拉伸圆孔板孔边裂纹应力强度因子解析解

裂纹尖端应力强度因子是判断裂纹扩展和结构失效的重要标准，探究拉伸荷载下圆孔与裂纹相互作用的裂纹尖端应力强度因子对材料断裂准则和残余强度分析具有重要意义。基于叠加原理和弹性力学初始解，采用Westergaard应力函数求得单轴拉伸圆孔板孔边裂纹应力强度因子的积分方程，使用切比雪夫多项式得到积分方程的近似解，运用Exponential函数对近似解修正得到裂纹尖端应力强度因子修正解；运用Abaqus对同一问题进行模拟分析并与修正解结果进行对比；分析了裂纹尺寸、圆孔半径、裂纹位置角以及裂纹倾角对裂纹尖端应力强度因子的影响。结果表明：修正解与Abaqus模拟解基本吻合；应力强度因子随裂纹尺寸和圆孔半径增大而增大，随裂纹位置角和裂纹倾角增大而减小。

Analytical solution of stress intensity factor for hole edge crack of a round hole plate

The crack tip stress intensity factor is an important criterion for judging crack extension and structural failure. Investigating the crack tip stress intensity factor for the interaction between circular hole and crack under tensile loading is of great significance for material fracture criterion and residual strength analysis. Based on the superposition principle and the initial solution of elastodynamics, the integral equation of the stress intensity factors of the crack at the edge of a uniaxially tensile circular hole plate is obtained by using the Westergaard stress function, and the approximate solution of the integral equation is obtained by using Chebyshev polynomials, and the approximate solution is modified by using the Exponential function to obtain the modified solution of the stress intensity factors at the crack tip; the same problem was simulated using Abaqus and compared with the corrected solution results; the effects of crack size, circular hole radius, crack location angle, and crack inclination on the stress intensity factor at the crack tip were analyzed. The results show that the modified solution and the Abaqus simulation solution basically agree; the stress intensity factors increases with the increase of crack size and circular hole radius, and decreases with the increase of crack location angle and crack inclination angle.