Analysis of the electric yielding zone of the anti-plane mode III crack problem in piezoelectric materials

作者：Xue Cun; Zhou Youhe^*; Yong Huadong

来源：Chinese Journal of Solid Mechanics, 2012, 33(5): 449-455.

• Anti-plane
• Electric displacement
• Mechanical displacements
• Mode III crack
• Relaxation models
• Strip model

The yielding zone of the anti-plane mode III crack problem in piezoelectric materials is analyzed in this paper. Based on the strip model, the expression of the electric yielding zone is derived. The boundary conditions along the yielding segments have two types: one is the mechanical displacement continuity condition and the other one is that the stress is assumed to be constant in the electric yielding zone. The latter eliminates the singularity of the electric field and the stress at the crack tip, which is coincident with the reality. The two different conditions have the same results. The energy release rates of the two types are also derived in this paper. The electric yielding zone is also obtained based on the electric displacement relaxation model which is similar to the stress relaxation model by Irwin. Comparing the results of the two different models, the yielding zone size obtained by the strip model is approximately equal to the result of the electric displacement relaxation model. Therefore, under the condition of the small deformation, the results are effective.

• 出版日期2012