JOURNAL OF MATERIALS SCIENCE 38 (2 0 0 3 ) 35 – 49 A three dimensional model for direct laser metal powder deposition and rapid prototyping M. LABUDOVIC Corning Lasertron, R & D, 11 Oak Park, M/S LZ-727, Bedford, MA 01730, USA E-mail: marko L@email.msn.com D. HU, R. KOVACEVIC Department of Mechanical Engineering, Southern Methodist University, P.O. Box 750337, Dallas, Texas, USA A three-dimensional model for direct laser metal powder deposition process and rapid prototyping is developed. Both numerical and analytical models are addressed. In the case of numerical modeling, the capabilities of ANSYS parametric design language were employed. The model calculates transient temperature profiles, dimensions of the fusion zone and residual stresses. Model simulations are compared with experimental results acquired on line using an ultra-high shutter speed camera which is able to acquire well-contrasted images of the molten pool, and off-line using metallographical and x-ray diffraction analyses. The experiments showed good agreement with the modeling. The results are discussed to provide suggestions for feedback control and reduction of residual stresses. C  2003 Kluwer Academic Publishers Nomenclature A Heat absorptivity of laser beam on metal surface C Specific heat (J/kg · K) d Diameter of the laser beam (m) d z , d x Length (width) of the laser beam in z (x ) direction (m) I Thermal flux density of laser beam (J/s · m 2 ) E Elastic modulus (N/mm 2 ) h Heat transfer coefficient (W/m 2 K) H Enthalphy (J/kg) H (.) Heaviside function (unit step function) k Boltzmann’s constant ( K = 1.38066 × 10 -23 Ws/K) K Heat conductivity (J/m · s · K) L f Latent heat of fusion (J/kg) P Laser beam power (J/s) P Surface pressure vector (N/m 2 ) ˙ q Rate of heat generation (J/s · m 3 ) ˙ q ii Tensor of heat flow derivatives (J/mm 3 s) ˙ Q v Volume-specific heat flow or source density (J/mm 3 s) Q Body force vector (N/m 3 ) r Distance from the center of the laser beam (m) r b Effective laser beam radius (m) S Area (m 2 ) S sl Area of the solid-liquid interface (m) t Time (s) T Temperature (K) ˙ T Cooling rate (K/s) u , v, w Displacement components in the x, y, z directions, respectively (m) u Displacement vector (m) V Volume (m 3 ) y m Molten pool depth (m) t Incremental time (s) α Thermal expansion coefficient (1/K) ρ Density (kg/m 3 ) ν Poisson’s ratio ε Emissivity δ(.) Dirac delta function ε Strain tensor in updated Lagrange configuration ˙ ε ii Tensor of elastic volumetric strain rates (1/s) ˙ ε vpij Tensor of viscoplastic strain rates (1/s) ξ Inelastic heat fraction σ Stefan-Boltzmann constant (σ = 5.670 × 10 -8 W/m 2 K 4 σ ) σ dij Deviatoric stress tensor (N/mm 2 ) σ Stress tensor in updated Lagrange configuration (N/m 2 ) ξ , ζ , χ Local coordinates 1. Introduction The direct laser metal powder deposition process is laser-assisted, direct metal manufacturing process for rapid prototyping under development at Southern Methodist University. The process is similar to the laser-engineered net shaping (LENS) TM process de- veloped at Sandia National Laboratories [1]. It in- corporates features from stereolithography and laser cladding, that use computer-aided design (CAD) file cross sections (stl file) to control the forming process. Metal-powder particles are delivered in an argon gas stream into the focus of the laser beam to form a molten 0022–2461 C  2003 Kluwer Academic Publishers 35