Prediction of residual stresses of second kind in deep drawing using an incremental two-scale material model

ABSTRACT

For modern engineering applications, the prediction of residual stresses is a starting-point for the subsequent optimisation of the design with regard to the process induced stresses on the macro and the grain scale. In this paper, a new approach for the numerically efficient prediction of phase-specific residual stresses (residual stresses of second kind) in two-phase materials is presented. The proposed model allows for a two-scale simulation of complex forming processes, solely based on the phase-specific constitutive equations. This enables the calculation of the average stresses and strains in each phase during the entire process and the prediction of the macroscopic material response. The numerical results are compared to experimental diffraction-based data of a bending bar and a deep drawn cup and are aligned better compared to existing models.

KEYWORDS:

• Duplex steel
• homogenisation
• residual stresses
• two-phase materials
• two-scale modelling
• metal forming

Acknowledgments

The authors thank S. Pulvermacher and J. Gibmeier from Institute of Applied Materials (IAM-WK), KIT for providing data from neutron diffraction experiments carried out at the instrument [email protected] under the experiment no. 1-02-199. This data is used in Figure 3. The research documented in this paper has been funded by the German Research Foundation (DFG) within the Priority Programme SPP2013 ‘Targeted Use of Forming Induced Residual Stresses in Metal Components’ (Grant: BO 1466/14-1). The support by the German Research Foundation (DFG) is gratefully acknowledged. The authors acknowledge support by the state of Baden-Württemberg through bwHPC.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research documented in this paper has been funded by the German Research Foundation (DFG) within the Priority Programme SPP2013 ‘Targeted Use of Forming Induced Residual Stresses in Metal Components’ [grant number BO 1466/14-1].