Yielding fracture mechanics

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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 σ Y 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, Δ c 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 Δ c or Jc is independent of geometry and the extent to which stable crack growth prevents the usage of one simple criterion of fracture for all structural configurations.

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