A finite element computation of fracture parameters for the crack problems with large-scale yielding

A global secant relaxation method was adopted for carrying out the incremental/iterative computations of fracture parameters for cracked structures with large-scale plastic yielding. The relaxation method has been used to improve the performances of the modified Newton-Raphson iteration in solving the system of nonlinear algebraic equations resulting from the finite element discretization of nonlinear structural problems. Numerical results have shown that this method has great numerical stability and is efficient in solving the problems for which highly accurate global and local convergences are needed. The convergency characteristics inherent in the global secant relaxation method are especially suitable for the analysis of a cracked ductile structure, since fully guaranteed global and local convergences are required to accurately obtain the fracture parameters in order to evaluate the fracture behaviour globally and locally. A numerical solution concerning a centre-cracked plate with an extremely ductile material property was performed. The performances of iterative computations were evaluated. And the correlations between different fracture parameters were studied which was mainly aimed at the objective of using displacement defined parameters to replace certain integral or differential parameters in evaluating the fracture behaviours through the computer assessment of FEM approximation.