Elastic-plastic fracture analysis and design using the finite element method

Abstract

Published stress analysis solutions for crack problems are reviewed under three headings — elastic, elastic-plastic, and finite element. Emphasis is laid on results which are of practical importance for fracture analysis. The review section is concluded with a critical survey of some commonly used fracture design procedures. Results obtained by the author using elastic-plastic finite element analysis are then presented. Correlations are given for J and COD in a range of edge and centre cracked tension geometries. Comparison is made with various estimation procedures. Problems involved in defining J and COD are fully enumerated and their significance and inter-relationship investigated. It is emphasised that J is not an available energy release rate in the presence of irreversible plastic deformation, and that its possible use as a fracture criterion rests solely on its ability to characterise the stress-strain environment at the crack tip. The relationship between J and near tip stress, strain, and displacement is examined. The author concludes that JIC is unlikely to be a geometry invariant fracture criterion, but that it may have considerable use as a scaling parameter for predicting the fracture behaviour of a large specimen from a much smaller but geometrically similar specimen. The possibility of providing a complete description of the crack tip environment by using J together with the geometry dependent non-singular stresses is indicated. Elastic-plastic analyses are presented for a number of structural geometries, including cracks emanating from a hole in a plate, cracks approaching a hole in a plate, and an internal crack in a thick walled cylinder. These results indicate that, provided net section yielding does not occur, J may be estimated from the nominal elastic stress distribution even if this locally exceeds yield. Recommended fracture design procedures are presented in the light of the above findings.