Thermoelasticity of mixed-mode cracks in layered transversely isotropic half-spaces

Abstract

A three-dimensional spectral formulation is developed for steady thermoelastic penny-shaped cracks embedded in layered transversely isotropic half-spaces, with arbitrary stacking sequences and mechanically compliant and thermally resistive interfaces. Its central feature is a complete crack-plane closure in which the symmetry of the prescribed traction does not, in general, determine the direction of the resulting displacement discontinuity. Fourier-Bessel harmonics, stable multilayer operators, and closed-form ring projections are combined to recover local stress-intensity factors and the elastic crack-driving force from near-front displacement-jump asymptotics. Excellent agreement is obtained with homogeneous analytical solutions. Applications are restricted to perfectly bonded architectures, and reveal distinct effects of elastic anisotropy, structural asymmetry, and crack position. In oriented α -Ti, anisotropy reduces the mechanical mode I energy-release rate by about 10.6% relative to an equivalent isotropic reference under the same temperature field. In an asymmetric layered medium, thermal loading generates a large axisymmetric radial crack-face discontinuity that becomes comparable to, and ultimately exceeds, the mechanical opening scale, producing strong mode II conversion. The mechanical-thermal interaction further produces a heat-flux-sign-dependent azimuthal modulation of the crack-driving force. Finally, in a representative coated superalloy architecture, varying the crack position within the top coat changes the mechanically induced energy-release rate from 32.5% shielding to 33.3% amplification relative to an infinite homogeneous APS-8YSZ reference. This transition in the crack-driving response is accompanied by a non-monotonic variation of the induced mode I and mode II mixity, arising from the competition between material contrast and free-surface effects. These results reveal the coupled influence of crack-front mode conversion, thermo-mechanical interaction, and position-dependent multilayer constraint on the fracture response.