Steady-state Thermo-elastic Field in An Infinite 1D Hexagonal Quasi-crystal Medium Containing A Penny-shaped Crack under Symmetric Heat Flux
This paper develops an analytical solution for the problem of an infinite 1D hexagonal quasi-crystal medium weakened by a penny-shaped crack and symmetrically subjected to a pair of heat flux on the upper and lower crack surfaces.Based on the general solution,the steady-state 3D thermo-elastic field in the quasi-crystal is obtained by the generalized potential theory method.Several important physical quantities on the cracked plane,such as crack surface displacements,normal stresses,and stress intensity factors,are obtained in closed forms.An illustrative numerical calculation is performed to verify the present analytical solution and to show the distribution of the 3D thermo-elastic field.It is indicated that the influence of the phason field on the results is pronounced and the phason field variables reduce to zero in the case of decoupling the phonon and phason fields.The present analytical solution can serve as a benchmark for various numerical codes for simulations of quasi-crystal fracture.
1D hexagonal quasi-crystalpenny-shaped crackheat fluxanalytical solutionpotential theory method
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