Effect of porosity defects on crack initiation and propagation behavior in SiC/AZ91D composites
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摘要: 采用内聚力模型及有限元分析方法，在含真实形貌SiC颗粒增强AZ91D镁基复合材料中引入孔隙缺陷，分析不同孔隙率及孔隙形状在单轴拉伸过程中对SiC/AZ91D复合材料力学行为的影响。结果表明：孔隙长径比为1时，孔隙率为0%、0.5%、1.0%、1.5%的复合材料的抗拉强度分别为351.214 MPa、339.452 MPa、325.735 MPa、306.791 MPa，抗拉强度随孔隙率的增加逐渐降低，复合材料中裂纹萌生和裂纹扩展时间均随孔隙率增加而提前。孔隙长径比越大，其尖端部位应力集中越严重，复合材料抗拉强度也越低。无孔隙缺陷的SiC/AZ91D复合材料裂纹萌生扩展机制是颗粒与基体交界处萌生微裂纹，微裂纹相互连接形成主裂纹绕开颗粒进行扩展致使材料断裂，含孔隙的SiC/AZ91D复合材料裂纹萌生扩展机制为微裂纹在孔隙周围萌生，与颗粒和基体交界处产生的微裂纹相互连接，汇集成主裂纹绕开颗粒扩展使材料断裂。Abstract: Using the finite element analysis method, this study introduced porosity defects into SiC/AZ91D magnesium matrix composites with realistic SiC particle morphology, and analyzed the influence of different porosity rates and shapes on the mechanical behavior of SiC/AZ91D composites during uniaxial tensile process. The results show that when the aspect ratio of the pore length to width is 1, the tensile strengths of the composites with void contents of 0%, 0.5%, 1.0%, and 1.5% are 351.214 MPa, 339.452 MPa, 325.735 MPa and 306.791 MPa, respectively. The tensile strength gradually decreases with the increase of porosity rate, and the initiation and propagation time of cracks in the composite material advances with the increase of porosity rate. As the aspect ratio of the pore length to width increases, the stress concentration at the tip of the pore becomes more severe, resulting in lower tensile strength of the composite material. The crack initiation and propagation mechanism in the SiC/AZ91D composite material without porosity defects involves the initiation of microcracks at the particle-matrix interface, followed by their interconnection to form a main crack, which propagates around the particles leading to material fracture. In the case of SiC/AZ91D composites with porosity, microcracks initiate around the pores and interconnect with microcracks generates at the particle-matrix interface, ultimately converging into a main crack that propagates around the particles, causing material fracture.
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Key words:
- SiC/AZ91D composites /
- crack initiation /
- crack extension /
- finite element analysis /
- porosity /
- cohesive model
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图 2 不同孔隙率的SiC/AZ91D镁基复合材料模型：(a) VC=0 (理想状况)；(b) VC=0.5%；(c) VC=1.0%；(d) VC=1.5%
Figure 2. Modeling diagram of SiC/AZ91D magnesium-based composite materials with different void contents: (a) VC=0 (Ideal condition); (b) VC=0.5%; (c) VC=1.0%; (d) VC=1.5%
图 3 SiC/AZ91D镁基复合材料模型及网格划分和载荷施加：(a) SiC/AZ91D模型；(b) 网格划分；(c) 载荷施加
Figure 3. Modeling, meshing and load application of SiC/AZ91D magnesium-based composite materials: (a) SiC/AZ91D model; (b) Meshing; (c) Load application
图 4 不同孔隙形状的SiC/AZ91D镁基复合材料模型：(a) 长径比r=1；(b) r=2；(c) r=4
Figure 4. Model of SiC/AZ91D magnesium-based composite materials with different pore shapes: (a) Aspect ratio of the pore length to width r=1; (b) r=2; (c) r=4
图 6 双线性内聚力模型
Figure 6. Bilinear cohesive zone model
$ {\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—Damage amount
图 7 拉伸过程中含不同孔隙率SiC/AZ91D镁基复合材料应力-应变曲线
Figure 7. Stress-strain curves of SiC/AZ91D magnesium-based composite materials with different void content during tensile process
图 8 拉伸过程中不同孔隙率SiC/AZ91D复合材料屈服应力值、抗拉强度和伸长率
Figure 8. Yield stress, tensile strength and elongation of SiC/AZ91D composite materials with different void contents during the tensile process
图 9 孔隙周围A、B、C方向示意图
Figure 9. Schematic diagram of the A, B, and C directions around the void
S—Quivalent stress (MPa)
