$t_{min}$ and $t_{max}$ are the maximal and minimal thickness of the Invar layer respectively. If there is no necking, $Z_{max} = 0$ whereas fragmentation is characterized by $Z_{max} = 1$

The micrographs obtained after 89 % reduction ratio are presented in Figure 2. The micrographs reveal three different advancements in necking:

- Configuration A: Invar layer has a large degree of necking ($Z_{max} = 0.8$)

- Configuration B: There is almost no necking ($Z_{max} = 0.1$)

- Configuration C: Invar layers are fragmented in the copper matrix ($Z_{max} = 1$)

<figure><img src="image_824.png" /><figcaption>Figure 2: Experimental results of the stackings at a rolling reduction of 89%</figcaption></figure>

Comparing configurations A and B, it is evident that as the volume fraction of Invar increases, necking is delayed ($Z_{max} = 0.8$ for A and $Z_{max} = 0.1$ for B). The comparison of A and C highlights the effect of the number of Invar layers on the apparition of necking: configuration C exhibits a fragmentation pattern ($Z_{max} = 1$), while configuration A is highly necked ($Z_{max} = 0.8$). Configurations B and C present the same volume fraction of Invar (25%), but different number of layers. Bilayer configuration C shows a higher degree of necking compared to the monolayer configuration B. The effect of Invar layer thickness on necking occurrence is consistent with the literature [4,5,11]. Hard layer volume fraction is widely used in the literature as an indicator to predict necking, as the maximal force-based criterion for necking varies linearly with this fraction [4,5,11]. This parameter is not sufficient to predict the necking of hard layers as necking occurrence depends also on the layer thickness.

Geometrical effects on necking occurrence have been identified, but they are combined with mechanical effects, such as hardness mismatch between soft and hard layers. As there is no reliable criterion to predict the necking of hard layers, finite element simulation of the process is a viable approach to optimize the manufacturing of composites with the expected structure. To model the process accurately, the mechanical behaviour of copper and Invar has to be determined, and this point is studied in the following section.

## Characterization of materials mechanical behaviour

### Approach:

Copper and Invar sheets used in the composite are obtained from rolling. This can induce crystallographic texture and mechanical anisotropy. Therefore, the mechanical behaviours of copper and Invar are determined as follows:

1) The strain hardening is obtained through tensile tests carried out at 200 °C (rolling temperature) along the rolling direction in quasi-static conditions;
2) Anisotropy is determined numerically with an elastoplastic self-consistent model [12] which takes into account the experimental crystallographic texture. This procedure allows an easy determination of properties out of the sheet plane, whereas complex instrumentation is required for thin sheets to obtain these properties through tensile tests.

Furthermore, composites are manufactured using a multi-cycle process, which includes a heat treatment before each warm rolling. While Invar is not sensitive to this thermal treatment (Table 1), copper is. Therefore, the evolution of the mechanical behaviour of the materials is studied as a function of the reduction applied to the sheets.

### Copper sheets:

The mechanical behaviour of copper sheets should be determined in the annealed state for modelling each rolling pass. The thermo-mechanical treatment applied to copper sheets for the first 3 reductions is illustrated in Figure 3. Considering uniform thickness reduction, the copper layer thickness for configuration A is 700 µm at the 1st pass entry, 385 µm at the 2nd pass entry, and 217 µm at the 3rd pass entry. Concerning configuration C, the copper layer thickness is: 400 µm at the 1st pass entry, 220 µm at the 2nd pass entry, and 125 µm at the 3rd pass entry. Amongst those thicknesses, three thicknesses are characterized (Figure 3):

1) Cu700: Copper from an annealed 700 µm thick sheet;

2) Cu400: Copper from an annealed 400 µm thick sheet;

3) Cu200: Copper from an annealed 200 µm thick sheet.

<figure><img src="image_817.png" /><figcaption>Figure 3: Thermo-mechanical treatment of copper sheets</figcaption></figure>

The microstructure of the plates is characterized by electron backscatter diffraction (EBSD) with a 1 µm step size. The results are treated using the software OIMTM. For that purpose, samples are polished and chemically attacked using a phosphoric acid solution before the observation. In order to get statistical results, the investigations are performed in the RD/TD plane.

Microstructures show a grain size drop (from approximately 150 µm to 35 µm) with annealing-rolling cycles (and copper thickness reduction from 700 to 200 µm) (Figure 4). Concerning crystallographic texture, with the annealing and the subsequent thickness reduction, texture becomes weaker, and orientations largely change since crystallographic direction along ND rotates from dominant <110> direction (green) to dominant <112> direction (purple). Grain shape remains isotropic due to recrystallization mechanisms during annealing. Copper keeps equivalent tensile behaviour whatever its thickness, meaning the hardening caused by the grain size diminution is compensated by the texture evolution. These tendencies are consistent with the literature [13-15]. It can be concluded that the copper strain hardening is reset at each cycle thanks to annealing. Strain hardening (in MPa) can be fitted by the following hardening function (in MPa) (Figure 4.b):
2) Anisotropy is determined numerically with an elastoplastic self-consistent model [12] which takes into account the experimental crystallographic texture. This procedure allows an easy determination of properties out of the sheet plane, whereas complex instrumentation is required for thin sheets to obtain these properties through tensile tests.

Furthermore, composites are manufactured using a multi-cycle process, which includes a heat treatment before each warm rolling. While Invar is not sensitive to this thermal treatment (Table 1), copper is. Therefore, the evolution of the mechanical behaviour of the materials is studied as a function of the reduction applied to the sheets.

### Copper sheets:

The mechanical behaviour of copper sheets should be determined in the annealed state for modelling each rolling pass. The thermo-mechanical treatment applied to copper sheets for the first 3 reductions is illustrated in Figure 3. Considering uniform thickness reduction, the copper layer thickness for configuration A is 700 µm at the 1st pass entry, 385 µm at the 2nd pass entry, and 217 µm at the 3rd pass entry. Concerning configuration C, the copper layer thickness is: 400 µm at the 1st pass entry, 220 µm at the 2nd pass entry, and 125 µm at the 3rd pass entry. Amongst those thicknesses, three thicknesses are characterized (Figure 3):

1) Cu700: Copper from an annealed 700 µm thick sheet;

2) Cu400: Copper from an annealed 400 µm thick sheet;

3) Cu200: Copper from an annealed 200 µm thick sheet.

<figure><img src="image_825.png" /><figcaption>Figure 3: Thermo-mechanical treatment of copper sheets</figcaption></figure>

The microstructure of the plates is characterized by electron backscatter diffraction (EBSD) with a 1 µm step size. The results are treated using the software OIMTM. For that purpose, samples are polished and chemically attacked using a phosphoric acid solution before the observation. In order to get statistical results, the investigations are performed in the RD/TD plane.

Microstructures show a grain size drop (from approximately 150 µm to 35 µm) with annealing-rolling cycles (and copper thickness reduction from 700 to 200 µm) (Figure 4). Concerning crystallographic texture, with the annealing and the subsequent thickness reduction, texture becomes weaker, and orientations largely change since crystallographic direction along ND rotates from dominant <110> direction (green) to dominant <112> direction (purple). Grain shape remains isotropic due to recrystallization mechanisms during annealing. Copper keeps equivalent tensile behaviour whatever its thickness, meaning the hardening caused by the grain size diminution is compensated by the texture evolution. These tendencies are consistent with the literature [13-15]. It can be concluded that the copper strain hardening is reset at each cycle thanks to annealing. Strain hardening (in MPa) can be fitted by the following hardening function (in MPa) (Figure 4.b):
$$R^{Cu}(p) = 35 + 39 * (1 - e^{-33.6*p}) + 237 * (1 - e^{-3.2*p}) \quad (3)$$

With *p* the cumulative equivalent plastic strain equal to plastic strain measured in tensile tests.

<figure><img src="image_818.png" /><figcaption>Figure 4: Copper characterisation: (a) ND-IPF maps and (b) stress-strain curves for different thicknesses</figcaption></figure>

Following [12], an elastic-plastic self-consistent (EPSC) model is used to obtain the yield strengths in different directions derived from the experimental crystallographic texture. Each grain is considered as an elastoplastic inclusion embedded in an elastoplastic homogeneous equivalent medium (HEM) whose properties are sought. The elastoplastic behaviour of the inclusion is defined by the glide on the 12 slip systems of the face-centered cubic crystal. The interaction equation between each grain and the HEM is obtained by solving the Eshelby problem of an elastoplastic inclusion in the HEM. If the single crystal behaviour, the orientation distribution, and grain morphology are known, the EPSC model gives the relationship between the stress rate and strain rate of the polycrystal. Using incremental time steps, it is possible to compute the elastoplastic behaviour of the polycrystal deformed by simple traction under different directions. The ratio between yield strengths of the HEM, i.e. copper, can be determined in different directions. The yield strengths along the rolling, transverse and normal directions and the yield strength at 45° across the transverse/rolling plane are called respectively $\sigma_{0R}$, $\sigma_{0T}$, $\sigma_{0N}$, $\sigma_{045TR}$. The yield strength $\sigma_{0R}$ is equal to 35 MPa as indicated in eq. (3). Results from EPSC calculations are presented in Table 2.

<table><caption>Table 2: Yield strength ratios for copper in 3 different mechanical states</caption><thead><tr><th></th><th>σ<sub>0T</sub> / σ<sub>0R</sub></th><th>σ<sub>0N</sub> / σ<sub>0R</sub></th><th>σ<sub>045TR</sub> / σ<sub>0L</sub></th></tr></thead><tbody><tr><td>Cu700</td><td>1.04</td><td>0.92</td><td>0.92</td></tr><tr><td>Cu400</td><td>1.01</td><td>1.01</td><td>1.02</td></tr><tr><td>Cu200</td><td>0.99</td><td>1.00</td><td>1.01</td></tr></tbody></table>

As shown in Table 2, mechanical anisotropy resulting from the crystallographic texture is rather low for the first state of copper, Cu700. For a larger reduction ratio, copper sheets can be considered isotropic. This can be explained by the texture evolution noticed in Figure 4. Initially, copper is textured at 700 µm, but it becomes isotropic at 400 and 200 µm. Based on these results, it can be inferred that copper sheets of lower thicknesses than 400 µm remain isotropic. Thus, for all the cycles, the copper is considered isotropic except when a Cu700 sheet is used.
$$R^{Cu}(p) = 35 + 39 * (1 - e^{-33.6*p}) + 237 * (1 - e^{-3.2*p}) \quad (3)$$

With *p* the cumulative equivalent plastic strain equal to plastic strain measured in tensile tests.

<figure><img src="image_826.png" /><figcaption>Figure 4: Copper characterisation: (a) ND-IPF maps and (b) stress-strain curves for different thicknesses</figcaption></figure>

Following [12], an elastic-plastic self-consistent (EPSC) model is used to obtain the yield strengths in different directions derived from the experimental crystallographic texture. Each grain is considered as an elastoplastic inclusion embedded in an elastoplastic homogeneous equivalent medium (HEM) whose properties are sought. The elastoplastic behaviour of the inclusion is defined by the glide on the 12 slip systems of the face-centered cubic crystal. The interaction equation between each grain and the HEM is obtained by solving the Eshelby problem of an elastoplastic inclusion in the HEM. If the single crystal behaviour, the orientation distribution, and grain morphology are known, the EPSC model gives the relationship between the stress rate and strain rate of the polycrystal. Using incremental time steps, it is possible to compute the elastoplastic behaviour of the polycrystal deformed by simple traction under different directions. The ratio between yield strengths of the HEM, i.e. copper, can be determined in different directions. The yield strengths along the rolling, transverse and normal directions and the yield strength at 45° across the transverse/rolling plane are called respectively $\sigma_{0R}$, $\sigma_{0T}$, $\sigma_{0N}$, $\sigma_{045TR}$. The yield strength $\sigma_{0R}$ is equal to 35 MPa as indicated in eq. (3). Results from EPSC calculations are presented in Table 2.

<table><caption>Table 2: Yield strength ratios for copper in 3 different mechanical states</caption><thead><tr><th></th><th>σ<sub>0T</sub> / σ<sub>0R</sub></th><th>σ<sub>0N</sub> / σ<sub>0R</sub></th><th>σ<sub>045TR</sub> / σ<sub>0L</sub></th></tr></thead><tbody><tr><td>Cu700</td><td>1.04</td><td>0.92</td><td>0.92</td></tr><tr><td>Cu400</td><td>1.01</td><td>1.01</td><td>1.02</td></tr><tr><td>Cu200</td><td>0.99</td><td>1.00</td><td>1.01</td></tr></tbody></table>

As shown in Table 2, mechanical anisotropy resulting from the crystallographic texture is rather low for the first state of copper, Cu700. For a larger reduction ratio, copper sheets can be considered isotropic. This can be explained by the texture evolution noticed in Figure 4. Initially, copper is textured at 700 µm, but it becomes isotropic at 400 and 200 µm. Based on these results, it can be inferred that copper sheets of lower thicknesses than 400 µm remain isotropic. Thus, for all the cycles, the copper is considered isotropic except when a Cu700 sheet is used.
Invar sheets:

Therefore, the evolution of the mechanical behaviour of Invar sheets as a function of thickness reduction will be essentially derived from strain hardening and texture development. Tensile tests have been performed at 200 °C on both 200 µm and 400 µm thick plates. Fracture elongation is lower than 1% which is consistent with the fact that Invar is not affected by heat treatment and its behaviour is characteristic of large strained metal. But this brittleness makes difficult hardening strain law determination. Thus, the evolution of hardness with a reduction ratio combined with a relation between hardness and yield strength is used to characterize the hardening law of Invar. A linear law is found and the strain hardening of Invar sheets is then defined by the hardening function defined for each roll cycle j as follows (MPa):

$$R_j^{\text{Invar}}(p, p_{0j}) = 680 + 65(p + p_{0j}) \qquad (4)$$

With p the cumulative equivalent plastic strain and $p_{0j}$ the equivalent plastic strain accumulated from the previous reduction (see Table 3):

$$p_{0j} = \frac{2}{\sqrt{3}} |\ln(1 - r_{j-1})| \quad \text{with } r_0 = 0 \qquad (5)$$

For Invar, crystallographic anisotropy (calculated from the EPSC model) can be considered negligible.

## Finite element modelling of multi-cycle rolling

Model design:

The finite element software Ansys 2023 R1 is used with the static procedure and updated Lagrangian formulation to solve problems with large strains and large displacements. The models are designed in 2D under the assumption of plane strain considering that experimentally the width enlargement is not significant.

As determined in the previous section, the mechanical behaviour of the copper needs to be reset at the start of each rolling cycle. As a result, simulating the reduction process from a 1.6 mm thick stacking to a 180 µm thick composite cannot be conducted in a single rolling pass, as commonly done in the existing literature [4,5]. To achieve the simulation of the multi-cycle process, a specific procedure is implemented: each rolling cycle is simulated from the deformed shape of the composite computed by the preceding rolling cycle simulation. For that purpose, the deformed sheet is loaded in the design module of the software; the ends of the sheet are removed with numerical tools and the remaining part is meshed in order to use it as the entry in the simulation of the following cycle as schemed in Figure 5. The procedure is repeated for each cycle. Only the simulation of the configuration C is presented in this paper.

<figure><img src="image_819.png" /><figcaption>Figure 5: Scheme of the numerical procedure used to simulate the forming cycle by cycle</figcaption></figure>

Stackings are meshed using reduced integration 8 nodes elements for most of the part. Layers are considered as one part, so that same nodes are shared at the interfaces between copper and
Invar sheets:

Therefore, the evolution of the mechanical behaviour of Invar sheets as a function of thickness reduction will be essentially derived from strain hardening and texture development. Tensile tests have been performed at 200 °C on both 200 µm and 400 µm thick plates. Fracture elongation is lower than 1% which is consistent with the fact that Invar is not affected by heat treatment and its behaviour is characteristic of large strained metal. But this brittleness makes difficult hardening strain law determination. Thus, the evolution of hardness with a reduction ratio combined with a relation between hardness and yield strength is used to characterize the hardening law of Invar. A linear law is found and the strain hardening of Invar sheets is then defined by the hardening function defined for each roll cycle j as follows (MPa):

$$R_j^{\text{Invar}}(p, p_{0j}) = 680 + 65(p + p_{0j}) \qquad (4)$$

With p the cumulative equivalent plastic strain and $p_{0j}$ the equivalent plastic strain accumulated from the previous reduction (see Table 3):

$$p_{0j} = \frac{2}{\sqrt{3}} |\ln(1 - r_{j-1})| \quad \text{with } r_0 = 0 \qquad (5)$$

For Invar, crystallographic anisotropy (calculated from the EPSC model) can be considered negligible.

## Finite element modelling of multi-cycle rolling

Model design:

The finite element software Ansys 2023 R1 is used with the static procedure and updated Lagrangian formulation to solve problems with large strains and large displacements. The models are designed in 2D under the assumption of plane strain considering that experimentally the width enlargement is not significant.

As determined in the previous section, the mechanical behaviour of the copper needs to be reset at the start of each rolling cycle. As a result, simulating the reduction process from a 1.6 mm thick stacking to a 180 µm thick composite cannot be conducted in a single rolling pass, as commonly done in the existing literature [4,5]. To achieve the simulation of the multi-cycle process, a specific procedure is implemented: each rolling cycle is simulated from the deformed shape of the composite computed by the preceding rolling cycle simulation. For that purpose, the deformed sheet is loaded in the design module of the software; the ends of the sheet are removed with numerical tools and the remaining part is meshed in order to use it as the entry in the simulation of the following cycle as schemed in Figure 5. The procedure is repeated for each cycle. Only the simulation of the configuration C is presented in this paper.

<figure><img src="image_827.png" /><figcaption>Figure 5: Scheme of the numerical procedure used to simulate the forming cycle by cycle</figcaption></figure>

Stackings are meshed using reduced integration 8 nodes elements for most of the part. Layers are considered as one part, so that same nodes are shared at the interfaces between copper and
Invar layers. The rolls are modelled as rigid bodies. The contact behaviour between rolls and the composite is modelled by a Coulomb model with a 0.2 friction coefficient.

The meshed part is positioned between the rolls and the loading is applied in two steps: 1) The rolls are displaced to simulate thickness reduction of the given cycle as experimentally applied (Table 3), and 2) a rotation is applied around the roll centre so that the composite moves into the roll-gap thanks to the friction between the roll and the plate. The rotation is specified to have at least five lengths of roll-grip (distance between the entry and exit of the rolls).

Thanks to the material characterization, the copper and Invar mechanical properties are experimentally defined at the start of each cycle. The effect of the annealing is taken into consideration with the laws previously defined in eq. (3) and (4). For copper, the properties are reset before each cycle and isotropy is considered as the copper layer thickness is initially 400 µm. For Invar, it is considered strain-hardened during the whole procedure since the annealing does not affect its mechanical properties.

<table><caption>Table 3: Roll reduction ratios $r_j\%$ and output thickness $h_j$ evolution during roll-bonding for the configuration C</caption><thead><tr><th>Cycle j</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th></tr></thead><tbody><tr><th>$h_j$ [mm]</th><td>880</td><td>500</td><td>350</td><td>250</td><td>180</td></tr><tr><th>$r_j\%$</th><td>45</td><td>69</td><td>79</td><td>85</td><td>89</td></tr></tbody></table>

Comparison to the experimental results:

The simulation and experimental results for configuration C after the 1st cycle, 3rd cycle and at the end of the forming i.e. after the 5th cycle, are shown in Figures 6a and 6b, respectively. Concerning the simulated results, for the 1st and 3rd cycle, almost equivalent necking coefficients ($Z_{max}$ = 0.2 for the 1st cycle and $Z_{max}$ = 0.3 for the 3rd cycle) and equal fragment sizes are observed. However, different types of plastic instability are spotted between the 1st and 3rd cycle, with a wavier pattern and more advanced necking in the latter simulation. For the 5th cycle simulation, a clear increase in maximal degree of necking is noted ($Z_{max}$ = 0.9). The same type of wavy pattern as the one in the 3rd cycle is visible, but with a more pronounced necking. Experimentally, the evolution is more progressive, and fragmentation of Invar layers is observed after the 5th cycle. Both experimentally and numerically, an increase of necking with the increase of thickness reduction is noticed.

In the comparison between simulated and experimental results, similar effects are observed, and overall, a good correlation between them is noticed in terms of the maximal degree of necking. Obviously, for the 5th cycle simulation, the fragmentation does not appear since no fracture criterion is defined in the simulation. However, it is important to remark that the fragment general aspect is like the experiment one.
Invar layers. The rolls are modelled as rigid bodies. The contact behaviour between rolls and the composite is modelled by a Coulomb model with a 0.2 friction coefficient.

The meshed part is positioned between the rolls and the loading is applied in two steps: 1) The rolls are displaced to simulate thickness reduction of the given cycle as experimentally applied (Table 3), and 2) a rotation is applied around the roll centre so that the composite moves into the roll-gap thanks to the friction between the roll and the plate. The rotation is specified to have at least five lengths of roll-grip (distance between the entry and exit of the rolls).

Thanks to the material characterization, the copper and Invar mechanical properties are experimentally defined at the start of each cycle. The effect of the annealing is taken into consideration with the laws previously defined in eq. (3) and (4). For copper, the properties are reset before each cycle and isotropy is considered as the copper layer thickness is initially 400 µm. For Invar, it is considered strain-hardened during the whole procedure since the annealing does not affect its mechanical properties.

