A disclination-based model for grain subdivision and its impact on the macroscopic mechanical behaviour of f.c.c. polycrystals (original) (raw)
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International Journal of Plasticity, 2005
Grain size is a critically important aspect of polycrystalline materials and experimental observations on Cu and Al polycrystals have shown that a Hall-Petchtype phenomenon does exist at the onset of plastic deformation. In this work, a parametric study is conducted to investigate the effect of microstructural and deformation-related length scales on the behaviour of such FCC polycrystals. It relies on a recently proposed non-local dislocation-mechanics based crystallographic theory to describe the evolution of dislocation mean spacings within each grain, and on finite element techniques to incorporate explicitly grain interaction effects. Polycrystals are modeled as representative volume elements (RVEs) containing up to 64 randomly oriented grains. Predictions obtained from RVEs of Cu polycrystals with different grain sizes are shown to be consistent with experimental data. Furthermore, mesh sensitivity studies revealed that, when there is a predominance of geometrically necessary dislocations (GNDs) relative to statistically-stored dislocations (SSDs), the polycrystal response becomes increasingly mesh sensitive. This was found to occur specially during the early stages of deformation in polycrystals with small grains.
Mechanics of Materials, 2006
In this study, evolution equations related to a heterogeneous microstructure that is physically representative of the densities and dimensions of dislocation-cells and walls have been formulated and coupled to a multiple-slip crystal plasticity formulation. Specialized finite-element methodologies have then been used to investigate how an imbalance in shear-strain amplitudes can result in deformation band formation in a cube-oriented aluminum single crystal subjected to strains of up to 30% under rolling deformation. It has been shown that a change in the microstructural morphology from matrix to transition bands occurs as the dislocation-cell size increases with decreases in the stored dislocation density and as a function of slip-system structure and orientation. Comparisons with experimental measurements and observations clearly indicate that the transition and matrix bands can occur in cube orientations as a consequence of shear strain imbalance on active slip-systems.
Grain orientation, deformation microstructure and flow stress
Materials Science and Engineering: A, 2008
Dislocation structures in deformed metals have been analyzed quantitatively by transmission electron microscopy, high-resolution electron microscopy and Kikuchi line analysis. A general pattern for the microstructural evolution with increasing strain has been established and structural parameters have been defined and quantified. It has been found that two dislocation patterns co-exist in all grains, however, with very different characteristics dependent on grain orientation. This correlation with the grain orientation has been applied in modeling of the tensile flow stress and the flow stress anisotropy of fcc polycrystals. In conclusion some future research areas are briefly outlined.
Effects of grain size and mechanical pretreatment on strain localization in FCC polycrystals
International Journal of Fatigue, 2001
Polycrystalline copper samples where the grains in the cross-section had crystallographic axes parallel to the load related to 'single slip' directions and three grain sizes, were ramp loaded and then step-tested to obtain their Cyclic Stress-Strain Curves (CSSCs). Plateaux were found for medium grain size at about 89 MPa, whereas large grained samples showed plateaux at 72 MPa, which correlated with the measured Taylor and Sachs factors, respectively. No plateaux were found when grains were smaller than 200 µm or ramp-loading stresses were below 87 MPa. Comparisons are made with nickel polycrystals and it is found that the plateaux in copper are narrower than those reported in nickel. The differences are attributed to a more homogeneous dislocation structure in nickel, due to lower elastic interactions across grain boundaries and easier cross-slip behavior as compared to copper.
Grain rotation dependent non-homogeneous deformation behavior in nanocrystalline materials
Materials Science and Engineering: A, 2010
Many experimental observations have indicated a transition from homogeneous to non-homogeneous plastic deformation on nanocrystalline materials. Based on a grain rotation theory of diffusionaccommodated grain-boundary sliding, a new phase mixture model was developed to predict the softening of nanocrystalline materials considering non-homogeneous plastic deformation due to shear bands subjected to quasi-static rates of loading. In this phase mixture model, nanocrystalline materials were treated as composites consisting of grain interior and grain boundary phases. Grain interior phase was divided into soft-grain interior part with soft orientation and hard-grain interior part with hard orientation. The grain rotation rate driving force for grain rotation was derived from energy considerations, including the dissipation induced by mass diffusion and that by GB sliding viscosity. The model predicts the effect of softening mechanism for total stress-strain relation; the grain size and mean maximum Schmid factor effect was considered in the phase mixture model. Further discussion was presented for calculation results and relative experimented observations.
