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假定膜内的残余拉应力足以使膜发生开裂,利用膜/基材料中含弹性界面层的剪滞模型,研究了脆性膜/基材料在残余应力作用下的开裂行为特征,探讨了膜内正应力、膜/基界面切应力的分布规律,获得了膜的裂纹密度与残余应力大小之间的解析表达式。在裂纹密度、材料的力学和几何参数确定的情况下,该解析表达式可以用来评估残余应力的大小。最后,分析了膜的裂纹密度与残余应力、膜的厚度、弹性模量、断裂强度以及界面层的切变模量之间的内在关联,绘出了这些参数影响膜裂纹密度的变化曲线。
Assuming that the residual tensile stress in the film is enough to cause the film to crack, the cracking behavior of the brittle film / matrix material under residual stress is studied by using the shear lag model with elastic interface layer in the film / base material. Stress and film / base interface shear stress, the analytical expression of the crack density and residual stress of the film was obtained. The analytical expression can be used to evaluate the residual stress in the case of crack density, mechanical and geometrical parameters of the material. Finally, the inherent correlation between the crack density and the residual stress, the film thickness, the elastic modulus, the fracture strength and the shear modulus of the interfacial layer were analyzed. The curves of the influence of these parameters on the crack density of the film were plotted.