Effective moduli for thermopiezoelectric materials with microcracks

Dilute, Self-Consistent (SC), Mori-Tanaka (MT) and differential micromechanics methods are developed for microcrack-weakened thermopiezoelectric solids. These methods are capable of determination of effective properties such as the conductivity, electroelastic moduli, thermal expansion and pyroelectric coefficients. The above material constants affected by the microcracks are derived by way of Stroh's formulation and some recently developed explicit solutions of a crack in an infinite piezoelectric solid subjected to remote thermal, electrical and elastic loads. In common with the corresponding uncoupled thermal, electric and elastical behavior, the dilute and Mori-Tanaka techniques give explicit estimates of the effective thermoelectroelastic moduli. The SC and differential schemes, however, give only implicit estimates, with nonlinear algebraic matrix equations, of the effective thermoelectroelastic moduli. Numerical results are given for a particular cracked material to examine the behavior of each of the four micromechanics models.