Effect of ultrasonic peening treatment on the fatigue behaviors of a magnesium alloy up to very high cycle regime

Yo Chen ,Fulin Liu ,Cho He ,Lng Li ,Chong Wng ,Yongjie Liu,* ,Qingyun Wng,c,*

a Failure Mechanics and Engineering Disaster Prevention and Mitigation Key Laboratory of Sichuan Province,Sichuan University,Chengdu 610065,China

b MOE Key Laboratory of Deep Earth Science and Engineering,College of Architecture and Environment,Sichuan University,Chengdu 610065,China

c Institute for Advanced Study,Chengdu University,Chengdu 610106,China

Abstract Ultrasonic fatigue tests are performed on a magnesium alloy with and without ultrasonic peening treatment (UPT).Surface enhancement layer leads to the complete change of crack initiation sites.However,crack initiation mechanism keeps the same and results in a single-faceted morphology at crack initiation site.Microcracks initiate as Mode II crack within the original grain,but deflec to Mode I crack outside of the original cracked grain.A threshold SIF value is proposed to evaluate the retarding effect of grain boundary on microcrack propagation.Outside of the original cracked grain,Mode I crack propagation below the threshold ΔKσ-th is responsible for the formation of fin granular area (FGA,a nano-grain layer).Based on the Numerous Cyclic Pressing (NCP) model,it is proposed that crack type should be another necessary condition for the formation of FGA.

Keywords: Ultrasonic peening treatment;Very-high-cycle fatigue;Crack initiation mechanism;Fine granular area;Nanograins.

1.Introduction

As one of lightest structural alloys [1],magnesium alloy shows the remarkable energy-saving value in aerospace,rail transit,automotive and other field [2].However,most of the industrial applications of Mg alloys at present are limited to the non-load bearing components [3].Expanding Mg alloys to the load-bearing components is indispensable to the further mass reduction.Unfortunately,the poor fatigue properties frequently restrict its widespread applications.

Surface enhancement is an effective approach to improve the fatigue resistance [4].Ultrasonic peening treatment (UPT)is a novel and promising surface technology [5].It can not only enhance mechanical properties but also reduce surface roughness.Therefore,it has stimulated public interest in its industrial application.During UPT process,ultrahigh frequency oscillations induced by ultrasonic generator are amplifie by a booster horn system.Then,the ultrasonic oscillations combined with a static loading are applied on target surface (see Fig.1).Generally,the oscillation frequency is at～20.0 kHz or more.This ultrahigh frequency oscillation makes it a quiet technology.Although the oscillation amplitude is only about several tens of micron at the tip,target surface receives a severe plastic deformation due to the ultrahigh impact speed[6].Beneath the target surface,harmful tensile residual stresses can be eliminated effectively and benefi cial compressive stresses are imposed accordingly.Compared with the traditional hammer peening and needle peening,it shows particular advantages in low noise,high-energy effi ciency,controllability,processing speed,affected depth,and uniform surface roughness [5].Therefore,UPT is a comfortable and effective surface technology to improve the fatigue performances of industrial component [7,8].

Fig.1.Schematic illustration of ultrasonic peening treatment (UPT)processing.

Long-life service and high reliability have become the future goal and also urgent need in modern manufacturing industry.Inevitably,fatigue damage,especially the very-highcycle fatigue (VHCF) problem,is threatening the long-life service reliability [9,10].The cyclic loading range of more than 107cycles is called very-high-cycle regime,and fatigue failure in such regime is define as VHCF failure,also named gigacycle fatigue failure [9].It is widely known that fatigue failure may happen beyond 107loading cycles (i.e.in the very-high-cycle regime) under a relatively low cyclic stress below the conventional fatigue limit [11,12].Therefore,the VHCF failure problem has been attracted extensive attentions and becomes a focus of researches.It is not only due to the broad engineering requirement but also the scientifi interest over the last two decades.For VHCF failure,it has been widely proved that crack initiation stage consumes most of the total fatigue life [13,14].As a result,crack initiation mechanism has become the key aspect of VHCF failure in scientifi significance In this study,the major novelty is to investigate the UPTed effect on the crack initiation mechanism of a magnesium alloy up to VHCF regime.

The main aims of this studying work are:(1) to determine the fatigue crack initiation and early propagation mechanisms in VHCF regime,(2) to determine whether the UPT processing affects the fatigue crack initiation mechanism,and (3) to reveal the connection between the macroscopic fatigue properties and the crack initiation mechanism.

2.Material and experimental methods

Fig.2.General microstructure along the extrusion direction.

Compared to AZ-series,ZK-series Mg alloy shows the superior strength and plasticity with the addition of Zr element as grain refine [15,16].It presents the great potentials to be utilized in load-bearing components.As a typical product,ZK60 Mg alloy with nominal compositions of Mg-6.0Zn-0.6Zr (wt.%)[17,18] has been investigated accordingly in this study.The as-received material was finall extracted from the hot-extruded sheet.The metallographic observations are prepared by mechanical grinding,electro-polishing (HClO4:Ethanol=1:9 vol,18 V,-20 °C,10 s) and chemical etching (Saturated picric acid alcohol:Acetic acid:Distilled water=5:1:2 vol,2 s).Fig.2 presents the microstructure along the extrusion direction.

Cyclic loading by conventional equipment is hard to reach the VHCF regime.For example,by a servo hydraulic testing system,it will consume～6.3 years up to 109cycles under the loading frequency of 5 Hz.Obviously,it is nearly an impossible task up to VHCF regime due to the unbearable time cost.Fortunately,the testing device used in this study is an ultrasonic fatigue testing system,which works at a loading frequency of 20.0 kHz [9].

