# Influence of shot-peening on the self-heating behavior and fatigue properties of 300M steel

Pierrick Lepitre, Louis-Maël Merlet, Cédric Doudard, Matthieu Dhondt,

Martin Surand, Sylvain Calloch

► To cite this version:

Pierrick Lepitre, Louis-Maël Merlet, Cédric Doudard, Matthieu Dhondt, Martin Surand, et al.. Influence of shot-peening on the self-heating behavior and fatigue properties of 300M steel. Mechanics of Materials, 2024, 199, pp.105174. 10.1016/j.mechmat.2024.105174. hal-05059009

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https://hal.univ-brest.fr/hal-05059009v1

Submitted on 7 May 2025

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Research paper

# Influence of shot-peening on the self-heating behavior and fatigue properties of 300M steel

Pierrick Lepitre<sup>a,b,*</sup>, Louis-Maël Merlet<sup>a</sup>, Cédric Doudard<sup>a</sup>, Matthieu Dhondt<sup>a</sup>, Martin Surand<sup>b</sup>, Sylvain Calloch<sup>a</sup>

<sup>a</sup> ENSTA Bretagne, IRDL, UMR CNRS 6027, 2 Rue François Verny, 29200, Brest, France

<sup>b</sup> Safran Landing Systems, 7 Rue Général Valérie André, 78140, Vélizy-Villacoublay, France

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

## ARTICLE INFO

Handling Editor: G Subhash

### Keywords:

Thermometry

Self-heating under cyclic loading

Intrinsic dissipation

Shot-peening

Residual stress

High cyclic fatigue

## ABSTRACT

Shot peening is an established cold working process used to introduce residual compressive stresses on a surface and is extensively studied using conventional fatigue tests. However, it has not been widely studied using the self-heating method. Specifically, the heterogeneity of the dissipation field has not been estimated, with only an average approach being used. Previous investigations in the case of 300M steel demonstrated that the effect of shot peening on the high cycle fatigue properties can be either beneficial or detrimental. This study proposes to apply the self-heating method on polished 300M and to investigate the effect of mean stress and shot peening on the dissipation behavior. A modified self-heating model is proposed and calibrated for 300M steel. Combined with residual stress profiles, a method to compute and determine the shot peening effect on self-heating behavior through single point surface measurements is proposed. Application on 300M steel shows excellent results, the over-dissipation being mainly due to the sub-surface compressive residual stresses. The self-heating method has proven useful to quickly estimate fatigue properties of polished 300M steel. Based on the understanding of the self-heating curve of shot peened 300M steel, a quantification of shot-peening effect on fatigue limit is discussed.

## 1. Introduction

Determining the effects of surface treatments and/or surface enhancements on the fatigue limit can be time and money consuming, as many process-parameters can influence the material fatigue properties. Generally, it is not industrially practicable to test the effects of every combination of every parameter. So only the most disadvantageous conditions are tested with a high level of statistical reliability, and other sets of parameters are usually covered by these conservative design rules.

As surface initiation is the main cause of 300M steel HCF (High Cycle Fatigue) rupture [Bag et al., 2020; Pei-ge et al., 1996; Xue et al., 2012], different treatments can be used to enhance the surface. These treatments include laser peening [Pistochini and Hill 2011], ultrasonic surface rolling [Dang et al., 2021] and more traditionally, shot peening [Pei-ge et al., 1996; Bag et al., 2019]. Shot peening introduces a high compressive residual stress state on the first 100 µm below the surface [Pistochini and Hill 2011; Bag et al., 2019], preventing initiation at the surface. The rupture mechanism shifts to internal initiation on inclusions

[Pistochini and Hill 2011; Bag et al., 2019]. This results in an improvement of fatigue properties under rotating bending tests [Pei-ge et al., 1996] or four-point bending tests [Pistochini and Hill 2011], where the stress concentrates on the surface. However, under axial tests, the effect of shot peening is less beneficial for high stress amplitudes (~$10^4–10^5$ cycles [Bag et al., 2020]) and could even be detrimental for HCF properties (~$10^5–10^6$ cycles [Bag et al., 2019]).

In this study, a fast method to characterize the HCF properties has been applied to polished and shot peened 300M steel. The so-called self-heating under cyclic loadings method (abbreviated as self-heating method) is based on the evolution of the test coupon temperature during cyclic loadings. Empirical analysis revealed a strong correlation with conventional fatigue tests on various steel grades (e.g. [Stromeyer, 1914; Moore and Kommers, 1921; Luong, 1998; Doudard, 2004; Munier et al., 2014; De Finis et al., 2015]), other metal alloys (e.g. [Giancane et al., 2009; Ezanno et al., 2010; Roué et al., 2018; Mostofizadeh et al., 2019]) or materials (e.g. [Luong, 2000; Le Saux et al., 2010; Kwiakowski et al., 2023; Teng, 2023]). For steel, a self-heating model has been built and validated on a broad range of steel grades [Munier et al., 2014;

<footnote>* Corresponding author. ENSTA Bretagne, IRDL, UMR CNRS 6027, 2 Rue François Verny, 29200, Brest, France.
E-mail address: pierrick.lepitre@ensta-bretagne.org (P. Lepitre).</footnote>
Doudard et al., 2005; Munier et al., 2017]. By modeling the dissipation, post-processing can predict the S/N curve with its scatter. The self-heating method has already been successfully applied on high-tensile strength steel [Louge et al., 2018; Zhao et al., 2022] but to the author's knowledge, not on 300M steel. Moreover, most of the studies used homogeneous configurations only. Some studies have applied the method for heterogenous configurations (coupon geometry [Doudard et al., 2010], surface carburizing [Graux, 2017], repairs by directed energy deposition [Balit et al., 2020], surface rolling [Cao et al., 2020] or welded joints [Florin et al., 2013; Wei et al., 2021]) but those studies consider a mean coupon temperature resulting from the homogenization of the intrinsic dissipation.

This study investigates the influence of shot peening on the dissipation of 300M steel. Test and post-processing protocols are proposed to estimate the intrinsic dissipated energy profile in the case of a heterogeneous configuration by using local temperature measurements. The influence of different mean stress levels on the self-heating curve is studied. The objective is to reconstruct the shot peened dissipation profile by interpreting shot peening through the stress profile. Using the mean stress self-heating curves, a simulated shot peened self-heating curve is computed and compared with the experimental one. To make informed predictions about the fatigue properties, understanding and modeling the changes of self-heating behavior due to shot peening is required.

