A Novel Crystal Plasticity FEM Framework and a Machine Learning Approach to Estimate Material Parameters and Dislocation Densities Under High Stress

The Crystal Plasticity-based Finite Element Method (CPFEM) is a well-established tool for modeling the microstructure of materials under deformation. Supported by Oxford and the UKAEA, we have developed an innovative crystal plasticity framework incorporating two different solvers (semi-implicit and explicit) that alternate their activity depending on the slip increments and Cauchy stress. This structure improves flexibility in addressing convergence issues compared to other codes and supports a comprehensive range of material constitutive laws to model slip, creep, strain hardening, and back stress [1].<br/><br/>Furthermore, our CPFEM code incorporates Machine Learning techniques to determine material properties by minimizing an objective-function. This function compares the results of experiments with simulations under different parametrizations of the material. As we incorporate more experiments, the precision of our model in characterizing the material improves. Among various optimization methods, we chose Nelder-Mead due its simplicity as it does not require mathematical derivatives of the objective function, and its fast convergence given the high time consumption of FEM simulations.<br/><br/>The length scale dependence of strength is governed by Geometrically Necessary Dislocations (GNDs). The GND densities are computed using the Nye’s tensor that reveals a rank-deficient coefficient matrix which is solved by a new method that restricts the GND solution to only the active slip systems. This method improves other alternatives such as: L2 minimization [Arsenlis Parks], slip gradient [Gerken Dawson] and other rate forms [Ma Roters]. Our approach gives consistent results across different simulations, including simple shear, uniaxial tension, and four-point bending [2].<br/><br/>Finally, using this framework, we have simulated the Bauschinger effect observed in copper monocrystal cantilever experiments during initial bending/straightening cycles [3]. The modified Orowan-Sleeswyk model revealed the best match between the micro cantilever Bauschinger experiments, suggesting non-ideal reversibility and storage of a fraction of GNDs as Statistically Stored Dislocations (SSDs) upon load reversal.<br/><br/>* Corresponding author. [email protected]<br/><br/>[1] OXFORD-UMAT: Multi-modal crystal plasticity framework for single and polycrystal finite element applications. Eralp Demir, Alvaro Martinez-Pechero, Chris Hardie, Edmund Tarleton. (Submitted to International Journal of Solids and Structures in 2024)<br/><br/>[2] Restraining geometrically-necessary dislocations to the active slip systems in a crystal plasticity-based finite element framework. Eralp Demir, Alvaro Martinez-Pechero, Chris Hardie, Edmund Tarleton. International Journal of Plasticity (2024).<br/><br/>[3] Mechanical and microstructural single-crystal Bauschinger effects: Observation of reversible plasticity in copper during bending. Eralp Demir and Dierk Raabe. Acta Materialia (2010).