Investigations on the changed intensity shot peening specimens machined from SS304: process characterization, fatigue modeling and failure analyses

Characterization on the surface morphology, residual stress relaxation and fatigue life prediction of the changed intensity shot peening specimens machined from SS304 were carried out. The present work aims, ﬁrst and foremost, to model the fatigue performance of shot peening specimens machined from SS304 in extra-low-, low- and high-cycle regime by clarifying the relaxation life component and fatigue life component with the total failure life, thereby successfully evaluating the fatigue performance of un-/0.1 mmA-/0.25 mmA-/0.4 mmA-peened components with satisfactory results in the whole cycle regime. It is, therefore, essential to provide a precise deﬁnition of the master life diagram on the purpose of evaluating the fatigue performance of shot peening components in service by linear interpolation of shot peening intensities considering the engineering applicability. Additionally, the characterization of multiple-fatigue crack initiation to failure was also identiﬁed by fractography analysis, which reasonably illustrated the non-conservative life prediction in the high-cycle regime.


Introduction
Introduction of shot peening to machined surface helps forming compressive residual stress, which plays a great role in improving fatigue performance. In view of this, shot peening is widely used in industry [1,2], and the discussion on its process characteristics is also available in [3,4].
Topics of shot peening are mumerous, mainly including three aspects: 1) Process characterization, which helps measuring the shot peening intensity, chractering surface morphologies as well as evaluating the residual stress; 2) Fatigue modeling, which requires experimental/numerical study on the service performance of shot peened components; 3) Failure analysis, which provides a verification for understanding the failure mechanism of shot peened components. Accrodingly, around the main topics involved in shot peening and their relevance is shown in Figure 1.
The 304 austenitic stainless steel (SS304) is one of the most widely used metallic materials and is processed into a variety of engineering structural components. Combined with shot peening treatments, its mechanical properties are further developed and play a more potential and valuable role in the practical service of engineering structures [5][6][7].
An enhanced fatigue performance by shot peening treatments has been systematically studied [8], including a se-rious of key issues on i) effect of variation of shot peening treatments on fatigue performance [9], ii) mechanism of residual stress relaxation caused by mechanical loading [10][11][12] and elevated thermal exposure [13], iii) failure of shot peened structure under complex loading conditions [14][15][16], iv) Degradation of fatigue performance due to increased surface roughness and shape distortion by shot peening treatments [17][18][19], v) study on the fatigue performance of the shot peening components characterized with complex structures [14], etc. Others, namely, the materialdependent and numerical calculation-dependent key issues on shot peening treatments are available in [20][21][22].
Although there are many reports on the fatigue performance of shot peened structures, the investigations on stress relaxation and failure under alternate loading needs special attention. In light of this, a series of investigations have taken efforts to further study these issues. Important but not the foremost, Dalaei et al. [10] studied the influence of shot peening on fatigue durability of normalized steel subjected to complicated loading conditions, including overloading and variable amplitude loading along with their influence on fatigue lifetime. In addition to the effect of shot peening treatments on fatigue performance, Kim et al. [23] experimentally studied fatigue performance of specimens machined from medium-carbon steel. The fatigue performance of shot peening specimens as well as the accompanied stress relaxation process was analyzed in the low-and high-cycle regime. In a series of papers Benedetti and coworkers systematically studied the fatigue of shot peened aluminum alloys. low-/high-/veryhigh cycle fatigue of aluminum alloys were experimentally carried out respectively [24,25]. Moreover, most of the available investigations on bending fatigue of shot peened aluminum alloys were also mainly attributed to Benedetti and coworkers [14][15][16]. The most recently reports by Lévesque et al. [26] highlight that defects in the structure and shot peening induced surface roughness together degraded the fatigue resistance of the structure, which is of great significance because it has opened the prologue of the research on the surface integrity and damage tolerance of shot peened structures.
As it was reported that the main purpose of the introduction of shot peening treatments is to increase the service life of the structure by introducing compressive residual stress on the surface of the material, the strategy of which is to increase the total failure life by introducing and extending the relaxation life as significantly as possible. It is, therefore, essential to clarify the relaxation life component and fatigue life component with the total failure life of shot peening specimens subjected to cyclic mechanical loads. However, only experimental investigations on illustrating the failure behavior together with the compressive residual stress relaxation and the fatigue process were available in [10][11][12]27], whereas, the modelled description is urgently needed in terms of the failure process of shot peening components subjected to cyclic mechanical loads. Meanwhile, with the increase of shot peening intensities, the surface roughness of the structure increases significantly, thereby leads to and intensifies the stress concentration, which, consequently accelerates the release of residual stress and reduce the fatigue life. It is designated as life transition phenomenon, which commonly occurs in the extra-low-/low-cycle regime as experimentally revealed in [28][29][30]. It is, therefore, essential to try to describe the fatigue performance in the extra-low-/low-cycle regime so as to comprehensively indicate the effect of life transition phenomenon on life prediction in this regime.
With respect to the mentioned challenges of the effect of shot peening treatments on fatigue performance, this paper developed a unified model by clarifying the relaxation life component and fatigue life component with the total failure life, thereby, successfully evaluated the fatigue performance of shot peening components in extra-low-, low-, and high-cycle regime and acquired satisfied life prediction results for various shot peening intensities. Based on the new proposed model accompanied with experimental investigation, the life transition phenomenon was also identified. Furthermore, a master life diagram on evaluating and predicting fatigue performance of shot peening specimens against various shot peening intensities in extra-low-, low-, and high-cycle fatigue life regime for SS304 was de-veloped on purpose of predicting or evaluating the fatigue life and performance of shot peened structures in service by linear interpolation of shot peening intensities. Additionally, characterization of multiple-fatigue initiation to failure was identified by fractography analysis, which reasonably illustrated the non-conservative life prediction in high-cycle regime.

