Bending of graded curved bars at elastic limits and beyond

Analytical and computational models are developed to predict the stress response of functionally graded curved bars under pure bending in elastic and partially plastic states of stress. In the analytical model, the modulus of elasticity and in the computational model, both the modulus of elasticity and the hardening parameter of the bar material are assumed to vary in the radial direction. The analytical model is based on Tresca’s yield criterion, its associated flow rule and ideal plastic material behavior, while the computational one is based on von Mises’ yield criterion, total deformation theory and a Swift type nonlinear hardening law. The models are verified not only in comparison to the published solutions, but also in comparison to each other. The results indicate that the variation of material properties, especially the variation of modulus of elasticity, strongly affects the deformation behavior of the bar. In a graded bar, yielding may commence at the inner, at the outer or simultaneously at both surfaces despite the fact that yielding initiates at the inner surface in a homogeneous bar.