One-dimensional nonlinear scattering by localized hysteretic damage and its application to damage characterization

Abstract

One-dimensional nonlinear scattering by a confined distribution of dislocations interacting with point defects distributed along their glide planes or their cores, and of microcracks with or without adhesion between their faces is predicted theoretically. The nonlinear properties of these forms of damage are modeled by macroscopic effective constitutive relationships, and a perturbation approach is used to solve the scattering problem. Backward and forward scattered fields are investigated and use of their main properties towards the development of selective imaging methods which are tailored to hysteretic material damage is briefly discussed. This model is also used to verify recent experimental results on steel samples containing small cracks or confined regions of macrograins. The mechanism associated to hysteresis of large grains is modeled by the interaction between dislocations and point defects along their glide planes. Theoretical predictions confirm that the exponent of a power law, which links the energy dissipated nonlinearly to the energy of a scaled linear field, is sensitive to the physical nature of damage. In turn, experimental findings are shown to provide convincing support to the effective constitutive relationships proposed in this work. Interactions of dislocations with glide and core PDs are characterized by different values of the exponent.

Keywords: Dislocations; Microcracks; Nonlinearity; Scattering.