Mechanical Properties of Metallic Materials Processed by Surface Severe Plastic Deformation

Abstract

This paper gives an overview about some mechanical properties of materials processed by surface severe plastic deformation (SSPD) techniques. SSPD processed materials are classified in terms of characteristics, and main generated parameters that determine the output properties of materials are presented. The influences of SSPD on mechanical properties of materials are then reviewed. Furthermore, the roles played by some parameters such as gradient microstructure, nanostructured layer, compressive residual stress (CRS) and surface integrity are highlighted by discussing their contributions. Finally, some conclusions are drawn and possible prospects for future research are underlined.

1. Surface Severe Plastic Deformation: State of the Art

In-service resistance of mechanical components is of primary importance due to increasing demand on security and economic issues. Most material failure occurs at surface, and its in-service resistance is determined by the material surface properties. Surface modification technologies have long been used to strengthen mechanical components with enhanced properties. Mechanical surface treatments are increasingly used to extend lives of engineering parts. These treatments are based on impact or contact loadings that can create severe plastic deformation in near surface region of parts.^1–7)

1.1 Methods and processes

The various methods based on surface severe plastic deformation (SSPD) presented in the literature are classified as deformation-based treatments. They generally rely on impact/contact loadings between media (solid or liquid) and material surface. Note that the techniques that use liquid media include essentially water jet peening (WJP)⁸⁾ and its derived methods. Typical SSPD based techniques essentially include shot peening (SP),^9–13) surface mechanical attrition treatment (SMAT),^14–18) ultrasonic shot peening (USP or USSP),^13,19–23) ultrasonic nanocrystal surface modification (UNSM),^24–27) ultrasonic impact peening or treatment (UIP^28,29) or UIT^30–32)), ultrasonic surface rolling process (USRP),^33–38) surface mechanical grinding treatment (SMGT),^39–41) surface mechanical rolling treatment (SMRT),^42–46) severe shot peening (SSP),^47–49) laser shock peening (LSP).^50–57) SP is one of the most studied and applied mechanical surface treatment techniques. It entails striking a surface unidirectionally with shot to generate severe plastic deformation. SMAT and USSP, often considered a variant of shot peening, involve repeated multi-directional impacts by solid balls on material surface. The multi-directional impacts with high kinetic energy allow transforming initial coarse grains (CG) into ultrafine grains (UFG) that can reach nanoscale. UNSM, UIP/UIT and USRP are based on high frequency contact of ultrasonic horn on material surface. SMGT and SMRT are also based on contact loading, and SMGT has a fixed tool head, whereas the tool head of SMRT can freely rotate leading to reduced friction. SSP is a sort of shot peening with a higher intensity, and is able to nanocrystallize material surface. LSP uses a laser beam to create plasma shock waves inducing compressive residual stress (CRS) in a thick layer on the surface of a structure. The difference between the above-mentioned techniques mainly lies in impact intensity and direction. This leads to the difference in obtained work-hardened layer and surface nanostructured layer.⁵⁸⁾ Some of typical SSPD techniques are illustrated in Fig. 1.

Fig. 1

Illustration of some typical SSPD processes: (a) air blast shot peening (ABSP),¹³⁾ (b) ultrasonic shot peening (USP),¹³⁾ and (c) ultrasonic nanocrystal surface modification (UNSM).²⁷⁾

1.2 Types of materials processed

A great number of materials have been studied to demonstrate their treatability and to understand the mechanisms of microstructure evolution. These materials are classified in a large range including steels,^{19,26,35,59–77)} copper and its alloys,^78–80) aluminum and its alloys,^20,81–85) magnesium and its alloys,^86–88) titanium and its alloys,^{25,34,89–95)} superalloys including IN718 alloy^96–101) and GH4169 alloy,¹⁰²⁾ uranium,³³⁾ metal-based composite materials,¹⁰³⁾ shape memory alloys NiTi,¹⁰⁴⁾ metallic glasses,^105–107) and medium entropy^108,109) as well as high entropy alloys.^110–113) Note that for alloys based on same elements but with different atomic structures, for example steels (ferritic, austenitic or martensitic phases) and Ti alloys (α, β or β metastable phases), their behavior while undergoing treatments could be very different. The SSPD techniques are usually applied to treat polycrystalline materials, but recently they have also been used to treat monocrystalline materials such as nickel based single crystal superalloys.^114–117) In some cases, attention should be paid to avoid the formation of micro-cracks due to over-treatment.^{33,60,118,119)}

As for microstructure evolution during treatments, a huge quantity of work can be found for materials of different atomic structures with a wide range of stacking fault energy (SFE). In fact, deformation mechanisms and subsequent grain refinement scenarios are strongly dependent on material’s atomic structure and its SFE. Different SFE can give rise to different dislocation activities. For example, for face-centered cubic (FCC) and body-centered cubic (BCC) metals, dislocation walls and cells are formed to accumulate strains, and sub-boundaries are formed to subdivide coarse grains if their SFE is high. For materials with medium or low SFE however, deformation-induced twinning plays an important role in deformation mechanism and grain subdivision.^120–122) For hexagonal close packed (HCP) materials, deformation-induced twinning appears to be prevailing because of the limited slip systems.¹²¹⁾ Deformation-induced phase transformation is also an important factor while considering the application of SSPD.^3,46,123)

More recently, SSPD started to be used to treat materials elaborated by advanced processes such as additive manufacturing. It is becoming a promising post-treatment approach to attenuate/eliminate the intrinsic defects generated during additive manufacturing.^124,125)

2. Microstructure and Features

In this section, microstructure and some main features including gradient microstructure, residual stresses, work hardening and surface integrity generated by SSPD will be presented.

2.1 Gradient microstructure

For SSPD processes, the imposed load is generally the highest at superficial region and decreases gradually with the depth. During these processes, highly active dislocation motion is induced, which progressively leads to grain refinement at the surface. In the bulk region far from the treated surface however, the material is not deformed and the material’s characteristics are unchanged. A gradient microstructure is thus obtained, from the treated surface to the interior region in general with three successive zones: (i) an ultrafine or nanocrystalline grained zone, (ii) a transition zone where grains are fragmented or subdivided, (iii) a deformed zone where initial grains are only plastically deformed.

More complex gradient features can be formed for materials which exhibit deformation-induced twinning and phase transformation. For these materials, there is a gradient distribution of twins and transformed phase,⁴⁶⁾ combined with the aforementioned gradient microstructure.⁶⁷⁾ An example of typical microstructure is presented in Fig. 2 for a SMATed 316L steel observed using electron backscatter diffraction (EBSD). Note that the change in microstructure from one zone to another is continuous, i.e. there is no clear frontiers between them.

Fig. 2

EBSD observation on the cross-section of a SMATed 316L steel: (a) non-deformed bulk region, (b) mechanically affected region showing three areas, i.e. (c) grains with plastic slips, (d) area with mixed grains, and (e) ultrafine grain area.⁷⁷⁾

Some SSPD processes are able to nanocrystallize the material at the surface of a structure. Nanocrystalline grains can increase the strength of materials, since the grain boundaries in nanocrystalline metals and alloys can effectively block dislocation motions.¹²⁶⁾ From an overall point of view, the formation of nanograined structures through mechanical surface treatment is due to plastic stain-induced grain refinement.¹²⁷⁾ More precisely, the nanocrystallization is governed by dislocation activities and dynamic recrystallization process^1,15,128) with high strain energy subgrains¹²⁹⁾ and heat production.¹³⁰⁾ For materials with high SFE, grain refinement is dominated by dislocation movement, whereas for materials with low SFE, the process is governed by deformation-induced twinning.¹³¹⁾ Dislocations in coarse grains multiply to form dislocation walls, and then gradually transform into low angle grain boundaries (LAGBs) which continue to absorb dislocations to form high angle grain boundaries (HAGBs).¹³²⁾ Twinning affects grain refinement via the interaction between twins and dislocations and twin/twin intersection,^133,134) resulting in the formation of equiaxed nanograins.^120,135) In some materials such as Ti, the dislocation bands generated by impacts change into equiaxed subgrains by dynamic recrystallization until the formation of nanostructured grains.¹⁾ For HCP materials, due to their limited number of slip systems, the effect of grain size should be considered, since it influences the critical resolved shear stress (CRSS) for twinning.¹³⁶⁾ The formation of refined grains can be further promoted by cryogenic temperature that can limit dynamic recovery and promote mechanical twinning.^137,138)

2.2 Residual stress

As presented in Section 2.1, there is a macroscopic plastic deformation gradient induced by SSPD. Because of this non-homogeneous plastic deformation, a coupled macroscopic residual stress field is generated in a structure. CRS is present in the near surface region, while tensile residual stress (TRS) is present in the interior to ensure a stress equilibrium of the whole structure. The distributions of the residual stresses induced by different SSPD processes are more or less similar to each other (see Fig. 3), due to the similarity of load modes and deformation mechanisms. CRS reaches its peak level beneath the treated surface, and then decreases with an increase in depth. The residual stress changes from compressive to tensile at a certain depth. However, quantitatively the CRS peak and the depth of CRS field obtained by various SSPD processes could be different from each other, mainly due to the differences in process nature and treatment conditions. The obtained residual stress profile depends also on the mechanical properties of materials to be treated.^139–142) The maximum CRS is higher in high yield strength alloys,^26,143) and a deeper CRS field can be obtained in alloys with higher elastic modulus and strain hardening exponent.²⁶⁾ Tensile residual stress (TRS) inside treated structures could be harmful as it can generate a positive mean stress locally and thus facilitate crack initiation. In some cases, a high magnitude of CRS may be less efficient in improving fatigue strength than its associated TRS in reducing fatigue strength.¹⁴⁴⁾

Fig. 3

Typical residual stress profile obtained by mechanical surface treatments. An experimentally obtained residual stress profile for a shot peened microalloyed steel is shown later in this paper (Fig. 13(b)).

2.3 Work hardening and hardness

Under the effect of SSPD, the hardness of the near surface region should be higher due to the generated work hardening and grain refinement.^48,145,146)

It is generally considered that work hardening induced by SSPD is beneficial for improving mechanical strength of materials due to the increased yield strength. However, if the SSPD processed materials undergo cyclic loading and exhibit Bauschinger effect, it would be necessary to distinguish isotropic hardening and kinematic hardening. Isotropic hardening is governed by short-range interactions of non-coplanar dislocations (forest hardening), while kinematic hardening stems from long-range dislocation interactions (through distant elastic fields). It is well known that back stress is associated with kinematic hardening, and if the material is loaded in the opposite direction of the back stress, its yield stress can be lower due to Bauschinger effect. Work hardening generated by SSPD can be divided into isotropic hardening and kinematic hardening depending on the material and its previous deformation history. Samih et al.¹⁴⁷⁾ highlighted using EBSD the distribution of geometrically necessary dislocation (GND) density in the near surface region of a 316L steel processed by SMAT. These GNDs generated by impacts could give rise to back stress responsible for kinematic hardening behavior, when the material is subsequently loaded.

Numerical simulation could be an effective approach to highlight the involvement of kinematic hardening in the SSPD processes. Zhou and Sun¹⁴⁸⁾ numerically investigated peening-induced work hardening gradient. They revealed that for a material which presents isotropic hardening and kinematic hardening behaviors, both the size and the position of the yield surface are changed due to shot peening. Accordingly, the peening-induced work hardening includes isotropic hardening (a scalar) and kinematic hardening (a tensor). It means that the kinematic hardening generated by SSPD can, to some extent, decrease the yield stress of a material, as highlighted by Zhou et al. on a cylindrical structure.¹⁴⁹⁾

2.4 Surface integrity

Surface integrity is one of the main factors determining the durability of mechanical components. When evaluating the effects of SSPD processes, it is important to consider the surface integrity, as it may induce local surface stress concentration and thus reduce fatigue performance.^150,151)

During treatments like UNSM and SMRT, large and rather uniform plastic deformation occurs at surface of materials, leading to much better surface integrity and as a consequence to superior fatigue performances. In contrast, some other treatment techniques could generate detrimental surface defects. The presence of these defects can attenuate the overall beneficial effect induced by other factors such as CRS. These surface defects can also increase the fatigue life scatter, which makes the life prediction more difficult while dimensioning mechanical components. Note that the initial roughness of materials to be treated could be an important factor because it influences the evolution of surface morphology and roughness and leads to different saturated roughness value.¹⁵²⁾

For certain SSPD processes, an over-treatment phenomenon could be observed for a given material to be treated. This potential over-treatment should be considered, since it could lead to the formation of surface defects and sometimes the occurrence of micro-cracks. For instance, in their study of a CoCrMo alloy, Brasileiro et al.¹⁵³⁾ revealed that for a same vibration amplitude and time duration, the SMAT treatment with 3 mm steel balls gave rise to the occurrence of micro-cracks at surface, while no such micro-cracks were detected for the specimens treated by 2 mm balls.

3. Mechanical Properties

Due to the SSPD induced microstructure modification and other generated parameters including residual stress, the SSPD processes are able to change the mechanical properties such as tensile properties, fatigue properties.

3.1 Tensile properties

3.1.1 Overall behavior

Tensile tests are usually conducted to investigate mechanical behavior in form of stress-strain curve. In the studies for 316L steel,¹⁵⁴⁾ pure Al¹⁵⁵⁾ and Mg–Gd alloy,¹²¹⁾ tensile tests were performed for specimens in form of sheet with a thickness ranging from 0.5 mm to 1 mm, treated with different SMAT intensities. Results show that compared with the as-received state, the SMATed specimens exhibit high level of yield stress and ultimate tensile strength (UTS), less pronounced strain hardening and reduced elongation to failure. An example of results obtained for the pure Al is given in Fig. 4.

Fig. 4

Tensile engineering stress-strain curves obtained for pure Al treated by SMAT with different intensities represented by different time durations in minutes.¹⁵⁵⁾

In SSPD processed materials, the mechanical behavior is mainly determined by plastic deformation and grain refinement induced by treatments. Large quantities of dislocations and ultrafine grains are two major sources of strengthening. The Taylor relationship can be used to describe the increase in yield stress σ_y caused by isotropic hardening related to intragranular dislocation interactions. The increase in yield stress caused by reduced grain size, can be estimated by the Hall-Petch law in the ordinary grain size range. The yield stress of a material processed by SSPD can be determined by:   

\begin{equation} \sigma_{y} = \sigma_{0} + \frac{k_{HP}}{\sqrt{d}} + M\alpha \mu b\sqrt{\rho} \end{equation} (1)

where σ₀ is the lattice friction stress; k_HP is the Hall-Petch slope; d is the grain size; M is the Taylor factor; α is a material constant; μ is the shear modulus; ρ is the dislocation density.

