Mechanical properties study of particles reinforced aluminum matrix composites by micro-indentation experiments

Chinese Journal of Aeronautics, (2014),27(2): 397–406

Chinese Society of Aeronautics and Astronautics & Beihang University

Chinese Journal of Aeronautics [email protected] www.sciencedirect.com

Mechanical properties study of particles reinforced aluminum matrix composites by micro-indentation experiments Yuan Zhanwei, Li Fuguo *, Zhang Peng, Chen Bo, Xue Fengmei State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, China Received 26 February 2013; revised 16 May 2013; accepted 6 November 2013 Available online 20 February 2014

KEYWORDS Aluminum matrix composites; FEM; Microhardness; Micro-indentation; Young’s modulus

Abstract By using instrumental micro-indentation technique, the microhardness and Young’s modulus of SiC particles reinforced aluminum matrix composites were investigated with microcompression-tester (MCT). The micro-indentation experiments were performed with different maximum loads, and with three loading speeds of 2.231, 4.462 and 19.368 mN/s respectively. During the investigation, matrix, particle and interface were tested by micro-indentation experiments. The results exhibit that the variations of Young’s modulus and microhardness at particle, matrix and interface were highly dependent on the loading conditions (maximum load and loading speed) and the locations of indentation. Micro-indentation hardness experiments of matrix show the indentation size effects, i.e. the indentation hardness decreased with the indentation depth increasing. During the analysis, the effect of loading conditions on Young’s modulus and microhardness were explained. Besides, the elastic–plastic properties of matrix were analyzed. The validity of calculated results was identified by finite element simulation. And the simulation results had been preliminarily analyzed from statistical aspect. ª 2014 Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA.

1. Introduction The micro-mechanical properties of materials have been a popular and interesting subject nowadays, since the material exhibits different properties from micro scale to macro scale, such as scale effect. Through indentation experiment, it is very * Corresponding author. Tel.: +86 29 88474117. E-mail address: [email protected] (F. Li). Peer review under responsibility of Editorial Committee of CJA.

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effective to explore the mechanical properties in micro scale.1 Discontinuous particles reinforced metal matrix composites (MMCs) have generated much interest recently due to their promising mechanical properties.2–9 The mechanical properties of MMCs generally depend on the microstructures of the materials, such as particle size effect.10,11 The optimization of the mechanical properties of composites is based on the knowledge of the relationship between the microstructure and the macroscopic response of MMCs. Up to now, though a considerable volume of literature regarding the microstructure and macroscopic mechanical behavior exists12–15; their micromechanical behavior between particles and matrix has not been examined in detail. From the design perspective as well as structure aspect, it is imperative to develop a detailed

1000-9361 ª 2014 Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA. http://dx.doi.org/10.1016/j.cja.2014.02.010

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understanding of the micro mechanical and elastic–plastic properties of MMCs. One of the widely used techniques for the evaluation of the elastic and plastic properties at both microscopic and macroscopic level is the depth-sensing instrumented indentation.16–20 It has long been recognized that instrumented indentation is a powerful technique for studying resistance of materials against deformation. For this reason, indentation has been widely used as an indirect method to characterize many fundamental mechanical properties of materials including Young’s modulus and hardness based on the experimentally determined load-unload curves (P–h).1,21–26 The first studies in this field can be traced back to the works of Ternovki et al. followed by the contributions of Nix et al.27,28 also Oliver and Pharr23, Lu and Suresh.29 Nowadays, this subject has been widely studied from theoretical and experimental investigations. For MMCs, scientists have been making preliminary exploration for both indentation experiments and simulations.30–36 In this paper, a study of instrumented microindentation for the characterization of MMCs is reported. The aim of the study is to explore the properties of MMC and to provide a thorough analysis of the deformation during loading/unloading under different conditions. 2. Experiments and theory 2.1. Experimental methods

particles (embossed) distributed scatteredly in matrix while assembling in some place and a few of black holes are the positions where particles dropped out during preparing specimens. Instrumented micro-indentation mechanical properties have been measured by using a Shimadzu micro-compression-tester type W501 (MCT) equipped with a Berkovich diamond indenter. And the morphologies of composite were examined by a TESCAN VEGAII-LMH scanning electron microscope (SEM). During the tests, specimens for indentation investigation were performed at different loads (10–25 mN, and 80–400 mN), different micro structures (particle, matrix and interface), and different loading speeds (2.231, 4.462 and 19.368 mN/s). Furthermore, the matrix in MMC has been much more focused in this study to explore the detail micromechanical behavior. The indentation load–displacement data obtained during one cycle of loading and unloading was recorded simultaneously. And the micro mechanical properties corresponding to the measuring point were then analyzed from the load–displacement curve. 2.2. Theory In the indentation field, Oliver and Pharr22,23 have shown their methods based on the Berkovich indenters. The law relating the applied load, P, to the penetration depth, h, follows Kick’s law: P ¼ Ch2

