# Cyber Enabled Manufacturing Systems (CeMs) for Small Lot Manufacture

### Abstract:

Selective laser sintering (SLS) is an additive manufacturing technique able to rapidly create parts directly from a CAD model using a laser to selectively fuse successive layers of powder. Defects can arise in SLS parts due to incomplete fusion of the powder layers or thermal stresses introduced by large temperature gradients during the part build. Accurate models of the SLS process are needed to ensure that high quality parts are produced and to allow new materials and designs to be used without requiring extensive experimentation. A multi-scale model of the SLS process is developed which couples a continuum finite volume method to predict temperature and melt history of a part with particle-scale models which predict effective material properties needed in the continuum model. A transient, three-dimensional, finite volume model is used to represent an SLS powder bed. A time-dependent Gaussian heat source is used to represent the laser. The heat equation is solved to produce a temperature profile of the powder bed. Powder layer additions are simulated by varying material properties. Temperature history results from the model are validated against experimental data available in the literature and good agreement is obtained. However, large uncertainties result from the uncertainties in the effective, bulk, material properties of the powder used as inputs. In order to computationally determine these material properties more accurately, a Discrete Element Model (DEM) is developed and implemented in the open source solver MFiX in which a small, representative domain is resolved at the particle level. Particles are modeled as spheres and representative domains are initialized with particles placed randomly. Particles fall under the influence of gravity, interact with each other via a spring-dashpot model and finally settle to form a packing structure. Effective optical properties are calculated using ray-tracing. Rays are fired downwards into the particle bed from random locations at the top of the domain. They are absorbed and reflected by the particles until their energy is adequately diminished or they exit the domain. The effective absorptivity and extinction coefficient are obtained from the resulting energy distribution in the bed. Effective thermal conductivity is calculated by modeling the heat transfer between particles in a bed with an imposed temperature gradient. A particle-particle contact conduction model, a particle-fluid-particle conduction model, and a view factor radiation model are used. The effective thermal conductivity is calculated from the steady state temperature distribution. Correlations along with uncertainties are developed to allow the effective absorptivity, extinction coefficient, and thermal conductivity to be accurately set in the SLS continuum model. Melt behavior of the particle bed is simulated using a hybrid continuum discrete model where un-melted particles are modeled using DEM and particle melt is modeled using a background mesh. As particles melt, they shrink and their lost mass is added to the appropriate mesh cell. The continuity, momentum, and energy equations are solved on the background mesh to predict the behavior of the melt. The laser source is modeled using the radiation transport equation (RTE) solved on the background mesh. Correlations are developed between the average temperature of the bed, the melt fraction, and the laser power for use in the SLS continuum model.

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