# Study on the influence of process parameters on the damage appearance during the push bench elongator process of super Cr13 tubes

GARCÍA GIL Eduardo<fnref n="1" />, a*, AGHAJANI DERAZKOLA Hamed<fnref n="1" />, b,
MURILLO-MARRODÁN Alberto<fnref n="1" />, c, and BARCO ATUTXA Jon<fnref n="2" />, d

**Keywords:** Hot Working, Martensitic Stainless Steel, Ductile Damage, FEM

**Abstract.** In this paper the hot forming of Super Cr 13 seamless tubes during push bench elongator process is analyzed by means of laboratory experimental study and Finite Element simulation. The objective is to understand the effect of the industrial process parameters on the tube quality and the risk of damage appearance. The results of a hot tensile test campaign have been used to characterize rheological behavior of the material under the hot working conditions, and for determining the critical constants for several damage laws: Latham & Cockcroft. Finally, a Finite Element Model, FEM, of the Push Bench Elongator process have been implemented and the effect of rollers geometry and friction coefficient on tube quality and damage appearance have been addressed.

## Introduction

In the Push Bench Elongator a hollow bloom, previously pierced in a Diescher Piercing Mill, is stretched by an inner mandrel which pulls from the head of the tube through several boxes of no driven rolls. As a consequence, the thickness of the tube is reduced, and its length is increased up to seven times its initial size. To meet the strict dimensional requirements the tube is finally rolled in the Sizing Mill. It is a complex process involving high temperatures and strain rates. The difficulty of the process is increased when high-performance materials are used for the tube, like the Super Cr 13 Martensitic Stainless Steels, MSS. This material, with higher resistance limit the productivity of the process due to its poor hot workability [1].

To improve process productivity and tube quality both, analytical and numerical models have been developed. Initial contributions were focussed on the flow of the material through the rolls and to improve process accuracy, mainly by analytical means. One of the first computational analysis was developed by Reggio et al. [2] and it analysed the heat transfer in the plug during the piercing process. Regarding the stretching of the tube in mandrel mills Yamane et al. [3] developed a numerical analysis of the seamless pipe process. In the paper, two of the main technical problems of mandrel mill are presented: necking and perforation of the tube wall, and “underfill”. The second phenomenon is deeply analysed, however, the former one, which involves material discontinuities is not. In fact, it is a defect typical of high alloy and Stainless Steels due to the different circumferential deformation states when passing below the rolls. More recent work deal with different and relevant aspects of the process but do not cover the problem of damage. Langbauer et al.[4] developed a mathematical model to predict the temperature distribution within the pipe cross section during the hot rolling process. With this model authors can predict the temperature of the material during the process to gain control on the final microstructure of the

<figure><img src="image_1247.png" /></figure>

<footnote n="1">¹Department of Mechanics, Design and Industrial Management, University of Deusto, 48007 Bilbao, Spain</footnote>

<footnote n="2">²Full Tubos Reunidos Group, Barrio, Sagarribai Kalea, s/n, 01470 Amurrio, Álava, Spain</footnote>

<footnote>a.e.garcia@deusto.es, b.h.aghajani@deusto.es, c.alberto.murillo@deusto.es,</footnote>

<footnote>d.jbarco@tubosreunidosgroup.com</footnote>
# Study on the influence of process parameters on the damage appearance during the push bench elongator process of super Cr13 tubes

GARCÍA GIL Eduardo<fnref n="1" />, a*, AGHAJANI DERAZKOLA Hamed<fnref n="1" />, b,
MURILLO-MARRODÁN Alberto<fnref n="1" />, c, and BARCO ATUTXA Jon<fnref n="2" />, d

**Keywords:** Hot Working, Martensitic Stainless Steel, Ductile Damage, FEM

**Abstract.** In this paper the hot forming of Super Cr 13 seamless tubes during push bench elongator process is analyzed by means of laboratory experimental study and Finite Element simulation. The objective is to understand the effect of the industrial process parameters on the tube quality and the risk of damage appearance. The results of a hot tensile test campaign have been used to characterize rheological behavior of the material under the hot working conditions, and for determining the critical constants for several damage laws: Latham & Cockcroft. Finally, a Finite Element Model, FEM, of the Push Bench Elongator process have been implemented and the effect of rollers geometry and friction coefficient on tube quality and damage appearance have been addressed.

**Introduction**

In the Push Bench Elongator a hollow bloom, previously pierced in a Diescher Piercing Mill, is stretched by an inner mandrel which pulls from the head of the tube through several boxes of no driven rolls. As a consequence, the thickness of the tube is reduced, and its length is increased up to seven times its initial size. To meet the strict dimensional requirements the tube is finally rolled in the Sizing Mill. It is a complex process involving high temperatures and strain rates. The difficulty of the process is increased when high-performance materials are used for the tube, like the Super Cr 13 Martensitic Stainless Steels, MSS. This material, with higher resistance limit the productivity of the process due to its poor hot workability [1].

To improve process productivity and tube quality both, analytical and numerical models have been developed. Initial contributions were focussed on the flow of the material through the rolls and to improve process accuracy, mainly by analytical means. One of the first computational analysis was developed by Reggio et al. [2] and it analysed the heat transfer in the plug during the piercing process. Regarding the stretching of the tube in mandrel mills Yamane et al. [3] developed a numerical analysis of the seamless pipe process. In the paper, two of the main technical problems of mandrel mill are presented: necking and perforation of the tube wall, and “underfill”. The second phenomenon is deeply analysed, however, the former one, which involves material discontinuities is not. In fact, it is a defect typical of high alloy and Stainless Steels due to the different circumferential deformation states when passing below the rolls. More recent work deal with different and relevant aspects of the process but do not cover the problem of damage. Langbauer et al.[4] developed a mathematical model to predict the temperature distribution within the pipe cross section during the hot rolling process. With this model authors can predict the temperature of the material during the process to gain control on the final microstructure of the

<figure><img src="image_1249.png" /></figure>

<footnote n="1">¹Department of Mechanics, Design and Industrial Management, University of Deusto, 48007 Bilbao, Spain</footnote>

<footnote n="2">²Full Tubos Reunidos Group, Barrio, Sagarribai Kalea, s/n, 01470 Amurrio, Álava, Spain</footnote>

<footnote>a.e.garcia@deusto.es, b.h.aghajani@deusto.es, c.alberto.murillo@deusto.es,</footnote>

<footnote>d.jbarco@tubosreunidosgroup.com</footnote>
material. The reducing rate distribution between stands is a topic repeatedly studied, Hu et al. [5] proposed a correction theory supported by FEM simulation and experimentation providing a new method for the definition of the reduction rate. The profile of the rolls gives a wide margin to improve the process as it is shown by Wey and Wu [6].

The perforation of the wall is an important problem in the hot rolling of seamless tubes, especially for stainless steels. The relevance of this defect was already highlighted in 2015 [3] but it has not been analysed in detail up to the moment. Consequently, in this paper a damage law is developed for the Super Cr13 MSS and implemented in a FEM of the Push Bench Elongator process to understand the effect of process parameters on the material flow and product quality. For that purpose, a hot tensile test campaign of Super Cr13 has been developed, with the flow curves obtained from the tests a rheological material behaviour law was developed. Additionally, the tension tests have been simulated using the constitutive law obtained and the models are used to adjust the critical damage values of the selected ductile fracture criterion, Latham & Cockcroft. Finally, a FEM of the Push Bench Elongator process of Super Cr 13 pipes has been implanted using experimental results to study the effect of process parameters such as friction, and ovality of the roll profile on pipe quality and integrity.

## Materials and Methods

Most of the works dealing with the simulation of hot forming processes use hot compression tests for the definition of the material constitutive law. In addition, for the study of damage, supplementary experimental tests are conducted in many cases. Pater and Gontarz [7], used hot compression tests for the definition of the material constitutive law, and hot tensile tests with pre-notched specimens for determining the damage criteria parameters. Muregesan and Jung [8] performed hot tensile tests with plane specimens for material characterization, and hot tensile test with pre-notched cylindrical specimens for damage model definition. By contrast, some other authors used solely hot tensile test for the definition of both, the material behaviour law and the damage criteria [9, 10]. During the stretch of the tube in the Push Bench Elongator the material is subjected to a combined state of stresses in which longitudinal tension loads have a primary role. In addition, the hole defect arisen during this kind of processes responds to tensile deformation of material [3]. Thus, for this study the results of the tension tests presented in [1] are used for the definition of both, the material constitutive law and the damage criteria. This experimental campaign consists of hot tensile test on Super Cr 13 MSS samples according to ASTM E 21-09 and ASTM E 04 standards. The composition of the alloy is shown in Table 1. The tested conditions are 900, 1000, and 1100 °C and strain rates of 0.01, 0.1, 1, and 10 s⁻¹, and the measured parameters were the load, the elongation and the temperature.

<table><caption>Table 1. Chemical composition and weight percentages of the super Cr 13 MSS samples tested.</caption><thead><tr><th>Element</th><th>C</th><th>Cr</th><th>Ni</th><th>Mn</th><th>Si</th><th>Mo</th><th>P</th><th>S</th><th>Ti</th><th>V</th><th>Fe</th></tr></thead><tbody><tr><td>Wt.%</td><td>0.03</td><td>11.5 to 13.5</td><td>4.5 to 6.5</td><td>0.5</td><td>0.5</td><td>1.5 to 3</td><td>0.02</td><td>0.005</td><td>0.01 to 0.5</td><td>0.5</td><td>Balance</td></tr></tbody></table>

## Hot Tensile Behavior

From the results of the tensile tests the stress-strain flow curves, shown in Fig. 1 have been obtained. As expected, results show a decrease in material resistance to flow with increasing temperature being the case of 0.1 s⁻¹ the one with higher peak stress values: 195 MPa, 94 MPa and 72 MPa for 900 °C, 1000 °C, and 1100 °C, respectively. The effect of strain rate on the material response does not follow a common trend (higher stress for higher strain rates), a fact due to recrystallization and precipitation phenomena deeply analysed in [1].
material. The reducing rate distribution between stands is a topic repeatedly studied, Hu et al. [5] proposed a correction theory supported by FEM simulation and experimentation providing a new method for the definition of the reduction rate. The profile of the rolls gives a wide margin to improve the process as it is shown by Wey and Wu [6].

The perforation of the wall is an important problem in the hot rolling of seamless tubes, especially for stainless steels. The relevance of this defect was already highlighted in 2015 [3] but it has not been analysed in detail up to the moment. Consequently, in this paper a damage law is developed for the Super Cr13 MSS and implemented in a FEM of the Push Bench Elongator process to understand the effect of process parameters on the material flow and product quality. For that purpose, a hot tensile test campaign of Super Cr13 has been developed, with the flow curves obtained from the tests a rheological material behaviour law was developed. Additionally, the tension tests have been simulated using the constitutive law obtained and the models are used to adjust the critical damage values of the selected ductile fracture criterion, Latham & Cockcroft. Finally, a FEM of the Push Bench Elongator process of Super Cr 13 pipes has been implanted using experimental results to study the effect of process parameters such as friction, and ovality of the roll profile on pipe quality and integrity.

## Materials and Methods

Most of the works dealing with the simulation of hot forming processes use hot compression tests for the definition of the material constitutive law. In addition, for the study of damage, supplementary experimental tests are conducted in many cases. Pater and Gontarz [7], used hot compression tests for the definition of the material constitutive law, and hot tensile tests with pre-notched specimens for determining the damage criteria parameters. Muregesan and Jung [8] performed hot tensile tests with plane specimens for material characterization, and hot tensile test with pre-notched cylindrical specimens for damage model definition. By contrast, some other authors used solely hot tensile test for the definition of both, the material behaviour law and the damage criteria [9, 10]. During the stretch of the tube in the Push Bench Elongator the material is subjected to a combined state of stresses in which longitudinal tension loads have a primary role. In addition, the hole defect arisen during this kind of processes responds to tensile deformation of material [3]. Thus, for this study the results of the tension tests presented in [1] are used for the definition of both, the material constitutive law and the damage criteria. This experimental campaign consists of hot tensile test on Super Cr 13 MSS samples according to ASTM E 21-09 and ASTM E 04 standards. The composition of the alloy is shown in Table 1. The tested conditions are 900, 1000, and 1100 °C and strain rates of 0.01, 0.1, 1, and 10 s⁻¹, and the measured parameters were the load, the elongation and the temperature.

<table><caption>Table 1. Chemical composition and weight percentages of the super Cr 13 MSS samples tested.</caption><thead><tr><th>Element</th><th>C</th><th>Cr</th><th>Ni</th><th>Mn</th><th>Si</th><th>Mo</th><th>P</th><th>S</th><th>Ti</th><th>V</th><th>Fe</th></tr></thead><tbody><tr><td>Wt.%</td><td>0.03</td><td>11.5 to 13.5</td><td>4.5 to 6.5</td><td>0.5</td><td>0.5</td><td>1.5 to 3</td><td>0.02</td><td>0.005</td><td>0.01 to 0.5</td><td>0.5</td><td>Balance</td></tr></tbody></table>

## Hot Tensile Behavior

From the results of the tensile tests the stress-strain flow curves, shown in Fig. 1 have been obtained. As expected, results show a decrease in material resistance to flow with increasing temperature being the case of 0.1 s⁻¹ the one with higher peak stress values: 195 MPa, 94 MPa and 72 MPa for 900 °C, 1000 °C, and 1100 °C, respectively. The effect of strain rate on the material response does not follow a common trend (higher stress for higher strain rates), a fact due to recrystallization and precipitation phenomena deeply analysed in [1].
<figure><img src="image_1248.png" /><figcaption>Fig. 1. Stress-Strain flow Curves of the hot tensile test of Super Cr 13 MSS at different strain rates: (A) 0.01 s⁻¹, (B) 0.1 s⁻¹, (C) 1 s⁻¹, (D) 10s⁻¹.</figcaption></figure>

These curves have been used for obtaining the function parameters describing the relationship between the flow stresses and the strain. In this case, the Hansel-Spittel constitutive model has been selected, according to Eq.1:

$$ \sigma = A \cdot e^{m1T} \cdot \varepsilon^{m2} \cdot \dot{\varepsilon}^{m3} \cdot e^{\frac{m4}{\varepsilon}}, \qquad (1) $$

Where A, m1, m2, m3, m4 are the coefficients of the constitutive equation, which have to be defined, and T is the temperature, ε is the strain and ˙ε is the strain rate. The coefficients A, m1, m2, m3, m4 have been determined by the Generalized Reduced Gradient (GRG2) optimization method implemented into Microsoft Excel. The optimized function for the determination of the coefficients was the quadratic error function. As a result of the optimization the parameters gathered in table 2 have been obtained. This material behaviour law has been implemented in Forge NxT 4.0 for the development of the models.
<figure><img src="image_1250.png" /><figcaption>Fig. 1. Stress-Strain flow Curves of the hot tensile test of Super Cr 13 MSS at different strain rates: (A) 0.01 s⁻¹, (B) 0.1 s⁻¹, (C) 1 s⁻¹, (D) 10s⁻¹.</figcaption></figure>

These curves have been used for obtaining the function parameters describing the relationship between the flow stresses and the strain. In this case, the Hansel-Spittel constitutive model has been selected, according to Eq.1:

$$ \sigma = A \cdot e^{m1T} \cdot \varepsilon^{m2} \cdot \dot{\varepsilon}^{m3} \cdot e^{\frac{m4}{\varepsilon}}, \qquad (1) $$

Where A, m1, m2, m3, m4 are the coefficients of the constitutive equation, which have to be defined, and T is the temperature, ε is the strain and ˙ε is the strain rate. The coefficients A, m1, m2, m3, m4 have been determined by the Generalized Reduced Gradient (GRG2) optimization method implemented into Microsoft Excel. The optimized function for the determination of the coefficients was the quadratic error function. As a result of the optimization the parameters gathered in table 2 have been obtained. This material behaviour law has been implemented in Forge NxT 4.0 for the development of the models.
<table><caption>Table 2. Hansel-Spittel Coefficients obtained for Super Cr 13 MSS</caption><tr><td>A</td><td>188397.6621</td></tr><tr><td>m1</td><td>-0.007936329</td></tr><tr><td>m2</td><td>-0.088440714</td></tr><tr><td>m3</td><td>0.062890826</td></tr><tr><td>m4</td><td>-0.006544786</td></tr></table>

## Calculation of Ductile Fracture Damage Criterion

During the deformation processes the limit of the material can be reached leading to the fracture of the material. The occurrence of ductile fracture during metal forming is related to modifications on microstructure, stress and strain states. Damage models relate the evolution of these variables with the development of damage in the material, and are usually described following an equation of the form shown below (2):

$$ \int_{0}^{\varepsilon_{f}} f(\sigma) d\varepsilon = C, \qquad (2) $$

where $f(\sigma)$ is a function describing the variation of stress as a function of strain, $\varepsilon_f$ is the strain limit, and C is the critical value of the damage criteria, at which the fracture occurs. In this study, the widely spread Latham & Cockcroft criterion is be used. It uses the following expression to compute damage:

$$ \int_{0}^{\varepsilon_{f}} \left( \frac{\sigma_{1}}{\sigma_{i}} \right) d\varepsilon = C, \qquad (3) $$

Where $\sigma_1$ is the first principal stress, and $\sigma_i$ is the effective stress. These parameters cannot be evaluated directly in the tensile test, because they are not constant during deformation, are strain dependant. Therefore, C is computed with the aid of FEM models developed in Forge NxT 4.0. The procedure is as follows: a 3D FEM model reproducing the parameters of the tension tests is created for each of the combination of tested conditions. According to the tested conditions, a total of 12 models have been created. For each model, the fracture damage parameters at the fracture strain are obtained giving as a result the C parameter for each condition. The limit strain has been obtained from the strain-stress graphs shown in Fig. 1.

The model consists of two rigid dies attached to the sample, which has plastic behaviour according to the Hansel-Spittel law with the coefficients of Table 2. The sample is meshed using 3D tetrahedral P1+linear elements with a bubble node with a generic size of 2 mm which is refined in the mid-section to 0.4 mm size, see Fig. 2A. The rest of the parameters are adjusted to reproduce test conditions of strain rate and temperature. The figure shows as well the results for the case of 1000°C and 0.01s-1 of equivalent strain (B), first principal stress (C), and strain rate (D).
<table><caption>Table 2. Hansel-Spittel Coefficients obtained for Super Cr 13 MSS</caption><tr><td>A</td><td>188397.6621</td></tr><tr><td>m1</td><td>-0.007936329</td></tr><tr><td>m2</td><td>-0.088440714</td></tr><tr><td>m3</td><td>0.062890826</td></tr><tr><td>m4</td><td>-0.006544786</td></tr></table>

Calculation of Ductile Fracture Damage Criterion

During the deformation processes the limit of the material can be reached leading to the fracture of the material. The occurrence of ductile fracture during metal forming is related to modifications on microstructure, stress and strain states. Damage models relate the evolution of these variables with the development of damage in the material, and are usually described following an equation of the form shown below (2):

$$ \int_{0}^{\varepsilon_{f}} f(\sigma) d\varepsilon = C, \qquad (2) $$

where $f(\sigma)$ is a function describing the variation of stress as a function of strain, $\varepsilon_f$ is the strain limit, and $C$ is the critical value of the damage criteria, at which the fracture occurs. In this study, the widely spread Latham & Cockcroft criterion is be used. It uses the following expression to compute damage:

$$ \int_{0}^{\varepsilon_{f}} \left(\frac{\sigma_{1}}{\sigma_{i}}\right) d\varepsilon = C, \qquad (3) $$

Where $\sigma_1$ is the first principal stress, and $\sigma_i$ is the effective stress. These parameters cannot be evaluated directly in the tensile test, because they are not constant during deformation, are strain dependant. Therefore, $C$ is computed with the aid of FEM models developed in Forge NxT 4.0. The procedure is as follows: a 3D FEM model reproducing the parameters of the tension tests is created for each of the combination of tested conditions. According to the tested conditions, a total of 12 models have been created. For each model, the fracture damage parameters at the fracture strain are obtained giving as a result the $C$ parameter for each condition. The limit strain has been obtained from the strain-stress graphs shown in Fig. 1.

The model consists of two rigid dies attached to the sample, which has plastic behaviour according to the Hansel-Spittel law with the coefficients of Table 2. The sample is meshed using 3D tetrahedral P1+linear elements with a bubble node with a generic size of 2 mm which is refined in the mid-section to 0.4 mm size, see Fig. 2A. The rest of the parameters are adjusted to reproduce test conditions of strain rate and temperature. The figure shows as well the results for the case of 1000°C and 0.01s-1 of equivalent strain (B), first principal stress (C), and strain rate (D).
<figure><img src="image_1249.png" /><figcaption>Fig. 2. Tensile test FE model and results for 1 s-1, 1000°C case: (A) the rigid dies and deformable meshed sample; (B) Equivalent strain; (C) Strain Rate; (D) First Principal Stress</figcaption></figure>
<figure><img src="image_1251.png" /><figcaption>Fig. 2. Tensile test FE model and results for 1 s-1, 1000°C case: (A) the rigid dies and deformable meshed sample; (B) Equivalent strain; (C) Strain Rate; (D) First Principal Stress</figcaption></figure>
As it can be seen the results are evenly distributed in the middle section of the sample, which allows obtaining the values of the principal and effective stress inserting a sensor in the middle section without risk of errors.

The results obtained from the application of the mentioned methodology for obtaining C are gathered in Table 3.

<table><caption>Table 3. FEM models test conditions, and C values obtained for each of the cases for Super Cr 13 MSS.</caption><thead><tr><td>Model #</td><td>Strain Rate</td><td>Tª [°C]</td><td>C</td></tr></thead><tbody><tr><td>1</td><td>0.01</td><td>900</td><td>0.17</td></tr><tr><td>2</td><td>0.01</td><td>1000</td><td>0.21</td></tr><tr><td>3</td><td>0.01</td><td>1100</td><td>0.21</td></tr><tr><td>4</td><td>0.1</td><td>900</td><td>0.2</td></tr><tr><td>5</td><td>0.1</td><td>1000</td><td>0.22</td></tr><tr><td>6</td><td>0.1</td><td>1100</td><td>0.22</td></tr><tr><td>7</td><td>1</td><td>900</td><td>0.12</td></tr><tr><td>8</td><td>1</td><td>1000</td><td>0.31</td></tr><tr><td>9</td><td>1</td><td>1100</td><td>0.33</td></tr><tr><td>10</td><td>10</td><td>900</td><td>0.13</td></tr><tr><td>11</td><td>10</td><td>1000</td><td>0.47</td></tr><tr><td>12</td><td>10</td><td>1100</td><td>0.47</td></tr></tbody></table>

The important finding of this procedure is the fact that the critical damage value is a function of strain rate and temperature, not only depends on the accumulated strain. As it can be seen the increasing temperature and strain rate lead to higher C values.

