PZT-4紧凑拉伸试样的断裂分析

FRACTURE ANALYSIS OF PZT-4 COMPACT TENSION SPECIMEN

基于线性压电材料的复势理论,通过解析分析,导出了一种分析有限压电板裂纹问题的解析数值方法.首先,计算了含中心裂纹有限板的断裂参数,与Woo和Wang的解析数值法(Int J Fract,1993,62:203～218)相比较,表明该方法具有很高的精度和很好的计算效率.随后,采用该方法和有限元法计算了PZT-4紧凑拉伸试样在绝缘裂纹面边界条件下断裂时的断裂参数,发现各断裂参数的临界值分散性很大,不能作为压电材料的单参数断裂准则.进而,针对试样真实的裂隙形状,采用有限元法计算了裂隙尖端的应力、电位移场,比较了裂隙内介质的介电性能对裂隙尖端场的影响,计算了带微裂纹的真实裂隙模型的断裂参数并进行了理论分析.

Based on a complex potential theory of linear piezoelectric materials and series expansion of the complex potential,a general method is proposed for solving the crack problem of a finite piezoelectric plate.By this method,fracture parameters such as the stress intensity factor,the electric displacement intensity factor and energy release rate et al.can be easily evaluated under the impermeable boundary condition.Numerical results of fracture parameters demonstrate that the proposed method gives satisfactory results compared with the existing solutions given by Woo and Wang for a central crack in a finite piezoelectric plate.This method is identified to be an accurate and efficient method.An experiment with a PZT-4 compact tension specimen has been modeled under the impermeable boundary condition by the present method,and the critical values of fracture parameters are greatly varied and not the material constants.Therefore,these fracture parameters are not used as the single-parameter fracture criterion for the piezoelectric material.Then,in terms of the PZT-4 compact tension specimen,the influence of permeability of the crack has been studied based on the results of finite element calculations.The finite element model of the PZT-4 compact tension specimen with an actual crack profile is analyzed for two different electric permeability of the medium in the crack cavity corresponding to an impermeable medium and silicone oil.The largest applied negative electric field and the corresponding mechanical load for fracture are considered.Finally,the crack profile in the PZT-4 compact tension specimen can be regarded to be composed of a notch and an ideal crack (so-called microcrack) in front of the notch.The model of this assumed crack profile has been analyzed by the finite element method.