圆盘状裂纹前缘塑性区尺寸及张开位移估计

Method to Estimate the Plastic Zone Size and Opening Displacement at the Tip of Penny Shaped Crack

将Ｄｕｇｄａｌｅ模型推广到三维裂纹问题计算了圆盘状裂纹前缘塑性区尺寸，并结合断裂力学中的Ｂａｒｅｎｂｌａｔ－Ｄｕｇｄａｌｅ裂纹模型和三维Ｊ－积分原理计算了圆盘状裂纹前缘张开位移，得到了Ｊ－积分与裂纹张开位移的关系。最后用非线性有限元方法对圆盘状裂纹的前缘塑性区尺寸作了数值分析，确定了公式中的未知常数，并对其正确性作了数值验证。

In this paper, a method is proposed to estimate the plastic zone size, by extending the Dugdale model to three dimensional (3D) crack problems and the crack opening displacement (COD) at the tip of a sptatial penny shaped crack by combining the Barenblatt Dugdale model with the principle of 3D J integral, then the relationship between J integral and COD is obtained. Finally, the reliability of the estimation in this paper is testified by calculating the plastic zone size at the tip of a sptatial penny shaped crack embedded in an infinite elastic perfect solid with nonlinear FEM and the unknown material constant is determined. The applicable domain of the Dugdale model is extended in this paper.