基于有限元的弹塑性裂纹数值分析

Numerical analysis of elastoplastic crack based on the finite element

在线弹性断裂力学和D-M模型的基础上,推导出了受单向拉伸含中心穿透裂纹的理想弹塑性材料J积分的解析式;通过ANSYS对弹塑性J积分进行数值计算,与推导出的解析解比较,表明了用有限元方法计算弹塑性J积分具有相当高的精度;分析了J积分与裂纹初始长度及外荷载的关系;对理想弹塑性材料塑性区大小进行了探讨,结果表明,塑性区尺寸随外荷载增大而增大,并且外荷载接近屈服应力时,裂纹塑性区尺寸趋近于无穷大,进入全面屈服。

Based on the linear elastic fracture mechanics and D--M model, J integral is derived under tension with center through-- thickness crack in the ideal elastic--plastic materials. Aiming at elastic--plastic J integral for numerical calculation through ANSYS, analysis and comparison with the deduced solution are made, showing that it is highly accurate by means of the finite element method to calculate the elastic plastic J integral .Then analysis of the relation between the J integral and the initial crack length and load is given.The ideal elastic--plastic materials＇ plastic zone size is studied and results show that the plastic zone size increases with the increase of load, and when the load is close to yield stress, crack plastic zone size approaches infinity, entering the overall yield.