Microstructure-based modeling and evaluation of dynamic behaviors of SiCp/2024Al composites①

YUAN Mei-ni，YANG Yan-qing，GONG Qiao-juan，LI Chao，LANG Xian-zhong，FAN Xue-ling

(1.College of Mechanical and Electrical Engineering，North University of China，Taiyuan 030051，China;2.State Key Laboratory of Solidification Processing，Northwestern Polytechnical University，Xi′an 710072，China;3.Department of Applied Chemistry，Yuncheng University，Yuncheng 030024，China;4.State Key Laboratory for Strength and Vibration of Mechanical Structures，Xi′an Jiaotong University，Xi′an 710049，China)

Microstructure-based modeling and evaluation of dynamic behaviors of SiCp/2024Al composites①

YUAN Mei-ni1，2，YANG Yan-qing2，GONG Qiao-juan3，LI Chao1，LANG Xian-zhong1，FAN Xue-ling4

(1.College of Mechanical and Electrical Engineering，North University of China，Taiyuan 030051，China;2.State Key Laboratory of Solidification Processing，Northwestern Polytechnical University，Xi′an 710072，China;3.Department of Applied Chemistry，Yuncheng University，Yuncheng 030024，China;4.State Key Laboratory for Strength and Vibration of Mechanical Structures，Xi′an Jiaotong University，Xi′an 710049，China)

Using the information of image processing and recognition，a microstructure-based finite element model(FEM)is established to evaluate the dynamic properties of SiCp/2024Al composites at strain rates ranging from 200 to 14 000 s-1.In the microstructure-based model，the irregular SiC particles are randomly distributed in the metal matrix.The results show that the flow stress of SiCp/2024Al composites with low particle volume fraction increases firstly to a maximum value and then decreases with the increasing of strain rate during adiabatic compression.The probable reason for the reduction of flow stress is that the inner damage and the heat softening of composites play a key role in the dynamic behavior of SiCp/2024Al composites at higher strain rates.Moreover，the configurations of SiC particles have dominate influence on the dynamical behavior of SiCp/2024Al composites.In particular，in cases of smaller strain(less than 0.62)，the angular particles have better strengthening effect than those of circle particles，however，in contrast，the strengthening effect of circle particles is more remarkable.

metallic composites;microstructure;finite element method;dynamic behavior

0 Introduction

Due to their high specific strength，high thermal conductivity and excellent abrasion resistance，etc.，particle reinforced metal matrix composites(PRMMC)are widelyused in aerospace，aviation and arms structural components.In these fields，PRMMC are inevitably suffered the high-speed crash and impact of bullets，birds and space dust，etc.Although the severity of PRMMC applications has dramatically increased in the past decade，dynamic behavior of PRMMC is still an overriding concern.In previous studies，the dynamic behaviors of PRMMC are commonly investigated using a simplified model，in which idealized particle shape and distribution are assumed based on the experimental data of complex particle morphology.Zhang J T，et al［1］analyzed the dynamic behaviors of Al2O3/6061-T6Al composites using the multi-particle 2D finite element method(FEM).Chen and Ghosh［2］established a unit cell model to study the deformation and damage in SiC/Al7075-T6 composites.Lim and Dunne［3］studied the dynamic mechanical properties of SiC/Al composites using the unit cell approach.Zhang H，et al［4］built an axisymmetric unit cell model to research the dynamic mechanical behaviors of PRMMC.However，in all of these simulations，the particle shapes were assumed as idealized sphere or ellipsoid.

However，the simplification of the complex structure does not allow for the study of the particle shape dependence of the dynamic behaviors of PRMMC composites.In this paper，with the usage of image processing，geometric modeling and finite element meshing，a 2D microstructurebased FEM was built to modeling and evaluation of the dynamic behaviors of SiCp/2024Al composites.

1 Finite element model

1.1 Microstructure-based model

The SEM photograph of SiCp/2024Al composites shown in Fig.1(a)is firstly converted to vector format using image processing and recognition technique［5］.Then，based on the image information，a computer aided drafting model is developed using Computer Aided Design(CAD)software，as shown in Fig.1(b).Finally，the 2D microstructure-based FEM is obtained by implementing the CAD model into commercial software ABAQUS.The corresponding finite element mesh is shown in Fig.1(c)，where the boundary conditions imposed on the microstructure-based FEM are also presented.

The dynamic compressive load is simulated by imposing displacement Uy(x，b)on all the nodes in y=b，given as Equ.(1).The node displacements at y=0 in Y direction are assumed to be zero as given in Equ.(2).The node displacements at x=a，y=0 in X direction is assumed to be zero as given in Equ.(3).

Fig.1 Stages of conversion of SEM image into FEM

where u is the displacement，Amp is the displacement as a function of times.

1.2 Material model

Al alloy is modeled by using the Johnson-Cook model.The flow stress in the Johnson-Cook model can be expressed as［5］:

where σ，ε，ε*，n are the dynamic flow stress，plastic strain，plastic strain rate and work hardening exponent，respectively;a，b，e and m are constants;Tmeltis melting temperature.

In addition，the JH-2 model is used to characterize SiC particle.The flow stress in the JH-2 model is expressed as［6］:

where A，B，C，M and N are all constants;P，PHEL，T and ε*are the actual pressure，the pressure at the HEL，the maximum tensile pressure and the plastic strain rate，respectively.The material parameters of Al and SiC are listed in Table 1.

Table 1 Material parameters of Al and SiC

2 Results and discussions

2.1 On strain rate effect

The predicted dynamic compressive stress-strain curves of SiCp/2024Al composites are shown in Fig.2 for various strain rates.In this section，the SiC particle volume fraction is assumed to 0.15.From Fig.2(a)，it can be seen clearly that the flow stresses of SiCp/2024Al composite increases as the strain rate increases from 200 to 6 200 s-1.Note that as the strain rate exceeds 3 200 s-1，the increases of flow stress slows down，which makes the difference between adjacent curves become not obvious.These phenomena consist with the experimental results by Perng C C，et al［7］.

