Crack initiation and propagation mechanism during uniaxial compression of SiC/AZ91D magnesium matrix composites
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摘要: 利用有限元分析软件Abaqus在有限元模型颗粒界面引入内聚力单元，研究了不同形状和不同体积分数SiC颗粒的SiC/AZ91D镁基复合材料在单轴压缩情况下裂纹萌生扩展机制。内聚力单元的引入避免了线弹性力学需要在试件中预制裂纹和裂纹尖端存在奇异性的弊端，提供了一种解决裂纹扩展问题的新手段。结果表明：圆形、原始形状和正方形颗粒SiC/AZ91D镁基复合材料抗压强度分别为474.853 MPa、435.783 MPa和397.211 MPa；其裂纹萌芽和断裂时间分别为施载后第15.6 μs、第14.4 μs、第12.6 μs和第22.2 μs、第20.4 μs、第18 μs；圆形颗粒复合材料裂纹扩展机制是基体损伤萌生的裂纹扩张导致材料断裂，而正方形和原始形状颗粒复合材料裂纹扩展机制是颗粒与基体交界处萌生裂纹，主裂纹和次生裂纹相互贯通，致使材料断裂；体积分数10vol%、15vol%和20vol%原始形状颗粒的SiC/AZ91D镁基复合材料裂纹萌芽和断裂时间分别在施载后第15.6 μs、第14.4 μs、第11.4 μs和第22.2 μs、第20.4 μs和第18 μs；颗粒体积分数的增加会加速SiC/AZ91D镁基复合材料的裂纹扩展过程。Abstract: The crack initiation and propagation mechanism of SiC/AZ91D magnesium matrix composites with different shapes and volume fractions of SiC particles under uniaxial compression was investigated by using the finite element analysis software Abaqus to introduce a cohesive force element into the interface of the finite element model. The introduction of cohesive force element avoids the defects of prefabrication crack and singularity of crack tip in linear elasticity, and provides a new method to solve the problem of crack propagation. The results show that the compressive strengths of circular, original shape and square SiC/AZ91D magnesium matrix composites are 474.853 MPa, 435.783 MPa and 397.211 MPa, respectively. The time of crack initiation and fracture are 15.6 μs, 14.4 μs, 12.6 μs, 22.2 μs, 20.4 μs, 18 μs after loading, respectively. The crack propagation mechanism of circular particle composites is the crack propagation initiated by matrix damage, which leads to material fracture, while the crack propagation mechanism of square and original shape particle composites is the crack initiation at the junction of particle and matrix, and the primary crack and secondary crack are connected with each other, which lead to material fracture. The crack initiation and fracture time of SiC/AZ91D magnesium matrix composites with 10vol%, 15vol% and 20vol% original shape particles are 15.6 μs, 14.4 μs, 11.4 μs, 22.2 μs, 20.4 μs and 18 μs after loading, respectively. The crack propagation process of SiC/AZ91D magnesium matrix composites is accelerated with the increase of particle volume fraction.
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Key words:
- SiC/AZ91D /
- finite element analysis /
- cohesion model /
- uniaxial compression /
- crack propagation
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图 2 SiCp/AZ91D镁基复合材料颗粒模型建立及网格划分和载荷施加
Figure 2. Establishment of particle model, meshing and load application of SiCp/AZ91D magnesium matrix composites
图 3 双线性内聚力模型[16]
Figure 3. Bilinear cohesive zone model[16]
$ {\delta }_{\mathrm{m}}^{\text{max}} $—Maximum value of the effective displacement; $ {\delta }_{\mathrm{m}}^{\mathrm{f}} $—Effective displacement at complete failure; $ {\delta }_{\mathrm{m}}^{0} $—Effective displacement at the initiation of damage; $ {\tau }_{\mathrm{m}}^{0} $—Maximum separation stress; K—Elasticity coefficient or spring constant; D—Damping coefficient
图 4 不同颗粒形状的SiC/AZ91D镁基复合材料模型图
Figure 4. Model diagrams of SiC/AZ91D magnesium matrix composites with different particle shapes
图 5 压缩过程中不同形状颗粒SiC/AZ91D镁基复合材料应力-应变曲线
Figure 5. Stress-strain curves of SiC/AZ91D magnesium matrix composites with different particle shapes during compression
图 6 压缩过程中不同形状颗粒SiC/AZ91D镁基复合材料屈服强度和抗压强度柱状图
Figure 6. Histogram of yield strength and compressive strength of SiC/AZ91D magnesium matrix composites with different particle shapes during compression
图 7 不同颗粒形状的SiC/AZ91D镁基复合材料裂纹长度随时间变化曲线
