Crystal Plasticity Modeling

Abstract

Among all material properties, the mechanical properties can, to date, probably be regarded as the most important ones. This not only holds for structural materials, but it is also true for many functional materials, which are in general also subjected to certain mechanical loads. The tailoring of mechanical properties is, therefore, a key aspect of this book. Within this process, the modeling of mechanical properties based on the microstructure of the material has gained a lot of importance during the past 50 years. With the increase of computational power, more and more physical aspects could be included in these modeling efforts. As the vast majority of structural materials is of crystalline nature, modeling of crystal elastoplasticity became a key topic. The elastic–plastic deformation of crystalline aggregates depends on the direction of loading, that is, crystals are mechanically anisotropic. This phenomenon is due to the anisotropy of the elastic behavior and the orientation dependence of the activation of the crystallographic deformation mechanisms (dislocations, twins, martensitic transformations). A consequence of crystalline anisotropy is that the associated mechanical phenomena such as shape change, crystallographic texture, strength, strain hardening, deformation-induced surface roughening, and damage also depend on the orientation. This is not a trivial statement as it implies that the mechanical parameters of crystalline matter are tensor quantities. Another major consequence of the single crystalline elastic–plastic anisotropy is that it adds up to produce macroscopically directional properties as well when the orientation distribution (crystallographic texture) of the grains in a polycrystal is not random. Figure 3.1 shows such an example of a plain carbon steel sheet with a preferred crystal orientation (here high probability for a crystallographic {1 1 1} plane being parallel to the sheet surface) after cup drawing. Plastic anisotropy leads to the formation of an uneven rim (referred to as ears or earing) and a heterogeneous distribution of material thinning during forming. It must be emphasized in this context that a random texture is not the rule but a rare exception in real materials. In other words, practically all crystalline materials reveal macroscopic anisotropy.