Effective prediction of residual stresses and deformations can ensure the quality of metal additive-manufactured parts. The traditional mesh-based finite element method (FEM) has been able to model many additive manufacturing processes with a correspondingly high fidelity. However, it is still deficient in other areas such as the simulation of complex boundary conditions, large deformations and crack extensions, interfacial motions, and phase transitions. Peridynamic, a nonlocal continuum theory whose governing equations are in the form of integral-differential equations, has the advantage of addressing the phenomenon of discontinuities. Numerous reports have been published on the evolution and application of the peridynamic theory after years of development. In this study, a three-dimensional peridynamic model is introduced to simulate the temperature field and deformation during laser additive manufacturing.

The basic thermophysical processes of laser additive manufacturing are considered in the peridynamic model. These include the coupling of thermal, material, and heat source models. First, the bond-based peridynamic governing equations are provided, including the coupled thermo-elasticity equation of motion and thermal diffusion. The time integration of the peridynamic motion and thermal diffusion equation is obtained by employing explicit forward and backward differences and forward difference techniques to obtain the velocity, displacement, and temperature, respectively. The simulation program is then created using the simulator generation system DELAB, which is used for calculating and analyzing the physical system of the particles. The Gaussian heat source and phase-change models in the heat transfer scenarios are used for the laser additive manufacturing process. In addition, a peridynamic volume correction procedure is considered. Finally, the model is validated for several individual physical processes, including the heat transfer model of the block and heating sphere model. The results indicate that the model is stable and accurate. This is expected to be used to simulate the laser additive manufacturing process.

A peridynamic model is demonstrated for simulations of the single-layer selective laser melting process. For the moving Gaussian heat source model with a 2-dimension plate, temperature and displacement variations along the x-direction are considered during the process. The high gradient temperature near the heat source is clearly displayed with the movement of the heat source in the x-direction (Fig. 13). The maximum displacement of the plate increases with the movement and constant action of the heat source (Fig. 14). The effect of the phase change on the temperature variation is presented, which shows that the maximum temperature is lower than the situation when phase change due to latent heat is considered (Fig. 16). For the single-layer powder bed model, a circular trajectory of the heat source is considered. The temperature field distribution at different times shows the shape of the melt pools at different trajectory locations (Fig. 18). A similar finite element model is created to verify the temperature field in the peridynamic model. The peridynamic-predicted results of the temperature variation at points P₁, P₂, and P₃ are in good agreement with the FEM model results obtained using ANSYS (Fig. 20).

We present a three-dimensional peridynamic model to simulate the temperature field and deformation during laser additive manufacturing. The basic thermophysical processes of laser additive manufacturing are considered in the model. These include the coupling of thermal, material, and heat source models. The model is validated for several individual physical processes. The obtained results show that the model is stable and accurate; the model can be used to simulate the laser additive manufacturing process. Finally, the peridynamic model is demonstrated for simulations of the single-layer selective laser process. Although this model has not been experimentally validated, it is a novel solution for simulating laser additive manufacturing. We expect that further studies based on this model will produce more feasible solutions to problems in the additive manufacturing process. Future efforts should utilize the peridynamic theory to overcome the difficulties in the simulation of laser additive manufacturing while considering the high-fidelity simulation with the traditional finite element method.