Crack Extension Force in a Piezoelectric Material

Abstract

A conservation law that leads to a path-independent integral of fracture mechanics is derived along with the governing equations and boundary conditions for linear piezoelectric materials. A closed-form solution to the antiplane fracture problem is obtained for an unbounded piezoelectric medium. The path-independent integral is evaluated at the crack tip to obtain the energy release rate for a mode III fracture problem. For a fixed value of the mechanical load, it is shown that the crack growth can be either enhanced or retarded depending on the magnitude, the direction, and the type of the applied electrical load. It is also shown that, for certain ratios of the applied electrical load to mechanical load, crack arrestment can be observed.

Anti-plane Green's functions and cracks for piezoelectric material with couple stress and electric field gradient effects

“…(45)- (48); (ii) The total stresses t r3 , t 3r , t θ3 and t 3θ and the in-plane electric displacements D r , D θ all exhibit the r −3/2 singularity near the crack tip. This singularity is much stronger than the classical square root singularity (Pak, 1990) and is in agreement with the results of Zhang et al (1998), Paulino et al (2003) and Yang, J.S. (2004) when the strain gradient or the electric field gradient effect is considered; (iii) The couple stresses m rr , m θθ , m rθ , m θr , the electric displacement D 3 , and Π rr , Π θθ , Π rθ all exhibit r −1/2 singularity near the crack tip.…”

“…(i) Similar to the classical mode III crack tip electroelastic field (Pak, 1990), the near-tip asymptotic electroelastic field in a piezoelectric material with both the couple stress and the electric field gradient effects is governed by two parameters B and D in Eqs. (45)- (48); (ii) The total stresses t r3 , t 3r , t θ3 and t 3θ and the in-plane electric displacements D r , D θ all exhibit the r −3/2 singularity near the crack tip.…”

Analysis of Mechanical and Electrical Damages in Piezoelectric Ceramics

“…Therefore, it is very important theoretically and practically for fracture analysis, reliability design and lifetime prediction of piezoelectric ceramics to investigate the fracture mechanism. On the basis of linear piezoelectric fracture mechanics, some solutions were obtained by Pak (1990Pak ( , 1992, Sosa and Pak (1990), Sosa (1991Sosa ( , 1992, Suo et al (1992), Suo (1993) and others, but they contradict the piezoelectric fracture experiments (Park and Sun, 1995;Heyer et al, 1998). The linear piezoelectric fracture mechanics predicted that the stress intensity factors were independent of the applied electric field, but the experimental results (Park and Sun, 1995;Heyer et al, 1998) showed that an existing electric field might impede or accelerate crack propagation, which was related to the applied electric field direction.…”

The energy release rate and the J-integral of an electrically insulated crack in a piezoelectric material

“…One can cite the work of Parton [1], Deeg [2], Pak [3], Sosa [4], Zhang and Hack [5], Suo et al [6], Park and Sun [7], Gao and Barnett [8], Zhang and Tong [9], Zhang et al [10], Ru [11], Gao and Fan [12], McMeeking [13,14], and others. Recently, an extensive summary of the previous work was presented in [15].…”