The contribution of grain refinement and that of work hardening to the mechanical strength of a structure can be more or less significant, depending on the dimension of the structure. For a thin sheet specimen, as illustrated in Fig. 4, the refined grains can play a dominant role because they occupy a large volume fraction, while for a specimen with a large dimension, the strengthening effect due to work hardened region can be predominant. In a 316L cylindrical structure with a diameter of 6 mm, the SMATed structure exhibits overall strengthening, but with an early yielding.¹⁴⁹⁾ This early yielding observed for the SMATed structure seems not to be consistent with other results presented in the literature, since both grain refinement and dislocations induced by SSPD can increase the yield stress of material according to eq. (1). To reveal the underlying reason, Zhou et al. performed numerical simulations using three different constitutive models including a model that they developed by incorporating a residual kinematic hardening tensor.¹⁴²⁾ The residual isotropic hardening (RIH) and the residual kinematic hardening (RKH) generated by impacts are numerically reconstructed based on the results of full SMAT process simulation coupling discrete element method (DEM) and finite element method (FEM). They revealed that RKH plays an important role in precisely predicting the mechanical behavior of the treated structure, especially the early yielding induced by peening treatments.

3.1.2 Local behavior

The local behavior of material in different layer is also important in terms of understanding the mechanical properties as well as modelling and predicting the behavior of gradient microstructure.

However, experimentally characterizing local behavior of SSPD processed structures is difficult, given the small thickness of different layer. Nevertheless, some attempts have been made in the literature.^156,157) In the work of Chen et al.¹⁵⁷⁾ regarding a 316L steel plate treated by SMAT, dogbone-shaped tensile specimen with a thickness of 15 µm was cut by using electro-discharging technique. This specimen contains essentially a nanostructured layer in which the average grain size is about 40 nm. The yield strength reaches as high as 1450 MPa, about 6 times that of the specimen in the as-received state, as shown in Fig. 5. However, in return, the elongation to failure is much reduced with only 3.4% (see Fig. 5), which implies that the ductility of the specimen was strongly degraded. Similar work was performed for commercial pure Ti processed by SMAT with a specimen of 20 µm in thickness prepared through electro-discharging and mechanical polishing.⁹¹⁾ Note that cutting specimens with thinner thickness is almost impossible, and the obtained mechanical behavior is often not local enough, i.e. it is the combination of material of different layers. It should also keep in mind that there exists an influence of specimen dimensions on tensile behavior.¹⁵⁸⁾

Fig. 5

Tensile true stress-strain curve for the SMAT processed specimen, compared with the curve obtained for the specimen in as-received state obtained for a 316L stainless steel.¹⁵⁷⁾

Nanoindentation was widely used to study the local behavior of materials such as thin films,^159,160) multi-phased materials.^161,162) This technique was also used to characterize the local behavior of gradient microstructure generated by SMAT.^163,164) However, the indenter heads with three-sided Berkovich or spherical tips cause complex stress field in the near contact region, and only typical loading-unloading curves can be obtained.^165,166) To obtain the stress-strain response in a more straightforward way, micro-pillar compression was used to investigate gradient microstructure generated by SMAT.¹⁶⁷⁾ The size of micro-pillars is so small that very local mechanical properties can be evaluated through this technique.

Numerical work has been performed to study the contributions of residual stress and work hardening on local behavior of material. In their work, Zhou et al.¹⁶⁸⁾ investigated the effects of residual stress and peening-induced work hardening including isotropic hardening and kinematic hardening on the tensile behavior of a cylindrical structure through FEM. The stress-strain curves at different depths can be drawn to provide information about local mechanical behavior. They highlighted that the presence of residual stress can significantly change the local stress state of material, as shown in Fig. 6.

Fig. 6

(a) Stress distribution within a cylindrical structure under tensile loading, (b) comparison between stress-strain curves obtained at different depths marked in (a).¹⁶⁸⁾

3.2 Fatigue properties

Fatigue is the most common failure mode of metallic materials in structural applications. Strengthening surface with SSPD has been recognized as an effective way to protect materials against fatigue failure. The effectiveness of these techniques depend strongly on some factors including treatment conditions, fatigue load level.

3.2.1 Cyclic plasticity and low cycle fatigue

Materials treated by SSPD were recently investigated under low cyclic fatigue (LCF). Zhou et al.¹⁶⁹⁾ studied the LCF properties of a 316L steel treated by SMAT with different intensities under various strain amplitudes. Stress amplitude evolution curves presented in Fig. 7 show that SMAT can significantly enhance the mechanical strength and change the cyclic hardening/softening behavior. It can be seen that under low stress amplitude (±0.5%) as shown in Fig. 7(a), the maximum stress amplitude is reached earlier for the SMATed specimens, and a longer softening phase occurs after the short period of initial hardening (see blue and red curves). Under high strain amplitude (±1.25%), the untreated specimen undergoes more obvious cyclic hardening than the SMATed specimens (Fig. 7(b)). It implies that the cyclic hardening property of the SSPD processed specimens is altered by the affected region.

Fig. 7

Cyclic stress amplitude evolution for specimens treated with different SMAT intensities under strain amplitudes of: (a) ±0.5% and (b) ±1.25%.¹⁶⁹⁾

In terms of fatigue life, under LCF the effects of SSPD are generally considered to be less beneficial and sometimes even controversial, and both improvement and degradation can occur depending on materials, treatment techniques and load levels.¹⁷⁰⁾ This is usually a result of high applied loads which can cause significant residual stress relaxation, and recovery of dislocations leading to a drop in strain hardening.¹⁴³⁾ In addition, the nanostructured or ultrafine grained layer might have a reduced LCF performance due to its poor ductility.¹⁷¹⁾ In a study focused on a 2014 aluminum alloy,¹⁷²⁾ significant increase in fatigue life was found for specimens treated by USSP, in particular at low strain amplitudes. After a treatment of 10 min, fatigue life is significantly increased for the samples tested at low total strain amplitudes (<0.55%). Such enhancement was also reported on a 7075 aluminum alloy (AA7075) according to Pandey et al.¹⁷³⁾ The results also revealed that the treatment conditions can be a strong influencing factor for fatigue life. The fatigue lives of the samples treated by USSP for 180 s are increased, while the ones of the samples treated for 300 s are reduced (Fig. 8). Similar results were obtained for a Ti–13Nb–13Zr alloy treated by USSP with different time durations.¹⁷⁴⁾ The improvement is due to a combined effect of grain refinement and CRS,¹⁷⁰⁾ while the negative effect on fatigue life is attributed to degraded surface roughness and surface damage caused by over-peening.^173,174)

Fig. 8

Total strain amplitude versus fatigue life plot for untreated and USSPed 7075 aluminum alloy (AA7075) samples. The specimens were treated respectively during 30, 60, 180 and 300 s.¹⁷³⁾

The effect of SSPD on LCF was also investigated for other alloys such as magnesium alloy,¹⁷⁵⁾ titanium alloys,^93,176) IN718 alloy,⁹⁸⁾ and AA7075 with different precipitation states.¹⁷⁷⁾ To summarize, both improvement and degradation have been observed depending on materials, treatment conditions and load amplitudes.^45,169,176) Under LCF, the residual stress relaxation occurs strongly during the first cycle,¹⁷⁸⁾ and the beneficial effect of CRS could be quickly reduced or even lost.

3.2.2 High cycle fatigue

In the range of HCF, the effects of SSPD were investigated for various materials under different cyclic loading conditions including uniaxial tension-compression, bending and rotating-bending, torsional and multiaxial loadings. An improvement in fatigue life can usually be observed. However, the level of improvement is strongly dependent on treatment conditions which can be optimized according to materials’ behavior.

Most work regarding the fatigue properties of SSPD processed materials was performed for laboratory specimens under uniaxial tension-compression loading. Some examples are given as follows. Ramos et al.¹⁷⁹⁾ reported that SMAT is able to improve the fatigue life of an AA7475-T7351 alloy. For SMATed specimens, the fatigue strength at 10⁶ cycles tested with a stress ratio R = 0 is improved by about 20%, while higher fatigue life enhancement is obtained with R = −1. The load ratio can have a significant effect on fatigue properties. Dureau et al.¹⁸⁰⁾ showed that for specimens in 316L steel treated by the same SMAT conditions, the fatigue limit was enhanced by +17% for R = −1, whereas it was reduced by −7% for R = +0.1. This deterioration of fatigue for R = +0.1 is ascribed to the fact that the compressive residual stress introduced by SMAT is not only totally removed, but instead replaced by a tensile residual stress profile.

The fatigue life of a SMATed 316L steel is increased by about 20% with respect to the non-SMATed counterparts, according to Roland et al.¹⁵⁴⁾ For 316L and 301LN steels, Uusitalo et al.¹⁸¹⁾ reported an increase in fatigue strength at 10⁷ cycles of about 50% after SMAT. Dureau et al.¹⁸²⁾ showed that the fatigue limit of a 304L steel treated by SMAT for 60 min was increased by approximately 20%, compared to the non-SMATed specimens polished to mirror finish. SMAT also improved the fatigue strength at 5 × 10⁶ cycles by 13.1% for a SS400 carbon steel.¹⁸³⁾ For a 316L steel processed by SMRT, clear increases in fatigue limit were highlighted especially for samples with smaller diameter (SMRT-3), compared to non-treated coarse grained (CG) samples, as shown in Fig. 9.

Fig. 9

S-N curves of different samples. SMRT-3 and SMRT-6 refer to SMRT samples with a diameter of 6 mm and 3 mm respectively, CG refers to coarse grains, and T refers to a uniaxial tensile straining of 3%.⁴²⁾

The enhancement in fatigue life obtained by SMAT was also reported by Gao et al.¹⁸⁴⁾ on an AA7075-T6. The fatigue strength at 1.20 × 10⁶ cycles for samples SMATed with 2 mm steel balls is improved by about 50% in comparison with the electropolished counterparts. However, the improvement caused by SMAT with 3 mm balls is less significant than that caused by 2 mm balls. In fact, surface observation highlighted that the treatment with 3 mm balls gives rise to micro-cracks due to an over-treatment.¹⁸⁴⁾ This phenomenon of over-treatment was also observed by Brasileiro et al.¹⁵³⁾ for a CoCrMo alloy SMATed with 3 mm balls, and it led to decreased fatigue lives compared to the treatment using 2 mm balls. A significant deterioration in fatigue life was also reported for an as-received spring steel treated by shot peening, which is due to the poor surface quality.¹⁸⁵⁾

The improvement due to SSPD was also observed for other metallic materials such as zirconium,¹⁸⁶⁾ nickel based alloys^187,188) and titanium alloy.¹⁸⁹⁾ Recently, SSPD was used as a post-treatment process to treat materials elaborated by additive manufacturing. For a selective laser melted Ti–6Al–4V alloy investigated by Yan et al.,¹⁹⁰⁾ fatigue resistance is enhanced by approximately 100% in comparison with the as-fabricated counterparts under stresses ranging from 290 to 580 MPa. The effects of SSPD on fatigue properties of structures such as welded joints have also been investigated. The improvement in fatigue strength of welded joints processed by SSPD has been observed in a large number of studies.^191–195) For instance, the fatigue strength at 10⁸ cycles of a low alloy steel treated by UIT is enhanced under the stress amplitudes from 370 to 410 MPa.²⁹⁾

The effects of SSPD on fatigue strength were also investigated under other loading conditions such as rotating bending^{60,153,182,196)} and torsional loading.¹⁹⁷⁾ Dureau et al.¹⁸²⁾ revealed that, the application of SMAT can bring an enhancement of about 30% in fatigue life under rotating bending compared with the initial ground state, and the improvement is more significant than the enhancement observed under tension-compression.

In terms of more complex loading conditions such as multiaxial loading, some studies were conducted on materials treated by shot peening^198,199) and SMRT.²⁰⁰⁾ Although enhancement in biaxial fatigue life was reported, few studies have been carried out on materials treated by other SSPD techniques. These aspects need to be investigated in future studies especially in terms of the involved mechanisms.

3.2.3 Very high cycle fatigue

Shiozawa and Lu²⁰¹⁾ performed rotary bending fatigue tests on a shot peened high-carbon–chromium bearing steel. The results showed that shot peening improved the fatigue lives in the region of high stress amplitude where crack initiation site changed from surface for untreated specimens to subsurface for shot peened specimens. However, no difference was observed in high cycle region where both most untreated and shot peened specimens had subsurface crack initiation.²⁰¹⁾ Myung et al.²⁰²⁾ showed that the effects of shot peening on the rotary bending fatigue life of a spring steel changed from positive in the HCF regime to negative in the VHCF regime, and most fish-eye fractures occur at sites deeper than the CRS zone. In other work, for example the one performed by Zhang et al.²⁰³⁾ for railway axle steels and the one performed by Suh et al.²⁰⁴⁾ for an AA7075-T651, they showed that shot peening improved the rotary bending fatigue strength of these materials in both HCF and VHCF regimes.

With the development of ultrasonic fatigue machine during the last decades, VHCF properties of materials processed by SSPD are being increasingly studied recently. Due to the fact that in general under VHCF, crack initiation site tends to occur in the interior of specimens at low stress ranges,²⁰⁵⁾ the beneficial effect of SSPD on prolonging fatigue life cannot be fully exhibited, and sometimes it is degraded or even becomes harmful. The VHCF strength of SSPD processed materials was investigated under uniaxial tension-compression loading in a number of studies.^184,206) It was shown that UNSM has significant positive effects on the HCF and VHCF properties of an AISI 310 stainless steel²⁰⁷⁾ and a Ti–6Al–4V titanium.²⁰⁸⁾ Suh et al.²⁰⁶⁾ revealed that for an AISI 4137 steel, the fatigue strength in the VHCF regime is increased up to 30%. Khan et al.²⁰⁷⁾ and Cao et al.²⁰⁸⁾ observed a surface crack failure mode for non-treated specimens, and it shifted to an interior crack failure mode after UNSM treatments especially in high fatigue life regime. In the study on a magnesium alloy processed by ultrasonic peening treatment (UPT), Chen et al.¹⁷⁵⁾ reported an overall increase in fatigue strength induced by UPT. However, the specimens processed by UPT all have an internal crack initiation site, i.e. far from surface.

