刚性-粘弹性材料界面Ⅰ型动态扩展裂纹的尖端场

Asymptotic Field of Mode I Dynamic Growing Crack Along Rigid/Viscoelastic Bi-material Interface

裂纹尖端渐近场的研究是断裂力学研究的重要课题之一。为了研究粘性效应作用下的界面动态扩展裂纹尖端渐近场,建立了刚性.粘弹性材料界面Ⅰ型动态扩展裂纹的力学模型;在稳态蠕变阶段,弹性变形和粘性变形同时在裂纹尖端场中占主导地位,应力和应变具有相同的奇异量级,即(σ,ε)∝r-1/(n-1)。当n→∞,幂硬化粘弹性材料动态扩展裂纹尖端场与Freund给出的理想塑性材料动态扩展裂纹尖端场具有相近的奇异量级;结合运动和协调方程,推导出粘弹性材料动态扩展裂尖场的控制方程。根据问题的边界条件和连续条件,通过数值计算,得到了裂纹尖端连续的分离变量形式的应力、应变和位移场。数值计算表明,裂纹尖端场主要受材料的蠕变指数n和马赫数M的控制,这为解决工程实践中所遇到的相应的问题和建立材料的破坏准则提供理论的参考。

The study of crack-tip asymptotical field is one of the important subjects of fracture mechanics. A mechanical model of dynamic growing interfacial crack of mode I between rigid material and viscoelas-tic material was established in order to investigate viscous effect in dynamic growing interfacial crack-tip asymptotic field. It is shown that in stable creep growing stage, elastic-deformation and visco-deformation are equally dominant in the near-tip field, the stress and strain have the same singularity, as(σ, ε)∞ r-1/(n-1) when n→∞ , the singularity of dynamic crack-tip field of viscoelastic power-hardening material in the dissertation is close formally to that of elastic-ideally plastic material given by Freund. Combining the movement and compatiblility equations, the governing equations in dynamic growing crack-tip field of the viscoelastic material was deduced. Through the numerical calculation, the asymptotic solution of the fully continuous separate variable formal of stress, stain and displacement in crack-tip field was obtained with boundary conditions and continuous conditions, and the results of numerical value of stress and strain in crack-tip field were obtained. The numerical results show that the near-tip field is mainly governed by the creep exponent n and Mach number M. The study will provide theoretical references for the corresponding problems encountered in engineering practices and the founding of fracture rule of material.