This paper is structured in four sections. First, the material and experimental setups are described with details on the coupons. The self-heating and fatigue tests, post-processing protocols, and stress measurements by X-ray diffraction are also listed. Second, the experimental results are presented. The self-heating curves of polished 300M steel, as well as the shot peened 300M steel, are presented at $R = -1$ and non-zero mean stresses. Third, the self-heating curve for polished steel at $R = -1$ is modeled with the two-mechanisms probabilistic self-heating model (shorten as self-heating model) [Munier et al., 2014]. A modified self-heating model is proposed to consider the mean stress influence. Combined with the residual stress profile, a simulated self-heating curve for a shot peened coupon is computed. The self-heating model is then used and validated on polished 300M steel to estimate fatigue properties. Finally, a fatigue model for shot peened 300M steel is built combining self-heating tests, residual stress profiles and optical microscopy observations of fatigue mechanisms. A first estimation of the shot peening effect on the fatigue limit is proposed and qualitatively validated with conventional fatigue data.

## Nomenclature

<table><tr><td>C<sub>p</sub></td><td>Specific heat</td></tr><tr><td>C<sub>the</sub></td><td>Thermo elastic coupling term</td></tr><tr><td>E<sub>d</sub></td><td>Dissipated energy density per cycle</td></tr><tr><td>E<sub>d,s</sub></td><td>Mean simulated dissipated energy density per cycle</td></tr><tr><td>F25</td><td>Test coupon with a 25 mm<sup>2</sup> cross-section</td></tr><tr><td>HCF</td><td>High Cycle fatigue</td></tr><tr><td>K<sub>t</sub></td><td>Stress concentration factor</td></tr><tr><td>P<sub>f,x</sub></td><td>Fatigue limit for a x probability of rupture</td></tr><tr><td>P<sub>f, 1/99%</sub></td><td>Fatigue limit range for 1 & 99 % probability of rupture estimated by self-heating</td></tr><tr><td>AE</td><td></td></tr><tr><td>R</td><td>Stress load ratio</td></tr><tr><td>RSD</td><td>Relative Standard Deviation</td></tr><tr><td>SP</td><td>Shot Peening</td></tr><tr><td>S<sub>0</sub></td><td>Normalizing stress of the self-heating model</td></tr><tr><td>S<sub>n</sub></td><td>Second regime modifying factor for the modified self-heating model</td></tr><tr><td>T<sub>bj</sub></td><td>Bottom jaw temperature</td></tr><tr><td>T<sub>cp</sub></td><td>Test coupon temperature</td></tr><tr><td>T<sub>tj</sub></td><td>Top jaw temperature</td></tr><tr><td>V</td><td>Coupon volume</td></tr><tr><td>YS<sub>0.2</sub></td><td>Conventional yield strength at 0.2 % plastic deformation</td></tr><tr><td>f<sub>r</sub></td><td>Loading frequency</td></tr><tr><td>m+2</td><td>Slope of the second regime of the self-heating model</td></tr><tr><td>p</td><td>Slope of the first regime of the self-heating model</td></tr><tr><td>r</td><td>Coupon radius</td></tr></table>

(continued on next column)

(continued)

<table><tr><td>t</td><td>Time</td></tr><tr><td>Γ</td><td>Gamma function</td></tr><tr><td>Δ</td><td>Intrinsic dissipation</td></tr><tr><td>α</td><td>Process intensity of the first regime of the self-heating model</td></tr><tr><td>β</td><td>Process intensity of the second regime of the self-heating model</td></tr><tr><td>θ</td><td>Mean test coupon temperature rise</td></tr><tr><td>θ<sub>stab</sub></td><td>Mean stabilized test coupon temperature rise</td></tr><tr><td>ρ</td><td>Density</td></tr><tr><td>σ<sub>AE</sub></td><td>Estimation of the fatigue limit by the self-heating model</td></tr><tr><td>σ<sub>D</sub></td><td>Mean conventional fatigue limit</td></tr><tr><td>σ<sub>a</sub></td><td>Loading amplitude</td></tr><tr><td>σ<sub>mean</sub></td><td>Mean stress</td></tr><tr><td>σ<sub>UTS</sub></td><td>Ultimate tensile strength</td></tr><tr><td>τ<sub>eq</sub></td><td>Thermal loss characteristic time</td></tr></table>

## 2. Experimental setup and methods

In this section, the material, the used test coupons, the instrumentation, and the test and post-processing protocols are presented.

### 2.1. Material

The 300M is a low-alloy ultra-high tensile strength steel ($YS_{0.2} > 1586$ MPa and $σ_{UTS} > 1931$ MPa [Aerospace Material Specification, 2022]). It has been used in aeronautics and aero-spatial industry since 1966 for bolts, landing gears, airframes, or drive shafts [Tomita 2000] due to its high mechanical and fatigue properties ($σ_D \approx 850 \pm 50$ MPa [Pei-ge et al., 1996; Xue et al., 2012; Ajaja et al., 2020]), and fracture toughness ($K_{IC} \approx 60$ MPa m$^{1/2}$ [Pistochini and Hill, 2011; Tomita, 2000]). Components are usually manufactured by machining of bars or forged parts produced from vacuum arc remelted ingots. After hot work, heat treatment includes the following steps: normalizing at 927 °C, austenizing at 871 °C followed by oil quenching, then double tempering at 302 °C [Aerospace Material Specification, 2022]. As a result, 300M steel exhibits a fine microstructure composed of martensite needles, some bainite and a few residual austenite at grain boundaries [Bag et al., 2019; Youngblood and Raghavan 1977] (Fig. 1). Its composition is given in Table 1.

### 2.2. Experimental protocol

For this study, all coupons have been extracted from the same forged bar compliant with the standard AMS 6257-G [Aerospace Material Specification, 2022]. Fatigue tests and surface roughness measurements

<figure><img src="image_3.png" /><figcaption>Fig. 1. EBSD observation of polished 300M.</figcaption></figure>
<table><caption>**Table 1**

Weight composition of 300M [Aerospace Material Specification, 2022].</caption><thead><tr><th>W<sub>t</sub> %</th><th>C</th><th>Mn</th><th>Si</th><th>P</th><th>S</th><th>Cr</th><th>Ni</th><th>Mo</th><th>Va</th><th>Cu</th><th>Fe</th></tr></thead><tbody><tr><td>Min</td><td>0.4</td><td>0.65</td><td>1.45</td><td>-</td><td>-</td><td>0.7</td><td>1.65</td><td>0.35</td><td>0.05</td><td>-</td><td>Balance</td></tr><tr><td>Max</td><td>0.44</td><td>0.9</td><td>1.8</td><td>0.01</td><td>0.008</td><td>0.95</td><td>2</td><td>0.45</td><td>0.1</td><td>0.35</td><td></td></tr></tbody></table>

were performed on smooth ($K_t = 1$) cylindrical coupons in longitudinal grain flow with a 25 mm² cross-section and a 15 mm gauge length (called F25, design Fig. 2) on two configurations.