<table><caption>Table 3: Roll reduction ratios $r_j\%$ and output thickness $h_j$ evolution during roll-bonding for the configuration C</caption><thead><tr><th>Cycle j</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th></tr></thead><tbody><tr><th>$h_j$ [mm]</th><td>880</td><td>500</td><td>350</td><td>250</td><td>180</td></tr><tr><th>$r_j\%$</th><td>45</td><td>69</td><td>79</td><td>85</td><td>89</td></tr></tbody></table>

Comparison to the experimental results:

The simulation and experimental results for configuration C after the 1st cycle, 3rd cycle and at the end of the forming i.e. after the 5th cycle, are shown in Figures 6a and 6b, respectively. Concerning the simulated results, for the 1st and 3rd cycle, almost equivalent necking coefficients ($Z_{max}$ = 0.2 for the 1st cycle and $Z_{max}$ = 0.3 for the 3rd cycle) and equal fragment sizes are observed. However, different types of plastic instability are spotted between the 1st and 3rd cycle, with a wavier pattern and more advanced necking in the latter simulation. For the 5th cycle simulation, a clear increase in maximal degree of necking is noted ($Z_{max}$ = 0.9). The same type of wavy pattern as the one in the 3rd cycle is visible, but with a more pronounced necking. Experimentally, the evolution is more progressive, and fragmentation of Invar layers is observed after the 5th cycle. Both experimentally and numerically, an increase of necking with the increase of thickness reduction is noticed.

In the comparison between simulated and experimental results, similar effects are observed, and overall, a good correlation between them is noticed in terms of the maximal degree of necking. Obviously, for the 5th cycle simulation, the fragmentation does not appear since no fracture criterion is defined in the simulation. However, it is important to remark that the fragment general aspect is like the experiment one.
<figure><img src="image_820.png" /><figcaption>Figure 6: (a) Simulated and (b) experimental results for configuration C at different $r_1$%</figcaption></figure>

## Conclusion

In this study, the effect of stacking parameters such as the number and thickness of Invar layers, which promote necking during roll-bonding of Invar and copper sheets has been studied. The following conclusions can be highlighted:

- For monolayer configurations, a lower thickness of the Invar layer enhances necking

- For a fixed volume fraction of Invar, a higher number of Invar layers favours necking

Hence, the volume fraction of the hard layer alone is insufficient for predicting the necking trend, contrary to common findings in the literature. The Invar layer thickness is likely to be an important parameter.

The finite element simulations of the multi-cycle process exhibit good agreement with experimental results. While this outcome needs confirmation for remaining configurations, these simulations hold the potential to efficiently model future setups, saving both time and materials.

## References

[1] Fekiri H, Esin VA, Maurel V, Köster A, Bienvenu Y. Microstructure evolution of innovative thermal bridge composite (i-TBC) for power electronics during elaboration. *Materials & Design*. 2018; 137:68-78. https://doi.org/10.1016/j.matdes.2017.10.009

[2] Luedtke A. Thermal Management Materials for High-Performance Applications. *Adv Eng Mater*. 2004; 6(3):142-144. https://doi.org/10.1002/adem.200300552

[3] Clérico P, Mininger X, Prévond L, Baudin T, Helbert AL. Compromise between magnetic shielding and mechanical strength of thin Al/Steel/Al sandwiches produced by cold roll bonding: Experimental and numerical approaches. *Journal of Alloys and Compounds*. 2019; 798:67-81. https://doi.org/10.1016/j.jallcom.2019.05.243
<figure><img src="image_828.png" /><figcaption>Figure 6: (a) Simulated and (b) experimental results for configuration C at different $r_j$%</figcaption></figure>

## Conclusion

In this study, the effect of stacking parameters such as the number and thickness of Invar layers, which promote necking during roll-bonding of Invar and copper sheets has been studied. The following conclusions can be highlighted:

- For monolayer configurations, a lower thickness of the Invar layer enhances necking

- For a fixed volume fraction of Invar, a higher number of Invar layers favours necking

Hence, the volume fraction of the hard layer alone is insufficient for predicting the necking trend, contrary to common findings in the literature. The Invar layer thickness is likely to be an important parameter.

The finite element simulations of the multi-cycle process exhibit good agreement with experimental results. While this outcome needs confirmation for remaining configurations, these simulations hold the potential to efficiently model future setups, saving both time and materials.

## References

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[2] Luedtke A. Thermal Management Materials for High-Performance Applications. *Adv Eng Mater.* 2004; 6(3):142-144. https://doi.org/10.1002/adem.200300552

[3] Clérico P, Mininger X, Prévond L, Baudin T, Helbert AL. Compromise between magnetic shielding and mechanical strength of thin Al/Steel/Al sandwiches produced by cold roll bonding: Experimental and numerical approaches. *Journal of Alloys and Compounds.* 2019; 798:67-81. https://doi.org/10.1016/j.jallcom.2019.05.243
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# Prevention of scaling by means of recycled process waste gases

GERKE Niklas¹,ª*, PEDDINGHAUS Julius¹,ᵇ, ROSENBUSCH Daniel¹,ᶜ, UHE Johanna¹,ᵈ, BRUNOTTE Kai¹,ᵉ and BEHRENS Bernd-Arno¹,ᵉ

¹Leibniz University Hannover, Institute of Forming Technology and Machines, An der Universität 2, 30823 Garbsen, Germany

ªgerke@ifum.uni-hannover.de, ᵇpeddinghaus@ifum.uni-hannover.de,

ᶜrosenbusch@ifum.uni-hannover.de, ᵈuhe@ifum.uni-hannover.de,

ᵉbrunotte@ifum.uni-hannover.de, ᶜbehrens@ifum.uni-hannover.de

**Keywords:** Retrofit, NoCarb, Hot Forming

**Abstract.** During hot forging of steel materials, the blanks are subjected to various heating processes. During these processes, scale is formed, which can lead to a mass loss of up to 3%. The additional mass required to compensate this material loss for a given forging component has a significant impact on the process emissions, as the production of the billet material has the highest impact on the overall CO₂ footprint of metal forming products [1]. Additionally, descaling operations such as upsetting are required to guarantee forging quality and process stability. At the same time, large quantities of process waste gas are emitted in the production of raw materials and components. These burnt gases have lower oxygen concentration due to the prior chemical combustion reaction. This work addresses the question, whether these burnt gases can be utilized as a forging process atmosphere. This would not only reduce material loss, but would also result in a reuse of the process waste gas. In order to retrofit existing forging infrastructure, a tooling system with a gas-tight enclosure was constructed and realized in a forming press. Defined gas combinations were fed into the enclosure to create an oxygen-reduced atmosphere. First, different gas combinations were investigated in annealing tests. The three most promising ones were then selected for the forging tests. The enclosure contained a heating, transport, forming and collecting unit. The blanks were fed in through a magazine and inductively heated to 1200 °C, formed and cooled under the defined atmosphere. In each atmosphere, 100 components were forged from the material 42CrMo4. Furthermore, it was investigated whether forming under a gas atmosphere has an influence on tool wear as scale can act as an abrasive. The investigations showed that both the surface of the starting material and the oxygen concentration of the atmosphere have a significant influence on scale formation. The amount of scale formed was reduced by up to 74% compared to an oxygen atmosphere. The adhesive layer on the upper dies was reduced with decreasing oxygen concentration. On the lower dies was an increased adhesive build-up.

**Introduction**

Considering current findings on climate change, resource efficiency and the reduction of CO₂ emissions are becoming increasingly important both politically and socially. Measures that contribute to climate and environmental protection are therefore of great interest in all fields [2]. In addition to purely economic parameters, these criteria are increasingly evolving into competitive factor in the business to business environment as well as in the end consumer market [3]. The EU Commission has proclaimed the vision of a climate-neutral economy by 2050 [4]. One of the largest emitters of greenhouse gases is the manufacturing industry. Large quantities of CO₂ are produced both during the manufacture of construction materials and the production of goods from these materials [5] as well as during the recycling of goods at the end of their life cycle [6]. The greatest saving potential is undoubtedly achieved by reducing the resources used, e. g. through a higher material efficiency factor (MEE). This is because only the materials that are actually needed

<figure><img src="image_821.png" /></figure>
# Prevention of scaling by means of recycled process waste gases

GERKE Niklas¹,ª*, PEDDINGHAUS Julius¹,ᵇ, ROSENBUSCH Daniel¹,ᶜ, UHE Johanna¹,ᵈ, BRUNOTTE Kai¹,ᵉ and BEHRENS Bernd-Arno¹,ᵉ

¹Leibniz University Hannover, Institute of Forming Technology and Machines, An der Universität 2, 30823 Garbsen, Germany

ªgerke@ifum.uni-hannover.de, ᵇpeddinghaus@ifum.uni-hannover.de,

ᶜrosenbusch@ifum.uni-hannover.de, ᵈuhe@ifum.uni-hannover.de,

ᵉbrunotte@ifum.uni-hannover.de, ᶜbehrens@ifum.uni-hannover.de

**Keywords:** Retrofit, NoCarb, Hot Forming

**Abstract.** During hot forging of steel materials, the blanks are subjected to various heating processes. During these processes, scale is formed, which can lead to a mass loss of up to 3%. The additional mass required to compensate this material loss for a given forging component has a significant impact on the process emissions, as the production of the billet material has the highest impact on the overall CO₂ footprint of metal forming products [1]. Additionally, descaling operations such as upsetting are required to guarantee forging quality and process stability. At the same time, large quantities of process waste gas are emitted in the production of raw materials and components. These burnt gases have lower oxygen concentration due to the prior chemical combustion reaction. This work addresses the question, whether these burnt gases can be utilized as a forging process atmosphere. This would not only reduce material loss, but would also result in a reuse of the process waste gas. In order to retrofit existing forging infrastructure, a tooling system with a gas-tight enclosure was constructed and realized in a forming press. Defined gas combinations were fed into the enclosure to create an oxygen-reduced atmosphere. First, different gas combinations were investigated in annealing tests. The three most promising ones were then selected for the forging tests. The enclosure contained a heating, transport, forming and collecting unit. The blanks were fed in through a magazine and inductively heated to 1200 °C, formed and cooled under the defined atmosphere. In each atmosphere, 100 components were forged from the material 42CrMo4. Furthermore, it was investigated whether forming under a gas atmosphere has an influence on tool wear as scale can act as an abrasive. The investigations showed that both the surface of the starting material and the oxygen concentration of the atmosphere have a significant influence on scale formation. The amount of scale formed was reduced by up to 74% compared to an oxygen atmosphere. The adhesive layer on the upper dies was reduced with decreasing oxygen concentration. On the lower dies was an increased adhesive build-up.

**Introduction**

Considering current findings on climate change, resource efficiency and the reduction of CO₂ emissions are becoming increasingly important both politically and socially. Measures that contribute to climate and environmental protection are therefore of great interest in all fields [2]. In addition to purely economic parameters, these criteria are increasingly evolving into competitive factor in the business to business environment as well as in the end consumer market [3]. The EU Commission has proclaimed the vision of a climate-neutral economy by 2050 [4]. One of the largest emitters of greenhouse gases is the manufacturing industry. Large quantities of CO₂ are produced both during the manufacture of construction materials and the production of goods from these materials [5] as well as during the recycling of goods at the end of their life cycle [6]. The greatest saving potential is undoubtedly achieved by reducing the resources used, e. g. through a higher material efficiency factor (MEE). This is because only the materials that are actually needed

<figure><img src="image_829.png" /></figure>
for a product should be produced. Further potential savings lie in lightweight construction and materials, the use of efficient, fully digitalised and automated production processes and the development of suitable reuse concepts, according to the cradle-to-cradle principle [7].

During hot forging of steel materials, oxidation of the raw parts results in pronounced scale formation, which leads to a significant loss of material (approx. 2% to 3% of the mass used) [8]. The scaled material is therefore no longer available for the manufacture of formed products and reduces the usable mass after forming.

The aim of these investigations is to carry out hot forging in an oxygen-reduced atmosphere in order to suppress the formation of scale. The study examines the use of low-oxygen, industrially emitted exhaust gases in an existing forming process. By reducing mass losses, the CO₂ footprint of the components produced can be lowered.

Scale or iron oxide is much harder and more brittle than steel and therefore acts as an abrasive in the tribological contact zone between die and billet during forging. It will also be investigated if lower quantities of scale also mean less abrasive wear on the tools and increase the service life of the tool. As the tool itself also contributes to the CO₂ footprint, its impact can be reduced by using it for an extended period and replacing it less often. By generally avoiding scale, upstream processes such as the upsetting for descaling or sand-blasting can also be completely removed from the process chain.

## Material and Methods

To determine the influence of the gas combinations on the scaling behaviour, a tempering test was carried out. To determine the difference in weight before and after annealing, the samples were weighed prior to and after the process. The scaling behaviour was quantified as a factor of the atmosphere by the weight loss. The samples were annealed in a sample holder in a previously purged inert gas furnace for 60 min at 1100 °C in the selected atmosphere. This temperature was chosen as it is a common hot forming temperature for steel [9]. This holding time in the furnace was significantly longer than in conventional industrial forging processes. It served to qualitatively assess the potential and pre-select the different gas compositions. After this time, the samples were transferred from the inert gas furnace to a cooling chamber, which was also purged with the same gas composition as the furnace. The sample holder was transported manually with a transfer time of approx. 5-8 s and came into contact with the ambient air during the transfer. The samples remained there until their temperature had fallen below 500 °C, as no significant scale formation takes place below this temperature [10, 11]. Depending on the process, process waste gases can have a wide variety of compositions. For this purpose, Huczkowski et al. simulated the compositions of flue gases produced during the technical combustion of fuels [12]. These are mainly composed of nitrogen (N₂), carbon dioxide (CO₂), water (H₂O), oxygen (O₂) and sulphur dioxide (SO₂). Lee and Choi modeled the waste gas composition of a heating process with the combination N₂+CO₂ (10%) + O₂ (5%) [13]. Gas combinations with different proportions of N₂, CO₂ and O₂ were selected to investigate the influence of different combustion processes. Nitrogen was used as the main gas and the proportions of carbon dioxide and oxygen were varied. A pure nitrogen atmosphere was also selected, which used in hardening or tempering processes, for example. Environmental statements from large hardening plants such as Reese (Härterei Reese Weimar GmbH & Co. KG, Weimar) or the BMW Group (BMW Group, Werk Dingolfing) show that these gases are emitted from the processes in significant quantities. The selected combinations are summarised in Table 1. Sulphur dioxide (SO₂) was not added as it represents a very small proportion in the sources used. Water (H₂O) would be separated during the preparation and cooling of the gases for the process, which is why it was also not added separately.
for a product should be produced. Further potential savings lie in lightweight construction and materials, the use of efficient, fully digitalised and automated production processes and the development of suitable reuse concepts, according to the cradle-to-cradle principle [7].

During hot forging of steel materials, oxidation of the raw parts results in pronounced scale formation, which leads to a significant loss of material (approx. 2% to 3% of the mass used) [8]. The scaled material is therefore no longer available for the manufacture of formed products and reduces the usable mass after forming.

The aim of these investigations is to carry out hot forging in an oxygen-reduced atmosphere in order to suppress the formation of scale. The study examines the use of low-oxygen, industrially emitted exhaust gases in an existing forming process. By reducing mass losses, the CO₂ footprint of the components produced can be lowered.

Scale or iron oxide is much harder and more brittle than steel and therefore acts as an abrasive in the tribological contact zone between die and billet during forging. It will also be investigated if lower quantities of scale also mean less abrasive wear on the tools and increase the service life of the tool. As the tool itself also contributes to the CO₂ footprint, its impact can be reduced by using it for an extended period and replacing it less often. By generally avoiding scale, upstream processes such as the upsetting for descaling or sand-blasting can also be completely removed from the process chain.

## Material and Methods

To determine the influence of the gas combinations on the scaling behaviour, a tempering test was carried out. To determine the difference in weight before and after annealing, the samples were weighed prior to and after the process. The scaling behaviour was quantified as a factor of the atmosphere by the weight loss. The samples were annealed in a sample holder in a previously purged inert gas furnace for 60 min at 1100 °C in the selected atmosphere. This temperature was chosen as it is a common hot forming temperature for steel [9]. This holding time in the furnace was significantly longer than in conventional industrial forging processes. It served to qualitatively assess the potential and pre-select the different gas compositions. After this time, the samples were transferred from the inert gas furnace to a cooling chamber, which was also purged with the same gas composition as the furnace. The sample holder was transported manually with a transfer time of approx. 5-8 s and came into contact with the ambient air during the transfer. The samples remained there until their temperature had fallen below 500 °C, as no significant scale formation takes place below this temperature [10, 11]. Depending on the process, process waste gases can have a wide variety of compositions. For this purpose, Huczkowski et al. simulated the compositions of flue gases produced during the technical combustion of fuels [12]. These are mainly composed of nitrogen (N₂), carbon dioxide (CO₂), water (H₂O), oxygen (O₂) and sulphur dioxide (SO₂). Lee and Choi modeled the waste gas composition of a heating process with the combination N₂+CO₂ (10%) + O₂ (5%) [13]. Gas combinations with different proportions of N₂, CO₂ and O₂ were selected to investigate the influence of different combustion processes. Nitrogen was used as the main gas and the proportions of carbon dioxide and oxygen were varied. A pure nitrogen atmosphere was also selected, which used in hardening or tempering processes, for example. Environmental statements from large hardening plants such as Reese (Härterei Reese Weimar GmbH & Co. KG, Weimar) or the BMW Group (BMW Group, Werk Dingolfing) show that these gases are emitted from the processes in significant quantities. The selected combinations are summarised in Table 1. Sulphur dioxide (SO₂) was not added as it represents a very small proportion in the sources used. Water (H₂O) would be separated during the preparation and cooling of the gases for the process, which is why it was also not added separately.
<table><caption>Table 1: Gas compositions used in annealing tests</caption><thead><tr><td>Test series</td><td>Gas composition</td></tr></thead><tbody><tr><td>A</td><td>Air atmosphere</td></tr><tr><td>B</td><td>N<sub>2</sub>+CO<sub>2</sub>(5%)+O<sub>2</sub>(10%)</td></tr><tr><td>C</td><td>N<sub>2</sub>+O<sub>2</sub>(10%)</td></tr><tr><td>D</td><td>N<sub>2</sub>+CO<sub>2</sub>(10%)+O<sub>2</sub>(5%)</td></tr><tr><td>E</td><td>N<sub>2</sub>+CO<sub>2</sub>(5%)+O<sub>2</sub>(5%)</td></tr><tr><td>F</td><td>N<sub>2</sub>+O<sub>2</sub>(5%)</td></tr><tr><td>G</td><td>N<sub>2</sub>+CO<sub>2</sub>(10%)</td></tr><tr><td>H</td><td>N<sub>2</sub>+CO<sub>2</sub>(5%)</td></tr><tr><td>I</td><td>N<sub>2</sub></td></tr></tbody></table>

For the tests, the material 42CrMo4 was selected in the variations bright (machined surface) and black (rolled) in order to simultaneously investigate the influence of the surface condition of the blanks on scaling. All cylindrical blanks for these tests had a diameter of 30 mm and a height of 40 mm. For the gas atmosphere, the aforementioned gas combinations of technical gases with corresponding purity were selected. In order to obtain a comprehensive picture of scaling, 24 samples were used for scaling tests in each material and gas combination. A gas mixing module was used to achieve the gas compositions. In this module, the quantity of each gas used could be set using digital flow rate regulators. The gases were then combined and fed into an inert gas furnace and a cooling chamber. By combining the gases before they were actually used, they were able to mix and thus minimise the separation of the gases in the different areas of the oven. A schematic representation of the gas flow displayed Fig. 1.

<figure><img src="image_822.png" /><figcaption>Figure 1: Schematic illustration of the gas flow</figcaption></figure>
<table><caption>Table 1: Gas compositions used in annealing tests</caption><thead><tr><td>Test series</td><td>Gas composition</td></tr></thead><tbody><tr><td>A</td><td>Air atmosphere</td></tr><tr><td>B</td><td>N<sub>2</sub>+CO<sub>2</sub>(5%)+O<sub>2</sub>(10%)</td></tr><tr><td>C</td><td>N<sub>2</sub>+O<sub>2</sub>(10%)</td></tr><tr><td>D</td><td>N<sub>2</sub>+CO<sub>2</sub>(10%)+O<sub>2</sub>(5%)</td></tr><tr><td>E</td><td>N<sub>2</sub>+CO<sub>2</sub>(5%)+O<sub>2</sub>(5%)</td></tr><tr><td>F</td><td>N<sub>2</sub>+O<sub>2</sub>(5%)</td></tr><tr><td>G</td><td>N<sub>2</sub>+CO<sub>2</sub>(10%)</td></tr><tr><td>H</td><td>N<sub>2</sub>+CO<sub>2</sub>(5%)</td></tr><tr><td>I</td><td>N<sub>2</sub></td></tr></tbody></table>

For the tests, the material 42CrMo4 was selected in the variations bright (machined surface) and black (rolled) in order to simultaneously investigate the influence of the surface condition of the blanks on scaling. All cylindrical blanks for these tests had a diameter of 30 mm and a height of 40 mm. For the gas atmosphere, the aforementioned gas combinations of technical gases with corresponding purity were selected. In order to obtain a comprehensive picture of scaling, 24 samples were used for scaling tests in each material and gas combination. A gas mixing module was used to achieve the gas compositions. In this module, the quantity of each gas used could be set using digital flow rate regulators. The gases were then combined and fed into an inert gas furnace and a cooling chamber. By combining the gases before they were actually used, they were able to mix and thus minimise the separation of the gases in the different areas of the oven. A schematic representation of the gas flow displayed Fig. 1.