Fatigue strength deterioration was observed as well in several studies. Gao et al.¹⁸⁴⁾ discovered that SMATed AA7075-T6 samples could have inferior fatigue lives compared to electropolished samples. The fatigue strengths at 1.82 × 10⁸ cycles are decreased respectively by 24.3% and 6.9% for samples treated by 3 mm and 2 mm steel balls. Interior crack initiation is observed in samples treated with 2 mm balls, while a surface-subsurface multi-initiation mode is observed in the ones treated with 3 mm balls, as shown in Fig. 10. A negative effect on VHCF strength as well as subsurface crack initiation especially under low stress levels was also highlighted for an AA2024-T351 processed by LSP.²⁰⁹⁾ For a Ni-based superalloy treated by shot peening, Qin et al.²¹⁰⁾ revealed that VHCF life was improved by shot peening. However, the improvement is degraded while further increasing the treatment intensity. In addition, crack initiation site shifted from surface to subsurface for shot peened specimens, which was caused by the excessive subsurface tensile residual stress.²¹⁰⁾ For an AA7075 treated by LSP, Sanchez et al.²¹¹⁾ reported a two-order magnitude increase in overall life, which is due to the crack initiation site changing from surface to subsurface since the surface is highly protected by LSP.

Fig. 10

S-N plot for the fatigue data points obtained with electropolished (EP) samples and samples SMATed with different conditions, namely Steel-2 (2 mm steel balls), Steel-3 (3 mm steel balls), and Steel-3 + mechanical polishing (MP).¹⁸⁴⁾

Recently, the VHCF properties of SSPD processed materials were investigated under other loading modes such as bending. For instance, Wang et al.²¹²⁾ investigated a LSP processed TC4 titanium alloy under three-point bending. They showed that the HCF properties are generally improved, whereas the VHCF properties can deteriorate for severe LSP conditions due to excessive grain refinement and subsurface failure mechanism.

In summary, the effects of SSPD seem to be dependent on materials and treatment conditions. For almost all the loading modes, there is a trend of crack initiation site shift from surface in HCF regime to subsurface in VHCF regime. In addition, for subsurface crack initiation cases, fish-eye pattern is frequently observed at crack origin, especially for materials that have metallurgical defects such as inclusions and crystallographic defects.^175,205,213) Note that there is also the involvement of environmental effects, since subsurface cracks initiate and propagate under vacuum until they reach the surface.²¹⁴⁾

3.2.4 Fatigue crack propagation

The effect of SSPD on fatigue crack propagation has also been investigated. For an AA2524 studied by Li et al.,²¹⁵⁾ the fatigue crack growth rate (FCGR) is significantly reduced by LSP under low load ratio (R = 0.1), and the reduction is not significant under high load ratio (R = 0.5). In the work regarding an IN718 and an AISI 301 steel performed by Klumpp et al.,⁹⁹⁾ a beneficial influence of shot peening on crack propagation was observed for the IN718, whereas it had detrimental effects for the AISI 301 steel. In both materials, the effects of shot peening vanished with increasing load ratio R. In their work of in-situ observation of cracking process for a spring steel, Wildeis et al.²¹⁶⁾ highlighted that CRS can imped the crack transition from short crack to long crack propagation. In their work performed for an AISI 4140 low alloy steel, Ozturk et al.²¹⁷⁾ showed that SSP had a positive effect and decreased FCGR by about 15% with respect to un-treated specimens.

Zhang et al.²¹⁸⁾ investigated the effect of USSP on both crack initiation and crack propagation for pure zirconium. For a given stress amplitude of 225 MPa, the initiation life and the propagation life for specimens treated during 45 min are respectively 3.1 times and 1.48 times those of untreated specimens, as shown in Fig. 11. It was also indicated that the lower the cyclic stress, the more obvious the improvement in fatigue initiation life. In the early stage of crack propagation, the CRS caused by SSPD can partially balance the imposed tensile stress, resulting in a reduction in the effective driving force for crack propagation.²¹⁹⁾

Fig. 11

Fatigue crack initiation life and propagation life of untreated (original) samples and samples USSP-treated with different time durations: (a) crack initiation life, (b) crack propagation life, for pure Zr.²¹⁸⁾

Wang et al.²²⁰⁾ studied the effect of shot peening on fatigue crack propagation of a Ti6Al4V alloy under a load ratio of 0.1. The results showed that the short crack propagation rate of shot peened specimen is decreased by 34–60%. This is because in addition to the beneficial effect of residual stress, the resistance to plastic deformation at crack tip is much higher due to work hardening.²²¹⁾ Similar result was obtained by Gao and Wu²²²⁾ for a shot peened AA7475-T7351 and the beneficial effect is attributed to the CRS. However, in the same work, Wang et al.²²⁰⁾ revealed that the long crack propagation rate tends to increase. In the work conducted by Yang et al.²²³⁾ for a CuNi₂Si alloy, they found significant increase in fatigue life mainly in the initiation and propagation stage of short cracks, and little effect on later stage of fatigue crack growth.

The above presented results seem to indicate that depending on materials, SSPD can improve fatigue crack growth resistance in the case where the plastic deformation at crack tip is not high. In the case where the beneficial effect due to CRS is not totally removed, the resistance to fatigue crack propagation can be improved.

4. Effects of Different Generated Parameters

In this section, the roles played by several main parameters including microstructure, residual stress and surface integrity will be presented in order to provide some elements about the damage mechanisms of SSPD processed materials.

4.1 Roles of microstructure

The plastic deformation induced by SSPD progressively varies with the depth from the treated surface. In some cases where the treatment intensity is high enough, there is also grain refinement caused by SSPD. These two aspects constitute the gradient microstructure.

4.1.1 Nanostructured layer

It is well documented that the nanostructured or ultrafine grained layer generated by SSPD has a hardness usually much higher than that of its coarse-grained counterpart. In the materials of grain size down to 100 nm, the Hall-Petch law with a constant slope is applicable to estimate the yield strength of materials.²²⁴⁾ When the grain size decreases below 100 nm, grain interior dislocation activities that commonly occur for materials with ordinary grain size tend to be more difficult.²²⁵⁾ This difficulty in activating dislocations gives the nanomaterials high yield strength, usually reflected by high hardness. In most cases of mechanical strengthening such as tension, fatigue, as presented in Section 3, the observed improvements benefit rather from this high yield strength and increase in hardness.

The nanostructured layer formed after grain refinement is considered to be one of the main factors in enhancing the mechanical strength of surface treated materials due to its high strength and its ability to retard the fatigue crack initiation.^226–228) As for the crack propagation resistance, grain refinement gives rise to a deleterious effect, according to systematic experiments realized by Hanlon et al.²²⁷⁾ They revealed that fatigue crack growth rate in nanocrystalline materials is higher than that in their coarse grained counterparts. In addition, crack path observation showed that grain refinement tends to cause a smoothening of fracture surface features.²²⁷⁾ This means that there are fewer obstacles to induce crack deflection in nanocrystalline materials.

The nanostructured layer is able to impede dislocation movement and avoid the formation of surface slip bands, as highlighted by Altenberger et al.²²⁹⁾ For a SMATed structure under tensile loading, Xing et al.²³⁰⁾ revealed that the movement of dislocations in the transition zone, as presented in Section 2.1, is arrested by the nanostructured layer. This dislocation arrest prevents the formation of slip bands at the structure’s surface due to the fact that the dislocation activities in the nanostructured layer are strongly restricted. This explanation can be supported by the investigation performed by Kattoura et al.²³¹⁾ for a 718Plus alloy processed by UNSM. They highlighted that the nanocrystalline layer along with other factors, creates a barrier that restricts the movement of dislocations to the surface, thus delaying crack nucleation due to intrusions and extrusions. The above presented observations seem to be confirmed by Park et al.²³²⁾ while studying the deformation behavior of harmonic structured materials composed of CG core and UFG shell. They revealed by using micro-digital image correlation (micro-DIC) that strain peaks are detected near core-shell boundaries, and this incompatibility is compensated by GNDs. This result could suggest that the movement of the dislocations developed inside CG core is arrested by the high strength UFG shell.

Since the nanostructured layer induced by surface treatment is generally associated with CRS and work hardening, it is challenging to separate its effect from those of other parameters. Post-treatment annealing can be applied to relieve residual stress in order to analyze the individual effect of the nanostructured layer.⁴¹⁾ However, it needs to pay attention to the stability of the nanostructured layer, while analyzing its effect on mechanical resistance especially under cyclic loading²³³⁾ or in an elevated temperature environment. Sun et al.⁷⁷⁾ investigated the potential changes of the microstructural characteristics generated by SMAT under subsequent LCF loading. It was found that in the nanostructured layer, no obvious microstructure changes were observed, which is considered to be related to the high dislocation slip resistance in nanocrystalline materials. For a ss400 carbon steel processed by SMAT under fatigue loading, Li et al.¹⁸³⁾ highlighted a drop in hardness in the nanostructured layer representing a fatigue induced softening. Even no marked grain coarsening is observed, the softening may result from substantial microstructural changes such as strain energy release related to the formation of initiation surface damage, decrease in dislocation density.²³⁴⁾

The thermal stability of nanostructured layer generated by SSPD has been largely studied. Roland et al.⁷⁴⁾ investigated the thermal stability of a 316L steel nanocrystallized by SMAT in the temperature range of 100°C to 800°C. It was shown that the grain size in the nanostructured layer remained unchanged up to 600°C. This result is consistent with that obtained by Todaka et al.¹³⁾ for various steels. Wu et al.²³⁵⁾ investigated, using an in-situ EBSD equipment, the thermal stability of a 316L steel processed by SMAT, especially the nanostructured layer. It was observed that the microstructure did not significantly evolve up to 720°C, and that the small grains were maintained. Thermal stability has also been studied for other materials such as pure Al^155,236) and its alloys,²³⁶⁾ and AZ31 Mg alloy.²³⁷⁾ It can be concluded from these studies that the thermal stability temperature of a material is more or less correlated with its melting temperature.

4.1.2 Gradient microstructure

A gradient microstructure from a nanostructured surface to a relatively coarser interior grain morphology can provide gradual transition from a surface layer resistant to HCF to a core which is more resistant to fatigue crack growth.²²⁸⁾ The external grain refined layer with high hardness has high fatigue crack initiation resistance, while the interior large-grained region has high fatigue crack growth resistance.¹⁰⁴⁾

For an industrial Zr treated by USSP under HCF, Zhang et al.²³⁸⁾ demonstrated that the high strength of surface gradient nanostructure could increase the crack initiation resistance. Furthermore, the surface nanocrystals grew and rotated gradually during fatigue loading, which is beneficial for slowing down the development of fatigue damage and prolonging crack initiation life. Gradient nano-grained (GNG) materials have shown synergetic high strength and ductility due to their gradient microstructure. In these GNG materials, the grain size changes from tens of nanometers in the surface region to tens of micrometers in the bulk. Through numerical simulation, Li et Soh²³⁹⁾ investigated the role of gradient size gradient (GSG) on tuning the strength, ductility and work hardening rate of a structure. This type of work allows to reveal the underlying deformation mechanisms controlling ductility and strengthening in terms of the spatial distribution and temporal evolution of microstructure and damage.²⁴⁰⁾ The gradient structure produces a synergetic strengthening and extra work hardening through enhancing both initial yielding and strain hardening,⁵²⁾ and there exists an optimum gradient structure volume fraction for the highest extra strain hardening and extra strengthening.²⁴¹⁾

In their investigation of a 316L steel treated by SMRT, Huang et al.⁴²⁾ revealed that the gradient nanostructured surface (GNS) region suppresses the initiation of cracks and accommodates a remarkable plastic strain amplitude during fatigue by reducing strain localization, resulting in the enhanced fatigue property.²⁴²⁾ Through analyzing experimental results, Li et al.¹²⁶⁾ concluded that the distribution and degree of structural gradient are two key factors determining the mechanical properties of GNS metals and alloys.

Ma et al.²⁴³⁾ investigated the effect of strength gradient on fatigue resistance of steels through a microstructural gradient generated by pre-torsion treatment. They highlighted that a negative strength gradient from an existing crack-like notch (the local strength gradually decreases with distance from the notch) leads to better resistance to fatigue crack initiation than a positive strength gradient (the local strength gradually increases with distance from notch), whereas a positive strength gradient is more effective at suppressing crack growth, as shown in Fig. 12. Finite element (FE) modelling of crack propagation showed that the microstructural gradient can significantly alter the stress distribution and plastic zone size near the crack tip.²⁴³⁾

Fig. 12

Cycles consumed for (a) crack initiation and (b) crack propagation for a 304 steel under the same test conditions for samples with different prepared states: as-received (as-rec), pre-tensioned gradient-free (ref), positively graded (+grad) and negatively graded (−grad).²⁴³⁾

As a SSPD processed structure has a negative strength gradient, it seems to be consistent with the fact that SSPD can usually improve fatigue life under HCF (as presented in Section 3.2.2) where a crack initiation stage is dominant. Under LCF however, the increase in fatigue life is often limited (as presented in Section 3.2.1), because in this case the fatigue life is mainly controlled by crack propagation and a negative strength gradient cannot play a beneficial role on delaying the crack growth. Through investigating the crack non-propagation of notched induction-hardened S38C steel, Zhang et al.²³⁸⁾ found that the gradient microstructure is one of the main factors responsible for inhibiting the fatigue crack propagation. FE modelling and experiment of crack propagation showed that gradient microstructured material has a smaller plastic zone and lower stress concentration in front of crack tip, resulting in slower crack propagation.⁴⁰⁾

4.2 Roles of residual stresses

It is generally recognized that CRS plays an important role in enhancing fatigue strength of materials especially under HCF. CRS is able to hinder or delay crack initiation and to some extent decrease propagation rate, so that an enhancement in fatigue life could be achieved.^186,244) Both crack initiation and propagation resistances can be enhanced by CRS through decreasing the effective external applied tensile stress.²⁴⁵⁾

In many cases, especially under low load levels, CRS is considered as mean stress²⁴⁶⁾ and is taken into account simply by summing with the external applied stress to get a resultant stress.¹⁴³⁾ In some other work, residual stress distribution is considered, along with SSPD induced work hardening, to modify the yield strength of materials, and the increased yield strength in the near surface region results in lower plastic strain amplitudes under stress controlled cyclic loading.²²⁹⁾

4.2.1 Surface crack initiation case

In the case where crack initiation occurs at surface even after SSPD processes, CRS can protect surface from initiating cracks. However, in practice this protection can be gradually degraded due to residual stress relaxation occurring during cyclic loading. After the compressive residual stress is relaxed to a certain level, the ordinary material damage process (i.e. without residual stress) begins. It is thus possible to divide the total fatigue life $N_{f}^{T}$ into two parts, namely the life dedicated to residual stress relaxation (relaxation life $N_{f}^{R}$), and the one ascribed to fatigue damage (fatigue life $N_{f}^{F}$), as proposed by Yang:²⁴⁷⁾   

\begin{equation} N_{f}^{T} = N_{f}^{R} + N_{f}^{F} \end{equation} (2)

Strictly speaking, the damage process can start during relaxation life. However, with this relation (eq. (2)), it is possible to qualitatively explain some results of fatigue tests.