The coming out of ultrasonic fatigue testing system should be a milestone in the fiel of VHCF researches.It is firstl developed at the Laboratory of Fatigue and Fracture Mechanics,Mechanics Institute for Technology and Advanced Materials(ITMA),National Conservatory of Arts and Crafts (CNAM),Paris [9].For the conventional fatigue devices,loading frequency is according to the external load system,which is different from the natural frequency of the loaded specimen.Obviously,fatigue specimen loaded by conventional devices is in forced vibration.However,for an ultrasonic fatigue testing system,the ultrahigh loading frequency (i.e.20 kHz) should be same to the natural frequency of loaded specimen along the loading direction [9].Therefore,fatigue specimens loaded by ultrasonic fatigue testing system are in resonant vibration.

In this study,fatigue tests are conducted by a commercial ultrasonic fatigue testing device(Shimadzu USF-2000)under a symmetrical push-pull loading condition (i.e.,stress ratioR=-1).A sine-wave cyclic loading is applied on the tested specimen.For the tested specimens,the inherent frequency along the loading direction has been specially designed according to vibration mechanics.By modal analysis using fi nite element method through commercial software ANSYS,the dimensions of the tested specimens are presented in Fig.3(a).Its natural frequency along the axial direction is close to the resonant frequency of 20.0 kHz.Then,the stress distribution is calculated by the Harmonic response analysis using finit element method through commercial software ANSYS.

Fig.3.Schematic diagram of (a) dimensions of ultrasonic fatigue specimen(units:mm);(b) the UPT processing.

The simulation results show that when a unit of vibration displacement is applied to the end of loaded specimen,the middle gauge section(i.e.20 mm in length seeing Fig.3(a))is applied with a stress amplitude of 2.7251 MPa.During fatigue testing,the target stress amplitudes are controlled by adjusting the vibration displacement at the end of the specimen.For example,a target stress of 120 MPa at the middle gauge section can be obtained by applying a vibration displacement of 44.04 μm (i.e.120/ 2.7251=44.04) at the end of the specimen.The firs book,“Gigacycle Fatigue in Mechanical Practice” -2004 by Claude Bathias and Paul C.Paris,details the loading principle of ultrasonic fatigue testing system and also the specimen design [9].

Specimens are sampled along the transverse direction of extruded sheet.In order to minimize the surface roughness caused by machining marks,low-stress mechanical polishing is employed along the loading direction of specimens.Then,the fina mirror surface is achieved by electro-polishing.Specimens are loaded in the range from 100 MPa to 145 MPa,and the maximum cyclic stress amplitude (i.e.145 MPa) reaches 62% of the tensile yield strength,48% of the tensile ultimate strength.The two group of specimens (i.e.with and without UPT processing) have been tested with three specimens for each stress level,respectively.Therefore,thirty specimens,in total,have been tested in this study.During fatigue testing,every specimen is loaded in ambient air environment up to 109cycles except for failure.

Fig.3((b) presents the UPTed paths schematically,which are along the loading direction of specimen.The UPT system is installed on a lathe carriage,which can precisely control the pin tip movement.During UPT processing,the axial static loading is 117.75 N,and the ultrasonic oscillation amplitude is 20 μm (22.18 kHz) at pin tip.The pin movement speed is 1500 mm/min,and the interval between two adjacent paths is 0.1 mm.The diameter of the cylindrical pin is 14 mm,and the curvature radius of pin top surface is 20 mm.

The UPTed surface roughness is investigated by an infinit Focus Optical 3D surface metrology (IFM G5,Alicona Imaging GmbH).The surface roughness is evaluated from 18 lines(12.5 mm in length per line) parallel to the loading direction.Microhardness-depth profil is determined by a nanoindenter (iNano,KLA),in which the allowable thermal drift rate,the target load,the target indentation strain rate and the hold maximum load time are set equal to 0.05 nm s-1,50 mN,0.2 s-1and 1 s,respectively.

Residual stresses distributions in the surface enhancement layer are evaluated by sin2ψmethod with an X-ray stress analyzer (Proto-LXRD),by removing the surface layer with electrolytic polishing step-by-step.In order to determine the peak position of in-depth residual stress,the polishing depth is carefully controlled by the polishing time of the removal process.Five positions at respective depths are measured.Then,the approximate distribution trend in depth is determined.To investigate the UPT effect on the fractography,all fatigue fracture surfaces are observed using a scanning electron microscope (SEM,JSM-6510LV) to identify the fatigue fracture behavior.The size and position of characteristic regions are measured through the obtained SEM photographs.In order to investigate the microscopic damage mechanism,focused ion beam (FIB) technique and transmission electron microscope (TEM,JEM-F200,Institute for Advanced Study,Chengdu University) are used to analysis the crack initiation mechanism.

3.Results and discussion

3.1.Surface integrity after UPT processing

In this study,the surface integrity is about the physical properties of the UPT-affected zone,such as:microstructure,surface roughness,hardness,and residual stresses distribution.

