A mesoscopic theory of dislocation and disclination fields for grain boundary-mediated crystal plasticity

Abstract

International audienceA 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

A continuum model for slip transfer at grain boundaries

“…Such non-locality was shown to have a strong impact on the elastic/plastic strain and rotation fields, both in the vicinity of grain boundaries and throughout the body. As already suggested above, it allowed retrieving such complex features as size and morphology effects, loading path-dependency, the Bauschinger effect and directional hardening in the plastic response of particle-reinforced alloys and thin polycrystalline fims [37,43,46], overall texture intensity and a β fiber more consistent with experimental observation in f.c.c. metals than the Taylor models [34], and shear strain localization in lamellar Al-Cu-Li alloys that conventional crystal plasticity fails to capture [47].…”

“…As a result, surface-dislocation-based modeling approaches fail to account for the structure and energy of high-angle boundaries, because they overlook their core properties. In addition, by allowing the accommodation of any tangential discontinuity of the elastic/plastic distortion and distortion rate, they tend to reduce grain-to-grain interactions, even for low-angle boundaries, with consequences on the prediction of texture evolution [34], size and Bauschinger effects [37,43,46] and plastic strain localization [47]. Here we similarly foresee consequences on slip transfer.…”

“…The method should be sufficiently versatile to allow its implementation in both a finite element framework and a spectral FFT-based method. Previous work on the account of tangential continuity of the plastic distortion rate include the finite element simulations of [37,40,41,43,50] and [46,47]. In a Galerkin scheme for the solution of Eq.…”

Validity of Crystal Plasticity Models Near Grain Boundaries: Contribution of Elastic Strain Measurements at Micron Scale

“…Strain rate effects on the slip transfer could also be considered [51]. It could be required to treat the grain boundary as a thin surface with specific properties or special kinematics conditions allowing sliding and torsion [16]. Another class of interfaces treatment could be to integrate grain boundaries as a non-local microstructural constituent with special properties per se [17].…”

Influence of the twin microstructure on the mechanical properties in magnetic shape memory alloys

“…Disclination plasticity and dynamics have been the topic of a number of recent studies, e.g. [20,21]. Here, we model the elastic fields of incoherent segments of twin boundaries as disclination dipoles.…”