Fracture mechanics of viscoelastic functionally graded materials

In this paper, the basic equations of viscoelasticity in functionally graded materials (FGMs) axe formulated. The "correspondence principle" is revisited and established for a class of FGMs where the relaxation moduli for shear and dilatation mu(x,t) and K(x, t) take separable forms in space and time, i.e. mu(x, t) = mu(0)mu(x)f(t) and K(x, t) = K(0)Kg(t), respectively, in which x is the position vector, t is the time, mu(0) and K-0 are materials constants, and mu(x), k(x), f (t) and g(t) are nondimensional functions. The "correspondence principle" states that the Laplace transforms of the nonhomogeneous viscoelastic variables can be obtained from the nonhomogeneous elastic variables by replacing mu(0) and K-0 with mu(0)pf(p) and K(0)pg(p), respectively, where f(p) and g(p) are the Laplace transforms of f (t) and g(t), respectively, and p is the transform variable. The final nonhomogeneous viscoelastic solution is realized by inverting the transformed solution. The "correspondence principle" is then applied to a crack in a viscoelastic FGM layer sandwiched between two dissimilar homogeneous viscoelastic layers under antiplane shear conditions. Results for stress intensity factors, including their time evolution, are presented considering the power law material model.