3.1.1.Microstructure

Fig.4 shows the microstructure of the UPT-affected zone on cross section after UPT processing,which is observed by optical microscope (OM).It should be noted that plastic deformations are invisible beneath the surface enhancement layer by OM.Therefore,the plastic deformations in Fig.4 should be induced by the UPT processing,rather than the inherent microstructure before UPT processing.It is seen that the microstructure near the UPTed free surface is almost indistinguishable (see Fig.4(b)).The UPTed surface suffers severe plastic deformations,and thus the granular microstructures can hardly be distinguished by OM.On the other hand,the granular microstructures become distinguishable gradually from the free surface to specimen interior.It means that the UPT-induced plastic deformation degree decreases accordingly from the surface to interior.Only some slight plastic deformations,indicated by arrows in Fig.4(c),are presented at the end of the UPT-affected zone.

Fig.4.Microstructure of UPT-affected zone.(a) Overall view on the cross section.(b)Magnifie observation near the UPTed surface shows severe plastic deformations.(c) Magnifie observation at the end of the UPT-affected zone shows some insignifican plastic deformations indicated by arrows.

The average thickness of the UPT-affected zone,measured from 15 points of 3 UPTed specimens,is determined to be～700 μm.For magnesium alloys,the affected depth induced by UPT is much deeper than the other surface techniques such as～35 μm for conventional shot peening,～65 μm for severe shot peening,～65 μm for repeened-severe shot peening[19].The UPTed ultrahigh frequency induces the ultrasonic oscillations at the pin tip,which leads to the high-speed impact with concentrated energy on a small target area.Thus,it is one of the UPTed advantages,which can induce a deeper plastic deformation layer.In this study,the UPT-affected layer(i.e.,～700 μm in depth) is referred to the “surface enhancement layer” as following.

3.1.2.Surface roughness

Surface roughness parameters in terms of the roughness average,Ra,root-mean-square roughness,Rq,and mean peak to valley height,Rz,are equal to 1.2475 μm,1.5726 μm,and 8.2955 μm,respectively.The UPTed surface roughness is smoother than that induced by the other surface peening techniques [5,20,21].

Fig.5.In-depth hardness distribution in the surface enhancement layer.

3.1.3.Hardness

Microhardness measurements are carried out to evaluate the basic mechanical performance of the UPT-induced surface enhancement layer.According to the depth of the surface enhancement layer,the in-depth microhardness is measured up to 700 μm,as shown in Fig.5.Owing to the UPT-induced severe plastic deformations,surface enhancement layer presents is a significan increasement in microhardness.The maximum hardness is～40% higher than the base material near the UPTed free surface,and it decreases gradually from surface to interior.This variation trend is basically consistent with the distribution of plastic deformation degree in the surface enhancement layer.

3.1.4.Residual stress

The in-depth residual stress distributions before and after cyclic loadings are corrected by the elasticity solution proposed by Moore and Evans [22] and the results are shown in Fig.6.After UPT processing,the compressive residual stress near the free surface is -41 MPa,and the maximum value is -83 MPa at the depth of 80 μm.However,after cyclic loadings,the residual stresses have been relaxed partially (see Fig.6).The residual stress near the free surface is -30 MPa,and the maximum value is -57 MPa at the depth of 150 μm.In previous studies,it is shown that residual stresses are commonly relaxed during the stress-controlled cyclic loadings[23,24],or even completely relaxed during the strain-controlled cyclic loadings [25].In this study,the maximum residual stress retains 69% of the original value after cyclic loadings.Generally,the relaxation degree increases with the increasing of cyclic stress level [23,25,26].In Fig.6,the evaluated results of residual stress are obtained from a specimen loaded at 145 MPa,which is the maximum applied stress of all tested specimens.Therefore,the retained residual stress loaded by the other stress levels should be higher theoretically.

Fig.6.In-depth residual stress distribution before and after fatigue loadings(σa=145 MPa,Nf=2.12 × 106 cycles).

Fig.7.S-N results before and after UPT processing with error bars and fitte curves.

3.2.S-N curves

Fig.7 presents the stress/life (S/N) results,in which fatigue life ranges from 104cycles to 109cycles with the loading stress amplitude from 100 MPa to 145 MPa.Since the different crack initiation sites before and after UPT processing,the UPT-affected zone(i.e.the surface enhancement layer～700 μm in depth) is artificiall define as “subsurface region” in the following,while the internal core zone surrounding by the surface enhancement layer refers to “interior core region”.In Fig.7,the black hollow and solid circles refer to a crack initiation from the free surface (i.e.surface failure,see Fig.8) and from the subsurface region (i.e.subsurface failure,see Fig.10),respectively.The red solid diamonds refer to a crack initiation from the interior core region (i.e.internal failure,see Fig.11).

Fig.8.A typical surface failure before UPT (σa=130 MPa,Nf=1.51 ×106 cycles).(a) Overall view of the fracture surface.(b-c) Magnification of the crack initiation site.(d) Schematic illustration accordingly.

The classical Basquin equation is used to fi the S-N data nonlinearly.The black and red lines in Fig.7 represent the fitte S-N curves before and after UPT processing,respectively.Both curves present a continuing downward trend,and there is no conventional fatigue limit accordingly.A benefi cial UPTed effect on improving fatigue properties can even up to the VHCF regime.However,with the increasing of fatigue life,the fitte curves before and after UPT processing become close gradually,indicating that the beneficia UPTed effect becomes insignifican accordingly.