- Polished to a mean surface roughness (Ra) of 0.2 µm;

- Shot peened with S230 shots to an Almen intensity between 8 and 16A for a 125 % coverage (abbreviated as shot peened or SP).

Fatigue and self-heating tests were performed on Amsler Vibrophore 50 (Zwick Roell, Ulm, Germany) at $f_r = 118$ Hz. For fatigue tests, a staircase with reloading for $10^7$ cycles at $R = 1$ and with a step of 25 MPa was performed. If rupture does not occur after $10^7$ cycles, the loading amplitude is increased by 25 MPa and the coupon is reloaded. For self-heating tests, blocks of increasing amplitude are applied until rupture (Fig. 3a). Each self-heating block is composed of five phases (Fig. 3b).

- Phase 1: Reach of the block mean stress, $\sigma_{mean}$;

- Phase 2: First holding time of at least $5\tau_{eq}$ to return to the thermal equilibrium, with $\tau_{eq}$ the characteristic thermal time;

- Phase 3: Start of the temperature acquisition and second holding time of 30 s;

- Phase 4: Cyclic loading at the block loading amplitude $\sigma_a$ during at least $4\tau_{eq}$;

- Phase 5: Cooling time of at least $5\tau_{eq}$.

$\tau_{eq}$ is determined experimentally and is approximately equal to 30 s for this coupon geometry, test machine and test protocol.

Self-heating tests are instrumented with three K-type thermocouples with a recording frequency of 1 Hz. Two are fixed on the top (to measure $T_t$) and bottom ($T_b$) machine jaws and the last one is fixed in the middle of the gauge length ($T_c$). The temperature is recorded during the third, fourth and fifth phases. To prevent environmental influence on the thermal loss, the test machine is protected from air flows and sudden temperature changes inside a box (Fig. 4).

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Design of a F25 coupon (all dimensions in mm).</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Test protocol for self-heating tests: blocks of increasing loading amplitude (a) and a close up to the five phases of a self-heating block (b).</figcaption></figure>

Fracture surfaces are observed by optical microscopy with a Keyence VHX-5000 equipped with VH-Z100 R/W/T lens (Keyence©, Osaka, Japan) for a magnification of ×500. Residual stress profiles are measured by X-ray diffraction with an AST X3000 device on the 156.4° peak of CrKα ray on three points of the coupon. Successive surface layers are removed by electro polishing to generate a depth profile.

## 2.3. Post processing protocol

By considering the specific Helmholtz free energy, for small temperature variation, small strains and linear thermal losses, the 0D heat equation can be written as

$$ \frac{d\theta}{dt} + \frac{\theta}{\tau_{eq}} = \frac{\Delta + C_{the}}{\rho C_p}, \qquad (1) $$

with $\theta$ the temperature difference between the coupon and the environment, $\tau_{eq}$ the characteristic time of the thermal loss, $\rho$ the density, $C_p$ the specific heat, $\Delta$ the intrinsic dissipation and $C_{the}$ the thermo-elastic coupling term [Doudard et al., 2005; Boulanger 2004].

As the loading frequency (118 Hz) is significantly higher than the thermocouple recording frequency (1 Hz) and as the mean thermo-elastic coupling term is null on a cycle, $C_{the}$ can be neglected. Moreover, a typical observation/acceptance for steel is that the temperature rise increases monotonically to a stabilized value, showing that the dissipation is constant per cycle [Doudard 2004]. Consequently, $\Delta$ can be written as

$$ \Delta = E_d * f_r, \qquad (2) $$

with $E_d$ the dissipated energy density per cycle, expressed in $\mu J.mm^{-3}$. $f_r$ is the frequency of the self-heating test. So, the temperature during a block of self-heating test should vary as a saturating exponential (and an exponential decay for the cool
<figure><img src="image_6.png" /><figcaption>Fig. 4. Experimental setup.</figcaption></figure>

down phase)

$$ \theta(t) = E_d \frac{f_r \tau_{eq}}{\rho C_p} \left( 1 - \exp\left(-\frac{t}{\tau_{eq}}\right) \right). \quad (3) $$

As the loading lasts at least 4τeq, θ reaches more than 98 % of its stabilization value, noted θstab. Then E_d can be computed as

$$ E_d = \theta_{\text{stab}} * \frac{\rho C_p}{f_r \tau_{eq}}. \quad (4) $$

Experimentally, θ is computed as

$$ \theta(t) = T_{cp}(t) - \frac{T_{ij}(t) + T_{bj}(t)}{2} - \hat{\theta}_{\text{mean}}, \quad (5) $$

With $\hat{\theta}_{mean}$ = average$_{t=0:30}$ $[T_{cp} - \frac{T_r + T_h}{2}]$, the mean temperature rise during the first 30 s of recording (third phase in Fig. 3b). To compute θstab, the average temperature on the last τeq of the loading (the fourth phase in Fig. 3b) is considered.

The thermal loss characteristic time τeq is estimated by identifying an exponential decay on the fifth phase on every self-heating block with a temperature rise greater than 0.5 K

$$ \theta(t) = C + A * \exp\left(-\frac{t}{\tau_{eq}}\right). \quad (6) $$

τeq depends only on the thermal boundary conditions and on the coupon geometry.

As the thermal environment is protected, it has been assumed that τeq is constant during a self-heating test. This assumption is verified later in this paper. A long self-heating loading block has been applied on a coupon and a first estimation of τeq is about 30 s. To compute E_d, ρ = 7800 kg m⁻³ and C_p = 445 J kg⁻¹ K⁻¹ are considered.

### 3. Self-heating experimental results

In this section, self-heating results are presented for the polished 300M steel, as for the shot peened configuration, at R = -1 and non-zero mean stress values.

#### 3.1. Polished 300M steel at R = -1 ($\sigma_{mean} = 0$ MPa)

The self-heating test protocol is applied to three polished 300M steel coupons. For one coupon, the temperature rise evolutions of each block are stacked up in Fig. 5 (from σa = 100 MPa to σa = 1025 MPa). The temperature rises vary according to a saturating exponential, as well as an exponential decay, validating the constant dissipated energy per cycle and linear thermal losses framework [Doudard and Calloch 2009]. The thermal signals are very clear as the measurement uncertainty on the stabilized temperature rise values is estimated at ± 10 mK. For each

<figure><img src="image_7.png" /><figcaption>Fig. 5. Stack up of the temperature rises over time for every loading block of polished 300M (f_r = 118 Hz, R = -1).</figcaption></figure>
loading block, $\theta_{\text{stab}}$ is retrieved and $\tau_{\text{eq}}$ is estimated for every block with $\theta_{\text{stab}} > 0.5$ K on the three coupons. Table 2 sums up the coupon and test information. For the same coupon, the maximum variation of estimated $\tau_{\text{eq}}$ is about $\pm 2$ s. The mean $\tau_{\text{eq}}$ varies very little between coupons, indicating well-controlled and repeatable thermal boundary conditions.

