Viscoplastic Self-consistent Polycrystal Model Research Articles

Study of Texture Development and Anisotropy of Mechanical Properties of API-X80 Line Pipe Steel for Spiral-Welded Pipe

This study has been conducted to analyze the effect of texture and microstructure on the anisotropy of yield strength and Charpy fracture toughness of an X80 line pipe steel. The texture and microstructure were investigated by X-ray diffractometer and electron backscattered diffraction (EBSD). The yield strength and impact energy were measured along 0o (longitudinal), 30o and 90o (transverse) to the rolling direction. It was found that the microstructure of the developed steel consisted of fine acicular and polygonal ferrite with small pearlite and martensite or retained austenite (MA constituents). The major components of textures were {332}<113> and {113}<110> orientations. In order to investigate the effect of both morphological and crystallographic texture on yield strength anisotropy, the prediction of the plastic property was carried out by using a viscoplastic self-consistent (VPSC) polycrystal model. The predicted anisotropy of yield strength with VPSC model assuming ellipsoidal grain shape was in a good agreement with experimental observation. EBSD results showed that the density of {001} cleavage planes of Charpy specimen, 30 degree to rolling direction, was the highest compared with that of other specimens. Therefore, the highest susceptibility to the cleavage fracture, i.e. increased ductile-brittle transition temperature, can be seen in the 30 degree direction.

Mechanical anisotropy and grain interaction in recrystallized aluminum

Axial compression tests up to 50 pct deformation were performed on rolled and fully recrystallized aluminum sheet stock (AA5754, AA5182, and AA6016) in the direction perpendicular to the sheet. Textures were measured using both X-rays and orientation imaging microscopy (OIM). In all three cases, a systematic in-plane anisotropy was observed, with more strain taking place in the transverse than in the rolling direction. Previous attempts to simulate this in-plane anisotropy for AA5754, starting from the X-ray initial textures and using a one-site polycrystal model, resulted in predictions of more deformation along the rolling than along the transverse direction. An analysis of the OIM textures indicates that there is a nonrandom spatial correlation of the recrystallization and retained rolling components. As a consequence, we implemented grain interaction and co-rotation in a viscoplastic self-consistent (VPSC) polycrystal model, in order to be able to account for orientation correlations. Such an approach allows us to describe the large- and small-angle misorientation distributions, as a function of deformation and to compare them with the available experimental evidence. Concerning the in-plane anisotropy, we conclude that it is very sensitive to details in the texture representation, rather than on grain interactions. Grain-interaction and co-rotation effects, however, have the effect of inducing less severe deformation textures, which is in better agreement with the experimental evidence.

A study of twinning in zirconium using neutron diffraction and polycrystalline modeling

An experimental study using neutron diffraction quantified the evolution of twinning in pure clockrolled zirconium that was subsequently deformed under uniaxial compression. The clock rolling introduced an initial texture of approximately 5 times random, and the compression specimens were cut with their loading axes nearly parallel to the predominant c-axes direction. Seven specimens deformed to strains between −2 and −17 pct and an undeformed specimen (0 pct strain) were examined. The deformation was performed at an applied strain rate of 0.001/s at 77 K. Twin volume fractions were estimated from diffraction data. Changes in texture and twin volume fractions were compared to predictions from a visco-plastic self-consistent (VPSC) polycrystal model, which described both slip and twinning. This work demonstrates the feasibility of using neutron diffraction to track the evolution of twinning. These results help benchmark the polycrystalline model, validate the description of twinning, and potentially lead to a better understanding of its role in hardening.

Modeling of textures and yield surfaces during recrystallization in IF steel sheets

A Monte Carlo technique was used to simulate primary recrystallization and grain growth in IF steels. In order to consider anisotropic properties of grain boundary energy and grain boundary mobility, functions of boundary misorientation were introduced. The yield surface of IF steels was calculated by coupling a visco-plastic self-consistent polycrystal model with a Monte Carlo technique.

Strain Hardening at Large Strains as Predicted by Dislocation Based Polycrystal Plasticity Model

A recent strain hardening model for late deformation stages (Estrin, Y., To´th, L.S., Molinari, A., and Bre´chet, Y., Acta Materialia, 1998, “A dislocation-based model for all hardening stages in large strain deformation,” Vol. 46, pp. 5509-5522) was generalized for the 3D case and for arbitrary strain paths. The model is based on a cellular dislocation arrangement in which a single- phase material is considered as a composite of a hard skeleton of cell walls and soft cell interiors. An important point in the approach is the evolution of the volume fraction of the cell walls which decreases with the deformation and gives rise to a plateau-like behavior (Stage IV) followed by a drop-off (Stage V) of the strain hardening rate observed at large strains. The hardening model was implemented into the viscoplastic self-consistent polycrystal model to predict hardening curves corresponding to different proportional loading paths. The calculated curves were evaluated to elucidate the path dependence of hardening.