Materials and specimens
The austenitic stainless steel 304 (SS304), a facecentered cubic structure (FCC), with chromium (chemical) content up to 17% and nickel (chemical) content about 8%, was studied in this paper and presented in Table 1.
In order to avoid the data dispersion of material mechanical properties between specimens, all specimens were obtained from a single bulk of the material. The raw material was cut from one round bar with a diameter of about 210 mm. The raw material was cut by electrical discharge machining (EDM) which was solution treated at 1050 • Cfor 30 minutes and water-cooled. The microstructure of SS304 is available in Figure 2, which clearly illustrates the grain size of SS304 that ranges from 100-150 µm. The forging billet of SS304 material was processed into tensile test specimens and fatigue test specimens, the shape and dimension of them are shown in Figure 3. All dimensions of specimens are in millimeters.

Shot peening treatments and performance characteri-
zation Investigations [31,32] indicated that the shot peening induced surface morphology of components degraded the fatigue performance since the surface might seriously distorted. Characterization of morphologies of specimens machined from SS304 with different shot peening intensities, namely un-, 0.1/0.25/0.4 mmA-peened based on the whitelight interference measuring technique (ZYGONexView, America, RMS repeatable precision of 0.005 nm, vertical scan range from 0 to 20 mm, vertical resolution of 0.1 nm and test accuracy of R a ≤ 0.1nm) are presented in Figure 4 respectively. Meanwhile, quantized 3D morphologies including surface roughness parameters such as the notch depth (α) and the notch width (2β) were statistically characterized and presented in Figure 5. The data show that although there is, in fact, an identically increasing trends for both α and β against shot peening intensities, the notch width exhibits increasing rates considerably higher than the notch depth data. Accordingly, Li et al. [33] correlated the notch characteristics with the stress concentration factor K t based on an empirical expression: which was commonly applied in characterizing the shot peening morphologies [34,35]. Illustration on the correlation between stress concentration factors and shot peening intensities calculated by Equation 1 is also available in Figure 5, which is well-described by with η 0 =1.0, η=0.265 and γ=0.2 respectively. The residual stress of specimens were measured by the X-ray Stress Analyser (LXRD, Proto, Canada) with  Mn-K α radiation, voltage of 30 kV, current of 20 mA, Cr filter and 311 diffraction plane (hkl) by using sin 2 ψ method. The hkl-depended X-ray diffraction elastic constants adopted here were 7.18 × 10 −6 MPa −1 and −1.20 × 10 −6 MPa −1 , respectively. About the residual stress measurement, the range of tilting angles (psi) is 0 • -±45 • . Moreover, in depth residual stress distribution of shot peened specimens is also required. Generally, The samples were electrochemically exfoliated by electropolishing machine, in which the electrolyte was saturated salt water, the working parameters of DC power supply were 15 V and 2 A, and the depth of electrochemistry corrosion was detected by digital micrometer. Accordingly, in depth residual stress distribution of as-treated specimens are depicted in Figure 6. The overall trends, apparently, are the same, but the remnant compressive residual stresses are completely different. The maximum compressive residual stresses σ R max,initial were designated as the initial values to resist fatigue failure. Therefore, the relationship between the initial compressive residual stress and shot peening intensities is illustrated and correlated by with satisfactory fitting results, where µ=861 and ξ=0.181 are both fitting parameters.

