Dynamics of Thermoelastic Stresses in Finite-Width Slab and Hollow Cylinder With a Growing or Receding Boundary Under an Arbitrary Temperature Transient

Abstract Thermoelastic stresses in a single-phase, finite-width slab or hollow cylinder with a constant-velocity growing or receding boundary were derived under a time dependent arbitrary thermal load. The analysis began by solving the conduction equation for a homogeneous, single-phase, finite-width slab subjected to a unit step temperature change with a growing or receding boundary in the Laplace domain. A series approximation was then employed for the inverse transformation to the time domain. The slab solution was extended to a cylindrical geometry via conformal mapping, with convection allowed at the fixed boundaries (the opposite face of the slab or the outer radius of the cylinder). Generalization to arbitrary temperature histories was accomplished using Duhamel's principle and Laplace convolution theorem. Integral elasticity equations were used to relate the transient temperature fields to the resulting thermoelastic stresses. Comparisons with finite element simulations showed excellent agreement, particularly for low to moderate growth/recession velocities. Due to the changing thickness, neither thermal nor stress fields attain steady-state conditions, especially when the growth or recession was higher. In such instances, the thermal and stress states tend to become linear with time, reflecting the constant velocity of growth/recession. The developed solutions should be applicable to thermal stresses during machining, wear, erosion, corrosion, and/or additive manufacturing, especially for lower temperature solid-state methods such as cold-spray.