Viscoelastic functionally graded materials subjected to antiplane shear fracture

In this paper, a crack in a strip of a viscoelastic functionally graded material is studied under antiplane shear conditions. The shear relaxation function of the material is assumed as μ = μ₀ exp(β y/h) f(t), where h is a length scale and f(t) is a nondimensional function of time t having either the form μ_∞/μ⁰exp(1-t/t₀)for a linear standard solid, or f(t)=(t₀/t)^q for a power-law material model. We also consider the shear relaxation function μ = μ₀ exp(β y/h)[t₀exp(δy/h)/t]^q in which the relaxation time depends on the Cartesian coordinate y exponentially. Thus this latter model represents a power-law material with position-dependent relaxation time. In the above expressions, the parameters β, μ₀, μ_∞, t₀; δ, q are material constants. An elastic crack problem is first solved and the correspondence principle (revisited) is used to obtain stress intensity factors for the viscoelastic functionally graded material. Formulas for stress intensity factors and crack displacement profiles are derived. Results for these quantities are discussed considering various material models and loading conditions.