title: Elastic-plastic interfacial crack problems
Creators: name: Li, Junhong
Publisher: name: University of Glasgow
Year: 1998
Subjects: subject: Materials science.

description: Plane strain asymptotic solutions for the stress fields of a stationary crack in a homogeneous isotropic material under mixed-mode loading have been constructed analytically. Without loss of generality the fields are taken to comprise elastic and plastic sectors. Slip line solutions have been developed for the plastic sectors and semi-infinite elastic wedge solutions for the elastic sectors. The fields, which exhibit full continuity of tractions, have been verified by numerical calculations based on modified boundary layer formulations. For mode I, the loss in constraint depends on the second order term in the Williams expansion (T). A compressive T stress results in the formation of an elastic wedge on the crack flanks and a loss of crack tip constraint. The relation between the loss of constraint and the structure of the asymptotic field has been determined analytically. These fields form the basis of a two parameter, constraint-based characterisation of mode I fields. For mixed mode fields in nonhardening and incompressible conditions, the loss of constraint has been correlated to plastic mode mixity. The asymptotic crack tip fields of a stationary crack located on the interface between a rigid body and an elastic-plastic matrix subject to mixed mode loading have been investigated under small scale yielding and incompressible deformation. The analysis does not require the assumption that plasticity fully surrounds the crack tip and satisfies continuity of stress, except for an allowable discontinuity in radial stress across the interface. Under negative mode mixities, the maximum hoop stress is located in the matrix and leads to the possibility that the crack may propagate into the matrix rather than along interface. The crack tip fields and hence the fracture toughness for this failure mode can be correlated with the fields and toughness in unconstrained mode I loading. The plane strain asymptotic stress fields of interface cracks in elastically matched but strength mismatched materials have been examined numerically and analytically under mixed mode loading. Stationary cracks located in the interface, as well as normal to the interface have been studied. A family of interface crack fields which depend on strength mismatch factor and phase angle have been constructed analytically in association with Prof. T-L Sham. These have been verified by a finite element method using boundary layer formations. For cracks normal to the interface, the crack tip stress field has been investigated by using boundary layer formulations under mode I with different levels of T stress and mixed mode loading. For weak and moderate strain hardening, the loss of constraint due to compressive T stress gives rise a family of fields which differ in a largely hydrostatic manner. This feature of mixed mode fields is similar to that of homogeneous materials. Both T and Mode II component cause a loss of constraint at the crack tip. All these fields have the same important feature, that they differ in a largely hydrostatic manner on the plane of the maximum principal stress. For stress controlled failure, these fields can be correlated with the homogeneous mode I small scale yielding field allowing constraint based homogeneous mode I failure criterion to be used for bi-material interface cracks as well cracks in homogenous materials under mixed mode loadings.