On nonlinear effects in fracture mechanics

Abstract

Linear elastic treatment of fracture is considered applicable for net section stress up to about 0.8 the uniaxial tensile yield stress. Crack front plastic yield is still small enough to be viewed and treated as a small perturbation to the local crack front elastic stress field. Assuming these same circumstances and adopting the same point of view, an approach is presented for incorporating the nonlinear effects of small scale crack front plastic yield and slow crack extension in determination of the energy release rate and fracture toughness. Deviation from linearity of the load-displacement record in a fracture toughness test offers a quantifiable measure of these effects and is used to calculate the energy release rate G ̃ , which turns out to have the form G ̃ = (1 + P ̃ )G , where G is Irwin's elastic energy release rate. The factor P ̃ is directly determined in each test case, and when added to unity defines a nonlinear correction C ̃ to G, which has a lower bound value of one. Fracture toughness values for one-eight inch thick 7075-T6 center cracked aluminum sheet based on this approach are compared with uncorrected values and with values obtained by the Irwin y ∗ method of plasticity correction.