<figure><img src="image_830.png" /><figcaption>Figure 1: Schematic illustration of the gas flow</figcaption></figure>
For further tests, three gas combinations were selected from the results. On the one hand, the variation with the lowest and the highest scale formation, as well as one a medium-level to verify the process. The surface variation with the stronger scale formation was used to amplify the influence of the gas for analytical purpose and focus on application scenarios with the most potential for improvement.

To carry out series forging tests under defined atmospheres, a tool system was developed which had an enclosure, a collecting container, a heating unit, a linear feed and dies adapted for the tests (Fig. 2). This tool was used in the Lasco SPR 500 screw press (LASCO Umformtechnik GmbH, Coburg) with a nominal force capacity of 5000 kN. A magazine, which feeds the components into the tool, allows continuous forging series to be carried out. In order to reproduce long-term behaviour under statistically verified conditions, forging series of 100 components per atmosphere were carried out. New dies were used for each forging series in order to be able to analyse the effects on die wear. The atmospheres were monitored using a lambda probe to check the oxygen content. Before starting the test series, the dies were preheated to 200 °C, as the basic tool temperature is normally between 100 °C and 250 °C [9]. As in the tempering test, the cylindrical blanks had a diameter of 30 mm and a height of 40 mm. They were heated to approx. 1200 °C using the integrated heating unit. In order to avoid contamination of the atmosphere, the tests were carried out under slight overpressure in the enclosure. A reference forging series in an air atmosphere was also carried out in addition to the three selected gas combinations.

<figure><img src="image_823.png" /><figcaption>Figure 2: Tool system and housing</figcaption></figure>

The samples were weighed before the test series were carried out. The blanks were then fed into the housing via a magazine and separated. The samples were pushed into the heating unit by the linear feed. After heating, the samples were pushed into the forging dies and the forming process was carried out. After forming, the samples were pushed onto a chute and collected in a cooled container. On average, the cycle time was approx. 40 s. The atmosphere in the collecting container was the same as in the process. The forged semi-finished products cooled down in the container and were then removed. As in the annealing tests, the scale was removed from the samples by subsequent blasting with glass beads of 90 – 150 µm. The samples were cleaned in
For further tests, three gas combinations were selected from the results. On the one hand, the variation with the lowest and the highest scale formation, as well as one a medium-level to verify the process. The surface variation with the stronger scale formation was used to amplify the influence of the gas for analytical purpose and focus on application scenarios with the most potential for improvement.

To carry out series forging tests under defined atmospheres, a tool system was developed which had an enclosure, a collecting container, a heating unit, a linear feed and dies adapted for the tests (Fig. 2). This tool was used in the Lasco SPR 500 screw press (LASCO Umformtechnik GmbH, Coburg) with a nominal force capacity of 5000 kN. A magazine, which feeds the components into the tool, allows continuous forging series to be carried out. In order to reproduce long-term behaviour under statistically verified conditions, forging series of 100 components per atmosphere were carried out. New dies were used for each forging series in order to be able to analyse the effects on die wear. The atmospheres were monitored using a lambda probe to check the oxygen content. Before starting the test series, the dies were preheated to 200 °C, as the basic tool temperature is normally between 100 °C and 250 °C [9]. As in the tempering test, the cylindrical blanks had a diameter of 30 mm and a height of 40 mm. They were heated to approx. 1200 °C using the integrated heating unit. In order to avoid contamination of the atmosphere, the tests were carried out under slight overpressure in the enclosure. A reference forging series in an air atmosphere was also carried out in addition to the three selected gas combinations.

<figure><img src="image_831.png" /><figcaption>Figure 2: Tool system and housing</figcaption></figure>

The samples were weighed before the test series were carried out. The blanks were then fed into the housing via a magazine and separated. The samples were pushed into the heating unit by the linear feed. After heating, the samples were pushed into the forging dies and the forming process was carried out. After forming, the samples were pushed onto a chute and collected in a cooled container. On average, the cycle time was approx. 40 s. The atmosphere in the collecting container was the same as in the process. The forged semi-finished products cooled down in the container and were then removed. As in the annealing tests, the scale was removed from the samples by subsequent blasting with glass beads of 90 – 150 µm. The samples were cleaned in
batches of 100 parts from the same series. The removal of non-scaled material was not considered significant due to the selected blasting medium [14]. The weight difference and thus the scale mass loss was determined by comparing the weight of the cleaned semi-finished products with the initial weight. The average material loss is calculated for each test series.

To evaluate the influence on the dies, the surfaces were scanned before and after the test series using the Keyence VR-3200 profilometer with a 12x magnification resulting in macroscopic and 3D images. The comparison of the 3D contours before and after the forging test series enables the overall changes in the tool surface structure resulting from the tribological conditions.

## Results

The weight loss in the tempering tests for the different process gas mixtures is displayed in Fig. 3 shows that weight loss decreases when oxygen and carbon dioxide content is reduced. In addition, the blank samples show a significantly lower weight loss than the black samples. A reduction in weight loss of over 50% could be determined for both the black and the blank samples. The relative weight loss in an air atmosphere was 0.5% for the blank samples and 0.6% for the black samples. This relative loss could be reduced to 0.2% for bare samples and 0.3% for black samples under pure nitrogen. The weight of the black samples before forming was 224.36 g with a standard deviation of 0.37 g, the weight of the blank samples 222.91 g with a standard deviation of 0.19 g. The standard deviation of the values shown in Fig. 3 varied depending on the surface and the gas composition used. It was between 0.30 g and 1 g for black surfaces and between 0.27 g and 0.51 g for blank surfaces.

<figure><img src="image_824.png" /><figcaption>Figure 3: Mass loss due to scale in annealing tests of 42CrMo4</figcaption></figure>

In the subsequent series of forging tests under the gas atmospheres A (air atmosphere), E (N₂+CO₂ (10%)+O₂ (5%)), H (N₂+CO₂ (5%)) and I (N₂) were selected. A significant reduction in
batches of 100 parts from the same series. The removal of non-scaled material was not considered significant due to the selected blasting medium [14]. The weight difference and thus the scale mass loss was determined by comparing the weight of the cleaned semi-finished products with the initial weight. The average material loss is calculated for each test series.

To evaluate the influence on the dies, the surfaces were scanned before and after the test series using the Keyence VR-3200 profilometer with a 12x magnification resulting in macroscopic and 3D images. The comparison of the 3D contours before and after the forging test series enables the overall changes in the tool surface structure resulting from the tribological conditions.

## Results

The weight loss in the tempering tests for the different process gas mixtures is displayed in Fig. 3 shows that weight loss decreases when oxygen and carbon dioxide content is reduced. In addition, the blank samples show a significantly lower weight loss than the black samples. A reduction in weight loss of over 50% could be determined for both the black and the blank samples. The relative weight loss in an air atmosphere was 0.5% for the blank samples and 0.6% for the black samples. This relative loss could be reduced to 0.2% for bare samples and 0.3% for black samples under pure nitrogen. The weight of the black samples before forming was 224.36 g with a standard deviation of 0.37 g, the weight of the blank samples 222.91 g with a standard deviation of 0.19 g. The standard deviation of the values shown in Fig. 3 varied depending on the surface and the gas composition used. It was between 0.30 g and 1 g for black surfaces and between 0.27 g and 0.51 g for blank surfaces.

<figure><img src="image_832.png" /><figcaption>Figure 3: Mass loss due to scale in annealing tests of 42CrMo4</figcaption></figure>

In the subsequent series of forging tests under the gas atmospheres A (air atmosphere), E (N₂+CO₂ (10%)+O₂ (5%)), H (N₂+CO₂ (5%)) and I (N₂) were selected. A significant reduction in
the loose scale around the tool compared to the reference series was already observed after completion of test series E (N₂+CO₂ (10%)+O₂ (5%)). In test series H (N₂+CO₂ (5%)) and I (N₂), virtually no chipped scale pieces could be detected around the die.

The evaluation of the component mass loss is shown in Fig. 4 for each test series. The mass loss decreases with decreasing oxygen and carbon dioxide content. The mass loss in air atmosphere was used as a reference. The relative mass loss decreases under the various atmospheres from over 1.6 g in an air atmosphere to less than 0.5 g in a pure nitrogen atmosphere. In percentage terms, the mass loss drops to approx. 74%. The average weight before forming was 224.52 g with a standard deviation of 3.35 g. After blast cleaning of the components, the mass loss shown in Fig. 4 was determined. The standard deviation of the weighed components was between 2.89 g and 3.28 g, depending on the gas composition.

<figure><img src="image_825.png" /><figcaption>Figure 4: Averaged mass loss of the parts due to scale</figcaption></figure>

Fig. 5 a-d shows the surface of the upper dies. It can be seen that material has been applied to all the dies. This appears to be most evident at die shown in Fig. 5 a. Another conspicuous feature is that there is an increased material adhesion on the ridge path in all the dies. This is particularly evident in Fig. 5 c, area 2. A slight erosion at the edges of this vertical swage channel, which is shown in Fig. 5 a, area 1, can be observed. Minor differences in height can be attributed to measurement inaccuracies. When the contours are superimposed, the reference height is minimally influenced by the average particle size of the spray. Nevertheless, it is observed that the amount of adhesions under the gas atmospheres is lower than in the air atmosphere. A decrease in adhesion can be observed for E (N₂+CO₂(5%)+O₂(5%)) and I (N₂) compared with the reference with air. It can be seen that a lower oxygen content tends to result in less adhesion on the upper die.
the loose scale around the tool compared to the reference series was already observed after completion of test series E (N₂+CO₂ (10%)+O₂ (5%)). In test series H (N₂+CO₂ (5%)) and I (N₂), virtually no chipped scale pieces could be detected around the die.

The evaluation of the component mass loss is shown in Fig. 4 for each test series. The mass loss decreases with decreasing oxygen and carbon dioxide content. The mass loss in air atmosphere was used as a reference. The relative mass loss decreases under the various atmospheres from over 1.6 g in an air atmosphere to less than 0.5 g in a pure nitrogen atmosphere. In percentage terms, the mass loss drops to approx. 74%. The average weight before forming was 224.52 g with a standard deviation of 3.35 g. After blast cleaning of the components, the mass loss shown in Fig. 4 was determined. The standard deviation of the weighed components was between 2.89 g and 3.28 g, depending on the gas composition.

<figure><img src="image_833.png" /><figcaption>Figure 4: Averaged mass loss of the parts due to scale</figcaption></figure>

Fig. 5 a-d shows the surface of the upper dies. It can be seen that material has been applied to all the dies. This appears to be most evident at die shown in Fig. 5 a. Another conspicuous feature is that there is an increased material adhesion on the ridge path in all the dies. This is particularly evident in Fig. 5 c, area 2. A slight erosion at the edges of this vertical swage channel, which is shown in Fig. 5 a, area 1, can be observed. Minor differences in height can be attributed to measurement inaccuracies. When the contours are superimposed, the reference height is minimally influenced by the average particle size of the spray. Nevertheless, it is observed that the amount of adhesions under the gas atmospheres is lower than in the air atmosphere. A decrease in adhesion can be observed for E (N₂+CO₂(5%)+O₂(5%)) and I (N₂) compared with the reference with air. It can be seen that a lower oxygen content tends to result in less adhesion on the upper die.
<figure><img src="image_826.png" /><figcaption>Figure 5: Contour comparison of the upper dies a) Air atmosphere b) N₂+CO₂(5%)+O₂(5%) c) N₂+CO₂(5%) d) N₂</figcaption></figure>

In addition to the upper dies, the lower dies were also analysed. These are shown in Fig. 6. It can be seen from these images that adhesion also occured on all dies. Areas with negative geometric deviations, as shown in Fig. 6 a, area 1, can be detected in all the dies. Compared to the other dies, the die shown in Fig. 6 c shows more significant adhesion. Material build-up in the area of the ridge path on the upper die occurs on all dies. A comparison of the lower dies A (Air atmosphere), E (N₂+CO₂(5%)+O₂(5%)) and I (N₂), as already carried out for the upper dies, did not reveal any reduction in build-up due to the use of a gas atmosphere. However, the areas with negative geometric deviations were reduced.

<figure><img src="image_827.png" /><figcaption>Figure 6: Contour comparison of the lower dies a) Air atmosphere b) N₂+CO₂(5%)+O₂(5%) c) N₂+CO₂(5%) d) N₂</figcaption></figure>

## Discussion

A tempering route was modelled using these gas combinations and the material 42CrMo4 in the variations "bright" and "black". The results showed that the reduction of oxygen and carbon dioxide with addition of nitrogen leads to a reduction in the amount of scale formed. The best results were initially achieved under a nitrogen atmosphere with 5% CO₂. It was expected that a pure nitrogen atmosphere would achieve the best results as no oxygen is available. The results
<figure><img src="image_834.png" /><figcaption>Figure 5: Contour comparison of the upper dies a) Air atmosphere b) N₂+CO₂(5%)+O₂(5%) c) N₂+CO₂(5%) d) N₂</figcaption></figure>

In addition to the upper dies, the lower dies were also analysed. These are shown in Fig. 6. It can be seen from these images that adhesion also occured on all dies. Areas with negative geometric deviations, as shown in Fig. 6 a, area 1, can be detected in all the dies. Compared to the other dies, the die shown in Fig. 6 c shows more significant adhesion. Material build-up in the area of the ridge path on the upper die occurs on all dies. A comparison of the lower dies A (Air atmosphere), E (N₂+CO₂(5%)+O₂(5%)) and I (N₂), as already carried out for the upper dies, did not reveal any reduction in build-up due to the use of a gas atmosphere. However, the areas with negative geometric deviations were reduced.

<figure><img src="image_835.png" /><figcaption>Figure 6: Contour comparison of the lower dies a) Air atmosphere b) N₂+CO₂(5%)+O₂(5%) c) N₂+CO₂(5%) d) N₂</figcaption></figure>

## Discussion

A tempering route was modelled using these gas combinations and the material 42CrMo4 in the variations "bright" and "black". The results showed that the reduction of oxygen and carbon dioxide with addition of nitrogen leads to a reduction in the amount of scale formed. The best results were initially achieved under a nitrogen atmosphere with 5% CO₂. It was expected that a pure nitrogen atmosphere would achieve the best results as no oxygen is available. The results
show, that oxidation is also inhibited under high temperatures when oxygen is bound as CO₂. Burnt gases with high CO₂ content therefore show high potential as an inert atmosphere in forging. The formation of scale can be reduced by using gases that lower the oxygen concentration in the process atmosphere. Whether the gases have an effect on the forged parts due to diffusion processes or a special atmosphere can be used in the production process must be checked on a case-by-case assessment.

Due to the deviating results, the pure nitrogen and the best atmosphere from the test were selected for further tests. An air atmosphere was also selected as a reference and a gas composition with N₂+CO₂ (5%)+O₂ (5%). It was found that bare surfaces tend to form less scale. This can be explained by the fact that the "bright" surfaces have a smaller specific surface area due to less roughness. Benefits in terms of reduced material loss in forging "bright" components are however not significant, as the material loss is merely shifted to an earlier stage in the process chain. The peeling process for blank steel rods naturally has high material loss as it is a chip removing method. The removed chips can however be more easily recycled than oxide scale. This method would significantly increase the CO₂ footprint of the component, as the additional process steps and recycling would also have to be included in the overall balance of the component. It is not a reasonable approach to reduce scaling and the CO₂-footprint and therefore not considered for the subsequent forging tests. For this reason, black samples were used for the further observations.

In subsequent series of tests, in which 100 parts were forged for each gas combination, it was shown that the lowest scale formation occurs under a pure nitrogen atmosphere, as expected. A scale reduction of approx. 1.1 g form the highest to the lowest result was achieved through the series of tests under the controlled atmospheres. This corresponds to a reduction of 74%. It was also shown that a partial reduction of the oxygen content has a significant effect on scale formation. Without the addition of oxygen, a certain amount of oxidation occurs. By reducing the oxygen content to a quarter of the normal level, more than half of the oxidation or the scale formed can be saved. The difference between CO₂ and N₂ is only relatively small. From this it can be deduced that the greatest improvements can be achieved if the residual oxygen concentration is minimized. This can be achieved with N₂ as well as CO₂.

No significant removal could be recognised in the contour comparisons of the upper dies. However, a clear build-up is recognisable in the area of the burr formation, which decreases as the amount of scale decreases. This can be explained by the fact that the scale forms a thermal protective layer that protects the sample against heat loss to the environment. Due to the absence of scale, it is possible that the components cool down faster and less adhesion occurs, as adhesive effects increase with temperature. The lower dies, on the other hand, exhibit negative geometric deviations in the centre of the dies, which also decrease with decreasing scale formation. This wear may be caused by scale which acts as an abrasive that is pressed into the surface of the die during the forging process. The reduction in abrasive wear was confirmed, which was particularly evident on the lower dies. The reduction in wear is attributed to the lowering of the scale content and the resulting reduction in the quantity of abrasive particles. Contrary to the effects on the upper dies, adhesion increases with decreasing scale. This result is possibly due to the fact that the lower dies surface has higher heat input than the upper dies, due to longer contact time with the billet before and after forging. Effects of increased adhesion with increasing die temperature have already been identified by Lorenz et al. [15]. The increased base temperature and the lack of a scale layer led to increased adhesion. This effect on the lower tool is also expected, since scale acts as an intermediate layer between billet and tool, preventing direct contact and chemical interaction, which can cause adhesion. The thermal and tribochemical effects can be solved by using lubricant. A separate adjustment is necessary as these have been atomised with compressed air up to now. One solution would be to substitute compressed air with pressurised inert or waste gas.
show, that oxidation is also inhibited under high temperatures when oxygen is bound as CO₂. Burnt gases with high CO₂ content therefore show high potential as an inert atmosphere in forging. The formation of scale can be reduced by using gases that lower the oxygen concentration in the process atmosphere. Whether the gases have an effect on the forged parts due to diffusion processes or a special atmosphere can be used in the production process must be checked on a case-by-case assessment.

Due to the deviating results, the pure nitrogen and the best atmosphere from the test were selected for further tests. An air atmosphere was also selected as a reference and a gas composition with N₂+CO₂ (5%) + O₂ (5%). It was found that bare surfaces tend to form less scale. This can be explained by the fact that the "bright" surfaces have a smaller specific surface area due to less roughness. Benefits in terms of reduced material loss in forging "bright" components are however not significant, as the material loss is merely shifted to an earlier stage in the process chain. The peeling process for blank steel rods naturally has high material loss as it is a chip removing method. The removed chips can however be more easily recycled than oxide scale. This method would significantly increase the CO₂ footprint of the component, as the additional process steps and recycling would also have to be included in the overall balance of the component. It is not a reasonable approach to reduce scaling and the CO₂-footprint and therefore not considered for the subsequent forging tests. For this reason, black samples were used for the further observations.

In subsequent series of tests, in which 100 parts were forged for each gas combination, it was shown that the lowest scale formation occurs under a pure nitrogen atmosphere, as expected. A scale reduction of approx. 1.1 g form the highest to the lowest result was achieved through the series of tests under the controlled atmospheres. This corresponds to a reduction of 74%. It was also shown that a partial reduction of the oxygen content has a significant effect on scale formation. Without the addition of oxygen, a certain amount of oxidation occurs. By reducing the oxygen content to a quarter of the normal level, more than half of the oxidation or the scale formed can be saved. The difference between CO₂ and N₂ is only relatively small. From this it can be deduced that the greatest improvements can be achieved if the residual oxygen concentration is minimized. This can be achieved with N₂ as well as CO₂.

No significant removal could be recognised in the contour comparisons of the upper dies. However, a clear build-up is recognisable in the area of the burr formation, which decreases as the amount of scale decreases. This can be explained by the fact that the scale forms a thermal protective layer that protects the sample against heat loss to the environment. Due to the absence of scale, it is possible that the components cool down faster and less adhesion occurs, as adhesive effects increase with temperature. The lower dies, on the other hand, exhibit negative geometric deviations in the centre of the dies, which also decrease with decreasing scale formation. This wear may be caused by scale which acts as an abrasive that is pressed into the surface of the die during the forging process. The reduction in abrasive wear was confirmed, which was particularly evident on the lower dies. The reduction in wear is attributed to the lowering of the scale content and the resulting reduction in the quantity of abrasive particles. Contrary to the effects on the upper dies, adhesion increases with decreasing scale. This result is possibly due to the fact that the lower dies surface has higher heat input than the upper dies, due to longer contact time with the billet before and after forging. Effects of increased adhesion with increasing die temperature have already been identified by Lorenz et al. [15]. The increased base temperature and the lack of a scale layer led to increased adhesion. This effect on the lower tool is also expected, since scale acts as an intermediate layer between billet and tool, preventing direct contact and chemical interaction, which can cause adhesion. The thermal and tribochemical effects can be solved by using lubricant. A separate adjustment is necessary as these have been atomised with compressed air up to now. One solution would be to substitute compressed air with pressurised inert or waste gas.
## Conclusions

It has been shown that offgases can be used to reduce scale formation. An influence of the component surface on scale formation could be shown. A scale reduction of up to 74% was achieved, which improves the CO₂ footprint of the components. The abrasive wear on tools was reduced by lowering the amount of scale. As a consequence, tool lifetimes can potentially be increased, further reducing the CO₂ footprint.

## Acknowledgements

This research and development project NoCarb-Forging - ErProFit (Number: 03LB3017) is funded by the Federal Ministry for Economic Affairs and Climate Action (BMWK) within the funding initiative "Technologietransfer-Programm Leichtbau (TTP LB)" (Lightweight construction technology transfer programme) and implemented by the Project Management Jüllich (PTJ). The author is responsible for the content of this publication. The authors thank the company "Gebr. Steller KG" for their support in this project.

