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=E0exp(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∞/E0)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=E0exp(βy/h)[t0exp(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 Poissonʹs ratio is assumed to have the form ν=ν0(1+γy/h)exp(βy/h)g(t), where ν0 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.