A hybrid approach for the efficient computation of polycrystalline yield loci with the accuracy of the crystal plasticity finite element method

Direct experimental evaluation of the anisotropic yield locus of a given material, representing the zeros of the material's yield function in the stress space, is arduous. It is much more practical to determine the yield locus by combining limited measurements of yield strengths with predictions from numerical models based on microstructural features such as the orientation distribution function (ODF; also referred to as the crystallographic texture). For the latter, several different strategies exist in the current literature. In this work, we develop and present a new hybrid method that combines the numerical efficiency and simplicity of the classical crystallographic yield locus (CYL) method with the accuracy of the computationally expensive crystal plasticity finite element method (CPFEM). The development of our hybrid approach is presented in two steps. In the first step, we demonstrate for diverse crystallographic textures that the proposed hybrid method is in good agreement with the shape of the predicted yield locus estimated by either CPFEM or experiments, even for pronounced plastic anisotropy. It is shown that the calibration of only two parameters of the CYL method with only two yield stresses for different load cases obtained from either CPFEM simulations or experiments produces a reliable computation of the polycrystal yield loci for diverse crystallographic textures. The accuracy of the hybrid approach is evaluated using the results from the previously established CPFEM method for the computation of the entire yield locus and also experiments. In the second step, the point cloud data of stress tensors on the yield loci predicted by the calibrated CYL method are interpolated within the deviatoric stress space by cubic splines such that a smooth yield function can be constructed. Since the produced yield locus from the hybrid approach is presented as a smooth function, this formulation can potentially be used as an anisotropic yield function for the standard continuum plasticity methods commonly used in finite element analysis.

Analysing the Interaction between Microscopic Deformation, Microstructure and Void Evolution of Near-α Titanium Alloys during Non-Superplastic Hot Deformation by an Integrated Crystal Plasticity Finite Element Model

High-efficiency and low-cost hot forming technologies for titanium alloys have been developed for producing complex-shaped, thin-walled tubular components under non-superplastic forming conditions. Under these forming conditions, there exist complex and highly integrated material evolution processes including microscopic heterogeneous deformation, microstructure evolution and damage behaviour. This paper presents an integrated crystal plasticity finite element model of near-α titanium alloys during non-superplastic hot deformation conditions considering grain boundary sliding (GBS), dynamic recrystallisation (DRX), as well as void evolution. The polycrystalline model of a near-α TA15 titanium alloy was established, containing α phase, β phase and grain boundary (GB) regions, in which the GB region was a visualised representation of GBS. The quantitative strength ratio between the GB regions and α phase was calculated according to the Zener–Holloman parameter Z and grain size, which determined the microscopic deformation behaviour. There were found to be two high microscopic strain regions in the α phase: intragranular deformation bands through the most favourable slipping and near the GBs through multiple slipping, which promoted continuous and discontinuous DRX, respectively. With the decrease in parameter Z or grain size, the activated dislocations accommodating GBS were found to no longer pile up inside the grain, but instead travel across the grain interior. Finally, methods to improve the macroscopic plastic formability were proposed for the difficult-to-form titanium alloys experiencing non-superplastic hot deformation.

Strain-Gradient Crystal Plasticity Finite Element Modeling of Slip Band Formation in α-Zirconium

Two methods for the determination of geometrically necessary dislocation (GND) densities are implemented in a lower-order strain-gradient crystal plasticity finite element model. The equations are implemented in user material (UMAT) subroutines. Method I has a direct and unique solution for the density of GNDs, while Method II has unlimited solutions, where an optimization technique is used to determine GND densities. The performance of each method for capturing the formation of slip bands based on the calculated GND maps is critically analyzed. First, the model parameters are identified using single crystal simulations. This is followed by importing the as-measured microstructure for a deformed α-zirconium specimen into the finite element solver to compare the numerical results obtained from the models to those measured experimentally using the high angular resolution electron backscatter diffraction technique. It is shown that both methods are capable of modeling the formation of slip bands that are parallel to those observed experimentally. Formation of such bands is observed in both GND maps and plastic shear strain maps without pre-determining the slip band domain. Further, there is a negligible difference between the calculated grain-scale stresses and elastic lattice rotations from the two methods, where the modeling results are close to the measured ones. However, the magnitudes and distributions of calculated GND densities from the two methods are very different.