Effect of void nucleation on microstructure and stress state in aluminum alloy tailor-welded blank

L.Xing ,M.Zhan,＊ ,P.F.Gao ,M.Li ,Y.D.Dong ,T.Y.Wang

a State Key Laboratory of Solidification Processing,School of Materials Science and Engineering,Northwestern Polytechnical University,Xi’an,710072,China

b Shaanxi Key Laboratory of High-Performance Precision Forming Technology and Equipment,Xi’an,710072,China

c Key Laboratory of High Performance Manufacturing for Aero Engine(Northwestern Polytechnical University),Ministry of Industry and Information Technology,Xi’an,710072,China

Keywords:Aluminum alloy Welded joint Void nucleation Microstructure Stress state Micromechanical model

ABSTRACT The microscopic damage initiation characteristic in welded joint greatly determines the subsequent damage evolution and fracture behavior of aluminum alloy tailor-welded blank (TWB) during plastic forming.In this study,the interactive dependence of void nucleation on microstructure and stress state in the welded joint of a 2219 aluminum alloy TWB was quantitatively explored by in-situ SEM testing.Moreover,a micromechanical model based on actual microstructure was adopted to reveal the underlying mechanisms from the perspective of microscopic heterogeneous deformation.The results showed that three void nucleation mechanisms,including particle-cracking,interface-debonding and matrix-cracking,coexisted in the deformation at different microstructure regions and stress states.The nucleation strain of each mechanism mainly depended on the particle volume fraction,grain size and stress triaxiality.Besides,the proportions of particle-cracking and interfacedebonding greatly varied with the grain size and particle volume fraction,and the variation law changed with the stress state.The proportion of matrix-cracking had a weak dependence on the microstructure,while increased with the stress triaxiality decreasing.It made the damage initiation in aluminum alloy welded joint transit from particle-cracking dominance to matrix-cracking dominance with the stress triaxiality decreasing.The micromechanical modeling results suggested that the changes of evolutions and distributions of Mises stress in particle,hydrostatic stress at interface and plastic strain in matrix with microstructure and stress state were responsible for the above effects.

1.Introduction

Aluminum alloy components with tailor-welded blank (TWB) have been widely used in the automotive and aircraft fields because of their advantages:easily achieve light-weight,low cost and short cycle forming[1-4].In the forming process of this kind of component,TWB often needs to undergo large plastic deformation.However,due to the great gradient distributions of microstructure and mechanical property in the welded joint,the deformation unevenness was intensified.It makes the ductile fracture of aluminum alloy TWB more likely to occur,which significantly reduces the forming quality and forming limit [5-7].Therefore,it is crucial to understand and master the fracture behavior in the plastic forming of aluminum alloy TWB,which provides a basis for improving the forming quality and forming limit.

By now,a series of researches on the aluminum alloy TWB have been conducted to reveal the fracture behavior in the plastic deformation.Lee et al.[8] investigated the dependence of fracture on weld zone (WZ)orientation as well as ductility and strength in the forming process of aluminum alloy TWB.It was concluded that the fracture is mainly affected by the ductility of WZ when the major principal loading direction is aligned with the WZ,otherwise,the strength of the WZ is more important.Nielsen[9]analyzed the dependence of fracture location on mechanical properties in different microstructure regions during tension deformation of aluminum alloy welded joint.Kim et al.[10]found that the fracture of TWB is determined by differences in flow stress and ductility of different microstructure regions.Shakeri et al.[11] and Negre et al.[12] investigated the crack propagation behavior of initial cracks in different microstructure regions of aluminum alloy welded joint.The above studies mainly focused on the macroscopic fracture behaviors in the plastic deformation of aluminum alloy TWB.Generally,the fracture is the external result of the microscopic damage evolution,including void nucleation,growth and coalescence [13,14].Nielsen et al.[15]and Simar et al.[16]analyzed the void feature on the fracture faces of different microstructure samples in aluminum alloy TWB.It was found that void coalescent by forming a large number of secondary voids between the primary voids for PZ and weld nugget zone (WNZ) with small particle size,whereas only primary voids necking were observed for heat affected zone (HAZ) with large particle size.Xing et al.[17]investigated the void growth and coalescence in aluminum alloy TWB and concluded that the void growth rate and coalescence criterion significantly vary with the microstructure and stress state.Meanwhile,their dependences on the microstructure are affected by the stress state.These studies focused on the void growth and coalescence processes in plastic deformation of aluminum alloy TWB.However,the details of void nucleation are still lacking.In particular,void nucleation,as damage initiation,determines the subsequent development of damage and plays an extremely important role in the fracture.Therefore,it is of great importance to explore the microscopic void nucleation behavior in the plastic forming of aluminum alloy TWB.