## Push Bench Elongator Process Analysis

The final step of this analysis is the application of the knowledge obtained from the laboratory tests to the study the Push Bench Elongator Process of Super Cr 13 seamless pipes. For that purpose, a 3D FE model of the process have been developed, following the indications of the industrial partner Tubos Reunidos s.l.u.

The main components of the Push Bench Elongator process are shown Fig. 3, considering the dimensions and relative disposition provided by the industrial partner, Tubos Reunidos s.l.u. It consists of an inner mandrel, and 10 stands of 3 rolls each. The rolls from one stand to the other are rotated 60º around tube axis, resulting in a staggered arrangement. The tube to be deformed is a hollow cylinder with the following initial dimensions:

* outer diameter = 206.2 mm,

* inner diameter = 154 mm,

* length = 4.27m.
As it can be seen the results are evenly distributed in the middle section of the sample, which allows obtaining the values of the principal and effective stress inserting a sensor in the middle section without risk of errors.

The results obtained from the application of the mentioned methodology for obtaining C are gathered in Table 3.

<table><caption>Table 3. FEM models test conditions, and C values obtained for each of the cases for Super Cr 13 MSS.</caption><thead><tr><td>Model #</td><td>Strain Rate</td><td>Tª [°C]</td><td>C</td></tr></thead><tbody><tr><td>1</td><td>0.01</td><td>900</td><td>0.17</td></tr><tr><td>2</td><td>0.01</td><td>1000</td><td>0.21</td></tr><tr><td>3</td><td>0.01</td><td>1100</td><td>0.21</td></tr><tr><td>4</td><td>0.1</td><td>900</td><td>0.2</td></tr><tr><td>5</td><td>0.1</td><td>1000</td><td>0.22</td></tr><tr><td>6</td><td>0.1</td><td>1100</td><td>0.22</td></tr><tr><td>7</td><td>1</td><td>900</td><td>0.12</td></tr><tr><td>8</td><td>1</td><td>1000</td><td>0.31</td></tr><tr><td>9</td><td>1</td><td>1100</td><td>0.33</td></tr><tr><td>10</td><td>10</td><td>900</td><td>0.13</td></tr><tr><td>11</td><td>10</td><td>1000</td><td>0.47</td></tr><tr><td>12</td><td>10</td><td>1100</td><td>0.47</td></tr></tbody></table>

The important finding of this procedure is the fact that the critical damage value is a function of strain rate and temperature, not only depends on the accumulated strain. As it can be seen the increasing temperature and strain rate lead to higher C values.

## Push Bench Elongator Process Analysis

The final step of this analysis is the application of the knowledge obtained from the laboratory tests to the study the Push Bench Elongator Process of Super Cr 13 seamless pipes. For that purpose, a 3D FE model of the process have been developed, following the indications of the industrial partner Tubos Reunidos s.l.u.

The main components of the Push Bench Elongator process are shown Fig. 3, considering the dimensions and relative disposition provided by the industrial partner, Tubos Reunidos s.l.u. It consists of an inner mandrel, and 10 stands of 3 rolls each. The rolls from one stand to the other are rotated 60º around tube axis, resulting in a staggered arrangement. The tube to be deformed is a hollow cylinder with the following initial dimensions:

* outer diameter = 206.2 mm,

* inner diameter = 154 mm,

* length = 4.27m.
<figure><img src="image_1250.png" /><figcaption>Fig. 3. Disposition of the elements of the Push Bench Elongation according to Tubos Reunidos.</figcaption></figure>

The rolls have two important goals in this process. On the one hand, they are in charge of reducing progressively the outer diameter of the tube, and, consequently, the thickness of the wall. The reduction of tube diameter between stands is a key parameter of the process. This reduction is higher at the begging of the process and smaller towards the end. At the same time, they have to guarantee the circumferential profile of the tube at the end of the process. For this reason, the profile of the rolls plays a main role during the process. The rolls have an elliptical profile, since the groove has a larger diameter than that of the flanges. As a consequence, the theoretical positions of the centres of the tube cylinder and the rolls are not coincident; there is an eccentricity to favour the material flow. This eccentricity is bigger at the beginning of the process in the initial stands (coinciding with the diameter reduction), and is reduced progressively to be null in the last stands, resulting that the profile of the rolls in the last stands is circular. The geometry of the rolls and the separation between stands is confidential information.

<figure><img src="image_1251.png" /><figcaption>Fig. 4. Detail of the mesh of the FE model: roll, tube, mandrel and mandrel head.</figcaption></figure>

Fig. 4 shows a detail of the meshed used for the FE model of the process, where the mandrel and its head, the tube and a roll of the first stand are plotted. The tube has been meshed with 3D tetrahedral P1+linear elements with a bubble node with a mesh size of 8 mm, with the aim of maintaining at least 3 elements in thickness of the tube, resulting in 115.538 elements. It is a deformable body according to Hansel-Spittel law and the coefficients gathered in Table 2. Rolls, and mandrel are rigid bodies with a mesh size of 12 mm, and 11 mm respectively.
<figure><img src="image_1252.png" /><figcaption>Fig. 3. Disposition of the elements of the Push Bench Elongation according to Tubos Reunidos.</figcaption></figure>

The rolls have two important goals in this process. On the one hand, they are in charge of reducing progressively the outer diameter of the tube, and, consequently, the thickness of the wall. The reduction of tube diameter between stands is a key parameter of the process. This reduction is higher at the begging of the process and smaller towards the end. At the same time, they have to guarantee the circumferential profile of the tube at the end of the process. For this reason, the profile of the rolls plays a main role during the process. The rolls have an elliptical profile, since the groove has a larger diameter than that of the flanges. As a consequence, the theoretical positions of the centres of the tube cylinder and the rolls are not coincident; there is an eccentricity to favour the material flow. This eccentricity is bigger at the beginning of the process in the initial stands (coinciding with the diameter reduction), and is reduced progressively to be null in the last stands, resulting that the profile of the rolls in the last stands is circular. The geometry of the rolls and the separation between stands is confidential information.

<figure><img src="image_1253.png" /><figcaption>Fig. 4. Detail of the mesh of the FE model: roll, tube, mandrel and mandrel head.</figcaption></figure>

Fig. 4 shows a detail of the meshed used for the FE model of the process, where the mandrel and its head, the tube and a roll of the first stand are plotted. The tube has been meshed with 3D tetrahedral P1+linear elements with a bubble node with a mesh size of 8 mm, with the aim of maintaining at least 3 elements in thickness of the tube, resulting in 115.538 elements. It is a deformable body according to Hansel-Spittel law and the coefficients gathered in Table 2. Rolls, and mandrel are rigid bodies with a mesh size of 12 mm, and 11 mm respectively.
As it can be seen in Fig. 4, the head of the mandrel is attached to the tube and has a linear velocity predefined of 5500 mm/min, during 40.000mm, to ensure the full tube to be rolled by the ten stands. The rolls have free rotation around their axis of symmetry.

Regarding the initial and boundary conditions, the initial temperatures are:

* tube: 1100°C,

* mandrel: 400°C,

* rolls and ambient: 50°C

The heat transfer coefficients, h, considered are gathered in Table 3.

<table><caption>Table 4. Heat transfer coefficients of FE model</caption><thead><tr><td>Components</td><td>h [W/m²·K]</td></tr></thead><tbody><tr><td>Roll-Tube</td><td>10.000</td></tr><tr><td>Mandrel-Tube</td><td>2.000</td></tr><tr><td>Ambient-Tube</td><td>10</td></tr></tbody></table>

For the friction between the rolls and the tube, and between the mandrel and the tube the Tresca friction law was selected, and friction coefficient of 0.3 for both contacts, according to experience.

The model above described has been used to assess the influence of two process parameters on the final tube geometry and risk of damage. The selected process parameters are: rolls ovality, and the friction coefficient. Two values of these parameters have been considered, resulting in 3 models, as described in Table 5:

<table><caption>Table 5. Description of the parameters used in the models</caption><thead><tr><td>Model Name</td><td>Coef. Friction</td><td>Ovality</td></tr></thead><tbody><tr><td>1. Base</td><td>0.3</td><td>1</td></tr><tr><td>2. ½ Friction</td><td>0.15</td><td>1</td></tr><tr><td>3. ½ Ovality</td><td>0.3</td><td>½</td></tr></tbody></table>

Thus, the comparison of the results of models 1 and 2, allows understanding the effect of friction. For this study, power consumption evolution and Latham and Cockcroft parameter are evaluated. The Latham and Cockcroft is an uncouple criteria, that is, it does affect material behavior due to damage. Its value is updated for every increment adding the damage increase between increments in each element of the mesh. On the other hand, the comparison of models 2 and 3 allows understanding the effect of ovality.

The ovality of the tube is related to that of the rolls, as it can be seen in Fig. 5, the ovality of models 1 and 3 are shown as well as the ovality of the rolls. The blue lines show the ovality of the original process, which lead to a final ovality on the tube that is relevant almost 50% higher than that of the rolls of the last stand. By contrast when the ovality in the last four stands is reduced to the half, the remaining ovality on the tube is reduced 65%.

The evolution of the wall thickness eccentricity is shown in Fig. 6 where the models 1 and 3 are compared, as well as the eccentricity of the rolls which are plotted in dashed lines. The blue lines correspond to the model 1, original, and there it can be seen that the wall thickness eccentricity increases greatly in after last stand, even though the eccentricity of the rolls remains constant. By contrast, in model 3 (red color) the eccentricity at the end increases slightly. Thus, a reduction of 50% of rolls ovality leads to a reduction of 64% in the final wall thickness eccentricity of the tube.
As it can be seen in Fig. 4, the head of the mandrel is attached to the tube and has a linear velocity predefined of 5500 mm/min, during 40.000mm, to ensure the full tube to be rolled by the ten stands. The rolls have free rotation around their axis of symmetry.

Regarding the initial and boundary conditions, the initial temperatures are:

* tube: 1100°C,

* mandrel: 400°C,

* rolls and ambient: 50°C

The heat transfer coefficients, h, considered are gathered in Table 3.

<table><caption>Table 4. Heat transfer coefficients of FE model</caption><thead><tr><td>Components</td><td>h [W/m²·K]</td></tr></thead><tbody><tr><td>Roll-Tube</td><td>10.000</td></tr><tr><td>Mandrel-Tube</td><td>2.000</td></tr><tr><td>Ambient-Tube</td><td>10</td></tr></tbody></table>

For the friction between the rolls and the tube, and between the mandrel and the tube the Tresca friction law was selected, and friction coefficient of 0.3 for both contacts, according to experience.

The model above described has been used to assess the influence of two process parameters on the final tube geometry and risk of damage. The selected process parameters are: rolls ovality, and the friction coefficient. Two values of these parameters have been considered, resulting in 3 models, as described in Table 5:

<table><caption>Table 5. Description of the parameters used in the models</caption><thead><tr><td>Model Name</td><td>Coef. Friction</td><td>Ovality</td></tr></thead><tbody><tr><td>1. Base</td><td>0.3</td><td>1</td></tr><tr><td>2. ½ Friction</td><td>0.15</td><td>1</td></tr><tr><td>3. ½ Ovality</td><td>0.3</td><td>½</td></tr></tbody></table>

Thus, the comparison of the results of models 1 and 2, allows understanding the effect of friction. For this study, power consumption evolution and Latham and Cockcroft parameter are evaluated. The Latham and Cockcroft is an uncouple criteria, that is, it does affect material behavior due to damage. Its value is updated for every increment adding the damage increase between increments in each element of the mesh. On the other hand, the comparison of models 2 and 3 allows understanding the effect of ovality.

The ovality of the tube is related to that of the rolls, as it can be seen in Fig. 5, the ovality of models 1 and 3 are shown as well as the ovality of the rolls. The blue lines show the ovality of the original process, which lead to a final ovality on the tube that is relevant almost 50% higher than that of the rolls of the last stand. By contrast when the ovality in the last four stands is reduced to the half, the remaining ovality on the tube is reduced 65%.

The evolution of the wall thickness eccentricity is shown in Fig. 6 where the models 1 and 3 are compared, as well as the eccentricity of the rolls which are plotted in dashed lines. The blue lines correspond to the model 1, original, and there it can be seen that the wall thickness eccentricity increases greatly in after last stand, even though the eccentricity of the rolls remains constant. By contrast, in model 3 (red color) the eccentricity at the end increases slightly. Thus, a reduction of 50% of rolls ovality leads to a reduction of 64% in the final wall thickness eccentricity of the tube.
<figure><img src="image_1252.png" /><figcaption>Fig. 5. Evolution of the ovality of the rolls and the tube during the forming process</figcaption></figure>

<figure><img src="image_1253.png" /><figcaption>Fig. 6. Wall thickness evolution for the two models studied: model 1 (original) blue lines, model 3 red line</figcaption></figure>

<figure><img src="image_1254.png" /><figcaption>Fig. 7. Evolution of Latham & Cockcroft parameters during the rolling process for model 3, friction coefficient 0.15; and model 1, friction coefficient 0.30</figcaption></figure>
<figure><img src="image_1254.png" /><figcaption>Fig. 5. Evolution of the ovality of the rolls and the tube during the forming process</figcaption></figure>

<figure><img src="image_1255.png" /><figcaption>Fig. 6. Wall thickness evolution for the two models studied: model 1 (original) blue lines, model 3 red line</figcaption></figure>

<figure><img src="image_1256.png" /><figcaption>Fig. 7. Evolution of Latham & Cockcroft parameters during the rolling process for model 3, friction coefficient 0.15; and model 1, friction coefficient 0.30</figcaption></figure>
## Summary

In this paper the Push Bench Elongator has been analysed and the effect of two process parameters, namely, on the quality of the tube and probability of material damage have been assessed. For that purpose, first, an experimental hot tension test campaign has been developed to characterize the behavior of super Cr 13 MSS was developed. From the curves obtained from the tests the coefficients of Hansel Spittel equation were adjusted. Additionally, the tension tests have been simulated for determining the critical damage values of the Latham & Cockcroft damage criteria. Results show that these critical values vary depending on strain rate and temperature. Finally, a FE model of the process has been developed to study the effect of friction and ovalization on the tube. Results show a very high impact of friction in damage, and that the reduction of rolls ovalization in the last stands of the process have relevant positive influence.

## References

[1] H. A. Derazkola, E. Garcia, A. Murillo-Marrodan, 'The effect of temperature and strain rate on the mechanical properties and microstructure of super Cr13 martensitic stainless steel', Journal of material reasech and technology, 2023. https://doi.org/10.1016/j.jmrt.2023.04.012

[2] M. Reggio, F. McKenty, L. Gravel, J. Cortes, and G. Morales, 'Computational analysis of the process for manufacturing seamless tubes', Applied Thermal Engineering, 2002. https://doi.org/10.1016/S1359-4311(01)00093-X

[3] A. Yamane, K. Yamane, and H. Shitamoto, 'Development of Numerical Analysis on Seamless Tube and Pipe Process', Nippon steel and Sumitomo Technical Report 107, 2015.

[4] R. Langbauer, 'Investigation of the temperature distribution in seamless low-alloy steel pipes during the hot rolling process', Advances in Industrial and Manufacturing Engineering, 2021. https://doi.org/10.1016/j.aime.2021.100038

[5] J. Hu, S. Yang, Y. Huang, X. Wang, and J. Chen, 'A New Correction Theory and Verification on the Reducing Rate Distribution for Seamless Tube Stretch-Reducing Process', Crystals 2022. https://doi.org/10.3390/cryst12091296

[6] Z. Wei, 'A new analytical model to predict the profile and stress distribution of tube in three-roll continuous retained mandrel rolling', Journal of Materials Processig Technology 2022. https://doi.org/10.1016/j.jmatprotec.2022.117491

[7] Z. Pater and A. Gontarz, 'Critical Damage Values of R200 and 100Cr6 Steels Obtained by Hot Tensile Testing', Materials 2019. https://doi.org/10.3390/ma12071011

[8] F. Lastname, F. Lastname, and F. Lastname, 'Johnson Cook Material and Failure Model Parameters Estimation of AISI-1045 Medium Carbon Steel for Metal Forming Applications', Materials 2019.

[9] H. Zhang, M. Meng, X. Yang, G. Lei, J. Jia, G. Wu, X. Zhang, J. Yu. 'Hot tensile deformation behavior and a fracture damage model of the wrought Mg-Gd-Y-Zn-Zr alloy. Journal of Materials Research and Technology, 2022. https://doi.org/10.1016/j.jmrt.2022.02.104

[10] H. Vafaeeenezhad, 'Using high temperature tensile testing data to analyze hot formability of Sn-5Sb alloy: instability and critical damage criteria'.
## Summary

In this paper the Push Bench Elongator has been analysed and the effect of two process parameters, namely, on the quality of the tube and probability of material damage have been assessed. For that purpose, first, an experimental hot tension test campaign has been developed to characterize the behavior of super Cr 13 MSS was developed. From the curves obtained from the tests the coefficients of Hansel Spittel equation were adjusted. Additionally, the tension tests have been simulated for determining the critical damage values of the Latham & Cockcroft damage criteria. Results show that these critical values vary depending on strain rate and temperature. Finally, a FE model of the process has been developed to study the effect of friction and ovalization on the tube. Results show a very high impact of friction in damage, and that the reduction of rolls ovalization in the last stands of the process have relevant positive influence.

## References

[1] H. A. Derazkola, E. Garcia, A. Murillo-Marrodan, 'The effect of temperature and strain rate on the mechanical properties and microstructure of super Cr13 martensitic stainless steel', Journal of material reasech and technology, 2023. https://doi.org/10.1016/j.jmrt.2023.04.012

[2] M. Reggio, F. McKenty, L. Gravel, J. Cortes, and G. Morales, 'Computational analysis of the process for manufacturing seamless tubes', Applied Thermal Engineering, 2002. https://doi.org/10.1016/S1359-4311(01)00093-X

[3] A. Yamane, K. Yamane, and H. Shitamoto, 'Development of Numerical Analysis on Seamless Tube and Pipe Process', Nippon steel and Sumitomo Technical Report 107, 2015.

[4] R. Langbauer, 'Investigation of the temperature distribution in seamless low-alloy steel pipes during the hot rolling process', Advances in Industrial and Manufacturing Engineering, 2021. https://doi.org/10.1016/j.aime.2021.100038

[5] J. Hu, S. Yang, Y. Huang, X. Wang, and J. Chen, 'A New Correction Theory and Verification on the Reducing Rate Distribution for Seamless Tube Stretch-Reducing Process', Crystals 2022. https://doi.org/10.3390/cryst12091296

[6] Z. Wei, 'A new analytical model to predict the profile and stress distribution of tube in three-roll continuous retained mandrel rolling', Journal of Materials Processig Technology 2022. https://doi.org/10.1016/j.jmatprotec.2022.117491

[7] Z. Pater and A. Gontarz, 'Critical Damage Values of R200 and 100Cr6 Steels Obtained by Hot Tensile Testing', Materials 2019. https://doi.org/10.3390/ma12071011

[8] F. Lastname, F. Lastname, and F. Lastname, 'Johnson Cook Material and Failure Model Parameters Estimation of AISI-1045 Medium Carbon Steel for Metal Forming Applications', Materials 2019.

[9] H. Zhang, M. Meng, X. Yang, G. Lei, J. Jia, G. Wu, X. Zhang, J. Yu. 'Hot tensile deformation behavior and a fracture damage model of the wrought Mg-Gd-Y-Zn-Zr alloy. Journal of Materials Research and Technology, 2022. https://doi.org/10.1016/j.jmrt.2022.02.104

[10] H. Vafaeeenezhad, 'Using high temperature tensile testing data to analyze hot formability of Sn-5Sb alloy: instability and critical damage criteria'.
# Investigation into the friction and wear behaviour of polymer coated steel

VENEMA Jenny¹,ª and KWAKKEL Henri¹,ᵇ

¹Tata Steel, Research & Development, PO BOX 10000, 1970 CA IJmuiden, The Netherlands

ªjenny.venema@tatasteeleurope.com, ᵇhenri.kwakkel@tatasteeleurope.com

**Keywords:** Polymer Coated Steel, Can Making, Wear, Tribology, Packaging

**Abstract.** In the packaging industry, polymer coated steel is used to produce cans and other containers. One of the limitations that can limit production rates is scuffing. Scuffing is local failure of the polymer coating. To understand the failure behaviour of this type of sheet coating, cans have been produced at a range of processing speeds and tribological tests have been performed on polymer coated steel. Linear friction tests were performed under various contact pressures and tool temperatures (20-195 °C). Scuffing generated by the tests were investigated using 3D topography measurements of the surfaces. Several parameters (coating, pressure and temperature) and their interaction determines the frictional and wear behaviour of the polymer. Temperature is a key parameter governing the coating wear phenomena. Surface measurements indicate that similar coating failure defects can be observed in both the linear friction test and in industrial-scale can making. The tests proved that polymer coatings can resist relatively high contact pressure conditions and temperatures. This makes polymer coated steel sheets applicable for a large range of packaging products.

**Introduction**

For the production of cans and other containers, polymer coated steels have many advantages. They possess good formability and no solvents are emitted during processing. They also offer protection of the metal substrate against the filled contents [1]. However, during processing at critically high velocities, local failure of the polymer coating can occur. This local failure of the polymer coating is called scuffing.

The production of a food can consists of several steps, including drawing, redrawing and ironing. The polymer coating is subjected to a large range of temperatures and pressures during each of these steps. In the draw and redraw step, the pressures and temperatures are low in comparison to the ironing step. In the ironing step, the polymer layer is subjected to high temperatures (> 100 °C), high strain rates (> 3000 1/s) and high hydrostatic pressure (>500 MPa) [2].

