<figure><img src="image_1.png" /></figure>

<figure><img src="image_2.png" /></figure>

# Fatigue Assessment of Quenched and Tempered Steels Based on Temperature and Micro-Magnetic Measurements

Srinivasa R. RAGHURAMAN<fnref n="1" />, Jonas A. ZIMAN<fnref n="1" />, Fabian WEBER<fnref n="1" />,<fnref n="2" />, Ayush SHRIVASTAVA<fnref n="3" />, Alexander GRAMLICH<fnref n="3" />, Ulrich KRUPP<fnref n="3" />, Peter STARKE<fnref n="1" />,<fnref n="2" />

## Abstract

Magnetic Barkhausen Noise measurements are advantageous for the fatigue characterisation of ferromagnetic materials since they can provide information regarding microstructure, residual stresses, hardness and the presence of microstructural defects. The fatigue characterisation of a quenched and tempered SAE 4140 steel was realised using a servo-hydraulic fatigue testing rig instrumented with an infrared camera and a Magnetic Barkhausen Noise sensor for capturing the material response. Magnetic Barkhausen measurements require correlation against a standardised measurement method such as X-ray diffraction technique. Therefore, micromagnetic measurements were carried out ex-situ at different fatigue stages and then correlated with X-ray diffraction data as well as thermographic data. Since the measured parameters correspond to the induced partial damage, they can be used in lifetime prediction methods and enable an accelerated estimation of the lifetime of materials, thus proving to be effective in monitoring the structural integrity of the material.

**Keywords:** Magnetic Barkhausen Noise, thermography, X-ray diffraction

## 1. Introduction

According to the International Energy Agency (IEA), forty percent of the demand for new steel results from the need to replace damaged steel components during service. High dwell times, expenses and effort required for maximum material utilization result in the majority of steel components being scrapped or recycled before the end of their structural integrity [1]. Achieving climate neutrality in the industry requires integration of Non-Destructive Testing (NDT) methods not only during production, but also throughout the entire material flow.

Various NDT methods are employed to assess the material degradation of components in service in terms of structural monitoring and residual life assessment. Some of these methods include thermography, micro-magnetic methods such as Magnetic Barkhausen Noise (MBN), Hall sensors or eddy current systems.

Thermography for fatigue assessment is based on the concept that, for a material subjected to mechanical loading, the change in temperature is a sum of an elastic part arising due to the thermoelastic effect and a plastic part when the applied load induced plastic deformation. The induced mechanical energy is transformed into the stored energy U and the heat energy component Q. According to Dengel [2], only a portion of approximately five percent of the mechanical work is used to increase the internal energy, whereas the remaining part is dissipated as heat through plastic deformation. Consequently, the change in temperature can be correlated with the cyclic deformation behaviour of metallic materials as a result of their high heat conduction rates.

When a ferromagnetic material is subjected to an external alternating magnetic field, its magnetic domains react by orienting themselves in the direction of applied magnetic field. This re-alignment is not a continuous and smooth process but rather tend to occur in discrete steps or jumps. These jumps or Barkhausen events are caused by obstacles, including defects such as

<footnote n="1">¹ Department of Materials Science and Materials Testing (WWHK), Institute QM³, University of Applied Sciences Kaiserslautern, Schoenstraße 11, 67659 Kaiserslautern, Rhineland-Palatinate, Germany;</footnote>

<footnote>Phone: +49 631 3724, Fax +49 631 3724 2105; srinivasa.raghuraman@hs-kl.de, jonas.ziman@hs-kl.de, fabian.weber@hs-kl.de, peter.starke@hs-kl.de;</footnote>

<footnote n="2">² Faculty of Natural Sciences and Technology, Saarland University, 66123 Saarbrucken, Germany</footnote>

