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# New perspectives in plasticity theory

Mon, 2007-10-01 17:05 - Amit Acharya

A field theory of dislocation mechanics and plasticity is illustrated through new results at the nano, meso, and macro scales. Specifically, dislocation nucleation, the occurrence of wave-type response in quasi-static plasticity, and a jump condition at material interfaces and its implications for analysis of deformation localization are discussed.

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## Comments

## Great paper!

Amit,

This is a wonderful paper!

I can't claim to have understood the entire content but still want to jot down a few questions for you. Since I'm interested in high rate phenomena in alloys, I was wondering

1) what happens when you add an inertia term to the momentum balance in your field dislocation equations.

2) where do obstacles (solute atoms and such) enter in your formulation.

3) what needs to be done to incorporate viscous drag effects (phonon drag etc.). It's probably there in the formulation but I can't see exactly where.

Biswajit

## RE: Biswajit's questions on (PM)FDM

Biswajit,

Glad you liked it. The answers tosay in a discrete DD setting, your questions:

1) inertia - just add the inertia term! OK seriously,

FDM - In fact this is a big advantage of this framework in dealing with stress fields of dislocations. This is because the stress fields of arbitrarily accelerating dislocations, even in isotropic, linear elastic, infinite bodies are very difficult to deal with (see Nabarro's Phil Mag paper on synthesis of dislocation stress...or something to that effect). When these qualifiers do not hold, then it is almost impossible, and practically, definitely so. This is however important as the Peach Koehler force on a dislocation depends upon the stress field from others and so the dynamics case, especially when you have very high strain rate deformation in mind, cannot be done very well, if at all (I don't think this point is well-appreciated, generally). The FDM framework does not have these shortcomings conceptually, but to be fair we need to show this in practice. We are actually working on the dynamic case at the current time, with earthquakes and nonconvex elasticity in mind, the latter to predict equilibrium dislocation cores and Peierls stress effects etc.

(P)MFDM - you again add the inertial term for the averaged motion as the avergaing operator and derivatives commute and the inertia term is linear. My feeling is that for high strain rate deformation, this setting will say non-trivial things about plastic deformation.

2) obstacles:

FDM - you explicitly represent the obstacles and the misfit stresses show up automatically in the framework, thus affecting disloction velocity. The fact that the setup actually can calculate stress fields of dislocations has been shown in Roy, Acharya (2005) JMPS.

(P)MFDM - the effects would go into the \bar V and L^p. For predictions of PLC effects due to breakaway from solutes, Armand Beaudoin, Satya Varadhan, and Claude Fressengeas have come up with a consitutive model and dynamical analysis that Satya has implemented within a slightly simplifed version of PMFDM. Satya is able to predict effects observed in PLC single crystal experiments of Neuhauser et al. in great detail I hear, and these are not easy for any theory or computation.

You should contact them for more details: abeaudoi@uiuc.edu, varadhan@uiuc.edu

3) Phonon drag effects:

FDM - the velocity law you would take would be V = XTalpha/B, B is a drag coeffcient and the driving force XTalpha is really Peach Koehler, but now per unit volume of core. (P)MFDM - it would go into the \bar V and L^p. If you would like to see how the Voce law fits into this framework (so that it may be easy for you to see connections with your MTS model) see the Roy and Acharya, PMFDM II paper (2006) JMPS.

- Amit