The physical behaviour of the polymer coating varies within the temperature range 20-200 °C. The polymer layer has a glass transition temperature of approximately 60°C. Above this temperature, the molecules become increasingly flexible as temperature rises, until the recrystallisation temperature is reached. Recrystallisation starts at around 100 °C and this lowers flexibility again. A melting trajectory takes place at approximately 200 °C - 250 °C. The tribological behaviour of the polymer layer during the drawing step can be investigated by linear friction testing. In this test, it is possible to assess performance at similar pressures and temperatures found in the drawing step. The strain is not taken into account in a linear friction test. Studying the tribological behaviour of the polymer layer during ironing is far more difficult due to the very high velocities, deformation and pressures. Van der Aa [3] build a strip ironing device to study the process forces and friction coefficients. The coefficient of friction decreases with decreasing die angle and increasing velocity.

<figure><img src="image_1255.png" /></figure>
# Investigation into the friction and wear behaviour of polymer coated steel

VENEMA Jenny¹,ª and KWAKKEL Henri¹,ᵇ

¹Tata Steel, Research & Development, PO BOX 10000, 1970 CA IJmuiden, The Netherlands

ªjenny.venema@tatasteeleurope.com, ᵇhenri.kwakkel@tatasteeleurope.com

**Keywords:** Polymer Coated Steel, Can Making, Wear, Tribology, Packaging

**Abstract.** In the packaging industry, polymer coated steel is used to produce cans and other containers. One of the limitations that can limit production rates is scuffing. Scuffing is local failure of the polymer coating. To understand the failure behaviour of this type of sheet coating, cans have been produced at a range of processing speeds and tribological tests have been performed on polymer coated steel. Linear friction tests were performed under various contact pressures and tool temperatures (20-195 °C). Scuffing generated by the tests were investigated using 3D topography measurements of the surfaces. Several parameters (coating, pressure and temperature) and their interaction determines the frictional and wear behaviour of the polymer. Temperature is a key parameter governing the coating wear phenomena. Surface measurements indicate that similar coating failure defects can be observed in both the linear friction test and in industrial-scale can making. The tests proved that polymer coatings can resist relatively high contact pressure conditions and temperatures. This makes polymer coated steel sheets applicable for a large range of packaging products.

**Introduction**

For the production of cans and other containers, polymer coated steels have many advantages. They possess good formability and no solvents are emitted during processing. They also offer protection of the metal substrate against the filled contents [1]. However, during processing at critically high velocities, local failure of the polymer coating can occur. This local failure of the polymer coating is called scuffing.

The production of a food can consists of several steps, including drawing, redrawing and ironing. The polymer coating is subjected to a large range of temperatures and pressures during each of these steps. In the draw and redraw step, the pressures and temperatures are low in comparison to the ironing step. In the ironing step, the polymer layer is subjected to high temperatures (> 100 °C), high strain rates (> 3000 1/s) and high hydrostatic pressure (>500 MPa) [2].

The physical behaviour of the polymer coating varies within the temperature range 20-200 °C. The polymer layer has a glass transition temperature of approximately 60°C. Above this temperature, the molecules become increasingly flexible as temperature rises, until the recrystallisation temperature is reached. Recrystallisation starts at around 100 °C and this lowers flexibility again. A melting trajectory takes place at approximately 200 °C - 250 °C. The tribological behaviour of the polymer layer during the drawing step can be investigated by linear friction testing. In this test, it is possible to assess performance at similar pressures and temperatures found in the drawing step. The strain is not taken into account in a linear friction test. Studying the tribological behaviour of the polymer layer during ironing is far more difficult due to the very high velocities, deformation and pressures. Van der Aa [3] build a strip ironing device to study the process forces and friction coefficients. The coefficient of friction decreases with decreasing die angle and increasing velocity.

<figure><img src="image_1257.png" /></figure>
The roughness development of polymer coated steels during deformation has been studied by several authors [4-6]. Faber [4] studied polymer-metal interfaces in bi-axially deformed ECCS/PET laminates and local delamination. Venema et al. [6] studied roughness development during several steps in the can making process. During the draw and redraw process, surface roughening occurs. In the first ironing stage, a large decrease in roughness is observed. In the second ironing step, scuffing was observed for one material. The behaviour of polymer coatings during ironing is relatively unknown and the recrystallisation (and other temperature related) behaviour of these coatings needs further investigation.

The aim of this paper is to investigate the effect of pressure and temperature on surface development and the risk of coating failure during can production. To gain further insights, cans were produced at several process speeds. Increasing process speed results in elevated processing temperatures. To assess both temperature and pressure effects on the polymer coating, linear friction tests were performed at a range of temperatures and pressures.

## Can making: Material and methods

Tests using a semi-industrial can making line were performed at several production velocities, ranging from 180 to 240 cans/minute. First, around 800 cans were produced to achieve a stable machine temperature. After reaching a stable situation, production speed was increased incrementally by 30 cans/minute after every 200 cans. At higher production speeds, increased temperatures will, at a critical moment, induce scuffing in the second ironing step.

The process includes waxing, blanking, drawing, redrawing and two steps of ironing. Fig. 1a shows the progression set. The electrostatic waxer applies wax at a temperature of 65 ° to both top (49.7 mg/m2) and bottom (218.1 mg/m2). The top side of the strip becomes the inside of the can. In the cupper, blanks are punched and cups are drawn. The cups are produced using the 'early lift off' principle. In the early lift off principle, the blank holder pressure is removed just before the flange material leaves the blank holder at the end of the stroke. This prevents the formation of polymer hairs as a result of the high surface pressure. In the bodymaker, a redraw step and two ironing steps occur. The tools of the bodymaker are internally cooled. The temperature of the can surface is measured between the two ironing rings by a digital infrared pyrometer, see Fig. 1b. Maximum temperatures measured are between 183 and 189 °C (at 167 and 200 cans/min respectively). Table 1 includes process settings.

<figure><img src="image_1256.png" /><figcaption>Fig. 1. a. Progression set. b. Bodymaker toolpack.</figcaption></figure>
The roughness development of polymer coated steels during deformation has been studied by several authors [4-6]. Faber [4] studied polymer-metal interfaces in bi-axially deformed ECCS/PET laminates and local delamination. Venema et al. [6] studied roughness development during several steps in the can making process. During the draw and redraw process, surface roughening occurs. In the first ironing stage, a large decrease in roughness is observed. In the second ironing step, scuffing was observed for one material. The behaviour of polymer coatings during ironing is relatively unknown and the recrystallisation (and other temperature related) behaviour of these coatings needs further investigation.

The aim of this paper is to investigate the effect of pressure and temperature on surface development and the risk of coating failure during can production. To gain further insights, cans were produced at several process speeds. Increasing process speed results in elevated processing temperatures. To assess both temperature and pressure effects on the polymer coating, linear friction tests were performed at a range of temperatures and pressures.

## Can making: Material and methods

Tests using a semi-industrial can making line were performed at several production velocities, ranging from 180 to 240 cans/minute. First, around 800 cans were produced to achieve a stable machine temperature. After reaching a stable situation, production speed was increased incrementally by 30 cans/minute after every 200 cans. At higher production speeds, increased temperatures will, at a critical moment, induce scuffing in the second ironing step.

The process includes waxing, blanking, drawing, redrawing and two steps of ironing. Fig. 1a shows the progression set. The electrostatic waxer applies wax at a temperature of 65 ° to both top (49.7 mg/m2) and bottom (218.1 mg/m2). The top side of the strip becomes the inside of the can. In the cupper, blanks are punched and cups are drawn. The cups are produced using the 'early lift off' principle. In the early lift off principle, the blank holder pressure is removed just before the flange material leaves the blank holder at the end of the stroke. This prevents the formation of polymer hairs as a result of the high surface pressure. In the bodymaker, a redraw step and two ironing steps occur. The tools of the bodymaker are internally cooled. The temperature of the can surface is measured between the two ironing rings by a digital infrared pyrometer, see Fig. 1b. Maximum temperatures measured are between 183 and 189 °C (at 167 and 200 cans/min respectively). Table 1 includes process settings.

<figure><img src="image_1258.png" /><figcaption>Fig. 1. a. Progression set. b. Bodymaker toolpack.</figcaption></figure>
<table><caption>Table 1. Process settings.</caption><thead><tr><th colspan="2">Copper</th><th colspan="2">Bodymaker</th></tr></thead><tbody><tr><td>Blank Holder force [bar]</td><td>1.17</td><td>Redraw diameter [mm]</td><td>66.41</td></tr><tr><td>Cupping speed [n/min]</td><td>140</td><td>Ironing ring 1 diameter [mm]</td><td>65.896</td></tr><tr><td>Punch size [mm]</td><td>88.71</td><td>Ironing ring 2 diameter [mm]</td><td>65.891</td></tr><tr><td>Blank size [mm]</td><td>149.94</td><td></td><td></td></tr><tr><td>Draw ratio [-]</td><td>1.69</td><td></td><td></td></tr></tbody></table>

Cans were produced from laminated Electrolytic Chromium Coated Steel (ECCS) with Poly-Ethylene Terephthalate (PET) on both sides (20 µm outside/30 µm inside) with a thickness of 0.25 mm. The wall thickness reduces after the first ironing ring to 0.168 mm (44% reduction) and after the second ironing ring to 0.158 mm (6% reduction).

Three dimensional topographical measurements were performed using the NanoFocus µsurf mobile confocal microscope. To enable measurement of the polymer coating, a thin layer of gold was sputtered onto the surface of the cans.

## Can making: Results

At a production speed of 240 cans/min, scuffing started to appear on the top side of the can. Fig. 2 shows the confocal measurements at position 100 mm from the base of the can. The appearance of the coating failure is not always exactly the same, and depends on the exact local conditions such as temperature, pressure and strain. In this investigation, a higher processing speed results in a higher surface roughness which is probably related to the increase in temperature. The surface roughness Sa (average of 3 measurement values) is 0.71 and 0.89 µm for 180 cans/min and 210 cans/min, respectively.

a.

<figure><img src="image_1257.png" /></figure>

b.

<figure><img src="image_1258.png" /></figure>

c.

<figure><img src="image_1259.png" /><figcaption>Fig. 2. Confocal measurement of surface of can at a. 180 cans/minute b. 210 cans/minute c. 240 cans/minute. Drawing direction from top to bottom.</figcaption></figure>

## Tribological investigation: Materials and methods

An experimental method was employed to evaluate the tribological behaviour of the polymer sheet coated material for a range of pressures and temperatures. The experiments were performed using a Linear Friction Tester (LFT) capable of providing controlled contact conditions between the tool surfaces and the polymer coated sheet, see Fig. 3a. Tool A (Sa = 0.12 ± 0.02) is cylindrical with a diameter 20 mm. Tool B (Sa = 0.12 ± 0.02) has a large radius of 300 mm. The tools were heated by an internal heating element to a specific temperature between 20 by 195 °C. The tools close upon the moving strip. The force builds up during the displacement of the strip. Tests with a normal force of 2, 4 and 8 kN were performed. The average coefficient of friction value was determined between 80-100 mm of the total drawing length of 105 mm.

A laminate of Electrolytic Chromium Coated Steel (ECCS) with Poly-Ethylene Terephthalate (PET) on both sides (20 µm inside/30 µm outside) with a thickness of 0.25 mm was used in the LFT investigation. Two sheets (50x300 mm) were pasted together with tape on the top and bottom
<table><caption>Table 1. Process settings.</caption><thead><tr><th colspan="2">Copper</th><th colspan="2">Bodymaker</th></tr></thead><tbody><tr><td>Blank Holder force [bar]</td><td>1.17</td><td>Redraw diameter [mm]</td><td>66.41</td></tr><tr><td>Cupping speed [n/min]</td><td>140</td><td>Ironing ring 1 diameter [mm]</td><td>65.896</td></tr><tr><td>Punch size [mm]</td><td>88.71</td><td>Ironing ring 2 diameter [mm]</td><td>65.891</td></tr><tr><td>Blank size [mm]</td><td>149.94</td><td></td><td></td></tr><tr><td>Draw ratio [-]</td><td>1.69</td><td></td><td></td></tr></tbody></table>

Cans were produced from laminated Electrolytic Chromium Coated Steel (ECCS) with Poly-Ethylene Terephthalate (PET) on both sides (20 µm outside/30 µm inside) with a thickness of 0.25 mm. The wall thickness reduces after the first ironing ring to 0.168 mm (44% reduction) and after the second ironing ring to 0.158 mm (6% reduction).

Three dimensional topographical measurements were performed using the NanoFocus µsurf mobile confocal microscope. To enable measurement of the polymer coating, a thin layer of gold was sputtered onto the surface of the cans.

## Can making: Results

At a production speed of 240 cans/min, scuffing started to appear on the top side of the can. Fig. 2 shows the confocal measurements at position 100 mm from the base of the can. The appearance of the coating failure is not always exactly the same, and depends on the exact local conditions such as temperature, pressure and strain. In this investigation, a higher processing speed results in a higher surface roughness which is probably related to the increase in temperature. The surface roughness Sa (average of 3 measurement values) is 0.71 and 0.89 µm for 180 cans/min and 210 cans/min, respectively.

a.

<figure><img src="image_1259.png" /></figure>

b.

<figure><img src="image_1260.png" /></figure>

c.

<figure><img src="image_1261.png" /><figcaption>Fig. 2. Confocal measurement of surface of can at a. 180 cans/minute b. 210 cans/minute c. 240 cans/minute. Drawing direction from top to bottom.</figcaption></figure>

## Tribological investigation: Materials and methods

An experimental method was employed to evaluate the tribological behaviour of the polymer sheet coated material for a range of pressures and temperatures. The experiments were performed using a Linear Friction Tester (LFT) capable of providing controlled contact conditions between the tool surfaces and the polymer coated sheet, see Fig. 3a. Tool A (Sa = 0.12 ± 0.02) is cylindrical with a diameter 20 mm. Tool B (Sa = 0.12 ± 0.02) has a large radius of 300 mm. The tools were heated by an internal heating element to a specific temperature between 20 by 195 °C. The tools close upon the moving strip. The force builds up during the displacement of the strip. Tests with a normal force of 2, 4 and 8 kN were performed. The average coefficient of friction value was determined between 80-100 mm of the total drawing length of 105 mm.

A laminate of Electrolytic Chromium Coated Steel (ECCS) with Poly-Ethylene Terephthalate (PET) on both sides (20 µm inside/30 µm outside) with a thickness of 0.25 mm was used in the LFT investigation. Two sheets (50x300 mm) were pasted together with tape on the top and bottom
before the test to ensure stability and avoid deformation. The 20 µm PET coating is in contact with the tools.

Three dimensional topographical measurements were performed using the NanoFocus µsurf mobile confocal microscope. To enable measurement of the polymer layer, a thin layer of gold was sputtered on the surface. The confocal measurements are performed at 50 mm sliding distance (middle) on both sides.

<figure><img src="image_1260.png" /><figcaption>Fig. 3. a. Schematic view test b. Normal force, tensile force and velocity versus displacement.</figcaption></figure>

## Tribological investigation: Results

To investigate scuffing behaviour, a matrix of LFT tests were performed at different pressures and temperatures. Scuffing is observed on both sides of the PET coated samples, however more severe scuffing is observed on the side in contact with Tool B (large radius). The contact area is higher for Tool B than for Tool A and more heat can, therefore, be transferred from the tool to the sheet. The pressure is lower on tool B which will have an opposite effect on the heat transfer. Besides heat transfer, contact pressure has also an effect on scuffing. Thus several aspects play a role, which are not easy to untangle due to the set-up of the test (different tool geometry on both sides). Finite element simulation could provide further insight into local temperature effects.

Fig. 4 shows surface appearance after testing at different temperatures. The confocal measurements shows a very smooth coating surface after testing at 150 °C. The surface roughness Sa is between 0.2 - 0.25 µm (depending on normal force) for temperatures of 20-100 °C. A large drop in surface roughness to a value of 0.1 µm occurs at 150 °C. This drop could be related to recrystallisation, but this needs further investigation.

<figure><img src="image_1261.png" /><figcaption>Fig. 4. Confocal measurements (2x2mm) sheet surface with tool temperature of a. 20 °C b. 200 °C c. 150 °C and d. 195 °C. Fn=4kN test – side with large radius tool</figcaption></figure>

Scuffing occurs at 195°C at loads of 4 and 8 kN. The scuffing is not homogeneous over the surface, thus the severity of the scuffing depends on the exact measurement position. The depth of the scuffing is approximately the coating thickness. At 2 kN, no scuffing is observed at any of the temperatures tested, only whitening (degradation) of the coating. The most severe scuffing is observed in the 4 kN test (Fig. 5).
before the test to ensure stability and avoid deformation. The 20 µm PET coating is in contact with the tools.

Three dimensional topographical measurements were performed using the NanoFocus µsurf mobile confocal microscope. To enable measurement of the polymer layer, a thin layer of gold was sputtered on the surface. The confocal measurements are performed at 50 mm sliding distance (middle) on both sides.

<figure><img src="image_1262.png" /><figcaption>Fig. 3. a. Schematic view test b. Normal force, tensile force and velocity versus displacement.</figcaption></figure>

**Tribological investigation: Results**

To investigate scuffing behaviour, a matrix of LFT tests were performed at different pressures and temperatures. Scuffing is observed on both sides of the PET coated samples, however more severe scuffing is observed on the side in contact with Tool B (large radius). The contact area is higher for Tool B than for Tool A and more heat can, therefore, be transferred from the tool to the sheet. The pressure is lower on tool B which will have an opposite effect on the heat transfer. Besides heat transfer, contact pressure has also an effect on scuffing. Thus several aspects play a role, which are not easy to untangle due to the set-up of the test (different tool geometry on both sides). Finite element simulation could provide further insight into local temperature effects.

Fig. 4 shows surface appearance after testing at different temperatures. The confocal measurements shows a very smooth coating surface after testing at 150 °C. The surface roughness Sa is between 0.2 - 0.25 µm (depending on normal force) for temperatures of 20-100 °C. A large drop in surface roughness to a value of 0.1 µm occurs at 150 °C. This drop could be related to recrystallisation, but this needs further investigation.

<figure><img src="image_1263.png" /><figcaption>Fig. 4. Confocal measurements (2x2mm) sheet surface with tool temperature of a. 20 °C b. 200 °C c. 150 °C and d. 195 °C. Fn=4kN test – side with large radius tool</figcaption></figure>

Scuffing occurs at 195°C at loads of 4 and 8 kN. The scuffing is not homogeneous over the surface, thus the severity of the scuffing depends on the exact measurement position. The depth of the scuffing is approximately the coating thickness. At 2 kN, no scuffing is observed at any of the temperatures tested, only whitening (degradation) of the coating. The most severe scuffing is observed in the 4 kN test (Fig. 5).
<figure><img src="image_1262.png" /><figcaption>Fig. 5. Photograph of samples for tool temperature of 195 °C with normal force of a. 2kN, b. 4 kN and c. 8 kN. Tool side with large radius. Drawing distance from right to left.</figcaption></figure>

## Tribological investigation: Coefficient of Friction (COF)

Fig. 6 shows the average COF between 80-100 mm drawing distance for all tests conducted. In general, between 20-150°C, the COF decreases as temperature increases. Beyond 150 °C, the COF increases again. At 2 kN force, a negative value is measured for 150 °C. This is unexpected and should be further investigated. Scuffing occurs at 195 °C for 4 and 8 kN normal load, and results in a sharp increase in COF. Degradation of the coating, but no severe scuffing, is observed for 2kN, this resulted a lower COF value than the two other higher normal forces at 195 °C. In general, a lower force results in a lower COF.

<figure><img src="image_1263.png" /><figcaption>Fig. 6. COF versus temperature.</figcaption></figure>

## Discussion

Scuffing occurs in the can making line during the second ironing step. The temperature of the can is ~ 185 °C between the first and second ironing step. Scuffing occurs in the LFT tests at a temperature of 195 °C for normal forces of 4 and 8 kN. The appearance of the scuffing defects generated is dependent on local conditions and is different for both tool sides in the LFT tests and for cans from different tests series (Fig. 7). However, similar appearances were observed in the can making line and the LFT test under some circumstances. Cross sectional analysis will be performed to investigate the failure mechanism found in both tests. The results of the LFT are encouraging and show that the test could provide a promising method for the investigation of scuffing.
<figure><img src="image_1264.png" /><figcaption>Fig. 5. Photograph of samples for tool temperature of 195 °C with normal force of a. 2kN, b. 4 kN and c. 8 kN. Tool side with large radius. Drawing distance from right to left.</figcaption></figure>

**Tribological investigation: Coefficient of Friction (COF)**

Fig. 6 shows the average COF between 80-100 mm drawing distance for all tests conducted. In general, between 20-150°C, the COF decreases as temperature increases. Beyond 150 °C, the COF increases again. At 2 kN force, a negative value is measured for 150 °C. This is unexpected and should be further investigated. Scuffing occurs at 195 °C for 4 and 8 kN normal load, and results in a sharp increase in COF. Degradation of the coating, but no severe scuffing, is observed for 2kN, this resulted a lower COF value than the two other higher normal forces at 195 °C. In general, a lower force results in a lower COF.

<figure><img src="image_1265.png" /><figcaption>Fig. 6. COF versus temperature.</figcaption></figure>

**Discussion**

Scuffing occurs in the can making line during the second ironing step. The temperature of the can is ~ 185 °C between the first and second ironing step. Scuffing occurs in the LFT tests at a temperature of 195 °C for normal forces of 4 and 8 kN. The appearance of the scuffing defects generated is dependent on local conditions and is different for both tool sides in the LFT tests and for cans from different tests series (Fig. 7). However, similar appearances were observed in the can making line and the LFT test under some circumstances. Cross sectional analysis will be performed to investigate the failure mechanism found in both tests. The results of the LFT are encouraging and show that the test could provide a promising method for the investigation of scuffing.
<figure><img src="image_1264.png" /><figcaption>Fig. 7. Confocal measurement 1 x 1 mm of a. Can from earlier investigation [6], b. Can 240 cans/min, c. LFT side Tool A, d. LFT side Tool B.</figcaption></figure>

## Conclusions and recommendation

A study was performed to investigate the tribological behaviour and surface appearance of PET coated steel at different can processing speeds, for a range of tool temperatures and pressures. The tribological behaviour of the PET coating is defined by a complex combination of mechanisms. Several parameters (coating, pressure, temperature) and their interaction determines the frictional behaviour of this product. Temperature is a key parameter governing the coating wear phenomena. In the LFT test, scuffing only occurs above a certain temperature level (195 °C). In can making tests, scuffing only occurred above a certain processing velocity. Pressure has also a clear effect on scuffing. Surface measurements indicate that similar coating failure defects can be observed in both the linear friction test and in industrial-scale can making. This needs to be investigated further by cross sectional analysis. The tests proved that the polymer coating can resist high contact pressure conditions and temperatures. This makes polymer coated steel sheets applicable for a large range of packaging products.