<footnote n="3">³ Steel Institute, RWTH Aachen University, Intzestraße 1, 52072 Aachen, North Rhine-Westphalia, Germany; ayush.shrivastava@iehk.rwth-aachen.de, alexander.gramlich@iehk.rwth-aachen.de, krupp@iehk.rwth-aachen.de</footnote>
dislocations and grain boundaries that act as pinning sites against domain wall motion and domain wall rotations [3]. MBN signals are highly sensitive to various parameters such as changes within the microstructure, residual stresses, plastic deformation, hardness and provide vital insights into the structural integrity and stress state of ferromagnetic materials. MBN is advantageous because it allows in-situ investigations and can be deployed in the field for on-site measurements due to its portability and versatility. The MBN technique, being stochastic in nature, needs to be standardised and correlated against an established conventional method. An analytical method such as X-ray diffraction (XRD) will be suitable for correlating MBN data since it can facilitate the measurement of parameters such as the residual stress and dislocation densities, which also play a huge role in MBN assessments.

The integration of thermography and micro-magnetic NDT-related methods is crucial for the fatigue assessment of a quenched and tempered steel SAE 4140 (DIN standard: 42CrMo4/1.7225) considered for this publication. In the High Cycle Fatigue (HCF) regime, fatigue damage is expected to be predominantly initiated on the surface and near surface regions [4, 5]. The data from thermography, MBN and XRD techniques supplemented by other analytical methods such as light microscopy, Scanning Electron Microscopy (SEM) will serve in the fatigue assessment and consequently the structural monitoring of components, leading to better resource management and sustainable engineering practices.

## 2. Materials and Methodology

### 2.1 Material

The material chosen for this research is a quenched and tempered SAE 4140 steel. As part of the specimen preparation, the material was heat treated by austenitizing at $T_{aus}$ = 880 °C and then by quenching until room temperature. This was followed by a tempering process ($T_{temp}$ = 550 °C and $t_{temp}$ = 90 min.), resulting in a distinctive tempered martensitic microstructure with martensitic lath structures. Figure 1(a) illustrates a band contrast image from an Electron Backscatter Diffraction (EBSD) analysis, which is a greyscale image that provides an assessment of the diffraction pattern quality and serves to visualize the tempered martensitic laths.

<figure><img src="image_3.png" /><figcaption>Figure 1: Microstructural investigations for the quenched and tempered SAE 4140 steel (initial condition): (a) Band contrast image to visualize the tempered martensitic microstructure; (b) EBSD-inverse pole figure mapping to represent the Prior Austenite Grain boundaries (PAGs)</figcaption></figure>

This microstructure results in a preferred combination of high strength and toughness and makes the material suitable for crankshafts, gear wheels and other technical applications that require high load resistance. Figure 1(b) contains the EBSD investigation results and illustrates the orientation distribution of Prior Austenite Grain boundaries (PAGs) with an average grain size of about 15 µm. Macro-hardness testing returned average hardness values of 379 HV (HV30).
## 2.2 Methodology

The methodology is split into two parts. The first part consists of carrying out Load Increase Tests (LIT) and Constant Amplitude Tests (CAT) for the initial fatigue characterisation of the fatigue behaviour and generating a trend S-N curve based on the Lifetime Prediction Method (LPM) MiDAcLife (Miner Damage Accumulation Lifetime Prediction). MiDAcLife obtains its inputs from a single LIT and is based on a modified approach of the linear damage accumulation model according to Palmgren and Miner [6]. This provides a basis for the determination of the stress amplitude for the execution of interrupted CATs in the second part, to gather information about the damage induced in different fatigue stages. These experiments were carried out stress-controlled, with a sinusoidal load-time function and a stress ratio of R = -1 on a servo-hydraulic fatigue testing rig (Shimadzu Deutschland GmbH, type EHF-U 50 kN) at room temperature.

