Simulation of polycrystalline Ceramics with Micro-Cracks
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Simulation of Polycrystalline Ceramics with Micro-Cracks Jianwu Cao, Yoshihisa Sakaida, Yasuo Nagano and Hiroshi Kawamoto Synergy Ceramics Laboratory, Fine Ceramics Research Association, 2-4-1, Mutsuno, Atsuta-ku Nagoya 456-8587, Japan ABSTRACT The micro FEM model, which was considered in the middle bottom of a four-point bending macro FEM model, was constructed from a SEM micrograph of an Al2O3-10vol%ZrO2 ceramic, in which the crystallographic information was given to each grain randomly. One micro-crack was introduced in the micro FEM model as a basic case to simulate the four-point bending strength. The strength was determined by the average stress in a one-grain size distance from the crack tip. Two types of micro-cracks were introduced in the model as a second micro-crack, and the strength was compared with the basic case. For the case in which the second crack is parallel to the first crack and apart from the first crack in horizontal direction, the strength was increasing with the second crack closer to the first crack. For the case in which the second crack is parallel to the first crack but apart from the first crack in vertical direction, the strength was decreasing with the second crack closer to the first crack. INTRODUCTION It is well established that micro-cracking can occur in ceramic materials due to residual stress during its fabrication processes and applied stress before its catastrophic failure [1,2]. The micro-cracks in Polycrystalline ceramics will propagate either intergranulary, along amorphous grain boundaries, or transgranulary, along cleavage planes of grains [3]. The micro-cracking and the interaction of micro-crackings will affect the mechanical properties of ceramics. In this study, a new analysis method that links macro properties with micro-cracking for heterogeneous ceramics has been developed. An average stress criterion of micro-crack propagation and the algorithm of micro-macro bridging simulation were discussed. A two-dimensional FEM model was constructed from SEM micrograph of an Al2O3-10vol%ZrO2 ceramics. The crystallographic information was given to each grain randomly. A micro-crack with same order in length as average grain size was introduced in the model. An attempt to simulate the relationship between micro cracking and macro mechanical behavior was made by relating the analysis result of four-point bending macro model and analysis results of crack propagation in micro model. SIMULATION METHOD Discussion of microcrack initiation criterion for FEM analysis Fracture of materials is a phenomenon that includes many different length scales. The geometry of the specimen and its microscopic dimensions determine the strength of the stress intensity at the crack tip and are equally important as the details of the grain boundary debonding or grain fracture in polycrystalline ceramics. Linear elastic fracture mechanics provides a quantitative description for fracture phenomena of engineering materials. It has been recognized from Griffith’s fundamental contributions that the stress-
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