Mechanical properties of SS304
Monotonic tensile tests were carried out to acquire the basic mechanical properties of SS304. Engineering stress/strain curves in terms of un-/0.1 mmA-/0.25 mmA-/0.4 mmA-peened specimens in monotonic tensile tests are presented in Figure 7, together with a detailed description in the earlier loading regime. The MTS-809 test system with an axial loading capacity of ±250kN equipped with non-contact laser extensometer was used to avoid additional damage on the peened surface. The solid round bar specimens (Figure 3 (a)) were tested and recorded in displacement control mode with a rate of 0.01 mm per second. The strong similarity between tensile curves of various shot peening intensities indicates a surface-independent monotonic tensile properties of SS304. Therefore, monotonic parameters (ultimate stress σ b , yield stress σ y , Young's modulus E, reduction in area ψ, elongation δ Poisson's ratio ν) of SS304 with errors are available in Table 2.

Fatigue testing and S-N curve
Sinusoidal (R = −1) load-controlled uniaxial fatigue tests were also performed with MTS-809 test system to evaluate the stress-strain responding during cyclic loading at room temperature and nominal frequency of 5 Hz. Various stress amplitudes corresponding to fatigue lives in the extra-low-, low-and high-cycle regime were considered for un-/0.1 mmA-/0.25 mmA-/0.4 mmA-peened specimens. Fatigue tests were terminated when specimens completely fractured or the number of cycles exceeded 10 6 . The number of un-/0.1 mmA-/0.25 mmA-/0.4 mmA-peened specimens are 15, 9, 11 and 13 respectively, based on which S − N curves with different shot peening intensities can be obtained.

Failure life prediction scheme for shot peening specimens subjected to cyclic mechanical loads
Fatigue performance of shot peening structures subjected to alternate loads is characterized with sophisticated mechanism since the damage caused by residual stress relaxation and fatigue is hardly to clarify. It is, therefore, essential to try to describe the total failure life (N T ) of shot peening specimen by dividing the total life into two parts, namely the relaxation life (N R f ) and fatigue life in which, the total life accords with the order of stress relaxation followed by fatigue failure. Strictly speaking, however, the damage caused by stress relaxation and fatigue will occur in the whole stage of cyclic loading. Additionally, the effect of relaxation is mainly in the initial stage of cyclic loading and gradually decreases with the progress of cyclic loading, while the effect of fatigue is mainly in the medium-long stage of cyclic loading and gradually increases with the progress of cyclic loading. In order to clarify the relaxation life and fatigue life from the total failure life so that the issue can be settled reasonably, Equation 4 is recommended in this paper.

