Discrete dislocation dynamics for crystal RVEs. Part 1: Periodic network kinematics

Modeling the evolution of representative dislocation structures under high thermo-mechanical conditions during Additive Manufacturing of Alloys

“…a simulation volume that is invariant with respect to the imposed PBCs. This definition is in alignment with the terminology used in the literature [5]. The results of these simulations provide an understanding of the requirements for simulation domains in mesoscale simulations as well as strategies for modifying simulation boundary conditions to over come numerical and computational challenges when the needed RVE size is large.…”

“…Thus, the concept of representative volume element (RVE) is typically employed in 3D DDD simulations where the domain edge-length is commonly limited to ∼ 1 to 20 µm and the time scale is limited to hundreds of nanoseconds to microseconds at most (i.e, a limit of ∼1-2% plastic strain). For this RVE concept, the simulation cell is defined as a "primary" cell of an infinite periodic array of supercells that are exact replicas of this primary cell (i.e, by employing periodic boundary conditions (PBCs) to the simulation domain) [5,6,7,8,9]. Examples of utilizing this concept include: simulations of the strain hardening in metals and metal-matrix composites [10,11,12]; quantifying the interactions of dislocations with alloying elements in complex alloys [7,13,6]; or studying the dislocation-precipitate interaction [14,15]; as well as many other applications.…”

“…Examples of utilizing this concept include: simulations of the strain hardening in metals and metal-matrix composites [10,11,12]; quantifying the interactions of dislocations with alloying elements in complex alloys [7,13,6]; or studying the dislocation-precipitate interaction [14,15]; as well as many other applications. The concept is also used for both single crystal simulations [5] and polycrystalline simulations [16,17,18]. However, it should be noted that the chosen RVE size could inadvertently influence the predictions in the characteristics of the evolving dislocation structure and the subsequent mechanical properties (e.g, yield strength, hardening rate, etc.).…”

“…However, on the level of mesoscopic dislocation-based plasticity simulations, these questions have received little attention. Existing studies mainly deal with the formulation and implementation of periodic boundary conditions to enforce the continuity of dislocation lines and dislocation flux throughout the deformation history [5,8] or address the self-annihilation of dislocation lines [19,20]. On the other hand, attempts to characterize and identify RVEs in mesoscale dislocation-based simulations under complex loading scenarios, such as in laser-based additive manufacturing, impose additional challenges associated with the multi-scale and multi-physics nature of the problem.…”

Microplasticity in inhomogeneous alloys

“…For simulating the collective dynamics of dislocations, Mechanics of Defect Evolution Library (MoDELib) is utilized [18]. We utilize RVE boundary conditions for DDD to simulate bulk plasticity in the alloy [19][20][21][22]. Constant elastic properties with elastic modulus and Poisson's ratio determined from Field et al [7] have been utilized for the coherency stresses and DDD calculations at room temperature.…”