受压圆孔板的闭合裂纹尖端应力强度因子解析解

研究多应力场相互作用下的裂纹尖端应力强度因子是断裂力学中的重要内容，探究压缩荷载下圆孔与裂纹相互作用下的裂纹尖端应力强度因子对受压材料断裂准则与强度的影响至关重要。在含圆孔板单轴压缩初始解的基础上，采用叠加原理推导得出了单轴压缩圆孔板的裂纹尖端应力强度因子积分方程，采用切比雪夫多项式推导得出了积分方程的近似解；运用有限元方法对同一问题进行分析，并与积分方程的近似解进行对比；分析了圆孔尺寸、裂纹尺寸、裂纹位置以及裂纹面摩擦系数对裂纹尖端应力强度因子的影响。结果表明：通过叠加原理得出的裂纹尖端应力强度因子解与有限元方法解基本吻合，证明了基于初始解与叠加原理得出的裂纹尖端应力强度因子积分方程的正确性；更大的裂纹尺寸和圆孔尺寸、与孔边更近的位置以及更小的裂纹面摩擦系数会造成更大的应力强度因子，同时，靠近孔边侧的裂纹应力强度因子波动相较于远离孔边侧更为明显。

Analytical solution of stress intensity factor for closed crack in compression circular hole plate

The study of the stress intensity factor at the crack tip under the interaction of multiple stress fields is an important part of fracture mechanics, the understanding of which is critical to the fracture criterion and strength analysis of compressed materials. On the basis of the initial solution of uniaxial compression of circular hole plate, the crack tip stress intensity factor integral equation of circular hole plate under uniaxial compression is derived by superposition principle, and the approximate solution of the integral equation is derived by Chebyshev polynomial. Then, the same problem is analyzed by finite element method, and the solution is compared with the approximate solution of the integral equation. Meanwhile, the effects of circular hole size, crack size, crack location and crack surface friction coefficient on the stress intensity factor at the crack tip are analyzed. The results show that the solution of the stress intensity factor at the crack tip obtained by the superposition principle is basically consistent with that of the finite element method, so the integral equation based on the initial solution and the superposition principle is proven correct. Larger crack size and circular hole size, closer to the hole edge and smaller crack surface friction coefficient all lead to greater stress intensity factors. Furthermore, the fluctuation of the crack stress intensity factor close to the hole edge is more obvious than that far away from the hole edge.