Characterization of residual stress relaxation process of shot peening specimens
Characterization of residual stress relaxation process of shot peening specimens have been discussed in some detail, e.g. in [11,12,27], among which the power criterion developed by Zhuang et al. was proved to give better description of residual stress evolution process by considering the effect of stress ratio and mechanical cyclic amplitude as well as the rapid relaxation behavior of residual stress in the first or first few cycles [27]. Initially, the power criterion proposed by Zhuang and Halford expressed as where σ R max is the maximum compressive residual stress along the depth direction from the peened surface, R is the stress ratio and σ a is the nominal stress amplitude introduced by cyclic mechanical loading. Moreover, α, ρ and κ are fitting parameters indicating the relaxation characteristics. N R ′ f (= N R f + 1) refers to the abscissa of the coordinate system corresponding to Equation 5. This operation of adding 1 to the value of relaxation life N R f is very meaningful, because it meets the requirements of describing relaxation process completely in logarithmic coordinate system. Apparently, before cyclic loading, namely Equation 5 can be simplified to σ R max = −|σ R max,initial | or σ R max = σ R max,initial . Degradation of fatigue life induced by deterioration of surface morphology after peening treatments has been highlight and experimentally reported [11,12,27], however, correlation between the shot peening intensities and residual stress relaxation behavior still needs further investigation. In light of this, K t , the stress concentration factor induced by peening treatments, was introduced to correlate the peened surface morphologies with the mechanical loads, which can be expressed as where σ M is the nominal stress of the peened specimen subjected to mechanical loads. σ M max is the maximum mechanical stress of the peened surface considering the stress concentration behavior. Substituting Equation 6 into Equation 5 yields the surface-dependent residual stress relaxation criterion as   (d)) illustrations on the relaxation process of shot peening specimens subjected to various mechanical cyclic loads. As it is shown in Figure 8(b), (c) and (d) that when the applied mechanical stress is greater than the fatigue limit or even the yield strength, the compressive residual stress will relax obviously after the first cycle, and then start to relax steadily. With the linear increase of the fatigue cycles (note that the abscissa in Figure 8 is in the form of logarithmic coordinate), the relaxation rate of residual stress will gradually decrease. When the residual stress is relaxed to 10% of the initial value (σ R max /σ R max,initial =0.1), it can be considered that the relaxation process is completely stable. At this time, fatigue begins to be the main factor leading to the failure of the peened specimens. It should be noted that measurements on residual stress evolution versus mechanical fatigue cycles up to 10 4 were carried out in this study, which presented strong liner trend in a considerable life range. However, it is necessary to measure the residual stress at higher cycles (more than 10 6 ), which may improve the predicted accuracy of residual stress relaxation  characteristics at low-stress levels. Accordingly, relaxation lives against mechanical loading amplitudes under various shot peening intensities were identified and presented in Figure 9 together with the cyclic run-out data, which, principally are in terms of infinite relaxation lives. Correlation between mechanical stress amplitude with relaxation life of shot peening specimens is modelled by where r and s are fitting parameters, r = 0.53, s = −0.033 for Q = 0.1 mmA, r = 0.552, s = −0.032 for Q = 0.25 mmA and r = 0.528, s = −0.021 for Q = 0.4 mmA, respectively. Therefore, the relaxation life (N R f ) is given by amplitude against the number of cycles to failure, comparing the S − N data for un-peened specimens with 0.1 where σ ′ f and b are fatigue strength coefficient and fatigue strength exponent, respectively. The correlation of fatigue parameters with monotonic tensile parameters to meet the feasibility of engineering structure life prediction is given in [36]. Therefore, the fatigue strength coefficient and fatigue strength exponent were obtained and presented in Table 2.
Stress amplitude and mean stress in the peening-induced notch root is separately illustrated in Equation 11, where σ M max and σ M min are maximum/minimum mechanical stress components respectively during the fatigue loading process. Since both the stable compressive residual stress σ R max,stable and stress concentration induced by shot peening were considered, σ M max and σ M min can be further given by The compatibility of Equation 12 and Equation 11 is em- ployed to derive Substituting Equation 13 into Equation 10 yields the fatigue life of shot peening specimens as Relating Equation 4, Equation 9 and Equation 14 finally gives with σ S < σ M < σ b , which reasonably give the loading possibilities between the fatigue limit σ S and the ultimate stress σ b . Basically, Equation 15 provides a successfully life prediction of specimens with various peening treatments in a wide life regime, 10 3 -10 6 . It is, however, essential to provide a fully description of fatigue performance of shot peening specimens, since the life transition phenomenon was identified in extra-low-/low-cycle regime (< 10 3 ), in which failure lifetime of peened specimens is significantly shorter than that of the un-peened specimens, meanwhile, improvement of fatigue performance was also identified in high-cycle regime (> 10 6 ), in which fatigue limits of peened specimens are significantly greater than that of the un-peened specimens. In light of this, a closer look at the monotonic tensile test in the perspective of the current investigation suggests that a monotonic tensile process is designated as a quarter of a fatigue cycle [36]. It is, therefore, reasonable to determine the upper limit of the S − N curve in extra-low cycle regime by taking a constant stress amplitude identical to the ultimate stress. Similarly, the lower limit of the S − N curve in high-cycle regime can be also determined by introducing the fatigue limits of various shot peening intensities into account. In view of the description of the S − N curve in the medium cycle regime, namely 10 3 -10 6 by Equation 15 and in accordance with the determination of the upper/lower limits of the S − N curve in extra-low/high-cycle regime, a unified model to evaluate fatigue performance of shot peening specimens in extra-low-, low-and high-cycle regime is given by and N H f are fatigue lives in extra-low-/highcycle regime. Since the fatigue limits of specimens against shot peening intensities are illustrated in Figure 10, which can be well described by a linear relationship

