Crystal Plasticity

Hi Hamanh:

Crystal plasticity theories act as complementary to the branch of classical plasticity theories, but the theories are formulated at a smaller length scale, usually microscopic. Continuum deformation is explained in terms of 'more' fundamental dislocation dynamics and their distributions. In crystal plasticity, dislocations (line defects) serve as the carriers of plastic strain, this is just the starting point of the theory.  There are many complicated issues involved, as crystal plasticity is a bottom up approach. That means, you describe the theories at microscopic scale, move to macroscopic scale  through an intermediate meso-scopic scale. More rigorous approach would be to start from a nanoscopic level (like, nucleation of dislocations, influence of hydrostatic stresses on dislocation core structure), but the problem only compounds to a larger one as you move up the length scale.

But majority of the crystal plasticity research involves in finding a proper approximation procedure to link microscopic state variables to their macroscopic counterparts. A few high-points of crystal plasticity theory are worth mentioning:

(i) Initial texture of the material. Texture is the preferential distribution of grain orienatations in polycrystalline materials. Mathematically, these are presented as Orientation Distribution Functions (ODF), Gauss-like distribution function in Orientation space. 

(ii) Approximation procedure: strain (compatibility) or stress (equilibrium). like in Taylor-Bishop-Hill procedure the local strain tensor is assumed to be same as macroscopic strain tensor. But this has a problem in selecting a set of slip systems, uniquely.

(iii) A procedure to select a set of crystallographic slip systems, like Asaro-Needleman's rate sensitive models.

 (iv) Constitutive Strain Hardening (Kocks' hardening theories or Voce type hardening theories are approximated). As more plastic shearing occurs on slip planes the crystal gets harder. Again there are a few theories to describe the stages of hardening (Stages - I, II, III, IV). Usually Stage-I can be ignored in a polycrystalline framework. Recovery, Cross-slip of dislocations are also considered.

(v) Dislocation patterning, phenomenological approach, Self-organized dislocation structures.

(vi) Deformation texture update & (vii) stress update

In a gross sense, crystal plasticity theories consider the rigors of the fundamental physics of inelastic deformation than classical plasticity. It only adds excitement to plasticity never subtracts :)

I tried to put a rough sketch of a very complicated field, as my ideas are sketchy too

-Atish

Hi Atish,

Do you know any good reference/idea about how to update texture in UMAT using crystal plasticity theory.

Thanks,

Alankar Ph.D. Student School of Mechanical and Materials Engineering Washington State University, Pullman

Hey Alankar,

Did you find any documentation about modifying the umat code for crystal plasticity? I am having some troubles myself too making it work for a polycrystal.

Thanks,

Toto