## References

[1] M.C. Ghattamaneni, S. Wernicke, T.S. Hainmann, H. Sulaiman, A.E. Tekkaya, Analysis, Prediction and Reduction of Emissions in an Industrial Hot Forming Process Chain for the Manufacture of Sheet Metal Components, Key Engineering Materials 926: 2342-2354 (2022). https://doi.org/10.4028/p-g7120f

[2] Directorate-General for Climate Action (DG CLIMA), Progress Report 2023 Climate Action Shifting gears: Increasing the pace of progress towards a green and prosperous future, (2023)

[3] R. L. Heron, R. Hayter, Knowledge, Industry and Environment: Institutions and Innovation in Territorial Perspective, Routledge (2018). https://doi.org/10.4324/9781315190327

[4] European Commission: A clean planet for all. A European strategic long-term vision for a prosperous, modern, competitive and climate neutral economy: COM (2018) 773 final (2018)

[5] V. C. Panagiotopoulou, P. Stavropoulos, G. Chryssolouris, A critical review on the environmental impact of manufacturing: a holistic perspective, The International Journal of Advanced Manufacturing Technology: 1-23 (2021). https://doi.org/10.1007/s00170-021-07980-w

[6] A. Damgaard, A. W. Larsen, T. H. Christensen, Recycling of metals: accounting of greenhouse gases and global warming contributions, Waste Management & Research 27.8: 773-780 (2009). https://doi.org/10.1177/0734242X09346838

[7] W. J. Mcdonough, M. Braungart, Cradle to cradle. Remaking the way we make things. 1. Ed. New York, NY: North Point Press (2002)

[8] M. Sartor, J. Schoppe, T. Khalil, Verringerung der Zunderbildung durch Beschichtungen. In: Schmiede Journal (2012)

[9] S. L. Semiatin, ASM Metals Handbook Vol 14 Forming and Forging (1996)

[10] L. S. Darken, R.W. Gurry, The System Iron-Oxygen.ll. Equilibrium and Thermodynamics of Liquid Oxide and other Phases, Journal of the American Chemical Society 68 (1946). https://doi.org/10.1021/ja01209a030

[11] R. Y. Chen, W. Y. D. Yeun, Review of the High-Temperature Oxidation of Iron and Carbon Steels in Air or Oxygen, Oxidation of Metals 59, Nr. 5-6, 433-468 (2003). https://doi.org/10.1023/A:1023685905159

[12] P. Huczkowski, L. Singheiser, J. Willem, Oxyfuel-Komponententwicklung und Prozessoptimierung, Teilprojekt P1TP3 Werkstoffe für Dampferzeugerheizflächen im Oxyfuel-
## Conclusions

It has been shown that offgases can be used to reduce scale formation. An influence of the component surface on scale formation could be shown. A scale reduction of up to 74% was achieved, which improves the CO₂ footprint of the components. The abrasive wear on tools was reduced by lowering the amount of scale. As a consequence, tool lifetimes can potentially be increased, further reducing the CO₂ footprint.

## Acknowledgements

This research and development project NoCarb-Forging - ErProFit (Number: 03LB3017) is funded by the Federal Ministry for Economic Affairs and Climate Action (BMWK) within the funding initiative "Technologietransfer-Programm Leichtbau (TTP LB)" (Lightweight construction technology transfer programme) and implemented by the Project Management Jüllich (PTJ). The author is responsible for the content of this publication. The authors thank the company "Gebr. Steller KG" for their support in this project.

## References

[1] M.C. Ghattamaneni, S. Wernicke, T.S. Hainmann, H. Sulaiman, A.E. Tekkaya, Analysis, Prediction and Reduction of Emissions in an Industrial Hot Forming Process Chain for the Manufacture of Sheet Metal Components, Key Engineering Materials 926: 2342-2354 (2022). https://doi.org/10.4028/p-g7120f

[2] Directorate-General for Climate Action (DG CLIMA), Progress Report 2023 Climate Action Shifting gears: Increasing the pace of progress towards a green and prosperous future, (2023)

[3] R. L. Heron, R. Hayter, Knowledge, Industry and Environment: Institutions and Innovation in Territorial Perspective, Routledge (2018). https://doi.org/10.4324/9781315190327

[4] European Commission: A clean planet for all. A European strategic long-term vision for a prosperous, modern, competitive and climate neutral economy: COM (2018) 773 final (2018)

[5] V. C. Panagiotopoulou, P. Stavropoulos, G. Chryssolouris, A critical review on the environmental impact of manufacturing: a holistic perspective, The International Journal of Advanced Manufacturing Technology: 1-23 (2021). https://doi.org/10.1007/s00170-021-07980-w

[6] A. Damgaard, A. W. Larsen, T. H. Christensen, Recycling of metals: accounting of greenhouse gases and global warming contributions, Waste Management & Research 27.8: 773-780 (2009). https://doi.org/10.1177/0734242X09346838

[7] W. J. Mcdonough, M. Braungart, Cradle to cradle. Remaking the way we make things. 1. Ed. New York, NY: North Point Press (2002)

[8] M. Sartor, J. Schoppe, T. Khalil, Verringerung der Zunderbildung durch Beschichtungen. In: Schmiede Journal (2012)

[9] S. L. Semiatin, ASM Metals Handbook Vol 14 Forming and Forging (1996)

[10] L. S. Darken, R.W. Gurry, The System Iron-Oxygen.ll. Equilibrium and Thermodynamics of Liquid Oxide and other Phases, Journal of the American Chemical Society 68 (1946). https://doi.org/10.1021/ja01209a030

[11] R. Y. Chen, W. Y. D. Yeun, Review of the High-Temperature Oxidation of Iron and Carbon Steels in Air or Oxygen, Oxidation of Metals 59, Nr. 5-6, 433-468 (2003). https://doi.org/10.1023/A:1023685905159

[12] P. Huczkowski, L. Singheiser, J. Willem, Oxyfuel-Komponententwicklung und Prozessoptimierung, Teilprojekt P1TP3 Werkstoffe für Dampferzeugerheizflächen im Oxyfuel-
Prozess Wirkung der Gasatmosphäre und der Beläge auf metallische Konstruktionswerkstoffe, Förderkennzeichen 03ET2026E, Jülich (2015)

[13] D.B. Lee, J.W. Choi, High Temperature Oxidation of Steels in Air and CO2-O2 Atmosphere. In: Oxidation of Metals 64 (2005). https://doi.org/10.1007/s11085-005-8530-8

[14] B.A. Behrens, L. Lippold., Influence of shot peened surfaces on friction in hot forging, Surface Topography: Metrology and Properties 6.4: 045005 (2018). https://doi.org/10.1088/2051-672X/aae91c

[15] U. Lorenz, K. Brunotte, J. Peddinghaus, B.A. Behrens, Investigation on Adhesion-Promoting Process Parameters in Steel Bulk Metal Forming., Congress of the German Academic Association for Production Technology. Cham: Springer International Publishing (2022). https://doi.org/10.1007/978-3-031-18318-8_10
Prozess Wirkung der Gasatmosphäre und der Beläge auf metallische Konstruktionswerkstoffe, Förderkennzeichen 03ET2026E, Jülich (2015)

[13] D.B. Lee, J.W. Choi, High Temperature Oxidation of Steels in Air and CO2–O2 Atmosphere. In: Oxidation of Metals 64 (2005). https://doi.org/10.1007/s11085-005-8530-8

[14] B.A. Behrens, L. Lippold., Influence of shot peened surfaces on friction in hot forging, Surface Topography: Metrology and Properties 6.4: 045005 (2018). https://doi.org/10.1088/2051-672X/aae91c

[15] U. Lorenz, K. Brunotte, J. Peddinghaus, B.A. Behrens, Investigation on Adhesion-Promoting Process Parameters in Steel Bulk Metal Forming., Congress of the German Academic Association for Production Technology. Cham: Springer International Publishing (2022). https://doi.org/10.1007/978-3-031-18318-8_10
# Surrogate model to describe temperature field in real-time for hot forging

MIDAOUI Aya<sup>1,a*</sup>, BAUDOUIN Cyrille<sup>1,b</sup>, DANGLADE Florence<sup>2,c</sup> and BIGOT Régis<sup>1,d</sup>

<sup>1</sup>HESAM Université, Arts et Métiers Institute of Technology, Université de Lorraine, LCFC, 57070 Metz, France

<sup>2</sup> HESAM Université, Arts et Métiers Institute of Technology, LISPEN, F-71100 Chalon-sur-Saône, France

<sup>a</sup>aya.midaoui@ensam.eu, <sup>b</sup>cyrille.baudouin@ensam.eu, <sup>c</sup>florence.danglade@ensam.eu,

<sup>d</sup>regis.bigot@ensam.eu

**Keywords:** Hot Forging, Proper Orthogonal Decomposition, Numerical Simulations, Surrogate Model, Real-Time Monitoring System

**Abstract.** In the context of certain metallic alloys, the conformity of the product depends on its metallurgical structure. Addressing this, the implementation of a real-time monitoring system to control the evolution of the metallurgical structure and the geometry of the cogging part is proposed. Focusing on the microstructure's dependence on temperature, this article outlines the requested steps for developing data-driven reduced models for describing the temperature field in the billet. These models use temperature data collected from predictive numerical simulations conducted using FORGE® software. Applying the Proper Orthogonal Decomposition (POD) technique, the images illustrating the temperature field are reconstructed through a 2D matrix-based framework. This matrix, derived from non-discretized elements issued from FORGE®, underwent discretization through an objective method, resulting in a size of 100*100. The utilization of the POD technique in this approach provides a parametric vector description, facilitating rapid image reconstruction through manipulation of vector system parameters. With just two vectors, we can effectively reconstruct the image representing the temperature field.

**Introduction**

Forging at high temperatures plays a crucial role in metallurgy, as hot deformation influences the microstructure of the product, which dictates product conformity and performance. The microstructure depends on several factors: temperature, deformation, deformation rate, and their temporal evolution [1], [2]. In this context, our focus is primarily on temperature.

Hot forming processes induce strong temperature gradients with rapid fluctuations over time. These variations arise from thermal exchanges with the tool, interaction with air at exposed surfaces, and adiabatic heating resulting from plastic deformation [3]. Each forging sequence involves a transfer time from the furnace to the press, a waiting time on the tooling, a shaping operation, and finally a cooling time. These fluctuations lead to both metallurgical and geometrical deviations from the intended target [4].

In the case of a manual cogging operation, our goal is to provide the operator with a temperature field mapping in real time to assist in decision-making. This system, using sensors and prediction models, will reconstruct in real-time the temperature field within a section (2D image plane) of the billet through extrapolation. Consequently, it will assist in adapting process control parameters during the operation.

While existing simulation models can predict temperature [5], the calculation time depends on the desired result accuracy, posing challenges when reactivity is essential [6]. This is especially

<figure><img src="image_828.png" /></figure>
# Surrogate model to describe temperature field in real-time for hot forging

MIDAOUI Aya<sup>1,a*</sup>, BAUDOUIN Cyrille<sup>1,b</sup>, DANGLADE Florence<sup>2,c</sup> and BIGOT Régis<sup>1,d</sup>

<sup>1</sup>HESAM Université, Arts et Métiers Institute of Technology, Université de Lorraine, LCFC, 57070 Metz, France

<sup>2</sup> HESAM Université, Arts et Métiers Institute of Technology, LISPEN, F-71100 Chalon-sur-Saône, France

<sup>a</sup>aya.midaoui@ensam.eu, <sup>b</sup>cyrille.baudouin@ensam.eu, <sup>c</sup>florence.danglade@ensam.eu,

<sup>d</sup>regis.bigot@ensam.eu

**Keywords:** Hot Forging, Proper Orthogonal Decomposition, Numerical Simulations, Surrogate Model, Real-Time Monitoring System

**Abstract.** In the context of certain metallic alloys, the conformity of the product depends on its metallurgical structure. Addressing this, the implementation of a real-time monitoring system to control the evolution of the metallurgical structure and the geometry of the cogging part is proposed. Focusing on the microstructure's dependence on temperature, this article outlines the requested steps for developing data-driven reduced models for describing the temperature field in the billet. These models use temperature data collected from predictive numerical simulations conducted using FORGE® software. Applying the Proper Orthogonal Decomposition (POD) technique, the images illustrating the temperature field are reconstructed through a 2D matrix-based framework. This matrix, derived from non-discretized elements issued from FORGE®, underwent discretization through an objective method, resulting in a size of 100*100. The utilization of the POD technique in this approach provides a parametric vector description, facilitating rapid image reconstruction through manipulation of vector system parameters. With just two vectors, we can effectively reconstruct the image representing the temperature field.

**Introduction**

Forging at high temperatures plays a crucial role in metallurgy, as hot deformation influences the microstructure of the product, which dictates product conformity and performance. The microstructure depends on several factors: temperature, deformation, deformation rate, and their temporal evolution [1], [2]. In this context, our focus is primarily on temperature.

Hot forming processes induce strong temperature gradients with rapid fluctuations over time. These variations arise from thermal exchanges with the tool, interaction with air at exposed surfaces, and adiabatic heating resulting from plastic deformation [3]. Each forging sequence involves a transfer time from the furnace to the press, a waiting time on the tooling, a shaping operation, and finally a cooling time. These fluctuations lead to both metallurgical and geometrical deviations from the intended target [4].

In the case of a manual cogging operation, our goal is to provide the operator with a temperature field mapping in real time to assist in decision-making. This system, using sensors and prediction models, will reconstruct in real-time the temperature field within a section (2D image plane) of the billet through extrapolation. Consequently, it will assist in adapting process control parameters during the operation.

While existing simulation models can predict temperature [5], the calculation time depends on the desired result accuracy, posing challenges when reactivity is essential [6]. This is especially

<figure><img src="image_836.png" /></figure>
pertinent in the case of hot forging, characterized by significant temperature shifts. Any delay in generating the temperature field image could result in the loss of crucial information for effective process control. So, surrogate models are employed to replace Finite Element Method (FEM) resolution by a simplified alternative description, that link essential connections between input variables and output responses. They are usually used for real time predictions, sticking an equilibrium between reactivity and accuracy [7], [8].

Some applications require surrogate models to describe fields, such as temperature field within air-conditioned spaces [9]. Proper Orthogonal Decomposition is used to construct such models by reducing their dimensionality, resulting in POD-based surrogate models[10], [11]. The Proper Orthogonal Decomposition (POD) is applied for image compression through a vectoral description. Sorting the vectors in the description basis by importance allows for a reduction in computational time, as only the dominant vectors are retained, effectively reducing the dimensionality of the basis. Although there has been extensive research on surrogate models in predicting temperature fields in architectural and energy contexts [12], [13], their applicability in forecasting temperature fields in metal forming processes has not been thoroughly investigated.

Hence, the focal point on this research lies in predicting temperature fields within metal processes. This work involves collecting temperature data from FORGE® Finite Element simulations as the initial step [14]. FORGE® is a numerical simulation software for forging (or shaping) operations, distinguished by its adaptive remeshing during simulations. To apply the Proper Orthogonal Decomposition (POD) technique, the mesh must maintain a constant number of points, and it is imperative to know the position of these points when reconstructing an image. Therefore, we propose a technique that transforms FORGE's unordered automatic mesh into a matrix-like structure representing the pixels of an image. Subsequently, the POD technique will be applied to determine a vector basis capable of describing the image, selecting the number of dominant vectors to optimize computation time. The image can then be reconstructed from this vector basis. In this paper, we will focus on the initial phases where the billet is not yet deformed. However, our goal is to generalize the techniques so that they are applicable to any section, even when deformation occurs. The aim of this research is to objectively determine the size of the matrix structure and subsequently the number of vectors required to reconstruct an image. The initial effort focused on establishing a tool capable of swiftly calculating this image at each time step, minimizing deviations from the numerical simulation, by setting criteria such as a temperature mean difference below 1°C and a gradient with pixel differences under 5 °C.

## Materials

Numerical simulations were performed using the commercial FORGE® software developed by Transvalor. As a first step, the focus is on monitoring the temperature field during the transfer of a billet, specifically made of XC35 steel with a diameter of 45 mm and a height of 65 mm, from the furnace to the press.

We suppose that the billet stays at least 30 minutes in the furnace, so it is assumed to have a homogeneous temperature of 1200 °C. Transported to the press using a gripper, the transfer time of the billet is estimated at a maximum of 8 s. FORGE® allows the adjustment of those various parameters, including the thickness of the gripper (20 mm) and the length of the contact surface (37 mm) between the gripper and the billet.

The contact between the gripper and the billet is considered partial, with specific pressure applied to prevent the piece from falling. In fact, the chosen heat transfer coefficient is estimated at 3000 W/m²K[14], and at 10 W/m²K between the air and the billet. The thermal conductivity of the material is 35.5 W/m²K. The room temperature is 25 °C, which is also the initial temperature of the gripper. Friction conditions follow a Coulomb limited Tresca Model (Eq. 1):
pertinent in the case of hot forging, characterized by significant temperature shifts. Any delay in generating the temperature field image could result in the loss of crucial information for effective process control. So, surrogate models are employed to replace Finite Element Method (FEM) resolution by a simplified alternative description, that link essential connections between input variables and output responses. They are usually used for real time predictions, sticking an equilibrium between reactivity and accuracy [7], [8].

Some applications require surrogate models to describe fields, such as temperature field within air-conditioned spaces [9]. Proper Orthogonal Decomposition is used to construct such models by reducing their dimensionality, resulting in POD-based surrogate models[10], [11]. The Proper Orthogonal Decomposition (POD) is applied for image compression through a vectoral description. Sorting the vectors in the description basis by importance allows for a reduction in computational time, as only the dominant vectors are retained, effectively reducing the dimensionality of the basis. Although there has been extensive research on surrogate models in predicting temperature fields in architectural and energy contexts [12], [13], their applicability in forecasting temperature fields in metal forming processes has not been thoroughly investigated.

Hence, the focal point on this research lies in predicting temperature fields within metal processes. This work involves collecting temperature data from FORGE® Finite Element simulations as the initial step [14]. FORGE® is a numerical simulation software for forging (or shaping) operations, distinguished by its adaptive remeshing during simulations. To apply the Proper Orthogonal Decomposition (POD) technique, the mesh must maintain a constant number of points, and it is imperative to know the position of these points when reconstructing an image. Therefore, we propose a technique that transforms FORGE's unordered automatic mesh into a matrix-like structure representing the pixels of an image. Subsequently, the POD technique will be applied to determine a vector basis capable of describing the image, selecting the number of dominant vectors to optimize computation time. The image can then be reconstructed from this vector basis. In this paper, we will focus on the initial phases where the billet is not yet deformed. However, our goal is to generalize the techniques so that they are applicable to any section, even when deformation occurs. The aim of this research is to objectively determine the size of the matrix structure and subsequently the number of vectors required to reconstruct an image. The initial effort focused on establishing a tool capable of swiftly calculating this image at each time step, minimizing deviations from the numerical simulation, by setting criteria such as a temperature mean difference below 1°C and a gradient with pixel differences under 5 °C.

## Materials

Numerical simulations were performed using the commercial FORGE® software developed by Transvalor. As a first step, the focus is on monitoring the temperature field during the transfer of a billet, specifically made of XC35 steel with a diameter of 45 mm and a height of 65 mm, from the furnace to the press.

We suppose that the billet stays at least 30 minutes in the furnace, so it is assumed to have a homogeneous temperature of 1200 °C. Transported to the press using a gripper, the transfer time of the billet is estimated at a maximum of 8 s. FORGE® allows the adjustment of those various parameters, including the thickness of the gripper (20 mm) and the length of the contact surface (37 mm) between the gripper and the billet.

The contact between the gripper and the billet is considered partial, with specific pressure applied to prevent the piece from falling. In fact, the chosen heat transfer coefficient is estimated at 3000 W/m²K[14], and at 10 W/m²K between the air and the billet. The thermal conductivity of the material is 35.5 W/m²K. The room temperature is 25 °C, which is also the initial temperature of the gripper. Friction conditions follow a Coulomb limited Tresca Model (Eq. 1):
$$ \tau = \min (\mu \cdot \sigma_n ; m \cdot \frac{\sigma_0}{\sqrt{3}}). \qquad (1) $$

where $\sigma_n$ is the contact pressure; $\mu$ and $m$ the friction coefficients, equal to 0.4 and 0.8, respectively.

Using finite element methods, the billet mesh is composed to tetrahedrons with a maximum mesh size of 1.14 mm and provides temperatures corresponding to each coordinate point (Xi, Yi, Zi) belonging to the mesh nodes (11190). These data are crucial for image reconstruction as they represent input parameters.

Time increments are defined at 0.5 s, resulting in 16-time steps ranging from 0.5 s to 8 s. Since each temperature field corresponds to a specific time, 16 images will represent the temperature fields.

## Methods

The methodology involves extracting temperature data from FORGE® simulation (Fig. 1a). Interpolations transform FORGE's mesh into ordered matrix image representing temperature field (Fig. 1b). Subsequently, the Proper Orthogonal Decomposition (POD) technique is applied to optimize computation time by selecting dominant vectors for image description (Fig. 1c)

<figure><img src="image_829.png" /><figcaption>Fig.1. Methodology.</figcaption></figure>

Ordered discretization (b). Given the irregular mesh in FORGE®, where the number of elements in the simulation's mesh depends on the billet's size, coupled with FORGE® regularly performing remeshing during simulations, it is uncommon to have a constant number of points and to track the evolution of the same point. Therefore, the decision was made to describe the temperature field of a section using a regular grid (Matrix image with pixels arranged in rows and columns.). For each calculation increment, the grid should represent the temperature field. To achieve this, various interpolation techniques were employed to recalculate the temperature at grid points that do not correspond to the coordinates of nodes extracted from the numerical simulation in FORGE®. The employed interpolation methods include Inverse Distance Weighting [15], nearest neighbor interpolation [16], 2D linear interpolation using Delaunay triangulation [17], cubic spline interpolation [18], and local polynomial interpolation.