A unified model to evaluate fatigue performance of shot peening specimens in extra-low-, low-and highcycle regime
with A=210.6 and B=136.7 are both fitting parameters. Therefore, a comparison of experimental and predicted failure lives of specimens with different shot peening intensities in extra-low-, low-and high-cycle regime is identified and available in Figure 11. Although insufficient data about the fatigue tests in extra-low cycle regime conducted were available to construct extremely convincing S − N curves. However, the life transition phenomenon caused by shot peening treatments has also been identified, which is consistent with the indication of the new model.  fatigue tests were carried out for 0 mmA and 0.4 mmA to verify the life transition phenomenon before and after shot peening. Although the predicted results are more conservative than the test results in this regime, it may be due to the introduction of strengthening behavior of materials under high stress amplitude loading.
Accordingly, both Figure 11 and Figure 12 presented the life prediction results of specimens with different shot peening intensities. In light of this, a master life diagram on evaluating and predicting fatigue performance of shot peening specimens against various shot peening intensities in extra-low-, low-, and high-cycle fatigue life regime for SS304 was developed on purpose of predicting or evaluating the fatigue life and performance of shot peened structures in service by linear interpolation of shot peening intensities. Although the fatigue tests in this paper are carried out under the condition of R = −1, the strategy in this paper can also be applied to the fatigue failure assessment of other stress ratios.

