13th International Conference on Fracture June 16–21, 2013, Beijing, China -9Figure 2. The temperature field around the crack tipversus time ( 0.5 =β 0 0 τ = ， 4 0 5 10 D = × ) Figure 3. The temperature field around the crack tipversus parameter β ( c h 0.5 = ， 0 0 τ = ， 4 0 5 10 D = × ) 5. Conclusions Research of Bilyk et al [5] revealed that applying high current on the conductor, the temperature of conductor is lager than the temperature just under force load. Then, this paper discusses the heating effect of the crack tip on piezoelectric medium under the high electric shock load. The thermal effect of a mode III crack in a functionally graded strip under the electric shock is investigated. This fracture analysis can be expressed through the superposition of two problems. The first problem refers to the dynamic behaviors of a functionally graded piezoelectric strip with central crack subjected to the electric shock. The second problem means the temperature field by calculating the power of point heat source around the crack tip. Firstly, without considering the related effect of temperature field, a theoretical model is developed for the dynamic fracture analysis of a functionally graded piezoelectric strip of a finite dimension with central crack subjected to the electric shock. The Laplace transformation and the Fourier transforms are applied to make the transient problem tractable, and singular integral equations is derived with the dislocation density functions of crack as the unknown functions. In particular, the closed-form expressions for the electric field intensity and electric displacements intensity in terms of fundamental functions are derived, which provide a scientific basis for the interpretation of the thermal effect. Secondly, within supposing that it is a heat insulation process in a short time, the thermal effect is calculated. For this problem, thermal field and electromechanical filed is decoupled. So the heat conduction equation contains no electromechanical quantity. Based on that the
RkJQdWJsaXNoZXIy MjM0NDE=