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# Anisotropic yield, plastic spin, and dislocation mechanics

(This paper is to appear in the IUTAM Procedia on "Linking scales in computations: from microstructure to macro-scale properties," edited by Oana Cazacu)

Amit Acharya, S. Jonathan Chapman

With a view towards utilization in macroscopic continuum models, an approximation to the root-mean-square of the driving force field on individual dislocations within a "representative volume element" is derived. The plastic flow field of individual dislocations is also similarly averaged. Even under strong simplifying assumptions, non-trivial results on the origin and nature of anisotropic macroscopic yielding, plastic spin, and the plastic flow rule (for single and polycrystalline bodies) are obtained. A particular result is the dependence of the plastic response of a material point of the averaged model on the *presence* of dislocations within it, an effect absent in conventional theories of plastic response (e.g.,* J*2 plasticity). Also noteworthy is the explicit geometric accounting of the indeterminacy of the slip-plane identity of the screw dislocation that appears to lead to some differences with conventional ideas.

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## Comments

## Re: Anisotropic yield, plastic spin, and dislocation mechanics

Is there any way of testing these theories experimentally? Can synchotron tomography be used?

-- Biswajit

## what good would it be otherwise?

Short answer for now.

You mention 'these' theories - I am assuming by that you mean MFDM and the averaged model discussed in the paper.

1) The averaged model is surely testable by experiment once one comes up with approximations for the evolution of the structure tensors that arise. But more importantly, because of its unambiguous microscopic link to the mechanism by which plastic deformation takes place, i.e. dislocation motion (without kinematic simplifications), it also suggests what experiments should be done to measure what. Moreover, for basically the same reason, it also provides a systematic route to improving theoretical approximations to plastic flow directions and yield criteria. For instance, the yield function developed (eqn 10) incorporates some non-schmid effects (look at eq. 8) almost with no extra work. There are matters of taste here, but this seems to me to be an improvement over anisotropic yield criteria that are based upon mathematical invariance of scalar valued functions of tensors with the resultant constants being fitted - in this picture, suppose the predcitions are not good enough when matched with experiments, then how does one improve and on what basis?

2) For the mesocale models, these are exciting times, see e.g.

http://www.aps.anl.gov/News/Conferences/2011/HEXD-MM/

With the advent of synchrotron measurements, it seems like one can put theoretical and simulation results on a one-to-one comparison path with corresponding in-situ, time-dependent experiments at the mesoscale.

I would like to say more about your question, but that commentary will have to wait till I find a little more time....