LAUSR

The final geometry and fatigue behavior of deep drawn components in service is strongly influenced by deformation-induced residual stresses. For multi-phase materials, besides macro residual stresses (first kind), phase-specific residual stresses (second kind) occur on the microscale of the material. In order to influence the component characteristics positively it is important to predict the distribution of the residual stresses on both scales. A two-scale simulation and measurement approach is presented which allows for an efficient determination and validation of the phase-specific residual stresses. Finite-element simulations are performed to predict the deformation-induced macro residual stresses. A numerically efficient mean-field homogenization is used to estimate the total strain, the plastic strain and the eigenstrain on the grain level based on macroscopic stress, strain and stiffness data. The simulated residual stresses are compared to experimental data. Macro residual stresses are determined by means of incremental hole drilling method, whereas phase-specific residual stresses are analyzed with use of X-ray diffraction according to the $$\sin ^2\psi$$sin2ψ method. The simulation and measurement approaches are applied to a representative deep-drawing process for the lean duplex stainless steel $$\mathrm {X2CrNiN23{-4}}$$X2CrNiN23-4, which consists of a ferritic and an austenitic phase both with the same volume fraction. The results indicate that the proposed two-scale simulation approach is well suited for the prediction of phase-specific residual stresses after a deep drawing process of lean duplex steel.