Figure 7. Curves of crack length of SiC/AZ91D magnesium matrix composites with different particle shapes over time
图 8 不同形状颗粒的SiC/AZ91D镁基复合材料在载荷施加后裂纹萌芽情况
Figure 8. Crack germination of SiC/AZ91D magnesium matrix composites with particles of different shapes after loading
S—Stress
图 9 不同形状颗粒的SiC/AZ91D镁基复合材料在载荷施加后裂纹扩展情况
Figure 9. Crack growth of SiC/AZ91D magnesium matrix composites with particles of different shapes after loading
图 10 颗粒体积分数不同的SiC/AZ91D镁基复合材料模型图
Figure 10. Model diagram of SiC/AZ91D magnesium matrix composites with different particle volume fraction
图 11 不同颗粒体积分数的SiC/AZ91D镁基复合材料压缩应力-应变曲线
Figure 11. Compression stress-strain curves of SiC/AZ91D composites with different particle volume fractions
图 12 不同颗粒体积分数的SiC/AZ91D镁基复合材料抗压强度和压缩率
Figure 12. Compressive strength and compressibility of SiC/AZ91D magnesium matrix composites with different particle volume fractions
图 13 不同颗粒体积分数的SiC/AZ91D镁基复合材料裂纹长度随时间变化的曲线
Figure 13. Curves of crack length versus time for SiC/AZ91D magnesium matrix composites with different volume fractions of particles
图 14 不同颗粒体积分数的SiC/AZ91D镁基复合材料在载荷施加后裂纹萌芽情况
Figure 14. Crack germination of SiC/AZ91D magnesium matrix composites with different volume fractions after loading
图 15 不同颗粒体积分数的SiC/AZ91D镁基复合材料在载荷施加后第17.4 μs裂纹扩展情况
Figure 15. Crack growth of SiC/AZ91D magnesium matrix composites with different particle volume fraction at 17.4 μs after loading
图 17 不同体积分数SiC颗粒增强AZ91D镁合金的模拟与实验压缩应力-应变曲线对比
Figure 17. Comparison of simulated and experimental compressive stress-strain curves of AZ91D magnesium alloy reinforced by SiC particles with different volume fractions
表 1 AZ91D镁合金和SiC颗粒的基本参数
Table 1. Basic parameters of AZ91D magnesium alloy and SiC particles
Material $ \rho $/(kg·m−3) E/GPa ν ${\sigma }_{\rm{b}}$/MPa AZ91D 1800 45 0.33 164 SiC 3215 450 0.17 2000 Notes: $ \rho $—Material density; E—Modulus of elasticity; ν—Poisson's ratio; $ {\sigma }_{\rm{b}} $—Tensile strength. 
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表 2 SiCp/AZ91D颗粒界面的本构模型参数
Table 2. Constitutive model parameters of SiCp/AZ91D particle interface
$ {t}_{\mathrm{n}}/\mathrm{M}\mathrm{P}\mathrm{a} $ $ {t}_{\mathrm{t}}/\mathrm{M}\mathrm{P}\mathrm{a} $ $ {\delta }_{\mathrm{m}\mathrm{a}\mathrm{x}}/\mathrm{m}\mathrm{m} $ $ {\delta }_{\mathrm{f}}/\mathrm{m}\mathrm{m} $ 400 400 0.00015 0.00005 Notes: $ {t}_{\mathrm{n}} $—Interface normal nominal stress; $ {t}_{\mathrm{t}} $—Interfacial tangential nominal stress; $ {\delta }_{\mathrm{m}\mathrm{a}\mathrm{x}} $—Destruction displacement; $ {\delta }_{\mathrm{f}} $—Material complete failure separation.
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表 3 AZ91D镁合金的Johnson-Cook (J-C)本构参数
Table 3. Johnson-Cook (J-C) constittive model parameters for AZ91D magnesium alloy
A/MPa $ B/\mathrm{M}\mathrm{P}\mathrm{a} $ n C $ {u}_{\mathrm{f}}^{\mathrm{p}\mathrm{l}} $/mm 164 600 0.283 0.021 0.00015 Notes: A—Yield strength of AZ91D matrix under static load; $ B $—Hardening constant; $ n $—Hardening exponent; $ C $—Strain rate constant; $ {u}_{\mathrm{f}}^{\mathrm{p}\mathrm{l}} $—Failure displacement.
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表 4 SiC颗粒的本构参数
Table 4. Constitutive parameters of SiC particles
$ {\sigma }_{\mathrm{f}}^{\mathrm{p}} $/MPa $ {e}_{\mathrm{f}}^{\mathrm{p}}/\mathrm{m}\mathrm{m} $ $ {e}_{\text{max}}^{\text{ck}} $/mm p 2000 0.2 0.2 2 Notes: $ {\sigma }_{{\rm{f}}}^{\mathrm{p}} $—Tensile strength; $ {e}_{{\rm{f}}}^{\mathrm{p}} $—Fracture strain; p and $ {e}_{\text{max}}^{\text{ck}} $—Material parameters used to control the shear retention.
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