Incremental Elastoplastic Solution for Thermal Cavity Expansion with Application in the Stress Analysis of Shrink Fits

Abstract

A general semi-analytical solution is developed for the time-dependent, axisymmetric problem of elastoplastic stress concentration around expanding cavities in the presence of heat conduction. The formulation is based on the incremental theory of plasticity within a Lagrangian framework of thermo-elastoplastic constitutive relations, while incorporating the von Mises yield criterion, strain hardening, and the associated flow rule. The transient heat conduction problem is treated through application of the Laplace integral transform. It is shown that the problem constitutive equations reduce to a system of three nonlinear ordinary differential equations describing the path-dependent evolution of the elastoplastic stress components with time. The long-time asymptotic solution provides the distribution of residual stresses. The proposed general solution for the thermal cavity expansion problem offers a rigorous benchmark for verification of relevant numerical solvers. The application of the proposed solution to the stress analysis of shrink-fit assemblies is demonstrated by examining the mechanical interaction between a solid shaft and a hollow hub, wherein the hub undergoes elastoplastic deformation due to the thermal expansion of the inner shaft. The results show that the strain-hardening parameter plays a critical role in controlling the extent of plastic deformation in the hub. Furthermore, a case study highlights the influence of constitutive behavior and stress-path dependency on the development of residual stresses in shrink-fit assemblies.