## References

[1] B. Boelen, H. den Hartog, H. van der Weijde, Product performance of polymer coated packaging steel, study of the mechanism of defect growth in cans. Progress in Organic Coatings 50 (2004) 40-46. https://doi.org/10.1016/j.porgcoat.2003.09.011

[2] J. Mulder, G.T. Nagy, P. Šuštarič, T. Šuštar and T. Rodič. (2010) AIP Conf. Proc. 1252 1 (2010), 762-769. https://doi.org/10.1063/1.3457632

[3] H.C.E van der Aa, M.A.H. van der Aa, P.J.G. Schreurs, F.P.T. Baaijens, W.J. van Veenen, An experimental and numerical study of the wall ironing process of polymer coated sheet metal, Mechanics of Materials 32 7 (2000) 423-443. https://doi.org/10.1016/S0167-6636(00)00013-2

[4] E. Faber, Nanotopography and morphology along metal-polymer interfaces. PhD thesis Rijksuniversiteit Groningen, 2014. ISBN 978-90-367-7457-4

[5] R. van Tijum, W. Vellinga, J.T.M De Hosson, Surface roughening of metal-polymer systems during plastic deformation, Acta Materialia. 55 (2007) 2757-2764. https://doi.org/10.1016/j.actamat.2006.12.013

[6] J. Venema, F. Jonker, R. Stegeman (2021), Roughness development of polymer coated steel during the production process of a can. Paper presented at ESAFORM 2021. 24th International Conference on Material Forming, Liège, Belgique. https://doi.org/10.25518/esaform21.1887
<figure><img src="image_1266.png" /><figcaption>Fig. 7. Confocal measurement 1 x 1 mm of a. Can from earlier investigation [6], b. Can 240 cans/min, c. LFT side Tool A, d. LFT side Tool B.</figcaption></figure>

## Conclusions and recommendation

A study was performed to investigate the tribological behaviour and surface appearance of PET coated steel at different can processing speeds, for a range of tool temperatures and pressures. The tribological behaviour of the PET coating is defined by a complex combination of mechanisms. Several parameters (coating, pressure, temperature) and their interaction determines the frictional behaviour of this product. Temperature is a key parameter governing the coating wear phenomena. In the LFT test, scuffing only occurs above a certain temperature level (195 °C). In can making tests, scuffing only occurred above a certain processing velocity. Pressure has also a clear effect on scuffing. Surface measurements indicate that similar coating failure defects can be observed in both the linear friction test and in industrial-scale can making. This needs to be investigated further by cross sectional analysis. The tests proved that the polymer coating can resist high contact pressure conditions and temperatures. This makes polymer coated steel sheets applicable for a large range of packaging products.

## References

[1] B. Boelen, H. den Hartog, H. van der Weijde, Product performance of polymer coated packaging steel, study of the mechanism of defect growth in cans. Progress in Organic Coatings 50 (2004) 40-46. https://doi.org/10.1016/j.porgcoat.2003.09.011

[2] J. Mulder, G.T. Nagy, P. Šuštarič, T. Šuštar and T. Rodič. (2010) AIP Conf. Proc. 1252 1 (2010), 762–769. https://doi.org/10.1063/1.3457632

[3] H.C.E van der Aa, M.A.H. van der Aa, P.J.G. Schreurs, F.P.T. Baaijens, W.J. van Veenen, An experimental and numerical study of the wall ironing process of polymer coated sheet metal, Mechanics of Materials 32 7 (2000) 423-443. https://doi.org/10.1016/S0167-6636(00)00013-2

[4] E. Faber, Nanotopography and morphology along metal-polymer interfaces. PhD thesis Rijksuniversiteit Groningen, 2014. ISBN 978-90-367-7457-4

[5] R. van Tijum, W. Vellinga, J.T.M De Hosson, Surface roughening of metal-polymer systems during plastic deformation, Acta Materialia. 55 (2007) 2757-2764. https://doi.org/10.1016/j.actamat.2006.12.013

[6] J. Venema, F. Jonker, R. Stegeman (2021), Roughness development of polymer coated steel during the production process of a can. Paper presented at ESAFORM 2021. 24th International Conference on Material Forming, Liège, Belgique. https://doi.org/10.25518/esaform21.1887
# A novel method to investigate tribological behaviors under transient temperatures using Pin-on-Cylinder tribometer and IR-thermography in glass forming

VU Anh Tuan¹,ᵃ*, GRUNWALD Tim²,ᵇ and BERGS Thomas¹,ᶜ

¹Fraunhofer Institute for Production Technology IPT, Aachen, Germany

²Manufacturing Technology Institute (MTI), RWTH Aachen University, Aachen, Germany

ᵃanh.tuan.vu@ipt.fraunhofer.de, ᵇtim.grunwald@ipt.fraunhofer.de,

ᶜthomas.bergs@ipt.fraunhofer.de

**Keywords:** Tribology, Friction, Contact Heat Transfer, Thermography, Glass Forming

**Abstract.** In high-temperature material forming, achieving high precision demands a nuanced understanding of thermal and mechanical interactions at the contact interface. Conventional methods, often involving separate measurements of friction and heat transfer coefficients, encounter challenges as the growing number of influencing factors amplifies experimental complexity. This research introduces an innovative approach enabling the simultaneous determination of both coefficients in a single experimental run. A specially designed pin-on-cylinder tribometer enables the measurement of transient friction forces resulting from temperature variations at the interface, recorded by an infrared thermographic camera. Inverse methods are developed to derive the friction and heat transfer coefficients from the acquired transient force and temperature data. The method expedites the determination of contact coefficients, providing an efficient avenue for numerical and analytical studies in hot forming processes.

**Introduction**

Glass manufacturers are facing ever-growing demands from the optics market, necessitating advancements in manufacturing technologies to satisfy requirements consisting of increased geometrical complexity, high accuracy, energy-efficient production, and low-cost products. Nonisothermal Glass Molding (NGM) has emerged as a promising solution, enabling cost-efficient production of complex precision glass optics [1,2]. NGM involves the compression of a heated glass preform between two mold halves with lower temperatures, resulting in intricate heat exchanges and complex deformation behaviors at the glass-mold interface [3]. To achieve the required accuracy for precision optics, a comprehensive understanding of thermal-mechanical phenomena at glass-mold contact boundary, including friction and thermal conductance, is crucial.

In previous studies, the characterization of contact coefficients involved separate measurements of friction and contact heat transfer coefficients. While earlier works primarily explored the temperature-dependent nature of friction in glass forming [4], the influence of factors such as pressure, sliding velocity, and surface finish were investigated [5]. Similarly, contact heat transfer coefficients have been measured, considering temperature, pressure, and surface roughness [6]. However, conventional methods encounter challenges as the increasing number of influencing factors leads to a considerable rise in the number of experiments. Furthermore, numerous test setups have been developed to characterize friction and contact heat transfer individually, contributing to the complexity of the experimental process. For example, ring compression [7], double shear test [8], and pin-on-disc [9] have been reported for the friction measurement. For the contact heat transfer measurement, both steady-state [10] and transient methods [11] have been explored. The latter method demonstrated a highly time-efficient approach for determining contact heat transfer coefficients, varying with temperature, pressure, and surface roughness.

<figure><img src="image_1265.png" /></figure>
# A novel method to investigate tribological behaviors under transient temperatures using Pin-on-Cylinder tribometer and IR-thermography in glass forming

VU Anh Tuan¹,ᵃ*, GRUNWALD Tim²,ᵇ and BERGS Thomas¹,ᶜ

¹Fraunhofer Institute for Production Technology IPT, Aachen, Germany

²Manufacturing Technology Institute (MTI), RWTH Aachen University, Aachen, Germany

ᵃanh.tuan.vu@ipt.fraunhofer.de, ᵇtim.grunwald@ipt.fraunhofer.de,

ᶜthomas.bergs@ipt.fraunhofer.de

**Keywords:** Tribology, Friction, Contact Heat Transfer, Thermography, Glass Forming

**Abstract.** In high-temperature material forming, achieving high precision demands a nuanced understanding of thermal and mechanical interactions at the contact interface. Conventional methods, often involving separate measurements of friction and heat transfer coefficients, encounter challenges as the growing number of influencing factors amplifies experimental complexity. This research introduces an innovative approach enabling the simultaneous determination of both coefficients in a single experimental run. A specially designed pin-on-cylinder tribometer enables the measurement of transient friction forces resulting from temperature variations at the interface, recorded by an infrared thermographic camera. Inverse methods are developed to derive the friction and heat transfer coefficients from the acquired transient force and temperature data. The method expedites the determination of contact coefficients, providing an efficient avenue for numerical and analytical studies in hot forming processes.

**Introduction**

Glass manufacturers are facing ever-growing demands from the optics market, necessitating advancements in manufacturing technologies to satisfy requirements consisting of increased geometrical complexity, high accuracy, energy-efficient production, and low-cost products. Nonisothermal Glass Molding (NGM) has emerged as a promising solution, enabling cost-efficient production of complex precision glass optics [1,2]. NGM involves the compression of a heated glass preform between two mold halves with lower temperatures, resulting in intricate heat exchanges and complex deformation behaviors at the glass-mold interface [3]. To achieve the required accuracy for precision optics, a comprehensive understanding of thermal-mechanical phenomena at glass-mold contact boundary, including friction and thermal conductance, is crucial.

In previous studies, the characterization of contact coefficients involved separate measurements of friction and contact heat transfer coefficients. While earlier works primarily explored the temperature-dependent nature of friction in glass forming [4], the influence of factors such as pressure, sliding velocity, and surface finish were investigated [5]. Similarly, contact heat transfer coefficients have been measured, considering temperature, pressure, and surface roughness [6]. However, conventional methods encounter challenges as the increasing number of influencing factors leads to a considerable rise in the number of experiments. Furthermore, numerous test setups have been developed to characterize friction and contact heat transfer individually, contributing to the complexity of the experimental process. For example, ring compression [7], double shear test [8], and pin-on-disc [9] have been reported for the friction measurement. For the contact heat transfer measurement, both steady-state [10] and transient methods [11] have been explored. The latter method demonstrated a highly time-efficient approach for determining contact heat transfer coefficients, varying with temperature, pressure, and surface roughness.

<figure><img src="image_1267.png" /></figure>

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under license by Materials Research Forum LLC.
This research addresses the limitations of conventional methods by introducing a novel approach using a Pin-on-Cylinder (PoC) tribometer. The tribometer, equipped with an infrared thermography camera (IR-camera), allows for the simultaneous measurement of transient temperatures of contacting materials near the contact point. By solving the inverse heat transfer problem, contact heat transfer coefficients can be derived from transient temperature measurements. Concurrently, the variation of transient friction force with temperature can be recorded, enabling the derivation of friction coefficients. The experimental setup and the application of inverse heat transfer solutions to determine friction and contact heat transfer coefficients are elaborated in the subsequent chapter. This innovative method offers a more efficient and integrated approach to characterizing contact coefficients in glass forming processes.

## Experimental setup

To achieve the research goal, this study constructed a novel tribometer based on the pin-on-cylinder principle. The tribometer incorporates the analogy method proposed for studying friction by Zemzemi et al. [12] and the inverse method for exploring transient contact heat transfer in glass forming using the IR-camera introduced by Vu et al. [13]. The new tribometer aims to investigate the process parameters as key factors influencing friction and heat transfer between glass and steel materials at elevated temperatures, emphasizing nonisothermal conditions where the temperatures of the glass and steel differ. This deliberate non-uniformity mimics realistic scenarios encountered in various glass forming processes, enhancing the study's practical relevance.

Fig. 1 introduces the tribometer setup and its key components. The apparatus, affixed to a lathe slide, featured a centered and securely clamped steel cylinder. To prevent the cylinder bending during operation, two rollers as a counter holder provided firm support. In the friction experiment, the cylinder was rotated ($\omega$), while the glass pin was constantly pressed onto the cylinder with a normal force ($F_N$) by a hydraulic unit and traversed linearly ($v$) along the cylinder. This dynamic combination of axial feed and rotational speed enabled the continual creation of new contact points as the pin traversed the cylinder. This process aimed to level surface roughness and induced material hardening through multiple traversals along the friction path. Moreover, the resulting helical trajectory of the pin on the cylinder allowed for the deformation of previously unaffected material, even after a full rotation of the cylinder.

<figure><img src="image_1266.png" /><figcaption>Fig. 1. Experimental setup and components of the PoC tribometer.</figcaption></figure>

**Heating methods.** Two distinct methods were employed for heating the specimens. The steel cylinder underwent induction heating by being placed within two copper rings, while the glass pin, held in a clamping holder, was heated using a heating cartridge. Additionally, to protect the force sensor, positioned directly behind the glass specimen, from thermal interference, a ceramic insulation was placed between the heating cartridge and the force sensor. This setup enabled the glass pin to be heated to temperatures exceeding the glass transition temperature $T_g$ ($T_g$ = 557 °C).
This research addresses the limitations of conventional methods by introducing a novel approach using a Pin-on-Cylinder (PoC) tribometer. The tribometer, equipped with an infrared thermography camera (IR-camera), allows for the simultaneous measurement of transient temperatures of contacting materials near the contact point. By solving the inverse heat transfer problem, contact heat transfer coefficients can be derived from transient temperature measurements. Concurrently, the variation of transient friction force with temperature can be recorded, enabling the derivation of friction coefficients. The experimental setup and the application of inverse heat transfer solutions to determine friction and contact heat transfer coefficients are elaborated in the subsequent chapter. This innovative method offers a more efficient and integrated approach to characterizing contact coefficients in glass forming processes.

## Experimental setup

To achieve the research goal, this study constructed a novel tribometer based on the pin-on-cylinder principle. The tribometer incorporates the analogy method proposed for studying friction by Zemzemi et al. [12] and the inverse method for exploring transient contact heat transfer in glass forming using the IR-camera introduced by Vu et al. [13]. The new tribometer aims to investigate the process parameters as key factors influencing friction and heat transfer between glass and steel materials at elevated temperatures, emphasizing nonisothermal conditions where the temperatures of the glass and steel differ. This deliberate non-uniformity mimics realistic scenarios encountered in various glass forming processes, enhancing the study's practical relevance.

Fig. 1 introduces the tribometer setup and its key components. The apparatus, affixed to a lathe slide, featured a centered and securely clamped steel cylinder. To prevent the cylinder bending during operation, two rollers as a counter holder provided firm support. In the friction experiment, the cylinder was rotated ($\omega$), while the glass pin was constantly pressed onto the cylinder with a normal force ($F_N$) by a hydraulic unit and traversed linearly ($\nu$) along the cylinder. This dynamic combination of axial feed and rotational speed enabled the continual creation of new contact points as the pin traversed the cylinder. This process aimed to level surface roughness and induced material hardening through multiple traversals along the friction path. Moreover, the resulting helical trajectory of the pin on the cylinder allowed for the deformation of previously unaffected material, even after a full rotation of the cylinder.

<figure><img src="image_1268.png" /><figcaption>Fig. 1. Experimental setup and components of the PoC tribometer.</figcaption></figure>

**Heating methods.** Two distinct methods were employed for heating the specimens. The steel cylinder underwent induction heating by being placed within two copper rings, while the glass pin, held in a clamping holder, was heated using a heating cartridge. Additionally, to protect the force sensor, positioned directly behind the glass specimen, from thermal interference, a ceramic insulation was placed between the heating cartridge and the force sensor. This setup enabled the glass pin to be heated to temperatures exceeding the glass transition temperature $T_g$ ($T_g = 557$ °C).
**Measuring data acquisition.** For precise measurement in the tribological tests, accurate data necessitates capturing process forces and temperature variations at the contact interface. Process forces were recorded using a three-component force measurement platform, capable of determining dynamic and static forces in three orthogonal directions ($F_x$, $F_y$, and $F_z$) as depicted in Fig. 1. This platform utilized piezo elements with force-proportional charge displacements, and the signals were processed by a charge amplifier and LabVIEW software. Variable amplification and filtering were applied, including a low-pass filter with a 1 kHz cut-off frequency. Simultaneously, transient temperatures of the glass and cylinder were monitored using an infrared thermographic camera (VarioCAM®HD head, InfraTec). The camera, with a temperature measuring range up to 2000°C and an accuracy of ±1°C, captured thermal radiation in the spectral range from 7.5 to 14 µm at a full-frame rate of 30 Hz. For the ease of imaging data analysis and accurate measurement data using IR thermographic techniques, both glass and cylinder surfaces were coated with high-temperature resistant black layers, possessing an emissivity of approximately 0.9. These thin black layers not only enhance measurement accuracy by minimizing the influence of surrounding radiation reflected at the measuring surfaces but also precisely determine the emissivity of both specimens across broad temperatures set for the IR-camera [13].

**Samples' preparation.** Contrasting with the PoC setup utilized in the prior work by Hild et al. [14], the tribometer employed in this present study involved an adaptation to essentially enable high-temperature tribological tests for glass-forming experiments. During these tests, deformation primarily occurred in the glass, making temperature homogeneity crucial for understanding the material behaviors of glass, specifically thermoviscoelastic deformation [15,16], and for subsequent inverse analysis. Hence, the pin was crafted from N-BK7 glass, a commonly used composition in glass molding processes, and a high-temperature-resistant steel grade, 1.4181 (AISI 314), was employed for the cylinder, given its widespread use as a mold material in NGM processes [17,18]. The thermal and mechanical properties of the materials used for the samples are given in Table 1. It is emphasized that prior to tribo-experiments, a sufficiently long heating period was carefully identified aiming to homogenize the temperatures of the specimens.

<table><caption>Table 1. Thermal- and mechanical properties of glass pin and steel cylinder</caption><thead><tr><td>Thermal properties</td><td>Unit</td><td>N-BK 7</td><td>1.4181 steel</td></tr></thead><tbody><tr><td>Density, ρ</td><td>kg/m³</td><td>2510</td><td>7900</td></tr><tr><td>Thermal conductivity, λ</td><td>W/mK</td><td>1.114</td><td>15</td></tr><tr><td>Specific heat, C<sub>p</sub></td><td>J/kgK</td><td>858</td><td>500</td></tr><tr><td>Young modulus, E</td><td>GPa</td><td>82</td><td>196</td></tr><tr><td>Poisson's ratio, ν</td><td></td><td>0.206</td><td>0.28</td></tr><tr><td>Glass transition temperature, T<sub>g</sub></td><td>°C</td><td>557</td><td>-</td></tr></tbody></table>

Although it is commonly agreed that surface roughness is a factor influencing on the thermal and mechanical phenomena at the contact interface, the present study does not explicitly consider its impact. Special attention was devoted to surface preparation, with the objective of ensuring identical surface roughness for all test samples. The glass specimens underwent fine grinding and polishing procedures following the specifications outlined in DIN ISO 10110, achieving the surface finish equivalent to P3 grade with Ra = 8-16 nm. The cylindrical samples were precision-machined through turning, followed by a subsequent polishing process achieving surface roughness varying in the range Ra = 40-80 nm (P2 grade).

**Methodology**

Building upon the newly developed PoC tribometer setup, this study introduces methods that enable the concurrent determination of contact heat transfer and friction coefficients in a single operation, through either *sequential approach* or *parallel approach*.
**Measuring data acquisition.** For precise measurement in the tribological tests, accurate data necessitates capturing process forces and temperature variations at the contact interface. Process forces were recorded using a three-component force measurement platform, capable of determining dynamic and static forces in three orthogonal directions ($F_x$, $F_y$, and $F_z$) as depicted in Fig. 1. This platform utilized piezo elements with force-proportional charge displacements, and the signals were processed by a charge amplifier and LabVIEW software. Variable amplification and filtering were applied, including a low-pass filter with a 1 kHz cut-off frequency. Simultaneously, transient temperatures of the glass and cylinder were monitored using an infrared thermographic camera (VarioCAM®HD head, InfraTec). The camera, with a temperature measuring range up to 2000°C and an accuracy of ±1°C, captured thermal radiation in the spectral range from 7.5 to 14 µm at a full-frame rate of 30 Hz. For the ease of imaging data analysis and accurate measurement data using IR thermographic techniques, both glass and cylinder surfaces were coated with high-temperature resistant black layers, possessing an emissivity of approximately 0.9. These thin black layers not only enhance measurement accuracy by minimizing the influence of surrounding radiation reflected at the measuring surfaces but also precisely determine the emissivity of both specimens across broad temperatures set for the IR-camera [13].

**Samples' preparation.** Contrasting with the PoC setup utilized in the prior work by Hild et al. [14], the tribometer employed in this present study involved an adaptation to essentially enable high-temperature tribological tests for glass-forming experiments. During these tests, deformation primarily occurred in the glass, making temperature homogeneity crucial for understanding the material behaviors of glass, specifically thermoviscoelastic deformation [15,16], and for subsequent inverse analysis. Hence, the pin was crafted from N-BK7 glass, a commonly used composition in glass molding processes, and a high-temperature-resistant steel grade, 1.4181 (AISI 314), was employed for the cylinder, given its widespread use as a mold material in NGM processes [17,18]. The thermal and mechanical properties of the materials used for the samples are given in Table 1. It is emphasized that prior to tribo-experiments, a sufficiently long heating period was carefully identified aiming to homogenize the temperatures of the specimens.

<table><caption>Table 1. Thermal- and mechanical properties of glass pin and steel cylinder</caption><thead><tr><td>Thermal properties</td><td>Unit</td><td>N-BK 7</td><td>1.4181 steel</td></tr></thead><tbody><tr><td>Density, ρ</td><td>kg/m³</td><td>2510</td><td>7900</td></tr><tr><td>Thermal conductivity, λ</td><td>W/mK</td><td>1.114</td><td>15</td></tr><tr><td>Specific heat, C<sub>p</sub></td><td>J/kgK</td><td>858</td><td>500</td></tr><tr><td>Young modulus, E</td><td>GPa</td><td>82</td><td>196</td></tr><tr><td>Poisson's ratio, ν</td><td>1</td><td>0.206</td><td>0.28</td></tr><tr><td>Glass transition temperature, T<sub>g</sub></td><td>°C</td><td>557</td><td>-</td></tr></tbody></table>

Although it is commonly agreed that surface roughness is a factor influencing on the thermal and mechanical phenomena at the contact interface, the present study does not explicitly consider its impact. Special attention was devoted to surface preparation, with the objective of ensuring identical surface roughness for all test samples. The glass specimens underwent fine grinding and polishing procedures following the specifications outlined in DIN ISO 10110, achieving the surface finish equivalent to P3 grade with Ra = 8-16 nm. The cylindrical samples were precision-machined through turning, followed by a subsequent polishing process achieving surface roughness varying in the range Ra = 40-80 nm (P2 grade).