In the case of LCF, the role of CRS is usually not significant in terms of fatigue life improvement, as presented in Section 3.2.1. This is mainly attributed to the more pronounced residual stress relaxation under high load levels.²⁴⁸⁾ The relaxation is caused by cyclic plastic deformation imposed during fatigue loading and its kinetics is dependent on several factors including the ductility of the studied material and the applied load level. Under LCF, when the load level is high, the relaxation takes place mainly in the first several cycles, and only a small proportion of residual stress can remain by the end of fatigue tests,^178,249) as illustrated in Fig. 13. It can thus be deduced that under LCF, $N_{f}^{R}$ is strongly reduced due to residual stress relaxation, and consequently the total fatigue life is mainly determined by $N_{f}^{F}$. Therefore, the effect of SSPD on fatigue life improvement should not be significant.

Fig. 13

(a) Evolution of residual stress at top surface as a function of number of cycles, with different load levels; (b) residual stress profiles at N = N_f/2 obtained with different load levels, for a micro alloyed steel.²⁴⁹⁾

By contrast, under HCF, as the imposed stress level is low, plastic deformation can hardly be observed in the macroscopic scale. Hence, the stress relaxation is insignificant, and a large proportion of CRS can remain even after the failure of materials.²⁵⁰⁾ These retained compressive surface residual stresses are able to extend materials’ lives. In this case, $N_{f}^{R}$ in eq. (2) can be much higher and there is a significant increase in total fatigue life $N_{f}^{T}$ due to SSPD. This improvement in fatigue life is ideally what we expect to obtain with the SSPD processes.

4.2.2 Subsurface crack initiation case

In another case where a very high CRS level is obtained by SSPD, there could be a drastic decrease in fatigue life associated with a crack initiation site shift from surface to subsurface, as highlighted in the literature.^214,251) As the crack initiation site is shifted to subsurface, CRS that is located in the near surface region cannot fully play its beneficial role even if it is not quickly relaxed by cyclic loading. Instead, the subsurface TRS which balances the CRS field is also quite high, and it promotes subsurface crack initiation^248,251) and thus reduces $N_{f}^{F}$ of eq. (2). In this case of subsurface crack initiation induced by high TRS level, the total fatigue life $N_{f}^{T}$ can be even smaller than that of its untreated counterpart, as illustrated by Gao et al. for an AA7075.¹⁸⁴⁾

Under much higher cycle fatigue especially VHCF, sometimes even for non SSPD treated structures, fatigue crack initiation site may be located in subsurface region or even interior of structures. It could be the case for materials with inclusions that play a role of stress raiser and thus facilitate subsurface initiation in the region of tensile residual stress.²⁵¹⁾ In such a case, SSPD processes may not be applicable to increase fatigue life, because the beneficial CRS in the near surface region evidently cannot play its role.

For the various cases presented above in this section, it is possible to qualitatively explain them through the following scenario. It can be assumed that the local fatigue strength of material is enhanced depending on the local CRS acting here. By referring to Fig. 3 obtained for a certain condition (material and treatment conditions), it is possible to roughly plot the distribution of local fatigue strength taking into accounting the residual stress profile.¹⁴⁴⁾ It can be deduced that:

• -    Surface-initiated crack propagates only if imposed stress curves do not intercept the estimated local fatigue strength curve. It corresponds to the cases of high stress amplitudes (surface crack initiation induced failure). In some cases cracks can initiate at surface but they do not propagate if the imposed stress is not high enough. The presence of non-propagating fatigue cracks which arrested at a certain depth was demonstrated by Guagliano and Vergani.²⁵²⁾
• -    Under lower stress amplitudes, the imposed stress curves can intercept the estimated local fatigue strength curves. In this case, only the subsurface cracks are able to expand, which leads to final fracture due to subsurface crack initiation.¹⁴⁴⁾

The above presented scenarios qualitatively illustrate the beneficial role played by CRS and the potential harmful role of the associated local TRS. However, it is worthwhile to note that in practice, stress concentration due to stress raisers such as inclusions can strongly influence the interior crack initiation processes by locally increasing the applied stress.²⁵¹⁾ In addition, the interaction between the residual stress field and the applied one should be more properly considered to assess subsurface crack initiation and the way in which residual stresses might relax.¹⁴³⁾

4.2.3 Residual stress versus other parameters

For SSPD processes, residual stress is generated along with other parameters such as work hardening, and grain refinement in some cases. There is still controversy about which parameter provides the major benefit in improving mechanical properties of materials. However, the individual effect of residual stress is rarely investigated since it is challenging to properly separate residual stress without changing other associated parameters. Nevertheless, some authors tried to provide information about this aspect.

Moon et al.²⁵³⁾ studied the respective effects of residual stress and microstructure on mechanical properties of gradient structured materials elaborated by UNSM. For this purpose, a UNSM treated specimen in pure Cu was heat treated (HT) at a temperature to release the residual stress. EBSD was used to ensure that the microstructure was not much changed in terms of grain size and grain boundary fraction. The results showed that gradient microstructure and residual stress respectively contribute to 80% and 20% increase in yield strength, compared to the non-treated sample. As yield stress plays an important role under stress-controlled HCF, it can be speculated that under fatigue loading, the contribution of the microstructure would be also dominant.

As for cyclic loading, recently Geng et al.⁴¹⁾ studied the respective contributions of GNS region and CRS with a Zr-4 alloy processed by SMGT. Similarly, they performed annealing to remove residual stress in order to investigate the individual effects of GNS and residual stress. The obtained S-N curves show that SMGT much increases the fatigue strength compared to coarse grained (CG) samples. After annealing, A-SMGTed (annealed + SMGTed) samples exhibit fatigue strength slightly lower than that of SMGTed samples without annealing, but still much higher than that of the CG samples. This result seems to indicate that removing residual stress did not much reduce the fatigue strength, and the increase in fatigue strength of the SMGTed samples is mainly attributed to the GNS layer. This observation for fatigue loading is consistent with the one reported above for tensile loading, and also consistent with the result obtained by Eleiche et al.²⁵⁴⁾ for a shot peened and annealed medium alloy steel. In the latter work, detailed analysis revealed that the GNS region improves the tension-compression fatigue strength by delaying crack initiation and decreasing crack propagation rate.

4.3 Roles of surface integrity and notch sensitivity

Surface integrity is generally a crucial factor influencing fatigue life. Rough surface or even micro-cracks induced by mechanical surface treatments could somehow deteriorate the fatigue strength of materials by causing stress concentration and promoting crack initiation.^255,256) The effect of surface roughness can thus be taken into account through stress concentration factor K_t, usually defined from roughness parameters:²⁵⁶⁾   

\begin{equation} K_{t} = 1 + 2.1(R_{t}/R_{sm}) \end{equation} (3)

where R_t and R_sm are roughness parameters. R_t is the difference between highest peak and deepest valley, and R_sm is the mean peak width. In practice, a specimen with a rough surface or even a micro-crack can be considered to be a notched specimen. In this case, the effect of roughness can be assessed using a fatigue strength reduction coefficient K_f defined as:   

\begin{equation} K_{f} = \frac{\sigma_{D(K_{t} = 1)}}{\sigma_{D(K_{t})}} \end{equation} (4)

where σ_D is the fatigue limit obtained for smooth specimens (K_t = 1) or notched specimens (K_t > 1).

According to the literature, the susceptibility to notch effect, i.e. the sensitivity to notch can be quantified using a factor q which is defined as:   

\begin{equation} q = \frac{K_{f} - 1}{K_{t} - 1} \end{equation} (5)

The factor q varies between 0 for materials non sensitive to notch and 1 for the case where the adaptation is totally absent.

Mechanical surface treatments can change the notch sensitivity of a notched material. For instance, through studying a TB6 Titanium alloy, Luo et al.²⁵⁷⁾ found that after shot peening, the fatigue limits of specimens with notches of K_t = 1 and K_t = 2 are increased by 33.5% and 22.2% respectively, and the notch sensitivity q is decreased by 48%. For an AW 7075 alloy processed by SSP, Jambor et al.²⁵⁸⁾ found that the fatigue strength of notched specimens is increased only in the range of very high cycles, and in the range of low cycles where the stress amplitudes are high, there is even a decrease in fatigue strength. This phenomenon can be attributed to the strong notch sensitivity of the AW7075 alloy. In their study, Maurel et al.¹⁵¹⁾ revealed that SMAT induced surface defects are extremely detrimental for the fatigue resistance of AA7075, compared to the counterparts of AA2024. Under HCF, the AA7075 specimens SMATed with 3 mm balls exhibited an inferior fatigue life compared to the ones SMATed with 2 mm balls, as highlighted by Gao et al.¹⁸⁴⁾

The notch sensitivity of a material could also be changed after it is nanocrystallized by SSPD. Furnish et al.²⁵⁹⁾ investigated fatigue stress concentration and notch sensitivity for nanocrystalline NiFe samples elaborated by electrodeposition. It was found that the notch sensitivity factors for the nanocrystalline material are more than two orders of magnitude larger than those for metals with similar notch sizes. It was concluded that this reduction in HCF life due to notch is caused by cyclically-induced abnormal grain growth, a predominant deformation and crack initiation mechanism. In their work performed by Lucas et al.²⁶⁰⁾ for an UFG copper produced by equal channel angular pressing (ECAP), they found also that the notch sensitivity of UFG copper is higher than that of its conventional counterpart, as shown in Fig. 14.

Fig. 14

Notch sensitivity factor q in dependence on notch radius for copper elaborated by ECAP and its conventional counterpart.²⁶⁰⁾

5. Conclusions and Prospects

In this paper, the mechanical properties including tension and fatigue in relation with different parameters were overviewed for materials processed by SSPD. Based on the elements reviewed and discussed in the present paper, some conclusions can be drawn and some prospects are given as follows:

1. (1)    SSPD has been widely studied for a large variety of metallic materials under different loading conditions, including monotonic and cyclic loadings. In general, an enhancement in mechanical strength after SSPD can be observed compared to the untreated state if the conditions of the SSPD processes are well chosen. However under fatigue loading, even if CRS plays a positive role, the presence of excessive roughness or even micro-cracks induced by over-peening could annihilate this beneficial effect.
2. (2)    The enhancement or deterioration of fatigue strength after SSPD is mainly attributed to the combined effect of gradient microstructure, CRS field and surface integrity. The nanostructured layer can play an important role in enhancing fatigue strength through increasing the yield stress of materials. CRS is also a crucial beneficial factor when the load level is not too high (so that the residual stress is not quickly relaxed) or too low (so that the crack initiation is shifted inwards). As for surface integrity, it is the main detrimental factor for fatigue resistance.
3. (3)    The microstructure changes in the SSPD affected region of various types of materials can be systematically investigated in order to understand the process of crack initiation including onset of microplastic deformation and its further development under cyclic loading. This type of information could be useful for understanding the inherent damage properties of SSPD processed materials, and to build a more quantitative strength limit distribution in the SSPD affected region.
4. (4)    In terms of modelling, work in microscopic scale for example using single crystal plasticity method and micro-macro transition method can be conducted to understand the effects of SSPD induced kinematic hardening on mechanical properties, especially the properties under cyclic loading. For this purpose, some well-designed experimental work should also be carried out, on the one hand to fit the parameters involved in the models, and on the other hand to validate the results of modelling and simulation.