Although the scope of the research project involves the investigation of the size effect with different specimen sizes, this paper concentrates on a single size specimen geometry with a test section diameter of 4 mm, a gauge length of 15 mm and a total specimen length of 150 mm. These specimens were subjected to LITs and CATs at a test frequency of 5 Hz. NDT methods based on temperature using an IR camera (Micro-Epsilon Messtechnik GmbH & Co. KG, type thermoIMAGER TIM QVGA HD) and electrical resistance measurements using the 4-wire method (power supply: Toellner, type TOE 7621) were applied to investigate the material response due to dynamic loading. Since the IR camera system is used for continuous monitoring (up to five days in some cases), the IR camera with a measurement resolution of 40 mK is sufficient for this purpose compared to a high-resolution camera. Since only the change in temperature is considered, the absolute temperature plays a minor role in the temperature calculations, and the measurement error therefore comprises of the resolution limit and the influences of the specimen surface. The stress amplitude of the interrupted CATs $\sigma_{a, PD}$ and the associated extent in terms of number of cycles were determined based on a trend S-N curve provided by the MiDAcLife method.

For specimens subjected to HCF loading, the development of damage characteristics in the surface area can be accessed in terms of the change in roughness arising from the occurrence of intrusions and extrusions, leading to the initiation and propagation of micro-cracks, development into macro-cracks and finally resulting in failure. To this end, light-, confocal- and scanning electron microscopic examinations were carried out at different fatigue stages and were compared to analyse the extent of the induced surface damage.

Besides that, specimens were subjected to interrupted CATs at different fatigue stages and load cycles and were investigated with further analytical NDT-related methods. Ex-situ investigations on these specimens with an MBN measuring system (Stresstech, type Rollscan 350) provided additional information regarding the current damage state to evaluate the influence of fatigue loading. The measurement parameters used are as follows:

* Magnetisation voltage $V_{pp}$ (voltage peak to peak) = 10 V

* Magnetisation frequency f = 100 Hz

* Sampling frequency $f_{sampling}$ = 6.140 MHz

The measured signals were filtered with a high pass and low pass filter of 10 and 1000 kHz and a duration of 10 half-cycles (bursts) was considered for further calculations.
Specimens were also investigated with XRD to obtain information about the surface residual stresses. For that purpose, XRD measurements (XRD Eigenmann GmbH, type Seifert Space XRD TS-4 research-edition X-ray diffractometer) were carried out with CrKα-radiation to investigate the diffraction peak corresponding to alpha-iron (α-Fe), with the focus of data
acquisition being on the Bragg angle of 156.09°. The information from XRD serves to correlate the MBN data pertaining to the induced fatigue damage. This correlation was also reflected in the thermographic data obtained from the IR camera and facilitates the non-destructive monitoring of the material.

# 3. Experimental Results and Discussion

## 3.1 Fatigue Characterisation of Quenched and Tempered Steel Grade SAE 4140

The results of the presented paper consist of an LIT and multiple CATs carried out at a testing frequency of 5 Hz. A detailed description of the MiDAcLife method for the generation of trend S-N curves, its implementation on a ferritic-bainitic steel, which is followed by its validation with other steels, is found in the research of Weber et al. [7]. The same procedure was executed equivalently for the quenched and tempered SAE 4140 steel considered within this publication. The LIT was carried out with an initial stress amplitude $\sigma_{a, start} = 500$ MPa, and the incremental load increase $\Delta\sigma_a$ for every 6000 cycles was 10 MPa. The LIT had run for twenty-four load steps till the specimen failed at a stress amplitude of 730 MPa, as depicted in Figure 2(a). The cyclic deformation curves show no considerable change in the material response until 640 MPa, after which the change in temperature $\Delta T$ starts to increase evidently. Based on this insight, an LIT not only facilitates the generation of S-N trend curves using MiDAcLife method (Figure 2(b)) but also provides an initial estimation of the fatigue limit, since the stage just before first increase in change in material response is considered to be the fatigue limit. This estimation also falls within the range of the fatigue limit expected from an average material hardness of 379 HV (HV30), which is approximately 645 MPa according to Murakami [8]. CATs at stress amplitudes of 650 MPa, 670 MPa, 690 MPa, and 700 MPa, respectively, were performed until specimen failure to serve as validation for the generated S-N curve. It was necessary to choose a stress amplitude which had a considerable fatigue life of at least $10^5$ cycles or more to enable interrupted CATs at different fatigue stages, taking into consideration the potential scatter in lifetime. Thus, the stress amplitude for interrupted CATs $\sigma_{a, PD}$ was chosen to be 650 MPa.

