Spatial correlation in grain misorientation distribution

On particle size effects: An internal length mean field approach using field dislocation mechanics

“…Such a description is consistent with the experimental evidence of long-range spatial correlations across grain boundaries [23]. Remarkably, it provides for "tangential continuity conditions" on the elastic distortion from the balance of lattice incompatibility across the interface, regardless of Hadamard's compatibility conditions [23][24][25]. Thus, a continuous description of grain boundaries is inherently non-local, as the limiting values of the elastic distortion on each side of the interface must have some relationship.…”

“…In a refined, non-singular description of the incompatibility between grains, interfacial dislocations should be discarded and, instead, the grain boundary area needs to be seen as an extended region sustaining a continuous distribution of GND densities on each side of the interface. Such a description is consistent with the experimental evidence of long-range spatial correlations across grain boundaries [23]. Remarkably, it provides for "tangential continuity conditions" on the elastic distortion from the balance of lattice incompatibility across the interface, regardless of Hadamard's compatibility conditions [23][24][25].…”

Tangential continuity of elastic/plastic curvature and strain at interfaces

“…However, this condition stops short of providing a characteristic thickness, or a length scale for the extent of the spatial correlations in neighboring grains. Such a characteristic length scale may be obtained from experiments, by analyzing the spatial correlations in the misorientations between neighbor grains (Beausir et al, 2009), or from the dynamics of dislocation and disclination densities in a complete field theory . In the numerical implementation of this theory in polycrystals, using for example the finite element method, the tangential continuity of the plastic strain rate and curvature rate tensors at grain boundaries may be seen as a penalty condition for the dynamics of the field variables.…”

“…It may be derived from dynamic calculations in the framework of the nonlocal elasto-plastic model . Experimental evidence of such a length scale was provided in various materials after diverse strain paths, in the form of the scaling range for the power law dependence of the probability density of a certain grain misorientation vs the inter-granular distance (Beausir et al, 2009). Similar continuity constraints can be obtained for the plastic curvature and plastic curvature rate.…”

“…In such context, tangential continuity should apply not only to the symmetric part of the plastic distortion rate tensor (the plastic strain rate tensor) but also to its skew-symmetric part (the plastic rotation rate tensor) (Acharya, 2007). Indeed, the tangential continuity conditions (56), (60), (61) differ from their counterparts in the theory of dislocation fields (Acharya, 2007;Beausir et al, 2009;Mach et al, 2010), because the elastic/plastic rotation and rotation rate tensors are undefined in a theory of crystal defects involving disclinations. Stated differently, the tangential continuity conditions (48), (51), (52) do not hold in the theory of dislocation fields because the elastic/plastic curvature and curvature rate tensors are assumed to be integrable in the latter.…”