WELDING RESEARCH salient features are presented here. The molten metal is assumed to be an incompressible, laminar, and Newtonian fluid. The liquid metal flow in the weld pool can be represented by the following momentum conservation equation (Refs. 30, 31): where is the density, t is the time, xi is the distance along the ith (i = 1, 2, and 3) orthogonal direction, uj is the velocity component along the j direction, is the effective viscosity, and Sj is the source term for the jth momentum equation and is given as = − ∂ ∂ + ∂ ∂ ( ) where p represents pressure, U is the welding speed, and is the coefficient of volume expansion. The third term represents the frictional dissipation in the mushy zone according to the Carman Kozeny equation for flow through a porous media (Refs. 32, 33) where fL is the liquid fraction, B is a very small computational constant to avoid division by zero, and C is a constant accounting for the mushy zone morphology a value of 1.6 × 104 was used in the present study (Ref. 34). The fourth term is the buoyancy source term (Refs. 23, 34, 35). The last term accounts for the relative motion of the workpiece relative 138-s WELDING JOURNAL / APRIL 2015, VOL. 94 to the laser and arc heat sources (Ref. 23). The following continuity equation is solved in conjunction with the momentum equation to obtain the pressure field. ∂(ρ ) ∂ A B In order to trace the weld pool liquid/ solid interface, i.e., the phase change, the total enthalpy H is represented by a sum of sensible heat h and latent heat content DH, i.e., H = h + DH u t u u x x u x S j i j i i j i j ( ) ρ ∂ ∂ +ρ ∂ ∂ = ∂ ∂ μ ∂ ∂ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + (1) S p x x u x C f f B u g T T U u x j j j j j L L j ref j j ( ) μ ∂ ∂ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − − + ⎛ ⎝ ⎜⎜ ⎞ ⎠ ⎟⎟ +ρ β − −ρ ∂ ∂ 1 (2) 2 3 u x i i =0 (3) Fig. 7 — Comparison of the calculated cooling rates of the fusion zone located 1 mm above the bottom surface for weld 3 with welding speed of 40.0 mm/s, laser arc separation distance of 1 mm, and weld 4 with welding speed of 40.0 mm/s, laser arc separation distance of 5 mm. Fig. 8 — Comparison of the optical microstructures of the top center of the fusion zone by different welding speeds. Magnification 500x. A — Welding speed of 20.0 mm/s, laser arc separation distance of 1 mm; B — welding speed of 30.0 mm/s, laser arc separation distance of 1 mm. The symbols , W, and a represent allotriomorphic, Widmanstätten, and acicular ferrite, respectively. Table 3 — Material Properties Used for the Calculation of Temperature and Velocity Fields (Ref. 29) Physical Property DH 36 Steel Boiling point (K) 3133 Solidus temperature (K) 1745 Liquidus temperature (K) 1785 Density (kg/m3) 7200 Thermal conductivity (W/mK) 21 Inverse Bremsstrahlung absorption coefficient (1/m) 100 Absorption coefficient (flat surface) 0.16 Molecular viscosity (Pas) 0.0067 Coefficient of thermal expansion (l/K) 1.96 x 105 Temperature coefficient of surface tension (N/m K) –0.5 x 103 Enthalpy of solid at melting point (J/kg) 1.20 x 106 Enthalpy of liquid at melting point (J/kg) 1.26 x 106 Specific heat of solid (J/kg K) 710.6 Specific heat of liquid (J/kg K) 836.0 A B Fig. 9 — Comparison of the optical microstructures of the fusion zone located 1 mm above the bottom surface by different laser arc separation distances. Magnification 500x. A — Welding speed of 40.0 mm/s, laser arc separation distance of 1 mm; B — welding speed of 40.0 mm/s, laser arc separation distance of 5 mm. The symbols , W, a, and M represent allotriomorphic, Widmanstätten, acicular ferrite, and martensite, respectively.
Welding Journal | April 2015
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