The asymptotic field of mode I quasi-static crack growth on the interface between a rigid and a pressure-sensitive material

Abstract

A mechanical model of the quasi-static interface of a mode I crack between a rigid and a pressure-sensitive viscoelastic material was established to investigate the mechanical characteristic of ship-building engineering bi-materials. In the stable growth stage, stress and strain have the same singularity, ie (σ, ε) ∞ r ^−1/(n−1). The variable-separable asymptotic solutions of stress and strain at the crack tip were obtained by adopting Airy’s stress function and the numerical results of stress and strain in the crack-tip field were obtained by the shooting method. The results showed that the near-tip fields are mainly governed by the power-hardening exponent n and the Poisson ratio ν of the pressure-sensitive material. The fracture criterion of mode I quasi-static crack growth in pressure-sensitive materials, according to the asymptotic analyses of the crack-tip field, can be viewed from the perspective of strain.

摘 要

为了研究船用工程复合材料的界面裂纹特性, 建立了刚性—压力敏感粘弹塑性材料I 型准静态扩展裂纹的力学模型. 在稳态扩展阶段, 应力和应变具有相同的奇异量级, 即 (σ, ɛ)∞r ^−1/(n−1). 引入Airy 应力函数, 通过渐近分析得出了裂纹尖端应力和应变的分离变量形式的渐近解, 并采用打靶法求得了裂纹尖端应力和应变的数值结果. 数值计算结果表明, 界面裂尖场主要受材料的泊松比和幂硬化指数的控制. 通过对裂纹尖端场的渐近分析, 从应变角度出发, 提出了刚性—压力敏感性材料界面I 型准静态扩展裂纹的断裂判据.