Correlation of fractography with fatigue performance
of shot peening specimens machined from SS304 Typical fracture surfaces of un-peened and peened (0.1 mmA, 0.25 mmA and 0.4 mmA) specimens were examined by FE-SEM (field emission electric scanning microscopy) technique. Figure 14 Figure 14. The results indicate that the failure of unpeened/peened specimens are characterized with multiple-fatigue initiations to failure. The characteristics of multi crack initiation are widely reported in shot peening specimens and components [11,25,29,30,37,38]. Generally, shot peening treatments induced surface roughness not only destroys the surface integrity of the peened specimens, but introduces a large number of notch characteristics, leading to stress concentration thereby makes these notches become the hot spot of fatigue failure of shot peened structures. Moreover, with the increase of shot peening intensities, the cross-section size of the peened specimen may also be changed, resulting in the distortion of the structure [31,32,39], which leads to the existence of multiple potentially dangerous nominal cross-sections of the specimen.
The characteristics of multi crack initiation are widely found in shot peening specimens and components [11,25,29,30,37,38]. Shot peening treatments make the roughness of peened surface increase, which not only destroys the surface integrity of the peened specimens, but introduces a large number of notch characteristics, leading to stress concentration, and makes these notches become the hot spot of fatigue failure of shot peening structures. Moreover, with the increase of shot peening intensity, the cross-section size of the peened specimen may also be changed, resulting in the distortion of the structure [31,32], which leads to the existence of multiple potentially dangerous nominal cross-sections of the specimen. Figure 15 extracts the morphology of the crack growth process and further indicates that multi crack initiation phenomenon may also occur on different cross-sections of the peened specimens. Therefore, Figure 14 and Figure 15 show two types of multi crack initiation phenomena respectively, namely multi crack initiation in the same nominal   cross-section and multi crack initiation in different nominal cross-section of the peened specimens. Since the total fatigue life of shot peening specimens considered the fatigue crack growth process, the multiple crack initiation phenomena will greatly reduce the crack growth life of shot peening specimens, which makes the predicted life is non-conservative with regard to the test life ( Figure 11, Figure 12). Figure 16 gives more detailed analysis on the characteristics of microstructures in the crack initiation position and crack propagation path. With respect to the fatigue crack initiation of the peened specimen subjected to cyclic mechanical loads, fracture collapsed at the anomalies of the surface/subsurface (Figure 16(a)). The red dash circled region indicates one of the cracking initiations, in which the anomaly is highlighted with S3. With the help of ED-S probe, cemical composition analysis of S3 confirmed the carbide aggregation which will significantly degrade the fatigue life of shot peen processed specimens machined from SS304. In Figure 14, randomly distributed small pits were identified as grain boundary inclusions in the accelerated crack growth stage, which present mostly between grains. Meanwhile, numerous granular inclusions are found in these pits. The detailed characteristics of them observed at higher magnification of microscope are available in Figure 16(b). As presented, these inclusions are small spherical particles with a diameter of ca.3 µm. The cemical composition of these spherical particles are identified as Manganese (Mn) by EDS probe, which is exactly the identity of the strengthening phase element of SS304.

Conclusions
In this paper, characterization and modeling on the shot peening process, surface morphology, residual stress relaxation and fatigue performance of shot peened specimen machined form SS304 were investigated and the following conclusions can be drawn: • Correlations between shot peening intensities and residual stress distributions and surface morphologies were quantitatively described.
• A life prediction model capable of clarifying the relaxation life component and fatigue life component was developed on evaluating the fatigue performance of shot peening components in extra-low-, low-, and high-cycle regime and acquired satisfied life prediction results for various shot peening intensities.
• The life transition phenomenon was found, which quantitatively clarified that shot peening is not necessarily beneficial to the fatigue life of the structure.
• Characterization of multiple-fatigue initiation to failure of shot peening specimens was identified by fractography analysis, which reasonably illustrated the non-conservative life prediction in high-cycle regime.

Acknowledgments
Thanks for the help of Residual Stress Analysis and Shot peening Enhancement Lab (RSA-SP Lab), Shanghai Jiaotong University in residual stress measurement.

Availability of data and material
All data generated or analyzed during this study are included in this published article.

Author contribution
Shun YANG contributed to the accessible experimental data analysis, life model establishment, literature review, manuscript writing and modification. RSA-SP Lab provided the service of residual stress measurement.

Declarations
Herewith the confirmation: The paper was and is not submitted for publication elsewhere. This paper has not been published elsewhere in its entirety, in part, or in a modified version. The paper was not submitted for possible publication elsewhere.