Double cantilever beam model for functionally graded materials based on two-dimensional theory of elasticity

This paper extends the double cantilever beam (DCB) model to functionally graded materials (FGMs) based on two-dimensional theory of elasticity. A theoretical approach is proposed to determine strain energy release rate of a crack in a layered FGM with exponential gradient perpendicular to the crack plane. Elasticity solutions of a functionally graded cantilever subjected to a concentrated force and a bending moment are derived for thickness-wise varying Young's modulus. Using the derived elasticity solutions, the energy release rate and stress intensity factor for an edge crack and a central crack parallel to the surface are obtained. Numerical results are given to show the influence of gradient index on fracture parameters.