Naprężenia Sprężysto-Plastyczne w Pierścieniu Wywołane Działaniem Pewnego Pola Temperatury

The object of the discussion is the elastic-plastic state of stress in a ring acted on by a steady-state temperature field. This field is axially symmetric. Assuming that Young's modulus E Poisson's ratio v, and the coefficient of thermal dilatation a do not depend on the temperature, radial stresses σrr and circumferential stresses σϕϕ are found. On the basis of the Tresca yield condition it is found that one or two regions of plastic behaviour may appear depending on the magnitude of the coefficient Ea|ΔT|σ3. If one plastic zone appears it is contained between the surface r = d and r = ξ. In the cases of two plastic zones they are separated by an elastic zone bounded by the surfaces r = ξ and r = n.
The quantities § and y are found from the equilibrium condition. The results obtained may be considered to be sufficiently accurate for temperatures of the ring not exceeding 250–350°C. For higher temperatures the dependency of E1, a and y on the temperature cannot be disregarded for most materials. The results obtained may then be treated as a first approximation to the accurate solution. The results are confronted with those obtained by Wilhoit for a ring insulated on the upper and lower surface. The results obtained by Wilhoit and those in the present paper are found to differ but slightly from the qualitative viewpoint.