Evaluation of non-linear sin²ψ distributions in residual stress analysis based on a scale-bridging mechanical modeling

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The aim of the research project is to clarify the open question of how a reliable determination of the residual stresses (RS) can be carried out in the case of a non-linear dependence of the experimental lattice strains on sin²ψ in the X-ray (residual) stress analysis of polycrystalline, single-phase and multi-phase metallic material states. To solve this problem, the influences of texture and plastic deformation are experimentally separated from each other by loading experiments. The loading experiments (laboratory and synchrotron experiments) are carried out uniaxially as well as biaxially in order to evaluate the influence of multiaxiality on the development of micro-RS. Three different material systems, Al alloy (fcc), ferritic steel (bcc) and duplex steel (bcc/fcc), are systematically investigated in the project. With the help of in situ loading experiments in the elastic and elasto-plastic range, comprehensive measurement data on the development of the micro-RS during plastic deformation are determined for the single- and two-phase materials of different crystal structures. In order to be able to additionally evaluate the influence of the texture on the formation of the micro-RS, the textures of the materials in the initial state are specifically varied by adjusting the rolling degree. With regard to the evaluation strategy to be developed for the RS analysis, the micro-RS are modeled via two-scale simulations and the distribution of the plastic strains is approximated via the orientation space by order reduction approaches such as Fourier coefficients. From a continuum mechanics perspective, the goal is to determine the expected value of the stress tensor or elastic distortion tensor as a function of crystal orientation. This two-scale problem is to be solved for non-textured and textured as well as single and multi-phase materials. Two routes are considered. In the first route, the plastic deformations are estimated with mean-field methods when the macroscopic load is applied and alternatively determined with full-field calculations (FFT) by including the crystallographic texture and the plastic distortions as residual strains. Due to the large computing time, the practical suitability of the methods in route 1 is not yet given. In the second route, the knowledge gained in route 1 on the statistical properties of the lattice stresses is to be modeled using a mean-field approach (singular approximation) and the maximum entropy method, without resolving the plastic sub-processes for the individual crystal orientations. For this, the statistical distributions of the natural strains induced by macroscopic plastic deformations must be identified in Route 1 and described by model functions. If successful, a practical model for calculating RS would be available as the end result.