In recent years,the researches on void nucleation in homogeneous materials have shown that the void nucleation strongly depends on the microstructure and stress state for aluminum alloy.Horstemeyer et al.[18]and Hannard et al.[19,20]found that the particle volume fraction and particle size have an impact on void nucleation for aluminum alloy by comparing the void number on the fracture face.In the study of Lassance et al.[21],it was stated that when the majority of particles with their long axis oriented at an angle smaller than 45°with respect to the main loading direction,the void mainly nucleates by the particle cracking.Whereas,the particle/matrix interface debonding mainly occurs for aluminum alloy.Landron et al.[22] and Cox et al.[23]concluded that the voids associated with particles are more likely to nucleate at higher triaxiality.However,the quantitative and in-depth dependences of void nucleation on microstructure and stress state are still lacking,and the underlying mechanism is unknown.Furthermore,for aluminum alloy welded joint,multiple microstructure parameters simultaneously vary in gradient,which may result in the different and more complicated dependences.Therefore,it is urgent to explore the dependences of void nucleation on the welded microstructure and stress state in the plastic deformation of aluminum alloy TWB.

In this study,the microscopic void nucleation behaviors in different microstructure regions of aluminum alloy welded joint were systematically investigated under various stress states based on in-situ SEM testing.The interactive dependences of void nucleation on the microstructure and stress state were quantitatively explored,in which the void type was distinguished.Moreover,the underlying mechanism was revealed through micromechanical simulation.This result laid the foundation for an understanding of the damage and fracture behaviors in the plastic forming of aluminum alloy TWB.

2.Experimental

2.1.Material

The material used in this work was an annealed 2219 aluminum alloy sheet with a thickness of 6 mm.The chemical compositions of this alloy are given in Table 1.The sheets were welded by friction stir welding (FSW) along the rolling direction,in which the welding speed and rotational speed were 200 mm/min and 700 r/min,respectively.

Table 1 Chemical compositions (wt.%)of the alloying elements in 2219 aluminum alloy.

2.2.Observation of microscopic damage initiation

In-situ SEM testing was conducted to capture the void nucleation during tensile deformations with various stress states.Three kinds of stress states tests,including uniaxial tension,0°shear and 90°shear,were conducted by using the specimens referred to Ref.[17].The average stress triaxiality(η)at these specimen center were 0.34,0.1 and 0.6,respectively.The tests were conducted on a MICROTEST-5000 tensile stage,which was mounted within a ZEISS SUPRA55 FE-SEM.In the initial stage deformation,the microstructure morphology in the center of the specimen was continuously recorded at small strain intervals to capture the void nucleation behavior.

2.3.Micromechanical model based on actual microstructure

In order to reveal the underlying mechanism of the dependences of damage initiation on microstructure and stress state,the micromechanical model which was developed earlier [17] was adopted to obtain the microscopic stress and strain distributions during deformation.In the model,the differences of the mechanical properties between the two constituent phases were considered.Among them,the Al2Cu particle was assumed to have a linear elastic material response,and the Al matrix was assumed to have elastic-plastic behavior with hardening governed by a Hollomon law.The specific values of material parameter were detailed in Ref.[17].

The micromechanical model was verified by comparing the predicted macroscopic response with the experimental results.It suggests that this model can predict the microscopic heterogeneous deformation during tensile deformation.During the analyses of simulated results,the quantitative data was extracted by running a programed script in ABAQUS post-processing.

3.Results and discussion

3.1.Microstructure in aluminum alloy tailor-welded blank

Fig.1 shows the macro and microstructure of the obtained FSW welded joint.According to the difference of microstructure,the welded joint could be divided into four regions,i.e.,WNZ,HAZ1,HAZ2 and PZ(Fig.1(a)).From Fig.1(b),the microstructures of each region were all the typical dual phase microstructures,consisting of Al matrix and Al2Cu particle.Their microstructure parameters were measured through Image-Pro Plus software based on the RGB index range of colors to automatically identify grain boundaries and particle morphology,as shown in Fig.1(c).It was found that for WNZ,the grain size was the smallest,while the particle volume fraction and particle size were the largest.For PZ,the particle volume fraction was the smallest,while the grain size was larger.