**Methodology**

Building upon the newly developed PoC tribometer setup, this study introduces methods that enable the concurrent determination of contact heat transfer and friction coefficients in a single operation, through either sequential approach or parallel approach.
<figure><img src="image_1267.png" /><figcaption>Fig. 2. (a) Thermographic image of a PoC experiment, (b) procedure of the sequential method and measuring points by the IR-camera, and (c) transient temperatures of the specimens during the contact heat transfer measurement.</figcaption></figure>

**Sequential approach.** This approach was designed to measure the contact heat transfer coefficient before conducting friction measurements in a quasi-isothermal process. Specifically, the glass and cylinder specimens were individually heated using the heating cartridge and induction, respectively, reaching predefined temperatures. Subsequently, the glass was brought into contact with the cylinder at a specified normal force, with no sliding velocity applied during the contact heat transfer measurement. Fig. 2a introduces a thermographic image of the specimens. Throughout the contact heat transfer measurement period, the IR-camera (see Fig. 2b) captured transient temperatures near the contact point, which were then utilized to calculate the contact heat transfer coefficient. The friction measurement began when the temperatures of the specimens were nearly identical. In this phase, a constant rotational speed of the cylinder and pin feed were applied, and process forces were collected under a constant normal force to derive the friction coefficients.

**Parallel approach.** This approach focused on measuring friction coefficients under a nonisothermal process, utilizing heat transfer at the glass-cylinder interface and variations in glass temperature at the contact point to derive the contact heat transfer coefficient. After heating, the specimens were brought into contact, initiating measurements of process forces and glass temperature. Throughout the measurement, the normal force and rotational speed are held constant.

**Inverse heat transfer solutions.** The contact heat transfer coefficient, quantifying the heat flow through the interface, hinges on the knowledge of two variables: the heat flux ($\dot{q}'$) and the temperature difference ($\Delta T$) as defined by Eq. 1. The latter is determined by the temperatures of the contacting materials—the glass specimen ($T_1$) and the cylinder ($T_2$). While the IR-camera allows measurement of transient temperatures, the heat flux remains unknown. For this reason, the coefficient cannot be directly measured through the thermographic method. Consequently, the derivation of the contact heat transfer coefficient necessitates inverse heat transfer solutions [19].

$$h_c = \frac{\dot{q}''}{\Delta T} = \frac{\dot{q}''}{T_1 - T_2} \qquad (1)$$

In sequential method, the contact point remains fixed throughout the contact heat transfer measurement. As a result, it permits the IR-camera to consistently capture the same measuring points of the glass and the cylinder near the contact interface during the measuring period. Fig. 2c shows a plot of transient temperature profiles of the measuring points during the recording period $t$, $T_{i,exp}(t)$ ($i = 1,2$). The objective of the inverse solution is to iteratively estimate the heat flux until achieving a precise calculation of the transient temperatures of the contacting materials. In each iteration, the temperature of each specimen is computed using the energy balance equation:

$$\rho \cdot C_p \cdot \frac{\partial T}{\partial t} = \lambda \cdot \frac{\partial^2 T}{\partial x^2} - h_{eff} \cdot \frac{P}{A} \cdot (T - T_{\infty}), \text{ with } \dot{q}'' = -\lambda \frac{\partial T}{\partial x}. \qquad (2)$$
<figure><img src="image_1269.png" /><figcaption>Fig. 2. (a) Thermographic image of a PoC experiment, (b) procedure of the sequential method and measuring points by the IR-camera, and (c) transient temperatures of the specimens during the contact heat transfer measurement.</figcaption></figure>

**Sequential approach.** This approach was designed to measure the contact heat transfer coefficient before conducting friction measurements in a quasi-isothermal process. Specifically, the glass and cylinder specimens were individually heated using the heating cartridge and induction, respectively, reaching predefined temperatures. Subsequently, the glass was brought into contact with the cylinder at a specified normal force, with no sliding velocity applied during the contact heat transfer measurement. Fig. 2a introduces a thermographic image of the specimens. Throughout the contact heat transfer measurement period, the IR-camera (see Fig. 2b) captured transient temperatures near the contact point, which were then utilized to calculate the contact heat transfer coefficient. The friction measurement began when the temperatures of the specimens were nearly identical. In this phase, a constant rotational speed of the cylinder and pin feed were applied, and process forces were collected under a constant normal force to derive the friction coefficients.

**Parallel approach.** This approach focused on measuring friction coefficients under a nonisothermal process, utilizing heat transfer at the glass-cylinder interface and variations in glass temperature at the contact point to derive the contact heat transfer coefficient. After heating, the specimens were brought into contact, initiating measurements of process forces and glass temperature. Throughout the measurement, the normal force and rotational speed are held constant.

**Inverse heat transfer solutions.** The contact heat transfer coefficient, quantifying the heat flow through the interface, hinges on the knowledge of two variables: the heat flux ($\dot{q}'$) and the temperature difference ($\Delta T$) as defined by Eq. 1. The latter is determined by the temperatures of the contacting materials—the glass specimen ($T_1$) and the cylinder ($T_2$). While the IR-camera allows measurement of transient temperatures, the heat flux remains unknown. For this reason, the coefficient cannot be directly measured through the thermographic method. Consequently, the derivation of the contact heat transfer coefficient necessitates inverse heat transfer solutions [19].

$$h_c = \frac{\dot{q}''}{\Delta T} = \frac{\dot{q}''}{T_1 - T_2} \qquad (1)$$

In sequential method, the contact point remains fixed throughout the contact heat transfer measurement. As a result, it permits the IR-camera to consistently capture the same measuring points of the glass and the cylinder near the contact interface during the measuring period. Fig. 2c shows a plot of transient temperature profiles of the measuring points during the recording period $t$, $T_{i,exp}(t)$ ($i = 1,2$). The objective of the inverse solution is to iteratively estimate the heat flux until achieving a precise calculation of the transient temperatures of the contacting materials. In each iteration, the temperature of each specimen is computed using the energy balance equation:

$$\rho \cdot C_p \cdot \frac{\partial T}{\partial t} = \lambda \cdot \frac{\partial^2 T}{\partial x^2} - h_{eff} \cdot \frac{P}{A} \cdot (T - T_{\infty}), \text{ with } \dot{q}'' = -\lambda \frac{\partial T}{\partial x}. \qquad (2)$$
where $\rho$, $C_p$ and $\lambda$ are the thermal properties of the specimens given in Table 1; $h_{eff}$ denotes the effective heat transfer coefficient, comprising of both convective and radiative heat losses to the environment at a specific ambient temperature $T_\infty$; $P$ and $A$ are the perimeter and area, respectively; and $x$ is the position where the node temperature is calculated.

Eq. (2) provides the computed temperatures throughout the measuring period of the specimens, referred as $T_{i,est}(t)$. If the disparity between the measured and computed temperatures exceeds an acceptable tolerance, the computed temperature requires correction by estimating a new heat flux through the conjugate gradient method [20]. This iterative procedure aims to refine the transient heat flux $\dot{q}''(t)$ by minimizing an objective function $\Omega(\dot{q}''(t))$, defined as:

$$ \Omega(\dot{q}''(t)) = \int_{0}^{t} (T_{i,exp}(\xi) - T_{i,est}(\xi))^2 d\xi \rightarrow \min. \quad (3) $$

In Eq. (3), $T_{i,exp}(\xi)$ and $T_{i,est}(\xi)$ are the vectors containing the measured and estimated temperatures, respectively, taken at a given time $\xi$ ($0 < \xi < t$). Fig. 3a illustrates the flowchart of the inverse procedure employed in the sequential method. Details of the iterative procedure for solving inverse heat transfer problem using the conjugate gradient method can be found in [13].

<figure><img src="image_1268.png" /><figcaption>Fig. 3. Flowcharts of inverse solutions for determining the contact heat transfer coefficients.</figcaption></figure>

In parallel approach, deriving the contact heat transfer coefficient from the direct temperature measurement of the contact pair proves more demanding. This difficulty arises because the cylinder rotates continuously during the measuring period of the contact heat transfer and friction coefficients. Because of the rotation, the glass pin consistently encounters new contact points on the cylinder, forming a helical friction path as schematically depicted in Fig. 1. Since the IR-camera was configured to measure temperatures at the contact points, the temperature of the glass pin can be recorded from a fixed point. However, the temperature reading of the cylinder follows the friction path, resulting in signal oscillations. Consequently, the oscillating measured data can pose an ill-posed problem when solving the inverse heat transfer using the conjugate gradient method [20], as approached in the sequential method.

To address this challenge, an FE-inverse approach was proposed. Specifically, a numerical model of the PoC setup was established to solve the nonlinear heat exchanges at the contact interface. The inputs for this model included the transient temperature measurements of the glass specimen $T_1(t)$ and the constant and homogeneous initial temperature of the cylinder $T_2(t = 0)$. Initially, an arbitrary contact heat transfer coefficient was given, which then allows for the estimation of temperatures at corresponding points on the glass as captured by the IR-camera. The estimated temperatures were then compared with those measured experimentally. Subsequent iterative simulations were carried out through a fully automated routine scripted in Python, aiming
where $\rho$, $C_p$ and $\lambda$ are the thermal properties of the specimens given in Table 1; $h_{eff}$ denotes the effective heat transfer coefficient, comprising of both convective and radiative heat losses to the environment at a specific ambient temperature $T_\infty$; $P$ and $A$ are the perimeter and area, respectively; and $x$ is the position where the node temperature is calculated.

Eq. (2) provides the computed temperatures throughout the measuring period of the specimens, referred as $T_{i,est}(t)$. If the disparity between the measured and computed temperatures exceeds an acceptable tolerance, the computed temperature requires correction by estimating a new heat flux through the conjugate gradient method [20]. This iterative procedure aims to refine the transient heat flux $\dot{q}''(t)$ by minimizing an objective function $\Omega(\dot{q}''(t))$, defined as:

$$ \Omega(\dot{q}''(t)) = \int_{0}^{t} (T_{i,exp}(\xi) - T_{i,est}(\xi))^2 d\xi \rightarrow \min. \quad (3) $$

In Eq. (3), $T_{i,exp}(\xi)$ and $T_{i,est}(\xi)$ are the vectors containing the measured and estimated temperatures, respectively, taken at a given time $\xi$ ($0 < \xi < t$). Fig. 3a illustrates the flowchart of the inverse procedure employed in the sequential method. Details of the iterative procedure for solving inverse heat transfer problem using the conjugate gradient method can be found in [13].

<figure><img src="image_1270.png" /><figcaption>Fig. 3. Flowcharts of inverse solutions for determining the contact heat transfer coefficients.</figcaption></figure>

In parallel approach, deriving the contact heat transfer coefficient from the direct temperature measurement of the contact pair proves more demanding. This difficulty arises because the cylinder rotates continuously during the measuring period of the contact heat transfer and friction coefficients. Because of the rotation, the glass pin consistently encounters new contact points on the cylinder, forming a helical friction path as schematically depicted in Fig. 1. Since the IR-camera was configured to measure temperatures at the contact points, the temperature of the glass pin can be recorded from a fixed point. However, the temperature reading of the cylinder follows the friction path, resulting in signal oscillations. Consequently, the oscillating measured data can pose an ill-posed problem when solving the inverse heat transfer using the conjugate gradient method [20], as approached in the sequential method.

To address this challenge, an FE-inverse approach was proposed. Specifically, a numerical model of the PoC setup was established to solve the nonlinear heat exchanges at the contact interface. The inputs for this model included the transient temperature measurements of the glass specimen $T_1(t)$ and the constant and homogeneous initial temperature of the cylinder $T_2(t = 0)$. Initially, an arbitrary contact heat transfer coefficient was given, which then allows for the estimation of temperatures at corresponding points on the glass as captured by the IR-camera. The estimated temperatures were then compared with those measured experimentally. Subsequent iterative simulations were carried out through a fully automated routine scripted in Python, aiming
to minimize the differences between the transient temperatures by updating new contact heat transfer coefficients. The flowchart of this procedure is described in Fig. 3b.

Finally, the derivation the friction coefficient using the PoC tribometer necessitates a particular procedure. As depicted in Fig. 1, the force sensors included the three components of the process force signals, from which the normal force and tangential force were computed. However, the measured tangential force encompassed not only the friction force but also the force required to deform the specimens. To calculate the actual friction coefficient, an iterative approach utilizing FEM simulations of the tribometer, as elucidated in [12], was performed. Initially, friction was modeled with the apparent friction coefficient calculated from experimentally measured process forces. The difference between the tangential force extracted from the simulation and the experimental data was assumed to be the force resulting from the samples' deformation. A new friction coefficient was then calculated from the experimental data, and this process repeated until the difference between the apparent friction coefficient from the simulation and the experimental value can be negligible. Leveraging the PoC apparatus and this computational approach, variations in the normal force, rotational speed, and specimen temperature allowed for the investigation of friction coefficients based on contact normal stress, relative velocity, and interfacial temperature.

## Results

The contact heat transfer coefficients determined through the sequential approach are shown in Fig. 4. In Fig. 4a, the transient contact heat transfer coefficient $h_c(t)$ is computed based on the measured transient temperatures of the two specimens. The plot presents the result of a contact pair where the initial temperatures of glass and cylinder are 550 °C and 500 °C (550/500 °C), respectively, under the applied pressure of 24 MPa. The transient coefficient exhibits a significant increase as soon as the glass pin contacted the cylinder, followed by a steady-state process. It is noteworthy that the initial surge in the coefficient aligns with the rise in contact pressure [11]. Once the predefined contact pressure was attained, the variation in the contact heat transfer coefficient became slight and stabilized after 4 seconds. Therefore, the plot exhibits the temperature variations of the contact pair within a 4-second period, and the coefficient was considered steady-state after this duration.

<figure><img src="image_1269.png" /></figure>

<figure><img src="image_1270.png" /><figcaption>Fig. 4. (a) Derivation of contact heat transfer coefficient from the measured temperatures in the sequential method, and (b) dependence of contact coefficients on pressure and initial temperatures of the contact pair.</figcaption></figure>

Furthermore, the influences of the contact pressure and the temperatures of the contact pair were examined, and the results are presented Fig. 4b. For these investigations, a glass temperature of 550 °C, close to the glass transition temperature $T_g$, was chosen for all experiments, while the cylinder temperatures were varied within the range of 350 °C to 500 °C. The results clearly demonstrate a strong dependency of the pair temperature on the contact heat transfer coefficients.
to minimize the differences between the transient temperatures by updating new contact heat transfer coefficients. The flowchart of this procedure is described in Fig. 3b.

Finally, the derivation of the friction coefficient using the PoC tribometer necessitates a particular procedure. As depicted in Fig. 1, the force sensors included the three components of the process force signals, from which the normal force and tangential force were computed. However, the measured tangential force encompassed not only the friction force but also the force required to deform the specimens. To calculate the actual friction coefficient, an iterative approach utilizing FEM simulations of the tribometer, as elucidated in [12], was performed. Initially, friction was modeled with the apparent friction coefficient calculated from experimentally measured process forces. The difference between the tangential force extracted from the simulation and the experimental data was assumed to be the force resulting from the samples' deformation. A new friction coefficient was then calculated from the experimental data, and this process repeated until the difference between the apparent friction coefficient from the simulation and the experimental value can be negligible. Leveraging the PoC apparatus and this computational approach, variations in the normal force, rotational speed, and specimen temperature allowed for the investigation of friction coefficients based on contact normal stress, relative velocity, and interfacial temperature.

## Results

The contact heat transfer coefficients determined through the sequential approach are shown in Fig. 4. In Fig. 4a, the transient contact heat transfer coefficient $h_c(t)$ is computed based on the measured transient temperatures of the two specimens. The plot presents the result of a contact pair where the initial temperatures of glass and cylinder are 550 °C and 500 °C (550/500 °C), respectively, under the applied pressure of 24 MPa. The transient coefficient exhibits a significant increase as soon as the glass pin contacted the cylinder, followed by a steady-state process. It is noteworthy that the initial surge in the coefficient aligns with the rise in contact pressure [11]. Once the predefined contact pressure was attained, the variation in the contact heat transfer coefficient became slight and stabilized after 4 seconds. Therefore, the plot exhibits the temperature variations of the contact pair within a 4-second period, and the coefficient was considered steady-state after this duration.

<figure><img src="image_1271.png" /></figure>

<figure><img src="image_1272.png" /><figcaption>Fig. 4. (a) Derivation of contact heat transfer coefficient from the measured temperatures in the sequential method, and (b) dependence of contact coefficients on pressure and initial temperatures of the contact pair.</figcaption></figure>

Furthermore, the influences of the contact pressure and the temperatures of the contact pair were examined, and the results are presented Fig. 4b. For these investigations, a glass temperature of 550 °C, close to the glass transition temperature $T_g$, was chosen for all experiments, while the cylinder temperatures were varied within the range of 350 °C to 500 °C. The results clearly demonstrate a strong dependency of the pair temperature on the contact heat transfer coefficients.
When the glass pin was brought into contact with a higher cylinder temperature, it led to a higher interfacial temperature. Consequently, the elevated interfacial temperature promoted deformation of the contact pair, resulting in an increased contact area. With the enlargement of the contact area, more heat transfer occurs through the contact. Moreover, the contact pressure additionally contributes to the growth of the contact area; hence, higher applied contact pressures increase the contact heat transfer coefficients. It is observed that the contact heat transfer coefficients linearly increase with the applied pressures at low interfacial temperatures. However, when the interfacial temperature is sufficiently high, such as 550/500 °C, where the interfacial temperature is close to the glass transient temperature $T_g$, the growth of contact heat transfer coefficients become nonlinear. The linear increase of the contact heat transfer coefficients in the low interfacial temperature range is attributed to the elastic behavior of the material pair, where the deformations of the pair linearly increase with the applied pressures. However, at a temperature in the glass transition region, the glass deformation is dominated by a viscoelastic response, which is thermal-history-, pressure-, and time-dependent [21]. Ultimately, the combined elastic-viscoelastic deformation behaviors of the material pair contribute to the nonlinear increase of the contact heat transfer coefficients concerning pressure and interfacial temperature.

In Fig. 4b, the pressures are referred to the locally normal contact stresses at the pin-cylinder contact point. The contact stresses were derived from the applied forces using the Hertzian theory of contact for sphere-cylinder elastic solids [22]. The material properties necessary for calculating the contact stress were obtained at room temperature, given in Table 1. In the present study, we assumed a constant contact pressure throughout the measuring period, corresponding to the initial applied force. This assumption implies that the contact area, influenced by the macroscopic deformation of glass, remained unchanged. The implications of any contact pressure variation resulting from the macroscopic deformation, governed by the stress relaxation phenomenon of glass, will be thoroughly discussed in the forthcoming paper.

<figure><img src="image_1271.png" /><figcaption>Fig. 5. Determination of contact heat transfer coefficient from the measured temperatures in the parallel method.</figcaption></figure>

Fig. 5 presents the results of inverse computation of the contact heat transfer coefficients in the parallel method. In Fig. 5a, the transient temperature profiles of two points (sensors) measured on the surface of the glass pin are plotted. The first point $T_{1,1}$ was extracted directly adjacent to the contact interface, and the other $T_{1,2}$ was positioned 1 mm further from the interface. As described in Fig. 3b, an FE model was built and served as the nonlinear numerical solver for the inverse contact heat transfer simulation. The iterative estimation of transient temperatures for the identified sensors involved varying the contact heat transfer coefficient.

The results demonstrate a noteworthy agreement between the estimated temperatures obtained through the FE model and experimental measurements, emphasizing the efficacy of the multi-
When the glass pin was brought into contact with a higher cylinder temperature, it led to a higher interfacial temperature. Consequently, the elevated interfacial temperature promoted deformation of the contact pair, resulting in an increased contact area. With the enlargement of the contact area, more heat transfer occurs through the contact. Moreover, the contact pressure additionally contributes to the growth of the contact area; hence, higher applied contact pressures increase the contact heat transfer coefficients. It is observed that the contact heat transfer coefficients linearly increase with the applied pressures at low interfacial temperatures. However, when the interfacial temperature is sufficiently high, such as 550/500 °C, where the interfacial temperature is close to the glass transient temperature $T_g$, the growth of contact heat transfer coefficients become nonlinear. The linear increase of the contact heat transfer coefficients in the low interfacial temperature range is attributed to the elastic behavior of the material pair, where the deformations of the pair linearly increase with the applied pressures. However, at a temperature in the glass transition region, the glass deformation is dominated by a viscoelastic response, which is thermal-history-, pressure-, and time-dependent [21]. Ultimately, the combined elastic-viscoelastic deformation behaviors of the material pair contribute to the nonlinear increase of the contact heat transfer coefficients concerning pressure and interfacial temperature.

In Fig. 4b, the pressures are referred to the locally normal contact stresses at the pin-cylinder contact point. The contact stresses were derived from the applied forces using the Hertzian theory of contact for sphere-cylinder elastic solids [22]. The material properties necessary for calculating the contact stress were obtained at room temperature, given in Table 1. In the present study, we assumed a constant contact pressure throughout the measuring period, corresponding to the initial applied force. This assumption implies that the contact area, influenced by the macroscopic deformation of glass, remained unchanged. The implications of any contact pressure variation resulting from the macroscopic deformation, governed by the stress relaxation phenomenon of glass, will be thoroughly discussed in the forthcoming paper.

<figure><img src="image_1273.png" /><figcaption>Fig. 5. Determination of contact heat transfer coefficient from the measured temperatures in the parallel method.</figcaption></figure>

Fig. 5 presents the results of inverse computation of the contact heat transfer coefficients in the parallel method. In Fig. 5a, the transient temperature profiles of two points (sensors) measured on the surface of the glass pin are plotted. The first point $T_{1,1}$ was extracted directly adjacent to the contact interface, and the other $T_{1,2}$ was positioned 1 mm further from the interface. As described in Fig. 3b, an FE model was built and served as the nonlinear numerical solver for the inverse contact heat transfer simulation. The iterative estimation of transient temperatures for the identified sensors involved varying the contact heat transfer coefficient.