In Fig.7 for specimens without UPT processing,with the increasing of fatigue life,the dominant failure mode transforms from surface failure to subsurface failure at a relatively low stress amplitude of 110 MPa.However,after UPT processing,there is only one failure mode (i.e.internal failure),in which fatigue crack only initiates from the interior core region (see Fig.11).For specimens with and without UPT processing,at the same stress amplitude,fatigue life of internal failure is almost one order of magnitude larger than that of surface failure (see Fig.7).For example,whenσaequals to 145 MPa,the average fatigue life of surface failures and internal failures is 1.44 × 105and 1.65 × 106cycles,respectively.Namely,there is a significan improvement of fatigue life in such condition.However,also at the same stress amplitude,average fatigue life of subsurface failures is much closer to that of internal failures (see Fig.7).For example,whenσaequals to 100 MPa,the average fatigue life of subsurface failures and internal failures is 2.56 × 108and 2.90 × 108cycles,respectively.Namely,UPT processing has insignifican effect on the improvement of fatigue life in such condition.Therefore,with the increasing of fatigue life,the UPT-enhanced effect becomes insignifican accordingly.

3.3.Fractographies

After fatigue tests,fracture surfaces of all the failed specimens are carefully examined by SEM.The three failure modes are:(1) Surface failure:crack initiation from free surface (see Fig.8),(2) Subsurface failure:crack initiation from subsurface region (see Fig.10),and (3) Internal failure:crack initiation from interior core region (see Fig.11).These three types of failure modes have also been indicated in Fig.7.

Fig.9.Element energy-dispersive spectroscopy (EDS) analyses on the surface of fatal facet.

It should be noted that although there are three types of failure mode due to the different crack initiation sites,all of them present a same crystallographic faceted morphology at the initiation site,as shown in Figs.8,10 and 11.Energy-dispersive spectroscopy (EDS),a chemical microanalysis technique used in conjunction with scanning electron microscopy (SEM,JSM-6510LV),is used to analysis the chemical elements on the surface of a faceted morphology.In Fig.9,the EDS results show that the element types and contents on the faceted surface are nearly equal to that of the original material matrix.Therefore,the facets should stem from the material matrix rather than from the non-metallic inclusions,which are frequently responsible for the VHCF crack initiations in high-strength steels [11,27].Since the observed crystallographic faceted morphologies are responsible for the finia failures as the crack initiation sites,they were named“fatal facet” as in our previous studies [17,18].

Fig.10 presents a typical example of subsurface failures.In Fig.10(c),it is seen that for the initial crack propagation outside of the fatal facet,a relatively rough surface morphology occurs on the left side of the fatal facet.Instead,a relatively smooth morphology occurs on the right side of the fatal facet,and some radial ridge morphologies are invisible there.Therefore,for the early crack propagation outside of fatal facet,there should be a competition in the propagation direction.Fatigue crack may firstl propagate towards to the free surface due to the limited confinemen effect at crack tip.

Fig.10.A typical subsurface failure before UPT (σa=110 MPa,Nf=5.06 × 107 cycles).(a) Overall view of the fracture surface.(b-c)Magnification of the crack initiation site.(d) Schematic illustration accordingly.

For VHCF failures,crack propagation rate is estimated to be＜10-8mm/cycle in general at the early propagation stage [28].According to the numerous cyclic pressing (NCP)model,crack tips at the ultra-slow propagation stage are subjected to the numerous cyclic pressings,resulting in the formation of rough morphology [11].Therefore,in Fig.10(c),crack firstl propagates towards to the free surface with the ultra-slow propagation rate,resulting in the formation of a rough surface morphology.However,once crack propagates beyond the free surface,it does not propagate in the internal vacuum-like environment,and crack propagation rate will be promoted due to the entry of air [29-31].Then,the ultraslow crack propagation stage [28] disappears accordingly,and crack starts to propagate towards to the interior of specimen(i.e.towards to the right side outside of the fatal facet).At this stage,crack tips will not be subjected to the numerous cyclic pressings,and thus the relative rough surface morphology disappears.The radial ridge morphology is formed on the right side of the fatal facet due to the relatively higher crack propagation rate.

Fig.11.A typical internal failure after UPT (σa=145 MPa,Nf=1.02 ×106 cycles).(a) Overall view of the fracture surface.(b-c) Magnification of the crack initiation site.(d) Schematic illustration accordingly.

Fig.12.A typical fish ye-like morphology on the fracture surface(σa=100 MPa,Nf=5.21 × 108 cycles).(a) Overall view of the fracture surface showing the characteristic region of large dark area.(b-c) Magnifi cations of the crack initiation site showing the characteristic region of small bright area (b) and fatal facet (c).(d) Schematic illustration of the fish-li e morphology accordingly.

After UPT processing,there is only internal failure mode,in which fatigue crack initiates from the interior core region of specimen,as shown in Fig.11.The fatal facet is located in the interior core region,surrounded by surface enhancement layer.It should be noted that the typical “fish-ye” characteristic is only observed in the internal failure mode (see Fig.12).

Fig.13.Topographic measurement of the fish-li e morphology(σa=120 MPa,Nf=2.60 × 107 cycles).(a) The target region observed by SEM.(b) 3D morphology.(c) Height result along the cross section in (b).(d) Enlarged window showing the detailed height result along the fatal facet.(e) Quantitative 3D morphology.(f) Schematic illustration of the characteristic areas on cross section.

As shown in Fig.12,the initial microcrack (i.e.the fatal facet in Fig.12(c))is located at the center of the fish-li e morphology.The fatal facet is surrounded by a relatively bright area with rough morphology characteristic,which is named“small bright area” (see Fig.12(b)).Outside of the small bright area,there is a region with a relatively smooth morphology characteristic,which is named “l(fā)arge dark area” (see Fig.12(a)).As a result,schematic illustration of the fish-li e morphology is shown in Fig.12(d),accordingly.

