陶瓷基复合材料基体唇形裂纹失效规律研究

Research on failure rules of the lip-shaped crack in a matrix of ceramic matrix composites

建立横向拉伸载荷下的唇形裂纹数学模型,采用复变函数的方法,通过保角映射,推导了唇形裂纹尖端应力场和位移场的解析解,建立了唇形裂纹的应力强度因子准则和最大能量释放率准则,结合算例分析陶瓷基复合材料基体唇形裂纹的几何参数、外载荷和纤维分布对失效准则的影响规律。结果表明,(1)裂纹尖端应力场和位移场的解析解与有限元计算结果进行对比,验证了方法的有效性;(2)相较于Griffith裂纹和椭圆裂纹,基于唇形裂纹的失效准则对裂纹尖端的敏感性更高,适用于预测脆性陶瓷基体裂纹的扩展;(3)对于不同几何参数的唇形裂纹,采用最大能量释放率准则的基体裂纹的扩展速率要大于应力强度因子准则。

The mathematical model of a lip-shaped crack under a transverse tensile load was established.Using the method of complex variable function,the analytical solution of the stress field and the displacement field of the lip-shaped crack tip was derived through the conformal mapping.The intensity factor criterion and the maximum energy release rate criterion were established.Combined with numerical examples,the influence of the lip-shaped crack geometric parameters,external load and the fiber distribution on the failure criterion was analyzed.The analytical solutions of the stress field and displacement field at the crack tip are compared with the finite element calculation results and effectiveness of the method is verified.Compared with the Griffith crack and elliptical crack.The sensitivity to the crack tip based on the failure criterion of the lip-shaped crack is higher,which is suitable for predicting the crack growth of a brittle ceramic matrix.For lip-shaped cracks with different geometric parameters,the growth rate of the matrix crack using the maximum energy release rate criterion is greater than the stress intensity factor criterion.