The sensitivity of J-integrals to material law variations for semi-elliptical surface cracks

Abstract

In finite element analysis of cracked bodies, it is quite common to represent the material law (stress-strain curve) in a simplified form e.g. bilinear approximation. Many steels, however, have a more complex material law, which includes a perfectly plastic region before work hardening. Two dimensional finite element analyses have shown that fracture parameters, such as the J-integral, are very sensitive to variation in material law for shallow cracks, and the writers have now commenced three dimensional analyses for surface semi-elliptical cracks in plates. Some computations have been made for specimens tested experimentally by Dodds and Read [1], and the results show that what appears to be a reasonable approximation of the material law is inadequate in modelling the deformation behaviour, and that more accurate modelling of the material law, especially the plastic part immediately after yield, which may include perfectly plastic behaviour, is required for reliable results.

J‐ESTIMATION FOR SEMI‐ELLIPTICAL SURFACE CRACKS IN WIDE PLATES UNDER DIRECT TENSION

“…The semielliptical crack had dimensions a/c=0.57, a/t=0.27. Very good agreement was obtained between the J computed at the deepest point of the crack and the experimental values quoted by Dodds and Read [12] (see [13] for more details of the comparison).…”

“…(1b) can be varied to provide a 'best fit' to actual stress-strain curves. It is well established [1,2,13] that J-strain behaviour is extremely sensitive to material law representation, and Lau et al [4] have proposed a method which can accurately fit a power law to the plastic part of any real stress-strain curve. Various values of n were included, although the emphasis was on low to medium work hardening materials.…”

J estimation for shallow semi‐elliptical surface cracks in wide plates under pure bending

“…In 2D work 1 –4 and 3D analysis of plates with finite widths, 20 the J versus strain curves were found to be very sensitive to material stress–strain modelling. When approximating the power hardening part of the stress–strain curve [Eq.…”