In Fig.13,a specimen with “fish-ye” characteristic is selected to examine the fractography features in detail.The roughness of fracture surfaces is measured by topography analysis technique using a noncontact optical 3D profle (IFM G5).The profile applies scanning white light interferometry technique to image and examine the morphology with a resolution of 10 nm on z (height) direction.

Fig.13(a) shows the crack initiation site in secondaryelectron-image mode by SEM.The fatal facet and the small bright area are cycled by dashed lines,respectively.The corresponding 3D morphology is shown in Fig.13(b) and (e).Fig.13(c) is the profil resulting from the section plane in Fig.13(b),which runs through the fatal facet.The fatal facet presents a width of 137 μm and a height of 135 μm (see Fig.13(d)).The fatal facet surface shows an angle of～45°against to the direction of maximum tensile stress,namely,close to the direction of maximum shear stress.Such slope angle means that crack nucleation stage of the fatal facet is driven by the shear stress,rather than the normal stress.However,surfaces of the small bright area and the large dark area are nearly perpendicular to the loading direction (see Fig.13(c)).As a result,the crack initiation and early propagation stage within the fatal facet are driven by the maximum shear stress.Then,outside of the fatal facet,crack propagation is driven by the maximum tensile stress.

The surface 3D morphology of “fish-ye” characteristic is shown In Fig.13(e).The fatal facet with a smooth surface is surrounded by the small bight area with a roughness surface,and the small bright area is surrounded by the large dark area with a relatively smooth surface.Schematic illustration of “fish-ye” characteristic is proposed in Fig.13(f),which presents the main crack with different roughness characteristics in each characteristic area.

3.4.Initial fatigue crack

In previous studies,the planar slip deformations play an important role in breaking the preferred orientation grain and result in the facet morphologies at crack initiation site[17,30].The observation of fatal facets at crack initiation sites is a direct way to reveal the crack initiation mechanism.Since the same faceted morphology at crack initiation site for the three failure modes (see Figs.8,10 and 11),it is believed that crack initiation mechanism keeps the same before and after UPT processing.

In Fig.14(c,d),a surface failure is observed from the side.Fig.14(a) presents the corresponding fracture morphology.It is seen that some sub-cracks are beneath the fracture surface,which are transgranular in the original single grain.A zigzag crack propagation path in total is seen along the fracture surface.It is similar to the crack path at the initial stage of internal failure(see Fig.13).Fatigue crack nearly initiates along the maximum shear stress direction (i.e.Mode II crack),and then deflect outside of the original cracked grain.It deflect to a direction perpendicular to the remote maximum principal stresses (i.e.Mode I crack).

Fig.14(c) shows a magnifie detail of side observation.Some planar-like cracks are formed beneath the fatal facet within the original cracked grain.Since the faceted morphology is strongly crystallographic on the planar slip systems[17,32-34],the planar-like cracks may be parallel to one trace of the available slip systems.It is found that the sub-cracks in Fig.14(b) are terminated at the grain boundary.Obviously,grain boundary retards the continuing propagation of such microcracks.In such case,grain size should affect the macroscopic fatigue properties,and grain refinemen may result in an improvement of fatigue strength.

Fig.14.Initial fatigue crack observation (σa=110 MPa,Nf=6.50 × 106 cycles).(a) Fracture surface observation showing the fatal facet at crack initiation site.(b) Side observation at the crack initiation site.(c) Magnificatio of the microcracks along the slip bands.

Fig.15.TEM analysis at fatigue crack initiation site (σa=120 MPa,Nf=2.60 × 107 cycles):(a) Locations of FIB-sliced samples at the fatal facet and the small bright area,respectively;(b-c) Magnification of the locations before FIB section;(d-e) The FIB-sliced samples;(f-g) The HRTEM images close to the topmost crack surface (＜350 nm),shown in (d-e)respectively.

Fig.15(a-c) presents the SEM images showing the morphology of an internal failure failed at Nf=2.60 × 107cycles with the stress amplitudeσa=120 MPa.It is seen from Fig.15(a-c) that the region containing a crack origin from a fatal facet,which is surrounded by a rough area (i.e.the small bright area in Figs.12 and 13).To further examine the fatal facet and the rough area,we observe the FIB-sliced samples(see Fig.15(d-e)),which are extracted from the target locations (see Fig.15(b,c)).The rough area presents a tortuous crack path (see Fig.15(d)),while the fatal facet presents a straight crack path (see Fig.15(e)).

In order to identify the microscopic nature of the different cracking morphologies,high-resolution TEM (HR-TEM)observations with selected area electron diffraction (SAED)examination are performed on the FIB-sliced samples.It is known that fatigue failures in VHCF regime are loaded at low stress amplitudes far below the tensile yield strength,and plastic deformations only occur and concentrate in some local areas.Therefore,the HR-TEM observations focus on a small local area near the crack surface (see Fig.15(d,e)),where plastic deformations are most likely to occur.For the FIB-sliced samples (see Fig.15(d,e)),the HR-TEM images in Fig.15(f,g) present the observation results close to the topmost crack surface (＜350 nm).