The rupture of coupon n° 3 (respectively n° 2) occurred during the $\sigma_a = 950$ MPa (resp. 1050 MPa) loading block. For coupon n° 1, the test was interrupted for $\sigma_a = 1200$ MPa due to an excessive temperature rise (>100 K). For this coupon, the rupture occurred during a reloading block at $\sigma_a = 1050$ MPa. Optical microscopy revealed a single surface initiation for the three coupons (Fig. 6). The dissipated energy density per cycle $E_d$ is computed using the mean $\tau_{\text{eq}}$ obtained from the coupon loading blocks. The self-heating curves are plotted in Fig. 7. There is almost no difference between the three experimental self-heating curves. Therefore, the tested volume can be considered representative of the material.

## 3.2. Polished 300M steel at $\sigma_{\text{mean}} \neq 0$

Self-heating tests are performed on five polished 300M steel coupons over different mean stress values from -800 MPa to +100 MPa (n° 4 to 8 in Table 2). The self-heating curves are plotted in Fig. 8. It can be noticed that the first part of the curve is not affected by the mean stress variation. On the second part, higher the absolute mean stress value, earlier and smoother the transition, resulting in higher dissipation. Tests were interrupted before rupture for the $\sigma_{\text{mean}} = -800$ MPa, -600 MPa and +100 MPa coupons due to an excessive temperature rise (>100 K). For other coupons, rupture is associated to a single surface initiation, similar to the one presented in Fig. 6. The five tests exhibit similar $\tau_{\text{eq}}$ as described previously (mean $\tau_{\text{eq}}$ of 28.8 ± 1.6 s, Table 2).

## 3.3. Shot peened 300M

A self-heating test is performed on a shot peened 300M steel coupon for $R = -1$ (coupon n°9). The self-heating curve is plotted in Fig. 9 and will be referred as the experimental shot peened self-heating curve. As for the polished 300M steel with mean stress variation, the first part of the curve is not affected by the shot peening, and the transition to the second part appears earlier and is smoother, resulting in higher dissipation. The coupon rupture occurs during the $\sigma_a = 1100$ MPa loading block. Optical microscopy shows an initiation on a single inclusion, leading to the formation of a fish eye (as shown Fig. 10). This initiation mechanism on a single inclusion is typical for shot peened 300M coupon under conventional fatigue testing. The test exhibits similar $\tau_{\text{eq}}$ as previously (mean $\tau_{\text{eq}} = 29.2$ s, Table 2).

# 4. Modeling

In this section, the self-heating model is applied to polished 300M steel and a modified self-heating model is proposed to take into account the mean stress effect on the self-heating behavior of polished 300M steel. Then, the residual stress profile of a shot peened 300M steel

<table><caption>**Table 2**
List of tested fatigue coupons.</caption><thead><tr><th>Coupon</th><th>Configuration</th><th>Test</th><th>Loading</th><th>Mean τ<sub>eq</sub></th></tr></thead><tbody><tr><td>N° 1</td><td>Polished</td><td>Self-Heating</td><td>R = -1</td><td>29.8 s</td></tr><tr><td>N° 2</td><td>Polished</td><td>Self-Heating</td><td>R = -1</td><td>28.9 s</td></tr><tr><td>N° 3</td><td>Polished</td><td>Self-Heating</td><td>R = -1</td><td>27.4 s</td></tr><tr><td>N° 4</td><td>Polished</td><td>Self-Heating</td><td>σ<sub>mean</sub> = -800 MPa</td><td>30.4 s</td></tr><tr><td>N° 5</td><td>Polished</td><td>Self-Heating</td><td>σ<sub>mean</sub> = -600 MPa</td><td>28.4 s</td></tr><tr><td>N° 6</td><td>Polished</td><td>Self-Heating</td><td>σ<sub>mean</sub> = -400 MPa</td><td>29.1 s</td></tr><tr><td>N° 7</td><td>Polished</td><td>Self-Heating</td><td>σ<sub>mean</sub> = -200 MPa</td><td>27.2 s</td></tr><tr><td>N° 8</td><td>Polished</td><td>Self-Heating</td><td>σ<sub>mean</sub> = +100 MPa</td><td>28.7 s</td></tr><tr><td>N° 9</td><td>Shot-peened</td><td>Self-Heating</td><td>R = -1</td><td>29.2 s</td></tr><tr><td>N° 10-16</td><td>Shot-peened</td><td>Staircase</td><td>R = -1</td><td>-</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Typical fracture surface of polished configuration (coupon n° 2, x 500, rupture during a self-heating test at the $\sigma_a = 1050$ MPa loading block).</figcaption></figure>

coupon is determined and modeled to be able to simulate a self-heating curve considering shot peening as a residual stress effect only.

## 4.1. Self-heating behavior of polished 300M

The self-heating model (SH model) [Munier et al., 2014] is based on a two-regimes dissipation composed of.

- A first regime, predominant at low loading amplitude [Munier et al., 2014],

- A second regime, predominant for higher loading amplitude and related to localized micro-plasticity [Munier et al., 2014; Doudard et al., 2005].

The total dissipation can be written as

$$E_d(\sigma_a) = \alpha^* \left(\frac{\sigma_a}{S_0}\right)^p + \beta^* \left(\frac{\sigma_a}{S_0}\right)^{m+2}, \quad (7)$$

with $S_0$ a normalizing parameter, $\alpha$ the intensity of the first regime, $p$ its slope in a log-log diagram, $\beta$ the second regime intensity and $m+2$ its slope, $m$ at $R = -1$ being the Weibull parameter of the material [Munier et al., 2014]. The two mechanisms responsible for the two regimes have been observed, modeled and simulated in the case of a high strength low-alloy steel, leading to Eq. (7) [Munier et al., 2014; Munier et al., 2017].

The identified curve parameters are reported in Table 3, and the model is plotted with the three self-heating curves in Fig. 11. The self-heating model describes very well the self-heating curves of polished 300M steel at $R = -1$.

Concerning the self-heating curves of polished 300M steel with mean stress, as mentioned previously.

- The first regime is not affected by the mean stress;

- The second regime is significantly affected by the mean stress, the higher the absolute mean stress, the earlier the transition between the 1st and the 2nd regime and the smoother is the second regime.

