Damage failure mechanism of unidirectional fiber reinforced SiCf/SiC composites under uniaxial tension
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摘要: 本文对纤维增强陶瓷基复合材料在单向载荷下的损伤失效机制进行了研究。根据常规的剪滞模型，引入库仑定律描述界面剪应力，根据能量平衡方法和断裂力学脱粘准则，计算了基体的稳态开裂应力和界面的脱粘长度。分析了不同剪滞模型下基体稳态开裂应力的区别和适用范围，讨论了界面剪应力、界面摩擦系数、界面脱粘能、纤维体积分数等对基体稳态开裂应力的影响。采用剪滞模型描述纤维增强陶瓷基复合材料在损伤后的细观结构应力场，根据基体裂纹随机演化方法确定基体裂纹的间距，根据断裂力学脱粘准则描述界面的脱粘行为，将剪滞模型和损伤模型结合预测了单向纤维增强陶瓷基复合材料在单轴载荷下的应力-应变曲线，讨论了各因素对应力-应变曲线的影响。Abstract: This paper studied the damage failure mechanism of fiber-reinforced ceramic composites under unidirectional loading. According to the conventional shear-lag model, Coulomb’s law was introduced to describe the interfacial shear stress. According to the energy balance method and the debonding criterion of fracture mechanics, the steady-state cracking stress of the matrix and the debonding length of the interface were calculated. The difference and applicable range of the steady-state cracking stress of the matrix under different shear lag models were analyzed, and the effects of the interfacial shear stress, the interfacial friction coefficient, the interfacial debonding energy, and the fiber volume fraction on the steady-state cracking stress of the matrix were discussed. The shear lag model was used to describe the microstructure stress field of the fiber-reinforced ceramic composites after damage, the distance between the matrix cracks was determined according to the random evolution method of matrix cracks, and the debonding behavior of the interface was described according to the fracture mechanics debonding criterion. Combined with the damage model, the stress-strain curve of unidirectional fiber-reinforced ceramic composites under unidirectional load was predicted, and the influence of various factors on the stress-strain curve was discussed.
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Key words:
- ceramic composites /
- continuous fiber reinforced /
- shear-lag model /
- fiber debonding /
- matrix cracking
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图 1 基体稳态开裂的裂纹尖端和裂纹尾迹图
Figure 1. Crack tip and crack trail of steady-state matrix cracking
σ—Uniform loading stress perpendicular to the crack surface
图 2 纤维增强陶瓷基复合材料裂纹尾迹桥连纤维等效体积单元示意图
Figure 2. Schematic diagram of representative volume element of fiber-reinforced ceramic composites with crack wake bridging fiber
Vf—Fiber volume fraction; v(0)—Relative displacement function; $\overline R$—Effective radius; r—Radial direction; θ—Tangents; z—Axial direction; ld—Debonding length; L—Matrix crack spacing; τi—Interfacial frictional shear stress
图 4 基体裂纹扩展与位置分布
Figure 4. Matrix crack propagation and distribution
m—Weibull modulus; σR—Matrix characteristic cracking stress
图 5 不同基体临界开裂应力下威布尔模量对最终裂纹间距的影响
Figure 5. Influence of Weibull modulus on final crack spacing under different matrix critical crack stresses
σmc—Steady-state cracking stress of matrix
图 6 SiC/CAS的各剪滞模型库仑摩擦系数μ与基体稳态开裂应力关系图(ξd=0、Vf=34vol%)
Figure 6. Relationship between Coulomb friction coefficient μ and matrix steady-state cracking stress for each shear-lag model of SiC/CAS(ξd=0, Vf=34vol%)
ACK—Aveston, Cooper and Kelly initials; BHE—Budiansky, Hutchinson and Evans initials
图 7 SiC/CAS的BHE模型与库仑摩擦剪滞模型ld对比图(ξd=0、Vf=34vol%)