International Journal of Solids and Structures, 2015
A coarse-grained extension of a recent nanoscale elasto-plastic model of polar dislocation and disclination density fields is developed to model grain boundary-mediated plasticity in polycrystals. At a small resolution length scale, the polar dislocation/disclination densities render continuously the discontinuities of the elastic displacements/rotations across grain boundaries. When the resolution length scale increases, the net polarities of a crystal defect ensemble decrease, perhaps to the point where no strain/curvature incompatibility is left in the body. The defect densities are then labeled ''statistical''. However both polar and statistical dislocation/disclination densities contribute to plastic flow, and a coarse-grained mesoscopic plastic curvature rate needs to be defined. In addition, whereas it is overlooked at nanoscale where grain boundaries are seen as continua, tangential continuity of the elastic/plastic curvature/strain rates across grain boundaries needs to be considered at mesoscale, because the latter are seen as singular discontinuity interfaces. It induces long-range, grain-to-grain, elastic/plastic interactions across interfaces. The mesoscale model allow preserving the essential features of the lower scale approach. In particular, it is shown that it allows accounting for such plastic deformation mechanisms as grain boundary migration and grain boundary misorientation variation by disclination motion and concurrent dislocation nucleation, when plasticity by dislocation glide is unavailable. Accumulation of polar defect densities in the vicinity of the grain boundaries and triple lines, leading to long-range inter-granular activation of slip and grain size effects, are also predicted by the model.
Mobility of grain boundary dislocations during the conservative untwisting of
Physical review. B, Condensed matter, 1996
We modeled the mobility of grain boundary dislocations ͑GBD's͒ during the untwisting of the ͓001͔ twist boundaries. Instead of assuming two semi-infinite crystals in calculating the grain boundary energy ͑i.e., the Read-Shockley approach͒ and therefore the driving force for untwisting, we assume equally spaced GBD's moving in the ͑001͒ boundary plane with the dislocations closest to the surface being pulled out by the image force. Experimental results from crystallite rotation in fcc gold were used to investigate the mobility of the GBD's. Two types of GBD motion were tested: viscous and thermally activated. The observed motions of the GBD's during untwisting can be described only as thermally activated. The Hirth-Lothe approach, which involves a thermally activated process overcoming the Peierls barrier, was applied to describe the mobility of GBD's during untwisting into the ⌺5 cusp/minimum ͑⌺ is the reciprocal of the density of the lattice sites in coincidence between two lattices at a misorientation͒ and the mobility of lattice dislocations ͕100͖ ͗110͘ during untwisting into the ⌺1 cusp/minimum. The Peierls barrier for GBD motion confined to the glide plane of the boundary ͑001͒ is significantly higher than that for lattice dislocations glide on ͕111͖ planes. From the untwisting rates, we estimate the energy barriers for GBD motions as 1.69 eV for ⌺1 and 1.84 eV for ⌺5 ͓001͔ twist boundaries. These results can explain the high yield stress and its sharp temperature dependence during plastic deformation of nanoparticle compacts of fcc metals. These results can also be used to estimate the largest size of crystallites that will rotate.
Acta Materialia 54 (2006) 2181
"We suggest a dislocation based constitutive model to incorporate the mechanical interaction between mobile dislocations and grain boundaries into a crystal plasticity finite element framework. The approach is based on the introduction of an additional activation energy into the rate equation for mobile dislocations in the vicinity of grain boundaries. The energy barrier is derived by using a geometrical model for thermally activated dislocation penetration events through grain boundaries. The model takes full account of the geometry of the grain boundaries and of the Schmid factors of the critically stressed incoming and outgoing slip systems and is formulated as a vectorial conservation law. The new model is applied to the case of 50% (frictionless) simple shear deformation of Al bicrystals with either a small, medium, or large angle grain boundary parallel to the shear plane. The simulations are in excellent agreement with the experiments in terms of the von Mises equivalent strain distributions and textures. The study reveals that the incorporation of the misorientation alone is not sufficient to describe the influence of grain boundaries on polycrystal micro-mechanics. We observe three mechanisms which jointly entail pronounced local hardening in front of grain boundaries (and other interfaces) beyond the classical kinematic hardening effect which is automatically included in all crystal plasticity finite element models owing to the change in the Schmid factor across grain boundaries. These are the accumulation of geometrically necessary dislocations (dynamic effect; see [Ma A, Roters F, Raabe D. A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations. Acta Mater 2006;58:2169–79]), the resistance against slip penetration (dynamic effect; this paper), and the change in the orientation spread (kinematic effect; this paper) in the vicinity of grain boundaries."