To describe these curves, a modified self-heating model is proposed

$$E_d(\sigma_a, \sigma_{\text{mean}}) = \alpha^* \left(\frac{\sigma_a}{S_0}\right)^p + \frac{\beta}{S_n(\sigma_{\text{mean}})^{m(\sigma_{\text{mean}})+2}} \left(\frac{\sigma_a}{S_0}\right)^{m(\sigma_{\text{mean}})+2}, \quad (8)$$
<figure><img src="image_9.png" /><figcaption>Fig. 7. Self-heating curves of polished 300M at R = -1 in linear (a) and log-log (b) graph.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 8. Self-heating curves of polished 300M for different mean stresses.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 9. Experimental self-heating curve of shot peened 300M F25 coupon at R = -1.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Fig. 10. Fracture surface of shot peened coupon n° 11 (x 500), rupture at $\sigma_a$ = 775 MPa for N = 7 375 000 cycles.</figcaption></figure>

<table><caption>**Table 3**
Self-heating model parameters for polished 300M over different mean stresses.</caption><thead><tr><th>Mean stress</th><th>α (μJ.mm<sup>-3</sup>. cycle<sup>-1</sup>)</th><th>p (-)</th><th>β (μJ.mm<sup>-3</sup>. cycle<sup>-1</sup>)</th><th>m (-)</th><th>S<sub>0</sub> (MPa)</th><th>S<sub>n</sub> (-)</th></tr></thead><tbody><tr><td>+100 MPa</td><td>2.97</td><td>2.1</td><td>0.62</td><td>28</td><td>1000</td><td>0.98</td></tr><tr><td>0 MPa (R = -1)</td><td>2.97</td><td>2.1</td><td>0.62</td><td>28</td><td>1000</td><td>1.00</td></tr><tr><td>-200 MPa</td><td>2.97</td><td>2.1</td><td>0.62</td><td>28</td><td>1000</td><td>0.97</td></tr><tr><td>-400 MPa</td><td>2.97</td><td>2.1</td><td>0.62</td><td>23</td><td>1000</td><td>0.91</td></tr><tr><td>-600 MPa</td><td>2.97</td><td>2.1</td><td>0.62</td><td>15</td><td>1000</td><td>0.82</td></tr><tr><td>-800 MPa</td><td>2.97</td><td>2.1</td><td>0.62</td><td>8</td><td>1000</td><td>0.69</td></tr></tbody></table>

with α, β and p fixed, $\frac{\beta}{S_n(\sigma_{mean})^{m(\sigma_{mean})+2}}$ being the modified second regime intensity. The parameters are summarized in Table 3, and the model is plotted with the self-heating curves in Fig. 12. To describe the m evolution, a piecewise affine model is chosen (Fig. 13a). To describe the $S_n$ evolution, a fourth-order polynomial is used (Fig. 13b).

## 4.2. Shot peened 300M residual stress profile

The profile of axial residual stress has been measured by X-ray diffraction and electro-polishing on a polished and shot-peened coupon (Fig. 14). The last point (at 300 µm) for the shot peened profile corresponds to the auto-equilibrated residual stress in the coupon bulk (assumed constant on the whole bulk). The profile is modeled by an affine three piecewise function.

## 4.3. Simulated shot peened 300M steel self-heating curve

The self-heating curve of a polished 300M steel coupon with an axial mean stress profile corresponding to the axial residual stress profile of a shot peened coupon can be computed by integrating the modified self-heating model along the radius. The mean dissipation of such configurations ($E_{d,s}$) is given by

$$E_{d,s}(\sigma_a) = \frac{2}{r^2} \int_{0}^{r} E_d(\sigma_a, \sigma_{mean}(r)) r dr \quad (9)$$

$$E_{d,s} = \frac{2}{r^2} \int_{0}^{r} \left( \alpha^* \left( \frac{\sigma_a}{S_0} \right)^p + \beta^* \left( \frac{\sigma_a}{S_0^* S_n(\sigma_{mean}(r))} \right)^{m(\sigma_{mean}(r))+2} \right) r dr \quad (10)$$

with r the radius. This integral is computed with a discretization step of 1 µm. The computed curve will be referred as the simulated shot peened self-heating curve.

Both the simulated and experimental curves are plotted in Fig. 15 with the polished 300M steel at R = -1 for comparison. The simulated curve is well correlated with the experimental curve. Until $\sigma_a$ = 1000 MPa, the maximum error is 0.3 µJ mm⁻³·cycle⁻¹ but quickly increases after this value due to the lack of data at high loading amplitude for higher residual stresses.

The effect of residual stress measurement errors is studied by considering an error of ±50 MPa. This error slightly modifies the intensity of the dissipation but not the global shape of the curve. The radius discretization is also small enough not to change the total dissipation. This shows that, in the case of 300M shot peened with the parameters described previously, the change in dissipation behavior can be attributed to the residual stress profile introduced by the shot peening.

Using the digital approach and choosing a depth threshold of 175 µm ($\sigma_{res} < 0$ MPa), the distribution of the dissipation between the bulk and the surfaces is plotted in Fig. 16. This shows that the change in self-heating behavior is mainly due to the surface. It initially represents 12 % of the coupon cross-section and increases with the stress amplitude once $\sigma_a$ = 600 MPa is reached. At $\sigma_a$ = 1000 MPa, the surface participates in 44 % of the total dissipation. It can be concluded that the effect of the shot peening on the 300M steel self-heating behavior is largely due to the compressive part of the residual stress profile.

## 5. Fatigue properties

In this section, the self-heating model is used to estimate the fatigue properties of polished 300M steel at R = -1 and a fatigue model is proposed to estimate the fatigue limit for shot peened 300M steel.

<figure><img src="image_13.png" /><figcaption>Fig. 11. Self-heating curves of polished 300M at R = -1 with the identified self-heating model.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Fig. 12. Self-heating curves of polished 300M for different mean stresses with the identification of the modified self-heating model.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 13. Experimental and fitted evolutions of the modified self-heating model parameters: m (a) and S<sub>n</sub> (b) as a function of σ<sub>mean</sub>.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 14. Axial residual stress profile of polished and shot peened coupons.</figcaption></figure>

Estimated values are compared with conventional fatigue data to validate the self-heating and the fatigue limit models.

