A general model of the equations of generalized thermo-microstretch for an infinite space weakened by a finite linear opening Mode-I crack are solving. The material is homogeneous isotropic elastic half space. The crack is subjected to prescribed temperature and stress distribution. The formulation is applied to generalized thermoelasticity theories, using mathematical analysis with the purview of the Lord-Åžhulman (LS involving one relaxation time) and Green-Lindsay (GL includes two relaxation times) theories with respect to the classical dynamical coupled theory (CD). The harmonic wave method has been used to getting the exact expression of Normal displacement, Normal stress force, couple stresses, microstress and temperature distribution. The variations of the considered fields with the horizontal distance are explained graphically. A comparison also is made between the three theories and for different depths.
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