Modeling plastic deformation of polycrystals

While most of the physical basis of plasticity in metals and alloys is now well identified and understood, quantitative prediction of the plastic behavior of a polycrystalline metal remains, despite the significant progress made in this field in recent decades, a very open field of research. The difficulty of such modeling has several origins, in particular:

• the highly non-linear nature of the phenomena associated with plasticity, and therefore of the equations describing them, whatever the scale adopted or the mechanism described (as opposed to linear elasticity, where we can simply write: σ = C : ε );

• the complex and varied nature of the physical mechanisms to be taken into account: creation, movement, annihilation and storage of dislocations, stacking on grain boundaries, crystal lattice rotations, formation of cellular substructures, creation of point defects, lattice friction... ;

• the simultaneous intervention of several characteristic scales (a few dislocations, cells, grains, etc.), each contributing in its own specific way to the macroscopic response;

• the considerable amplitude of plastic deformation and the associated significant changes in the metallurgical state of the material: crystallographic and morphological textures, "plastic heterogenization" through cell formation, etc. Moreover, these modifications are highly dependent on the loading path followed (swaging, expansion, uniaxial tension, etc.).

One could attempt a continuous transition from dislocation to polycrystal... But while the static behavior of a single dislocation or even a continuous distribution of dislocations is well known, the same cannot be said of the complex, evolving system of interacting dislocations that would need to be taken into account to reach the polycrystal scale. This is why the proponents of the transition from single crystal to polycrystal (Sachs, Taylor and others) have devised a more global approach, focusing from the outset on the grain scale and only indirectly describing, on average, the collective behavior of intragranular dislocations via crystallographic plastic slip.

The concepts of reduced cission and critical cission introduced by Schmid led to the development of what has since been called crystalline plasticity, an approach according to which grain behavior is described by relationships between cissions on different sliding systems and their plastic sliding. The next step, within the framework of continuum mechanics, is to make the transition from the "mesoscopic" level (the grain) to the macroscopic level of the polycrystalline volume element, taking into account intergranular interactions, polycrystal...