A new look at energy release rates for quasistatically propagating cracks in inelastic materials

A mapping technique is used to derive an integral expression for the energy release rate for a quasistatically propagating crack. The derivation does not depend on any assumptions in regard to the contitutive behavior of the material. It leads to a contour integral around the crack tip, plus an area integral over the region enclosed by this contour. Only the stress and displacement fields appear in the integrands. Although for stationary crack solutions known to the authors the area integral is not convergent, for propagating crack solutions in elastoplastic material, the integrals are convergent, and lead to zero energy release rate. This confirms conclusions by Rice from an independent point of view.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42773/1/10704_2004_Article_BF00012388.pd

Influences of non-singular stresses on plane-stress near-tip fields for pressure-sensitive materials and applications to transformation toughened ceramics

In this paper, we investigate the effects of the non-singular stress ( T stress) on the mode I near-tip fields for elastic perfectly plastic pressure-sensitive materials under plane-stress and small-scale yielding conditions. The T stress is the normal stress parallel to the crack faces. The yield criterion for pressure-sensitive materials is described by a linear combination of the effective stress and the hydrostatic stress. Plastic dilatancy is introduced by the normality flow rule. The results of our finite element computations based on a two-parameter boundary layer formulation show that the total angular span of the plastic sectors of the near-tip fields increases with increasing T stress for materials with moderately large pressure sensitivity. The T stress also has significant effects on the sizes and shapes of the plastic zones. The height of the plastic zone increases substantially as the T stress increases, especially for materials with large pressure sensitivity. When the plastic strains are considered to be finite as for transformation toughened ceramics, the results of our finite element computations indicate that the phase transformation zones for strong transformation ceramics with large pressure sensitivity can be approximated by those for elastic-plastic materials with no limit on plastic strains. When the T stress and the stress intensity factor K are prescribed in the two-parameter boundary layer formulation to simulate the crack-tip constraint condition for a single-edge notch bend specimen of zirconia ceramics, our finite element computation shows a spear shape of the phase transformation zone which agrees well with the corresponding experimental observation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42782/1/10704_2004_Article_BF00018779.pd