29. Strain Gradient Crystal Plasticity: Intergranular Microstructure Formation

This chapter addresses the formation and evolution of inhomogeneous plastic deformation field between grains in polycrystalline metals by focusing on continuum scale modeling of dislocation-grain boundary interactions within a strain gradient crystal plasticity (SGCP) framework. Thermodynamically consistent extension of a particular strain gradient plasticity model, addressed previously (see also, e.g., Yalcinkaya et al, J Mech Phys Solids 59:1–17, 2011), is presented which incorporates the effect of grain boundaries on plastic slip evolution explicitly. Among various choices, a potential-type non-dissipative grain boundary description in terms of grain boundary Burgers tensor (see, e.g., Gurtin, J Mech Phys Solids 56:640–662, 2008) is preferred since this is the essential descriptor to capture both the misorientation and grain boundary orientation effects. A mixed finite element formulation is used to discretize the problem in which both displacements and plastic slips are considered as primary variables. For the treatment of grain boundaries within the solution algorithm, an interface element is formulated. The capabilities of the framework is demonstrated through 3D bi-crystal and polycrystal examples, and potential extensions and currently pursued multi-scale modeling efforts are briefly discussed in the closure.