In order to explore the void nucleation behaviors in different microstructure,we took four groups specimens from the above regions,which were named as PM (in PZ),HAM1 (in HAZ1),HAM2 (in HAZ2)and WNM(in WNZ),respectively.

3.2.Microscopic damage analysis

In terms of void nucleation,the nucleation mechanism (type),nucleation strain and proportion of different types of voids are three critical indexes.Their characteristics in different microstructures and stress states were quantitatively analyzed to reveal the nonuniform damage initiation in welded joint.Furthermore,the underlyingmechanisms for their different nucleation behaviors were discussed based on the evolutions and distributions of microscopic stress and strain during deformation.

Fig.1.Macroscopical characteristic of 2219 aluminum alloy FSW welded joint (a),and microstructures (b) and microstructural parameters (c) of various regions.

3.2.1.Void nucleation mechanism

The stress-strain curves for in-situ testing under uniaxial tension are shown in Fig.2(a),three strains in figure were marked to capture the void nucleation characteristic.The microstructures at these strains were continuously recorded,as shown in Fig.2(b).It was observed that there were three types of void nucleation mechanisms for any microstructure specimen,including the particle/matrix interface-debonding (yellow arrow),particle-cracking (red arrow) and matrix-cracking (green arrow).Their nucleation were closely related to the microscopic heterogeneous deformation.As can be seen,a significant deformation mismatch existed between the particle and matrix (red circle in Fig.2(І)),which resulted in the stress concentration (red circle in Fig.2 (ІІ))and the variation of hydrostatic stress(Fig.2(ІІІ))at the interface.When the stress exceeded the interfacial strength,as well,the hydrostatic stress at the interface was a large positive value(red circle in Fig.2(ІІІ)),the debonding at the interface occurred.For the particle-cracking void,its nucleation was determined by the larger Mises stress in particle(white circle in Fig.2(ІІ)).When the stress exceeded the strength of the particle,the cracking was formed[24,25].As for the cracking in matrix,it was usually caused in two ways.One was the cracking of grain boundary,which was related to the stress concentration caused by the dislocation pile-up at the grain boundary.The other was the cracking of grain,which was associated with the stress concentration caused by the crossing of multiple slip bands in the interior of grains[26,27].Since the micromechanical simulation did not consider grains and their crystallographic orientation,these uneven stress and strain distributions within grains could not be presented from the current model.

Fig.3 shows the microstructures of PM and WNM at the initial deformation stage under 0°shear and 90°shear tensile conditions.It was seen that the void nucleation mechanisms under 0°shear and 90°also presented the particle/matrix interface-debonding,particle-cracking and matrix-cracking.These indicated that the void nucleation mechanism did not vary with the stress state in the plastic deformation of aluminum alloy TWB.

3.2.2.Void nucleation strain

The nucleation strain refers to the minimum strain when the void appears,which determines the critical condition for the damage initiation.In this section,the nucleation strains of the above three types of voids were counted by recording the strains when these voids appeared under different microstructure specimens and stress states,as shown in Fig.4.These statistics were based on three groups of in-situ SEM tensile tests with two observation locations on each test.

From Fig.4(a),the nucleation strain of the matrix-cracking void was overall higher than those of interface-debonding and particle-cracking voids for each microstructure specimen.This was because its nucleation was related to the dislocation pile-up and crossing of the slip band,which were mainly formed at a larger strain.The result meant that the particle-cracking and interface-debonding occurred first,while the matrix-cracking formed later in the plastic deformation of aluminum alloy welded joint.Besides,it can be seen from Fig.4(a) that the nucleation strain of each type of void was quite different in four microstructure specimens under uniaxial tension.Coincidentally,they were all the smallest in PM and the largest in WNM,presenting an increasing trend from PM to HAM and then to WNM.Combining the difference of microstructural parameters in four regions(Fig.1),it was found that as a whole,the nucleation strains of three types of voids all gradually decreased with the increase of grain size and the decrease of particle volume fraction.These variations were related to the difference in microscopic heterogeneous deformation under different microstructure parameters,which will be discussed in detail below.

Fig.2.Stress-strain curves for in-situ tensile testing(a),and microstructures of PM(b),HAM2(c),HAM1(d)and WNM(e)at the strain of 0.02(1),0.04(2)and 0.08(3) under uniaxial tension.

