Yielding fracture mechanics

TLDR: In this paper, the crack opening displacement, Δ, and the J contour integral are proposed for describing the stresses and deformation at the tip of a sharp crack embedded in a region of yielding material.

Abstract: Yielding fracture mechanics seeks to find a relationship between applied stress, crack size and material toughness that is independent of the geometry of a component when fracture occurs after significant degree of yielding. The crack opening displacement, Δ, and the J contour integral are two proposals for describing the stresses and deformation at the tip of a sharp crack embedded in a region of yielding material. The concepts can be related in the form J = M σ YΔ where σY is the uniaxial yield stress, and M a factor with a value between about 1 and 2.5. The concepts are still under development. Either term can be chosen as a measure of the severity of crack tip deformation in a given material with the onset of crack growth in monotonic loading occurring at a critical value, Δc or Jc, for a given thickness. Experimental evidence so far is in broad support of this picture but there remains uncertainty over the degree to which Δc or Jc is independent of geometry and the extent to which stable crac...