The specimens investigated (aluminum alloy reinforced by 15% SiC particles) were made by a powder metallurgy route. The raw aluminum was prepared by atomized powder, and then mixed with SiC particle. After hot extrusion (extrusion ratio is 9.8 to 1, at extrusion temperature 773 K), the SiCp/Al composite was obtained. Before testing, the specimens have been annealed at 673 K for 2 h. The content of matrix is shown in Table 1. In this composite, the particle size distributed within the range of 1–12 lm, and the major size is 3–8 lm; the particle aspect ratio lies around 1–2 after statistic analysis by the maximum/minimum axis ratio. The metallographic structure of the study material is shown in Fig. 1. In this figure, the

Table 1 Chemical composition of matrix in SiC particle reinforced Al matrix composites. Element

Cu

Mg

Mn

Fe

Si

Zn

Ti

Al

wt.%

4.10

0.64

0.54

0.37

0.34

0.10

0.02

Bal.

ð1Þ

where C is loading curvature which depends on elastic and plastic material properties, as well as indenter geometry. Similarly, the unloading curve follows a simple power-law relation determined by a least square fitting procedure: P ¼ B  ðh  hf Þm

ð2Þ

where B and m are fitting parameters and hf is the residual depth after complete unloading. The elastic contact stiffness, S, is given by the first derivative at the peak load of unloading curve:  dP S ¼  ð3Þ dh h¼hm where hm is maximum penetration depth. The depth, along which contact is made between the indenter and the specimen, can be estimated and given by hc ¼ hm  c

Pm S

ð4Þ

where Pm is the peak load at the onset of unloading, and c is a tip-dependent geometry factor, which is equal to 0.72 for a conical indenter, 0.75 for a Berkovich indenter and 1 for a flat cylindrical indenter.1,23,37,38 From the knowledge of hc and taking into account the indenter shape, the developed contact area, A, can be given by39 A ¼ 24:56h2c

ð5Þ *

Then the indentation modulus, E , is expressed as pffiffiffi p S  E ¼  pffiffiffiffi 2b A Fig. 1

SEM metallographic structure of MMC.

23

ð6Þ

where b is a constant associated with the indenter shape. It has been used to account for deviations in stiffness caused by the

Mechanical properties study of particles reinforced aluminum matrix composites by micro-indentation experiments lack of axial symmetry for pyramidal indenters.23 For a Berkovich indenter, the value of b is between 1.034 and 1.09.1 The Young’s modulus E and hardness H of the specimen can be expressed by  1 1 1  m2i E ¼ ð1  m2 Þ   ð7Þ Ei E H¼

Pm A

ð8Þ

where m is the Poisson’s ratio of the specimen, and Ei and mi are the Young’s modulus and the Poisson’s ratio of the indenter, respectively. The properties of the indenter are: Young’s modulus Ei = 1147 GPa and Poisson’s ratio mi = 0.07. Combined Eq. (6) with Eq. (7), the Young’s modulus of specimen can be determined finally, and the hardness can be calculated from Eq. (8). 3. Results and discussion 3.1. Micro-mechanical properties of different micro structures in MMC Usually, the conventional Young’s modulus values for SiC particles and Al alloy are 440 GPa and 70 GPa, respectively. In terms of composites of SiC particles and Al alloy, the composites Young’s modulus EC can be calculated according to the rule of mixtures in the Halpin-Tsai equation10 with particle Young’s modulus Ep, matrix Young’s modulus Em and particle volume Vp, EC ¼

