Experimental comparison of residual stresses for a thermomechanical model for the simulation of selective laser melting

Abstract

Selective laser melting (SLM) is an additive manufacturing process in which multiple, successive layers of metal powders are heated via laser in order to build a part. Modeling of SLM requires consideration of the complex interaction between heat transfer and solid mechanics. The present work describes the authors initial efforts to validate their first generation model, as described in Hodge et al. [1]. In particular, the comparison of model-generated solid mechanics results, including both deformation and stresses, is presented. Additionally, results of various perturbations of the process parameters and modeling strategies are discussed.

Introduction

This article presents preliminary validation of the solid mechanics response within a thermo-mechanical model for part-scale simulation of selective laser melting (SLM) additive manufacturing. This model was previously documented in Hodge et al. [1].

The continuum model consists of the balance of thermal energy, a moving boundary problem associated with phase change, the balances of mass and linear momentum, and the associated constitutive relations. The numerical formulation is a weighted residual formulation [2], solved in a Lagrangian frame, and with an incremental solution method [3]. The details of solving these kinds of problems can be found elsewhere [4], [5], [6]. There are numerous methods for coupling independent physical models in order to solve multi-physics problems. The examples presented in the current work were all solved using a staggered solution scheme [4], [7], [8].

The Diablo code [9] is an implicit finite element code building on the decades of experience with nonlinear, large-deformation solid mechanics at Lawrence Livermore National Laboratory (LLNL). It serves as a vehicle for extending our well-established discretization technologies to a message passing/parallel software architecture. The platform target is large, commodity CPU-based clusters where we now typically utilize 128–512 CPUs, and can exercise thousands. In creating this Fortran 95 program, we have concentrated on solid/structural mechanics and heat transfer, while embracing a more general multi-physics perspective allowing future extensions. Its Lagrangian finite element options currently comprise low-order continuum (hex), shells (quad) and two-nodes beams. A growing set of material models is available to represent nonlinear stress and thermal response, complemented with appropriate element quadrature rules to mitigate numerical locking. Our team and its predecessors have a long history of advancing numerical methods for contact problems simulating the interactions of unbounded material interfaces. Highly stable and robust mortar formulations [10] can accommodate large, arbitrary relative motions while representing typical engineering responses, such as friction and interface conductivity that varies with pressure and/or gap size. As an implicit code, Diablo is aimed toward relatively low-rate problems, including those exhibiting both quasi-static and static responses. Time integration is accomplished via the standard Newmark method [11] for solid mechanics and with a generalized alpha-method [12] for heat transfer. These time integrators require repeated solution of coupled linear systems of equations. To provide users with options to trade-off performance and robustness, both iterative and direct linear solvers are available and specifiable on a per-physics basis. Simulations comprising multiple field equations are solved through an operator splitting construct. The active sub-problems are solved successively within each time step until the sub-problems simultaneously converge. Multiple strategies are available to drive the nonlinear solution process for each of the individual field problems.

This paper will proceed as follows: the next section presents a brief description of the physical problem, as well as its mathematical representation. Section 3 will describe changes to the material properties, relative to [1], used to generate the results presented herein. Finally, Section 4 presents the results for three build cases, two being the same geometry with different orientations relative to the build plate. The comparisons in Section 4 include modeling versus experiment results, as well as various permutations of the models (alternate processing parameters, mesh refinement).