PLASTIC INTENSITY FACTORS FOR CRACKED PLATESt

An elastic-plastic analysis is performed for two problems relevant to fracture mechanics: a semi­ infinite body with an edge crack in a far out-of-plane shearing field and an infinite plate under plane stress conditions containing a finite line crack in a remote tensile field. Amplitudes of the dominant singularity in the plastic region at the crack tip, the plastic stress and strain intensity factors, are calculated for applied stress levels approaching the yield stress. A technique is developed for using the dominant singular solution in conjunction with the finite element method to make accurate calculations for the near-tip fields. Addition­ ally, a comparative study of deformation theory with flow theory is performed for cracks in an anti-plane shear field. Elastic fracture mechanics is extended to high levels of applied stress for which the plastic zone is no longer small compared to the crack length by relating the critical stress for fracture initiation to the plastic intensity factors. INTRODUCTION AN ELASTiC-plastic analysis of plates of hardening material containing cracks will be carried out. This analysis is then employed to extend classical fracture mechanics to the case when the plastic zone about the crack tip can no longer be considered small. Work pertinent to this area of fracture mechanics has been reviewed by McClintock and Irwinj l] and very recently by Rice [2]. Initiation of crack growth depends on the stress and strain fields in the immediate vicinity of the crack tip. For the cases considered in the present study, cracks in remote anti-plane shear and tensile fields, these near-tip solutions are known except for their amplitudes, the plastic stress and strain intensity factors which relate the be­ havior at the crack tip to the geometry and applied stress. In the small scale yielding range, when the plastic zone about the crack tip is small in comparison with the crack length, the plastic intensity factors can be related directly to the elastic stress intensity factor. Results of this type, which will be further discussed, are due to Hult and McClintock[3], Neuber[4] and Rice[5] for the anti-plane shear case and to Rice and Rosengren[6] and Hutchinson [7, 8] for the tensile case. At higher values of applied stress, in what will be referred to as the large scale yielding range, the plastic zone is no longer small compared to the crack length and the elastic stress intensity factor is no longer relevant without some modification. Use of plastic intensity factors is in no way restricted by the extent of the plastic zone; and thus the concept of a critical value of the plastic stress or strain intensity factor can be introduced and employed in much the same way as the elastic stress intensity factor is used in classical fracture mechanics. A numerical procedure is developed here which combines details of the dominant singularity in the plastic region with the finite element technique for accurate computation of the plastic intensity factors. Standard numerical techniques which have been applied to these crack prob­ lems with no special treatment for the singularity at the crack tip fail to give accurate solutions about the tip, the region of prime interest. [Presented at the Third National Symposium on Fracture Mechanics, Lehigh University, Bethlehem, Pa., August 25-27, 1969. 435