Fig.2 Stress-strain behaviors of SiCp/Al composites at different strain rate

In contrast，when the strain rate exceeds 6 200 s-1，the flow stresses of SiCp/Al composites decreases with the increasing of strain rate，as shown in Fig.2(b).Since inner damage and matrix heat softening occur in SiCp/2024Al composites during the adiabatic compression，which is believed to induce the reduction of flow stress under higher strain rates.The SEM photographs of SiCp/Al composites can show the locally melting phenomenon of matrix［8］.Yao Z，et al［9］also found that there were some cavities，micro-cracks，particle fracture and the matrix softening performance in SiCp/2024Al composites using SEM.Leduc and Bao［10］，Zhou and Xia［11］also found that thermal softening has an obvious influence on the flow stress in PRMMC.

According to the above analysis，we can conclude that once the strain rate exceeds a critical strain rate，the flow stress of SiCp/2024Al composites decreases with the increasing of strain rate.The relationship between the critical strain rate and the SiC particle volume fraction is shown in Fig.3.It can be seen that the critical strain rate decreases with increasing SiC particle volume fraction.SiC particles in PRMMC can hardly be deformed，thus almost all the deformation is confined to the matrix in the composite.As a result，higher particle volume fraction composites experience more strain than these of lower particle volume fractions，which leads to the decrease of the critical strain rate as SiC particle volume fraction increases.

Fig.3 Relationship between the critical strain rate and SiC particle volume fraction

2.2 On particle shape effect

The dynamic compression simulationsofSiCp/2024Al composite containing different particle shapes are performed，and the numerical results are shown in Fig.4.The results indicate that when the strain is less than 0.62，the original，square and hexagon particles(i.e.angular particle)have more significant strengthening effect than that of circle particle.The reason is that the constraint of angular particle is high，which results in the high local stress concentration phenomenon，and thus the composite is more beneficial to matrix hardening.

In contrast，circle particle provides more stress and strengthening for strain level larger than 0.62.It is reasonable since larger local stress is resulted by the stress concentration phenomenon when the strain is higher than 0.62.Once the local stress is larger than the fracture stress of angular particle，fracture occurs in angular particles.However，the circle particles result in relative lower local stress concentration phenomenon and local stress.Thus few circle particles are failed.Our results that compared with circle particle fracture can be easily triggered for angular particle coincide with those of Song S G，et al［12］.

2.3 On particle volume fraction effect

The dynamic compression simulationsofSiCp/2024Al composites with different SiC particle volume fractions are conducted，as shown in Fig.5.It can be clearly seen that and the elastic modulus of SiCp/Al composites increases rapidly with the increasing SiC particle volume fraction.In the meanwhile，the flow stres-strain curve of SiCp/2024Al composites also increases as the SiC particle volume fraction increases.The reason is that the higher the SiC particle volume fraction is，the more the grain refinement and dislocations interaction in matrix are，which results in the higher level of flow stress in PRMMC.According to Orowan dislocation theory，the curvature radius of dislocation also increases with increasing particle volume fraction，which leads to a higher flow stress.

Fig.4 Stress-strain behaviors of SiCp/Al composites for different particle shapes

Fig.5 Stress-strain behaviors of SiCp/Al composites for different SiC particle volume fractions

3 Conclusions

(1)The flow stress of SiCp/2024Al composites increases firstly and then decreases with the increasing of strain rate.

(2)When the strain is less than 0.62，the strengthening effect of angular particle is much more significant than that of circle particle.However，in contrast，the circle particle can provide more strengthening effect when the strain is larger than 0.62.

(3)Both the flow stress and the elastic modulus of SiCp/2024Al composites increase as the particle volume fraction increases.

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(编辑:薛永利)

SiCp/2024Al复合材料微观结构建模及动态力学性能评估

原梅妮1，2，杨延清2，弓巧娟3，李 超1，郎贤忠1，范学领4
(1.中北大学机电工程学院，太原 030051;2.西北工业大学 凝固技术国家重点实验室，西安 710072;3.运城学院应用化学系，运城 030024;4.西安交通大学强度与振动实验室，西安 710049)

借助图像处理和识别技术，建立复合材料真实微观结构的有限元模型，并运用该模型分析计算SiCp/2024Al复合材料在应变速率为200～14 000 s-1下的动态力学性能。在真实微观结构的有限元模型中，无规则的SiC颗粒自由分布在铝合金基体材料中，SiC颗粒形貌保持原状。有限元模拟结果表明，动态压缩过程中，低体积分数的SiCp/2024Al复合材料流变应力随着应变速率的增加呈现先升高后降低的趋势。在较高应变率下，SiCp/2024Al复合材料流变应力出现降低趋势是由于复合材料内部损失或铝合金基体热软化甚至局部熔化导致的。当应变低于0.62时，带有棱角的SiC颗粒比圆形SiC颗粒强化效果好，当应变大于0.62时，情况正好相反。

金属基复合材料;微观结构;有限元方法;动态力学性能

V257 Document Code:A Article ID:1006-2793(2014)04-0541-04

10.7673/j.issn.1006-2793.2014.04.021

date:2014-03-13;Revised date:2014-05-07.

Foundation:Natural Science of China(51201155);Natural Science of Shanxi Province(2012011019-1，2012011007-1);Chinese Education Ministry Foundation for Doctors(20101420120006).

Biography:YUAN Mei-ni(1974—)，female，professor，speciality:Mechanical properties of composition.E-mail:mnyuan@126.com