According to the stated in Section 3.2.1,the nucleation of particlecracking void was associated with the Mises stress in particle (MS-P).For the interface-debonding void,its nucleation was attributed to the significant deformation mismatch between the particle and matrix(Fig.2 (І)).This deformation mismatch led to the variation of hydrostatic stress at the interface (Fig.2 (ІІІ)).When the hydrostatic stress reached the positive value,it meant that the volume of material would expand.In other words,the larger hydrostatic stress at the interface meant the higher probability of interface debonding.Thus,the hydrostatic stress at the interface could be adopted to evaluate the nucleation of interface-debonding void.Kadkhodapour et al.[28] and Horstemeyer et al.[29]stated that the maximums of these two stresses could be used to evaluate the corresponding nucleation strain.The larger the maximums of two stress were,the smaller the nucleation strain would be for the two types of voids.For the matrix-cracking void,its two nucleation ways,including the cracking of grain boundary caused by the dislocation pile-up and the cracking of grain caused by the crossing of multiple slip bands in the interior of grains,were both related to the plastic deformation in matrix.The dramatic local plastic deformation would increase the possibility of matrix cracking.Thus,the nucleation strain of the matrix-cracking void was related to the maximum of equivalent plastic strain in matrix (PEEQ-M) [30].The larger the maximum of PEEQ-M corresponded to the smaller nucleation strain for the matrix-cracking void.Therefore,the maximum of MS-P,maximum of HS-I and maximum of PEEQ-M will be discussed to reveal the mechanism of the dependences of nucleation strain.

Fig.5 shows the evolutions of the maximum of MS-P,maximum of HS-I and maximum of PEEQ-M in various microstructure specimens and stress states.It was seen from Fig.5(a) that the maximum of MS-P was the smallest in WNM and the largest in PM in the initial deformation stage under uniaxial tension,and it showed an increasing trend with the increase of grain size and the decrease of particle volume fraction.These were related to the change of load sharing between matrix and particle.As the grain size increased,the stress required for matrix deformation would decrease,so that the stress in particle increased.Besides,the decrease of particle volume fraction resulted in fewer particles to share the load,which would make the stress in particle increase.Thus,the maximum of MS-P showed an increasing trend with the grain size increasing and the particle volume fraction decreasing.These would promote the nucleation of particle-cracking void and decrease the nucleation strain.From Fig.5(b)and(c),it was seen that the maximum of HS-I and maximum of PEEQ-M also were the smallest in WNM and the largest in PM under uniaxial tension,presenting an increasing trend with the increase of grain size and the decrease of particle volume fraction.These were related to the plastic deformation in matrix.As the particle volume fraction decreased,the suppression of particle to the deformation in matrix would be weakened,which promoted the plastic deformation in matrix.This on the one hand propelled the maximum of PEEQ-M to exhibit an increasing trend.On the other hand,it intensified the deformation incompatibility between matrix and particle,which then led to larger tensile stress at the particle/matrix interface on the side of the tensile direction.Accordingly,the local stress triaxiality at the interface got larger,and the HS-I increased in accompany.Thus,the maximum of HS-I also presented an increasing trend.Consequently,these variations led to the nucleation strains of interface-debonding and matrix-cracking voids decrease with the grain size increasing and the particle volume fraction decreasing.

Fig.3.Microstructures of PM (1) and WNM (2) at the initial deformation stage under 0° shear (a) and 90°shear (b).

Fig.4.Nucleation strains of three types of voids in four microstructure specimens under uniaxial tension (a),PM and WNM under various stress states (b).

According to Fig.4(b),it can be seen that the nucleation strain of each type of void increased with stress triaxiality for each microstructure specimen.It was noted that the stress states studied in this work were all under plane stress loading conditions.The variations of nucleation strain with stress triaxiality were related to the differences of the maximum of MS-P,maximum of HS-I and maximum of PEEQ-M.From Fig.5,it was visible that the values of these three parameters gradually decreased with the stress triaxiality increasing.This was because under plane stress loading,as the stress triaxiality increased from 0.1 to 0.6,the shear stress component gradually decreased.This would weaken the non-uniformity of deformation between the matrix and particle,which further reduced the above three parameters.These variations let to the nucleation strains of three types of voids present an increasing trend with the stress triaxiality.Extraordinarily,an abnormal law occurred for the maximum of PEEQ-M under 90°shear(Fig.5(c)):its value was larger than that under uniaxial tension,while the anomaly was not mapped to the nucleation strain.The reason for this inconsistent may be that there was a part of compressive strain in 90°shear deformation,which suppressed the generation of the void.Therefore,although the maximum of PEEQ-M under 90°shear was larger,the nucleation strain of matrix cracking was larger.Besides,it was also found from Fig.4(b) that the nucleation strains of each type of void in WNM were both greater than those in PM under 0°and 90°shear stress states,which were consistent with those under uniaxial tension.These results indicated that the void nucleation strain of each type of void was related to the stress state,and this dependence was not affected by microstructure.Moreover,the stress state also did not affect the dependence on microstructure.