In Fig.15(f) for the HR-TEM result underneath the rough area,the discontinuous diffraction rings shown in the SAED pattern suggest a random crystallographic orientation of the formed nanograins,which are marked by blue circles.In addition,the HR-TEM result also reveals the formation of an amorphous phase surrounding the nanograins,as suggested by the typical amorphous SAED pattern in Fig.15(f).On the other hand,in Fig.15(g) for the HR-TEM result underneath the fatal facet,the SAED pattern suggest a single crystallographic orientation,and the basal plane has been plotted based on the electron diffraction in the HR-TEM image.Importantly,the fracture surface (see Fig.15(e)) is perfectly correlated with the basal plane,indicating a close relationship between basal slip and the formation of fatal facet.

Generally,at room temperature,both basal slip and tensile twinning are prone to be activated at a low stress amplitude along their respective shearing planes in magnesium crystals[35].Simultaneously,crystallographic orientation is another key factor determining the occurrence of slip or twinning for crystal materials.In this study,the basal plane inclines nearly along the maximum shear stress direction with a high Schmidt factor.Therefore,it results in the reduced probability of tensile twinning within the initial cracked grain.Furthermore,it could be expected that only basal slip would be activated in the well-oriented initial grain if the applied cyclic stress decreases to a certain amplitude [34].As the current loading condition,the stress amplitudes are much lower than the tensile yield strength.Therefore,it is concluded that fatigue crack initiates from the slip bands along the basal plane,resulting in the formation of fatal facet on the fracture surface.

It is known that for VHCF failures,cracks are prone to initiate at specimen subsurface or interior with a distinct feature of so-called ‘‘fish-ye’’ embracing ‘‘Fine Granular Area(FGA) [36]’’.During the ultra-long period of cyclic loadings up to VHCF regime,the formation of FGA,i.e.the stage of crack initiation and early growth,almost consumes larger than 95% of total fatigue life [11,12,28].Therefore,the investigations of VHCF behavior are based on the essential characteristic related to the damage mechanism within FGA [11,13,37].In previous studies,an average grain size of about several tens of nanometers is observed in the topmost layer beneath the FGA surface [38,39].However,in this study,such nanograins are only observed beneath the small bright area,rather than the fatal facet (see Fig.15).Therefore,in this study,FGA corresponds to the small bright area with rough surface morphology,and the formation mechanism of the fatal facet should be different from that of the FGA.

Fig.16.Fatigue damage observation of a run-out specimen (σa=100 MPa,Nf=1.00 × 109 cycles).

Several mechanisms have been proposed for the formation of FGA,especially the “Numerous Cyclic Pressing (NCP)model [11]”.It is regarded that the formation mechanism of the crack initiation characteristic region of FGA is the numerous cyclic pressings between the two originated crack surfaces associated with crack closure.Nano-grain layer in FGA region is formed in the cases of negative stress ratios with the numerous cyclic pressings loaded up to VHCF regime [11].In this study,the fatal facet is surrounded by the FGA(i.e.the small bright area with nanograins),and obviously meeting the above conditions for FGA formation (i.e.the negative stress ratio and a large number of cyclic loadings up to the VHCF regime).However,there is no nano-grain layer beneath the fatal facet.

As discussion in the above section,it is known that the formation of the fatal facet is driven by the shear stress as Mode II cracking,while the formation of the small bright area is driven by the normal stress as Mode I cracking.For Mode II crack,the crack closure between the two originated crack surfaces is almost negligible as compare to Mode I crack.Therefore,according to the NCP model [11] and the current studying work,crack type should also be an another necessary condition for the formation of FGA.Only Mode I cracking will lead to the formation of FGA with nano-grain layer beneath the crack surface.

3.5.Microcracks to be stopped at or break through the grain boundary?

Fig.17.Variations in the SIF range at the periphery of the fatal facet (ΔKτ-FF) depending on the fatigue life (a) and stress amplitude (b).

Fatigue damage of a run-out specimen (i.e.loading up to 109cycles) at stress level of 100 MPa is also observed from the side.As shown in Fig.16,fatigue damages are in the form of slip bands,which show a tendency to saturation.It is seen that numbers of microcracks are formed along the slip bands,but the microcracks and slip bands are stopped at the grain boundary.Once one of the fatigue damages breaks through the grain boundary,it may lead to the finall fatigue failure as that shown in Fig.14.However,what is the critical criterion for determining whether the fatigue damages to be stopped at or break through the grain boundary?

From the aforementioned discussion,it is known that the planar slips along the maximum shear stress leads to the formation of fatal facet (see Figs.13 and 14).Obviously,it is a shear-type crack at the crack initiation site.From the perspective of fracture mechanics,it is a Mode II crack for the formation of the fatal facet.However,once one of the microcracks breaks through the grain boundary,it transforms into a Mode I crack (see Fig.13).The crack surfaces outside of the fatal facet are perpendicular to the loading direction.Therefore,in order to know the driving force for fatigue crack propagation at the crack tip when microcracks reach the grain boundary,it is necessary to evaluate the stress intensity factor(SIF) rangeΔKat the periphery of the fatal facets.

Quantitative facture surface analyses are performed by means of fracture mechanics.Theparameter model is adopted to conduct fracture mechanics analysis on the calculation method for SIF.As approximating a crack in an infinit body,ΔKfor a Mode II crack of the fatal facets is calculated as follows:

whereτrepresents the shear stress andis the square root of the area projected on the plane parallel to the shear stress direction.Combing the above Eq.(1) [40],the SIF range at the periphery of the fatal facets (ΔKτ-FF) for the internal failures after UPT are determined and are presented in Fig.17.

