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The methcxl of integral transforms is used in this work to solve for both the temperature distribution and the stress function for several axially symmetric fracture mechanics problems. The problems considered are symmetric in temperature and stresses with respect to the plane of the crack. Due to the mixed boundary conditions in the plane of the crack, this method leads to two sets of dual integral equations. One of these is a result of solving the conduction problem, and the other occurs in the solution of the thermoelastic problem. In this work, the problem of determining stress intensity factors for an axially symmetric problem of an external circumferential crack in a long cylinder of finite radius is solved. The crack is opened up by a temperature applied on the crack face. Each set of dual integral equations is formulated into a Fredholm integral equation of the second kind. The solution to the integral equation for the thermoelastic problem is directly related to the stress intensity factor for a crack of a given size. Each Fredholm integral equation is discretized into matrix form using an appropriate quadrature rule. The axially symmetric problem of an infinite linearly elastic-perfectly plastic body with an external crack is considered. An applied temperature on the crack surface gives rise to thermal stresses in the body. To account for small-scale plastic deformation near the crack tip, Dugdale's hypothesis is used. The size of the plastic zone, the temperature field, the normal stresses in the plane of the crack, and the displacement of the crack surface are found for several applied temperatures. An estimate of the plastic zone size for the finite cylinder is determined by extending the previous analysis using Dugdale's hypothesis.

Thermal stresses in axially symmetric fracture mechanics problems for bodies with an external crack