Em ð1 þ 2sqVp Þ 1  qVp

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SiC particle, matrix, and interfaces. For particles, the penetration curves are shallow in contrast to deep penetrations to those in the interfaces, and deeper for matrix. In regard to different micro structures of this composite, the indentation sizes are dissimilar. And the variations of the shape of the curves (especially for the indentation depth) illustrated the specific mechanical behavior. Fig. 3(a) plots a detailed description of P–h curves for particle. From this figure, it can be found that before position ‘A’, the load curve is flat, and then transits to an abrupt curve after position ‘A’. For this phenomenon, it is different from pure material, which is smooth transition like standard curves (such as parabola). And this discrepancy may be related to particle as a ‘second indenter’ to matrix during indentation (see Fig. 3(b)). At the beginning of indentation of particle, with the load increasing the particle moved down with indenter, like an indenter to ‘push’ the interface (or matrix), and thus the P–h curves mainly captured the indentation property of interfaces or matrix. After ‘compaction’, the P–h curves would mainly show the property of particle. In the case of interfaces, the P–h curves sometimes are shown as a similar pattern to particle (see Fig. 4(a)). Before position ‘B’, the P–h curves mainly captured the indentation property of matrix. Not until the indenter slides to neighboring particles, does the curve become sharper after position ‘B’ (see Fig. 4(b)). Fig. 5 shows the SEM metallographic structure of the MMC after indentation experiments. In terms of matrix, the indentation is similar to the normal material (see Fig. 5(a));

ð9Þ

where q¼

ðEp =Em  1Þ ðEp =Em Þ þ 2s

and s is the particle aspect ratio. Here, the particle aspect ratio s is about 1–2; and particle Young’s modulus Ep = 440 GPa, matrix Young’s modulus Em = 70 GPa and particle volume Vp = 15%, so the Young’s modulus of this composite is 92.22–99.23 GPa according to the rule of mixtures. Under one load condition, the experiments were executed for several times (deviant indentation curves have been excluded), and the curves of the load versus the penetration depth are displayed in Fig. 2 for different micro structures as

Fig. 2 Examples of P–h curves of different micro structures in MMC at loading speed 2.231 mN/s.

Fig. 3 A detailed description for indentation experiments of the case of particle.

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Fig. 4 A detailed description for indentation experiments of the case at interface.

Z. Yuan et al. however, for particle, it shows difference, i.e., it may be related to ‘second indenter’ to matrix or particle damage during indentation. Fig. 5(b) displays typical cracking at the corner of particle, resulting from the large displacement of the indenter in the particle. This may be due to stress concentration in particle and will strongly influence the tested results which are different from the normal pure particle indenter test.19 Using the methods related in Section 2, the microhardness and Young’s modulus were calculated. For indentation experimental results, the Young’s modulus and hardness of these micro structures were different and distributed in a wide range. For SiC particle and Al alloy matrix, the mean Young’s modulus values were 334.7 GPa (from 268.4 GPa to 435.8 GPa) and 76.8 GPa (from 65.1 GPa to 96.2 GPa) respectively, at the load of 20 mN. As far as particle is concerned, the mean Young’s modulus values was less than the theoretical result and the discrepancy was 25%. In terms of Al matrix, the mean Young’s modulus values were slightly greater than theoretical value. According to the mixture rule, the experimental results of matrix were less than the results of mixture rule. Similar to Ref.,35 this effect may be due to the addition of particles. The comparison of the instrumented Young’s modulus values and conventional Young’s modulus value show a significant discrepancy. It is material and load dependent. The difference between the theoretical and experiment results of Young’s modulus is due to the rule of mixtures. In comparison with Young’s modulus, the mean microhardness of SiC particles and Al alloy matrix is 32.56 GPa (from 21.2 GPa to 49.3 GPa) and 1.58 GPa (from 1.28 GPa to 1.78 GPa) at the load of 20 mN. The experimental and theoretical studies reveal that the failure of the MMCs usually occurs at the interface between the particle and the matrix.40–42 Therefore, it is imperative to investigate the mechanical behavior of interface. The results of interfaces are that the mean Young’s modulus values are 73.13 GPa in range from 53.27 GPa to 90.23 GPa at the load 20 mN. In contrast with the Young’s modulus value of the matrix, it is slightly lower than that at the matrix. And this may be due to the combination of interface ‘looser’ rather than structure of matrix. Furthermore, the average microhardness at interface is 3.13 GPa in range from 1.68 GPa to 5.27 GPa. It is harder than matrix since that more dislocations are concentrated around SiC particles because of the mismatch between particle and matrix. And, the extra dislocations add resistance to deformation during indentation. 3.2. Effect of loading speed on the Young’s modulus and microhardness of matrix

Fig. 5 SEM metallographic structure of MMC (a) indentation positions during micro-indentation experiments; (b) SiC particle fracture after indentation experiments.

