Shocks and slip systems: Predictions from a mesoscale theory of continuum dislocation dynamics

Abstract

Exploring a recently developed mesoscale continuum theory of dislocation dynamics, we derive three predictions about plasticity and grain boundary formation in crystals. (1) There is a residual stress jump across grain boundaries and plasticity-induced cell walls as they form, which self-consistently acts to attract neighboring dislocations; residual stress in this theory appears as a remnant of the driving force behind wall formation under both polygonization and plastic deformation. We derive the predicted asymptotic late-time dynamics of the grain-boundary formation process. (2) During grain boundary formation at high temperatures, there is a predicted cusp in the elastic energy density. (3) In early stages of plasticity, when only one type of dislocation is active (single-slip), cell walls do not form in the theory; instead we predict the formation of a hitherto unrecognized jump singularity in the dislocation density. r

A single theory for some quasi-static, supersonic, atomic, and tectonic scale applications of dislocations

“…In effect, the linear elastic stress and the core term tend to prevent a sharp discontinuity and the driving force from the non-convex η term promotes the discontinuity, and it is the balance between these thermodynamic forces that sets the dislocation core width at equilibrium. Interestingly, it can be shown that while in the presence of just one component of plastic distortion only the linear elastic term suffices to give a finite core width (paralleling a fundamental result due to Peierls, 1940), with more than one component, the core regularization from the α term is essential Acharya and Tartar (2011) and Limkumnerd and Sethna (2008). It is to be noted that the core energy is a fundamental physical ingredient of our model and not simply a mathematical regularization.…”

New Perspectives in Plasticity Theory: Dislocation Nucleation, Waves, and Partial Continuity of Plastic Strain Rate

“…A series of works by Limkumnerd and Sethna [8][9][10] that have since appeared is based on essentially the same theory as recognized by the authors [10]. Motivated by their numerical results, these authors suggest that the theory admits singularities in the Nye tensor field even when the elastic response is linear, an interesting claim that would be well worth establishing rigorously.…”

“…such that T 4 curl W 6 grad g (10) and the orthogonality condition holds. In passing, we note that the boundary condition (8) 2 implies 2curl W3n 4 0 on 6 B, a condition that is useful in proving the decomposition (10).…”

Statistical approach to dislocation dynamics: From dislocation correlations to a multiple-slip continuum theory of plasticity

“…Several variations of this work-all of which reduce to the same two-dimensional theory-also exist for threedimensional dislocation systems. [6][7][8][9] Although having laid out the foundation for possible interactions of many-dislocation configurations, Groma's pioneering work did not investigate these correlated effects in detail. Zaiser et al 10 explicitly considered the evolution of dislocation correlations by extending Groma's theory for systems of single-slip, parallel edge dislocations.…”