三维数值流形法在裂纹扩展中的应用研究

运用三维数值流形法（3D NMM）进行三维裂纹扩展分析，并采用C++语言编写了相应的程序。充分利用三维数值流形法模拟裂纹扩展的优势，只需要更新裂纹尖端线附近的边界环路和流形单元，不需要使用阶跃函数。根据三维数值流形法计算得到的应力结果，应用非局部求迹方法分析每个裂纹尖端的破坏状态，如果发生破坏则沿垂直于其最大主应力方向扩展。针对裂纹扩展后的不同状况，采用四边形或三角形推进法。裂纹扩展后为了使变形后的面保持平面，必须对新生成的面进行三角化分割。对诸如单边裂纹、平行钱币型裂纹和倾斜钱币型裂纹扩展问题进行数值模拟。计算结果表明，采用三维数值流形法进行裂纹扩展模拟是可行的，文中方法对裂纹尖端线非闭合和闭合的情形均适用，且文中方法对于裂纹尖端线位于单元内部的非平面裂纹扩展也是有效的。

Application of three-dimensional numerical manifold method to crack propagation

The three-dimensional crack propagation is analyzed by the three-dimensional numerical manifold method (3D NMM) and the corresponding program with C++ is established. By taking the advantages of 3D NMM in crack propagation, only crack shells and manifold elements are required to be updated without the use of Heaviside function. According to the stress obtained from 3D NMM, the nonlocal crack tracing method is used to analyze the failure state of every crack tip. If failure occurs, the crack propagates along the direction perpendicular to the maximum principal stress. Quadrilateral or triangle tracing method is selected according to the situation during propagation. In order to make the deformed surface remain plane, triangulation of new generated face is needed. The edge crack, horizontal penny-shaped crack and inclined penny-shaped crack are simulated. It is feasible that simulating crack propagation with 3D NMM. Furthermore, the proposed method is suitable for cases of nonclosed and closed crack tip line and is also effective for the nonplanar 3D crack growth where the crack tip line is located in an element.