Usually, it is empirically verified that a straightforward way of determining whether the load-depth curves obtained on the material are satisfactory or not is to compare different curves under the same experimental conditions. Therefore, the indents are performed at another loading speed again (shown in Fig. 6). Accordingly, the results of Young’s modulus and microhardness are plotted in Figs. 7 and 8. These results indicate that the Young’s modulus increase with the increasing loading speed; however, the relevance between microhardness and loading speed is inconspicuous. Also, the results reveal that the Young’s modulus and microhardness decrease with the increasing load. This may be related to the matrix damage and microhardness size effect and need further investigation.

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Fig. 8 Influence of indenter load and loading speed on the microhardness of matrix.

Fig. 6

P–h curves of matrix at different loading speeds. Fig. 9 P–h curves of matrix obtained in the indenter load ranging from 80 to 400 mN at the loading speed of 19.368 mN/s.

Fig. 7 Influence of indenter load and loading speed on the Young’s modulus of matrix.

3.3. Effect of load on the Young’s modulus and microhardness of matrix In order to investigate the effect of load on the mechanical property of matrix of the MMC, additional experiments at loading speed 19.368 mN/s have been carried out, and the load-unload curves (P–h) are plotted in Fig. 9. Fig. 10(a) plots the Young’s modulus versus load. It can be found that the Young’s modulus decreases with load increasing. And the microhardness shows the similar tendency as Young’s modulus

(see Fig. 10(b)). The decreasing effect of Young’s modulus with load increasing may be related to the material damage43 and it will be investigated in future study. And for the phenomenon of microhardness decreasing with load (indentation depth), it is associated with size effect during indentation experiment in micro scale.28 The relation between square of the microhardness and h1, by combining the results of low load as shown in Fig. 6, is plotted in Fig. 11. It suggests that the square of the microhardness plotted against the reciprocal of the indentation depth is a linear relation, which indicates a considerable indentation size effect. According to Nix and Gao28, the relation between the microhardness (H) and the indentation depth (h) is given by rffiffiffiffiffiffiffiffiffiffiffiffiffi H h ¼ 1þ ð10Þ h H0 In this equation H0 is the hardness that would arise from the statistically stored dislocations and h* is characteristic length parameter, which can be written as pffiffiffi pffiffiffiffiffi H0 ¼ 3 3alb qS ð11Þ h ¼

 2 81 2 l ba tan2 h 2 H0

ð12Þ

where a is a empirical coefficient, l the shear modulus, and b the Burgers vector. From Fig. 11, H0 and h* in the case of loading speed being 19.368 mN/s can be calculated according to the

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Fig. 12 Density of total dislocations and geometrically necessary dislocations at different indenter depth.

Fig. 10 Micro-mechanical properties of matrix in MMC from 80 mN to 400 mN at loading speed of 19.368 mN/s.

Fig. 11 Depth dependence of the hardness of matrix under different loading conditions.

where qT is the total dislocations density under indenter, and qS the density of statistically stored dislocations, which is associated with the homogeneous deformation of materials; qG is the density of geometrically necessary dislocations, which is related to plastic shear gradient to meet the geometric matching of inhomogeneous deformation.11,28,44 By using Eq. (11), the density of statistically stored dislocations of this material is obtained as qS = 1.586 · 1015m2. Combining Eq. (13) with Eq. (14), the density of total dislocations under indenter, qT, and the density of geometrically necessary dislocations qG are inferred respectively (shown in Fig. 12). From this figure, the total dislocations and geometrically necessary dislocations concurrently decrease with increasing indenter displacement. During indentation experiments, when the studied materials undergo lower load, the permeated depth is shallower, and qG has a greater proportion effect on material deformation, increasing the deformation resistance.28,45 With the load increased, the density of statistically stored dislocations kept the same magnitude. However, the average geometrically necessary dislocations with increasing depth reduced to a larger extent, because average geometrically necessary dislocations decreased with h1.28 So, with the increase of depth, the hardness of materials fails down and caused indentation size effect. The proportion of geometrically necessary dislocation became small which can even be neglected until the indentation depth is large enough. So the indentation size effect vanished. The hardness of material is mainly related to statistically stored dislocations in macro scale. 3.4. Elastic–plastic properties of matrix in SiCp/Al To solve the ‘‘reverse problem’’ of predicting the elastic–plastic

