模拟脆性材料动态裂纹扩展的非连续变形分析方法

非连续变形分析方法(DDA)属于隐式离散元法,通过引入虚拟节理可以模拟材料从连续到破坏全过程。尝试将DDA方法应用于脆性材料动态裂纹扩展问题。采用基于Voronoi多边形离散的DDA方法进行模拟。由于Voronoi多边形会存在较多短边,采用原始DDA程序计算时短边会优先发生破坏。针对该问题通过引入均布弹簧算法,在一定程度上减轻了过多短边发生破坏的问题。其次,为了能够定量分析动态裂纹扩展,提出了一套参数标定方案。该方案通过单轴压缩试验进行弹性参数标定,通过带切槽半圆盘试验进行强度参数标定。利用标定后的参数模拟的带切槽半圆盘,裂纹扩展路径与试验结果高度一致。最后,基于标定的参数,模拟了几类典型脆性材料的动态裂纹扩展问题,包括自相似裂纹扩展、裂纹分叉和紧凑拉伸试验。模拟结果表明,DDA方法能够较好地再现自相似裂纹扩展时裂纹扩展速度保持不变的规律,可以真实地模拟出脆性材料的裂纹分叉现象,并成功模拟了不同加载速度下紧凑拉伸试验中不同的破坏模式。这些算例验证了DDA方法在模拟脆性材料动态裂纹扩展问题的可行性,为后续相关应用打下了基础。

Numerical study on dynamic crack propagation of brittle materials by discontinuous deformation analysis

The discontinuous deformation analysis(DDA),as an implicit discrete element method,can simulate the evolution process from continuum to failure by introducing the virtual joint technology.In this study,the DDA method is modified and applied to the dynamic crack propagation problem of brittle materials.Firstly,the DDA with Voronoi discretization is adopted.Since there are many short edges in the Voronoi discretization,these edges will fail preferentially using the original DDA algorithm.A uniform spring algorthim for the DDA is proposed to solve this issue.Then,a parameter calibration scheme is presented.The uniaxial compression and a semi-circular bend(SCB) with a pre-existing crack are used to calibrate the elastic parameters and the strength parameters,respectively.Based on the calibrated parameters,the predicted crack propagation paths of SCB are highly consistent with the test results.Finally,several dynamic crack propagation problems for brittle materials,such as self-similar crack propagation,crack branching and compact tensile tests,are simulated based on the calibrated parameters.The proposed DDA method can reproduce the phenomenon of crack propagation with the constant speed for the self-similar crack and the crack branching phenomenon under dynamic loading.Meanwhile,different failure patterns for compact tensile tests under different loading speeds are reproduced successfully.The results verify the feasibility of the DDA for dynamic crack propagation of brittle materials,and pave the way for future engineering applications.