5.1. Polished 300M at R = -1

The mean fatigue limit σ<sub>D</sub> for polished 300M at R = -1 can be estimated as the loading amplitude for which the dissipated energy caused by the second regime is detectable, i.e., higher than the
<figure><img src="image_17.png" /><figcaption>Fig. 15. Experimental and simulated self-heating curves for shot peened 300M on F25 coupon at R = -1.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Fig. 16. Repartition of the dissipated energy density on shot peened 300M between the bulk and the surface.</figcaption></figure>

dissipated energy density uncertainty. Once the stabilized temperature rise and $\tau_{eq}$ uncertainties are set, this uncertainty can be estimated to $\pm 0.02 \mu J \text{ mm}^{-3} \text{ cycle}^{-1}$. Fig. 17 shows the second self-heating regime (computed as the self-heating curve minus the first regime) and the associated threshold.

As the self-heating model predicts a fatigue limit varying as a Weibull law [Doudard et al., 2005], showed that the relative standard deviation (RSD) of the fatigue limit can be computed as (with $\Gamma$ the gamma function)

$$RSD = \frac{\sqrt{\Gamma\left(1 + \frac{2}{m}\right) - \Gamma^2\left(1 + \frac{1}{m}\right)}}{\Gamma\left(1 + \frac{1}{m}\right)} \quad (11)$$

Using the parameters given in Table 3, the mean fatigue limit estimated by the self-heating test is $\sigma_{AE} = 897 \text{ MPa}$ and the relative standard deviation is estimated to 4.5 % (standard deviation of 40 MPa). To determine fatigue limit for various rupture probabilities, the Weibull distribution gives [Munier 2012]

<figure><img src="image_19.png" /><figcaption>Fig. 17. Second self-heating regime for polished 300M and dissipation uncertainty threshold.</figcaption></figure>
$$ \frac{\ln(1-x)}{\ln(1-0.5)} = \left( \frac{\sigma_D (P_{fx})^* \Gamma \left( 1 + \frac{1}{m} \right)}{\sigma_D^* \ln(2) \frac{1}{m}} \right)^m \quad (12) $$

The fatigue limits at 1 and 99 % of rupture probability are $P_{f,1/99\%AE} = [776 ; 966] MPa$. To validate the model, a different database of conventional fatigue tests on 300M steel is used. It provides an estimation of the mean fatigue limit at 2 x 10⁶ cycles of $\sigma_D = 886 \pm 37$ MPa and a standard deviation of 80 ± 58 MPa. The self-heating model is well correlated with conventional fatigue tests, as the results are in the confidence interval for both the mean fatigue limit and its standard deviation. The fatigue data employed has been obtained from several test campaigns performed on different machines and using coupons obtained from various material heats. This can explain a higher scattering than self-heating tests performed on one single material heat and the same machine.

## 5.2. Shot peened 300M

As the configuration is highly heterogeneous, the self-heating model cannot be directly applied to estimate the fatigue properties of shot peened 300M. In fact, the shot peened area is over represented in the mean dissipation but is protected against fatigue initiation. To assess the HCF properties, a staircase with reloading on seven coupons has been performed (10⁷ cycles, step of 25 MPa and first loading of 750 MPa). Fig. 18 represents the loading sequence. Optical microscopy shows that for the 7 coupons, the initiation occurs in the bulk on an inclusion, as shown in Fig. 10. Using the maximum likelihood method for staircase with reloading [Roué 2020], the mean fatigue limit is estimated at 770 ± 30 MPa, a reduction of 116 ± 67 MPa compared to polished 300M steel.

For the studied shot peening process parameters, on 300M steel F25 coupons, the shot peening reduces the HCF properties. An explanation can be that for polished 300M, the surface initiation and the internal initiation mechanisms are very close [Xue et al., 2012]. The shot peening protects the surface by creating a high compressive residual stress (~ 1 000 MPa) area just below the surface which prevents the propagation of surface cracks. However, because of auto-equilibrium of the stress field, shot peening creates a low-tension stress on the whole bulk (~ 85 MPa), facilitating the initiation and propagation of internal cracks.

Three effects of the shot peening on the 300M have been listed.

- Change of fatigue mechanism, switching from surface initiation to internal initiation;

- A small volume effect, as the entire subsurface is protected by compressive stresses;

- The tension residual stress in the bulk, which favors the internal initiation and propagation of cracks.

For the change of fatigue mechanism, as both can occur for polished

300M for HCF lifespan, it has been assumed that it does not affect the fatigue limit. For the volume effect, by considering that an area with residual stress lower than -100 MPa cannot produce a crack initiation, the effective volume of a F25 shot peened coupon is 0.9*V. It results in an increase of the fatigue limit of +0.4 % (~ + 3 MPa) [Munier 2012]

$$ \sigma_D(V_1) = \sigma_D(V_2) * (V_2/V_1)^{\frac{1}{m}} \quad (13) $$

For the tension residual stress effect, it has been assumed that the decrease of the fatigue limit corresponds to the decrease due to an additional mean stress of 85 MPa (the tension residual stress in bulk). By assuming that polished 300M steel follows the Goodman line

$$ \frac{\sigma_{mean}}{\sigma_{UTS}} + \frac{\sigma_D(\sigma_{mean})}{\sigma_D} = 1, \quad (14) $$

$\sigma_D(+ 85 MPa) = 886 * (1 - \frac{85}{1931}) \approx 847 MPa$. The fatigue limit reduction due to the tension residual stress is about -39 MPa (-4 %). By cumulating the two last effects, the fatigue limit reduction is about -36 MPa (-4 %), which is consistent in term of trend and order of magnitude with the experimental one, -116 ± 67 MPa (-13 ± 7 %). The consideration of the fatigue mechanism change will surely improve the prediction quality and could be later investigated.

## 6. Conclusion

In this paper, a self-heating test and post-processing protocol have been established to estimate the mean dissipated energy density per cycle of homogeneous and heterogeneous configurations. On polished 300M steel at R = -1, the self-heating curve has been proven to be repeatable. Then, the effects of mean stress and shot peening on the self-heating behavior of 300M steel have been studied. Both have similar effect: they do not affect the self-heating first regime (low loading amplitudes) but increase the dissipation for the second regime (higher loading amplitudes) and smoothen the transition between both regimes.

Polished 300M steel at R = -1 follows the self-heating model developed by Munier. A modified self-heating model taking into account the effect of mean stress has been proposed and applied on polished 300M steel. Self-heating model parameters have been identified for a range of mean stress from +100 MPa to -800 MPa, supported by the identification of the model parameters evolution against the mean stress. For the shot peened configuration, a simulated self-heating curve has been produced, using residual stress profile obtained by XRD and electro-polishing. It represents the mean dissipation of a polished 300M F25 coupon with an axial mean stress profile corresponding to the axial residual stress profile of a shot peened F25 coupon. The simulated curve is almost identical to the experimental self-heating curve of a shot peened F25 coupon. It indicates that, for the studied 300M, changes in dissipation behavior induced by shot peening are almost exclusively caused by the residual stresses. Moreover, the dissipation distribution between the sub-surface and the bulk showed that changes in dissipation

<figure><img src="image_20.png" /><figcaption>Fig. 18. Sequence of non-rupture and rupture for the staircase on shot peened 300M.</figcaption></figure>
behavior are mainly due to the sub-surface, corresponding to the high compressive residual stress area. Therefore, the self-heating curve of a 300M shot peened configuration conveys the mean information on the sub-surface residual stress value.