REFERENCES

• 1)   M.  Wen,  G.  Liu,  J.  Gu,  W.  Guan and  J.  Lu: Appl. Surf. Sci. 255 (2009) 6097–6102. doi:10.1016/j.apsusc.2009.01.048
• 2)   H.W.  Zhang,  L.  Wang,  Z.K.  Hei,  G.  Liu,  J.  Lu and  K.  Lu: Zeitschrift fuer Met. Res. Adv. Tech. 94 (2003) 1143–1147.
• 3)   M.  Novelli,  J.J.  Fundenberger,  P.  Bocher and  T.  Grosdidier: Appl. Surf. Sci. 389 (2016) 1169–1174. doi:10.1016/j.apsusc.2016.08.009
• 4)   O.  Unal and  R.  Varol: Appl. Surf. Sci. 351 (2015) 289–295. doi:10.1016/j.apsusc.2015.05.093
• 5)   J.E.  Merwin and  K.L.  Johnson: Proc. Inst. Mech. Eng. 177 (1963) 676–690. doi:10.1243/PIME_PROC_1963_177_052_02
• 6)   C.C.  Wong,  A.  Hartawan and  W.K.  Teo: Procedia CIRP 13 (2014) 350–354. doi:10.1016/j.procir.2014.04.059
• 7)   K.  Edalati et al.: Mater. Res. Lett. 10 (2022) 163–256. doi:10.1080/21663831.2022.2029779
• 8)   D.  Arola,  M.L.  Mccain,  S.  Kunaporn and  M.  Ramulu: Wear 249 (2001) 943–950. doi:10.1016/S0043-1648(01)00826-2
• 9)   M.  Umemoto,  Y.  Todaka and  K.  Tsuchiya: Mater. Trans. 44 (2003) 1488–1493. doi:10.2320/matertrans.44.1488
• 10)   J.L.  Liu,  M.  Umemoto,  Y.  Todaka and  K.  Tsuchiya: J. Mater. Sci. 42 (2007) 7716–7720. doi:10.1007/s10853-007-1659-x
• 11)   J.  Champaigne: Shot Peen. Mag. 20 (2006) 12–38.
• 12)   O.  Unal and  R.  Varol: Appl. Surf. Sci. 351 (2015) 289–295. doi:10.1016/j.apsusc.2015.05.093
• 13)   Y.  Todaka,  M.  Umemoto and  K.  Tsuchiya: Mater. Trans. 45 (2004) 376–379. doi:10.2320/matertrans.45.376
• 14)   K.  Lu and  J.  Lu: Mater. Sci. Eng. A 375–377 (2004) 38–45. doi:10.1016/j.msea.2003.10.261
• 15)   Y.  Wei,  B.  Liu,  L.  Hou,  B.  Xu and  G.  Liu: J. Alloy. Compd. 452 (2008) 336–342. doi:10.1016/j.jallcom.2006.11.079
• 16)   Y.  Lin,  J.  Lu,  L.  Wang,  T.  Xu and  Q.  Xue: Acta Mater. 54 (2006) 5599–5605. doi:10.1016/j.actamat.2006.08.014
• 17)   H.W.  Zhang,  Z.K.  Hei,  G.  Liu,  J.  Lu and  K.  Lu: Acta Mater. 51 (2003) 1871–1881. doi:10.1016/S1359-6454(02)00594-3
• 18)   T.  Grosdidier and  M.  Novelli: Mater. Trans. 60 (2019) 1344–1355. doi:10.2320/matertrans.MF201929
• 19)   G.  Liu,  J.  Lu and  K.  Lu: Mater. Sci. Eng. A 286 (2000) 91–95. doi:10.1016/S0921-5093(00)00686-9
• 20)   X.  Wu,  N.  Tao,  Y.  Hong,  B.  Xu,  J.  Lu and  K.  Lu: Acta Mater. 50 (2002) 2075–2084. doi:10.1016/S1359-6454(02)00051-4
• 21)   F.  Yin,  M.  Rakita,  S.  Hu and  Q.  Han: Surf. Eng. 33 (2017) 651–666. doi:10.1080/02670844.2017.1278838
• 22)   M.  Rakita,  M.  Wang,  Q.  Han,  Y.  Liu and  F.  Yin: Int. J. Comput. Mater. Sci. Surf. Eng. 5 (2013) 189. doi:10.1504/IJCMSSE.2013.056948
• 23)   G.  Liu,  J.  Lu and  K.  Lu: Mater. Sci. Eng. A 286 (2000) 91–95. doi:10.1016/S0921-5093(00)00686-9
• 24)   Y.  Li,  Z.  Lu,  T.  Li,  D.  Li,  J.  Lu,  P.K.  Liaw and  Y.  Zou: Metals 10 (2020) 1–13. doi:10.3390/met10060831
• 25)   R.  Liu,  S.  Yuan,  N.  Lin and  Q.  Zeng: J. Mater. Res. Technol. 11 (2021) 351–377. doi:10.1016/j.jmrt.2021.01.013
• 26)   M.K.  Khan,  M.E.  Fitzpatrick,  Q.Y.  Wang,  Y.S.  Pyoun and  A.  Amanov: Fatigue Fract. Eng. Mater. Struct. 41 (2018) 844–855. doi:10.1111/ffe.12732
• 27)   M.S.  Kim,  S.H.  Park,  Y.S.  Pyun and  D.S.  Shim: J. Mater. Res. Technol. 9 (2020) 15102–15122. doi:10.1016/j.jmrt.2020.10.092
• 28)   B.N.  Mordyuk and  G.I.  Prokopenko: J. Sound Vib. 308 (2007) 855–866. doi:10.1016/j.jsv.2007.03.054
• 29)   J.  Lago,  L.  Trško,  M.  Jambor,  F.  Nový,  O.  Bokůvka,  M.  Mičian and  F.  Pastorek: Metals 9 (2019) 619. doi:10.3390/met9060619
• 30)   S.  Roy,  J.W.  Fisher and  B.T.  Yen: Int. J. Fatigue 25 (2003) 1239–1247. doi:10.1016/S0142-1123(03)00151-8
• 31)   Z.  Fan,  H.  Xu,  D.  Li,  L.  Zhang and  L.  Liao: Procedia Eng. 27 (2012) 1718–1722. doi:10.1016/j.proeng.2011.12.641
• 32)   S.  Roy and  J.  Fisher: Int. J. Steel Struct. 5 (2005) 241–252.
• 33)   D.  Chen,  J.  Liu,  D.  Chen,  R.  Li,  C.  Ma,  M.  Wang,  P.  Dong,  D.  Lang,  Y.  Hu and  K.  Liu: Mater. Chem. Phys. 279 (2022) 125741. doi:10.1016/j.matchemphys.2022.125741
• 34)   N.  Ao,  D.  Liu,  X.  Zhang,  J.  Zhang and  S.  Wu: Int. J. Fatigue 158 (2022) 106732. doi:10.1016/j.ijfatigue.2022.106732
• 35)   D.  Liu,  D.  Liu,  X.  Zhang,  C.  Liu and  N.  Ao: Mater. Sci. Eng. A 726 (2018) 69–81. doi:10.1016/j.msea.2018.04.033
• 36)   C.  Duan,  S.  Qu,  X.  Hu,  S.  Jia and  X.  Li: Int. J. Fatigue 158 (2022) 106733. doi:10.1016/j.ijfatigue.2022.106733
• 37)   M.  Han,  H.  Zhang,  Z.  Yan,  K.  Li and  W.  Wang: Mater. Lett. 328 (2022) 133200. doi:10.1016/j.matlet.2022.133200
• 38)   J.  Zou,  Y.  Liang,  Y.  Jiang,  C.  Yin,  C.  Huang,  D.  Liu,  Z.  Zhu and  Y.  Wu: Int. J. Fatigue 167 (2023) 107383. doi:10.1016/j.ijfatigue.2022.107383
• 39)   W.L.  Li,  N.R.  Tao and  K.  Lu: Scr. Mater. 59 (2008) 546–549. doi:10.1016/j.scriptamat.2008.05.003
• 40)   C.  Yang,  X.  Jiang,  W.  Zhang and  X.  Wang: Mater. Charact. 194 (2022) 112493. doi:10.1016/j.matchar.2022.112493
• 41)   D.  Geng,  Q.  Sun,  C.  Xin and  L.  Xiao: Nanomaterials 11 (2021) 3125. doi:10.3390/nano11113125
• 42)   H.W.  Huang,  Z.B.  Wang,  J.  Lu and  K.  Lu: Acta Mater. 87 (2015) 150–160. doi:10.1016/j.actamat.2014.12.057
• 43)   K.  Zhang,  Z.B.  Wang and  K.  Lu: Mater. Res. Lett. 5 (2017) 258–266. doi:10.1080/21663831.2016.1253625
• 44)   Z.  Liu,  H.  Zhang,  Z.  Yan,  P.K.  Liaw and  P.  Dong: Mater. Sci. Eng. A 822 (2021) 141669. doi:10.1016/j.msea.2021.141669
• 45)   L.  Carneiro,  X.  Wang and  Y.  Jiang: Int. J. Fatigue 134 (2020) 105469. doi:10.1016/j.ijfatigue.2019.105469
• 46)   Y.B.  Lei,  Z.B.  Wang,  J.L.  Xu and  K.  Lu: Acta Mater. 168 (2019) 133–142. doi:10.1016/j.actamat.2019.02.008
• 47)   S.  Bagherifard and  M.  Guagliano: Eng. Fract. Mech. 81 (2012) 56–68. doi:10.1016/j.engfracmech.2011.06.011
• 48)   S.  Bagheri and  M.  Guagliano: Surf. Eng. 25 (2009) 3–14. doi:10.1179/026708408X334087
• 49)   S.  Bagherifard,  I.  Fernandez-Pariente,  R.  Ghelichi and  M.  Guagliano: Int. J. Fatigue 65 (2014) 64–70. doi:10.1016/j.ijfatigue.2013.08.022
• 50)   C.S.  Montross,  T.  Wei,  L.  Ye,  G.  Clark and  Y.W.  Mai: Int. J. Fatigue 24 (2002) 1021–1036. doi:10.1016/S0142-1123(02)00022-1
• 51)   Y.K.  Zhang,  J.Z.  Lu,  X.D.  Ren,  H.B.  Yao and  H.X.  Yao: Mater. Des. 30 (2009) 1697–1703. doi:10.1016/j.matdes.2008.07.017
• 52)   J.  Zhao,  X.  Pan,  J.  Li,  Z.  Huang,  Q.  Kan,  G.  Kang,  L.  Zhou and  X.  Zhang: Int. J. Mech. Sci. 213 (2022) 106874. doi:10.1016/j.ijmecsci.2021.106874
• 53)   H.F.  Lu,  K.Y.  Luo,  L.J.  Wu,  C.Y.  Cui and  J.Z.  Lu: J. Alloy. Compd. 770 (2019) 732–741. doi:10.1016/j.jallcom.2018.08.161
• 54)   P.K.  Dwivedi,  R.  Vinjamuri,  A.K.  Rai,  P.  Ganesh,  K.  Ranganathan,  K.S.  Bindra and  K.  Dutta: Int. J. Fatigue 163 (2022) 107033. doi:10.1016/j.ijfatigue.2022.107033
• 55)   K.  Yang,  Q.  Huang,  B.  Zhong,  Q.  Wang,  Q.  Chen,  Y.  Chen,  N.  Su and  H.  Liu: Int. J. Fatigue 141 (2020) 105868. doi:10.1016/j.ijfatigue.2020.105868
• 56)   E.  Maawad,  H.G.  Brokmeier,  L.  Wagner,  Y.  Sano and  C.  Genzel: Surf. Coat. Technol. 205 (2011) 3644–3650. doi:10.1016/j.surfcoat.2011.01.001
• 57)   H.  Gu,  P.  Yan,  L.  Jiao,  S.  Chen,  Y.  Song,  S.  Zou and  X.  Wang: Int. J. Fatigue 166 (2023) 107241. doi:10.1016/j.ijfatigue.2022.107241
• 58)   K.  Dai and  L.  Shaw: Mater. Sci. Eng. A 463 (2007) 46–53. doi:10.1016/j.msea.2006.07.159
• 59)   A.M.  Gatey,  S.S.  Hosmani and  R.P.  Singh: Surf. Eng. 32 (2016) 69–78. doi:10.1179/1743294415Y.0000000056
• 60)   B.  Wu,  J.  Zhang,  L.  Zhang,  Y.S.  Pyoun and  R.I.  Murakami: Appl. Surf. Sci. 321 (2014) 318–330. doi:10.1016/j.apsusc.2014.09.068
• 61)   X.  Yang,  X.  Ling and  J.  Zhou: Int. J. Fatigue 61 (2014) 28–38. doi:10.1016/j.ijfatigue.2013.12.003
• 62)   K.  Miková,  S.  Bagherifard,  O.  Bokuvka,  M.  Guagliano and  L.  Trško: Int. J. Fatigue 55 (2013) 33–42. doi:10.1016/j.ijfatigue.2013.04.021
• 63)   F.  Yin,  S.  Hu,  L.  Hua,  X.  Wang,  S.  Suslov and  Q.  Han: Metall. Mater. Trans. A 46 (2015) 1253–1261. doi:10.1007/s11661-014-2689-z
• 64)   S.  Bagherifard,  S.  Slawik,  I.  Fernández-Pariente,  C.  Pauly,  F.  Mücklich and  M.  Guagliano: Mater. Des. 102 (2016) 68–77. doi:10.1016/j.matdes.2016.03.162
• 65)   D.M.  Ba,  S.N.  Ma,  F.J.  Meng and  C.Q.  Li: Surf. Coat. Technol. 202 (2007) 254–260. doi:10.1016/j.surfcoat.2007.05.033
• 66)   D.  Li,  Y.  Wei,  L.  Hou and  W.  Lin: J. Iron Steel Res. Int. 19 (2012) 38–46. doi:10.1016/S1006-706X(12)60071-5
• 67)   M.  Novelli,  P.  Bocher and  T.  Grosdidier: Mater. Charact. 139 (2018) 197–207. doi:10.1016/j.matchar.2018.02.028
• 68)   S.  Lu,  Z.  Wang and  K.  Lu: J. Mater. Sci. Technol. 26 (2010) 258–263. doi:10.1016/S1005-0302(10)60043-6
• 69)   W.  Liu,  C.  Zhang,  Z.  Yang and  Z.  Xia: Appl. Surf. Sci. 292 (2014) 556–562. doi:10.1016/j.apsusc.2013.12.008