<figure><img src="image_4.png" /><figcaption>Figure 2: (a) Cyclic deformation curve based on thermographic data for an LIT; (b) Trend S-N curve generated according to MiDAcLife and the chosen stress amplitude $\sigma_{a, PD}$ for interrupted CATs</figcaption></figure>

## 3.2 Thermographic Investigations at Different Fatigue Stages

CATs until failure and interrupted CATs at a stress amplitude of 650 MPa were carried out on multiple specimens, and the corresponding thermographic data at every 1,000 cycles are plotted in Figure 3. The CATs carried out until failure show a considerable increase in temperature due to the material degradation and consequently the cyclic softening behaviour, followed by failure. The interrupted CATs of specimens 1 and 2 (Figure 3(b), (c)) exhibit a similar trend where the change in temperature $\Delta T$ increases steadily in both the fatigue stages and is followed by a sudden upsurge in the second stage just before failure. Specimens 1 and 2 were interrupted
at different fatigue stages with normalised number of cycles Nnorm of 0.76 and 0.97, respectively. These values are based on the total fatigue life of the corresponding specimens and are subject to scatter in lifetime. Both specimens exhibit non-linear increases in temperature change, which indicates plastic deformation in the first partially fatigued stage. The already accumulated material degradation in both specimens has paved the way to a drastic increase in temperature, culminating in specimen failure in the second stage. This was evident in specimen 2, where the second stage was particularly fleeting.

<figure><img src="image_5.png" /><figcaption>Figure 3: (a) Thermographic data of CATs at 650 MPa till failure; (b), (c) & (d) Thermographic data of interrupted CATs at different fatigue stages for different specimens</figcaption></figure>

Specimens 3 and 4 were cyclically loaded until they were interrupted at Nnorm = 0.55 and 0.72 and at Nnorm = 0.25 and 0.33, respectively. As seen in Figure 3(d), specimen 3 shows a considerable increase across all the fatigue stages as depicted by solid rectangular data points. In order to investigate the material reactions specifically in earlier stages, partial fatigue damage was induced on specimen 4. The course of temperature change, which is plotted with solid round data points, is relatively stable, showing a meagre increase for each fatigue stage and an abrupt increase just before failure. In all the cases, temperature increase was the highest when specimen failure was imminent. As this study involves MBN and XRD investigations in addition to the thermographic data, and owing to the time-consuming nature of XRD measurements, specimens with only two and three partially fatigued stages were taken into consideration for the scope of this research.

## 3.3 MBN Investigations at Different Fatigue Stages

The MBN measurements were taken at different fatigue stages to assess the change in micro-magnetic parameters due to induced fatigue damage after proper specimen preparation, including material demagnetisation and reference air measurements. The changes in MBN measurand parameters such as effective voltage ΔV<sub>RMS</sub> and coercivity ΔH<sub>CM</sub> at various fatigue stages, plotted against normalised number of load cycles N<sub>norm</sub> are illustrated in Figure 4(a) and Figure 4(b), respectively.
<figure><img src="image_6.png" /><figcaption>Figure 4: MBN parameters plotted at different fatigue stages; (a) Development of changes in effective voltage $\Delta V_{\text{RMS}}$ due to the fatigue damage induced at different stages; (b) Degradation of change in coercivity $\Delta H_{\text{CM}}$ due to induced fatigue damage at various stages</figcaption></figure>

