Analysis of delamination fatigue growth for delaminated piezoelectric elasto-plastic laminated beams under hygrothermal conditions

A nonlinear analysis model of fatigue delamination growth for piezoelectric elasto-plastic laminated beams under hygrothermal conditions is presented. Based on the incremental elasto-plastic constitutive equations, the incremental nonlinear governing equations of the piezoelectric elasto-plastic laminated beams with delamination are derived when taking into account the hygrothermal environments, transverse shear deformation, geometrical nonlinearity and piezoelectric effect. According to the elasto-plastic fracture dynamics and J-integral theory, the energy-release-rate along the delamination is obtained. Then, applying the Paris law, the delamination growth rate is obtained and the delamination growth lengths along the delamination fronts under cyclic loads are finally determined by using the cyclic skip method. The equations are solved by the finite difference method and iterative method as a whole. Effects of voltages, variation of temperature and humidity, delamination length and depth on the energy-release-rate and delamination growth length for the piezoelectric elasto-plastic laminated beams are discussed in numerical examples.