Additive manufacturing (AM) is rapidly emerging as a feasible manufacturing method. The material is deposited in a layer-by-layer approach, enabling complex-shaped parts to be manufactured. However, the printed parts are typically distorted to some extent due to the residual stresses from the manufacturing stage. These residual stresses are a result of the material’s temperature fluctuations during the layer-by-layer deposition: as the material is heated, it expands, and when cooled, it shrinks. To address this issue, models have been developed capable of simulating the entire AM process. By employing modeling techniques, process optimization can be achieved by identifying suitable process parameters, eliminating the need for time-consuming trial-and-error experimentation. One of the enabling technologies to these models is the finite element method (FEM) where the deposited material and build plate is treated as a continuum discretized by finite elements (FE). This work provides an overview of the finite element models for AM and the couplings that can be made to predict the residual stresses and distortions of printed components more accurately. The coupling can be made on different scales, including the micro-, meso-, or part-scale. Micro-scale finite element models coupled with cellular automata models (FE-CA), initially developed by Gandin and Rappaz (1997), can predict the grain texture after solidification. Meso-scale models such as thermal models can predict the temperature history from the chosen scanning strategy. Subsequently, thermo-mechanical models can predict residual stresses and distortions. When it comes to predicting the distortions on a part-scale level, thermo-mechanical layer-by-layer lumping and inherent strain method can be used to reduce the computational time. The coupled thermo-mechanical FE models can be used with a physically based material model which is based on the material’s dislocation structure. For example, Lindgren et al. (2017) developed a dislocation density-based plasticity model. Here, FE-CA models can provide information about the grain orientation and grain size which are important parameters involving the strain hardening in a physically based model where the Taylor orientation factor is needed, and the Hall-Petch effect where the grain size is needed. Phase composition can be provided by a thermo-metallurgical model. Furthermore, the change in dislocation density is proportional to the plastic strain rate which is obtained from the meso- or part-scale thermo-mechanical model itself. Additionally, thermal activation can assist dislocations when passing obstacles such as precipitates or solutes, hence the prediction of an accurate temperature field is an important input to the physically based model.

REFERENCES:

Gandin, Ch.-A., Rappaz, M., 1997. A 3D Cellular Automaton algorithm for the prediction of dendritic grain growth. Acta Materialia. pp. 2187-2195.

Lindgren, L.-E., Hao, Q., Wedberg, D., 2017. Improved and simplified dislocation density based plasticity model for AISI 316L. Mechanics of Materials. pp. 68-76.