<figure><img src="image_7.png" /></figure>

As depicted in Figure 4(a), the $\Delta V_{\text{RMS}}$ values tend to increase with increasing number of load cycles, showing that they increase with increasing plastic deformation due to dynamic loading. This trend is also reflected in the thermographic data for this material, where the change in temperature increases with the loading cycles as well. Plastic deformation causes nucleation, local clustering of dislocations at earlier stages. Further increase in plastic deformation results in dislocation annihilations, micro-crack initiation and propagation and further transition into macro-cracks [9]. The rates of increase in $\Delta V_{\text{RMS}}$ are relatively higher in specimens 1, 2 and 4, where the MBN measurements were taken at $N_{\text{norm}} = 0.76, 0.97, 0.25$ and $0.33$ respectively. Specimen 3 on the other hand, was interrupted at $N_{\text{norm}} = 0.55$ and $0.72$. In specimen 3, the $\Delta V_{\text{RMS}}$ increased slightly before falling further down at the second interruption stage. This can be attributed to the increase in pinning sites because of dislocation tangles, which restrict the domain wall movement, leading to reduced MBN activity. For specimen 4, $\Delta V_{\text{RMS}}$ initially increased and then showed a pronounced rise at the second interruption stage. Both trends are consistent with findings reported in the literature regarding the effects of dynamic loading on $\Delta V_{\text{RMS}}$ [10, 11].

In Figure 4(b), the change in coercivity $\Delta H_{\text{CM}}$ exhibits a trend opposite in nature to that of the change in effective voltage $\Delta V_{\text{RMS}}$. Specimen 2 shows the strongest reduction in coercivity, indicating since the material has softened the most due to cyclic loading, thus requiring the least coercive field intensity to affect the magnetisation of the material. In contrast, specimens 1, 3, and 4, which experienced fewer load cycles, retain higher coercivity values. The increase in $\Delta H_{\text{CM}}$ for specimen 4 in the first partially fatigued stage deviates from this general inverse relationship. Overall, increasing material degradation due to plastic deformation leads to higher $\Delta V_{\text{RMS}}$ values and lower $\Delta H_{\text{CM}}$ values.

## 3.4 XRD Investigations at Different Fatigue Stages

Residual stresses were calculated from XRD analysis of the specimens at different fatigue stages in the axial direction at three points along the gauge length, and the average values are plotted in Figure 5(a) and (b). A pronounced reduction of compressive residual stresses occurs during fatigue loading. Furthermore, specimens with higher initial compressive stresses exhibit faster relaxation rates, most notably specimen 4. Residual stress relaxation depends on the interaction of several factors, including the amplitude of the applied cyclic loading, the loading mode, the number of cycles and the surface finishing process. Since the relaxation is associated with dislocation movement, it is therefore correlated with the plastic strain accumulation. Most of the residual stress relaxation takes place in the initial cycles, followed by further gradual relaxation along the lifetime [12].
<figure><img src="image_8.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 5: (a) Surface residual stresses $\sigma_{RS}$ due to dynamic loading at different fatigue stages; (b) Deterioration of residual stresses $\Delta\sigma_{RS}$ at different fatigue stages</figcaption></figure>

### 3.5 Correlation of MBN and XRD Data

Compressive residual stresses play a vital role in determining the fatigue life of a specimen by facilitating crack closure and delaying crack propagation, while tensile residual forces have an adverse effect on the lifetime [13]. As MBN measurand parameters are sensitive to residual stresses, and since the XRD technique is a well-established method of measuring the residual stresses, XRD data can consequently be used for the correlation of MBN data. The $\Delta V_{RMS}$ and $\Delta H_{CM}$ values as a function of normalised fatigue life are plotted in Figure 6(a) and Figure 6(b), respectively, along with the change in residual stresses $\Delta\sigma_{RS}$.

<figure><img src="image_10.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 6: Correlation of residual stress values $\Delta\sigma_{RS}$ at different stages of dynamic loading with (a) change in effective voltage $\Delta V_{RMS}$; (b) Change in coercivity $\Delta H_{CM}$</figcaption></figure>

The $\Delta V_{RMS}$ values tend to increase as the compressive residual stresses diminish. This trend is supported by previous literature from Jagadish et al. [14]. The $\Delta H_{CM}$ values behave opposite in nature to that of $\Delta V_{RMS}$ and decrease with decreasing compressive residual stresses. The first partially fatigued stage for specimen 4 offers a notable contradiction to this trend. It is significant that the information provided by the MBN and XRD methods pertain to the surface area, while the thermography also provides information about the changes in the bulk of the specimen. The material response is influenced by the plastically deformed volume, which in turn depends on the specimen geometry.