The results demonstrate a noteworthy agreement between the estimated temperatures obtained through the FE model and experimental measurements, emphasizing the efficacy of the multi-
objective solution. The convergence plot in Fig. 5b shows that approximately 40 iterations suffice to optimize the contact heat transfer coefficient, emphasizing the efficiency of the proposed approach. The derived contact heat transfer coefficient for this example in the parallel method was found comparable to that obtained through the sequential approach.

Finally, Fig. 6 presents the process forces obtained during the friction measurement (Fig. 6a) and the resultant Coulomb friction coefficients derived from these measured forces across various contact temperature experiments (Fig. 6b). The Coulomb’s friction law was considered, a choice supported by its extensive application in prior research, underscoring its efficacy in predicting the macroscopic deformation of glass and the form accuracy of molded glass optics. This relevance persists even under high contact pressures typical in glass forming processes [7,10]. The friction coefficients, shown in Fig. 6b, are calculated upon reaching the predefined normal force, with error bars indicating the oscillation inherent in the recorded forces throughout the friction measurement.

<figure><img src="image_1272.png" /><figcaption>Fig. 6. (a) Process forces during the friction measurement, and (b) friction coefficient vs. temperature.</figcaption></figure>

The results illustrate a noticeable escalation in the friction coefficient with increasing contact temperature, consistent with observations in previous works [5]. However, our findings reveal a more pronounced change in the friction coefficient at temperatures well below the glass transition temperature $T_g$, while the effect becomes less significant at temperatures near $T_g$. At low temperature range near room temperature, glass exhibits significant elasticity, leading to hard contact at the interface. Ploughing, arising from the sliding of two solid surfaces at both macroscopic and microscopic levels, contributes as the primary mechanism, resulting in a monotonic increase in friction forces. The more noticeable increase of friction coefficients in the following temperature range is explained by the surface fracturing of the glass specimens. In this range, glass is not in the glass transition, inherently exhibiting brittleness without significant deformation before fracturing occurs. In contrast, as temperature rises further, approaching the glass transition region (near $T_g$), the variation in friction becomes less significant. This can be elucidated by the fact that the increase in friction caused by fracturing is mitigated by the substantial reduction in the modulus and hardness of the steel pin. Moreover, the primary influence on friction in this temperature range is the relaxation phenomenon inherited by the viscoelastic deformation of glass. Due to the stress relaxation, the flow stress tends to decrease after small straining when it is approaching the glass transition region.

The current study aims to present a method that facilitates the simultaneous determination of contact heat transfer and friction coefficients within the PoC tribometer. The findings, depicted in Fig. 6, highlights the influences of temperature on frictional behavior near the glass transition temperature, demonstrating consistent findings with prior investigations using alternative methods
objective solution. The convergence plot in Fig. 5b shows that approximately 40 iterations suffice to optimize the contact heat transfer coefficient, emphasizing the efficiency of the proposed approach. The derived contact heat transfer coefficient for this example in the parallel method was found comparable to that obtained through the sequential approach.

Finally, Fig. 6 presents the process forces obtained during the friction measurement (Fig. 6a) and the resultant Coulomb friction coefficients derived from these measured forces across various contact temperature experiments (Fig. 6b). The Coulomb’s friction law was considered, a choice supported by its extensive application in prior research, underscoring its efficacy in predicting the macroscopic deformation of glass and the form accuracy of molded glass optics. This relevance persists even under high contact pressures typical in glass forming processes [7,10]. The friction coefficients, shown in Fig. 6b, are calculated upon reaching the predefined normal force, with error bars indicating the oscillation inherent in the recorded forces throughout the friction measurement.

<figure><img src="image_1274.png" /></figure>

<figure><img src="image_1275.png" /><figcaption>Fig. 6. (a) Process forces during the friction measurement, and (b) friction coefficient vs. temperature.</figcaption></figure>

The results illustrate a noticeable escalation in the friction coefficient with increasing contact temperature, consistent with observations in previous works [5]. However, our findings reveal a more pronounced change in the friction coefficient at temperatures well below the glass transition temperature $T_g$, while the effect becomes less significant at temperatures near $T_g$. At low temperature range near room temperature, glass exhibits significant elasticity, leading to hard contact at the interface. Ploughing, arising from the sliding of two solid surfaces at both macroscopic and microscopic levels, contributes as the primary mechanism, resulting in a monotonic increase in friction forces. The more noticeable increase of friction coefficients in the following temperature range is explained by the surface fracturing of the glass specimens. In this range, glass is not in the glass transition, inherently exhibiting brittleness without significant deformation before fracturing occurs. In contrast, as temperature rises further, approaching the glass transition region (near $T_g$), the variation in friction becomes less significant. This can be elucidated by the fact that the increase in friction caused by fracturing is mitigated by the substantial reduction in the modulus and hardness of the steel pin. Moreover, the primary influence on friction in this temperature range is the relaxation phenomenon inherited by the viscoelastic deformation of glass. Due to the stress relaxation, the flow stress tends to decrease after small straining when it is approaching the glass transition region.

The current study aims to present a method that facilitates the simultaneous determination of contact heat transfer and friction coefficients within the PoC tribometer. The findings, depicted in Fig. 6, highlights the influences of temperature on frictional behavior near the glass transition temperature, demonstrating consistent findings with prior investigations using alternative methods
like the pin-on-disc tribometer [23]. In further study, comprehensive insights into temperature- and pressure-dependent friction coefficients within the glass transition region will be discussed.

## Summary

This study addresses the essential understanding of thermal-mechanical interactions at contact interfaces, a crucial aspect in controlling material forming processes. A novel characterization method is introduced, enabling the simultaneous determination of contact heat transfer and friction coefficients using a single tribometer and a singular operational run. Two distinct approaches are presented, each necessitating a specific inverse method. Utilizing the proposed tribometer setup and methodology, critical factors influencing contact coefficients can be explored. The versatility of this setup extends its applicability to diverse material forming processes, providing an efficient means to comprehend these processes and enhance product quality control.

## Acknowledgement

This research was supported by the German Research Foundation (DFG) under the project »FriPGM«. Grant number: 456107969.

## References

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[2] H. Kreilkamp, A.T. Vu, O. Dambon, N.F. Klocke, Non-Isothermal Glass Molding of Complex Led Optics, in: S.K. Sundaram (Ed.), 77th Conf. on Glass Problems, Wiley, 2017, pp. 141–149. https://doi.org/10.1002/9781119417507.ch13

[3] A.T. Vu, G. Liu, H. Kreilkamp, O. Dambon, F. Klocke, Numerical modeling-based design of the newly developed nonisothermal glass molding process for complex glass optics, in: Glass Service (Ed.), 13th International Seminar on Furnace Design – Operation & Process Simulation, Czech Republic, 2015, p.376–390.

[4] B. Ananthasayanam, D. Joshi, M. Stairiker, M. Tardiff, K.C. Richardson, P.F. Joseph, High temperature friction characterization for viscoelastic glass contacting a mold, Journal of Non-Crystalline Solids 385 (2014) 100–110. https://doi.org/10.1016/j.jnoncrysol.2013.11.007

[5] P. Mosaddegh, S. Akbarzadeh, M. Zareei, H. Reiszadeh, Tribological behavior of BK7 optical glass at elevated temperatures, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 233 (2019) 580–592. https://doi.org/10.1177/1350650118788756

[6] A.T. Vu, S. Gulati, P.-A. Vogel, T. Grunwald, T. Bergs, Machine learning-based predictive modeling of contact heat transfer, Int. Journal of Heat and Mass Transfer 174 (2021) 121300. https://doi.org/10.1016/j.ijheatmasstransfer.2021.121300

[7] A. Sarhadi, J.H. Hattel, H.N. Hansen, Evaluation of the viscoelastic behaviour and glass/mould interface friction coefficient in the wafer based precision glass moulding, Journal of Materials Processing Technology 214 (2014) 1427–1435. https://doi.org/10.1016/j.jmatprotec.2014.02.008

[8] P. Mosaddegh, J.C. Ziegert, Friction measurement in precision glass molding: An experimental study, Journal of Non-Crystalline Solids 357 (2011) 3221–3225. https://doi.org/10.1016/j.jnoncrysol.2011.05.012
like the pin-on-disc tribometer [23]. In further study, comprehensive insights into temperature- and pressure-dependent friction coefficients within the glass transition region will be discussed.

## Summary

This study addresses the essential understanding of thermal-mechanical interactions at contact interfaces, a crucial aspect in controlling material forming processes. A novel characterization method is introduced, enabling the simultaneous determination of contact heat transfer and friction coefficients using a single tribometer and a singular operational run. Two distinct approaches are presented, each necessitating a specific inverse method. Utilizing the proposed tribometer setup and methodology, critical factors influencing contact coefficients can be explored. The versatility of this setup extends its applicability to diverse material forming processes, providing an efficient means to comprehend these processes and enhance product quality control.

## Acknowledgement

This research was supported by the German Research Foundation (DFG) under the project »FriPGM«. Grant number: 456107969.

## References

[1] H. Kreilkamp, A.T. Vu, O. Dambon, F. Klocke, Replicative manufacturing of complex lighting optics by non-isothermal glass molding, in: D.H. Krevor (Eds.), Polymer Optics and Molded Glass Optics: Design, Fabrication, and Materials 2016, SPIE, 2016, 99490B. https://doi.org/10.1117/12.2235848

[2] H. Kreilkamp, A.T. Vu, O. Dambon, N.F. Klocke, Non-Isothermal Glass Molding of Complex Led Optics, in: S.K. Sundaram (Ed.), 77th Conf. on Glass Problems, Wiley, 2017, pp. 141–149. https://doi.org/10.1002/9781119417507.ch13

[3] A.T. Vu, G. Liu, H. Kreilkamp, O. Dambon, F. Klocke, Numerical modeling-based design of the newly developed nonisothermal glass molding process for complex glass optics, in: Glass Service (Ed.), 13th International Seminar on Furnace Design – Operation & Process Simulation, Czech Republic, 2015, p.376–390.

[4] B. Ananthasayanam, D. Joshi, M. Stairiker, M. Tardiff, K.C. Richardson, P.F. Joseph, High temperature friction characterization for viscoelastic glass contacting a mold, Journal of Non-Crystalline Solids 385 (2014) 100–110. https://doi.org/10.1016/j.jnoncrysol.2013.11.007

[5] P. Mosaddegh, S. Akbarzadeh, M. Zareei, H. Reiszadeh, Tribological behavior of BK7 optical glass at elevated temperatures, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 233 (2019) 580–592. https://doi.org/10.1177/1350650118788756

[6] A.T. Vu, S. Gulati, P.-A. Vogel, T. Grunwald, T. Bergs, Machine learning-based predictive modeling of contact heat transfer, Int. Journal of Heat and Mass Transfer 174 (2021) 121300. https://doi.org/10.1016/j.ijheatmasstransfer.2021.121300

[7] A. Sarhadi, J.H. Hattel, H.N. Hansen, Evaluation of the viscoelastic behaviour and glass/mould interface friction coefficient in the wafer based precision glass moulding, Journal of Materials Processing Technology 214 (2014) 1427–1435. https://doi.org/10.1016/j.jmatprotec.2014.02.008

[8] P. Mosaddegh, J.C. Ziegert, Friction measurement in precision glass molding: An experimental study, Journal of Non-Crystalline Solids 357 (2011) 3221–3225. https://doi.org/10.1016/j.jnoncrysol.2011.05.012
[9] J. Zhou, H. Xu, C. Zhu, W. Ai, X. Liu, K. Liu, High-temperature friction characteristics of N-BK7 glass and their correlation with viscoelastic loss modulus, Ceramics International 47 (2021) 21414-21424. https://doi.org/10.1016/j.ceramint.2021.04.151

[10] T.D. Pallicity, A.T. Vu, K. Ramesh, P. Mahajan, G. Liu, O. Dambon, Birefringence measurement for validation of simulation of precision glass molding process, J Am Ceram Soc 100 (2017) 4680-4698. https://doi.org/10.1111/jace.15010

[11] A.T. Vu, T. Helmig, A.N. Vu, Y. Frekers, T. Grunwald, R. Kneer, T. Bergs, Numerical and experimental determinations of contact heat transfer coefficients in nonisothermal glass molding, J Am Ceram Soc 103 (2020) 1258-1269. https://doi.org/10.1111/jace.16756

[12] F. Zemzemi, J. Rech, W. Ben Salem, A. Dogui, P. Kapsa, Identification of a friction model at tool/chip/workpiece interfaces in dry machining of AISI4142 treated steels, Journal of Materials Processing Technology 209 (2009) 3978-3990. https://doi.org/10.1016/j.jmatprotec.2008.09.019

[13] A.T. Vu, A.N. Vu, G. Liu, T. Grunwald, O. Dambon, F. Klocke, T. Bergs, Experimental investigation of contact heat transfer coefficients in nonisothermal glass molding by infrared thermography, J Am Ceram Soc 102 (2019) 2116-2134. https://doi.org/10.1111/jace.16029

[14] R. Hild, D. Trauth, P. Mattfeld, S. Bastürk, T. Brögelmann, N. Kruppe, K. Bobzin et al., Trockenumformung strukturierter Halbzeuge aus 16MnCr5 und 42CrMo4*/Dry forming of surface structured workpiece made of 16MnCr5 and 42CrMo4 - Determination of friction shear stress by means of a pin-on-cylinder Tribometer, wt 106 (2016) 712-718. https://doi.org/10.37544/1436-4980-2016-10-38

[15] A.T. Vu, A.N. Vu, T. Grunwald, T. Bergs, Modeling of thermo-viscoelastic material behavior of glass over a wide temperature range in glass compression molding, J Am Ceram Soc 103 (2020) 2791-2807. https://doi.org/10.1111/jace.16963

[16] A.T. Vu, T. Grunwald, T. Bergs, Thermo-viscoelastic Modeling of Nonequilibrium Material Behavior of Glass in Nonisothermal Glass Molding, Proc. Manufacturing 47 (2020) 1561-1568. https://doi.org/10.1016/j.promfg.2020.04.350

[17] A.T. Vu, H. Kreilkamp, O. Dambon, F. Klocke, Nonisothermal glass molding for the cost-efficient production of precision freeform optics, Opt. Eng 55 (2016) 71207. https://doi.org/10.1117/1.OE.55.7.071207

[18] A.T. Vu, P.A. Vogel, A. Siva Subramanian, T. Grunwald, T. Bergs, Real-Time Quality Control in Thin Glass Forming Using Infrared Thermography and Deep Learning, KEM 926 (2022) 2312-2321. https://doi.org/10.4028/p-5w9vr9

[19] C. Fieberg, R. Kneer, Determination of thermal contact resistance from transient temperature measurements, International Journal of Heat and Mass Transfer 51 (2008) 1017-1023. https://doi.org/10.1016/j.ijheatmasstransfer.2007.05.004

[20] M.N. Ozisik, H. Orlande, A.J. Kassab, Inverse Heat Transfer: Fundamentals and Applications, Applied Mechanics Reviews 55 (2002) B18-B19. https://doi.org/10.1115/1.1445337

[21] A.T. Vu, R.d.l.A. Avila Hernandez, T. Grunwald, T. Bergs, Modeling nonequilibrium thermoviscoelastic material behaviors of glass in nonisothermal glass molding, J Am Ceram Soc 105 (2022) 6799-6815. https://doi.org/10.1111/jace.18605

[22] V.L. Popov, Contact Mechanics and Friction, Springer Berlin Heidelberg, Berlin, Heidelberg, 2010.

[23] P. Chizhik, M. Friedrichs, D. Dietzel, A. Schirmeisen, Tribological Analysis of Contacts Between Glass and Tungsten Carbide Near the Glass Transition Temperature, Tribol Lett 68 (2020). https://doi.org/10.1007/s11249-020-01363-0
[9] J. Zhou, H. Xu, C. Zhu, W. Ai, X. Liu, K. Liu, High-temperature friction characteristics of N-BK7 glass and their correlation with viscoelastic loss modulus, Ceramics International 47 (2021) 21414-21424. https://doi.org/10.1016/j.ceramint.2021.04.151

[10] T.D. Pallicity, A.T. Vu, K. Ramesh, P. Mahajan, G. Liu, O. Dambon, Birefringence measurement for validation of simulation of precision glass molding process, J Am Ceram Soc 100 (2017) 4680-4698. https://doi.org/10.1111/jace.15010

[11] A.T. Vu, T. Helmig, A.N. Vu, Y. Frekers, T. Grunwald, R. Kneer, T. Bergs, Numerical and experimental determinations of contact heat transfer coefficients in nonisothermal glass molding, J Am Ceram Soc 103 (2020) 1258-1269. https://doi.org/10.1111/jace.16756

[12] F. Zemzemi, J. Rech, W. Ben Salem, A. Dogui, P. Kapsa, Identification of a friction model at tool/chip/workpiece interfaces in dry machining of AISI4142 treated steels, Journal of Materials Processing Technology 209 (2009) 3978-3990. https://doi.org/10.1016/j.jmatprotec.2008.09.019

[13] A.T. Vu, A.N. Vu, G. Liu, T. Grunwald, O. Dambon, F. Klocke, T. Bergs, Experimental investigation of contact heat transfer coefficients in nonisothermal glass molding by infrared thermography, J Am Ceram Soc 102 (2019) 2116-2134. https://doi.org/10.1111/jace.16029

[14] R. Hild, D. Trauth, P. Mattfeld, S. Bastürk, T. Brögelmann, N. Kruppe, K. Bobzin et al., Trockenumformung strukturierter Halbzeuge aus 16MnCr5 und 42CrMo4*/Dry forming of surface structured workpiece made of 16MnCr5 and 42CrMo4 - Determination of friction shear stress by means of a pin-on-cylinder Tribometer, wt 106 (2016) 712-718. https://doi.org/10.37544/1436-4980-2016-10-38

[15] A.T. Vu, A.N. Vu, T. Grunwald, T. Bergs, Modeling of thermo-viscoelastic material behavior of glass over a wide temperature range in glass compression molding, J Am Ceram Soc 103 (2020) 2791-2807. https://doi.org/10.1111/jace.16963

[16] A.T. Vu, T. Grunwald, T. Bergs, Thermo-viscoelastic Modeling of Nonequilibrium Material Behavior of Glass in Nonisothermal Glass Molding, Proc. Manufacturing 47 (2020) 1561-1568. https://doi.org/10.1016/j.promfg.2020.04.350

[17] A.T. Vu, H. Kreilkamp, O. Dambon, F. Klocke, Nonisothermal glass molding for the cost-efficient production of precision freeform optics, Opt. Eng 55 (2016) 71207. https://doi.org/10.1117/1.OE.55.7.071207

[18] A.T. Vu, P.A. Vogel, A. Siva Subramanian, T. Grunwald, T. Bergs, Real-Time Quality Control in Thin Glass Forming Using Infrared Thermography and Deep Learning, KEM 926 (2022) 2312-2321. https://doi.org/10.4028/p-5w9vr9

[19] C. Fieberg, R. Kneer, Determination of thermal contact resistance from transient temperature measurements, International Journal of Heat and Mass Transfer 51 (2008) 1017-1023. https://doi.org/10.1016/j.ijheatmasstransfer.2007.05.004

[20] M.N. Ozisik, H. Orlande, A.J. Kassab, Inverse Heat Transfer: Fundamentals and Applications, Applied Mechanics Reviews 55 (2002) B18-B19. https://doi.org/10.1115/1.1445337

[21] A.T. Vu, R.d.l.A. Avila Hernandez, T. Grunwald, T. Bergs, Modeling nonequilibrium thermoviscoelastic material behaviors of glass in nonisothermal glass molding, J Am Ceram Soc 105 (2022) 6799-6815. https://doi.org/10.1111/jace.18605

[22] V.L. Popov, Contact Mechanics and Friction, Springer Berlin Heidelberg, Berlin, Heidelberg, 2010.

[23] P. Chizhik, M. Friedrichs, D. Dietzel, A. Schirmeisen, Tribological Analysis of Contacts Between Glass and Tungsten Carbide Near the Glass Transition Temperature, Tribol Lett 68 (2020). https://doi.org/10.1007/s11249-020-01363-0
Incremental and sheet metal forming

<figure><img src="image_1273.png" /></figure>
Incremental and sheet metal forming

<figure><img src="image_1276.png" /></figure>
# Effects of triaxiality and lode parameter on deep drawing process

GÜZELDEREN Tolunay¹, a * and DARENDELILER Haluk², b

¹TRMOTOR Power Systems Corp., Hacettepe Technocity, F Block, 06800 Çankaya, Ankara, Turkey

²Department of Mechanical Engineering, Middle East Technical University, 06810 Ankara, Turkey

a tolunaygzldrn@gmail.com, b hdarende@metu.edu.tr

**Keywords:** Triaxiality, Lode Parameter, Deep-Drawing

**Abstract.** The aim of this study is to explore the effects of stress triaxiality and Lode angle parameter as a function of the cup height in the deep drawing process. For this purpose, deep drawing of square cups made of AISI304 steel are analyzed numerically by using von Mises and Hill'48 yield criteria with isotropic hardening. The fracture of the sheet is predicted by applying the Johnson-Cook and the Hosford-Coulomb ductile criteria. The results obtained by using the finite element method are presented in terms of effective plastic strain, triaxiality and Lode angle parameter distributions for the deformed blank. The tensile, compressive and shear nature of the deformation is evaluated by referring the corresponding triaxiality and Lode angle parameter values.

**Introduction**

Stress state is one of the important factors that affect the deformation and failure of the metals. Recent researches have shown that stress triaxiality and Lode angle are two critical parameters of the stress state. The effects of triaxiality and Lode parameter on deformation behavior of the materials have been studied extensively. Xue and Wierzbicki [1] have developed a fracture criterion with the effect of Lode angle and stress triaxiality and Mirone et. al. [2] has developed a yield criterion with the effect of Lode angle and stress triaxiality. Bao and Wierzbicki [3], carried out a series of experiments on the aluminum alloy Al2024-T351 and it was shown that stress triaxiality, in addition to strain intensity, is the most critical factor affecting the start of ductile fracture. The mechanism of fracture for negative stress triaxialities is determined by shear. For large triaxialities, void growth is the major failure mode. However, for low stress triaxialities between the two regimes described above, a mix of shear and void growth modes may arise. Early investigations by McClintock [4] and Rice and Tracey [5] demonstrated that the stress triaxiality controls the formation of voids by using a porous plasticity model with the void volume as an internal variable that was proposed by Gurson [6]. In Bai and Wierzbicki's [7] study, it was shown that the third invariant and hydrostatic pressure have an effect on material behavior. Moreover, the proposed 3D asymmetric fracture locus was validated by the test results of Bao [8] on aluminum 2024-T351 and A710 steel. Hancock and MacKenzie [9], examined the relationship between the ductility and stress triaxiality of three different steels. In the Bai and Wierzbicki's work [10], the modified Mohr-Coulomb model used by relating to the Lode angle and stress triaxiality. The aim of this study is to find out the effects of stress triaxiality and Lode parameter on deep drawing processes by using Von Mises and Hill'48 yield criteria combined with Johnson-Cook and Hosford-Coulomb ductile failure criteria. For this purpose, square blanks made of AISI 304 steel were used. Analyzes were performed by a commercial finite element software.