A study of through-thickness texture gradients in rolled sheets

A method to simulate shear effects and through-thickness texture gradients in rolled sheet materials is introduced. The strain history during a rolling pass is idealized by superimposing a sine-shaped evolution of the \(\dot \varepsilon \)13 shear component to a plane-strain state. These generic strain histories are enforced in a visco-plastic self-consistent (VPSC) polycrystal deformation model to simulate texture evolution as a function of through-thickness position. The VPSC scheme is deemed superior to a full constraints (FC) or relaxed constraints (RC) approach, because it allows one to fully prescribe diagonal and shear-strain-rate components while still accounting for grain-shape effects. The idealized strain states are validated by comparison with deformation histories obtained through finite-element method (FEM) calculations. The through-thickness texture gradients are accounted for by introducing a relative variation of the sine-shaped \(\dot \varepsilon \)13 shear with respect to the plane-strain component. The simulation results are validated, in turn, by comparison with typical examples of through-thickness texture gradients observed experimentally in rolled plates and in sheets of fcc and bcc materials.

Macroscopic anisotropy in AA5019A sheets

The macroscopic anisotropy for typical texture components in aluminum alloys and AA5019A sheet samples (H48 and O temper conditions) were investigated. In order to simultaneously consider the effects of morphological texture and crystallographic texture on macroscopic anisotropy, predictions of plastic properties were carried out using a full-constraints Taylor model and a visco-plastic self-consistent (VPSC) polycrystal model. The yield stress and r-value (width-to-thickness plastic strain ratio in uniaxial tension) anisotropy predicted using the VPSC model were in good agreement with experimental data.

Calculation of intergranular stresses based on a large-strain viscoplastic self-consistent polycrystal model

We present here an extension of the viscoplastic self-consistent (VPSC) polycrystal model for the calculation of the intergranular Cauchy stresses in an aggregate. This method, which is based on the self-consistent treatment of incompressible aggregates proposed in 1987 by Molinari et al, is formulated using the inclusion formalism and full anisotropy is incorporated into it. The complete stress state in the grains is obtained by computing the deviatoric and the hydrostatic local deviations with respect to the overall corresponding magnitudes applied to the polycrystal. The extended VPSC model, followed by an elastic self-consistent unloading, is used to obtain the intergranular residual strains in the aggregate after large plastic deformation. The texture evolution and the hardening of the material are explicitly taken into account in the model. As an application, the model is used to predict intergranular residual states in Incoloy-800 plate after uniaxial deformation.

Modelling fabric development along the GRIP ice core, central Greenland

The preferred c-axes orientation (fabric) observed in cold polar ice is induced by intracrystalline slip only when the grain-boundary migration rate is low enough (i.e. corresponding to grain growth or rotation recrystallization regimes). Fabrics reflect the entire thermomechanical history of the ice and strongly influence its mechanical behaviour. Large viscoplastic anisotropy is always associated with pronounced fabrics. We use a viscoplastic self-consistent (VPSC) polycrystal deformation model to calculate fabric development. In this model, stress- and strain-rate fields are not uniform within the polycrystal and both equilibrium and compatibility conditions are fulfilled. We compare fabrics measured on thin sections along the GRIP ice core (central Greenland) with those calculated down to a depth of 2800 m. Behaviours predicted by uniform stress and uniform strain bounds are presented for comparison. Predictions of the VPSC model are in close agreement with measurements within the upper 650 m, which corresponds to the entire grain-growth zone. Deeper clown, the simulated fabric strength appears to be too high. A simple calculation shows that this discrepancy may be fully attributed to the effects of rotation recrystallization.

Modelling fabric development along the GRIP ice core, central Greenland

The preferredc-axes orientation (fabric) observed in cold polar ice is induced by intracrystalline slip only when the grain-boundary migration rate is low enough (i.e. corresponding to grain growth or rotation recrystallization regimes). Fabrics reflect the entire thermomechanical history of the ice and strongly influence its mechanical behaviour. Large viscoplastic anisotropy is always associated with pronounced fabrics. We use a viscoplastic self-consistent (VPSC) polycrystal deformation model to calculate fabric development. In this model, stress- and strain-rate fields are not uniform within the polycrystal and both equilibrium and compatibility conditions are fulfilled. We compare fabrics measured on thin sections along the GRIP ice core (central Greenland) with those calculated down to a depth of 2800 m. Behaviours predicted by uniform stress and uniform strain bounds are presented for comparison. Predictions of the VPSC model are in close agreement with measurements within the upper 650 m, which corresponds to the entire grain-growth zone. Deeper clown, the simulated fabric strength appears to be too high. A simple calculation shows that this discrepancy may be fully attributed to the effects of rotation recrystallization.