Non-linear elastic characterisation of a high strength bainitic roller bearing steel

A small but not negligible non-linear elastic behaviour was detected when investigating cyclic uniaxial push–pull experiments on a high strength bainitic steel. Cyclic torsion experiments led to the conclusion that the shear modulus was relatively constant. A non-linear elastic model was implemented where the bulk modulus was extended with a second order term related to the elastic dilatation and where the shear modulus was constant. The material presented a strength differential effect (SDE), with larger yield stress in compression than in tension. Consequently, the non-linear elastic model was combined with a plasticity model that incorporated a Drucker–Prager yield surface, non-associated flow rule and combined non-linear hardening. Expressions that include non-linear elasticity were derived for the elastic–plastic hardening and the compliance tensors. The extended material model predicted the elastic–plastic results from cyclic push–pull experiments. Also, a phenomenological analysis of the cyclic elastic response showed isotropic damage in the elastic moduli. The steady-state damage increased linearly with the cyclic plastic strain range.