含中心裂纹的有限加筋板Dugdale模型

Dugdale Model Analysis on Finite Internally Cracked Plate with Stiffened Edges

建立了含中心裂纹有限板弹塑性断裂问题分析的Dugdale模型,基于Muskhelishvili关于平面弹性力学解析函数解法,运用线弹性理论的叠加原理对Dugdale模型进行求解。以裂纹尖端开口位移值为弹塑性情况下表述裂纹力学特征的断裂参数,经过实例计算,给出了不同裂纹长度、不同载荷作用下含中心裂纹有限加筋板的系列断裂参数值。

The Dugdale model for finite internally cracked plate with stiffened edges under tension is studied in this paper. The CTOD (Crack Tip Opening Displacement) of the Dugdale model is used for an analytical separation into two fracture modes according to linear elastic superposition theorem: one is the problem that finite cracked stiffened plate is subject to rectangular distribution traction σY acting on the crack border, and the other is the problem that finite cracked stiffened plate is subject to uniaxial tension stress and behaves in a purely elastic manner, which can be solved independently and then recom-bined for the complete solution. A discrete stiffened plate model is constructed in the invesgiation, ignoring the bending effect, the tangential traction along two sides of the cracked plate is converted into the tension body force of the strip stiffener, then the problem about finite cracked stiffened plate is converted to the problem about finite cracked plate. Based on the knowledge of the Muskehelishvili's complex variable function for plane problem of elasticity, the eigenfunction expansion variational method is used to solve the problem of the finite cracked plate. The boundary tangential traction along the two sides of the plate is approximately expressed by a discretization, after considering the compatibility condition of the displacement between the edge of the cracked plate and the strip, the boundary tangential traction is obtained. By using the condition of bounded stresses at the carck tip proposed by Dugdale model, the relation between the plastic zone length on the crack tip and the applied stress is approximately evaluated, and the fracture parameter CTOD is obtained. One example is given. The numerical results show that the effect of the stiffened edge is changed with the crack length. Elastic-plastic fracture problems of finite cracked plate with stiffened edge are solved.