A viscoelastic functionally graded strip containing a crack subjected to in-plane loading

In this paper, a crack in a viscoelastic strip of a functionally graded material (FGM) is studied under tensile loading conditions. The extensional relaxation modulus is assumed as E = E₀ exp(βy/h)f(t), where h is a scale length and f(t) is a nondimensional function of time t either having the form f(t) = E_∞/E₀ + (1 - E_∞/E_o) exp(-t/t₀) for a linear standard solid or f(t) = (t₀/t)^q for a power law material model, where E₀, E_∞, β, t₀ and q are material constants. An extensional relaxation function in the form E = E₀ exp(βy/h)[t₀ exp(δy/h)/t]^q is also considered, in which the relaxation time depends on the Cartesian coordinate y exponentially with δ being a material constant describing the gradation of the relaxation time. The Poisson's ratio is assumed to have the form v = v₀(1 + γy/h) exp(βy/h)g(t), where v₀ and γ are material constants, and g(t) is a nondimensional function of time t. An elastic FGM crack problem is first solved and the "correspondence principle" is used to obtain both mode I and mode II stress intensity factors, and the crack opening/sliding displacements for the viscoelastic FGM considering various material models.