图 10 孔隙周围基体A、B、C 方向应力随施载时间变化曲线
Figure 10. Stress variation curves with respect to loading time in the A, B, and C directions of the matrix around the void
图 11 含不同孔隙率 SiC/AZ91D 复合材料裂纹长度随时间变化曲线
Figure 11. Crack length variation curves with respect to time in SiC/AZ91D composite materials with different void contents
图 12 不同孔隙率的SiC/AZ91D复合材料裂纹扩展路径：(a) VC=0%；(b) VC=0.5%；(c) VC=1.0%；(d) VC=1.5%
Figure 12. Crack propagation paths in SiC/AZ91D composite materials with different void contents: (a) VC=0%; (b) VC=0.5%; (c) VC=1.0%; (d) VC=1.5%
图 13 含不同孔隙形状的SiC/AZ91D复合材料的拉伸应力-应变曲线
Figure 13. Stress-strain curves during tension of SiC/AZ91D composite materials with different void shapes
图 14 拉伸过程中含不同孔隙形状SiC/AZ91D 复合材料抗拉强度和伸长率
Figure 14. Tensile strength and elongation of SiC/AZ91D composite materials with different void shapes during the tensile process
图 15 含不同形状孔隙的复合材料同一区域的应力场：(a) r=1；(b) r=2；(c) r=4
Figure 15. Stress field in the same region of composite materials with different void shapes: (a) r=1; (b) r=2; (c) r=4
图 16 含不同孔隙形状 SiC/AZ91D 复合材料裂纹长度随时间变化曲线
Figure 16. Crack length variation curves with respect to time in SiC/AZ91D composite materials with different void shapes
图 17 含不同形状孔隙的SiC/AZ91D复合材料的裂纹扩展路径：(a) r=1；(b) r=2；(c) r=4
Figure 17. Crack propagation paths in SiC/AZ91D composite materials with different void shapes: (a) r=1; (b) r=2; (c) r=4
图 20 实验使用的WDW-E100D微机控制电子万能试验机
Figure 20. WDW-E100D microcomputer-controlled electronic universal testing machine used in the experiment
图 21 含不同孔隙率的SiC/AZ91D复合材料仿真与实验拉伸应力-应变曲线对比
Figure 21. Comparison of simulated and experimental stress-strain curves during tensile testing of SiC/AZ91D composite materials with different void contents
图 22 含不同孔隙率SiC/AZ91D复合材料拉伸应力-应变误差带图：(a) VC=0.5%；(b) VC=1.0%；(c) VC=1.5%
Figure 22. Tensile stress-strain error band diagram of SiC/AZ91D composite materials with different void contents: (a) VC=0.5%; (b) VC=1.0%; (c) VC=1.5%
表 1 排水法测量的SiC/AZ91D复合材料孔隙率(VC)
Table 1. Void content (VC) measurement for SiC/AZ91D composite material using drainage method
Sample serial number VC/% 1 1.56 2 0.84 3 0.85 4 1.62 5 0.83 6 0.41 7 1.65 8 0.94 9 0.48 10 1.18 
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表 2 AZ91D镁合金和SiC颗粒的基本参数
Table 2. Basic parameters of AZ91D magnesium alloy and SiC particles
Material $ \rho $/(kg·m−3) E/GPa $ \mu $ σb/MPa AZ91D 1800 45 0.33 164 SiC 3215 450 0.17 2000 Notes: $ \rho $—Material density; E—Modulus of elasticity; $ \mu $—Poisson's ratio; σb—Tensile strength.
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表 3 SiC/AZ91D颗粒-界面的本构模型参数
Table 3. Constitutive model parameters of SiC/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 4 AZ91D镁合金的Johnson-Cook (J-C)本构参数
Table 4. Johnson-Cook (J-C) constitutive model parameters for AZ9ID magnesium alloy
A/MPa B/MPa n C ${u}_{{\rm{f}}}^{\mathrm{p}\mathrm{l} }/{\rm{mm} }$ 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 5 SiC颗粒本构模型及失效参数
Table 5. Constitutive model and failure parameters of SiC particles
Parameter Value G/GPa 193 A0 0.96 B0 0.35 C0 0.009 M 1 N 0.65 T1/MPa 750 SFMAX/MPa 1300 LHE/MPa 11700 PHEL/MPa 5130 D1 0.48 D2 0.48 K1 220000 K2 361000 K3 0 Notes: G—Shear modulus; A0—Strength parameter before damage; B0—Strength parameter when damage occurs; C0—Strain rate constant; M—Pressure index when damage occurs; N—Pressure index when no damage occurs; T1—Cut-off pressure; SFMAX—Maximum fracture strength; LHE—Hugoniot elastic limit; PHEL—Hugoniot elastic limit pressure; D1, D2—Fracture constant; K1, K2, K3—Material parameter.
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