Modeling of the Fracture Properties of Brittle Functionally Graded Materials


Functionally graded materials (FGMs), like other composites, are designed to achieve levels of performance superior to that of homogeneous materials by combining the desirable properties of each constituent phase. To offset the adverse effects of discontinuities in layered composites, the composition of an FGM is varied over length scales that are significant in comparison to the overall dimensions of the body. The shape of this material gradient is an important parameter in determining the properties of an FGM structure. At small length scales the shape of the gradient is of little importance, and the mechanics are dominated by the size, shape and interface conditions of a particle of one material embedded in the matrix of another. Mechanics analyses of an FGM usually emphasize the larger-scaled phenomenon and treat the FGM as an inhomogeneous material, employing only the "effective" properties of the composite at any given location. It is through the variation of these effective material properties (such as modulus) that the nature of the spatial variations of the constituents affects the thermomechanical behavior of the FGMs.


on Statistical RKR Modeling of Mixed-Mode Fracture in Brittle FGMs:

Limitations on the use of the mixed-mode delaminating beam test specimen: Effects of the size of the region of K-dominance by T.L. Becker, J.M. McNaney, R.M. Cannon and R.O. Ritchie. Mechanics of Materials, 1997.

FGM '98 Paper HTML PDF
Slides from USNCCM '99 HTML PDF
(sorry, HTML slides look best with M$ Internet Explorer)

An approximate method for residual stress calculation in functionally graded materials by T.L.Becker Jr., R.M.Cannon, R.O.Ritchie, Mechanics of Materials 32(2000), pp. 85-97

Finite crack kinking and T-stresses in fuctionally graded materials by T.L. Becker Jr., R.M. Cannon, and R.O. Ritchie. International Journal of Solids and Structures, 2001

Statistical Fracture Modeling: Crack Path and Fracture Criteria with Application to Homogeneous and Functionally Graded Materials by T. L. Becker, Jr., R. M. Cannon, and R. O. Ritchie, Engineering Fracture Mechanics, vol. 69, 2002, pp. 1521-1555


Ritchie Group
Dept of MSME , UC Berkeley

Last updated 8/03