<figure><img src="image_1274.png" /></figure>
# Effects of triaxiality and lode parameter on deep drawing process

GÜZELDEREN Tolunay¹, a * and DARENDELILER Haluk², b

¹TRMOTOR Power Systems Corp., Hacettepe Technocity, F Block, 06800 Çankaya, Ankara, Turkey

²Department of Mechanical Engineering, Middle East Technical University, 06810 Ankara, Turkey

a tolunaygzldrn@gmail.com, b hdarende@metu.edu.tr

**Keywords:** Triaxiality, Lode Parameter, Deep-Drawing

**Abstract.** The aim of this study is to explore the effects of stress triaxiality and Lode angle parameter as a function of the cup height in the deep drawing process. For this purpose, deep drawing of square cups made of AISI304 steel are analyzed numerically by using von Mises and Hill'48 yield criteria with isotropic hardening. The fracture of the sheet is predicted by applying the Johnson-Cook and the Hosford-Coulomb ductile criteria. The results obtained by using the finite element method are presented in terms of effective plastic strain, triaxiality and Lode angle parameter distributions for the deformed blank. The tensile, compressive and shear nature of the deformation is evaluated by referring the corresponding triaxiality and Lode angle parameter values.

**Introduction**

Stress state is one of the important factors that affect the deformation and failure of the metals. Recent researches have shown that stress triaxiality and Lode angle are two critical parameters of the stress state. The effects of triaxiality and Lode parameter on deformation behavior of the materials have been studied extensively. Xue and Wierzbicki [1] have developed a fracture criterion with the effect of Lode angle and stress triaxiality and Mirone et. al. [2] has developed a yield criterion with the effect of Lode angle and stress triaxiality. Bao and Wierzbicki [3], carried out a series of experiments on the aluminum alloy Al2024-T351 and it was shown that stress triaxiality, in addition to strain intensity, is the most critical factor affecting the start of ductile fracture. The mechanism of fracture for negative stress triaxialities is determined by shear. For large triaxialities, void growth is the major failure mode. However, for low stress triaxialities between the two regimes described above, a mix of shear and void growth modes may arise. Early investigations by McClintock [4] and Rice and Tracey [5] demonstrated that the stress triaxiality controls the formation of voids by using a porous plasticity model with the void volume as an internal variable that was proposed by Gurson [6]. In Bai and Wierzbicki's [7] study, it was shown that the third invariant and hydrostatic pressure have an effect on material behavior. Moreover, the proposed 3D asymmetric fracture locus was validated by the test results of Bao [8] on aluminum 2024-T351 and A710 steel. Hancock and MacKenzie [9], examined the relationship between the ductility and stress triaxiality of three different steels. In the Bai and Wierzbicki's work [10], the modified Mohr-Coulomb model used by relating to the Lode angle and stress triaxiality. The aim of this study is to find out the effects of stress triaxiality and Lode parameter on deep drawing processes by using Von Mises and Hill'48 yield criteria combined with Johnson-Cook and Hosford-Coulomb ductile failure criteria. For this purpose, square blanks made of AISI 304 steel were used. Analyzes were performed by a commercial finite element software.

<figure><img src="image_1277.png" /></figure>
## Theory

The yield and ductile fracture criteria that are used in this study and the equations related with triaxality and Lode angle are presented in this section.

**Yield Criteria:** In this study, von-Mises and Hill'48 yield criteria are used with isotropic hardening assumption. The von Mises yield criterion is given below

$$ \left(\frac{3}{2} \sigma'_{ij} \sigma'_{ij}\right)^{1/2} = \sigma_y \qquad (1) $$

where $\sigma'_{ij}$ are the deviatoric stresses and $\sigma_y$ is the yield strength. The Hill'48 yield criterion is

$$ 2f = F(\sigma_{yy} - \sigma_{zz})^2 + G(\sigma_{zz} - \sigma_{xx})^2 + H(\sigma_{xx} - \sigma_{yy})^2 + 2L\sigma_{yz}^2 + 2M\sigma_{xz}^2 + 2N\sigma_{xy}^2 - 1 \qquad (2) $$

and the constants $F, G, H, L, M$ and $N$ are calculated experimentally.

**Ductile Fracture Criteria:** Two ductile fracture criteria are used in the analyses; Johnson-Cook and Hosford-Coulomb. The Johnson-Cook criterion is

$$ \bar{\varepsilon}_D^p = [d_1 + d_2 \exp(-d_3 \eta)] [1 + d_4 \ln(\dot{\bar{\varepsilon}}^{pl}/\dot{\varepsilon}_0)] (1 + d_5 \hat{\theta}) \qquad (3) $$

where, $\bar{\varepsilon}_D^p$ is the equivalent plastic strain at fracture, $\eta$ is the stress triaxiality and $\hat{\theta}$ is the nondimensional temperature defined as,

$$ \hat{\theta} \equiv \begin{cases} 0 & \text{for } \theta < \theta_{\text{transition}} \\ (\theta - \theta_{\text{transition}})/(\theta_{\text{melt}} - \theta_{\text{transition}}) & \text{for } \theta_{\text{transition}} < \theta < \theta_{\text{melt}} \\ 1 & \text{for } \theta > \theta_{\text{melt}} \end{cases} $$

here $d_1, d_2, d_3, d_4, d_5$ are the failure parameters, $\theta_{\text{melt}}$ is the melting temperature, $\theta_{\text{transition}}$ is the transition temperature and $\dot{\varepsilon}_0$ is the reference strain rate. According to the Hosford-Coulomb criterion the equivalent plastic strain at the onset of damage $\bar{\varepsilon}_D^p$ is

$$ \bar{\varepsilon}_D^p = b \left[ 1 + d \ln \left( \frac{\dot{\bar{\varepsilon}}^p}{\dot{\varepsilon}_0} \right) \right] (1 + c)^{1/n} \left\{ \frac{1}{2} \left[ (f_1 - f_2)^a + (f_2 - f_3)^a + (f_1 - f_3)^a \right] \right\}^{1/a} + c(2\eta + f_1 + f_3)^{-1/n} \qquad (4) $$

In the above equation $a, b, c, d$ and $n$ are material parameters, $\dot{\varepsilon}_0$ is the reference strain rate and $f_1, f_2, f_3$ are functions of the Lode angle parameter.

**Triaxiality and Lode Parameter:** Stress triaxiality is given as

$$ \eta = \frac{\sigma_m}{\bar{\sigma}_{VM}} $$

where $\sigma_m = \sigma_{ii}/3$ is the mean stress, $\bar{\sigma}_{VM}$, is equivalent von Mises stress. The Lode parameter $L$ is given in terms of the principal stresses $\sigma_i$ as,

$$ L = \frac{2\sigma_2 - \sigma_1 - \sigma_3}{\sigma_1 - \sigma_3} $$

Using the normalized third deviatoric stress invariant $\xi$, the Lode angle $\theta$ can be presented as
## Theory

The yield and ductile fracture criteria that are used in this study and the equations related with triaxality and Lode angle are presented in this section.

**Yield Criteria:** In this study, von-Mises and Hill'48 yield criteria are used with isotropic hardening assumption. The von Mises yield criterion is given below

$$ \left(\frac{3}{2} \sigma'_{ij} \sigma'_{ij}\right)^{1/2} = \sigma_y \qquad (1) $$

where $\sigma'_{ij}$ are the deviatoric stresses and $\sigma_y$ is the yield strength. The Hill'48 yield criterion is

$$ 2f = F(\sigma_{yy} - \sigma_{zz})^2 + G(\sigma_{zz} - \sigma_{xx})^2 + H(\sigma_{xx} - \sigma_{yy})^2 + 2L\sigma_{yz}^2 + 2M\sigma_{xz}^2 + 2N\sigma_{xy}^2 - 1 \qquad (2) $$

and the constants $F, G, H, L, M$ and $N$ are calculated experimentally.

**Ductile Fracture Criteria:** Two ductile fracture criteria are used in the analyses; Johnson-Cook and Hosford-Coulomb. The Johnson-Cook criterion is

$$ \bar{\varepsilon}_D^p = [d_1 + d_2 \exp(-d_3 \eta)] [1 + d_4 \ln(\dot{\bar{\varepsilon}}^{pl} / \dot{\varepsilon}_0)] (1 + d_5 \hat{\theta}) \qquad (3) $$

where, $\bar{\varepsilon}_D^p$ is the equivalent plastic strain at fracture, $\eta$ is the stress triaxiality and $\hat{\theta}$ is the nondimensional temperature defined as,

$$ \hat{\theta} = \begin{cases} 0 & \text{for } \theta < \theta_{\text{transition}} \\ (\theta - \theta_{\text{transition}})/(\theta_{\text{melt}} - \theta_{\text{transition}}) & \text{for } \theta_{\text{transition}} < \theta < \theta_{\text{melt}} \\ 1 & \text{for } \theta > \theta_{\text{melt}} \end{cases} $$

here $d_1, d_2, d_3, d_4, d_5$ are the failure parameters, $\theta_{\text{melt}}$ is the melting temperature, $\theta_{\text{transition}}$ is the transition temperature and $\dot{\varepsilon}_0$ is the reference strain rate. According to the Hosford-Coulomb criterion the equivalent plastic strain at the onset of damage $\bar{\varepsilon}_D^p$ is

$$ \bar{\varepsilon}_D^p = b \left[ 1 + d \ln \left( \frac{\dot{\bar{\varepsilon}}^p}{\dot{\varepsilon}_0} \right) \right] (1 + c)^{1/n} \left\{ \frac{1}{2} \left[ (f_1 - f_2)^a + (f_2 - f_3)^a + (f_1 - f_3)^a \right] \right\}^{1/a} + c(2\eta + f_1 + f_3)^{-1/n} \qquad (4) $$

In the above equation $a, b, c, d$ and $n$ are material parameters, $\dot{\varepsilon}_0$ is the reference strain rate and $f_1, f_2, f_3$ are functions of the Lode angle parameter.

**Triaxiality and Lode Parameter:** Stress triaxiality is given as

$$ \eta = \frac{\sigma_m}{\bar{\sigma}_{VM}} $$

where $\sigma_m = \sigma_{ii}/3$ is the mean stress, $\bar{\sigma}_{VM}$, is equivalent von Mises stress. The Lode parameter $L$ is given in terms of the principal stresses $\sigma_i$ as,

$$ L = \frac{2\sigma_2 - \sigma_1 - \sigma_3}{\sigma_1 - \sigma_3} $$

Using the normalized third deviatoric stress invariant $\xi$, the Lode angle $\theta$ can be presented as
$$ \theta = \frac{1}{3} \cos^{-1} \xi = \frac{1}{3} \arccos \left( \frac{3\sqrt{3} J_3}{2 \sqrt{J_2^3}} \right) $$

where $J_2$ and $J_3$ are second and third invariants of the deviatoric stresses. Since the range of the Lode angle is $0 \le \theta \le \pi/3$, the range of $\xi$ is $-1 \le \xi \le 1$. Further, the Lode angle parameter is $\bar{\theta}$ ($-1 \le \bar{\theta} \le 1$) can be formulated as shown below

$$ \bar{\theta} = 1 - \frac{2}{\pi} \arccos \left( \frac{3\sqrt{3} J_3}{2 \sqrt{J_2^3}} \right) = 1 - \frac{6\theta}{\pi} $$

## Finite Element Analysis

In the finite element analysis of the square cup drawing a commercial program is used. Due to symmetry conditions, quarter of the square blanks are modelled by using 6400 eight-node brick elements with reduced integration. The punch, die and blank holder are assumed as rigid parts. The dimensions of the blank, punch and die are given in Table 1.

<table><caption>Table 1. The dimensions of the blank, punch and die</caption><tr><td>Blank size [mm]</td><td>80 x 80</td></tr><tr><td>Sheet thickness [mm]</td><td>1</td></tr><tr><td>Punch dimensions [mm]</td><td>40 x 40</td></tr><tr><td>Punch shoulder radius [mm]</td><td>4.5</td></tr><tr><td>Punch corner radius [mm]</td><td>10</td></tr><tr><td>Die dimensions [mm]</td><td>42.5 x 42.5</td></tr><tr><td>Die shoulder radius [mm]</td><td>4.5</td></tr><tr><td>Die corner radius [mm]</td><td>11.25</td></tr></table>

The AISI304 stainless steel alloy is used in the analysis with elastic modulus $E = 207.8$ MPa, Poisson's ratio $\nu = 0.3$ and yield strength $\sigma_y = 280$ MPa. The true strain-true stress curve is digitized and entered the program. The anisotropy coefficients for the material are; $r_0 = 0.923$, $r_{45} = 1.011$, $r_{90} = 0.840$. Coefficients of Johnson-Cook damage initiation criterion and the Hosford-Coulomb damage initiation criterion given in Table 2 and Table 3, respectively.

<table><caption>Table 2. Johnson-Cook damage initiation coefficients for AISI-304</caption><tr><td>$\dot{\epsilon}_0$</td><td>$\theta_{melt}$ [K]</td><td>$\theta_{transition}$ [K]</td><td>$d_1$</td><td>$d_2, d_3, d_5$</td><td>$d_4$</td></tr><tr><td>1</td><td>1673</td><td>1000</td><td>0.69</td><td>0</td><td>0.0546</td></tr></table>

<table><caption>Table 3. Hosford-Coulomb coefficients for AISI-304</caption><tr><td>a</td><td>b</td><td>c</td><td>n</td><td>d</td><td>$\dot{\epsilon}_0$</td></tr><tr><td>0.623</td><td>1.671</td><td>0.096</td><td>0.1</td><td>0.193</td><td>1</td></tr></table>

## Results and Discussion

The results are given for two different cases.

**Case 1:** For this case, Hill'48 yield criterion is applied with the Johnson-Cook ductile fracture criterion. It is observed that the fracture has started at 20 mm punch travel as shown Fig. 1. The variations of equivalent plastic strain and thickness strain, stress triaxiality, and Lode angle
$$ \theta = \frac{1}{3} \cos^{-1} \xi = \frac{1}{3} \arccos \left( \frac{3\sqrt{3} J_3}{2 \sqrt{J_2^3}} \right) $$

where $J_2$ and $J_3$ are second and third invariants of the deviatoric stresses. Since the range of the Lode angle is $0 \le \theta \le \pi/3$, the range of $\xi$ is $-1 \le \xi \le 1$. Further, the Lode angle parameter is $\bar{\theta}$ ($-1 \le \bar{\theta} \le 1$) can be formulated as shown below

$$ \bar{\theta} = 1 - \frac{2}{\pi} \arccos \left( \frac{3\sqrt{3} J_3}{2 \sqrt{J_2^3}} \right) = 1 - \frac{6\theta}{\pi} $$

## Finite Element Analysis

In the finite element analysis of the square cup drawing a commercial program is used. Due to symmetry conditions, quarter of the square blanks are modelled by using 6400 eight-node brick elements with reduced integration. The punch, die and blank holder are assumed as rigid parts. The dimensions of the blank, punch and die are given in Table 1.

<table><caption>Table 1. The dimensions of the blank, punch and die</caption><tr><td>Blank size [mm]</td><td>80 x 80</td></tr><tr><td>Sheet thickness [mm]</td><td>1</td></tr><tr><td>Punch dimensions [mm]</td><td>40 x 40</td></tr><tr><td>Punch shoulder radius [mm]</td><td>4.5</td></tr><tr><td>Punch corner radius [mm]</td><td>10</td></tr><tr><td>Die dimensions [mm]</td><td>42.5 x 42.5</td></tr><tr><td>Die shoulder radius [mm]</td><td>4.5</td></tr><tr><td>Die corner radius [mm]</td><td>11.25</td></tr></table>

The AISI304 stainless steel alloy is used in the analysis with elastic modulus $E = 207.8$ MPa, Poisson's ratio $\nu = 0.3$ and yield strength $\sigma_y = 280$ MPa. The true strain-true stress curve is digitized and entered the program. The anisotropy coefficients for the material are; $r_0 = 0.923$, $r_{45} = 1.011$, $r_{90} = 0.840$. Coefficients of Johnson-Cook damage initiation criterion and the Hosford-Coulomb damage initiation criterion given in Table 2 and Table 3, respectively.

<table><caption>Table 2. Johnson-Cook damage initiation coefficients for AISI-304</caption><tr><td>$\dot{\epsilon}_0$</td><td>$\theta_{melt}$ [K]</td><td>$\theta_{transition}$ [K]</td><td>$d_1$</td><td>$d_2, d_3, d_5$</td><td>$d_4$</td></tr><tr><td>1</td><td>1673</td><td>1000</td><td>0.69</td><td>0</td><td>0.0546</td></tr></table>

<table><caption>Table 3. Hosford-Coulomb coefficients for AISI-304</caption><tr><td>a</td><td>b</td><td>c</td><td>n</td><td>d</td><td>$\dot{\epsilon}_0$</td></tr><tr><td>0.623</td><td>1.671</td><td>0.096</td><td>0.1</td><td>0.193</td><td>1</td></tr></table>

## Results and Discussion

The results are given for two different cases.

**Case 1:** For this case, Hill'48 yield criterion is applied with the Johnson-Cook ductile fracture criterion. It is observed that the fracture has started at 20 mm punch travel as shown Fig. 1. The variations of equivalent plastic strain and thickness strain, stress triaxiality, and Lode angle
parameter values for the diagonal direction of the cup are presented as a function of the distance from the center of the blank up to the fracture in Fig. 2, Fig. 3 and Fig. 4, respectively. Further, the variation of stress triaxiality and Lode angle parameter values with respect to equivalent plastic strain are given by considering both von Mises and Hill'48 criteria as the metal deforms until failure for the element that fractured first in Fig. 5(a) and Fig 5(b), respectively.

<figure><img src="image_1275.png" /><figcaption>Fig. 1. The deformed cup just after the fracture (Johnson-Cook)</figcaption></figure>

<figure><img src="image_1276.png" /><figcaption>Fig. 2. The variations of equivalent and thickness plastic strain values along the diagonal of the cup at 20 mm cup height (Johnson-Cook)</figcaption></figure>
parameter values for the diagonal direction of the cup are presented as a function of the distance from the center of the blank up to the fracture in Fig. 2, Fig. 3 and Fig. 4, respectively. Further, the variation of stress triaxiality and Lode angle parameter values with respect to equivalent plastic strain are given by considering both von Mises and Hill'48 criteria as the metal deforms until failure for the element that fractured first in Fig. 5(a) and Fig 5(b), respectively.

<figure><img src="image_1278.png" /><figcaption>Fig. 1. The deformed cup just after the fracture (Johnson-Cook)</figcaption></figure>

<figure><img src="image_1279.png" /><figcaption>Fig. 2. The variations of equivalent and thickness plastic strain values along the diagonal of the cup at 20 mm cup height (Johnson-Cook)</figcaption></figure>
<figure><img src="image_1277.png" /><figcaption>Fig. 3. The variation stress triaxiality values along the diagonal of the cup at 20 mm cup height (Johnson-Cook)</figcaption></figure>

<figure><img src="image_1278.png" /><figcaption>Fig. 4. The variation of Lode Angle Parameter along the diagonal of the blank at 20 mm cup height (Johnson-Cook)</figcaption></figure>

<figure><img src="image_1279.png" /><figcaption>Fig. 5. Variation of the (a) stress triaxiality and (b) Lode angle parameter with respect to equivalent plastic strain for the first fractured element (Johnson-Cook)</figcaption></figure>

In the diagonal direction, when the pre-rupture state of the sheet is examined, it is observed that equi-biaxial tension state dominates up to a distance of 20 mm from the center of initial blank. It is noted that the stress situation of the region changes from tension to shear from punch corner to die corner. After 35 mm from the center of the initial blank, there is a change of stress state from
<figure><img src="image_1280.png" /><figcaption>Fig. 3. The variation stress triaxiality values along the diagonal of the cup at 20 mm cup height (Johnson-Cook)</figcaption></figure>

<figure><img src="image_1281.png" /><figcaption>Fig. 4. The variation of Lode Angle Parameter along the diagonal of the blank at 20 mm cup height (Johnson-Cook)</figcaption></figure>

<figure><img src="image_1282.png" /><figcaption>Fig. 5. Variation of the (a) stress triaxiality and (b) Lode angle parameter with respect to equivalent plastic strain for the first fractured element (Johnson-Cook)</figcaption></figure>

In the diagonal direction, when the pre-rupture state of the sheet is examined, it is observed that equi-biaxial tension state dominates up to a distance of 20 mm from the center of initial blank. It is noted that the stress situation of the region changes from tension to shear from punch corner to die corner. After 35 mm from the center of the initial blank, there is a change of stress state from
compression to equi-biaxial compression. Following this, the values of the Lode angle parameter and the triaxiality both increasing and became positive. Finally, fracture occurs in the punch shoulder in tension state.

**Case 2:** In this case, Hill'48 yield criterion is applied with the Hosford-Coulomb ductile fracture criterion. It is seen that the fracture has started at 16 mm punch travel as shown in Fig. 6. The variations of equivalent plastic strain and thickness plastic strain, stress triaxiality, and Lode angle parameter values are presented as a function of the distance from the center of the initial blank up to the fracture for the diagonal direction of the cup in Fig. 7, Fig. 8 and Fig. 9, respectively. Further, the variations of stress triaxiality and Lode angle parameter values with respect to equivalent plastic strain are given by considering both von Mises and Hill'48 criteria as a function of the deformation of the element that fractured first in Fig. 10(a) and Fig 10(b), respectively.

