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

Abstract

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= E 0exp( 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 ∞/ E 0+(1− E ∞/ E 0)exp(− t/ t 0) for a linear standard solid or f( t)=( t 0/ t) q for a power law material model, where E 0, E ∞, β, t 0 and q are material constants. An extensional relaxation function in the form E= E 0exp( βy/ h)[ t 0exp( 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 ν= ν 0(1+ γy/ h)exp( βy/ h) g( t), where ν 0 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.