A theoretical study was performed of mode II delamination in a multilayered functionally graded beam configuration with considering the material non-linearity. The fracture was analysed by the J-integral approach. Two laws (quadratic and exponential) for variation of the modulus of elasticity along the beam height were applied. The J-integral closed form non-linear analytical solutions derived were verified by performing analyses of the strain energy release rate with taking into account the material non-linearity. Parametric investigations of mode II non-linear fracture were conducted. It was found that material non-linearity leads to increase of the J-integral value. Therefore, the non-linear behaviour of material has to be taken into account in fracture mechanics-based safety design of functionally graded structural members. The present paper contributes to the understanding of non-linear fracture in functionally graded materials. The results obtained can be used for optimization of functionally graded beam structures with respect to the fracture performance.

中文翻译：

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弹塑性功能梯度多层梁的分层断裂分析

考虑到材料的非线性，对多层功能梯度梁配置中的模式II分层进行了理论研究。通过J-积分方法分析骨折。应用了两个定律（二次和指数）来改变弹性模量沿梁的高度。通过考虑材料非线性对应变能释放速率进行分析，验证了导出的J积分闭合形式非线性解析解。进行了II型非线性断裂的参数研究。发现材料非线性导致J积分值的增加。因此，在功能梯度结构构件的基于断裂力学的安全设计中，必须考虑材料的非线性行为。本文有助于理解功能梯度材料中的非线性断裂。获得的结果可用于在断裂性能方面优化功能渐变梁结构。