The choice of the interpolation method relies on the examination of the error between numerical simulation temperature values and those interpolated at the same coordinates, as well as the Pearson correlation coefficient that measures the linear correlation between two sets of data.

The next step is to objectively determine the size of the structured grid (rectangular) needed to describe the temperature field. To achieve this objective, an analysis is undertaken to establish objective criteria that will define the number of points required on this grid.

Across various grids of different sizes, memory space, computation time, the average of differences of the mean temperatures (Eq. 2), and the maximum of differences of the mean temperatures (Eq. 3) for the 16-time steps (corresponding to the 16 images representing the temperature field) between interpolated temperature values corresponding to changes in grid size $\hat{T}_{grid}$ ranging from 10x10 to 100 x100 and the numerical simulation tool temperature $\hat{T}_{fem}$ values were calculated.
$$ \tau = \min (\mu \cdot \sigma_n ; m \cdot \frac{\sigma_0}{\sqrt{3}}). \qquad (1) $$

where $\sigma_n$ is the contact pressure; $\mu$ and $m$ the friction coefficients, equal to 0.4 and 0.8, respectively.

Using finite element methods, the billet mesh is composed to tetrahedrons with a maximum mesh size of 1.14 mm and provides temperatures corresponding to each coordinate point (Xi, Yi, Zi) belonging to the mesh nodes (11190). These data are crucial for image reconstruction as they represent input parameters.

Time increments are defined at 0.5 s, resulting in 16-time steps ranging from 0.5 s to 8 s. Since each temperature field corresponds to a specific time, 16 images will represent the temperature fields.

## Methods

The methodology involves extracting temperature data from FORGE® simulation (Fig. 1a). Interpolations transform FORGE's mesh into ordered matrix image representing temperature field (Fig. 1b). Subsequently, the Proper Orthogonal Decomposition (POD) technique is applied to optimize computation time by selecting dominant vectors for image description (Fig. 1c)

<figure><img src="image_837.png" /><figcaption>Fig.1. Methodology.</figcaption></figure>

Ordered discretization (b). Given the irregular mesh in FORGE®, where the number of elements in the simulation's mesh depends on the billet's size, coupled with FORGE® regularly performing remeshing during simulations, it is uncommon to have a constant number of points and to track the evolution of the same point. Therefore, the decision was made to describe the temperature field of a section using a regular grid (Matrix image with pixels arranged in rows and columns.). For each calculation increment, the grid should represent the temperature field. To achieve this, various interpolation techniques were employed to recalculate the temperature at grid points that do not correspond to the coordinates of nodes extracted from the numerical simulation in FORGE®. The employed interpolation methods include Inverse Distance Weighting [15], nearest neighbor interpolation [16], 2D linear interpolation using Delaunay triangulation [17], cubic spline interpolation [18], and local polynomial interpolation.

The choice of the interpolation method relies on the examination of the error between numerical simulation temperature values and those interpolated at the same coordinates, as well as the Pearson correlation coefficient that measures the linear correlation between two sets of data.

The next step is to objectively determine the size of the structured grid (rectangular) needed to describe the temperature field. To achieve this objective, an analysis is undertaken to establish objective criteria that will define the number of points required on this grid.

Across various grids of different sizes, memory space, computation time, the average of differences of the mean temperatures (Eq. 2), and the maximum of differences of the mean temperatures (Eq. 3) for the 16-time steps (corresponding to the 16 images representing the temperature field) between interpolated temperature values corresponding to changes in grid size $\hat{T}_{grid}$ ranging from 10x10 to 100 x100 and the numerical simulation tool temperature $\hat{T}_{fem}$ values were calculated.
$$ \frac{\sum_{k=1}^{16} |\hat{T}_{fem_k} - \hat{T}_{grid_k}|}{16} \qquad (2) $$

$$ max_{k=1}^{16} (|\hat{T}_{fem_k} - \hat{T}_{grid_k}|) \qquad (3) $$

A study has also been conducted on the visual aspect of the reconstructed image. To assess the quality of the reconstructed image, the criterion considered is the study of image sharpness. To quantify this quality, the Sobel operator is employed [19], which serves to measure the sharpness of the image by calculating the intensity gradients (Eq. 5) of the image with respect to its horizontal (Eq. 4.1) and vertical (Eq. 4.2) coordinates.

$$ G_x = \begin{bmatrix} -1 & 0 & 1 \\ -2 & 0 & 2 \\ -1 & 0 & 1 \end{bmatrix} * A \quad G_y = \begin{bmatrix} -1 & -2 & -1 \\ 0 & 0 & 0 \\ 1 & 2 & 1 \end{bmatrix} * A \qquad (4.1 4.2) $$

$$ G = \sqrt{\text{gradient}(x)^2 + \text{gradient}(y)^2} \qquad (5) $$

The mean gradient magnitude curve is computed for each grid image, spanning dimensions from 10x10 to 100x100. This curve provides an assessment of the image's overall sharpness. A heightened gradient magnitude signals abrupt intensity changes between pixels, indicating significant variations in the image. Conversely, a lower magnitude denotes a smoother image, where transitions between pixel grayscale levels are more gradual.

In this context, a low gradient magnitude is of particular importance, as it indicates subtle intensity variations between pixels. This is relevant in our case because the observed temperature changes are minimal. Therefore, an image displaying a low gradient intensity is more pertinent for our analytical objective.

Proper Orthogonal Decomposition (c). At this point, we have successfully reconstructed each image (for every increment) in a pixelated format. Our current objective is to represent the entire set of these images using a unified vector basis. To achieve this, we leverage the image collection and apply the POD technique. As a vector-based method, POD enables us to derive a vector basis, allowing us to describe each image through a linear combination of these vectors. Consequently, this approach ensures a brief computational time in the end. This technique, originating from image processing (as a temperature field can be viewed as an image), involves describing a mesh with a constant number of nodes through a linear combination of eigenvectors. The Proper Orthogonal Decomposition technique serves this purpose, enabling the characterization of fields through a parameterized vector system that captures their predominant features or patterns[20]. By deliberately selecting the most influential vectors, often referred to as modes, this technique effectively reduces the volume of data required for precise representation of temperature fields.

After reconstructing the 16 grids, they are assembled into a matrix where each column represents all the points at a given increment, and each row depicts the temperature evolution at each point over the course of the 16 increments.

Using Proper Orthogonal Decomposition (POD), the most influential vectors are extracted, commonly known as eigenvectors. These eigenvectors are sorted in descending order based on their corresponding eigenvalues. The model reduction technique involves retaining only a reduced yet significant number of eigenvectors to accelerate the computation and refreshing of the image. Subsequently, images could be generated with reconstructions using varying numbers of modes: 1 mode, 2 modes, 5 modes, etc. The initial task is to identify the minimum number of modes necessary to achieve the reconstruction of the temperature matrix with the deviation less than 5
$$ \frac{\sum_{k=1}^{16} |\hat{T}_{fem_k} - \hat{T}_{grid_k}|}{16} \qquad (2) $$

$$ \max_{k=1}^{16} (|\hat{T}_{fem_k} - \hat{T}_{grid_k}|) \qquad (3) $$

A study has also been conducted on the visual aspect of the reconstructed image. To assess the quality of the reconstructed image, the criterion considered is the study of image sharpness. To quantify this quality, the Sobel operator is employed [19], which serves to measure the sharpness of the image by calculating the intensity gradients (Eq. 5) of the image with respect to its horizontal (Eq. 4.1) and vertical (Eq. 4.2) coordinates.

$$ G_x = \begin{bmatrix} -1 & 0 & 1 \\ -2 & 0 & 2 \\ -1 & 0 & 1 \end{bmatrix} * A \quad G_y = \begin{bmatrix} -1 & -2 & -1 \\ 0 & 0 & 0 \\ 1 & 2 & 1 \end{bmatrix} * A \qquad (4.14.2) $$

$$ G = \sqrt{\text{gradient}(x)^2 + \text{gradient}(y)^2} \qquad (5) $$

The mean gradient magnitude curve is computed for each grid image, spanning dimensions from 10x10 to 100x100. This curve provides an assessment of the image's overall sharpness. A heightened gradient magnitude signals abrupt intensity changes between pixels, indicating significant variations in the image. Conversely, a lower magnitude denotes a smoother image, where transitions between pixel grayscale levels are more gradual.

In this context, a low gradient magnitude is of particular importance, as it indicates subtle intensity variations between pixels. This is relevant in our case because the observed temperature changes are minimal. Therefore, an image displaying a low gradient intensity is more pertinent for our analytical objective.

Proper Orthogonal Decomposition (c). At this point, we have successfully reconstructed each image (for every increment) in a pixelated format. Our current objective is to represent the entire set of these images using a unified vector basis. To achieve this, we leverage the image collection and apply the POD technique. As a vector-based method, POD enables us to derive a vector basis, allowing us to describe each image through a linear combination of these vectors. Consequently, this approach ensures a brief computational time in the end. This technique, originating from image processing (as a temperature field can be viewed as an image), involves describing a mesh with a constant number of nodes through a linear combination of eigenvectors. The Proper Orthogonal Decomposition technique serves this purpose, enabling the characterization of fields through a parameterized vector system that captures their predominant features or patterns[20]. By deliberately selecting the most influential vectors, often referred to as modes, this technique effectively reduces the volume of data required for precise representation of temperature fields.

After reconstructing the 16 grids, they are assembled into a matrix where each column represents all the points at a given increment, and each row depicts the temperature evolution at each point over the course of the 16 increments.

Using Proper Orthogonal Decomposition (POD), the most influential vectors are extracted, commonly known as eigenvectors. These eigenvectors are sorted in descending order based on their corresponding eigenvalues. The model reduction technique involves retaining only a reduced yet significant number of eigenvectors to accelerate the computation and refreshing of the image. Subsequently, images could be generated with reconstructions using varying numbers of modes: 1 mode, 2 modes, 5 modes, etc. The initial task is to identify the minimum number of modes necessary to achieve the reconstruction of the temperature matrix with the deviation less than 5
°C. This evaluation involves comparing each reconstructed image from different modes with the selected regular grid image.

At the end of this section, pivotal questions emerge, steering the trajectory of our investigation. Firstly, what interpolation technique best ensures the precision of our data representation? Secondly, what grid size strikes the optimal balance, achieving a maximum temperature difference of 1 °C and an average maximum gradient of 5 °C? Finally, how many proper vectors are required for a lossless image reconstruction, with a maximum temperature difference of 5 °C? These questions serve as crucial benchmarks, guiding our pursuit of effective methodologies and contributing to the broader applicability of our techniques, even in scenarios involving deformation.

## Results

Optimal Interpolation Technique. After a thorough evaluation of the various interpolation methods (Fig. 2) discussed in the previous paragraph, it is concluded 2D linear interpolation based on Delaunay triangulation emerges as the optimal approach for temperature prediction in this case. This conclusion is drawn as it consistently demonstrated the smallest average deviation (0.12 for the average of deviations across all 16-time steps) and the Pearson coefficient closest to 1 (0.9990 for the average of Pearson coefficients for all time steps). It's worth noting that a Pearson coefficient of 1 indicates a perfect linear correlation.

<figure><img src="image_830.png" /><figcaption>Fig. 2. Comparative study of average deviation of temperature (°C) and Pearson coefficient for various interpolations</figcaption></figure>

Grid Size for Max Temperature Difference of 1 °C and Average Gradient of 5 °C. Analyzing the computation time for grids ranging from 10x10 to 100x100 reveals minimal change, hovering between 0.111 s and 0.116 s. Similarly, when examining memory space, the variance is not substantial, fluctuating between 164.7 Mo and 166 Mo. Since these metrics show negligible differences, our focus shifts to evaluating the other criteria mentioned earlier to determine the dimension of the structured (rectangular) grid needed to describe the temperature field with a deviation of less than 1 °C compared to the numerical simulation, the result is that a grid of at least (100\*100) points is required to meet the criteria (Fig. 3).

A study was also conducted on the visual quality of the reconstructed image to ensure it is not overly "pixelated". According to the equation (Eq. 5), the vertical and horizontal gradients (Fig. 4) for two grid (50\*50) and (100\*100) are obtained below. The appearance of the image is influenced by cold spots generated by the clamps.

In our case, the objective is to generate an image where the temperature variation between 2 pixels should be less than 5 °C.
°C. This evaluation involves comparing each reconstructed image from different modes with the selected regular grid image.

At the end of this section, pivotal questions emerge, steering the trajectory of our investigation. Firstly, what interpolation technique best ensures the precision of our data representation? Secondly, what grid size strikes the optimal balance, achieving a maximum temperature difference of 1 °C and an average maximum gradient of 5 °C? Finally, how many proper vectors are required for a lossless image reconstruction, with a maximum temperature difference of 5 °C? These questions serve as crucial benchmarks, guiding our pursuit of effective methodologies and contributing to the broader applicability of our techniques, even in scenarios involving deformation.

## Results

Optimal Interpolation Technique. After a thorough evaluation of the various interpolation methods (Fig. 2) discussed in the previous paragraph, it is concluded 2D linear interpolation based on Delaunay triangulation emerges as the optimal approach for temperature prediction in this case. This conclusion is drawn as it consistently demonstrated the smallest average deviation (0.12 for the average of deviations across all 16-time steps) and the Pearson coefficient closest to 1 (0.9990 for the average of Pearson coefficients for all time steps). It's worth noting that a Pearson coefficient of 1 indicates a perfect linear correlation.

<figure><img src="image_838.png" /><figcaption>Fig. 2. Comparative study of average deviation of temperature (°C) and Pearson coefficient for various interpolations</figcaption></figure>

Grid Size for Max Temperature Difference of 1 °C and Average Gradient of 5 °C. Analyzing the computation time for grids ranging from 10x10 to 100x100 reveals minimal change, hovering between 0.111 s and 0.116 s. Similarly, when examining memory space, the variance is not substantial, fluctuating between 164.7 Mo and 166 Mo. Since these metrics show negligible differences, our focus shifts to evaluating the other criteria mentioned earlier to determine the dimension of the structured (rectangular) grid needed to describe the temperature field with a deviation of less than 1 °C compared to the numerical simulation, the result is that a grid of at least (100\*100) points is required to meet the criteria (Fig. 3).

A study was also conducted on the visual quality of the reconstructed image to ensure it is not overly "pixelated". According to the equation (Eq. 5), the vertical and horizontal gradients (Fig. 4) for two grid (50\*50) and (100\*100) are obtained below. The appearance of the image is influenced by cold spots generated by the clamps.

In our case, the objective is to generate an image where the temperature variation between 2 pixels should be less than 5 °C.
<figure><img src="image_831.png" /><figcaption>Fig. 3. Evaluation of mean (a) and maximal (b) deviations from the average temperature depending on grid size.</figcaption></figure>

The analysis of the gradient magnitude reveals that when there is a temperature variation of less than 5 °C between two pixels, it is advisable to use a grid size of at least 100x100 (Fig. 4). The combination of all criteria leads to a choice of 100*100.

<figure><img src="image_832.png" /><figcaption>Fig. 4. Curve of the mean gradient magnitude and images pixelized of temperature field for 2 grid sizes.</figcaption></figure>

Number of eigenvectors for Lossless Image Reconstruction. In this section, the approach involves reconstructing an image with a vectorized description using different numbers of eigenvectors ranging from 1 to 16. The process includes taking the collection of 16 images and generating a reconstructed image for each case. The evaluation focuses on examining the maximum error at a specific point between the reconstructed image and the pixelated image (100*100) (Fig. 5). Subsequently, the maximum error across all time increments (16) is determined.

To achieve a maximum error of 5 °C, the addition of eigenvectors is deemed necessary; however, this comes at the expense of increased computation time. Opting for a compromise, a reduction of 6 °C is accepted, resulting in a conservation of vectors and a corresponding reduction
<figure><img src="image_839.png" /><figcaption>Fig. 3. Evaluation of mean (a) and maximal (b) deviations from the average temperature depending on grid size.</figcaption></figure>

The analysis of the gradient magnitude reveals that when there is a temperature variation of less than 5 °C between two pixels, it is advisable to use a grid size of at least 100x100 (Fig. 4). The combination of all criteria leads to a choice of 100*100.

<figure><img src="image_840.png" /><figcaption>Fig. 4. Curve of the mean gradient magnitude and images pixelized of temperature field for 2 grid sizes.</figcaption></figure>

Number of eigenvectors for Lossless Image Reconstruction. In this section, the approach involves reconstructing an image with a vectorized description using different numbers of eigenvectors ranging from 1 to 16. The process includes taking the collection of 16 images and generating a reconstructed image for each case. The evaluation focuses on examining the maximum error at a specific point between the reconstructed image and the pixelated image (100*100) (Fig. 5). Subsequently, the maximum error across all time increments (16) is determined.

To achieve a maximum error of 5 °C, the addition of eigenvectors is deemed necessary; however, this comes at the expense of increased computation time. Opting for a compromise, a reduction of 6 °C is accepted, resulting in a conservation of vectors and a corresponding reduction
in computational expenses. Considering the ambient temperature is 1200 °C and the current error stands at 6 °C, this signifies a deviation margin of approximately 0.5%. Consequently, the decision has been made to adhere to 2 eigenvectors striking a balance between precision and computational load. Nonetheless, in cases where specific requirements demand heightened accuracy, the option to include more modes remains available. While this approach doesn't inherently introduce greater technical complexity, it does entail a trade-off with increased computation time.

<figure><img src="image_833.png" /><figcaption>Fig. 5. Maximal deviation of temperature based on the number of eigenvectors.</figcaption></figure>

With these 2 eigenvectors, and by interpolation, the temperature image can be reconstructed at any given time. The ensuing figure (Fig. 6) illustrate the coefficients of these 2 eigenvectors over time.

<figure><img src="image_834.png" /><figcaption>Fig. 6. Eigenvectors values resulting from POD.</figcaption></figure>

<figure><img src="image_835.png" /><figcaption>Fig. 7. Temperature field represented by ordered matrix image(a), and by vector image(b), and the difference(c).</figcaption></figure>

The figure 7 depicts the temperature field represented by ordered matrix image (Fig. 7a), and by vector image (Fig. 7b), as well as the difference between the two (Fig. 7c). It appears that there
in computational expenses. Considering the ambient temperature is 1200 °C and the current error stands at 6 °C, this signifies a deviation margin of approximately 0.5%. Consequently, the decision has been made to adhere to 2 eigenvectors striking a balance between precision and computational load. Nonetheless, in cases where specific requirements demand heightened accuracy, the option to include more modes remains available. While this approach doesn't inherently introduce greater technical complexity, it does entail a trade-off with increased computation time.

<figure><img src="image_841.png" /><figcaption>Fig. 5. Maximal deviation of temperature based on the number of eigenvectors.</figcaption></figure>

With these 2 eigenvectors, and by interpolation, the temperature image can be reconstructed at any given time. The ensuing figure (Fig. 6) illustrate the coefficients of these 2 eigenvectors over time.

<figure><img src="image_842.png" /><figcaption>Fig. 6. Eigenvectors values resulting from POD.</figcaption></figure>

<figure><img src="image_843.png" /><figcaption>Fig. 7. Temperature field represented by ordered matrix image(a), and by vector image(b), and the difference(c).</figcaption></figure>

The figure 7 depicts the temperature field represented by ordered matrix image (Fig. 7a), and by vector image (Fig. 7b), as well as the difference between the two (Fig. 7c). It appears that there
are some numerical errors that warrant a more detailed analysis of the interpolation algorithms. Despite the field exhibiting a constant evolution, there are occasional discrepancies that do not follow a consistent trend. Further scrutiny of the interpolation algorithms is necessary to address these discrepancies and ensure a more accurate representation of the temperature field.

## Discussion

To represent temperature fields, several considerations arise:

*   **Interpolation Method:** The process of discretizing and standardizing temperature fields involves inherent errors, making the careful selection of an appropriate interpolation method crucial to minimize these inaccuracies. In our study, we chose a method based on Delaunay triangulation to perform the interpolation. While this approach addresses many concerns, it is essential to acknowledge the potential edge effects that may arise. It is important to note that the technique remains applicable in a three-dimensional (3D) context, offering versatility in addressing temperature variations throughout the spatial domain.

*   **The Grid Size Selection:** The selection of an appropriate grid size is a crucial factor, influencing our ability to accurately capture the entire temperature field akin to the finite element simulation. In our investigation, a grid size of 100x100 stands out as the most fitting choice. This particular grid size ensures a sufficient number of elements to closely replicate the nuances of the finite element simulation's temperature distribution. However, it's worth noting that the grid size can be easily adapted by modifying the criteria. It would be judicious to consider the sensor sensitivity when adjusting the grid size to align with the measurements we will be able to obtain

*   **Number of Modes (eigenvectors):** Careful thought needs to be given to choosing the number of modes, considering their sensitivity to variations in the temperature field. While vector addition is computationally efficient, it is crucial to note that we are not restricted to a specific number of modes. However, it's essential to acknowledge that recalculating an image quickly is feasible. Still, due to various assumptions made, such as thermal exchanges, we cannot solely rely on post-furnace time for image recalculation. Additionally, having temperature measurements is necessary to recalibrate the coefficients of the vector combination at measurement points, enabling the propagation of the image across the entire section.

