Effects of thickness variations on the thermal elastoplastic behavior of annular discs

Metallic annular discs with their outer boundary fully constrained are studied with newly derived semi-analytical solutions for the effects of thickness variations under thermal loading and unloading. The plane stress and axisymmetric assumptions were adopted, and the thickness of the disk depends on the radius hyperbolically with an exponent n. Furthermore, it is assumed that the stress state is two dimensional and temperature is uniform in the domain. The solutions include the elastic, elastic-plastic and plastic-collapse behavior, depending on the values of temperature. The von Mises type yield criterion is adopted in this work. The material properties, Young's modulus, yield stress and thermal expansion coefficient, are assumed temperature dependent, while the Poisson's ratio is assumed to be temperature independent. It is found that for any n values, if the normalized hole radius a greater than 0.6, the normalized temperature difference between the elastically reversible temperature and plastic collapse temperature is a monotonically decreasing function of inner radius. For small holes, the n values have strong effects on the normalized temperature difference. Furthermore, it is shown that thickness variations may have stronger effects on the strain distributions when temperature-dependent material properties are considered.