• 70)   D.A.  Lesyk,  H.  Soyama,  B.N.  Mordyuk,  V.V.  Dzhemelinskyi,  S.  Martinez,  N.I.  Khripta and  A.  Lamikiz: J. Mater. Eng. Perform. 28 (2019) 5307–5322. doi:10.1007/s11665-019-04273-y
• 71)   M.  Umemoto,  K.  Todaka and  K.  Tsuchiya: Mater. Sci. Eng. A 375–377 (2004) 899–904. doi:10.1016/j.msea.2003.10.198
• 72)   W.Y.  Tsai,  J.C.  Huang,  Y.J.  Gao,  Y.L.  Chung and  G.R.  Huang: Scr. Mater. 103 (2015) 45–48. doi:10.1016/j.scriptamat.2015.03.003
• 73)   A.  Wick,  V.  Schulze and  O.  Vöhringer: Mater. Sci. Eng. A 293 (2000) 191–197. doi:10.1016/S0921-5093(00)01035-2
• 74)   T.  Roland,  D.  Retraint,  K.  Lu and  J.  Lu: Mater. Sci. Eng. A 445–446 (2007) 281–288. doi:10.1016/j.msea.2006.09.041
• 75)   B.  Wu,  P.  Wang,  Y.S.  Pyoun,  J.  Zhang and  R.  Murakami: Surf. Coat. Technol. 213 (2012) 271–277. doi:10.1016/j.surfcoat.2012.10.063
• 76)   X.J.  Cao,  Y.S.  Pyoun and  R.  Murakami: Appl. Surf. Sci. 256 (2010) 6297–6303. doi:10.1016/j.apsusc.2010.04.007
• 77)   Z.  Sun,  D.  Retraint,  T.  Baudin,  A.L.  Helbert,  F.  Brisset,  M.  Chemkhi,  J.  Zhou and  P.  Kanouté: Mater. Charact. 124 (2017) 117–121. doi:10.1016/j.matchar.2016.12.017
• 78)   Y.S.  Zhang,  Z.  Han,  K.  Wang and  K.  Lu: Wear 260 (2006) 942–948. doi:10.1016/j.wear.2005.06.010
• 79)   L.  Yang,  N.R.  Tao,  K.  Lu and  L.  Lu: Scr. Mater. 68 (2013) 801–804. doi:10.1016/j.scriptamat.2013.01.031
• 80)   M.  Sato,  N.  Tsuji,  Y.  Minamino and  Y.  Koizumi: Sci. Technol. Adv. Mater. 5 (2004) 145–152. doi:10.1016/j.stam.2003.10.015
• 81)   M.  Mhaede: Mater. Des. 41 (2012) 61–66. doi:10.1016/j.matdes.2012.04.056
• 82)   V.  Pandey,  J.K.  Singh,  K.  Chattopadhyay,  N.C.S.  Srinivas and  V.  Singh: J. Alloy. Compd. 723 (2017) 826–840. doi:10.1016/j.jallcom.2017.06.310
• 83)   B.  Hadzima,  F.  Novy,  L.  Trsko,  F.  Pastorek,  M.  Jambor and  S.  Fintova: Int. J. Adv. Manuf. Technol. 93 (2017) 3315–3323. doi:10.1007/s00170-017-0776-1
• 84)   P.  Dong,  Z.  Liu,  X.  Zhai,  Z.  Yan,  W.  Wang and  P.K.  Liaw: Int. J. Fatigue 124 (2019) 15–25. doi:10.1016/j.ijfatigue.2019.02.023
• 85)   X.  An,  C.A.  Rodopoulos,  E.S.  Statnikov,  V.N.  Vitazev and  O.V.  Komlkov: J. Mater. Eng. Perform. 15 (2006) 355–364. doi:10.1361/105994906X108693
• 86)   J.  Zhang,  Y.  Jian,  X.  Zhao,  D.  Meng,  F.  Pan and  Q.  Han: J. Magnes. Alloy. 9 (2021) 1187–1200. doi:10.1016/j.jma.2020.11.012
• 87)   A.  Amanov,  O.V.  Penkov,  Y.S.  Pyun and  D.E.  Kim: Tribol. Int. 54 (2012) 106–113. doi:10.1016/j.triboint.2012.04.024
• 88)   G.  Chen,  J.  Gao,  Y.  Cui,  H.  Gao,  X.  Guo and  S.  Wu: J. Alloy. Compd. 735 (2018) 536–546. doi:10.1016/j.jallcom.2017.11.141
• 89)   L.  Jin,  W.  Cui,  X.  Song and  L.  Zhou: Appl. Surf. Sci. 347 (2015) 553–560. doi:10.1016/j.apsusc.2015.04.137
• 90)   Y.-F.  Li,  C.  Chen,  J.  Ranabhat and  Y.-F.  Shen: Rare Met. 42 (2023) 1343–1352. doi:10.1007/s12598-017-0988-4
• 91)   M.  Wen,  G.  Liu,  J.  Gu,  W.  Guan and  J.  Lu: Surf. Coat. Technol. 202 (2008) 4728–4733. doi:10.1016/j.surfcoat.2008.04.054
• 92)   S.  Yao,  G.  Wang,  H.  Yu,  J.  Wang,  K.  Li,  S.  Liu,  X.  Zhang and  S.  Tu: Int. J. Fatigue 164 (2022) 107076. doi:10.1016/j.ijfatigue.2022.107076
• 93)   P.  Kumar,  G.S.  Mahobia,  V.  Singh and  K.  Chattopadhyay: Int. J. Fatigue 166 (2023) 107289. doi:10.1016/j.ijfatigue.2022.107289
• 94)   D.  He,  L.  Li,  Y.  Zhang,  J.  Chi,  H.  Zhang,  R.  Sun,  Z.  Che,  H.  Zhang and  W.  Guo: J. Alloy. Compd. 935 (2023) 168139. doi:10.1016/j.jallcom.2022.168139
• 95)   A.  Heinzelmeier,  A.  Guitton,  M.  Novelli,  W.  Yu and  T.  Grosdidier: J. Alloy. Compd. 950 (2023) 169946. doi:10.1016/j.jallcom.2023.169946
• 96)   S.  Anand Kumar,  S.  Ganesh Sundara Raman and  T.S.N.  Sankara Narayanan: Trans. Indian Inst. Met. 65 (2012) 473–477. doi:10.1007/s12666-012-0154-5
• 97)   A.  Amanov,  Y.S.  Pyun,  J.H.  Kim,  C.M.  Suh,  I.S.  Cho,  H.D.  Kim,  Q.  Wang and  M.K.  Khan: Fatigue Fract. Eng. Mater. Struct. 38 (2015) 1266–1273. doi:10.1111/ffe.12330
• 98)   S.  Kumar,  K.  Chattopadhyay,  V.  Singh,  D.V.V.  Satyanarayana and  V.  Kumar: Mater. Charact. 159 (2020) 110066. doi:10.1016/j.matchar.2019.110066
• 99)   A.  Klumpp,  M.  Ruf,  S.  Dietrich and  V.  Schulze: Eng. Fract. Mech. 269 (2022) 108551. doi:10.1016/j.engfracmech.2022.108551
• 100)   S.  Kumar,  G.  Sudhakar Rao,  K.  Chattopadhyay,  G.S.  Mahobia,  N.C.  Santhi Srinivas and  V.  Singh: Mater. Des. 62 (2014) 76–82. doi:10.1016/j.matdes.2014.04.084
• 101)   A.  Gill,  A.  Telang,  S.R.  Mannava,  D.  Qian,  Y.S.  Pyoun,  H.  Soyama and  V.K.  Vasudevan: Mater. Sci. Eng. A 576 (2013) 346–355. doi:10.1016/j.msea.2013.04.021
• 102)   Z.  Qin,  B.  Li,  R.  Chen,  H.  Zhang,  H.  Xue,  C.  Yao,  L.  Tan,  Z.  Qin,  B.  Li,  R.  Chen,  H.  Zhang,  H.  Xue and  C.  Yao: Int. J. Fatigue 168 (2023) 107429. doi:10.1016/j.ijfatigue.2022.107429
• 103)   I.  Karademir,  O.  Unal,  S.  Ates,  H.  Gokce and  M.S.  Gok: Acta Phys. Pol. A 131 (2017) 487–489. doi:10.12693/APhysPolA.131.487
• 104)   P.  Wei,  P.  Hua,  M.  Xia,  K.  Yan,  H.  Lin,  S.  Yi,  J.  Lu,  F.  Ren and  Q.  Sun: Acta Mater. 240 (2022) 118269. doi:10.1016/j.actamat.2022.118269
• 105)   S.  González,  J.  Fornell,  E.  Pellicer,  S.  Suriñach,  M.D.  Baró,  A.L.  Greer,  F.J.  Belzunce and  J.  Sort: Appl. Phys. Lett. 103 (2013) 211907. doi:10.1063/1.4833017
• 106)   R.  Wei,  L.  Chen,  J.  Tao,  S.  Guo,  Z.  Han and  F.  Li: Mater. Trans. 58 (2017) 757–760. doi:10.2320/matertrans.M2016349
• 107)   T.G.  Nieh,  Y.  Yang,  J.  Lu and  C.T.  Liu: Prog. Nat. Sci. Mater. Int. 22 (2012) 355–363. doi:10.1016/j.pnsc.2012.09.006
• 108)   N.  Liang,  X.  Wang,  Y.  Cao,  Y.  Li,  Y.  Zhu and  Y.  Zhao: Entropy 22 (2020) 1074. doi:10.3390/e22101074
• 109)   W.  Lu,  X.  Luo,  D.  Ning,  M.  Wang,  C.  Yang,  M.  Li,  Y.  Yang,  P.  Li and  B.  Huang: J. Mater. Sci. Technol. 112 (2022) 195–201. doi:10.1016/j.jmst.2021.09.058
• 110)   Z.  Wang,  L.  Guo,  W.  Xia,  Z.  Yuan,  Y.  Cao,  S.  Ni and  M.  Song: Mater. Charact. 161 (2020) 110169. doi:10.1016/j.matchar.2020.110169
• 111)   L.  Guo,  W.  Wu,  S.  Ni,  Z.  Yuan,  Y.  Cao,  Z.  Wang and  M.  Song: J. Alloy. Compd. 841 (2020) 155688. doi:10.1016/j.jallcom.2020.155688
• 112)   Z.  An,  S.  Mao,  Y.  Liu,  H.  Zhou,  Y.  Zhai,  Z.  Tian,  C.  Liu,  Z.  Zhang and  X.  Han: J. Mater. Sci. Technol. 92 (2021) 195–207. doi:10.1016/j.jmst.2021.02.059
• 113)   Y.  Chen,  J.  Du,  S.  Deng,  L.  Tian and  K.  Hu: J. Alloy. Compd. 934 (2023) 168023. doi:10.1016/j.jallcom.2022.168023
• 114)   X.  Wang,  S.  Ma,  D.  Hu,  C.  Xu,  X.  Luo and  Z.  Tang: Int. J. Fatigue 156 (2022) 106675. doi:10.1016/j.ijfatigue.2021.106675
• 115)  A. Morançais, M. Fèvre, M. Francois, N. Guel, S. Kruch, P. Kanouté and A. Longuet: 13th Int. Symp. Superalloys (Superalloys 2016) (2016).
• 116)   S.  Sun,  L.  Li,  C.  Hu,  Q.  Li and  T.  Yuan: Tribol. Lett. 70 (2022) 1–13. doi:10.1007/s11249-022-01637-9
• 117)   X.  Wang,  C.  Xu,  A.  Zhai,  M.  Liu,  X.  Huang,  K.  Tian,  X.  Luo,  C.  Liu,  Z.  Tang and  Z.  Zhao: J. Alloy. Compd. 933 (2023) 167796. doi:10.1016/j.jallcom.2022.167796
• 118)   Y.M.  Xing and  J.  Lu: J. Mater. Process. Technol. 152 (2004) 56–61. doi:10.1016/j.jmatprotec.2004.02.057
• 119)   S.  Kumar,  K.  Chattopadhyay,  S.R.  Singh and  V.  Singh: Int. J. Surface Sci. Eng. 11 (2017) 23–35. doi:10.1504/IJSURFSE.2017.082949
• 120)   N.R.  Tao,  Z.B.  Wang,  W.P.  Tong,  M.L.  Sui,  J.  Lu and  K.  Lu: Acta Mater. 50 (2002) 4603–4616. doi:10.1016/S1359-6454(02)00310-5
• 121)   X.Y.  Shi,  Y.  Liu,  D.J.  Li,  B.  Chen,  X.Q.  Zeng,  J.  Lu and  W.J.  Ding: Mater. Sci. Eng. A 630 (2015) 146–154. doi:10.1016/j.msea.2015.02.009
• 122)   N.R.  Tao and  K.  Lu: Scr. Mater. 60 (2009) 1039–1043. doi:10.1016/j.scriptamat.2009.02.008
• 123)   M.  Rostami,  R.  Miresmaeili and  A.  Heydari Astaraee: Met. Mater. Int. 29 (2023) 948–967. doi:10.1007/s12540-022-01286-6
• 124)   M.  Kahlin,  H.  Ansell,  D.  Basu,  A.  Kerwin,  L.  Newton,  B.  Smith and  J.J.  Moverare: Int. J. Fatigue 134 (2020) 105497. doi:10.1016/j.ijfatigue.2020.105497
• 125)   Q.  Portella,  M.  Chemkhi and  D.  Retraint: Mater. Charact. 167 (2020) 110463. doi:10.1016/j.matchar.2020.110463
• 126)   X.  Li,  L.  Lu,  J.  Li,  X.  Zhang and  H.  Gao: Nat. Rev. Mater. 5 (2020) 706–723. doi:10.1038/s41578-020-0212-2
• 127)   K.  Wang,  N.R.  Tao,  G.  Liu,  J.  Lu and  K.  Lu: Acta Mater. 54 (2006) 5281–5291. doi:10.1016/j.actamat.2006.07.013
• 128)   S.  Bahl,  S.  Suwas,  T.  Ungàr and  K.  Chatterjee: Acta Mater. 122 (2017) 138–151. doi:10.1016/j.actamat.2016.09.041
• 129)   H.Q.  Sun,  Y.N.  Shi,  M.X.  Zhang and  K.  Lu: Acta Mater. 55 (2007) 975–982. doi:10.1016/j.actamat.2006.09.018
• 130)   H.  Liu,  J.  Gan,  C.  Jiang,  W.  Wu and  M.  Guagliano: Surf. Coat. Technol. 441 (2022) 128601. doi:10.1016/j.surfcoat.2022.128601
• 131)   X.  Yang,  H.  Pan,  J.  Zhang,  H.  Gao,  B.  Shu,  Y.  Gong and  X.  Zhu: Mater. Trans. 60 (2019) 1543–1552. doi:10.2320/matertrans.MF201911