Since Proper Orthogonal Decomposition (POD) enables the faithful reconstruction of an image of temperature field consistent with finite element simulations, we propose to extend this methodology to subsequent phases with the same interpolation method, and grid size. This includes the positioning of the billet onto the press and its subsequent shaping.

The scientific challenge at this stage lies in chaining reduced models without necessarily having to redo the numerical experimental plan from the beginning of the process. We also plan to extend our modeling to a three-dimensional representation of the temperature field. Additionally, the introduction of a deformable mesh will need to be considered, particularly when working on cogging operations.

Next, the alignment of reduced models with reality, involving the adjustment of linear combination parameters based on temperature measurement data, poses an additional scientific challenge. Simultaneously, we are exploring two distinct paths to address this challenge:

a) Continuation of the Process: Despite the scientific challenges, our focus remains on advancing the process to generate an image at various stages, irrespective of the phase of the manufacturing process. This involves refining the models and incorporating real-time temperature data, ensuring a comprehensive representation.
are some numerical errors that warrant a more detailed analysis of the interpolation algorithms. Despite the field exhibiting a constant evolution, there are occasional discrepancies that do not follow a consistent trend. Further scrutiny of the interpolation algorithms is necessary to address these discrepancies and ensure a more accurate representation of the temperature field.

## Discussion

To represent temperature fields, several considerations arise:

* **Interpolation Method:** The process of discretizing and standardizing temperature fields involves inherent errors, making the careful selection of an appropriate interpolation method crucial to minimize these inaccuracies. In our study, we chose a method based on Delaunay triangulation to perform the interpolation. While this approach addresses many concerns, it is essential to acknowledge the potential edge effects that may arise. It is important to note that the technique remains applicable in a three-dimensional (3D) context, offering versatility in addressing temperature variations throughout the spatial domain.

* **The Grid Size Selection:** The selection of an appropriate grid size is a crucial factor, influencing our ability to accurately capture the entire temperature field akin to the finite element simulation. In our investigation, a grid size of 100x100 stands out as the most fitting choice. This particular grid size ensures a sufficient number of elements to closely replicate the nuances of the finite element simulation's temperature distribution. However, it's worth noting that the grid size can be easily adapted by modifying the criteria. It would be judicious to consider the sensor sensitivity when adjusting the grid size to align with the measurements we will be able to obtain

* **Number of Modes (eigenvectors):** Careful thought needs to be given to choosing the number of modes, considering their sensitivity to variations in the temperature field. While vector addition is computationally efficient, it is crucial to note that we are not restricted to a specific number of modes. However, it's essential to acknowledge that recalculating an image quickly is feasible. Still, due to various assumptions made, such as thermal exchanges, we cannot solely rely on post-furnace time for image recalculation. Additionally, having temperature measurements is necessary to recalibrate the coefficients of the vector combination at measurement points, enabling the propagation of the image across the entire section.

Since Proper Orthogonal Decomposition (POD) enables the faithful reconstruction of an image of temperature field consistent with finite element simulations, we propose to extend this methodology to subsequent phases with the same interpolation method, and grid size. This includes the positioning of the billet onto the press and its subsequent shaping.

The scientific challenge at this stage lies in chaining reduced models without necessarily having to redo the numerical experimental plan from the beginning of the process. We also plan to extend our modeling to a three-dimensional representation of the temperature field. Additionally, the introduction of a deformable mesh will need to be considered, particularly when working on cogging operations.

Next, the alignment of reduced models with reality, involving the adjustment of linear combination parameters based on temperature measurement data, poses an additional scientific challenge. Simultaneously, we are exploring two distinct paths to address this challenge:

a) Continuation of the Process: Despite the scientific challenges, our focus remains on advancing the process to generate an image at various stages, irrespective of the phase of the manufacturing process. This involves refining the models and incorporating real-time temperature data, ensuring a comprehensive representation.
b) Demonstrator Development: In parallel, we are working towards the development of a demonstrator that integrates sensors for real-time data collection and visualization. However, we recognize the importance of adapting the form of feedback for optimal operator interpretation. Traditional image returns might not be the most straightforward. Therefore, alternative presentation forms, often referred to as metaphors, are being explored.

Ultimately, our long-term goal is to create additional metamodels predicting various fields impacting the microstructure. Real-time presentation of grain sizes and deformations directly to the blacksmith could offer substantial benefits. The success of these solutions will be validated through the creation of a demonstrator once all the necessary tools are operational. This approach allows us to materialize our vision of integrating augmented reality to assist operators in decision-making.

## Conclusion

This paper deals with a methodology to obtain a picture representing a temperature field of a billet section in real-time during a forging process. Our research illustrates the capability of describing an image using a vector system, effectively reduced through the application of Proper Orthogonal Decomposition (POD) techniques. However, achieving this necessitates an image with a consistent and known number of points in space. We have established a methodology to reconstruct a 2D matrix image from a non-uniformly distributed Finite Element Method (FEM) mesh. This methodology enables the objective determination of tool parameters, including grid size and the number of vectors employed, ensuring a standardized and principled approach to image reconstruction.

## Acknowledgments

I extend my sincere thanks to CETIM (Centre Technique des Industries Mécaniques) and the Region Grand Est for their financial support in funding this thesis. Their contribution has been instrumental in the successful completion of my research.

## References

[1] H. Clemens, S. Mayer, et C. Scheu, « Microstructure and Properties of Engineering Materials », in Neutrons and Synchrotron Radiation in Engineering Materials Science, John Wiley & Sons, Ltd, 2017, p. 1-20.

[2] G. Y. Lai, W. E. Wood, R. A. Clark, V. F. Zackay, et E. R. Parker, « The effect of austenitizing temperature on the microstructure and mechanical properties of as-quenched 4340 steel », Metall Trans, vol. 5, no 7, p. 1663-1670, juill. 1974. https://doi.org/10.1007/BF02646340

[3] R. Douglas et D. Kuhlmann, « Guidelines for precision hot forging with applications », Journal of Materials Processing Technology, vol. 98, no 2, p. 182-188, janv. 2000. https://doi.org/10.1016/S0924-0136(99)00197-1

[4] Z. Allam, E. Becker, C. Baudouin, R. Bigot, et P. Krumpipe, « Forging Process Control: Influence of Key Parameters Variation on Product Specifications Deviations », Procedia Engineering, vol. 81, p. 2524-2529, janv. 2014. https://doi.org/10.1016/j.proeng.2014.10.361

[5] Y. C. Gerstenmaier et G. Wachutka, « Time dependent temperature effects calculated using eigenfunctions and eigenvalues of the heat conduction equation », Microelectronics Journal, 2001.

[6] J. Yin, R. Hu, et X. Shu, « Closed-die forging process of copper alloy valve body: finite element simulation and experiments », Journal of Materials Research and Technology, vol. 10, p. 1339-1347, janv. 2021. https://doi.org/10.1016/j.jmrt.2020.12.087
b) Demonstrator Development: In parallel, we are working towards the development of a demonstrator that integrates sensors for real-time data collection and visualization. However, we recognize the importance of adapting the form of feedback for optimal operator interpretation. Traditional image returns might not be the most straightforward. Therefore, alternative presentation forms, often referred to as metaphors, are being explored.

Ultimately, our long-term goal is to create additional metamodels predicting various fields impacting the microstructure. Real-time presentation of grain sizes and deformations directly to the blacksmith could offer substantial benefits. The success of these solutions will be validated through the creation of a demonstrator once all the necessary tools are operational. This approach allows us to materialize our vision of integrating augmented reality to assist operators in decision-making.

## Conclusion

This paper deals with a methodology to obtain a picture representing a temperature field of a billet section in real-time during a forging process. Our research illustrates the capability of describing an image using a vector system, effectively reduced through the application of Proper Orthogonal Decomposition (POD) techniques. However, achieving this necessitates an image with a consistent and known number of points in space. We have established a methodology to reconstruct a 2D matrix image from a non-uniformly distributed Finite Element Method (FEM) mesh. This methodology enables the objective determination of tool parameters, including grid size and the number of vectors employed, ensuring a standardized and principled approach to image reconstruction.

## Acknowledgments

I extend my sincere thanks to CETIM (Centre Technique des Industries Mécaniques) and the Region Grand Est for their financial support in funding this thesis. Their contribution has been instrumental in the successful completion of my research.

## References

[1] H. Clemens, S. Mayer, et C. Scheu, « Microstructure and Properties of Engineering Materials », in Neutrons and Synchrotron Radiation in Engineering Materials Science, John Wiley & Sons, Ltd, 2017, p. 1-20.

[2] G. Y. Lai, W. E. Wood, R. A. Clark, V. F. Zackay, et E. R. Parker, « The effect of austenitizing temperature on the microstructure and mechanical properties of as-quenched 4340 steel », Metall Trans, vol. 5, no 7, p. 1663-1670, juill. 1974. https://doi.org/10.1007/BF02646340

[3] R. Douglas et D. Kuhlmann, « Guidelines for precision hot forging with applications », Journal of Materials Processing Technology, vol. 98, no 2, p. 182-188, janv. 2000. https://doi.org/10.1016/S0924-0136(99)00197-1

[4] Z. Allam, E. Becker, C. Baudouin, R. Bigot, et P. Krumpipe, « Forging Process Control: Influence of Key Parameters Variation on Product Specifications Deviations », Procedia Engineering, vol. 81, p. 2524-2529, janv. 2014. https://doi.org/10.1016/j.proeng.2014.10.361

[5] Y. C. Gerstenmaier et G. Wachutka, « Time dependent temperature effects calculated using eigenfunctions and eigenvalues of the heat conduction equation », Microelectronics Journal, 2001.

[6] J. Yin, R. Hu, et X. Shu, « Closed-die forging process of copper alloy valve body: finite element simulation and experiments », Journal of Materials Research and Technology, vol. 10, p. 1339-1347, janv. 2021. https://doi.org/10.1016/j.jmrt.2020.12.087
[7] P. Ruane, P. Walsh, et J. Cosgrove, « Development of a digital model and metamodel to improve the performance of an automated manufacturing line », Journal of Manufacturing Systems, vol. 65, p. 538-549, oct. 2022. https://doi.org/10.1016/j.jmsy.2022.10.011

[8] L. Jia, R. Alizadeh, J. Hao, G. Wang, J. K. Allen, et F. Mistree, « A rule-based method for automated surrogate model selection », Advanced Engineering Informatics, vol. 45, p. 101123, août 2020. https://doi.org/10.1016/j.aei.2020.101123

[9] B. Jiang, H. Gong, H. Qin, et M. Zhu, « Attention-LSTM architecture combined with Bayesian hyperparameter optimization for indoor temperature prediction », Building and Environment, vol. 224, p. 109536, oct. 2022. https://doi.org/10.1016/j.buildenv.2022.109536

[10] B. M. de Gooijer, J. Havinga, H. J. M. Geijselaers, et A. H. van den Boogaard, « Evaluation of POD based surrogate models of fields resulting from nonlinear FEM simulations », Advanced Modeling and Simulation in Engineering Sciences, vol. 8, no 1, p. 25, nov. 2021. https://doi.org/10.1186/s40323-021-00210-8

[11] D. Uribe, C. Baudouin, C. Durand, et R. Bigot, « Predictive control for a single-blow cold upsetting using surrogate modeling for a digital twin », Int J Mater Form, vol. 17, no 1, p. 7, déc. 2023. https://doi.org/10.1007/s12289-023-01803-x

[12] W. Yoo, M. J. Clayton, et W. Yan, « ESMUST: EnergyPlus-driven surrogate model for urban surface temperature prediction », Building and Environment, vol. 229, p. 109935, févr. 2023. https://doi.org/10.1016/j.buildenv.2022.109935

[13] Y. Liu, G. Lin, J. Guo, et J. Zhu, « Dynamic prediction of fuel temperature in aircraft fuel tanks based on surrogate », Applied Thermal Engineering, vol. 215, p. 118926, oct. 2022. https://doi.org/10.1016/j.applthermaleng.2022.118926

[14] T. S.A, « Ressources | FORGE® ». https://www.transvalor.com/fr/ressources/tag/forge (consulté le août 22, 2023).

[15] A. Saha, B. S. Gupta, S. Patidar, et N. Martínez-Villegas, « Spatial distribution based on optimal interpolation techniques and assessment of contamination risk for toxic metals in the surface soil », Journal of South American Earth Sciences, vol. 115, p. 103763, avr. 2022. https://doi.org/10.1016/j.jsames.2022.103763

[16] R. M. Di Biase, A. Marcelli, S. Franceschi, A. Bartolini, et L. Fattorini, « Design-based mapping of plant species presence, association, and richness by nearest-neighbour interpolation », Spatial Statistics, vol. 51, p. 100660, oct. 2022. https://doi.org/10.1016/j.spasta.2022.100660

[17] Y. Liu et G. Yin, « The Delaunay triangulation learner and its ensembles », Computational Statistics & Data Analysis, vol. 152, p. 107030, déc. 2020. https://doi.org/10.1016/j.csda.2020.107030

[18] M. Sun, L. Lan, C.-G. Zhu, et F. Lei, « Cubic spline interpolation with optimal end conditions », Journal of Computational and Applied Mathematics, vol. 425, p. 115039, juin 2023. https://doi.org/10.1016/j.cam.2022.115039

[19] O. Vincent et O. Folorunso, « A Descriptive Algorithm for Sobel Image Edge Detection », présenté à InSITE 2009: Informing Science + IT Education Conference, 2009. https://doi.org/10.28945/3351.

[20] S. L. Brunton et J. N. Kutz, « Data Driven Science & Engineering », 2017.
[7] P. Ruane, P. Walsh, et J. Cosgrove, « Development of a digital model and metamodel to improve the performance of an automated manufacturing line », Journal of Manufacturing Systems, vol. 65, p. 538-549, oct. 2022. https://doi.org/10.1016/j.jmsy.2022.10.011

[8] L. Jia, R. Alizadeh, J. Hao, G. Wang, J. K. Allen, et F. Mistree, « A rule-based method for automated surrogate model selection », Advanced Engineering Informatics, vol. 45, p. 101123, août 2020. https://doi.org/10.1016/j.aei.2020.101123

[9] B. Jiang, H. Gong, H. Qin, et M. Zhu, « Attention-LSTM architecture combined with Bayesian hyperparameter optimization for indoor temperature prediction », Building and Environment, vol. 224, p. 109536, oct. 2022. https://doi.org/10.1016/j.buildenv.2022.109536

[10] B. M. de Gooijer, J. Havinga, H. J. M. Geijselaers, et A. H. van den Boogaard, « Evaluation of POD based surrogate models of fields resulting from nonlinear FEM simulations », Advanced Modeling and Simulation in Engineering Sciences, vol. 8, no 1, p. 25, nov. 2021. https://doi.org/10.1186/s40323-021-00210-8

[11] D. Uribe, C. Baudouin, C. Durand, et R. Bigot, « Predictive control for a single-blow cold upsetting using surrogate modeling for a digital twin », Int J Mater Form, vol. 17, no 1, p. 7, déc. 2023. https://doi.org/10.1007/s12289-023-01803-x

[12] W. Yoo, M. J. Clayton, et W. Yan, « ESMUST: EnergyPlus-driven surrogate model for urban surface temperature prediction », Building and Environment, vol. 229, p. 109935, févr. 2023. https://doi.org/10.1016/j.buildenv.2022.109935

[13] Y. Liu, G. Lin, J. Guo, et J. Zhu, « Dynamic prediction of fuel temperature in aircraft fuel tanks based on surrogate », Applied Thermal Engineering, vol. 215, p. 118926, oct. 2022. https://doi.org/10.1016/j.applthermaleng.2022.118926

[14] T. S.A. « Ressources | FORGE® ». https://www.transvalor.com/fr/ressources/tag/forge (consulté le août 22, 2023).

[15] A. Saha, B. S. Gupta, S. Patidar, et N. Martínez-Villegas, « Spatial distribution based on optimal interpolation techniques and assessment of contamination risk for toxic metals in the surface soil », Journal of South American Earth Sciences, vol. 115, p. 103763, avr. 2022. https://doi.org/10.1016/j.jsames.2022.103763

[16] R. M. Di Biase, A. Marcelli, S. Franceschi, A. Bartolini, et L. Fattorini, « Design-based mapping of plant species presence, association, and richness by nearest-neighbour interpolation », Spatial Statistics, vol. 51, p. 100660, oct. 2022. https://doi.org/10.1016/j.spasta.2022.100660

[17] Y. Liu et G. Yin, « The Delaunay triangulation learner and its ensembles », Computational Statistics & Data Analysis, vol. 152, p. 107030, déc. 2020. https://doi.org/10.1016/j.csda.2020.107030

[18] M. Sun, L. Lan, C.-G. Zhu, et F. Lei, « Cubic spline interpolation with optimal end conditions », Journal of Computational and Applied Mathematics, vol. 425, p. 115039, juin 2023. https://doi.org/10.1016/j.cam.2022.115039

[19] O. Vincent et O. Folorunso, « A Descriptive Algorithm for Sobel Image Edge Detection », présenté à InSITE 2009: Informing Science + IT Education Conference, 2009. https://doi.org/10.28945/3351.

[20] S. L. Brunton et J. N. Kutz, « Data Driven Science & Engineering », 2017.
# Effects of Co ratio on fatigue life of WC-Co die inserts used in cold forming operations

HIZLI Burak<sup>1,2,a*</sup>, OZTURK Kubra<sup>1,2,b</sup>, INCE Umut<sup>2,c</sup>

<sup>1</sup>Department of Metallurgical and Materials Engineering, Dokuz Eylül University, İzmir, Türkiye

<sup>2</sup>R&D Center, Norm İzmir Civata San. ve Tic. A.Ş., AOSB, İzmir, Türkiye

<sup>a</sup>burak.hizli@normfasteners.com, <sup>b</sup>kubra.ozturk@normfasteners.com,

<sup>c</sup>umut.ince@normfasteners.com

**Keywords:** WC-Co, Co Ratio, Fatigue Life, Cold Forming

**Abstract.** Production of fasteners via cold forming requires high forming forces, which induce significant stresses in dies. Therefore, die performance becomes a critical parameter of the fastener production process. Estimation of die life with high accuracy allows to enhance production efficiency and reduce die-related expenditures. Generally, WC-Co hardmetals consisting of 4-30% Co content as a binder are highly preferred in cold forming operations. WC-Co metal-ceramic composite materials offer high wear resistance against frictional forces, high compressive strength, and lower elastic deformation to resist excessive contact pressures, which are primary requirements for cold-forming dies. In this study, experimental investigations were conducted for the determination and comparison of fatigue performance at three different stress amplitudes, utilizing three-point bending fatigue testing with two different grades of WC-Co hardmetals. After the experiments, Goodman-Haigh diagrams were obtained from the experimental results to be utilized in predictive die-life calculations.

**Introduction**

Tungsten carbide-cobalt materials are ceramic-matrix composite materials with high wear resistance, consisting of a WC as a hard phase and Co as a soft binding phase. Low cobalt content in a hardmetal causes large gaps between WC grains, resulting in a material with lower toughness and resistance to fatigue [1]. Various combinations are formed depending on the content of the Co binder, and they are used in different industries according to the needs, ranging from automotive parts production to the mining sector [1, 2]. Die materials used in the cold forming process require high fracture toughness to prevent crack propagation, wear resistance, and high fatigue strength due to the high forming forces that create significant stresses in the dies. [2]. As a consequence, die life has a direct and significant impact on several factors, including mass production, production plans, costs, and customer satisfaction. In the studies conducted in the literature on this subject, Tanrikulu et al. examined three-point bending fatigue tests on specimens of WC-20 wt.% Co, which are often used in cold forging dies, with a loading ratio (R) of 0.1, and constructed Morrow-Haigh diagrams to determine the fatigue life. Through comparison of three-point bending test results with production line dies, their model accurately predicted fatigue life with a deviation of only 5.6 % [3]. The research conducted by Klünser et al. investigated various grades with variations in WC grain size and Co binder content, ranging from 0.2 to 1.3 µm and 6 to 12 wt.%, respectively. They demonstrated that the fatigue crack growth behavior of a hardmetal alloy with an ultra-fine WC grain size showed a dependency on the stress ratio. The threshold stress intensity factor range for fatigue crack growth from inhomogeneities was found to vary with stress ratios, with values of 4.3, 6.2, and 9 MPa for R=0.1, -1, and -3, respectively [4]. Ferreira et al. examined the mechanical behavior of WC-Co materials with different Co ratios (R=0.05 and R=0.5) and demonstrated the influence of Co content on ductility and brittleness [5]. Mikado et al. investigated

<figure><img src="image_836.png" /></figure>
# Effects of Co ratio on fatigue life of WC-Co die inserts used in cold forming operations

HIZLI Burak<sup>1,2,a*</sup>, OZTURK Kubra<sup>1,2,b</sup>, INCE Umut<sup>2,c</sup>

<sup>1</sup>Department of Metallurgical and Materials Engineering, Dokuz Eylül University, İzmir, Türkiye

<sup>2</sup>R&D Center, Norm İzmir Civata San. ve Tic. A.Ş., AOSB, İzmir, Türkiye

<sup>a</sup>burak.hizli@normfasteners.com, <sup>b</sup>kubra.ozturk@normfasteners.com,

<sup>c</sup>umut.ince@normfasteners.com

**Keywords:** WC-Co, Co Ratio, Fatigue Life, Cold Forming

**Abstract.** Production of fasteners via cold forming requires high forming forces, which induce significant stresses in dies. Therefore, die performance becomes a critical parameter of the fastener production process. Estimation of die life with high accuracy allows to enhance production efficiency and reduce die-related expenditures. Generally, WC-Co hardmetals consisting of 4-30% Co content as a binder are highly preferred in cold forming operations. WC-Co metal-ceramic composite materials offer high wear resistance against frictional forces, high compressive strength, and lower elastic deformation to resist excessive contact pressures, which are primary requirements for cold-forming dies. In this study, experimental investigations were conducted for the determination and comparison of fatigue performance at three different stress amplitudes, utilizing three-point bending fatigue testing with two different grades of WC-Co hardmetals. After the experiments, Goodman-Haigh diagrams were obtained from the experimental results to be utilized in predictive die-life calculations.