model described in Ref.28 The value of H0 is 0.770 GPa, and characteristic length parameter is h* = 1.196 lm when a is taken as 0.5; shear modulus l is 26.3 GPa, and Burgers vector b is 0.283 nm for Aluminum, tan h = 0.358.28 In Taylor relation, the deformation resistance and the hardness can be estimated by28 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi s ¼ alb qT ¼ alb qG þ qS ð13Þ pffiffiffi pffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi H ¼ 3 3s ¼ 3 3alb qG þ qS

ð14Þ

properties from the obtained indentation P–h curves, Dao et al.21 has proposed a complete set of explicit analytical method. For soft specimens, the stress–strain relation is assumed to be the following Hooker elastic and power-law plastic formula:1,21,37,38  r¼

Ee Ren

r 6 ry r P ry

ð15Þ

where R is a strength coefficient, n the strain hardening exponent, and ry initial yield stress. As is known, total strain

Mechanical properties study of particles reinforced aluminum matrix composites by micro-indentation experiments is composed of yield strain ey and plastic strain ep, i.e. e = ey + ep, then Eq. (15) can be rewritten as1,21 8 r 6 ry < Ee n r¼ ð16Þ E : ry 1 þ ep r > ry ry According to Dao et al.21, the dimensionless functions are used to describe the constitutive behavior:    E C P1 ;n ¼ ð17Þ rr rr     dP E  ¼ E hP ;n 2 rr dh h¼hm

ð18Þ

Eq. (17) and Eq. (18) are associated with loading curve and unloading curve, respectively, where C is loading curvature, and dP j ¼ S is unloading curvature at h = hm; rr is the repdh h¼hm resentative stress at ep = er for the description of loading curvature. When er = 0.033, P1 is independent of hardening exponent n and can be given by1,21    E C ¼  P1 E r0:033   3   2 E E ¼ 1:131 ln þ 13:635 ln r0:033 r0:033    E þ 29:267 ð19Þ  30:594 ln r0:033

403

Combining Eq. (19) with Eq. (20), the strain hardening exponent n and initial yield stress ry can be solved. The tested curves in the case of loading speed 19.368 mN/s (shown in Fig. 9) are applied to this method. And the obtained parameters were that the strain hardening exponents are 0.384–0.399; yield stress ranges from 80.70 MPa to 96.11 MPa, of matrix in this MMC, as shown in Fig. 13. And the average values of strain hardening exponent and initial yield stress are 0.389 and 85.66 MPa respectively at these loads. 3.5. Finite element analysis verification In order to verify the material property, finite element analysis has been carried out. A two-dimensional axisymmetric finite element model was constructed to simulate the indentation process by using the general finite element package ABAQUS. The indenter was assumed to be an equivalent cone, and the tip apex angle h was chosen as 70.3 for Berkovich indenter.21,23 Fig. 14 is the designed model with size of 20 lm · 20 lm, which contains 2500 elements using quadrilateral elements (CAX4R). For the sake of simulation accuracy, a finer squared mesh was designed near the contact region and a gradually coarser rectangular mesh was used further from the contact region. After finite element simulations, the examples of load– displacement curves are presented in Fig. 15. From this figure, the curves are in good agreement, respectively.

And P2 can be rewritten as    E S P2 ;n ¼  E hm rr ¼ ð1:40557n3 þ 0:77526n2 þ 0:15830n    3 E þ ð17:93006n3  0:06831Þ ln r0:033  9:22091n2  2:37733n  2 E þ ð79:99715n3 þ 0:86295Þ ln r0:033 þ 40:55620n2 þ 9:00157n  2:54543Þ    E þ ð122:65069n3  ln r0:033 2

 63:88418n  9:58936n þ 6:20045Þ

Fig. 13

Values of n and ry at different indenter loads.

Fig. 14

Model of micro-indentation experiments.

ð20Þ

Figure 15

Comparison of experimental and simulation results.

