A Pseudo-Linear Analysis of Yielding and Crack Growth: Strain Energy Density Criterion

Abstract

A typical phenomenon of ductile fracture is the process of crack initiation, slow growth and final termination. This process, being sensitive to the rate of loading, results in global nonlinearity of the load and displacement as the material may be damaged locally by yielding and/or fracture. The progressive damage of material being a path dependent process requires the stress and failure analysis be performed in tandem for each increment of loading. This is accomplished by a finite element procedure in conjunction with the strain energy density criterion. The configuration of a through crack under a rising load is analyzed where yielding of the elements near the crack are assumed to coincide with ΔW/ΔV reaching some critical value (ΔW/ΔV)y. This is translated into a permanent change of local stiffness for each increment of loading. Further damage of the material will be distinguished by the local value of (ΔW/ΔV). The nonuniform segment of crack growth is assumed to occur along the path of ΔW/ΔV being a relative minimum regardless of whether the material separates elastically or plastically and is assumed to be governed by the condition S1/rl = S2/r2 = --- = Sc/rc = (ΔW/ΔV) c * where (ΔW/ΔV) c * is the relative strain energy density. The strain energy density of virgin undamaged material is (ΔW/ΔV)c. The pseudolinear stress and failure analysis lead to a nonlinear response of load and displacement for the cracked medium. It is shown that for materials with a relatively low value of critical strain energy density more damage is inflicted due to crack growth or fracture than yielding while the reverse holds for materials with a relatively high value of critical strain energy density.