Large Deformation and Strain Gradient Fracture Analysis of Double Cantilever Beams with Piezoelectric Effect

Abstract

This paper examines the size-dependent fracture of a piezoelectric double cantilever beam (DCB) specimen based on large deformation–strain gradient theory. The governing equations with relevant boundary conditions for a piezoelectric cantilever beam with simultaneous consideration of surface piezoelectricity, surface elasticity, surface residual stress, and large deformation are obtained and solved numerically. These results are further utilized to investigate the fracture behavior of a DCB. Results show that the strain gradient effect is more pronounced when the beam height is less than the material length scale parameter. The strain gradient model anticipates significant stiffening behavior at micro/nanoscales. The effect of the surface residual stress is more substantial than that of surface elasticity and surface piezoelectricity. The study further established that the strain energy release rate of the short-circuit boundary condition is larger than that of open-circuit boundary condition. Using strain gradient model, the effect of the uncracked part of DCB is more noticeable on a smaller scale and should not be ignored even for slender beams.