Application of the grain boundary formulation and image processing-based algorithm in micro-mechanical analysis of piezoelectric ceramic

Abstract

The main subject of this paper is the micro-mechanical analysis of a piezoelectric ceramic. In micro-mechanical analyses, it is very important to have knowledge about the real and natural micro-structure of materials. Therefore, the barium titanate powder was prepared using the solid-state technique, and pellets and beams were manufactured by uniaxial and isostatic pressing. The boundary element method (BEM) is used in order to be combined with three different grain boundary formulations for investigation of micro-mechanics and crack nucleation and evaluation in piezoelectric ceramic. In order to develop a numerical programming algorithm, suitable models of polycrystalline aggregate have to be discretised for the BEM analysis. Hence, original comprehensive algorithms are designed on the basis of image processing methods. Several assumptions are made to model the grain boundary in micro-scale. In the first step, before having any cracks, the traction equilibrium and displacement compatibility are governing equations. When the onset micro-crack starts to initiate, one mixed-mode potential based cohesive law is applied to model grain boundaries and investigate the intergranular crack nucleation and evolution. Upon interface failure, a frictional law is utilised in order to study separation, sliding or sticking between micro-crack surfaces. Several numerical experiments on barium titanate polycrystalline aggregate are presented to show the effectiveness of image processing-based discretisation algorithms and grain boundary formulation in micro-mechanical analysis.