3.2.3.Proportion of void type

The proportion of void type reflects the difference in the density of various types of void after deformation,where density refers to the number of void per unit area.It has an important effect on fracture behavior.In this section,the density of each type of void near the fracture surface after deformation was counted to obtain the proportions of three types of voids in different microstructure specimens and stress states,as shown in Fig.6.

Fig.5.Evolutions of the maximum of Mises stress in particle(a),maximum of hydrostatic stress at interface(b)and maximum of equivalent plastic strain in matrix(c) for various microstructures and stress states.

According to Fig.6(a),it can be observed that under uniaxial tension,the particle-cracking was the dominant damage initiation in each microstructure specimen,and the interface-debonding was occasional.However,the proportions of each type of void were quite different in four microstructure specimens.In the case of the particle-cracking void,its proportion was the highest in HAM2 and the lowest in PM.For interface-debonding void,the law of its proportion was exactly opposite to that of the particle-cracking void.For the matrix-cracking void,its proportions in four microstructure specimens differed slightly.These results suggested that the proportions of particle-cracking and interfacedebonding voids significantly varied with the microstructure under uniaxial tension,while that of the matrix-cracking void had a weak dependence on the microstructure.

The proportion of void nucleation type was related to the distribution frequency of microscopic stress and strain in the whole observed region.According to the front analyses,the proportions of particlecracking,interface-debonding and matrix-cracking voids were associated with the distribution frequency of MS-P,HS-I and PEEQ-M,respectively.It has been reported that the particle Al2Cu was usually a brittle phase at room temperature,whose fracture resistance was lower than 680 MPa[31].Thus,the frequency of MS-P greater than 680 MPa was concerned to evaluate the proportion of particle-cracking void.For the proportion of interface-debonding void,it was generally known that HS-I≤0 meant no damage and HS-I＞0 indicated that void may be generated.Thus,the frequency of HS-I ≤0 was focused.In terms of the proportion of matrix-cracking void,the frequencies of PEEQ-M greater than 0.25 were concerned,because the difference in void density significantly increased when PEEQ-M was greater than 0.25 for different microstructures.

Fig.6.Proportions of the density of three types voids in four microstructures under uniaxial tension (a),and PM and WNM under various stress states (b).

Fig.7.Distributions of Mises stress in particle(a),hydrostatic stress at interface(b),equivalent plastic strain in matrix(c)under uniaxial tension,and evolutions of average Mises stress in particle (d) and distributions of hydrostatic stress at interface under various stress states.

Fig.7 shows the quantitative distributions and evolution of MS-P,HS-I and PEEQ-M for different microstructures at the later stage of various stress states deformations.From Fig.7(a),it was found that the frequency of MS-P greater than 680 MPa varied greatly with microstructure under uniaxial tension.According to the difference of microstructural parameters,it was found that the frequency mainly relied on the grain size and particle volume fraction,showing an increasing trend with them.As a result,the frequency reached the largest in HAM2,causing the highest proportion of particle-cracking void in HAM2 under uniaxial tension.According to Fig.7(b),the frequency of hydrostatic stress less than 0 varied with microstructure and overall showed an increasing trend with the grain size and particle volume fraction under uniaxial tension.Consequently,it presented as the highest in HAM2 and the lowest in PM,further producing the lowest proportion of interfacedebonding void in HAM2 and the highest proportion in PM under uniaxial tension.From Fig.7(c),the frequencies of strain greater than 0.25 changed little with microstructure,which made the less dependence of the proportion of matrix-cracking void on microstructure under uniaxial tension.