<figure><img src="image_1280.png" /><figcaption>Fig. 6. The deformed cup just after the fracture (Hosford-Coulomb)</figcaption></figure>

<figure><img src="image_1281.png" /><figcaption>Fig. 7. The variations of equivalent and thickness plastic strain values along the diagonal of the cup at 16 mm cup height (Hosford-Coulomb)</figcaption></figure>

In the diagonal direction, as in the transverse and rolling directions, equi-biaxial stress condition is observed under the punch. When the pre-rupture state of sheet is examined, it is seen that equi-biaxial stress conditions dominates up to 16 mm from the center of the blank. At the punch shoulder, stress state changes from tension to shear while triaxiality values are decreasing. After this region, Lode angle parameter values are decreasing, and triaxiality values are increasing followed by a limited drop towards the blank corner. Fracture occurs at the punch shoulder in tension situation.
compression to equi-biaxial compression. Following this, the values of the Lode angle parameter and the triaxiality both increasing and became positive. Finally, fracture occurs in the punch shoulder in tension state.

**Case 2:** In this case, Hill'48 yield criterion is applied with the Hosford-Coulomb ductile fracture criterion. It is seen that the fracture has started at 16 mm punch travel as shown in Fig. 6. The variations of equivalent plastic strain and thickness plastic strain, stress triaxiality, and Lode angle parameter values are presented as a function of the distance from the center of the initial blank up to the fracture for the diagonal direction of the cup in Fig. 7, Fig. 8 and Fig. 9, respectively. Further, the variations of stress triaxiality and Lode angle parameter values with respect to equivalent plastic strain are given by considering both von Mises and Hill'48 criteria as a function of the deformation of the element that fractured first in Fig. 10(a) and Fig 10(b), respectively.

<figure><img src="image_1283.png" /><figcaption>Fig. 6. The deformed cup just after the fracture (Hosford-Coulomb)</figcaption></figure>

<figure><img src="image_1284.png" /><figcaption>Fig. 7. The variations of equivalent and thickness plastic strain values along the diagonal of the cup at 16 mm cup height (Hosford-Coulomb)</figcaption></figure>

In the diagonal direction, as in the transverse and rolling directions, equi-biaxial stress condition is observed under the punch. When the pre-rupture state of sheet is examined, it is seen that equi-biaxial stress conditions dominates up to 16 mm from the center of the blank. At the punch shoulder, stress state changes from tension to shear while triaxiality values are decreasing. After this region, Lode angle parameter values are decreasing, and triaxiality values are increasing followed by a limited drop towards the blank corner. Fracture occurs at the punch shoulder in tension situation.
<figure><img src="image_1282.png" /><figcaption>Fig. 8. The variation stress triaxiality values along the diagonal of the cup at 16 mm cup height (Hosford-Coulomb)</figcaption></figure>

<figure><img src="image_1283.png" /><figcaption>Figure 9. The variation of Lode Angle Parameter along the diagonal of the blank at 16 mm cup height (Hosford-Coulomb)</figcaption></figure>

<figure><img src="image_1284.png" /><figcaption>Fig. 10. Variation of the (a) stress triaxiality and (b) Lode angle parameter with respect to equivalent plastic strain for the first fractured element (Hosford-Coulomb)</figcaption></figure>

## Conclusions

In this study, von Mises and Hill'48 yield criteria, and Johnson-Cook and Hosford-Coulomb ductile fracture criteria are considered to simulate the square cup drawing process for AISI304 sheet materials. The following conclusions are acquired referring to the diagonal direction since all square cups fractured along the diagonal direction:
<figure><img src="image_1285.png" /><figcaption>Fig. 8. The variation stress triaxiality values along the diagonal of the cup at 16 mm cup height (Hosford-Coulomb)</figcaption></figure>

<figure><img src="image_1286.png" /><figcaption>Figure 9. The variation of Lode Angle Parameter along the diagonal of the blank at 16 mm cup height (Hosford-Coulomb)</figcaption></figure>

<figure><img src="image_1287.png" /><figcaption>Fig. 10. Variation of the (a) stress triaxiality and (b) Lode angle parameter with respect to equivalent plastic strain for the first fractured element (Hosford-Coulomb)</figcaption></figure>

**Conclusions**

In this study, von Mises and Hill'48 yield criteria, and Johnson-Cook and Hosford-Coulomb ductile fracture criteria are considered to simulate the square cup drawing process for AISI304 sheet materials. The following conclusions are acquired referring to the diagonal direction since all square cups fractured along the diagonal direction:
1. The part of the sheet under the punch is in equi-biaxial tension condition.

2. On the punch shoulder the sheet is in tension and the dominant deformation type changes from equi-biaxial tension to uniaxial tension as the distance from the center of the blank increases.

3. At the clearance between the die and the punch, the sheet is in tension and the uniaxial tension condition is the dominant deformation type.

4. On the die shoulder the deformation type changes from tension to compression.

5. Under the blank holder the sheet is in compression condition; however, the thickness decreases towards the rim.

6. High variations are observed for the lode angle parameter and stress triaxiality values in the region between die and punch.

7. Significant differences are observed in determining the fracture point depending on the ductile fracture criterion and yield criterion used.

8. It is observed that triaxiality and Lode angle parameter values can be efficiently used to determine the deformation nature of the cup drawing and determine the fracture.

## References

[1] L. Xue, T. Wierzbicki, Ductile fracture initiation and propagation modeling using damage plasticity theory, Eng. Fract. Mech. 75(11) (2008) 3276-3293. doi: 10.1016/j.engfracmech.2007.08.012

[2] G. Mirone, R. Barbagallo, D. Corallo, A new yield criteria including the effect of Lode angle and stress triaxiality, Procedia Struct. Integr. 2 (2016) 3684-3696. doi: 10.1016/j.prostr.2016.06.458

[3] Y. Bao, T. Wierzbicki, On fracture locus in the equivalent strain and stress triaxiality space, Int. J. Mech. Sci. 46(1) (2004) 81-98. doi: 10.1016/j.ijmecsci.2004.02.006

[4] F.A. McClintock, A criterion of ductile fracture by growth of holes, J. Appl. Mech. 35 (1968) 363-371.

[5] J.R. Rice, D.M. Tracey, On the ductile enlargement of voids in triaxial stress fields, J Mech Phys Solids 17 (1969) 201-217.

[6] A.L. Gurson, Continuum theory of ductile rupture by void nucleation and growth. Part I: Yield criteria and flow rules for porous ductile media, J. Eng. Mater. Technol. 99 (1975) 2-15.

[7] Y. Bai, T. Wierzbicki, A new model of metal plasticity and fracture with pressure and Lode dependence, Int. J. Plast. 24(6) (2008) 1071-1096. doi: 10.1016/j.ijplas.2007.09.004

[8] Y. Bao, Prediction of Ductile Crack Formation in Uncracked Bodies, PhD Thesis, 2003.

[9] J.W. Hancock and A.C. Mackenzie, On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress states, J. Mech. Phys. Solids. 24, (1976) 147-160.

[10] Y. Bai, T. Wierzbicki, Application of extended Mohr-Coulomb criterion to ductile fracture, Int. J. Fract. 161(1) (2010) 1-20. doi: 10.1007/s10704-009-9422-8
1. The part of the sheet under the punch is in equi-biaxial tension condition.

2. On the punch shoulder the sheet is in tension and the dominant deformation type changes from equi-biaxial tension to uniaxial tension as the distance from the center of the blank increases.

3. At the clearance between the die and the punch, the sheet is in tension and the uniaxial tension condition is the dominant deformation type.

4. On the die shoulder the deformation type changes from tension to compression.

5. Under the blank holder the sheet is in compression condition; however, the thickness decreases towards the rim.

6. High variations are observed for the lode angle parameter and stress triaxiality values in the region between die and punch.

7. Significant differences are observed in determining the fracture point depending on the ductile fracture criterion and yield criterion used.

8. It is observed that triaxiality and Lode angle parameter values can be efficiently used to determine the deformation nature of the cup drawing and determine the fracture.

## References

[1] L. Xue, T. Wierzbicki, Ductile fracture initiation and propagation modeling using damage plasticity theory, Eng. Fract. Mech. 75(11) (2008) 3276-3293. doi: 10.1016/j.engfracmech.2007.08.012

[2] G. Mirone, R. Barbagallo, D. Corallo, A new yield criteria including the effect of Lode angle and stress triaxiality, Procedia Struct. Integr. 2 (2016) 3684-3696. doi: 10.1016/j.prostr.2016.06.458

[3] Y. Bao, T. Wierzbicki, On fracture locus in the equivalent strain and stress triaxiality space, Int. J. Mech. Sci. 46(1) (2004) 81-98. doi: 10.1016/j.ijmecsci.2004.02.006

[4] F.A. McClintock, A criterion of ductile fracture by growth of holes, J. Appl. Mech. 35 (1968) 363-371.

[5] J.R. Rice, D.M. Tracey, On the ductile enlargement of voids in triaxial stress fields, J Mech Phys Solids 17 (1969) 201-217.

[6] A.L. Gurson, Continuum theory of ductile rupture by void nucleation and growth. Part I: Yield criteria and flow rules for porous ductile media, J. Eng. Mater. Technol. 99 (1975) 2-15.

[7] Y. Bai, T. Wierzbicki, A new model of metal plasticity and fracture with pressure and Lode dependence, Int. J. Plast. 24(6) (2008) 1071-1096. doi: 10.1016/j.ijplas.2007.09.004

[8] Y. Bao, Prediction of Ductile Crack Formation in Uncracked Bodies, PhD Thesis, 2003.

[9] J.W. Hancock and A.C. Mackenzie, On the mechanisms of ductile failure in high-strength steels subjected to multi-axial stress states, J. Mech. Phys. Solids. 24, (1976) 147-160.

[10] Y. Bai, T. Wierzbicki, Application of extended Mohr-Coulomb criterion to ductile fracture, Int. J. Fract. 161(1) (2010) 1-20. doi: 10.1007/s10704-009-9422-8
# Shear cutting: Model-based prediction of material parameters based on synthetic process force signals

RIEMER Matthias<fnref n="1" />,ᵃ*, SILBERMANN Katja<fnref n="1" />,ᵇ, KRÄUSEL Verena<fnref n="1" />,ᶜ, LANGHAMMER Dominic<fnref n="2" />,ᵈ and KOSCHMIDER Agnes<fnref n="2" />,ᵉ

**Keywords:** Shear Cutting, Punching Force, Synthetic Data, Model-Based Process Monitoring, Machine-Learning

**Abstract.** Data-driven process monitoring is an approach in the field of forming technology for increasing process efficiency. In shear cutting processes surrogate models based on process force signals can be used for process monitoring. Currently, the data basis for developing such models has to be generated within experiments. The generation of synthetic training data using numerical methods seems to be a more efficient alternative approach. In this work, it is investigated whether virtual training data for the prediction of material properties can be generated by numerical methods. An FE model of the investigated shear cutting process has been designed and validated based on experiments. It is shown that especially the consideration of the tool stiffness has a significant influence on the simulated process force signal. The validated FE model is used to generate synthetic training data. Based on this data, different prediction models are trained to predict the material model parameters based on the force signals. Different model types are compared and the hyperparameters are optimized for the preferred model.

**Introduction**

In the field of forming-based production of sheet metal components, increasing component complexity and the use of novel materials are leading to narrow process windows [1]. On the one hand, this requires a highly accurate process design and, on the other hand, leads to reduced process robustness due to transient scattering of process inputs and conditions. The sources of scatter can be divided into the categories of material variability, tooling variability, process variability, lubrication and random variabilities like incorrect positioning of the sheet [2]. One of the most essential category on process robustness are fluctuating material properties [3]. Process robustness can be increased by restricting the material and process specification. However, this results in significantly increased production costs. Another approach to increase process robustness is model-based process monitoring and model-based adaptive process control using process-data based digital twins [4]. Acquiring the material properties of the semi-finished product being processed is an essential prerequisite for implementing these digital twins. Ideally, this should be done directly in the process (inline). Currently, the use of eddy current sensors is an established inline-capable method. This method is based on the correlation between local electromagnetic properties and the mechanical properties of the sheet metal [5]. One disadvantage of this method is the high calibration and hardware integration effort. An alternative method, investigated by

<figure><img src="image_1285.png" /></figure>

<footnote n="1">¹Fraunhofer Institute for Machine Tools and Forming Technology IWU, Reichenhainer Strasse 88, 09126 Chemnitz, Germany</footnote>

<footnote n="2">²University of Bayreuth, Group Business Informatics and Process Analytics, Wittelsbacherring 10, 95444 Bayreuth, Germany</footnote>

<footnote>ᵃmatthias.riemer@iwu.fraunhofer.de, ᵇkatja.silbermann@iwu.fraunhofer.de,</footnote>

<footnote>ᶜverena.kraeusel@iwu.fraunhofer.de, ᵈdominic.langhammer@uni-bayreuth.de,</footnote>

<footnote>ᵉagnes.koschmider@uni-bayreuth.de</footnote>
# Shear cutting: Model-based prediction of material parameters based on synthetic process force signals

RIEMER Matthias¹, a*, SILBERMANN Katja¹, b, KRÄUSEL Verena¹, c, LANGHAMMER Dominic², d and KOSCHMIDER Agnes², e

¹Fraunhofer Institute for Machine Tools and Forming Technology IWU, Reichenhainer Strasse 88, 09126 Chemnitz, Germany

²University of Bayreuth, Group Business Informatics and Process Analytics, Wittelsbacherring 10, 95444 Bayreuth, Germany

**Keywords:** Shear Cutting, Punching Force, Synthetic Data, Model-Based Process Monitoring, Machine-Learning

**Abstract.** Data-driven process monitoring is an approach in the field of forming technology for increasing process efficiency. In shear cutting processes surrogate models based on process force signals can be used for process monitoring. Currently, the data basis for developing such models has to be generated within experiments. The generation of synthetic training data using numerical methods seems to be a more efficient alternative approach. In this work, it is investigated whether virtual training data for the prediction of material properties can be generated by numerical methods. An FE model of the investigated shear cutting process has been designed and validated based on experiments. It is shown that especially the consideration of the tool stiffness has a significant influence on the simulated process force signal. The validated FE model is used to generate synthetic training data. Based on this data, different prediction models are trained to predict the material model parameters based on the force signals. Different model types are compared and the hyperparameters are optimized for the preferred model.

**Introduction**

In the field of forming-based production of sheet metal components, increasing component complexity and the use of novel materials are leading to narrow process windows [1]. On the one hand, this requires a highly accurate process design and, on the other hand, leads to reduced process robustness due to transient scattering of process inputs and conditions. The sources of scatter can be divided into the categories of material variability, tooling variability, process variability, lubrication and random variabilities like incorrect positioning of the sheet [2]. One of the most essential category on process robustness are fluctuating material properties [3]. Process robustness can be increased by restricting the material and process specification. However, this results in significantly increased production costs. Another approach to increase process robustness is model-based process monitoring and model-based adaptive process control using process-data based digital twins [4]. Acquiring the material properties of the semi-finished product being processed is an essential prerequisite for implementing these digital twins. Ideally, this should be done directly in the process (inline). Currently, the use of eddy current sensors is an established inline-capable method. This method is based on the correlation between local electromagnetic properties and the mechanical properties of the sheet metal [5]. One disadvantage of this method is the high calibration and hardware integration effort. An alternative method, investigated by

<figure><img src="image_1288.png" /></figure>

<footnote>a matthias.riemer@iwu.fraunhofer.de, b katja.silbermann@iwu.fraunhofer.de,</footnote>

<footnote>c verena.kraeusel@iwu.fraunhofer.de, d dominic.langhammer@uni-bayreuth.de,</footnote>

<footnote>e agnes.koschmider@uni-bayreuth.de</footnote>
Scheneck and others, involves predicting the mechanical properties of semi-finished sheet metal products by analyzing the cutting force curves during shear cutting [6]. This method has the advantage that shearing operations are carried out on almost any sheet metal component. The approach's in-line capability is guaranteed, and only the appropriate measurement technology needs to be integrated. Surrogate models are used to derive the mechanical parameters from the recorded force-displacement curves. In Scheneck's study, an artificial neural network (ANN) was used to predict several mechanical properties, including tensile strength (R<sub>m</sub>), yield strengths (R<sub>p0.2</sub>), elongations at break (A<sub>t</sub>) and strain hardening exponent (n) of different sheet materials. The results showed a high level of agreement between the predicted values from the cutting force curves and the actual measurements obtained from the tensile test. However, generating training data with sufficient quantity and high variance remains a significant challenge in this approach. The overall objective is to investigate to what extent prediction models can be generated on the basis of virtual training data to predict the material parameters by analyzing the cutting force curve. To achieve this, three different material batches of micro-alloyed fine-grained structural steel S500MC (1.0984) were used to determine experimentally both the cutting force curves for the punching operation as well as the mechanical material properties in conventional tensile test. An FE model was established for the punching operation and calibrated using experimental data from one of the material batches. The training database is developed by running simulations with varied material model parameters. Prediction models are then trained using this data to predict mechanical characteristics. At the end, various prediction models are trained and their performance is compared.

**Material Characterization and experimental investigations**

The tests were conducted using S500MC material with a nominal thickness of t = 3.2 mm. The material batches analyzed were obtained from an actual production line and are available in a strip width of b = 78 mm. Initially, conventional tensile tests were performed on the available material batches according to ISO 6892-1:2016. Figure 1 shows the resulting stress-strain diagrams. Test specimens were taken only in the rolling direction due to the dimensions of the available semi-finished products. Each batch of material was tested with four samples. Table 1 summarizes the mean values of the mechanical properties determined for each batch. Batches 1 and 3 show fundamentally similar behavior in the tensile test, but the samples from batch 3 experience has higher stress levels. Batch 2, on the other hand, shows significantly different deformation behavior and slight hardening.

<figure><img src="image_1286.png" /><figcaption>Fig. 1: Stress-strain curves from tensile tests for the investigated material</figcaption></figure>
Scheneck and others, involves predicting the mechanical properties of semi-finished sheet metal products by analyzing the cutting force curves during shear cutting [6]. This method has the advantage that shearing operations are carried out on almost any sheet metal component. The approach's in-line capability is guaranteed, and only the appropriate measurement technology needs to be integrated. Surrogate models are used to derive the mechanical parameters from the recorded force-displacement curves. In Scheneck's study, an artificial neural network (ANN) was used to predict several mechanical properties, including tensile strength (R<sub>m</sub>), yield strengths (R<sub>p0.2</sub>), elongations at break (A<sub>t</sub>) and strain hardening exponent (n) of different sheet materials. The results showed a high level of agreement between the predicted values from the cutting force curves and the actual measurements obtained from the tensile test. However, generating training data with sufficient quantity and high variance remains a significant challenge in this approach. The overall objective is to investigate to what extent prediction models can be generated on the basis of virtual training data to predict the material parameters by analyzing the cutting force curve. To achieve this, three different material batches of micro-alloyed fine-grained structural steel S500MC (1.0984) were used to determine experimentally both the cutting force curves for the punching operation as well as the mechanical material properties in conventional tensile test. An FE model was established for the punching operation and calibrated using experimental data from one of the material batches. The training database is developed by running simulations with varied material model parameters. Prediction models are then trained using this data to predict mechanical characteristics. At the end, various prediction models are trained and their performance is compared.

## Material Characterization and experimental investigations

The tests were conducted using S500MC material with a nominal thickness of t = 3.2 mm. The material batches analyzed were obtained from an actual production line and are available in a strip width of b = 78 mm. Initially, conventional tensile tests were performed on the available material batches according to ISO 6892-1:2016. Figure 1 shows the resulting stress-strain diagrams. Test specimens were taken only in the rolling direction due to the dimensions of the available semi-finished products. Each batch of material was tested with four samples. Table 1 summarizes the mean values of the mechanical properties determined for each batch. Batches 1 and 3 show fundamentally similar behavior in the tensile test, but the samples from batch 3 experience has higher stress levels. Batch 2, on the other hand, shows significantly different deformation behavior and slight hardening.

<figure><img src="image_1289.png" /><figcaption>Fig. 1: Stress-strain curves from tensile tests for the investigated material</figcaption></figure>
<table><caption>Table 1: Material characteristics for the investigated material batches</caption><thead><tr><th>Material Batch</th><th>t<br>(mm)</th><th>E<br>(GPa)</th><th>R<sub>p0.2</sub><br>(MPa)</th><th>R<sub>m</sub><br>(MPa)</th><th>r<sub>2-20/Ag</sub></th><th>A<sub>t</sub><br>(%)</th></tr></thead><tbody><tr><td>Batch 1</td><td>3.17</td><td>189</td><td>571</td><td>636</td><td>0.66</td><td>16.4</td></tr><tr><td>Batch 2</td><td>3.22</td><td>180</td><td>640</td><td>662</td><td>0.67</td><td>9.1</td></tr><tr><td>Batch 3</td><td>3.13</td><td>187</td><td>593</td><td>675</td><td>0.64</td><td>15.5</td></tr></tbody></table>

Shear cutting tests were conducted on the three material batches under consideration, and the resulting force-displacement curves were recorded. The tests were performed on a test press at the Fraunhofer IWU using a specialized measuring tool. The tool incorporates a load cell directly into the force flow of the cutting punch, while displacement is measured using a laser triangulation sensor. Figure 2 displays used the tool and the main process parameters. Figure 3 shows five force-displacement curves for each material batch. The graph shows the cutting force in relationship to the displacement of the punch relative to the specimen. It includes both the actual working stroke (positive forces) and the back stroke (negative forces). The curves recorded for the different batches exhibit significant differences. This indicates that the force-displacement curves are fundamentally suitable for detecting the different deformation behavior of the material batches.

<figure><img src="image_1287.png" /><figcaption>Fig. 2: Section view of used cutting tool and main experimental parameters</figcaption></figure>

<table><thead><tr><th colspan="2">tool components</th></tr></thead><tbody><tr><td>A</td><td>tool guidance</td></tr><tr><td>B</td><td>die</td></tr><tr><td>C</td><td>blank holder plate</td></tr><tr><td>D</td><td>cylindrical punch</td></tr><tr><td>E</td><td>load cell MEGATRON KMC100K 200kN</td></tr><tr><td>F</td><td>laser triangulation sensor MICRO-EPSILON optoNCDT 1420</td></tr></tbody><thead><tr><th colspan="2">experimental parameters</th></tr></thead><tbody><tr><td>punch diameter</td><td>5.8 mm (material: HSS)</td></tr><tr><td>clearance</td><td>0.125 mm</td></tr><tr><td>die velocity</td><td>3.5 mm/s</td></tr><tr><td>blank holder force</td><td>21 kN</td></tr></tbody></table>

<figure><img src="image_1288.png" /><figcaption>Fig. 3: Experimentally obtained cutting force signals for the 3 investigated material batches</figcaption></figure>