Ⅰ-Ⅱ复合型多裂纹板的应力强度因子分析
Analyzing Stress Intensity Factors of a Plate with Multiple Mixed-mode Cracks

利用有限元方法求解多裂纹板的应力强度因子，讨论了板的尺寸、裂纹长度比、裂纹间距比对应力强度因子的影响。通过单裂纹的数值解与解析解的对比，证明了有限元位移外推法求解应力强度因子的有效性。计算结果表明：两侧裂纹长度越小、离中心裂纹越远，对中心裂纹尖端应力强度因子的影响就越小；当板的尺寸W/a>8时可视为无限大平板，忽略板尺寸的影响；当L/b>9或h/b>6时，两侧裂纹对中心裂纹影响很小，可忽略裂纹之间的相互影响而分开考虑。
The paper obtains the stress intensity factors (SIF) of a plate with multiple mixed-mode cracks with the displacement extrapolation method and the finite element method, and studies in detail the effects of some parameters on the SIF, which include the length of rectangular plate, crack length, crack separation ratio. Comparing the simulation results with the analytical solutions, we demonstrate the feasibility of the displacement extrapolation method. The side crack of small size and the large crack separation ratio have little effect on the SIF of a central crack. It can be seen as an infinite plate when the length of rectangular plate is eight times larger than the crack length. The three cracks can be seen as a single crack separately when the horizontal distance L or vertical distance h is six times or nine times larger than the crack length b. The reason is that the interaction among multiple mixed-mode cracks can be ignored when L/b>9 or h/b>6