Figure 7. Comparison of BHE model and Coulomb friction shear-lag model for ld (ξd=0, Vf=34vol%) of SiC/CAS
图 8 SiC/CAS库仑摩擦剪滞模型不同泊松比v的基体稳态开裂应力关系图(ξd=0、Vf=34vol%)
Figure 8. Relationship between Poisson’s ratio v and matrix steady-state cracking stress of SiC/CAS using Coulomb friction shear-lag model(ξd=0, Vf=0.34vol%)
图 9 SiC/CAS库仑摩擦剪滞模型不同泊松比v的基体稳态开裂脱粘长度关系图(ξd=0、Vf=34vol%)
Figure 9. Relationship between the steady-state cracking stress debonding length ld and Poisson’s ratio v of SiC/CAS using Coulomb friction shear-lag model (ξd=0, Vf=34vol%)
图 10 SiC/CAS的各剪滞模型纤维体积分数Vf与基体稳态开裂应力关系图(ξd=0、μ=1、基体泊松比νm=0.25)
Figure 10. Relationship between fiber volume fraction Vf and matrix steady-state cracking stress of each shear-lag model of SiC/CAS(ξd=0, μ=1, Poisson's ratio of matrix νm=0.25)
图 11 SiC/CAS的各剪滞模型纤维体积分数与稳态开裂脱粘长度ld关系图(ξd=0、μ=1、νm=0.25)
Figure 11. Relationship between fiber volume fraction and steady-state cracking debonding length ld for each shear-lag model of SiC/CAS(ξd=0, μ=1, νm=0.25)
图 12 SiC/CAS复合材料不同韧度比下界面剪应力对基体稳态开裂应力的影响(Vf=34vol%)
Figure 12. Effect of interfacial shear stress on matrix steady-state cracking stress of SiC/CAS composites under different toughness ratios (Vf=34vol%)
图 13 SiC/CAS复合材料不同韧度比下界面剪应力对界面脱粘长度的影响(Vf=34vol%)
Figure 13. Effect of interfacial shear stress on interfacial debonding length under different toughness ratios of SiC/CAS composites (Vf=34vol%)
图 14 两种剪滞模型对SiC/CAS单轴拉伸的应力-应变曲线模拟
Figure 14. Simulation of stress-strain curves of two shear-lag models for uniaxial tension of SiC/CAS
图 15 不同界面剪切力对SiC/CAS单轴拉伸应力-应变曲线的影响
Figure 15. Effect of different interfacial shear forces on uniaxial tensile stress-strain curves of SiC/CAS
图 16 不同界面剪切力对SiC/CAS单轴拉伸时裂纹密度的影响
Figure 16. Effect of different interfacial shear forces on the crack density of SiC/CAS under uniaxial tension
图 17 不同相对韧度对SiC/CAS单轴拉伸应力-应变曲线的影响
Figure 17. Effect of different relative toughness on uniaxial tensile stress-strain curve of SiC/CAS
图 18 不同纤维体积分数Vf对SiC/CAS单轴拉伸应力-应变曲线的影响
Figure 18. Effect of different fiber volume fraction Vf on uniaxial tensile stress-strain curve of SiC/CAS
图 19 不同泊松比(ν=νm=νf)对SiC/CAS单轴拉伸应力-应变曲线的影响
Figure 19. Effect of different Poisson’s ratio (ν=νm=νf) on uniaxial tensile stress-strain curve of SiC/CAS
νf—Poisson's ratio of fibers
表 1 单向纤维增强陶瓷基复合材料(CMCs)各组分参数
Table 1. Parameters of constituents of unidirectional fiber reinforced ceramic matrix composites (CMCs)
SiC/CAS[24,38] SiC/CAS[24,39] SiC/CAS-II[24,40] Radius of the fiber a/μm 7.5 7.5 7.5 Fiber volume fraction Vf/vol% 34 37 30 Fibre elastic modulusEf /GPa 190 200 200 Elastic modulus of matrix Em/GPa 90 97 98 Fracture energy of matrix ξm/(J·m-2) 6 6 6 Debonding energy of interface ξd/(J·m-2) 0.8 0.4 0.4 Thermal expansion coefficient of fiber αf/℃−1 3.3×10−6 4×10−6 4×10−6 Thermal expansion coefficient of matrix αm/℃−1 4.6×10−6 5×10−6 5×10−6 Temperature difference between composite
preparation and working condition ΔT/℃−1000 −1000 −1000 Weibull modulus of matrix m 5 5 7 Constant frictional shear stress τs/MPa 10 15 20 Weibull modulus of fiber mf 3.6 3.6 3.0 Matrix characteristic strength σc/MPa 2.0 2.0 2.0 Final strength of composites σUTS/MPa
(Experiment)395 447 350 Final strength of composites σUTS/MPa
(Theory)464.76 505.77 399.63 Error/% 17.66 13.15 14.18 
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