ICF100630OR FUNCTIONALLY GRADED MATERIALS: EFFECT OF ELASTIC HETEROGENEITY ON THE TOUGHNESS V. Cannillo1 and W. C. Carter 2 1 University of Modena and Reggio Emilia, Modena, Italy 2 Dept. of Materials Science and Engineering, Massachusetts Institute of Technology, USA ABSTRACT It has been demonstrated that gradients in the elastic modulus of a surface can affect the toughness of that surface [1,2]. Specifically, experimental results have correlated enhanced toughness with engineered gradients created by co-sintering a depth-dependent admixture of constituent particles with different elastic stiffnesses. While such engineered composites have average gradients that match the calculated optimal gradient, the composite microstructure will have variations in its lateral (in-surface-plane) properties and variations about the optimal gradient. The discrete nature of the particulate composites gives "stochastically graded" microstructures. In this work, we numerically analyze the effect of stochasticity on the predicted optimal material properties and their variation. We achieve this analysis by generating a series of microstructures that have the same average surface gradient, but with variable placement of the second phase. An image-based computational tool, OOF [3] which maps material microstructures onto finite element meshes, is used to determine the local stress state. The microstructural stress is used in conjunction with a statistical representation of failure. The effect of damage accumulation on the microstructural stresses is calculated iteratively. We characterize the effect of stochastic placement of second phase particles on the toughness of these materials with a specified gradient in their surface elastic coefficients and we investigate the stability of a surface crack in such materials. KEYWORDS Microstructure, finite elements, functionally graded materials, Weibull statistics INTRODUCTION Functionally graded materials (FGM) are composites that display spatially varying properties in one thickness direction and may be characterized by spatial microstructure variations. The spatial microstructures variations are usually achieved through a non uniform distribution of the second phase and these variations can be tailored in order achieve favorable responses to prescribed thermo-mechanical loads. FGM have received recent interest due to their particular properties: functionally graded surfaces provide new microstructural designs for enhanced surface damage resistance performance in ceramic materials. In particular, Giannakopoulos et al. [1,2] demonstrated that gradients in the elastic modulus of a surface can affect the toughness of that surface. In their experimental work, enhanced toughness has
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