Materials Science Forum Vols. 702-703

Abstract: The 'stack' model of a rate-independent rigid-plastic polycrystalline material is developed. In the 'stack' model, stacks of N neighboring sub-grain domains collectively accommodate the imposed macroscopic deformation while enforcing the velocity and traction continuity condition with its neighbors. The developed 'stack' model is applied to simulate the two-dimensional polycrystalline aggregate under macroscopically imposed plane-strain tension. The effect of inter- and intra-grain interactions on qualitative and quantitative variations in the predicted macroscopic stress-strain response and texture evolution are presented. The diminishing trend of constraint on individual sub-grain domains and texturing rate with stack size N, and saturation for large N also given.

Abstract: In this work microstructure evolution in a columnar polycrystal of pure aluminum is studied using a microstructure sensitive crystal plasticity finite element model (CPFEM). In the model, based upon the kinematics of crystal deformation and dislocation interaction laws, dislocation generation and annihilation are modeled. Dislocation densities evolve in the form of closed loops and are tracked as state variables, leading to spatially inhomogeneous dislocation densities that show patterning in the dislocation structures. The hardening law is based on the strength of junctions between dislocations on specific slip systems. The CPFEM model is able to show the anisotropic hardening behavior of aluminum single crystals. The measures of accumulated plastic strain in the experiment and the simulation are compared with varying degrees of success.

Abstract: A rigid-plastic rate-independent crystal plasticity based `stack of domains' model of a single crystal is developed to capture local deformation inhomogeneity and sub-structure formation when subjected to macroscopically homogeneous imposed deformation. This model regards the single crystal as a linear stack of domains with planar shaped domain boundaries. The domains of the model single crystal collectively accommodate the imposed deformation and individual domains maintain velocity and traction continuity with its neighbors. The lattice orientation of individual domains perturbed and that perturbation triggers the inhomogeneity of plastic slip amongst domains. Mobility of domain boundaries relative to the material and a differential hardening law that accounts for the orientational instability of individual domains are also considered in the model. The developed model is applied to predict the formation of banding in initially copper (C), rotated cube (RC) and Goss (G) orientated single crystals when subjected to plane strain deformation and the predictions are compared with the experimental literature.

Abstract: The flow stress behavior of a bake-hardenable steel during a few simple shear cycles is investigated using a crystal plasticity model. The simple shear test provides a stable way to reverse the loading direction. Stress reversals were accompanied with a lower yield stress, i.e., the Bauschinger effect, followed by a transient hardening stage with a plateau region and, permanent softening. The origins of these three distinct stages are discussed using a crystal plasticity model. To this end, the representative discrete grain set is tuned to capture such behavior by coupling slip system hardening appropriately. The simulated results are compared with experimental forward-reverse simple shear stress-strain curves. It is shown that the characteristic flow stress stages are linked to texture evolution and to the Bauschinger effect acting on the different slip systems.

Abstract: The classical definition of lattice rotation leads in some cases to different textures than the definition based on the preservation of orientations of selected sample directions and/or planes. For example, if classical {111} slip is taken into account for f.c.c. materials, the former approach enables to predict both copper and brass types of rolling texture, while classical approach predicts only the first one. The analysis of rolling texture formation is done for two types of lattice rotation in function of grain-matrix interaction parameter used in a deformation model. Predicted textures and correlation factors estimating the similarity of predicted and experimental textures are presented.

Abstract: This paper summarizes a recent review about the brass-type texture and its deviation from the copper-type texture by the present author and R.K. Ray – with somewhat sharpened conclusions.

Abstract: The microstructural and crystallographic aspects, reflected at the macroscopic scale on yield surface and its subsequent evolution, are reappraised by application of crystal plasticity simulations. Strain hardening rule in the slip system is coupled to cope with latent hardening and Bauschinger effect. Uniaxial tension simulation on an isotropic polycrystalline aggregate leads to anisotropic strain hardening. Typical elements of phenomenological plastic anisotropy and hardening rules such as expansion, kinematic shift and distortion of the yield surface, are shown to be featured in crystal plasticity by tuning the slip system hardening rules appropriately.

Abstract: A new selection criterion to explain the activation of the twinning variant is proposed. This criterion is based on the calculation of the deformation energy to create a primary twin. The calculation takes into account the effect of the grain size using a Hall-Petch type relation. This criterion allows to obtain a very good prediction for the variant selection. The calculations are compared with the experimental results obtained on T40 (ASTM grade 2) deformed by Channel Die compression.

Abstract: Several multilevel plasticity models that make use of the crystallographic texture have been developed in the past for the prediction of deformation textures. State-of-the-art models that consider grain interaction, such as Alamel and VPSC, are known to give superior deformation texture predictions compared to the well-known (full constraint) Taylor model. In this paper, these models are assessed on a different basis, namely their ability to predict plastic anisotropy in single-phase steel sheet. A wide range of mechanical tests is considered: uniaxial tension, plane strain tension, simple shear and sheet normal compression. Furthermore, the sensitivity of the anisotropy predictions is analyzed, considering the variability in textures measured by routine XRD. The considered grain interaction models clearly produce improved predictions of plastic anisotropy over the Taylor model.

Abstract: The twinning behavior of a commercial Ti-6Al-4V alloy is studied using a combined experimental and numerical approach. An extensive microstructural investigation was performed to identify and quantify the active twin systems. The mechanical behavior as a function of initial texture and strain rate was then modeled using a visco-plastic self-consistent crystal plasticity code (VPSC7). Earlier obtained quasi-static and dynamic data served to fit the parameters of the model, giving good agreement. However, even if the model gave qualitatively good predictions of the stress-strain curves and the texture evolution for the different loadings, the calculated twin fractions differed considerably of the experimental results.