交叉型裂纹扩展的近场动力学分析

Peridynamics analysis of intersecting cracks propagation

为了研究交叉型裂纹的扩展模式及主次裂纹长度比值对裂纹扩展模式的影响,基于近场动力学(peridynamics,PD)理论建立模型,在本构方程中引入长程力作用,采用体积修正提高计算精度。基于该数学模型编写Fortran程序对含交叉型裂纹二维板的裂纹扩展进行数值模拟。以T形交叉型裂纹为例,分析拉伸载荷作用下主次裂纹长度比值对裂纹扩展的影响,计算无量纲应力强度因子并与解析解进行对比。结果表明:近场动力学方法可以很好地对T形裂纹的结构裂纹扩展进行模拟;主次裂纹长度比值增大,裂纹扩展速率有减小的趋势,并且由次裂纹引发的裂纹扩展夹角有增大的趋势。

To research the influence of propagation mode and ratio of main and secondary crack lengths on the intersecting cracks,modeling was established based on the peridynamics(PD)theory.The long range force is introduced into the constitutive equation,and the accuracy of the calculation is improved by interface correction and volume correction.Based on this model,the numerical simulation of two-dimensional plate crack growth with intersecting cracks was carried out,and the structural crack growth of T-shaped cracks was simulated.The different effects of length ratio of main crack and secondary crack on crack growth under tensile conditions are analyzed.Nondimensional stress intensity factors were calculated and compared with the analytical solutions.Peridynamics theoretical method can well simulate the structural crack growth of T-shaped cracks.When the ratio of primary to secondary crack length increases,the crack growth rate tends to decrease and the crack growth angle caused by secondary crack tends to increase.