Using the self-heating model, the mean fatigue limit and its scattering have been computed for polished 300M at $R = -1$ within two days. To validate the estimation, an additional conventional fatigue database has been used. With $\sigma_{AE} = 897$ MPa (compared to $\sigma_D = 886 \pm 37$ MPa from conventional fatigue test database) and a standard deviation of 40 MPa (compared to $80 \pm 58$ MPa), the self-heating analysis is validated to quickly obtain fatigue properties for polished 300M steel at $R = -1$. For shot peened 300M steel, the dissipation is heterogeneous and the surface (i.e. area with compressive residual stresses) is a main contributor. However, the surface does not participate in the crack initiation process so the self-heating curve is not relevant for fatigue properties. A staircase with reloading tests has been performed on seven shot peened coupons, showing a fatigue limit reduction of $-116 \pm 67$ MPa ($-13 \pm 7\%$). It has been attributed to three phenomena: the fatigue mechanism change (from surface to internal initiation), a volume effect and the tension residual stress in the bulk. The first one has been considered negligible, leading to a fatigue limit reduction of $-36$ MPa ($-4\%$), less than the value estimated by conventional fatigue tests. However, the model gives the right trend and order of magnitude by only testing few coupons.

## CRediT authorship contribution statement

**Pierrick Lepitre:** Writing – review & editing, Writing – original draft, Methodology, Investigation.
**Louis-Maël Merlet:** Methodology.
**Cédric Doudard:** Writing – review & editing, Supervision, Methodology.
**Matthieu Dhondt:** Writing – review & editing, Supervision.
**Martin Surand:** Writing – review & editing, Supervision.
**Sylvain Calloch:** Writing – review & editing, Supervision, Methodology.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

A part of this study belongs to the “Self-Heating” ANR-Safran-Naval Group research chair (grant no. ANR-20-CHIN-0002), involving Safran Aircraft Engines, Safran Landing Systems, SafranTech, Naval Group, ENSTA Bretagne (IRDL), and Institut Pprime.

## Data availability

The authors do not have permission to share data.

## References

* Aerospace Material Specification, 2022. Steel bars, forgings, and tubing 1.6Si - 0.82Cr - 1.8Ni - 0.40Mo - 0.08V (0.40 - 0.44C) consumable electrode vacuum remelted normalized and tempered. AMS6257-G.

* Ajaja, J., Jomaa, W., Bocher, P., Chromik, R.R., Brochu, M., 2020. High cycle fatigue behavior of hard turned 300 M ultra-high strength steel. Int. J. Fatig. 131. https://doi.org/10.1016/j.ijfatigue.2019.105380.

* Bag, A., Delbergue, D., Bocher, P., Lévesque, M., Brochu, M., 2019. Statistical analysis of high cycle fatigue life and inclusion size distribution in shot peened 300M steel. Int. J. Fatig. 118, 126-138. https://doi.org/10.1016/j.ijfatigue.2018.08.009.

* Bag, A., Delbergue, D., Ajaja, J., Bocher, P., Lévesque, M., Brochu, M., 2020. Effect of different shot peening conditions on the fatigue life of 300 M steel submitted to high stress amplitudes. Int. J. Fatig. 130. https://doi.org/10.1016/j.ijfatigue.2019.105274.

* Balit, Y., Joly, L.-R., Szmytka, F., Durbecq, S., Charkaluk, E., Constantinescu, A., 2020. Self-heating behavior during cyclic loadings of 316L stainless steel specimens manufactured or repaired by Directed Energy Deposition. Materials Science and Engineering: A 786. https://doi.org/10.1016/j.msea.2020.139476.

* Boulanger, T., 2004. Calorimetric analysis of dissipative and thermoelastic effects associated with the fatigue behavior of steels. Int. J. Fatig. 26, 221-229. https://doi.org/10.1016/S0142-1123(03)00171-3.

* Cao, Y., Moumni, Z., Zhu, J., Zhang, Y., You, Y., Zhang, W., 2020. Comparative investigation of the fatigue limit of additive-manufactured and rolled 316 steel based on self-heating approach. Eng. Fract. Mech. 223. https://doi.org/10.1016/j.engfracmech.2019.106746.

* Dang, J., An, Q., Lian, G., Zuo, Z., Li, Y., Wang, H., Chen, M., 2021. Surface modification and its effect on the tensile and fatigue properties of 300M steel subjected to ultrasonic surface rolling process. Surf. Coating. Technol. 422. https://doi.org/10.1016/j.surfcoat.2021.127566.

* De Finis, R., Palumbo, D., Ancona, F., Galietti, U., 2015. Fatigue limit evaluation of various martensitic stainless steels with new robust thermographic data analysis. Int. J. Fatig. 74, 88-96. https://doi.org/10.1016/j.ijfatigue.2014.12.010.

* Doudard, C., 2004. Détermination rapide des propriétés en fatigue à grand nombre de cycles à partir d'essais d'auto-échauffement. Ph.D. thesis, Mécanique - Génie civile, École Normale Supérieure de Cachan.

* Doudard, C., Calloch, S., 2009. Influence of hardening type on self-heating of metallic materials under cyclic loadings at low amplitude. Eur. J. Mech. Solid. 2, 233-240 https://doi.org/10.1016/j.euromechsol.2008.08.002.

* Doudard, C., Calloch, S., Cugy, P., Galtier, A., Hild, F., 2005. A Probabilistic Two-Scale Model for High-Cycle Fatigue Life Predictions Fatigue and Fracture of Engineering Materials and Structures, vol. 28, pp. 279-288. https://doi.org/10.1111/j.1460-2695.2005.00854.x.

* Doudard, C., Calloch, S., Hild, F., Roux, S., 2010. Identification of heat source fields from infra-red thermography: determination of self-heating in a dual-phase steel by using a dog bone sample. Mech. Mater. 42 (1), 55-62. https://doi.org/10.1016/j.mechmat.2009.09.005.

* Ezanno, A., Doudard, C., Calloch, S., Millot, T., Heuzé, J.-L., 2010. Fast characterization of high-cycle fatigue properties of a cast copper-aluminum alloy by self-heating measurements under cyclic loadings. Procedia Eng. 2, 967-976. https://doi.org/10.1016/j.proeng.2010.03.105.