## 4. Conclusion

The correlation between X-ray diffraction data and Magnetic Barkhausen Noise data is highly advantageous as it enables faster field deployment of damage assessments using non-
destructive testing. This results in lesser effort in maintenance, reducing the chances of premature scrapping, encourages sustainability and improved resource management. Further refinement of this correlation is possible by considering more fatigue stages as well as other parameters that affect Magnetic Barkhausen Noise signals, such as dislocation densities, surface roughness, hardness as well as the measurement frequency. While the Magnetic Barkhausen Noise measurements show promise, the incorporation of other non-destructive techniques like electrical resistance measurements, eddy current measurements, ultrasound can bolster thermographic and micro-magnetic based measurement techniques and facilitate reliable fatigue assessments

## Acknowledgements

The authors would like to thank the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) for the funding and support of the research project (STA 1133/20-1 | KR 1999/52-1). The authors would also like to thank the University of Applied Sciences Kaiserslautern, for its financial support in procuring the test infrastructure. Finally, thanks go to the company Shimadzu Deutschland GmbH, Stresstech GmbH, EVIDENT Europe GmbH and XRD Eigenmann GmbH for their technical support.

## References

[1] D. R. Cooper, A. C. Skelton, M. C. Moynihan, and J. M. Allwood, "Component level strategies for exploiting the lifespan of steel in products," Resources, Conservation and Recycling 84 (2014).

[2] D. Dengel and H. Hang, "Die Temperatur als Indikator von Deformationsvorgängen im Werkstoff," HTM Journal of Heat Treatment and Materials 30 (1975).

[3] H. Barkhausen, "Einheitliche Bezeichnungen für die bei Vakuumröhren vorkommenden Größen," Archiv f. Elektrotechnik 8 (1919).

[4] D. Radaj, M. Vormwald, "Ermüdungsfestigkeit: Grundlagen für Ingenieure", 3rd ed., (2007).

[5] J. Polák, T. Lepistö, P. Kettunen, "Surface topography and crack initiation in emerging persistent slip bands in copper single crystals," Materials Science and Engineering 74 (1985).

[6] M. A. Miner, "Cumulative Damage in Fatigue," Journal of Applied Mechanics 12 (1945).

[7] F. Weber and P. Starke, "MiDAcLife – Ein neues Lebensdauerprognoseverfahren basierend auf der Kombination zerstörungsfreier Messverfahren und (nicht)linearer Schadensakkumulationsansätze," in Zerstörungsfreie Materialprüfung. DGZfP-Jahrestagung, Date: 2024/05/06-2025/05/08, Location: Osnabrück, Germany.

[8] Y. Murakami, "Metal fatigue: Effects of small defects and nonmetallic inclusions", 2nd ed., (2019).

[9] J. Schijve, "Fatigue of Structures and Materials" (2009), Location: Dordrecht, Netherlands.

[10] S. Sagar, N. Parida, S. Das, G. Dobmann, and D. Bhattacharya, "Magnetic Barkhausen emission to evaluate fatigue damage in a low carbon structural steel," International Journal of Fatigue 27 (2005).

[11] N. Baak, "Mikromagnetische Charakterisierung des Ermüdungsverhaltens und der Eigenspannungsrelaxation tiefgebohrter Proben des Vergütungsstahls 42CrMo4", PhD, TU Dortmund

[12] Kodama. S, "The behavior of residual stress during fatigue stress cycles", International Conference on Mechanical Behavior of Metals II, Location: Kyoto, Japan, (1972).

[13] L. Wagner, G. Lütjering, and V. Sedláček, "Fatigue Crack Growth Retardation in an Al Alloy 2024 in a Residual Compressive Stress Field," International Conference on Residual Stresses 1 (1989).

[14] C. Jagadish, L. Clapham, and D. L. Atherton, "Influence of uniaxial elastic stress on power spectrum and pulse height distribution of surface Barkhausen noise in pipeline steel," IEEE Transactions on Magnetics 26 (1990).