CUED: Cambridge Centre for Micromechanics - Technical Report Abstracts

University of Cambridge > Engineering Department > MMD > CCM > Publications > Abstracts

Microstructure in the near-tip process zone for an impermeable macrocrack in piezoelectric materials

Qida Liu¹ , Yi-Heng Chen¹, Tian Jian Lu²
¹School of School of Civil Engineering and Mechanics, Xi'an Jiaotong University, 710049, P. R. China; (e-mail:qidaliu2000@yahoo.com.cn)
²Department of Engineering, University of Cambridge
Trumpington St., Cambridge CB2 1PZ, UK
CUED technical report, CUED/C-MICROMECH/TR.92, February 2004.

This paper deals with the influence of microstructure, e.g., microcracks, on the near-tip stress-electric field for an impermeable macrocrack in piezoelectric materials. Firstly, we propose an extension technique of the pseudo-traction method originally developed by Chen (1984) and Horii and Nemat-Nasser (1985,1987). A new method called the pseudo-traction electric displacement method (PTEDM) is summarized briefly (Chen and Han, 1999a, b), from which the interaction problem between the near-tip microcracks and an impermeable macrocrack could be solved. Secondly, we focus our attention on the different electric boundary conditions along the near-tip microcracks, say, the permeable model (Parton, 1976) or impermeable model (Deeg, 1980). By following the conclusion of Park and Sun (1995a,b), a macrocrack could be modeled as impermeable one when a cracked specimen is put in insulating oil (Jiang and Sun, 2001). Whereas by following the conclusion of McMeeking (1999), the preexisting microcracks due to poling or other sources could be modeled as permeable slit cracks, in which the crack surface opening is very small. Thirdly, following to the work of Xu and Rajapakse (2001), we present some mathematical treatments to solve the interaction problem between the near-tip permeable microcracks and an impermeable macrocrack. Thus, an extension technique of the PTEDM originally proposed by Chen and Han (1999a, b) is needed, which shows some different aspects from those done by Chen and Han (1999a,b) and by Zeng and Rajapakse (2000). Fourthly, based on the conservation law of the J -integral, we reuse the consistency check proposed by Chen and Han (1999a,b) to examine the results of the new technique. It is found that the results are actually confirmed in the present case with a permeable microcrack near the tip of an impermeable macrocrack. Fifthly, the influence of the permeable microcrack on the macrocrack tip parameters such as the stress intensity factor (SIF), electric displacement intensity factor (EDIF), and mechanical strain energy release rate (MSERR) are plotted in figures and compared in detail with those given by Chen and Han (1999a, b) previously under the impermeable microcrack model. It is concluded that divergences between the present permeable microcrack model and the previous impermeable microcrack model of Chen and Han (1999a,b) are remarkable under combined electric-mechanical loading. It is concluded that under the positive electric loading, the disturbance of the permeable microcracks on the near-tip stress-electric field is always much smaller than that given in the previous impermeable model, whereas under the negative electric loading, this disturbance becomes quite complicated. In our present investigation only positive influence of electric loading is found, i.e., the positive electric loading promotes crack growth and the negative impedes crack growth, and there is no evidence for the existence of the converse influence even though two different kinds of microstructures are considered. Some discussions and remarks are presented in detail.

Keywords: Piezoelectric material, macrocrack, microcrack, microstructure, conservation law, the J-integral, integral equation, stress intensity factor, electric displacement intensity factor, shielding effect, mechanical strain energy release rate.