Photothermoelastic study of stress concentrations in a plate with internal heating

This paper describes a photothermoelastic method for simulating, in a three-dimensional model, the temperature gradients that occur in structural parts subjected to internal heating such as is frequently encountered in certain areas of nuclear-reactor design. The method is applied to a plate which has a step change in thickness and sustains a nonlinear temperature gradient through its thickness. The shapes of the gradients simulate internal heating of the plate material. The values for the highest stresses on the free surfaces of the plate, within the thickness of the plate, and at the root of the step are presented in graphical form for a range of internal heat-generated conditions. Thermal-stress-concentration factors are presented for a step change in the thickness of a plate under this type of heating. Its design significance is discussed. The same stress and stress-concentration values are shown to also apply to nonnuclear problems. During shut-down in conventional thermal plants, when the walls sustain linear steady-state temperature drops across their thicknesses, temperature profiles exactly analogous to those presented in this paper occur. The stresses can then be computed from the values presented here.