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To estimate the errors between experimental results and predicted results, two parameters are defined as the correlation coefficient R2 and the average absolute relative error (AARE):37,38 P

2  Pexp ÞðPip  Pp Þ R2 ¼ PN PN i i i¼1 ðPexp  Pexp Þ i¼1 ðPp  Pp Þ N i i¼1 ðPexp

  i N  i 1X Pexp  Pp  AARE ¼   100%  N i¼1  Piexp 

ð21Þ

ð22Þ

the elements whose plastic strain greater than 0.05 are statistically analyzed as 8 N X > > > V Vk ep ¼ > > > k > > ! > > N < X 1 rep ¼ Vep rk Vk ð23Þ > > k > > ! > > N X > > 1 > > epk Vk epk > 0:05 : ep ¼ Vep k

where Piexp is the experimental finding, and Pexp the average value of experimental results; correspondingly Pip is the predicated value and Pp the average value of predicated results; N is the total number of data employed in the investigation. Through computation, the average R2 is found to be 98.02%, and average absolute relative error (AARE) is 9.45% which reflects the good prediction capabilities of the proposed method. 3.6. Statistical analysis of simulation results Fig. 16 plots the distribution of Mises stress and Equivalent plastic strain (PEEQ) at the maximum load of 200 mN, respectively. Under indenter, the shape of the isoline of stress distribution with different values is similar, and PEEQ shows the same characteristics. In the position of indenter tip, the stress of matrix is comparatively larger with stress concentration, as PEEQ concentration exists in the same zone. In order to describe the stress and PEEQ statistically during indentation,

Fig. 16 Distribution of von Mises stress and PEEQ under indenter tip at the maximum load of 200 mN.

Fig. 17 Statistical results of elements when plastic strain is greater than 0.05.

Mechanical properties study of particles reinforced aluminum matrix composites by micro-indentation experiments Where Vep is the total element volume of PEEQ greater than 0.05, Vk represents the kth element and N indicates number of total elements; rk and epk are the flow stress and plastic strain of kth element as required; rep and ep are the average flow stress and plastic strain of statistical analysis, respectively. After calculation, Fig. 17(a) depicts that at different depth, the volume ratio of statistical volume of elements when plastic strain is greater than 0.05 (loads) to the total volume of all elements. There is no doubt that volume ratio increases with the depth or loads, as the plastic deformation zone increases. Fig. 17(b) plots the statistical result of Mises stress and plastic strain of required elements. The statistical stress and plastic strain increase along with the increasing depth, and both of them have the same increasing trend. The average stress and plastic strain are shown in Fig. 17(c). Along with the increase of depth, the average plastic materials decrease approximately, although this trend is not very clear, so was the average stress. And the reason may be related to material properties (elastic modulus, strain hardening exponent, yield stress) and loading condition, and needs further quantitative research. 4. Conclusions

(1) For different micro structures, the load-unload (P–h) curves show different characteristics from both the shape and the indentation size. With regard to Young’s modulus, the value of particle is lower than theoretical result in contrast to that the matrix is greater than theoretical result of aluminum at the load of 20 mN. And the result of interfaces is close to that at matrix. In terms of microhardness, it decreases progressively from particles, interfaces to matrix. (2) Under the same test conditions, the Young’s modulus and microhardness decline with increasing loading speed. With the load increasing, the hardness shows size effect, i.e., the indentation hardness decreases with the indentation depth increasing. By the way, the density of total dislocations and geometrically necessary dislocations during indentation is calculated according to Nix and Gao.28 (3) Furthermore, the elastic–plastic properties of matrix are explored through the method proposed by Dao. And the results show that the strain hardening exponents are 0.384–0.399, and yield stress is from 80.70 MPa to 96.11 MPa. In order to verify the validation of the results, a FEM simulation was carried out with different loads. And P–h curves from FEM simulation are in good agreement with experiments. Also, the simulation results have been preliminarily analyzed from statistical aspect. It can be found that with the increase of depths (loads), the volume ratio, the total statistical stress and plastic strain of zone with PEEQ greater than 0.05 also increase. While after the average, the relationship between average stress, plastic strain and loading depth (load) is not very clear, which needs further quantitative research.

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Yuan Zhanwei is a Ph.D. candidate in School of Materials Science and Engineering, Northwestern Polytechnical University. His main research interests lie in shape characterization and mechanical properties of SiCp/Al composites. Li Fuguo is a professor with Ph.D. degree in State Key Laboratory of Solidification Processing, Northwestern Polytechnical University. His main research interests are integrated technologies of design and control of the forming process for aeronautical materials, as well as process coupling computation method of multi-scale and multi-physics of materials forming process.