• 132)   X.  Yue,  S.  Hu,  X.  Wang,  Y.  Liu,  F.  Yin and  L.  Hua: Mater. Sci. Eng. A 836 (2022) 142721. doi:10.1016/j.msea.2022.142721
• 133)   N.  Tao,  H.  Zhang,  J.  Lu and  K.  Lu: Mater. Trans. 44 (2003) 1919–1925. doi:10.2320/matertrans.44.1919
• 134)   J.Z.  Lu,  L.J.  Wu,  G.F.  Sun,  K.Y.  Luo,  Y.K.  Zhang,  J.  Cai,  C.Y.  Cui and  X.M.  Luo: Acta Mater. 127 (2017) 252–266. doi:10.1016/j.actamat.2017.01.050
• 135)   L.  Kang,  X.  Mi,  X.  Zhang,  L.  Xin,  Y.  Lu and  T.  Shoji: Mater. Charact. 195 (2023) 112498. doi:10.1016/j.matchar.2022.112498
• 136)   X.  Wu,  N.  Tao,  Y.  Hong,  G.  Liu,  B.  Xu,  J.  Lu and  K.  Lu: Acta Mater. 53 (2005) 681–691. doi:10.1016/j.actamat.2004.10.021
• 137)   Y.  Shen,  C.  Wen,  X.  Yang,  Y.  Pang,  L.  Sun,  J.  Tao,  Y.  Gong and  X.  Zhu: J. Mater. Eng. Perform. 24 (2015) 5058–5064. doi:10.1007/s11665-015-1797-2
• 138)   K.A.  Darling,  M.A.  Tschopp,  A.J.  Roberts,  J.P.  Ligda and  L.J.  Kecskes: Scr. Mater. 69 (2013) 461–464. doi:10.1016/j.scriptamat.2013.05.036
• 139)   Y.K.  Gao,  M.  Yao and  J.K.  Li: Metall. Mater. Trans. A 33 (2002) 1775–1778. doi:10.1007/s11661-002-0186-2
• 140)   S.  Wang,  Y.  Li,  M.  Yao and  R.  Wang: J. Mater. Process. Technol. 73 (1998) 64–73. doi:10.1016/S0924-0136(97)00213-6
• 141)   J.  Zhou,  K.  Cui and  Z.  Sun: Int. J. Solids Struct. 254–255 (2022) 111934. doi:10.1016/j.ijsolstr.2022.111934
• 142)   J.  Zhou,  K.  Cui,  Z.  Xu,  Z.  Sun,  B.  Guelorget and  D.  Retraint: Int. J. Mech. Sci. 233 (2022) 107688. doi:10.1016/j.ijmecsci.2022.107688
• 143)   K.A.  Soady: Mater. Sci. Technol. 29 (2013) 637–651. doi:10.1179/1743284713Y.0000000222
• 144)   P.  Starker,  H.  Wohlfahrt and  E.  Macherauch: Fatigue Fract. Eng. Mater. Struct. 1 (1979) 319–327. doi:10.1111/j.1460-2695.1979.tb00388.x
• 145)   D.  Gallitelli,  D.  Retraint and  E.  Rouhaud: Adv. Mater. Res. 996 (2014) 964–968. doi:10.4028/www.scientific.net/AMR.996.964
• 146)   P.  Gao,  Z.  Sun and  D.  Retraint: Metals 12 (2022) 775. doi:10.3390/met12050775
• 147)   Y.  Samih,  B.  Beausir,  B.  Bolle and  T.  Grosdidier: Mater. Charact. 83 (2013) 129–138. doi:10.1016/j.matchar.2013.06.006
• 148)   J.  Zhou and  Z.  Sun: Int. J. Solids Struct. 244–245 (2022) 111586. doi:10.1016/j.ijsolstr.2022.111586
• 149)   J.  Zhou,  X.  Xu,  Z.  Sun,  D.  Retraint and  X.  Zhang: Int. J. Solids Struct. 262–263 (2023) 112063. doi:10.1016/j.ijsolstr.2022.112063
• 150)   J.  Zhou,  D.  Retraint,  Z.  Sun and  P.  Kanouté: Surf. Coat. Technol. 349 (2018) 556–566. doi:10.1016/j.surfcoat.2018.06.041
• 151)   P.  Maurel,  L.  Weiss,  T.  Grosdidier and  P.  Bocher: Int. J. Fatigue 140 (2020) 105792. doi:10.1016/j.ijfatigue.2020.105792
• 152)   B.  Arifvianto Suyitno and  M.  Mahardika: Appl. Surf. Sci. 258 (2012) 4538–4543. doi:10.1016/j.apsusc.2012.01.021
• 153)   L.  Brasileiro,  Z.  Sun,  C.  Mabru,  R.  Chieragatti,  G.  Proust and  D.  Retraint: Procedia Struct. Integr. 38 (2022) 283–291. doi:10.1016/j.prostr.2022.03.029
• 154)   T.  Roland,  D.  Retraint,  K.  Lu and  J.  Lu: Scr. Mater. 54 (2006) 1949–1954. doi:10.1016/j.scriptamat.2006.01.049
• 155)   Y.  Liu,  B.  Jin and  J.  Lu: Mater. Sci. Eng. A 636 (2015) 446–451. doi:10.1016/j.msea.2015.03.068
• 156)   Y.M.  Wang,  K.  Wang,  D.  Pan,  K.  Lu,  K.J.  Hemker and  E.  Ma: Scr. Mater. 48 (2003) 1581–1586. doi:10.1016/S1359-6462(03)00159-3
• 157)   X.H.  Chen,  J.  Lu,  L.  Lu and  K.  Lu: Scr. Mater. 52 (2005) 1039–1044. doi:10.1016/j.scriptamat.2005.01.023
• 158)   Y.H.  Zhao,  Y.Z.  Guo,  Q.  Wei,  A.M.  Dangelewicz,  C.  Xu,  Y.T.  Zhu,  T.G.  Langdon,  Y.Z.  Zhou and  E.J.  Lavernia: Scr. Mater. 59 (2008) 627–630. doi:10.1016/j.scriptamat.2008.05.031
• 159)   D.  Mercier,  V.  Mandrillon,  G.  Parry,  M.  Verdier,  R.  Estevez,  Y.  Bréchet and  T.  Maindron: Thin Solid Films 638 (2017) 34–47. doi:10.1016/j.tsf.2017.07.040
• 160)   W.D.  Nix: Mater. Sci. Eng. A 234–236 (1997) 37–44. doi:10.1016/S0921-5093(97)00176-7
• 161)   Y.  Choi,  W.  Yong Choo and  D.  Kwon: Scr. Mater. 45 (2001) 1401–1406. doi:10.1016/S1359-6462(01)01176-9
• 162)   H.  ur Rehman,  K.  Durst,  S.  Neumeier,  A.B.  Parsa,  A.  Kostka,  G.  Eggeler and  M.  Göken: Mater. Sci. Eng. A 634 (2015) 202–208. doi:10.1016/j.msea.2015.03.045
• 163)   Y.  Wu,  B.  Guelorget,  Z.  Sun,  R.  Déturche and  D.  Retraint: Mater. Charact. 155 (2019) 109788. doi:10.1016/j.matchar.2019.109788
• 164)   Y.M.  Wang,  W.  Zhuang,  H.P.  Yang and  C.H.  Zhang: Rare Met. 38 (2019) 824–831. doi:10.1007/s12598-019-01302-6
• 165)   M.J.  Mayo,  R.W.  Siegel,  A.  Narayanasamy and  W.D.  Nix: J. Mater. Res. 5 (2011) 107.
• 166)   M.  Kolb,  J.M.  Wheeler,  H.N.  Mathur,  S.  Neumeier,  S.  Korte-Kerzel,  F.  Pyczak,  J.  Michler and  M.  Göken: Mater. Sci. Eng. A 665 (2016) 135–140. doi:10.1016/j.msea.2016.04.026
• 167)   Z.  Sun,  D.  Retraint,  B.  Guelorget and  L.  Waltz: Mater. Tech. 103 (2015) 304. doi:10.1051/mattech/2015028
• 168)   J.  Zhou,  Z.  Sun,  P.  Kanouté and  D.  Retraint: Mech. Mater. 127 (2018) 100–111. doi:10.1016/j.mechmat.2018.09.005
• 169)   J.  Zhou,  Z.  Sun,  P.  Kanouté and  D.  Retraint: Int. J. Fatigue 103 (2017) 309–317. doi:10.1016/j.ijfatigue.2017.06.011
• 170)   C.S.  Kumar,  K.  Chattopadhyay,  V.  Singh and  G.S.  Mahobia: Mater. Today Commun. 25 (2020) 101576. doi:10.1016/j.mtcomm.2020.101576
• 171)   H.  Mughrabi,  H.W.  Höppel and  M.  Kautz: Scr. Mater. 51 (2004) 807–812. doi:10.1016/j.scriptamat.2004.05.012
• 172)   V.  Pandey,  G.S.  Rao,  K.  Chattopadhyay,  N.C.  Santhi Srinivas and  V.  Singh: Mater. Sci. Eng. A 647 (2015) 201–211. doi:10.1016/j.msea.2015.09.021
• 173)   V.  Pandey,  K.  Chattopadhyay,  N.C.  Santhi Srinivas and  V.  Singh: Int. J. Fatigue 103 (2017) 426–435. doi:10.1016/j.ijfatigue.2017.06.033
• 174)   P.  Kumar,  G.S.  Mahobia,  V.  Singh and  K.  Chattopadhyay: Mater. Res. Express 6 (2019) 125413. doi:10.1088/2053-1591/ab59fd
• 175)   Y.  Chen,  F.  Liu,  C.  He,  L.  Li,  C.  Wang,  Y.  Liu and  Q.  Wang: J. Magnes. Alloy. 10 (2022) 614–626. doi:10.1016/j.jma.2021.07.028
• 176)   S.  Kumar,  K.  Chattopadhyay and  V.  Singh: J. Alloy. Compd. 724 (2017) 187–197. doi:10.1016/j.jallcom.2017.07.014
• 177)   V.  Pandey,  M.K.  Singh,  J.  Basu,  K.  Chattopadhyay,  N.C.S.  Srinivas and  V.  Singh: Surf. Coat. Technol. 404 (2020) 126431. doi:10.1016/j.surfcoat.2020.126431
• 178)   R.C.  McClung: Fatigue Fract. Eng. Mater. Struct. 30 (2007) 173–205. doi:10.1111/j.1460-2695.2007.01102.x
• 179)   R.  Ramos,  N.  Ferreira,  J.A.M.  Ferreira,  C.  Capela and  A.C.  Batista: Int. J. Fatigue 92 (2016) 87–95. doi:10.1016/j.ijfatigue.2016.06.022
• 180)   C.  Dureau,  M.  Arzaghi,  R.  Massion,  Y.  Nadot and  T.  Grosdidier: Mater. Sci. Eng. A 840 (2022) 142916. doi:10.1016/j.msea.2022.142916
• 181)   J.  Uusitalo,  L.P.  Karjalainen,  D.  Retraint and  M.  Palosaari: Mater. Sci. Forum 604–605 (2009) 239–248. doi:10.4028/www.scientific.net/MSF.604-605.239
• 182)   C.  Dureau,  M.  Novelli,  M.  Arzaghi,  R.  Massion,  P.  Bocher,  Y.  Nadot and  T.  Grosdidier: Metals 10 (2020) 100. doi:10.3390/met10010100
• 183)   D.  Li,  H.N.  Chen and  H.  Xu: Appl. Surf. Sci. 255 (2009) 3811–3816. doi:10.1016/j.apsusc.2008.10.037
• 184)   T.  Gao,  Z.  Sun,  H.  Xue and  D.  Retraint: Int. J. Fatigue 139 (2020) 105798. doi:10.1016/j.ijfatigue.2020.105798
• 185)   B.  Xia,  B.  Wang,  P.  Zhang,  C.  Ren,  Q.  Duan,  X.  Li and  Z.  Zhang: Int. J. Fatigue 161 (2022) 106891. doi:10.1016/j.ijfatigue.2022.106891
• 186)   C.  Zhang,  G.  Song,  Y.  Wang,  M.  Zheng,  G.  Xiao and  J.  Yang: Mater. Sci. Eng. A 794 (2020).
• 187)   J.W.  Tian,  J.C.  Villegas,  W.  Yuan,  D.  Fielden,  L.  Shaw,  P.K.  Liaw and  D.L.  Klarstrom: Mater. Sci. Eng. A 468–470 (2007) 164–170. doi:10.1016/j.msea.2006.10.150
• 188)   J.C.  Villegas,  L.L.  Shaw,  K.  Dai,  W.  Yuan,  J.  Tian,  P.K.  Liaw and  D.L.  Klarstrom: Philos. Mag. Lett. 85 (2005) 427–438. doi:10.1080/09500830500311705
• 189)   B.N.  Mordyuk and  G.I.  Prokopenko: Mater. Sci. Eng. A 437 (2006) 396–405. doi:10.1016/j.msea.2006.07.119
• 190)   X.  Yan,  S.  Yin,  C.  Chen,  R.  Jenkins,  R.  Lupoi,  R.  Bolot,  W.  Ma,  M.  Kuang,  H.  Liao,  J.  Lu and  M.  Liu: Mater. Res. Lett. 7 (2019) 327–333. doi:10.1080/21663831.2019.1609110
• 191)   D.  Li,  H.N.  Chen and  H.  Xu: Surf. Eng. 25 (2009) 15–20. doi:10.1179/174329409X389335
• 192)   D.  Yin,  D.  Wang,  H.  Jing and  L.  Huo: Mater. Des. 31 (2010) 3299–3307. doi:10.1016/j.matdes.2010.02.006
• 193)   Y.  Wang,  M.  Huang,  L.  Zhou,  Z.  Cong and  H.  Gao: J. Mater. Sci. Technol. 25 (2009) 513–515.
• 194)   X.  Zhao,  D.  Wang and  L.  Huo: Mater. Des. 32 (2011) 88–96. doi:10.1016/j.matdes.2010.06.030
• 195)   L.  An,  Y.T.  Sun,  S.P.  Lu and  Z.B.  Wang: Acta Metall. Sin. (Engl. Lett.) 33 (2020) 1252–1258. doi:10.1007/s40195-020-01046-8
