Investigation of transient thermal-mechanical behavior of a cracked viscoelastic material using time-fractional dual-phase-lag theory

In the past decade, viscoelastic materials (like polymer composites, biological tissues, rubber, etc.) have been increasingly used in a variety of industries due to their excellent multifunctional properties. In this work, by extending the fractional calculus to dual-phase-lag (DPL) heat conduction theory, the transient thermal-mechanical response in cracked viscoelastic materials under thermal shock is analyzed. With the aids of Fourier and Laplace transform, the thermal-viscoelastic problem is converted into a system of singular integral equations with Cauchy kernels of the first kind, which are then solved numerically. The parametric study is performed and the numerical results of temperatures, intensity factors of temperature gradient (IFTG) and stress intensity factors (SIFs) around the crack tips, are shown graphically to illustrate the effects of time fractional order, thermal lags and viscoelastic relaxation on the thermoelastic response.