半圆形初始裂纹在交变拉伸载荷下的裂尖应力场数值模拟

Numerical simulation of tip stress field of semi-circular initial crack subjected to alternating tensile loads

[目的]为研究板结构中初始裂纹深度沿板厚方向分布不均匀的问题,[方法]基于三维虚拟裂纹闭合技术(VCCT),以半圆形初始裂纹为例,对其在交变拉伸载荷作用下的裂尖应力场进行数值模拟。[结果]结果表明:对于裂纹水平面的应力场,在发生塑性变形的区域,计算点的von Mises等效应力随着距裂尖距离的增大而减小,两者之间呈线性或双线性关系;在未发生塑性变形的区域,该应力值基本上是裂尖距离的三次函数。对于裂纹横断面,裂纹总是沿裂纹边缘形状的法向方向扩展,且应力峰值出现在裂纹边缘,裂纹内部应力值随着距裂纹中心的距离呈现高度的非线性分布,而外部应力值则随着距裂纹中心距离的增大而减小。当该距离超过裂纹半径的1.67倍时,应力集中消失;当拉伸载荷为2/3和1/3倍材料屈服应力时,裂纹边缘的应力峰值总是分别等于载荷的1.45倍和2倍。[结论]研究结果可为考虑初始裂纹的板结构的疲劳强度计算提供参考。

[Objectives]In order to research the uneven distribution problem of initial crack depth along the thickness direction of a plate,[Methods]based on the 3D Virtual Crack Closure Technique(VCCT),this paper takes a semi-circular crack as an example for carrying out a numerical simulation on the tip stress field of a crack subjected to alternating tensile loads.[Results]For the horizontal equivalent stress field of the crack in the plastic deformation area,it is found that the von Mises equivalent stress at the calculation point decreases as the distance from the crack tip increases,where it is basically subjected to linear or bilinear distribution.However,the stress of the crack in the non-plastic deformation area is the cubic function of the distance.The cross-section of the crack always extends in the normal direction along the crack's edge,where it is subjected to maximum stress.The internal stress features a highly nonlinear distribution with regard to the distance from the center of the crack,and the external stress decreases as the distance increases.As the distance reaches up to 1.67 times greater than the crack radius,the concentration of stress disappears.As the tensile loads are 2/3 and 1/3 times greater than the material yield stress,the maximum stress at the edge of the crack is always equal to 1.45 and 2 times the load respectively.[Conclusions]The results of this paper can provide valuable references for the ultimate strength calculation of plate structures with initial cracks.