Conference Agenda

The motion of dislocations has been determined to be one of the main mechanisms leading to inelastic deformation in crystalline materials. Their motion is affected by other crystal imperfections, e.g., at grain boundaries their advancement is hindered due to misalignment between the crystals' slip systems. The pile-up that occurs at the boundaries can lead to yielding inside the adjacent grains or intergranular fracture. The damage induced by the latter acts as a precursor to failure at the macroscopic scale. As such, a formulation capable of describing the interaction between the aforementioned crystal imperfections could provide a feasible tool to predict failure of components made from crystalline materials.

To this end, a gradient crystal plasticity formulation which accounts for grain misorientation is enhanced by considering the grain boundary as a cohesive interface and by introducing a damage variable influencing the interaction between adjacent grains. Numerical examples demonstrating the material response based on the proposed formulation are presented and discussed.

Heat treatment plays an essential role in the production of cold-work steel parts. While the material properties are adjusted by the heat treatment, side effects like distortion and residual stresses have to be controlled. A good prediction of the heat treatment plays a major role in reducing the necessary grinding time in subsequent finishing operations. Optimising the heat treatment process has the potential to save energy in the furnaces. This presentation discusses the application of simplified material models for the finite element (FE) simulation of quenching. The formation of martensite is covered by a purely temperature dependent Koistinen-Marburger model, whereas the diffusive formation of Bainite is modelled with an incrementally isothermal Johnson-Mehl-Avrami-Kolmogorov relation [1]. Both models are used in rate format and solved monolithically. The thermal-mechanical-microstructural-coupling implemented in the FE-software Abaqus is presented alongside numerical examples.

[1] de Oliveira, W.P., Savi, M.A., Pacheco, P.M.C.L., 2013. Finite element method applied to the quenching of steel cylinders using a multi-phase constitutive model. Arch Appl Mech 83, 1013–1037. https://doi.org/10.1007/s00419-013-0733-x

Modeling single crystal plasticity is essential for understanding the behavior of polycrystalline materials such as metals and alloys. The mechanical properties of such materials depend on the microstructure of individual grains and their interaction through grain boundaries. Single crystal plasticity aims to model the behavior of an individual grain based on the microscopic lattice structure. It can be expressed mathematically using the concept of multisurface plasticity. Applying the principle of maximum plastic dissipation leads to an optimization problem where the individual slip systems of the crystal, represented by yield criteria, define the constraints of the optimization problem.

In the framework of rate-independent crystal plasticity models, the set of active slip systems is possibly non-unique, which makes the algorithmic treatment challenging. Typical approaches are either based on an active set search using various regularization techniques [3] or simplifying the problem in such a way that it becomes unique [1]. In computationally extensive simulations, the problem needs to be evaluated multiple times. Therefore, a stable, robust, and efficient algorithm is required to obtain satisfactory results.

Recently, an alternative strategy based on the infeasible primal-dual interior point method (IPDIPM [2] has been presented in [4], which handles the ill-posed problem without perturbation techniques. Through the introduction of slack variables, a stabilization of the conventional active set search approach is reached. The introduction of barrier terms with related barrier parameters continuously penalizes the violation of the feasibility of the intermediate solution. This talk especially focuses on the treatment of the barrier parameter and the related speed of convergence.

[1] M. Arminjon. A Regular Form of the Schmid Law. Application to the Ambiguity Problem. Textures and Microstructures, 14:1121–1128, 1991.

[2] A. S. El-Bakry, R. A. Tapia, T. Tsuchiya, and Y. Zhang. Journal of Optimization Theory and Applications, 89(3):507–541, 1996.

[3] C. Miehe and J. Schr ̈oder. A comparative study of stress update algorithms for rate-independent and rate-dependent crystal plasticity. International Journal for Numerical Methods in Engineering, 50:273–298, 2001.

[4] L. Scheunemann, P. Nigro, J. Schröder, and P. Pimenta. A novel algorithm for rate independent small strain crystal plasticity based on the infeasible primal-dual interior point method. International Journal of Plasticity, 124:1–19, 2020.