非奇异应力对中央含V形切口试样断裂性能的影响

Effect of non-singular stress on the brittle fracture of the centrally sharp V-notched specimen

采用Williams渐近展开式表达V形切口尖端附近区域的位移场和应力场,将其代入弹性力学基本方程中,应力奇异性指数及其对应的位移和应力角函数由求解常微分方程组获得。由于在远离切口尖端的区域无应力奇异性,将切口尖端应力奇异性区域移出后,应用边界元法分析无应力奇异性的剩余结构;将Williams渐近展开式与弹性力学边界积分方程结合,解出切口尖端附近应力奇异性区域的各应力场渐近展开项系数,从而获得切口尖端附近区域的完整应力场;基于此,研究了非奇异应力项对中央含V形切口试样的表观断裂韧度和临界荷载预测值的影响。结果表明:考虑非奇异应力项时,脆性断裂的表观断裂韧度和临界荷载的预测值要比忽略非奇异应力项时的预测值更接近实验值。

The displacement and stress fields of the characteristic radius region near a notch tip are expressed by the Williams asymptotic expansions. After the series expansions are substituted into the governing equations in elasticity, the stress singularity order and the corresponding angle function can be obtained by solving the characteristic differential equations. Due to the fact that there is no stress singularity in the region far from the crack tip, the boundary element method is used to analyze the remaining region excluding the crack tip. The coefficients in the Williams series expansions can be calculated by associating the expansions with the boundary integral equations. Then the singular stress terms and the non-singular stress terms in the crack tip region can be conveniently obtained. Thus the effect of the non-singular stress on the apparent fracture toughness and the critical loading for the centrally sharp V-notched specimen problem are discussed. Numerical results obtained indicate that the predicted critical loading and fracture toughness of V-notched structures are closer to the test results than the predicted ones only considering the singular stress when the non-singular stress is taken into consideration.