Micromorphic crystal plasticity

Abstract

The micromorphic approach to crystal plasticity represents an extension of the micropolar (Cosserat) framework, which is presented in a separate chapter. Cosserat crystal plasticity is contained as a special constrained case in the same way as the Cosserat theory is a special restricted case of Eringen's micromorphic model, as explained also in a separate chapter. The micromorphic theory is presented along the lines of Aslan et al. (Int J Eng Sci 49:1311- 1325, 2011) and Forest et al. (Micromorphic approach to crystal plasticity and phase transformation. In: Schroeder J, Hackl K (eds) Plasticity and beyond. CISM international centre for mechanical sciences, courses and lectures, vol 550, Springer, pp 131-198, 2014) and compared to the micropolar model in some applications. These extensions of conventional crystal plasticity aim at incorporating the dislocation density tensor introduced by Kröner (Initial studies of a plasticity theory based upon statistical mechanics. In: Kanninen M, Adler W, Rosenfield A, Jaffee R (eds) Inelastic behaviour of solids. McGraw-Hill, pp 137-147, 1969). and Cermelli and Gurtin (J Mech Phys Solids 49:1539- 1568, 2001) into the constitutive framework. The concept of dislocation density tensor is equivalent to that of the so-called geometrically necessary dislocations (GND) introduced by Ashby (The deformation of plastically non-homogeneous alloys. In: Kelly A, Nicholson R (eds) Strengthening methods in crystals. Applied Science Publishers, London, pp 137-192, 1971). The applications presented in this chapter deal with pile-up formation in laminate microstructures and strain localization phenomena in polycrystals.