Keywords: material models, computer modelling, FEM, FEA, rapid prototyping, stereolithography, materials characterization, multi- and inter-disciplinary optimization.

In the rapid prototyping (RP) stereolithography (SL) process, parts are fabricated in a layer-by-layer technique by curing photopolymer resins with a UV laser. A laser beam scans across the vat surface, providing UV radiation that initiates the photopolymerization reactions in the SL resin. During the reaction, monomer is consumed, polymer is produced, and heat is generated. Since the resin is a liquid, the monomer and polymer molecules may diffuse. A better understanding of the SL process is needed in order to improve this technology.

The improvement of stereolithography (SL) material polymerisation relies on a better understanding of process fundamentals. The actual SL resin cure model relates laser beam exposure to the cured photopolymeric resin using a simple threshold approach [1]. This model ignores a variety of transient thermal and chemical effects that can influence final material properties and part geometry. SL cure resin is a time-varying process that is governed by complex, exothermic chemical reactions that have multiple reaction pathways.

Most commercial SL resins are now combinations of acrylates, epoxies, their photoinitiators, and other additives, as referenced by several researchers [2-4]. Acrylates react through a free radical mechanism, while epoxies react cationically. Radical photopolimerization is a chain reaction that consists of three main steps: photoinitiation, propagation, and termination. SL reactions are known to be exothermic, raising the temperature of the resin significantly. The governing energy balance consists of transient, conduction, and generation terms that yield the temperature distribution in the resin.

In this research, made in the Laboratory of Modelling Prototypes, a more rigorous SL cure model is developed that captures effects that are ignored in the threshold model. This new model incorporates photoinitiation rates, reaction rates, diffusion, and spatial temperature distributions. Process simulations are performed using the finite element method (FEM) with a standard software package.

Normally three cure cases could be investigated: single-scan-single-layer, multiple-scan-single-layer and single-scan-multiple-layer (stack of scans). These three cases cover the basic processes in SL. The governing equations are valid for each case, but the boundary and initial conditions will differ.

The FEM simulations and the finite element analysis (FEA) provide very good insight into the mechanisms of SL cure reactions, particularly the variation of quantities over time. An analytical model of SL resin cure involving heat conduction and diffusion is presented in this paper. The SL cure model is formulated as a set of partial differential equations, with initial conditions specified based on the chemistry and physics of laser exposure and photoinitiation. This model is then solved using the finite element method.

With the SL cure model it is possible to investigate the spatial and temporal distributions of monomer and polymer concentrations, molecular weights, cross-link densities, and degree of cure, which are necessary to characterize the cured material properties.

Simulations using FEM were conducted to determine the time-dependent distributions of monomer and polymer concentrations and degree of cure, as well as reaction rates. A time dependent solver was used for this problem, with time step correction algorithm. Triangular, quadratic, Lagrange elements were selected for domain discretization.

From the simulations by FEM, are represented time-dependent profiles of temperature, monomer concentration, and radical concentration. The rates of reactions (propagation, termination) and component consumption are also analysed. Furthermore, it is possible to investigate the effect of process and material parameters on the SL precision and speed.

Based on the sensitivity analysis, it is a little unexpected that only several material properties and process variables affect the resolution significantly. The sensitivities of results to changes in resin compositions and other input parameters are presented.

1

Jacobs P.F., "Rapid Prototyping & Manufacturing: Fundamentals of Stereolithography", Society of Manufacturing Engineers, Dearborn, MI, 1992.

2

Chartoff, R.P., Schultz, J.W., Ullett J.S., "Processing and Properties of Novel Liquid Crystal Resins for Stereolithography", RADTECH report, 12(4), 20-25, July 1998.

3

Broer, D.J., Mol, G.N., Challa, "Temperature Effects on the Kinetics of Photoinitiated Polymerization of Dimethacrylates", Polymer, 32, 690-695, 1991. doi:10.1016/0032-3861(91)90482-X

4

Pogue, R.T., Chartoff, R.P., "Novel Liquid Crystal for Stereolithography: Reaction Rates and Photopolymerization Conversion", Proceedings of the 1997 Solid Freeform Fabrication Symposium, Austin, TX, April, 1997.

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