The values ofΔKτ-FFvary from 0.63 to 1.26 MPa√m for the internal failures,and display a slight decreasing tendency with respect to the failure life (see Fig.17(a)).For VHCF failure,the initiation and early propagation of short fatigue cracks are active far below the threshold SIF value(ΔKth) [28,33].The threshold SIF value (ΔKth) is determined by theΔKvalue at the crack propagation rate of 10-10m/cycle [41].In this study,the fatal facets are formed by the shear-type crack propagation (i.e.Mode II crack) at crack nucleation site.Therefore,fatigue crack propagation rate at this stage should be controlled by the SIF range for Mode II crack (ΔKτ) rather than that for Mode I crack(ΔKσ).

For Mode II crack,from the underlying physical principles,Mode II threshold (ΔKτ-th) is expressed as a simple formula[42]:

where μ is shear modulus,bis Burgers vector,andnais a goniometrical coefficient It determines the threshold of intrinsic material resistance for Mode II crack propagation.In this study,it is assumed that the surfaces of the fatal facets are parallel to the maximum shear stress direction as that shown in Figs.13 and 14,and thusna=1.For magnesium alloys,b≈0.3186 nm,μ ≈18 GPa [43],the predicted intrinsic threshold is calculated to beΔKτ-th=0.32 MPa√m by Eq.2,which is also presented in Fig.17.

In Fig.17,the SIF ranges at the periphery of the fatal facets (i.e.ΔKτ-FF) are shown to be higher than the Mode II crack propagation threshold (ΔKτ-th).It is reasonable that Mode II microcracks within the original cracked grain can propagate through the grain boundary in the failed specimens.However,for a run-out specimen (i.e.survival even up to 109cycles),the microcracks are stopped at the grain boundary (see Fig.16).It is assumed that such microcracks in Fig.16 follows as a semi-circular shape in a semi-infinit body,and the effect of crack closure is negligible.Thus,the SIF value at the crack tip when it reaches the grain boundary is obtained by the formula:

whereτrepresents the shear stress andis the square root of the area projected on the plane parallel to the shear stress direction.The effective sizeof the longest microcrack in Fig.16 is about 26.58 μm,and thus the SIF value at the crack tip is about 0.49 MPa√m according to Eq.3[40].Obviously,it is larger than the threshold SIF value(ΔKτ-th=0.32 MPa√m),but smaller than the minimum SIF value 0.63 MPa√m at the periphery of a fatal facet (a failed specimen loaded at the same stress level 100 MPa),as shown in Fig.17(b).

From the above discussion,the microcrack propagations are stopped at the grain boundary for the run-out specimen(see Fig.16)with the SIF value 0.49 MPa√m at the crack tip,while the minimum SIF value 0.63 MPa√m at the periphery of the fatal facet can lead to a fina failure (see Fig.17).Therefore,it is concluded that the grain boundary provides a threshold SIF value for stopping crack propagation,which should be in the range from 0.49 to 0.63 MPa√m.When the driving force of crack growth at crack tip is larger than the above threshold,microcracks will break through the grain boundary.When the driving force at crack tip is smaller than the above threshold,microcracks will be stopped at the grain boundary and lead to an infinit life.It should be noted that in this study the above threshold value is determined in the range from 0.49 to 0.63 MPa√m,rather than a certain value.

3.6.The formation of the small bright area

From the aforementioned discussion,it is known that when one of the initial microcracks(Mode II crack)within the original cracked grain breaks through the grain boundary,it will transform to a Mode I crack.Therefore,crack propagation outside of the fatal facet should be controlled by the SIF range for Mode I crack (ΔKσ),rather than Mode II crack(ΔKτ).Thus,the SIF value for a Mode I crack at the periphery of the small bright area is obtained by the formula:

whereσrefers to the applied cyclic stress,andis the square root of the area projected on the plane normal to the loading direction.

For the internal failures after UPT,the values ofΔKσ-SBAvary from 1.57 to 1.99 MPa√m according to Eq.4 [44],as shown in Fig.18.It is worth noting that the values ofΔKσ-SBAare almost constant with an average value of 1.80 MPa√m for failure cycles between 106and 109.

From the viewpoint of dislocation emission,Mode I crack propagation threshold (ΔKσ-th) corresponds to a crack propagation rate of one Burgers vector per cycle,below which dislocation emission is retarded [41,43].Note that if the crack propagation distance is below one Burgers vector during cycling,it will be easily recovered under the combination effect of lattice force and reversal loading.If the propagation distance is larger than one Burgers vector,it will be difficul to recover completely.Therefore,below and above the threshold,crack propagation rate and facture surface morphology will differ definitel [43].In the present study,it is seen that the morphology of the small bright area is quite different from the other regions on fracture surface,as shown in Figs.12 and 13.The surface roughness on the small bright area is larger than that of the other areas.

Fig.18.Variations in the SIF range at the periphery of the small bright area(ΔKσ-SBA) depending on the fatigue life.

The threshold SIF value for Mode I crack (ΔKσ-th) of Mg alloys is available from a vast amount of fatigue crack propagation experiments.It should be noted that for the internal failures,fatigue crack nucleation and early propagation occur in the internal vacuum-like environment at specimen interior.Therefore,fatigue crack propagation experiment for evaluating the thresholdΔKσ-thof internal failures should be conducted in vacuum environment.Through literature investigation,Mode I crack propagation experiment of an extruded Mg alloy is conducted in vacuum environment with the same stress ratio (R=-1) by ultrasonic fatigue testing system [45].The correspondingΔKσ-this measured to be 1.90 MPa√m [45].In this study,the average value ofΔKσ-SBA(1.80 MPa√m) at the periphery of the small bright area is close to the above threshold SIF valueΔKσ-th(1.90 MPa√m).The small bright area should be formed during early crack propagation stage,and the large dark area corresponds to the stable crack propagation stage,which can be described by Paris law.The early crack propagation stage is strongly sensitive to microstructure,and fatigue crack propagates at an extremely low and fluctuatin growth rate [43].Therefore,fatigue crack propagation below the thresholdΔKσ-thleads to the formation of the small bright area,which displays a distinguishing roughness morphology on the fracture surface.