**Introduction**

Tungsten carbide-cobalt materials are ceramic-matrix composite materials with high wear resistance, consisting of a WC as a hard phase and Co as a soft binding phase. Low cobalt content in a hardmetal causes large gaps between WC grains, resulting in a material with lower toughness and resistance to fatigue [1]. Various combinations are formed depending on the content of the Co binder, and they are used in different industries according to the needs, ranging from automotive parts production to the mining sector [1, 2]. Die materials used in the cold forming process require high fracture toughness to prevent crack propagation, wear resistance, and high fatigue strength due to the high forming forces that create significant stresses in the dies. [2]. As a consequence, die life has a direct and significant impact on several factors, including mass production, production plans, costs, and customer satisfaction. In the studies conducted in the literature on this subject, Tanrikulu et al. examined three-point bending fatigue tests on specimens of WC-20 wt.% Co, which are often used in cold forging dies, with a loading ratio (R) of 0.1, and constructed Morrow-Haigh diagrams to determine the fatigue life. Through comparison of three-point bending test results with production line dies, their model accurately predicted fatigue life with a deviation of only 5.6 % [3]. The research conducted by Klünser et al. investigated various grades with variations in WC grain size and Co binder content, ranging from 0.2 to 1.3 µm and 6 to 12 wt.%, respectively. They demonstrated that the fatigue crack growth behavior of a hardmetal alloy with an ultra-fine WC grain size showed a dependency on the stress ratio. The threshold stress intensity factor range for fatigue crack growth from inhomogeneities was found to vary with stress ratios, with values of 4.3, 6.2, and 9 MPa for R=0.1, -1, and -3, respectively [4]. Ferreira et al. examined the mechanical behavior of WC-Co materials with different Co ratios (R=0.05 and R=0.5) and demonstrated the influence of Co content on ductility and brittleness [5]. Mikado et al. investigated

<figure><img src="image_844.png" /></figure>
the fatigue strength of WC-Co materials using a three-point bending test with R=0.5 and analyzed S-N diagrams [6]. A study by Torres et al. aimed to assess the fatigue behavior of a fine-grained WC-10 wt.% Co hardmetal. It specifically examined the influence of mean stress on the fatigue limit of hardmetals, suggesting that this influence could be elucidated through a Goodman-like relationship [7]. Li et al. examined the fatigue strengths of WC-Co samples with Co binder contents ranging from 3 to 20 wt. % were compared based on their Co content. Having an in-depth knowledge of the mechanical properties of WC-Co will enable companies to determine the most suitable composite structure for various types of industrial processes [8]. Therefore, the fatigue performance of two different grades of WC-Co hardmetals was meticulously investigated and compared in this study. Experimental investigations were conducted for the determination and comparison of fatigue performances at three different stress amplitudes, utilizing three-point bending fatigue testing with two different grades of WC-Co hardmetals. After the completion of experiments, Goodman-Haigh diagrams were obtained from the experimental results.

## Materials & Methods

In this study, different grades of WC-Co materials that have Co contents of 19 and 26% were used in the experiments in order to reveal the fatigue life performance of die inserts used in heading and upsetting operations. Referenced grades were supplied from Boehlerit GmbH & Co.KG with corresponding product range numbers of GB40 and GB56, respectively. The chemical compositions, and mechanical and physical properties of these grades shared by the supplier are given in Table 1. All the test samples were produced by sintering WC powder with Co binder using special molds and HIPed to fabricate the test samples without machining.

<table><caption>Table 1. Properties of referenced grades.</caption><thead><tr><th rowspan="2">Grade</th><th colspan="3">Chemical Composition<br>[wt. %]</th><th rowspan="2">Density<br>[g/cm³]</th><th rowspan="2">Hardness<br>HV 30<br>[MPa]</th><th rowspan="2">Compressive<br>Strength<br>[MPa]</th><th rowspan="2">Transverse<br>Rupture<br>Strength<br>[MPa]</th><th rowspan="2">Fracture<br>Toughness<br>[MNm<sup>-3/2</sup>]</th><th rowspan="2">Elastic<br>Modulus<br>[GPa]</th><th rowspan="2">Thermal<br>Expansion<br>Coefficient<br>[10<sup>-6</sup> / K]</th></tr><tr><th>WC</th><th>Co</th><th>Other</th></tr></thead><tbody><tr><td>GB40</td><td>Balanced</td><td>19</td><td>&lt;0.2</td><td>13.60</td><td>950</td><td>4,000</td><td>2800</td><td>≥ 24</td><td>530</td><td>6</td></tr><tr><td>GB56</td><td>Balanced</td><td>26</td><td>&lt;0.2</td><td>13.05</td><td>815</td><td>3,200</td><td>2700</td><td>≥ 24</td><td>490</td><td>6.5</td></tr></tbody></table>

It is crucial to decrease the surface roughness of forming dies in order to prevent excessive frictional effects that could cause high forming forces and, in return, lower the die life during cold forming. Therefore, prior to testing stage, the surfaces of the test samples were grinded and polished to obtain surface conditions similar to forming dies. Surface preparations were completed in two steps: (i) grinding of each surface with 220+ grid diamond disc under 40 N for 3 min. at 400 rpm, and (ii) polishing of each surface with 9 – 3 µm diamond disc under 25 N for 5 min. at 400 rpm. Surface preparation steps were carried out using Metkon Forcipol 102 grinding and polishing machine with Metkon Forcimat 102 automatic head. Following the microstructural observations, the surface roughness of grinded and polished surfaces of samples was measured by Mitutoyo Surftest SJ 210 portable surface roughness measurement instrument in terms of R<sub>a</sub>, R<sub>q</sub>, and R<sub>z</sub> values. During the measurements, roughness values of the polished surfaces were measured with a straight line pattern over a sampling length of 4.8 mm, in accordance with ISO 1997. Additionally, microstructural observations were conducted on samples of both grades using Zeiss Axio Imager.M2m optical microscope on the polished surfaces.

Fatigue life tests were carried out on prismatic test samples using a three-point bending test apparatus adapted to Zwick Roell Amsler 250 FP 5100 high-frequency fatigue testing machine. Test samples were produced according to Type B as given in ISO 3327:2009, whose nominal dimensions are 20x6.5x5.25 mm [9]. Test samples and fatigue testing stage are illustrated in Fig.
the fatigue strength of WC-Co materials using a three-point bending test with R=0.5 and analyzed S-N diagrams [6]. A study by Torres et al. aimed to assess the fatigue behavior of a fine-grained WC-10 wt.% Co hardmetal. It specifically examined the influence of mean stress on the fatigue limit of hardmetals, suggesting that this influence could be elucidated through a Goodman-like relationship [7]. Li et al. examined the fatigue strengths of WC-Co samples with Co binder contents ranging from 3 to 20 wt. % were compared based on their Co content. Having an in-depth knowledge of the mechanical properties of WC-Co will enable companies to determine the most suitable composite structure for various types of industrial processes [8]. Therefore, the fatigue performance of two different grades of WC-Co hardmetals was meticulously investigated and compared in this study. Experimental investigations were conducted for the determination and comparison of fatigue performances at three different stress amplitudes, utilizing three-point bending fatigue testing with two different grades of WC-Co hardmetals. After the completion of experiments, Goodman-Haigh diagrams were obtained from the experimental results.

## Materials & Methods

In this study, different grades of WC-Co materials that have Co contents of 19 and 26% were used in the experiments in order to reveal the fatigue life performance of die inserts used in heading and upsetting operations. Referenced grades were supplied from Boehlerit GmbH & Co.KG with corresponding product range numbers of GB40 and GB56, respectively. The chemical compositions, and mechanical and physical properties of these grades shared by the supplier are given in Table 1. All the test samples were produced by sintering WC powder with Co binder using special molds and HIPed to fabricate the test samples without machining.

<table><caption>Table 1. Properties of referenced grades.</caption><thead><tr><th rowspan="2">Grade</th><th colspan="3">Chemical Composition<br>[wt. %]</th><th rowspan="2">Density<br>[g/cm³]</th><th rowspan="2">Hardness<br>HV 30<br>[MPa]</th><th rowspan="2">Compressive<br>Strength<br>[MPa]</th><th rowspan="2">Transverse<br>Rupture<br>Strength<br>[MPa]</th><th rowspan="2">Fracture<br>Toughness<br>[MNm⁻³/²]</th><th rowspan="2">Elastic<br>Modulus<br>[GPa]</th><th rowspan="2">Thermal<br>Expansion<br>Coefficient<br>[10⁻⁶ / K]</th></tr><tr><th>WC</th><th>Co</th><th>Other</th></tr></thead><tbody><tr><td>GB40</td><td>Balanced</td><td>19</td><td>&lt;0.2</td><td>13.60</td><td>950</td><td>4,000</td><td>2800</td><td>≥ 24</td><td>530</td><td>6</td></tr><tr><td>GB56</td><td>Balanced</td><td>26</td><td>&lt;0.2</td><td>13.05</td><td>815</td><td>3,200</td><td>2700</td><td>≥ 24</td><td>490</td><td>6.5</td></tr></tbody></table>

It is crucial to decrease the surface roughness of forming dies in order to prevent excessive frictional effects that could cause high forming forces and, in return, lower the die life during cold forming. Therefore, prior to testing stage, the surfaces of the test samples were grinded and polished to obtain surface conditions similar to forming dies. Surface preparations were completed in two steps: (i) grinding of each surface with 220+ grid diamond disc under 40 N for 3 min. at 400 rpm, and (ii) polishing of each surface with 9 – 3 µm diamond disc under 25 N for 5 min. at 400 rpm. Surface preparation steps were carried out using Metkon Forcipol 102 grinding and polishing machine with Metkon Forcimat 102 automatic head. Following the microstructural observations, the surface roughness of grinded and polished surfaces of samples was measured by Mitutoyo Surftest SJ 210 portable surface roughness measurement instrument in terms of R<sub>a</sub>, R<sub>q</sub>, and R<sub>z</sub> values. During the measurements, roughness values of the polished surfaces were measured with a straight line pattern over a sampling length of 4.8 mm, in accordance with ISO 1997. Additionally, microstructural observations were conducted on samples of both grades using Zeiss Axio Imager.M2m optical microscope on the polished surfaces.

Fatigue life tests were carried out on prismatic test samples using a three-point bending test apparatus adapted to Zwick Roell Amsler 250 FP 5100 high-frequency fatigue testing machine. Test samples were produced according to Type B as given in ISO 3327:2009, whose nominal dimensions are 20x6.5x5.25 mm [9]. Test samples and fatigue testing stage are illustrated in Fig.
1a and Fig. 1b, respectively. Stress amplitudes in fatigue tests were determined as 750, 800, and 850 MPa in order to observe the fatigue behavior in a wide range of loading conditions. Stress ratios (R) were determined using minimum stress ($\sigma_{min}$) and maximum stress ($\sigma_{max}$) values in a cycle as given in Eq. 1. Mean stresses ($\sigma_m$) and stress amplitudes ($\sigma_a$) were sequentially calculated by the formulas in Eq. 2 and Eq. 3 as given below.

$$R = \frac{\sigma_{min}}{\sigma_{max}} \qquad (1)$$

$$\sigma_m = \frac{\sigma_{max} + \sigma_{min}}{2} \qquad (2)$$

$$\sigma_a = \frac{\sigma_{max} - \sigma_{min}}{2} \qquad (3)$$

Maximum and minimum loads in fatigue tests were calculated for corresponding maximum and minimum stress values based on stress ratios of R=0.1 and R=0.2 by using Eq. 4 which is given in ISO 3327:2009 as;

$$R_{bm} = \frac{3kFl}{2bh^2} \qquad (4)$$

where $R_{bm}$ is transverse rupture strength in MPa, F is the force applied to the test piece in N, k is the correction factor to compensate for the chamfer, l is the distance between supports, b is the width of test piece perpendicular to its height, and h is the height of test piece parallel to the direction of application of the test force, respectively. k value was taken as 1, as described in the standard for test samples having chamfer of 0,15 to 0,2 mm.

<figure><img src="image_837.png" /></figure>
1a and Fig. 1b, respectively. Stress amplitudes in fatigue tests were determined as 750, 800, and 850 MPa in order to observe the fatigue behavior in a wide range of loading conditions. Stress ratios (R) were determined using minimum stress ($\sigma_{min}$) and maximum stress ($\sigma_{max}$) values in a cycle as given in Eq. 1. Mean stresses ($\sigma_m$) and stress amplitudes ($\sigma_a$) were sequentially calculated by the formulas in Eq. 2 and Eq. 3 as given below.

$$R = \frac{\sigma_{min}}{\sigma_{max}} \qquad (1)$$

$$\sigma_m = \frac{\sigma_{max} + \sigma_{min}}{2} \qquad (2)$$

$$\sigma_a = \frac{\sigma_{max} - \sigma_{min}}{2} \qquad (3)$$

Maximum and minimum loads in fatigue tests were calculated for corresponding maximum and minimum stress values based on stress ratios of R=0.1 and R=0.2 by using Eq. 4 which is given in ISO 3327:2009 as;

$$R_{bm} = \frac{3kFl}{2bh^2} \qquad (4)$$

where $R_{bm}$ is transverse rupture strength in MPa, F is the force applied to the test piece in N, k is the correction factor to compensate for the chamfer, l is the distance between supports, b is the width of test piece perpendicular to its height, and h is the height of test piece parallel to the direction of application of the test force, respectively. k value was taken as 1, as described in the standard for test samples having chamfer of 0,15 to 0,2 mm.

<figure><img src="image_845.png" /></figure>
<figure><img src="image_838.png" /><figcaption>Fig. 1. (a) Dimensions of prismatic samples used in the testing stage and (b) testing fixtures used in fatigue tests and sample positioning.</figcaption></figure>

Calculated static and dynamic forces in fatigue tests corresponding to maximum, minimum, and mean stress values are given in Table 2. The endurance limit for fatigue tests was accepted as 5,000,000 cycles. The average fatigue performance of each set was determined from consistent 3 test results. S-N curves and Goodman-Haigh diagrams were obtained and compared from test results of each grade in order to correlate test results with life cycles of forming dies during the cold forming operations.

<table><caption>Table 2. Fatigue test parameters and corresponding static and dynamic loads.</caption><thead><tr><th>Stress Ratio [R]</th><th>Stress Amplitude, σ<sub>a</sub> [MPa]</th><th>Min. Stress, σ<sub>min</sub> [MPa]</th><th>Max. Stress, σ<sub>max</sub> [MPa]</th><th>Mean Stress, σ<sub>m</sub> [MPa]</th><th>Static Load [kN]</th><th>Dynamic Load [kN]</th></tr></thead><tbody><tr><td rowspan="3">0.1</td><td>850</td><td>188.9</td><td>1,888.9</td><td>1,038.9</td><td>6.20</td><td>5.08</td></tr><tr><td>800</td><td>177.8</td><td>1,777.8</td><td>977.8</td><td>5.84</td><td>4.78</td></tr><tr><td>750</td><td>166.7</td><td>1,666.7</td><td>916.7</td><td>5.47</td><td>4.48</td></tr><tr><td rowspan="3">0.2</td><td>850</td><td>425</td><td>2,125</td><td>1,275</td><td>7.61</td><td>5.08</td></tr><tr><td>800</td><td>400</td><td>2,000</td><td>1,200</td><td>7.17</td><td>4.78</td></tr><tr><td>750</td><td>375</td><td>1,875</td><td>1,125</td><td>6.72</td><td>4.48</td></tr></tbody></table>

## Results & Discussions

OM micrographs of both grades are shown in Fig 2a and 2b, respectively. WC powders in Co binder exhibited homogeneous distributions regardless of the amount of Co binder. However, the difference in the amount of Co binder depending on grade was identified from the micrographs. WC powders with an average particle size of 6.6 µm were used during the fabrication of GB40 samples. For GB56 samples, the average particle size of WC particles was found as 6.1 µm.
<figure><img src="image_846.png" /><figcaption>Fig. 1. (a) Dimensions of prismatic samples used in the testing stage and (b) testing fixtures used in fatigue tests and sample positioning.</figcaption></figure>

Calculated static and dynamic forces in fatigue tests corresponding to maximum, minimum, and mean stress values are given in Table 2. The endurance limit for fatigue tests was accepted as 5,000,000 cycles. The average fatigue performance of each set was determined from consistent 3 test results. S-N curves and Goodman-Haigh diagrams were obtained and compared from test results of each grade in order to correlate test results with life cycles of forming dies during the cold forming operations.

<table><caption>Table 2. Fatigue test parameters and corresponding static and dynamic loads.</caption><thead><tr><th>Stress Ratio [R]</th><th>Stress Amplitude, σ<sub>a</sub> [MPa]</th><th>Min. Stress, σ<sub>min</sub> [MPa]</th><th>Max. Stress, σ<sub>max</sub> [MPa]</th><th>Mean Stress, σ<sub>m</sub> [MPa]</th><th>Static Load [kN]</th><th>Dynamic Load [kN]</th></tr></thead><tbody><tr><td rowspan="3">0.1</td><td>850</td><td>188.9</td><td>1,888.9</td><td>1,038.9</td><td>6.20</td><td>5.08</td></tr><tr><td>800</td><td>177.8</td><td>1,777.8</td><td>977.8</td><td>5.84</td><td>4.78</td></tr><tr><td>750</td><td>166.7</td><td>1,666.7</td><td>916.7</td><td>5.47</td><td>4.48</td></tr><tr><td rowspan="3">0.2</td><td>850</td><td>425</td><td>2,125</td><td>1,275</td><td>7.61</td><td>5.08</td></tr><tr><td>800</td><td>400</td><td>2,000</td><td>1,200</td><td>7.17</td><td>4.78</td></tr><tr><td>750</td><td>375</td><td>1,875</td><td>1,125</td><td>6.72</td><td>4.48</td></tr></tbody></table>

## Results & Discussions

OM micrographs of both grades are shown in Fig 2a and 2b, respectively. WC powders in Co binder exhibited homogenous distributions regardless of the amount of Co binder. However, the difference in the amount of Co binder depending on grade was identified from the micrographs. WC powders with an average particle size of 6.6 µm were used during the fabrication of GB40 samples. For GB56 samples, the average particle size of WC particles was found as 6.1 µm.
<figure><img src="image_839.png" /><figcaption>Fig. 2. OM micrographs of (a) GB40 and (b) GB56.</figcaption></figure>

Surface roughness results obtained from grinded and polished samples are given in Table 3.
According to the results, it was seen that values exhibited convergent and even superior values
compared to those of forming dies. Also, surface roughness results were in well-conforming
manner to surface conditions outlined in ISO 3327:2009, which is defined as not exceeding R_a
limit of 0,4 µm. These findings are evident that failure in fatigue tests is expected to originate from
inner defects rather than surface conditions.
<figure><img src="image_847.png" /><figcaption>Fig. 2. OM micrographs of (a) GB40 and (b) GB56.</figcaption></figure>

Surface roughness results obtained from grinded and polished samples are given in Table 3.
According to the results, it was seen that values exhibited convergent and even superior values
compared to those of forming dies. Also, surface roughness results were in well-conforming
manner to surface conditions outlined in ISO 3327:2009, which is defined as not exceeding R_a
limit of 0,4 µm. These findings are evident that failure in fatigue tests is expected to originate from
inner defects rather than surface conditions.
<table><caption>Table 3. R<sub>a</sub>, R<sub>q</sub>, and R<sub>z</sub> values of test samples.</caption><thead><tr><th>Grade</th><th>R<sub>a</sub> (μm)</th><th>R<sub>q</sub> (μm)</th><th>R<sub>z</sub> (μm)</th></tr></thead><tbody><tr><td>GB40</td><td>0.036 ± 0.010</td><td>0.044 ± 0.05</td><td>0.255 ± 0.031</td></tr><tr><td>GB56</td><td>0.046 ± 0.021</td><td>0.058 ± 0.026</td><td>0.275 ± 0.098</td></tr></tbody></table>

Three-point bending fatigue test results of GB40 and GB56 insert materials are listed in Tables 4 and 5 in detail, respectively. For both grades, fatigue test results showed a consistent manner with each other considering stress ratio, stress amplitude, and hardness increase with Co content decrease.

