An elastic-plastic finite element solution for a cracked plate

In this paper, the finite element method is applied to a center-cracked plate subject to opening mode tensile loading. A complete elastic-plastic plane-stress solution for strain hardening materials obeying a Von Mises yield condition and Prandtl-Reuss stress-strain relations is obtained using only constant strain elements. An accurate representation of the stress-strain field even at distances very close to the crack-tip, is achieved by the use of a mesh arrangement in which the size of the elements decreases in a geometric series as the crack tip is approached. The numerical solution is compared with and used to discuss the range of validity of the well-known HRR (Hutchinson-Rice-Rosengren) crack tip solution valid for small scale yielding. The influence of different amounts of hardening and the effect of changes in the mesh arrangements are also considered. Features of the finite element algorithm which reduce the total computing time are discussed. The finite element program is executed on a CRAY-1 computer and the effect of vectorization on computational speed is discussed for this problem.

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