For the results under various stress states,it was found from Fig.6(b)that the results of proportion under 90°shear were similar to those under uniaxial tension for each microstructure specimen,displaying the particle-cracking dominance.With the decrease of stress triaxiality,the proportion of particle-cracking void gradually decreased,while that of matrix-cracking void increased for each microstructure specimen.For the decrease of the proportion of particle-cracking,it was related to the evolutions of average MS-P.Fig.7(d) shows the evolutions of average MS-P for PM and WNM under various stress states.It was seen that the average MS-P was weakened as stress triaxiality decreasing for any microstructure specimen,which resulted in a low probability of particle cracking.Regarding the increase of the proportion of matrix-cracking,it was mainly attributed to the increases in the shear stress component in deformation.The shear stress had a promoting effect for the cracking of grain boundary,which further made the proportion of matrix-cracking void gradually increase.As a result,the matrix-cracking transformed into the dominant void nucleation mechanism under 0°shear.The transition of the dominant nucleation mechanism with stress triaxiality will greatly determine the macroscopic fracture behavior,whose reason will be discussed below.

Besides,it was also found in Fig.6(b) that for the interfacedebonding void,the proportion in WNM was larger under 90°shear,while smaller under uniaxial tension than that in PM.It was related to the relations of average MS-P between PM and WNM varied with stress state (Fig.7(d)):PM presented smaller average MS-P under uniaxial tension,while a larger value under 90°shear than WNM.This resulted in the dependence of the proportion of particle-cracking void on microstructure changing with stress state.Similarly,for the particle-cracking void,the relation of proportion between PM and WNM under 90°shear also varied compared to that under uniaxial tension.It was ascribed to the variation of HS-I,as shown in Fig.7(e).The frequency of HS-I less than 0 for WNM was higher than that for PM under uniaxial tension,while this was reversed under 90°shear,which made the dependence of the proportion of interface-debonding void on microstructure varying.These results indicated that the dependences of the proportions of particle-cracking and interface-debonding voids on microstructure varied with the stress state.

3.3.Fracture morphology

As mentioned above,the proportion of void type had an important effect on the fracture behavior.Xing et al.[17]stated that under uniaxial tension,with the increase of the proportion of particle-cracking void,ligament shearing between voids was promoted during the fracture.To clarify the effect the proportion of void type on fracture behavior of various microstructure specimens,the fracture morphology was observed.Fig.8 shows the fracture morphologies of the above four microstructure specimens under uniaxial tension.As can be seen from Fig.8,the number of quasi-cleavage surface formed by the ligament shearing was the largest for HAM2,which was attributed to the highest proportion of particle-cracking void in HAM2(Fig.6(a)).However,the number of quasi-cleavage surface was the smallest in PM,which was due to the smallest proportion of particle-cracking void in PM (Fig.6(a)).These verify that the fracture behavior of material was closely related to the proportion of void type.

4.Conclusion

The interactive dependence of void nucleation on microstructure and stress state in 2219 aluminum alloy tailor-welded blank have been quantitatively explored and explained through the in-situ SEM testing and micromechanical modeling.

(1) The nucleation strains of particle-cracking,interface-debonding and matrix-cracking voids all show a decreasing trend with the increase of grain size and the decrease of particle volume fraction,which make them present the smallest value in parent zone and the largest value in weld nugget zone.Meanwhile,all these nucleation strains increase with stress triaxiality under plane stress loading.These results are mainly attributed to the variations of the maximum of Mises stress in particle (MS-P),maximum of hydrostatic stress at interface(HS-I)and maximum of equivalent plastic strain in matrix (PEEQ-M) with the microstructure and stress state.

(2) As the grain size and particle volume fraction increase,the proportion of particle-cracking void increases,while the proportion of interface-debonding void decreases under uniaxial tension.These result in the highest proportion of particle-cracking void and the lowest proportion of interface-debonding void in heat affected zone-2 under uniaxial tension.However,the above variation laws are reversed under 90°shear deformation.For the proportion of matrix-cracking void,it has a weak dependence on the microstructure,while increases with the decrease of stress triaxiality.It makes the damage initiation transits from particlecracking dominance to matrix-cracking dominance with the stress triaxiality decreasing.The underlying reasons for these effects are that the distribution frequencies of MS-P,HS-I and PEEQ-M vary with microstructure and stress state.

Fig.8.Fracture morphologies of PM (a),HAM2 (b),HAM1 (c) and WNM (d) under uniaxial tension.

Declaration of competing interest

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

Acknowledgments

The authors acknowledge support from the National Science Fund for Distinguished Young Scholars of China(51625505),the Key Program Project of the Joint Fund of Astronomy and National Science Foundation of China (Project U1537203) and the Research Fund of the State Key Laboratory of Solidification Processing(NWPU),China(Grant No.2019-TZ-02).