Analytical and numerical evaluation of crack-tip plasticity of an axisymmetrically loaded penny-shaped crack

作者：Chaiyat Sumitra; Jin Xiaoqing; Keer Leon M^*; Kiattikomol Kraiwood

来源：Comptes Rendus Mecanique, 2008, 336(1-2): 54-68.

DOI：10.1016/j.crme.2007.10.015

• penny-shaped crack
• crack tip plasticity
• Dugdale approach
• Tresca criterion
• Von Mises criterion

Analytical and numerical approaches are used to solve an axisymmetric crack problem with a refined Barenblatt-Dugdale approach. The analytical method utilizes potential theory in classical linear elasticity, where a suitable potential is selected for the treatment of the mixed boundary problem. The closed-form solution for the problem with constant pressure applied near the tip of a penny-shaped crack is studied to illustrate the methodology of the analysis and also to provide a fundamental solution for the numerical approach. Taking advantage of the superposition principle, an exact solution is derived to predict the extent of the plastic zone where a Tresca yield condition is imposed, which also provides a useful benchmark for the numerical study presented in the second part. For an axisymmetric crack, the numerical discretization is required only in the radial direction, which renders the programming work efficient. Through an iterative scheme, the numerical method is able to determine the size of the crack tip plasticity, which is governed by the nonlinear von Mises criterion. The relationships between the applied load and the length of the plastic zone are compared for three different yielding conditions.

• 出版日期2008-2
• 单位西北大学