<table><caption>Table 4. Fatigue test results of GB40 samples.</caption><thead><tr><th>Stress Ratio [R]</th><th>Static Load [kN]</th><th>Dynamic Load [kN]</th><th>Stress Amplitude [MPa]</th><th>Cycles to Failure</th><th>Average Cycles to Failure</th></tr></thead><tbody><tr><td rowspan="7">0.1</td><td>6.20</td><td>5.08</td><td>850</td><td>268,396</td><td rowspan="3">438,316 ± 221,767</td></tr><tr><td>6.20</td><td>5.08</td><td>850</td><td>357,366</td></tr><tr><td>6.20</td><td>5.08</td><td>850</td><td>689,185</td></tr><tr><td>5.84</td><td>4.78</td><td>800</td><td>772,647</td><td rowspan="3">2,144,884 ± 2,473,221</td></tr><tr><td>5.84</td><td>4.78</td><td>800</td><td>662,006</td></tr><tr><td>5.84</td><td>4.78</td><td>800</td><td>5,000,000</td></tr><tr><td rowspan="3">0.2</td><td>5.47</td><td>4.48</td><td>750</td><td>5,000,000</td><td rowspan="2">5,000,000</td></tr><tr><td>5.47</td><td>4.48</td><td>750</td><td>5,000,000</td></tr><tr><td>5.47</td><td>4.48</td><td>750</td><td>5,000,000</td></tr><tr><td rowspan="8">0.2</td><td>7.61</td><td>5.08</td><td>850</td><td>179,076</td><td rowspan="3">174,419 ± 74,119</td></tr><tr><td>7.61</td><td>5.08</td><td>850</td><td>98,081</td></tr><tr><td>7.61</td><td>5.08</td><td>850</td><td>246,101</td></tr><tr><td>7.17</td><td>4.78</td><td>800</td><td>431,630</td><td rowspan="3">310,732 ± 136,040</td></tr><tr><td>7.17</td><td>4.78</td><td>800</td><td>163,423</td></tr><tr><td>7.17</td><td>4.78</td><td>800</td><td>337,144</td></tr><tr><td>6.72</td><td>4.48</td><td>750</td><td>463,139</td><td rowspan="3">700,656 ± 205,850</td></tr><tr><td>6.72</td><td>4.48</td><td>750</td><td>811,459</td></tr><tr><td>6.72</td><td>4.48</td><td>750</td><td>827,372</td></tr></tbody></table>

<table><caption>Table 5. Fatigue test results of GB56 samples.</caption><thead><tr><th>Stress Ratio [R]</th><th>Static Load [kN]</th><th>Dynamic Load [kN]</th><th>Stress Amplitude [MPa]</th><th>Cycles to Failure</th><th>Average Cycles to Failure</th></tr></thead><tbody><tr><td rowspan="3">0.1</td><td>6.20</td><td>5.08</td><td>850</td><td>114,737</td><td rowspan="3">87,383 ± 36,755</td></tr><tr><td>6.20</td><td>5.08</td><td>850</td><td>45,603</td></tr><tr><td>6.20</td><td>5.08</td><td>850</td><td>101,808</td></tr><tr><td>0.1</td><td>5.84</td><td>4.78</td><td>800</td><td>208,056</td><td></td></tr></tbody></table>
<table><caption>Table 3. R<sub>a</sub>, R<sub>q</sub>, and R<sub>z</sub> values of test samples.</caption><thead><tr><th>Grade</th><th>R<sub>a</sub> (μm)</th><th>R<sub>q</sub> (μm)</th><th>R<sub>z</sub> (μm)</th></tr></thead><tbody><tr><td>GB40</td><td>0.036 ± 0.010</td><td>0.044 ± 0.05</td><td>0.255 ± 0.031</td></tr><tr><td>GB56</td><td>0.046 ± 0.021</td><td>0.058 ± 0.026</td><td>0.275 ± 0.098</td></tr></tbody></table>

Three-point bending fatigue test results of GB40 and GB56 insert materials are listed in Tables 4 and 5 in detail, respectively. For both grades, fatigue test results showed a consistent manner with each other considering stress ratio, stress amplitude, and hardness increase with Co content decrease.

<table><caption>Table 4. Fatigue test results of GB40 samples.</caption><thead><tr><th>Stress Ratio [R]</th><th>Static Load [kN]</th><th>Dynamic Load [kN]</th><th>Stress Amplitude [MPa]</th><th>Cycles to Failure</th><th>Average Cycles to Failure</th></tr></thead><tbody><tr><td rowspan="7">0.1</td><td>6.20</td><td>5.08</td><td>850</td><td>268,396</td><td rowspan="3">438,316 ± 221,767</td></tr><tr><td>6.20</td><td>5.08</td><td>850</td><td>357,366</td></tr><tr><td>6.20</td><td>5.08</td><td>850</td><td>689,185</td></tr><tr><td>5.84</td><td>4.78</td><td>800</td><td>772,647</td><td rowspan="3">2,144,884 ± 2,473,221</td></tr><tr><td>5.84</td><td>4.78</td><td>800</td><td>662,006</td></tr><tr><td>5.84</td><td>4.78</td><td>800</td><td>5,000,000</td></tr><tr><td rowspan="6">0.2</td><td>5.47</td><td>4.48</td><td>750</td><td>5,000,000</td><td rowspan="2">5,000,000</td></tr><tr><td>5.47</td><td>4.48</td><td>750</td><td>5,000,000</td></tr><tr><td>5.47</td><td>4.48</td><td>750</td><td>5,000,000</td><td></td></tr><tr><td>7.61</td><td>5.08</td><td>850</td><td>179,076</td><td rowspan="3">174,419 ± 74,119</td></tr><tr><td>7.61</td><td>5.08</td><td>850</td><td>98,081</td></tr><tr><td>7.61</td><td>5.08</td><td>850</td><td>246,101</td></tr><tr><td rowspan="6">0.1</td><td>7.17</td><td>4.78</td><td>800</td><td>431,630</td><td rowspan="3">310,732 ± 136,040</td></tr><tr><td>7.17</td><td>4.78</td><td>800</td><td>163,423</td></tr><tr><td>7.17</td><td>4.78</td><td>800</td><td>337,144</td></tr><tr><td>6.72</td><td>4.48</td><td>750</td><td>463,139</td><td rowspan="3">700,656 ± 205,850</td></tr><tr><td>6.72</td><td>4.48</td><td>750</td><td>811,459</td></tr><tr><td>6.72</td><td>4.48</td><td>750</td><td>827,372</td></tr></tbody></table>

<table><caption>Table 5. Fatigue test results of GB56 samples.</caption><thead><tr><th>Stress Ratio [R]</th><th>Static Load [kN]</th><th>Dynamic Load [kN]</th><th>Stress Amplitude [MPa]</th><th>Cycles to Failure</th><th>Average Cycles to Failure</th></tr></thead><tbody><tr><td rowspan="3">0.1</td><td>6.20</td><td>5.08</td><td>850</td><td>114,737</td><td rowspan="3">87,383 ± 36,755</td></tr><tr><td>6.20</td><td>5.08</td><td>850</td><td>45,603</td></tr><tr><td>6.20</td><td>5.08</td><td>850</td><td>101,808</td></tr><tr><td>0.1</td><td>5.84</td><td>4.78</td><td>800</td><td>208,056</td><td></td></tr></tbody></table>
<table><tbody><tr><td></td><td>5.84</td><td>4.78</td><td>800</td><td>65,142</td><td>127,365 ±<br/>73,225</td></tr><tr><td></td><td>5.84</td><td>4.78</td><td>800</td><td>108,896</td><td></td></tr><tr><td></td><td>5.47</td><td>4.48</td><td>750</td><td>97,394</td><td></td></tr><tr><td></td><td>5.47</td><td>4.48</td><td>750</td><td>497,502</td><td>269,746 ±<br/>205,725</td></tr><tr><td></td><td>5.47</td><td>4.48</td><td>750</td><td>214,342</td><td></td></tr><tr><td rowspan="8">0.2</td><td>7.61</td><td>5.08</td><td>850</td><td>22,276</td><td rowspan="3">25,083 ±<br/>8,244</td></tr><tr><td>7.61</td><td>5.08</td><td>850</td><td>34,365</td></tr><tr><td>7.61</td><td>5.08</td><td>850</td><td>18,609</td></tr><tr><td>7.17</td><td>4.78</td><td>800</td><td>100,492</td><td rowspan="3">74,994 ±<br/>22,536</td></tr><tr><td>7.17</td><td>4.78</td><td>800</td><td>66,745</td></tr><tr><td>7.17</td><td>4.78</td><td>800</td><td>57,744</td></tr><tr><td>6.72</td><td>4.48</td><td>750</td><td>122,389</td><td rowspan="3">123,889 ±<br/>53,824</td></tr><tr><td>6.72</td><td>4.48</td><td>750</td><td>70,831</td></tr><tr><td>6.72</td><td>4.48</td><td>750</td><td>178,448</td></tr></tbody></table>

According to fatigue test parameters given in Table 2, maximum, minimum and mean stress levels considerably altered as the stress ratio increased to R=0.2. Because of this reason, cycles to failure in R=0.2 were significantly decreased compared to cycles acquired from R=0.1 tests. It is generally anticipated that WC-Co grades with higher binder content exhibit greater toughness than grades with lower binder content, resulting in improved performance in resisting higher forming loads during cold forming operations. Consequently, WC-Co grades with higher binder content demonstrate increased resistance to cyclic loads, as evidenced by an extended cycle-to-failure capability. Additionally, lower binder content leads to increased brittleness, so toughness decreases. However, in contrast to having a lower binder content than the other grade, the results of GB40 grade were well above those obtained from GB56 grade, considering both stress ratios and each stress amplitude. Despite GB56 tests, several tests on GB40 grade which were conducted at various stress amplitudes and stress ratios resulted in run-out and reaching the endurance limit. These results were attributed to the probability of the existence of <0.2 % other elements such as Cr and Mo in GB40 grade that improve the material properties. As comparing the two referenced grades, GB40 results exhibited noticeable scattering in all test sets, even higher in test sets of low mean stress-stress amplitudes. It is noteworthy to be said that inner defects and their severeness become critical influencing criteria in terms of fatigue performance and eventual cycles to failure. For any stress combinations lying within the limit areas of R=0.2 with stress amplitude of 750 MPa and R=0.1 with stress amplitude of 800 MPa evidently showed the effect of the previous statement. Additionally, having slightly bigger sized WC powders by GB40 was predicated as an accompanied factor to result in better fatigue performance than GB56 due to lowering crack propagation rates. These outcomes would be further investigated and verified through elemental analysis and examination of fracture surfaces. Also, test results would be confirmed in real-world applications for usage in die life simulations and production trials of die inserts built by using GB40 and GB56 grades.

Following the testing stage, obtained test results were employed to draw Goodman-Haigh diagrams that would be utilized in die life estimations of WC-Co die inserts. Respective diagrams for both GB40 and GB56 grades are illustrated in Fig. 3 and Fig. 4. With the help of these diagrams, die lifespans and safe stress limits could be estimated based on determined areas separated by fitted lines of cycle-to-failure limits, also identifying the corresponding mean stress-stress amplitude ranges in which the die insert could perform reliably.
<table><tbody><tr><td></td><td>5.84</td><td>4.78</td><td>800</td><td>65,142</td><td>127,365 ±<br/>73,225</td></tr><tr><td></td><td>5.84</td><td>4.78</td><td>800</td><td>108,896</td><td></td></tr><tr><td></td><td>5.47</td><td>4.48</td><td>750</td><td>97,394</td><td></td></tr><tr><td></td><td>5.47</td><td>4.48</td><td>750</td><td>497,502</td><td>269,746 ±<br/>205,725</td></tr><tr><td></td><td>5.47</td><td>4.48</td><td>750</td><td>214,342</td><td></td></tr><tr><td rowspan="8">0.2</td><td>7.61</td><td>5.08</td><td>850</td><td>22,276</td><td rowspan="3">25,083 ±<br/>8,244</td></tr><tr><td>7.61</td><td>5.08</td><td>850</td><td>34,365</td></tr><tr><td>7.61</td><td>5.08</td><td>850</td><td>18,609</td></tr><tr><td>7.17</td><td>4.78</td><td>800</td><td>100,492</td><td rowspan="3">74,994 ±<br/>22,536</td></tr><tr><td>7.17</td><td>4.78</td><td>800</td><td>66,745</td></tr><tr><td>7.17</td><td>4.78</td><td>800</td><td>57,744</td></tr><tr><td>6.72</td><td>4.48</td><td>750</td><td>122,389</td><td rowspan="3">123,889 ±<br/>53,824</td></tr><tr><td>6.72</td><td>4.48</td><td>750</td><td>70,831</td></tr><tr><td>6.72</td><td>4.48</td><td>750</td><td>178,448</td></tr></tbody></table>

According to fatigue test parameters given in Table 2, maximum, minimum and mean stress levels considerably altered as the stress ratio increased to R=0.2. Because of this reason, cycles to failure in R=0.2 were significantly decreased compared to cycles acquired from R=0.1 tests. It is generally anticipated that WC-Co grades with higher binder content exhibit greater toughness than grades with lower binder content, resulting in improved performance in resisting higher forming loads during cold forming operations. Consequently, WC-Co grades with higher binder content demonstrate increased resistance to cyclic loads, as evidenced by an extended cycle-to-failure capability. Additionally, lower binder content leads to increased brittleness, so toughness decreases. However, in contrast to having a lower binder content than the other grade, the results of GB40 grade were well above those obtained from GB56 grade, considering both stress ratios and each stress amplitude. Despite GB56 tests, several tests on GB40 grade which were conducted at various stress amplitudes and stress ratios resulted in run-out and reaching the endurance limit. These results were attributed to the probability of the existence of <0.2 % other elements such as Cr and Mo in GB40 grade that improve the material properties. As comparing the two referenced grades, GB40 results exhibited noticeable scattering in all test sets, even higher in test sets of low mean stress-stress amplitudes. It is noteworthy to be said that inner defects and their severeness become critical influencing criteria in terms of fatigue performance and eventual cycles to failure. For any stress combinations lying within the limit areas of R=0.2 with stress amplitude of 750 MPa and R=0.1 with stress amplitude of 800 MPa evidently showed the effect of the previous statement. Additionally, having slightly bigger sized WC powders by GB40 was predicated as an accompanied factor to result in better fatigue performance than GB56 due to lowering crack propagation rates. These outcomes would be further investigated and verified through elemental analysis and examination of fracture surfaces. Also, test results would be confirmed in real-world applications for usage in die life simulations and production trials of die inserts built by using GB40 and GB56 grades.

Following the testing stage, obtained test results were employed to draw Goodman-Haigh diagrams that would be utilized in die life estimations of WC-Co die inserts. Respective diagrams for both GB40 and GB56 grades are illustrated in Fig. 3 and Fig. 4. With the help of these diagrams, die lifespans and safe stress limits could be estimated based on determined areas separated by fitted lines of cycle-to-failure limits, also identifying the corresponding mean stress-stress amplitude ranges in which the die insert could perform reliably.
<figure><img src="image_840.png" /><figcaption>Fig. 3. Goodman-Haigh diagram of GB40 grade for R=0.1 and R=0.2.</figcaption></figure>

<figure><img src="image_841.png" /><figcaption>Fig. 4. Goodman-Haigh diagram of GB56 grade for R=0.1 and R=0.2.</figcaption></figure>

As the fatigue tests at R=-1 stress ratio could not be conducted for the three-point bend samples of hardmetals, the transverse rupture strength of such hardmetals was utilized as static failure strength instead of the ultimate tensile strength value in the Goodman-Haigh graph. In contrast to diagrams that are drawn for materials with infinite fatigue life, diagrams for hardmetals help to define stress limits and corresponding fatigue life limits. Therefore, fitted lines based on mean
<figure><img src="image_848.png" /><figcaption>Fig. 3. Goodman-Haigh diagram of GB40 grade for R=0.1 and R=0.2.</figcaption></figure>

<figure><img src="image_849.png" /><figcaption>Fig. 4. Goodman-Haigh diagram of GB56 grade for R=0.1 and R=0.2.</figcaption></figure>

As the fatigue tests at R=-1 stress ratio could not be conducted for the three-point bend samples of hardmetals, the transverse rupture strength of such hardmetals was utilized as static failure strength instead of the ultimate tensile strength value in the Goodman-Haigh graph. In contrast to diagrams that are drawn for materials with infinite fatigue life, diagrams for hardmetals help to define stress limits and corresponding fatigue life limits. Therefore, fitted lines based on mean
stress-stress amplitude values illustrate the most probable cycles until failure due to fatigue and life zones placed on each fitted line are restricted with other lines that show a lower fatigue life. The Goodman-Haigh diagrams were extended to include the compression zone, facilitating the adjustment of the acquired lines to the compression characteristics of the material. With the utilization of the shrink-fitting process in cold forming dies, there is a need for a comprehensive fatigue life map that takes into account the compressive stresses present in the core material of WC-Co die inserts due to shrink-fitting. The compressive strength of the material represents the static failure strength on the compression zone of the diagram, which was taken as 4,000 MPa and 3,200 MPa for GB40 and GB56, respectively. The diagrams given in Fig. 3 and Fig. 4 would directly be used to predict the most probable fatigue lifes of GB40 and GB56 in the case of being exposed to several means stress and stress amplitude combinations. Additionally, fatigue life limits for the R=-1 stress ratio could be determined from where the fitted limit lines meet the stress amplitude axis and then S-N diagrams would be drawn for each stress amplitude accordingly. Though the fatigue endurance limit of GB40 was found as 1096 MPa directly from diagrams for zero mean stress condition, the determination of the fatigue endurance limit of GB56 required further tests in lower mean stress-stress amplitude values rather than those reported above.

## Conclusions

In the scope of this study, two different grades of WC-Co materials that sequentially have Co contents of 19 and 26% were tested and investigated to understand the effects of Co content on the fatigue life of WC-Co die inserts, which are highly preferred materials in heading and upsetting operations due to high resistance against frictional forces and high contact pressures, superior compressive strength, and lower elastic deformation under forming forces. The following conclusions can be extracted from the experimental results and Goodman-Haigh diagrams:

* Fatigue tests were conducted after reaching lower surface roughness values in order not to cause failure by the surface defects, originating from inner flaws and defects.

* GB40 (WC-19 wt.% Co) grade exhibited better fatigue performance compared to GB56 (WC-26 wt.% Co) in contrast to its increased sensitivity to brittleness due to less binder content and higher hardness.

* Superior test results obtained from GB40 grade were attributed to the probability of existence of <0.2 % other elements such as Cr and Mo. The addition of such elements in WC-Co grade is likely to improve the material properties including fatigue resistance.

* As the Co content decreased, the standard deviation for the same sets increased.

* Goodman-Haigh diagram of both GB40 and GB56 grades were drawn by utilizing experimental results. Die life estimations and determination of safe stress limits could be made based on determined areas separated by fitted lines of cycle-to-failure limits, also identifying the corresponding mean stress-stress amplitude ranges in which the die insert could perform reliably.

* Stress amplitude values read for R=-1 stress ratio conditions when the respective limit lines cross the vertical axis in Goodman-Haigh diagrams could be used to construct an S-N diagram of zero mean stress condition.

The aforementioned experimental outcomes would be further investigated and verified through elemental analysis, and examination of fracture surfaces. Fatigue test results are planned to be confirmed in real-world applications for usage in die life simulations and production trials of dies built by using GB40 and GB56 grade die inserts as a part of future investigations.
stress-stress amplitude values illustrate the most probable cycles until failure due to fatigue and life zones placed on each fitted line are restricted with other lines that show a lower fatigue life. The Goodman-Haigh diagrams were extended to include the compression zone, facilitating the adjustment of the acquired lines to the compression characteristics of the material. With the utilization of the shrink-fitting process in cold forming dies, there is a need for a comprehensive fatigue life map that takes into account the compressive stresses present in the core material of WC-Co die inserts due to shrink-fitting. The compressive strength of the material represents the static failure strength on the compression zone of the diagram, which was taken as 4,000 MPa and 3,200 MPa for GB40 and GB56, respectively. The diagrams given in Fig. 3 and Fig. 4 would directly be used to predict the most probable fatigue lifes of GB40 and GB56 in the case of being exposed to several means stress and stress amplitude combinations. Additionally, fatigue life limits for the R=-1 stress ratio could be determined from where the fitted limit lines meet the stress amplitude axis and then S-N diagrams would be drawn for each stress amplitude accordingly. Though the fatigue endurance limit of GB40 was found as 1096 MPa directly from diagrams for zero mean stress condition, the determination of the fatigue endurance limit of GB56 required further tests in lower mean stress-stress amplitude values rather than those reported above.

## Conclusions

In the scope of this study, two different grades of WC-Co materials that sequentially have Co contents of 19 and 26% were tested and investigated to understand the effects of Co content on the fatigue life of WC-Co die inserts, which are highly preferred materials in heading and upsetting operations due to high resistance against frictional forces and high contact pressures, superior compressive strength, and lower elastic deformation under forming forces. The following conclusions can be extracted from the experimental results and Goodman-Haigh diagrams:

* Fatigue tests were conducted after reaching lower surface roughness values in order not to cause failure by the surface defects, originating from inner flaws and defects.

* GB40 (WC-19 wt.% Co) grade exhibited better fatigue performance compared to GB56 (WC-26 wt.% Co) in contrast to its increased sensitivity to brittleness due to less binder content and higher hardness.

* Superior test results obtained from GB40 grade were attributed to the probability of existence of <0.2 % other elements such as Cr and Mo. The addition of such elements in WC-Co grade is likely to improve the material properties including fatigue resistance.

* As the Co content decreased, the standard deviation for the same sets increased.

* Goodman-Haigh diagram of both GB40 and GB56 grades were drawn by utilizing experimental results. Die life estimations and determination of safe stress limits could be made based on determined areas separated by fitted lines of cycle-to-failure limits, also identifying the corresponding mean stress-stress amplitude ranges in which the die insert could perform reliably.

* Stress amplitude values read for R=-1 stress ratio conditions when the respective limit lines cross the vertical axis in Goodman-Haigh diagrams could be used to construct an S-N diagram of zero mean stress condition.

The aforementioned experimental outcomes would be further investigated and verified through elemental analysis, and examination of fracture surfaces. Fatigue test results are planned to be confirmed in real-world applications for usage in die life simulations and production trials of dies built by using GB40 and GB56 grade die inserts as a part of future investigations.