• 196)   T.  Kakiuchi,  Y.  Uematsu,  N.  Hasegawa and  E.  Kondoh: J. Soc. Mater. Sci. Japan 65 (2016) 325–330. doi:10.2472/jsms.65.325
• 197)   Y.  Li,  D.  Retraint,  P.  Gao,  H.  Xue,  T.  Gao and  Z.  Sun: Metals 12 (2022) 785. doi:10.3390/met12050785
• 198)   M.  Benedetti,  V.  Fontanari,  M.  Bandini and  D.  Taylor: Int. J. Fatigue 61 (2014) 271–282. doi:10.1016/j.ijfatigue.2013.10.020
• 199)   M.  Benedetti,  V.  Fontanari,  M.  Allahkarami,  J.C.  Hanan and  M.  Bandini: Int. J. Fatigue 93 (2016) 133–147. doi:10.1016/j.ijfatigue.2016.08.015
• 200)   C.  Xin,  Q.  Sun,  L.  Xiao and  J.  Sun: J. Mater. Sci. 53 (2018) 12492–12503. doi:10.1007/s10853-018-2391-4
• 201)   K.  Shiozawa and  L.  Lu: Fatigue Fract. Eng. Mater. Struct. 25 (2002) 813–822. doi:10.1046/j.1460-2695.2002.00567.x
• 202)   N.J.  Myung,  L.  Wang and  N.S.  Choi: J. Mech. Sci. Technol. 35 (2021) 4963–4973. doi:10.1007/s12206-021-1015-0
• 203)   J.W.  Zhang,  L.T.  Lu,  K.  Shiozawa,  X.L.  Shen,  H.F.  Yi and  W.H.  Zhang: Mater. Sci. Eng. A 528 (2011) 1615–1622. doi:10.1016/j.msea.2010.10.086
• 204)   M.S.  Suh,  C.H.  Suh,  S.H.  Nahm and  C.M.  Suh: Adv. Mech. Eng. 7 (2015). doi:10.1155/2014/126848
• 205)   S.  Nishijima and  K.  Kanazawa: Fatigue Fract. Eng. Mater. Struct. 22 (1999) 601–607. doi:10.1046/j.1460-2695.1999.00206.x
• 206)   M.S.  Suh,  C.M.  Suh and  Y.S.  Pyun: Fatigue Fract. Eng. Mater. Struct. 36 (2013) 769–778. doi:10.1111/ffe.12045
• 207)   M.K.  Khan,  Y.J.  Liu,  Q.Y.  Wang,  Y.S.  Pyun and  R.  Kayumov: Fatigue Fract. Eng. Mater. Struct. 39 (2016) 427–438. doi:10.1111/ffe.12367
• 208)   X.  Cao,  L.  Xu,  X.  Xu and  Q.  Wang: Metals 8 (2018) 77. doi:10.3390/met8010077
• 209)   Z.  Qin,  B.  Li,  X.  Huang,  H.  Zhang,  R.  Chen,  M.  Adeel and  H.  Xue: Opt. Laser Technol. 149 (2022) 107897. doi:10.1016/j.optlastec.2022.107897
• 210)   Z.  Qin,  B.  Li,  R.  Chen,  H.  Zhang,  H.  Xue,  C.  Yao and  L.  Tan: Int. J. Fatigue 168 (2023) 107429. doi:10.1016/j.ijfatigue.2022.107429
• 211)   A.G.  Sanchez,  C.  You,  M.  Leering,  D.  Glaser,  D.  Furfari,  M.E.  Fitzpatrick,  J.  Wharton and  P.A.S.  Reed: Int. J. Fatigue 143 (2021) 106025. doi:10.1016/j.ijfatigue.2020.106025
• 212)   B.  Wang,  L.  Cheng and  D.  Li: Int. J. Fatigue 156 (2022) 106668. doi:10.1016/j.ijfatigue.2021.106668
• 213)   Q.Y.  Wang,  C.  Bathias,  N.  Kawagoishi and  Q.  Chen: Int. J. Fatigue 24 (2002) 1269–1274. doi:10.1016/S0142-1123(02)00037-3
• 214)  T. Dörr and L. Wagner: International Scientific Committee on Shot Peening-6 (ICSP-6), (1996) pp. 223–242.
• 215)   S.  Li,  W.  Liang,  H.  Yan,  Y.  Wang and  C.  Gu: Eng. Fract. Mech. 268 (2022) 108477. doi:10.1016/j.engfracmech.2022.108477
• 216)   A.  Wildeis,  H.J.  Christ and  R.  Brandt: Metals 12 (2022) 1085. doi:10.3390/met12071085
• 217)   M.  Ozturk,  F.  Husem,  I.  Karademir,  E.  Maleki,  A.  Amanov and  O.  Unal: Vacuum 207 (2023) 111552. doi:10.1016/j.vacuum.2022.111552
• 218)   C.  Zhang,  G.  Song,  Y.  Wang,  M.  Zheng,  G.  Xiao and  J.  Yang: Mater. Sci. Eng. A 794 (2020) 139831. doi:10.1016/j.msea.2020.139831
• 219)   Z.  Qin,  B.  Li,  H.  Zhang,  T.  Youani Andre Wilfried,  T.  Gao and  H.  Xue: Eng. Fail. Anal. 133 (2022) 106010. doi:10.1016/j.engfailanal.2021.106010
• 220)   Y.  Wang,  Y.  Zhang,  G.  Song,  W.  Niu,  Z.  Xu and  C.  Huang: Mater. Today Commun. 25 (2020) 101430. doi:10.1016/j.mtcomm.2020.101430
• 221)   E.R.  de los Rios,  A.  Walley,  M.T.  Milan and  G.  Hammersley: Int. J. Fatigue 17 (1995) 493–499. doi:10.1016/0142-1123(95)00044-T
• 222)   Y.K.  Gao and  X.R.  Wu: Acta Mater. 59 (2011) 3737–3747. doi:10.1016/j.actamat.2011.03.013
• 223)   B.  Yang,  B.  Feng,  Y.  Li,  Z.  Liao,  J.  Zhang,  S.  Xiao,  G.  Yang and  T.  Zhu: J. Traffic Transp. Eng. 21 (2021) 163–171 (in Chinese).
• 224)   K.S.  Kumar,  H.  Van Swygenhoven and  S.  Suresh: Acta Mater. 51 (2003) 5743–5774. doi:10.1016/j.actamat.2003.08.032
• 225)   Y.J.  Wei and  L.  Anand: J. Mechan. Phys. Solids 52 (2004) 2587–2616. doi:10.1016/j.jmps.2004.04.006
• 226)   N.  Shamsaei and  A.  Fatemi: Mater. Sci. Eng. A 527 (2010) 3015–3024. doi:10.1016/j.msea.2010.01.056
• 227)   T.  Hanlon,  E.D.  Tabachnikova and  S.  Suresh: Int. J. Fatigue 27 (2005) 1147–1158. doi:10.1016/j.ijfatigue.2005.06.035
• 228)   T.  Hanlon,  Y.N.  Kwon and  S.  Suresh: Scr. Mater. 49 (2003) 675–680. doi:10.1016/S1359-6462(03)00393-2
• 229)   I.  Altenberger,  B.  Scholtes,  U.  Martin and  H.  Oettel: Mater. Sci. Eng. A 264 (1999) 1–16. doi:10.1016/S0921-5093(98)01121-6
• 230)   Y.M.  Xing,  K.  Lu and  J.  Lu: Proc. Asian Pacific Conf. Fract. Strength Int. Conf. Adv. Technol. Exp. Mech. (2001) 863–867. doi:10.1299/jsmeatemapcfs.2.01.03.0_863
• 231)   M.  Kattoura,  A.  Telang,  S.R.  Mannava,  D.  Qian and  V.K.  Vasudevan: Mater. Sci. Eng. A 711 (2018) 364–377. doi:10.1016/j.msea.2017.11.043
• 232)   H.K.  Park,  K.  Ameyama,  J.  Yoo,  H.  Hwang and  H.S.  Kim: Mater. Res. Lett. 6 (2018) 261–267. doi:10.1080/21663831.2018.1439115
• 233)   M.W.  Kapp,  O.  Renk,  T.  Leitner,  P.  Ghosh,  B.  Yang and  R.  Pippan: J. Mater. Res. 32 (2017) 4317–4326. doi:10.1557/jmr.2017.273
• 234)   M.  Goto,  S.Z.  Han,  T.  Yakushiji,  S.S.  Kim and  C.Y.  Lim: Int. J. Fatigue 30 (2008) 1333–1344. doi:10.1016/j.ijfatigue.2007.11.001
• 235)   Y.  Wu,  Z.  Sun,  F.  Brisset,  T.  Baudin,  A.L.  Helbert and  D.  Retraint: Mater. Lett. 263 (2020) 127249. doi:10.1016/j.matlet.2019.127249
• 236)   H.  Chang,  P.M.  Kelly,  Y.  Shi and  M.  Zhang: Surf. Coat. Technol. 206 (2012) 3970–3980. doi:10.1016/j.surfcoat.2012.03.069
• 237)   J.  Xu,  Y.  Liu,  B.  Jin,  J.  Li,  S.  Zhai,  X.  Yang and  J.  Lu: Acta Metall. Sin. (Engl. Lett.) 28 (2015) 1162–1169. doi:10.1007/s40195-015-0308-7
• 238)   H.  Zhang,  S.  Wu,  N.  Ao,  J.  Zhang,  H.  Li,  L.  Zhou,  P.  Xu and  Y.  Su: Int. J. Fatigue 166 (2023) 107296. doi:10.1016/j.ijfatigue.2022.107296
• 239)   J.  Li and  A.K.  Soh: Int. J. Plast. 39 (2012) 88–102. doi:10.1016/j.ijplas.2012.06.004
• 240)   X.  Lu,  X.  Zhang,  M.  Shi,  F.  Roters,  G.  Kang and  D.  Raabe: Int. J. Plast. 113 (2019) 52–73. doi:10.1016/j.ijplas.2018.09.007
• 241)   X.  Yang,  X.  Ma,  J.  Moering,  H.  Zhou,  W.  Wang,  Y.  Gong,  J.  Tao,  Y.  Zhu and  X.  Zhu: Mater. Sci. Eng. A 645 (2015) 280–285. doi:10.1016/j.msea.2015.08.037
• 242)   J.H.  Yan,  Y.F.  Du and  Y.L.  Feng: Suxing Gongcheng Xuebao/J. Plast. Eng. 29 (2022) 1–13.
• 243)   Z.  Ma,  J.  Liu,  G.  Wang,  H.  Wang,  Y.  Wei and  H.  Gao: Sci. Rep. 6 (2016) 1–11.
• 244)   Y.  Ochi,  K.  Masaki,  T.  Matsumura and  T.  Sekino: Int. J. Fatigue 23 (2001) 441–448. doi:10.1016/S0142-1123(00)00110-9
• 245)   J.  Arakawa,  A.  Sugeta,  H.  Akebono,  Y.  Hayashi,  R.  Tanegashima,  M.  Kakuta and  M.  Kato: Surf. Eng. 30 (2014) 662–669. doi:10.1179/1743294414Y.0000000308
• 246)   M.  Benedetti,  T.  Bortolamedi,  V.  Fontanari and  F.  Frendo: Int. J. Fatigue 26 (2004) 889–897. doi:10.1016/j.ijfatigue.2003.12.003
• 247)   S.  Yang: Int. J. Adv. Manuf. Technol. 120 (2022) 5041–5056. doi:10.1007/s00170-022-09063-w
• 248)   L.  Wagner: Mater. Sci. Eng. A 263 (1999) 210–216. doi:10.1016/S0921-5093(98)01168-X
• 249)   K.  Dalaei,  B.  Karlsson and  L.E.  Svensson: Mater. Sci. Eng. A 528 (2011) 1008–1015. doi:10.1016/j.msea.2010.09.050
• 250)   Y.  Shimatani,  K.  Shiozawa,  T.  Nakada,  T.  Yoshimoto and  L.  Lu: Int. J. Fatigue 33 (2011) 122–131. doi:10.1016/j.ijfatigue.2010.07.009
• 251)   M.A.S.  Torres and  H.J.C.  Voorwald: Int. J. Fatigue 24 (2002) 877–886. doi:10.1016/S0142-1123(01)00205-5
• 252)   M.  Guagliano and  L.  Vergani: Eng. Fract. Mech. 71 (2004) 501–512. doi:10.1016/S0013-7944(03)00017-1
• 253)   J.H.  Moon,  S.M.  Baek,  S.G.  Lee,  Y.  Seong,  A.  Amanov,  S.  Lee and  H.S.  Kim: Mater. Res. Lett. 7 (2019) 97–102. doi:10.1080/21663831.2018.1560370
• 254)   A.M.  Eleiche,  M.M.  Megahed and  N.M.  Abd-Allah: J. Mater. Process. Technol. 113 (2001) 502–508. doi:10.1016/S0924-0136(01)00601-X
• 255)   S.A.  Kumar,  S.G.S.  Raman and  T.S.N.S.  Narayanan: Trans. Indian Inst. Met. 67 (2014) 137–141. doi:10.1007/s12666-013-0322-2
• 256)   J.K.  Li,  Y.  Mei,  W.  Duo and  W.  Renzhi: Fatigue Fract. Eng. Mater. Struct. 15 (1992) 1271–1279. doi:10.1111/j.1460-2695.1992.tb01262.x
• 257)   X.  Luo,  C.  Zhao,  X.  Zha,  J.  Guo,  X.  Wang,  Z.  Tang and  B.  Yu: Mater. Reports 35 (2021) 12114–12118 (in Chinese).
• 258)   M.  Jambor,  L.  Trško,  J.  Klusák,  S.  Fintová,  D.  Kajánek,  F.  Nový and  O.  Bokůvka: Metals 10 (2020) 1262. doi:10.3390/met10091262
• 259)   T.A.  Furnish,  B.L.  Boyce,  J.A.  Sharon,  C.J.  O’Brien,  B.G.  Clark,  C.L.  Arrington and  J.R.  Pillars: J. Mater. Res. 31 (2016) 740–752. doi:10.1557/jmr.2016.66
• 260)   P.  Lukáš,  L.  Kunz and  M.  Svoboda: Mater. Sci. Eng. A 391 (2005) 337–341. doi:10.1016/j.msea.2004.09.052