Advances in Polycrystal Plasticity: How do 10 Billion Crystals Co-deform?

Crystalline materials reveal highly anisotropic mechanical behavior1-6. Examples are metals, geological substances, semiconductors, superconductors, or semi-crystalline polymers. Large scale crystalline anisotropy has four major sources. First, crystals reveal intrinsic elastic reversible anisotropy due to the orientation dependence of the atomic bonds.

Simulation study on the influence of texture on earing in steel

We present a numerical study on the influence of crystallographic texture on the earing behavior of a low carbon steel during cup drawing. The simulations are conducted by using the texture component crystal plasticity finite element method which accounts for the full elastic-plastic anisotropy of the material and for the explicit incorporation of texture including texture update. Several important texture components that typically occur in commercial steel sheets were selected for the study. By assigning different spherical scatter widths to them the resulting ear profiles were calculated under consideration of texture evolution. The study reveals that 8, 6, or 4 ears can evolve during cup drawing depending on the starting texture. An increasing number of ears reduces the absolute ear height. The effect of the orientation scatter width (texture sharpness) on the sharpness of the ear profiles was also studied. It was observed that an increase in the orientation scatter of certain texture components entails a drop in ear sharpness while for others the effect is opposite.

Simulation of textures and Lankford values for face centered cubic polycrystaline metals by using a modified Taylor model

This report presents a modified Taylor model is presented which statistically considers grain interaction in a polycrystalline aggregate in terms of a standard deviation for the symmetric part of the velocity gradient. The model can be solved using a Newton iteration method. We simulate crystallographic rolling textures and the anisotropy arising from uniaxial tension tests (Lankford values for different directions in the rolling sheet plane). The results reveal in part a good agreement with experimental data.

Measurement of plastic strains by 3D image correlation photogrammetry at the grain scale

Polycrystals with columnar coarse grains are plastically compressed in a channel die for imposing an external plane-strain state. The spatial distribution of the accumulated plastic surface strains in the deformed polycrystals is determined by measuring the displacement fields using 3D quantitative image correlation photogrammetry. For this purpose digital stereological image pairs of the sample surface are taken at the beginning and after each deformation step. The displacement field is derived from them by applying an image analysis method based on pattern recognition to the data before and after straining. The three components of the plastic displacement vector field are used to derive the surface portion of the plastic strain tensor field. The microtexture of the specimens is determined by analysis of electron back scattering patterns obtained in a scanning electron microscope. The experiments are interpreted by comparing them to corresponding crystal plasticity finite element simulations.

Experimental Investigation of the Deformation Behavior of Aluminium-Bicrystals

This Max-Planck project report discusses the deformation behaviour of an aluminium-bicrystal with a symmetrical <112> tilt boundary and an initial misorientation of 8.7°. The specimen was compressed in a channel die to 30% engineering thickness reduction at room temperature. Afterwards the crystal orientations were determined by electron backscatter diffraction (EBSD) and the plastic strain distribution was measured by photogrametry. It was found that the two abutting crystals close to the grain boundary rotate towards each other, whereas the grain interiors increase their mutual misorientation during plastic loading.

Crystal Plasticity Finite Element Simulations of Grain Interaction and Orientation Fragmentation during Plastic Deformation of BCC Metals

Deformation of a grain in polycrystalline metals is restricted or forced by deformation of neighbor grains during plastic deformation processes. It also gives influence to deformation of neighbor grains at the same time. Interaction between grains causes inhomogeneous local deformation and texture during plastic deformation. Prediction of inhomogeneous local deformation and texture is important in understanding of recrystallization texture. Taylor-type polycrystal models which have been employed in prediction of texture evolution can not count on grain interaction. In this work, a finite element simulation based on the crystal plasticity has been carried out to investigate the effect of grain interaction on local deformation and texture evolution. An artificially configured BCC bicrystal that consists of a crystal located at center and a surrounding neighbor crystal has been employed in plane strain compression simulation. Several pairs of specific orientations have been chosen for initial orientations of the bicrystal. Deformation and texture evolution of the center crystal in the bicrystal have been investigated changing the initial orientation of the surrounding crystal. The simulation results show that deformation and texture evolution near crystal boundary can be different from those at the center region of the crystal. Orientation fragmentation, which results in great lattice curvature is observed in a center grain with an initial metastable orientation. Simulation shows that a metastable crystal always breaks up during deformation and the grain interaction changes only the pattern of grain breakup.

Recrystallization Simulation by Coupling of a Crystal Plasticity FEM with a Cellular Automaton Method

The report presents an approach for simulating primary static recrystallization which is based on coupling a viscoplastic crystal plasticity finite element model with a probabilistic kinetic cellular automaton. The crystal plasticity finite element model accounts for crystallographic slip and for the rotation of the crystal lattice during plastic deformation. The model uses space and time as independent variables and the crystal orientation and the accumulated slip as dependent variables. The ambiguity in the selection of the active slip systems is avoided by using a viscoplastic formulation which assumes that the slip rate on a slip system is related to the resolved shear stress through a power*law relation. The equations are cast in an updated Lagrangian framework. The model has been implemented as a user subroutine in the commercial finite element code Abaqus. The cellular automaton uses a switching rule which is formulated as a probabilistic analogue of the linearized symmetric Turnbull kinetic equation for the motion of sharp grain boundaries. The actual decision about a switching event is made using a Monte Carlo step. The automaton uses space and time as independent variables and the crystal orientation and a stored energy measure as dependent variables. The kinetics produced by the switching algorithm are scaled through the mesh size, the grain boundary mobility, and the driving force data. Coupling of the two models is realized by: translating the state variables used in the finite element plasticity model into state variables used in the cellular automaton; mapping the finite element integration point locations on the quadratic cellular automaton mesh; using the resulting cell size, maximum driving force and maximum grain boundary mobility occuring in the region for determining the length scale, time step, and local switching probabilities in the automaton; and identifying an appropriate nucleation criterion. The coupling method is applied to the simulation of texture and microstructure evolution in a heterogeneously deformed high purity aluminum polycrystal during static primary recrystallization considering local grain boundary mobilities and driving forces.