3.7.Fatigue performance improvement after UPT processing

Since crack initiation stage consumes most of the total fatigue life in VHCF regime,it should be paid much attention to [13,14].After UPT processing,all crack initiation sites are located in the interior core region beneath surface enhancement layer,as shown in Figs.11 and 12.The UPTed effect on fatigue crack initiation stage is mainly ascribed to two aspects:the residual stress (see Fig.6) and the plastic deformation (see Fig.4) in surface enhancement layer.The compressive residual stress can reduce the true driving force for crack initiation in surface enhancement layer[46].Surface enhancement layer,subjected to plastic deformations,should store high-density dislocations [47].The high-density dislocations improve the fatigue resistance of surface enhancement layer.In other words,the UPT-introduced high-density dislocations will extend the fatigue crack initiation life in the surface enhancement layer.Contrarily,the interior core region is not affected by the UPT processing,and presents the intrinsic material resistance for fatigue crack initiation.Therefore,the UPT processing makes fatigue cracks only initiate from the interior core region beneath the surface enhancement layer.

Based on the above discussion,it is found that for specimens with and without UPT processing,crack initiation sites possess the same intrinsic material resistance for fatigue crack initiation.However,UPT processing also improves the fatigue performance as shown in Fig.7,especially at higher stress levels.In the elasticity theory,crack propagation in the internal core region is nearly under plane strain condition,while crack propagation in the surface layer is prone to under plane stress condition.It means that confinemen effect at crack tip for crack propagation should be stronger when fatigue crack initiates from the interior core region.Therefore,the stronger confinemen effect at crack tip leads to an increase in the fatigue life when fatigue crack initiates from the interior core region.

On the other hand,from the perspective of environmental effect,ambient air can accelerate the crack propagation rate,while the internal vacuum-like environment will decelerate the crack propagation rate [29-31].In this study,surface failure initiates from the free surface,and crack initiation stage occurs in the ambient air environment.Contrarily,internal failure initiates from the interior core region,and crack initiation stage occurs in the internal vacuum-like environment.Therefore,in Fig.7,at high stress levels,internal failures present longer fatigue life in comparison to the surface failures due to the environmental effect.In other words,UPT processing makes the significan improvement of fatigue life at higher stress levels.

However,at lower stress levels,the UPT processing seems to have insignifican effect on fatigue life improvement.It is shown that at lower stress levels,fatigue failure of specimens without UPT processing is dominated by the subsurface failure mode,in which crack initiation stage occurs in the subsurface region.It should be noted that crack initiation in the subsurface region also occurs in the vacuum-like environment.It means that crack initiation stage of subsurface failure and internal failure occurs in the same vacuum-like environment.Therefore,environmental effect is insignifican at the lower stress levels.Under this condition,only the confinemen effect at crack tip improves the fatigue life of internal failure.As a result,UPT processing makes insignifican improvement of fatigue life at lower stress levels.

4.Conclusion

In this study,the UPTed effect on fatigue behaviors of a Mg alloy up to VHCF regime is studied by ultrasonic fatigue tests.The crack initiation and early propagation mechanisms are addressed in detail by failure analyses.The main conclusions are as follows:

(1) The UPT-affected zone can reach about～700 μm in depth,which is much deeper than that induced by the traditional surface strengthening techniques.All the surface and subsurface failures before UPT processing shift to the internal failures after UPT processing.It is attributed to the compressive residual stress and severe plastic deformation in the surface enhancement layer.

(2) The fatal facets are formed at crack initiation sites,and the initiation mechanism is strongly crystallographic on the planar slip systems along the maximum shear stress direction.At the crack initiation stage as Mode II crack,although the deformation localization led to multiple microcrack initiation on the slip planes,the grain boundary provides a threshold SIF value to prevent microcracks from breaking through the grain boundary,which is in the range from 0.49 to 0.63 MPa√m.At the crack early propagation stage as Mode I crack,crack propagation belowΔKσ-this the reason why the small bright area forms and displays a distinguishable roughness morphology.

(3) TEM results show that the fatal facet surface is parallel to the basal plane,and the formation of fatal facet results from the deformation localizations of basal slips.It is found that nanograins only occurs beneath the small bright area (i.e.beneath the distinguishable roughness surface),rather than the fatal facet.Based on the Numerous Cyclic Pressing (NCP) model,it is proposed that the formation of fine-granula-area (FGA) in very-high-cycle fatigue (VHCF) regime is only associated with the Mode I crack at the early crack propagation stage.

Acknowledgement

This work was supported by the National Natural Science Foundation of China (Nos.12102280,12172238,11832007,12022208,12072212,and 52003181),the Science&Technology Support Program of Sichuan Province(Nos.2020YJ0230,and 2021YJ0555) and the Fundamental Research Funds for the Central Universities of China (No.2021SCU12129).We also appreciate the Institute for Advanced Study,Chengdu University,for their assistance in TEM characterization(JEMF200).