Nondestructive evaluation of cracks in conducting magnetoelastic materials

Abstract

Theoretical analysis of the alternating current flow around the crack appearing in the loaded material is given. The effective conductivity near the crack has been found to be nonhomogencous, so the phenomenon of accumulation of the charge appears there. The charge density of accumulated charge near the crack is given. The potential drop has been calculated taking into account the effect of load (stress intensity factor) of the material for three basic modes of a cracked body: opening, sliding, and tearing. The nonhomogeneous conductivity tensors are reported for all modes. The analysis is based on general rotationally invariant nonlinear magnetoelastic equations (energy balance equation, Clausius—Duhem formula, and Gibbs function expansion). Bilinear constitutive relations for large quantities of the bias (loading) have been given and linear, but parametric constitutive formulas for small-field variables (superposed over the bias, for example current) have been derived in the reference or intermediate frame. The obtained effective material tensors of the biased magnetoelastic media, such as effective elastic, piezomagnetic, permeability tensors, as well as effective conductivity, allow to treat any other small-field phenomena in the intermediate frame in the same manner as the linear phenomena for the free (unbiased) media with the only change of material parameters.