* Florin, P., Facchinetti, M., Doudard, C., Calloch, S., 2013. Fast fatigue properties identification by “self-heating” method: application to automotive welded joints. Procedia Eng. 66, 676-683. https://doi.org/10.1016/j.proeng.2013.12.120.

* Giancane, S., Chrysochoos, A., Dattoma, V., Wattrisse, B., 2009. Deformation and dissipated energies for high cycle fatigue of 2024-T3 aluminum alloy. Theor. Appl. Fract. Mech. 52-2, 117-121. https://doi.org/10.1016/j.tafmec.2009.08.004.

* Graux, N., 2017. Caractérisation et modélisation des propriétés à la fatigue à grand nombre de cycles des aciers cémentés à partir d'essais d'auto-échauffement sous sollicitations cycliques. Mécanique des matériaux, Université de Bretagne Occidentale. Ph.D. thesis.

* Kwiakowski, V., Le Saux, M., Le Saux, V., Leclercq, S., Marco, Y., 2023. Fatigue of short carbon fiber reinforced PEEK under compression: influence of the load ratio and predictions from heat buildup measurements. Fatig. Fract. Eng. Mater. Struct. 46-7, 2396-2410. https://doi.org/10.1111/ffe.14003.

* Le Saux, V., Marco, Y., Calloch, S., Doudard, C., Charrier, P., 2010. Fast evaluation of the fatigue lifetime of rubber-like materials based on a heat build-up protocol and micro-tomography measurements. Int. J. Fatig. 32, 1582-1590. https://doi.org/10.1016/j.ijfatigue.2010.02.014.

* Louge, J., Doudard, C., Calloch, S., Weber, B., 2018. Study of load history effects on the high cycle fatigue properties of high-strength low-alloy steel from self-heating measurements. In: MATEC Web of Conferences, vol. 165. https://doi.org/10.1051/matecconf/201816514016.

* Luong, M.P., 1998. Fatigue limit evaluation of metals using an infrared thermographic technique. Mech. Mater. 28, 155-163. https://doi.org/10.1016/S0167-6636(97)00047-1.

* Luong, M.P., 2000. Infrared thermography of the damage of natural gut string. Proceedings of the 2000 International Conference on Quantitative InfraRed Thermography. https://doi.org/10.21611/qirt.2000.05.

* Moore, H.F., Kommers, J.B., 1921. Fatigue of metals under repeated stress. Chem. Metall. Eng. 25, 1141-1144.

* Mostofizadeh, P., Kadkhodaei, M., Arbab Chirani, S., Saint-Sulpice, L., Rokbani, M., Bouraoui, T., Calloch, S., 2019. Fatigue analysis of shape memory alloys by self-heating method. Int. J. Mech. Sci. 156, 329-341. https://doi.org/10.1016/j.ijmecsci.2019.04.012.

* Munier, R., 2012. Etude de la fatigue des aciers lainés à partir de l'auto-échauffement sous sollicitation cyclique : essais, observations, modélisation et influence d'une pré- déformation plastique. Mécanique des matériaux, Université de Bretagne Occidentale. Ph.D. thesis.

* Munier, R., Doudard, C., Calloch, S., Weber, B., 2014. Determination of high cycle fatigue properties of a wide range of steel sheet grades from self-heating measurements. Int. J. Fatig. 63, 46-61. https://doi.org/10.1016/j.ijfatigue.2014.01.004.

* Munier, R., Doudard, C., Calloch, S., Weber, B., 2017. Identification of the micro- plasticity mechanisms at the origin of self-heating under cyclic loading with low stress amplitude. Int. J. Fatig. 103, 122-135. https://doi.org/10.1016/j.ijfatigue.2017.05.027.

* Pei-ge, S., Mei, Y., Xiang-bin, L., Ji-lai, R., Ren-zhi, W., 1996. Qualitative analysis about effect of shot peening on fatigue limit of a 300M steel under the rotating bending condition. In: The Shot Peener Magazine. San Francisco, pp. 290-295.

* Pistochini, T.E., Hill, M.R., 2011. Effect of laser peening on fatigue performance in 300M steel. Fatig. Fract. Eng. Mater. Struct. 34, 521-533. https://doi.org/10.1111/j.1460-2695.2010.01544.x.

* Roué, V., 2020. Détermination rapide des propriétés en fatigue à grand nombre de cycles à partir de mesures d'auto-échauffement sous sollicitations cycliques : application
aux alliages métalliques pour turboréacteurs aéronautique. Ph.D. thesis. Matériaux et structures en mécanique, École nationale supérieure de techniques avancées Bretagne.

Roué, V., Doudard, D., Calloch, S., Montel, F., Pujol D'Andrebo, Q., Corpace, F., 2018. Rapid determination of the high cycle fatigue properties of high temperature aeronautical alloys by self-heating measurements. MATEC Web Conf. 165. https://doi.org/10.1051/matecconf/201816522022.

Stromeyer, C.E., 1914. The determination of fatigue limits under alternating stress conditions. Proc. R. Soc. Lond. A 90, 411–425.

Teng, Z., 2023. Thermo-based fatigue life prediction: a review. Fatig. Fract. Eng. Mater. Struct. 46 (9), 3121–3144. https://doi.org/10.1111/ffe.140793144TENG.

Tomita, Y., 2000. Development of fracture toughness of ultrahigh strength, medium carbon, low alloy steels for aerospace applications. Int. Mater. Rev. 45, 27–37. https://doi.org/10.1179/095066000771048791.

Wei, W., Li, C., Sun, Y., Xu, H., Yang, X., 2021. Investigation of the self-heating of Q460 butt joints and an S-N curve modeling method based on infrared thermographic data for high-cycle fatigue. Metals 11, 232. https://doi.org/10.3390/met11020232.

Xue, H., Liu, P., Chen, P., Wang, J., 2012. Fatigue life assessment of a high strength steel 300 M in the gigacycle regime. Theoretical and Applied Mechanics Letters 2. https://doi.org/10.1063/2.1203106.

Youngblood, J.L., Raghavan, M., 1977. Correlation of microstructure with mechanical properties of 300m steel. Metall. Trans. A 8, 1439–1448. https://doi.org/10.1007/BF02642857.

Zhao, A., Xie, J., Zhao, Y., Liu, C., Zhu, J., Qian, G., Wang, S., Hong, Y., 2022. Fatigue limit evaluation via infrared thermography for a high strength steel with two strength levels. Eng. Fract. Mech. 268. https://doi.org/10.1016/j.engfracmech.2022.108460.