Crystal plasticity modelling and simulation of yield surfaces of aluminium alloys

Abstract

Nowadays, advanced technologies are employed to adjust various microstructural features to produce materials for specific needs. Modelling and simulation have become essential tools in materials science and engineering, offering the massive potential to comprehend, investigate and design advanced materials. Efficient mean-field and comprehensive full-field simulation techniques weigh in material design to build a helpful relation between processing, microstructure, and mechanical properties. In this context, the ongoing trend of developing multi-physics simulation tools, aided by advanced supercomputing and statistical analysis, enables the investigation of high-resolution low-scale phenomena. As such, in this PhD thesis, an efficient virtual laboratory for crystal plasticity simulations is introduced, using the spectral solver in the DAMASK open software, which is used to investigate the anisotropic behavior of metals, with a main focus on yield surfaces. A yield surface is a 5-dimensional surface in the 6-dimensional stress space and represents the critical stress state separating elastic and plastic yielding. Eventually, the influence of pre-deformation and hard particles/voids on the shape of the yield surfaces is studied. In Part 1, the virtual laboratory for probing the yield points for desired stress directions is introduced. Calculations are used for the calibration of yield surfaces. The required spatial resolution is assessed based on a comparison with the previously published crystal plasticity finite element method (CPFEM) and experimental results for three different aluminium alloys (AA1050, AA3103-O, and AA3103H18) with 1000 and 2500 grains in a representative volume element. The results of the crystal plasticity fast Fourier transform (CPFFT) method agree well with CPFEM. The elongated grain morphology of the AA3103H18 alloy was found to have a negligible effect on predicted anisotropy. An analysis was made on the number of tests required for properly calibrating the Yld2004-18p orthotropic yield surface. It was found that 32 virtual tests, along either uniformly distributed strain-rate or stress directions but obeying the orthotropic symmetry of the Yld2004-18p yield surface, make a good compromise between accuracy and computation time. Randomly chosen directions have a significantly larger error and require more virtual tests for a similarly good calibration of the yield surface. Since a preselected set of strain-rate directions does not require extra iterations, it is the preferred choice for calibrating the full-stress-based Yld2004-18p. However, for calibrations of the plate confined to a plane-stress condition, stress directions must be specified to be sure to be in this stress subspace. Part 2 includes studies on the effects of pre-deformations on the plastic anisotropy of polycrystals. The influence of material strength, work hardening, and texture are discussed. It is concluded that the predictions obtained with a spectral solver compare reasonably well with a simple aggregate Taylor model. The full-field solutions provide accuracy but do not significantly alter the behavior. An assessment is made of the origin of anelasticity and Bauschinger effects at small strains, considering two mechanisms. Firstly, there is a built-in composite effect in crystal elasto-plastic simulations due to the mixture of elastically and plastically loaded grains. Secondly, latent hardening of active forward compared to reverse slip systems, i.e., kinematic hardening of slip systems, will contribute similarly to the Bauschinger effect. Based on analyses of the computed selected cases and comparison to previously published measurements, it is concluded that both mechanisms are vital for interpreting conventional yield surfaces. In Part 3 the idea was to capture the Bauschinger effect caused by second-phase particles or voids in the full-field open software DAMASK crystal plasticity framework. The model does this by including a back-stress of the critical resolved shear stress in a single-phase simulation, instead of explicitly resolving the second-phase particles in the system. The back-stress model is calibrated based on the behavior observed in detailed crystal plasticity simulations featuring hard, non-shearable spherical particles or voids. A simplified representation involves a periodic box containing one such spherical particle within the crystal, considering periodic boundary conditions equivalent to a uniform regular distribution of particles or voids throughout the crystal. This serves as an idealized approximation of a particle distribution with a specified mean size and particle volume fraction. To explore the Bauschinger effect, tensile-compression tests are simulated with 5% and 10% volume fractions of particles, along with 1%, 2%, and 5% pre-strain. The findings indicate that an increasing volume fraction amplifies the Bauschinger effect, observed in cases involving both particles and voids. However, an increase in pre-strain only influences the Bauschinger effect in scenarios with particles, not in cases involving voids.