WELDING RESEARCH = − γ d d 2 2 + ρ + γ APRIL 2015 / WELDING JOURNAL 139-s (Ref. 36). The sensible heat h is expressed as h = CpdT, where Cp is the specific heat and T is the temperature. The latent heat content DH is given as DH = fLL, where L is the latent heat of fusion. The liquid fraction fL is assumed to vary linearly with temperature for simplicity (Ref. 23) and is given as ⎪⎪ where TL and TS are the liquidus and solidus temperature, respectively. Thus, the thermal energy transportation in the weld workpiece can be expressed by the following modified energy equation: h (5) ( ) ρ∂ ∂ where k is the thermal conductivity. The source term Sh is due to the latent heat content and is given as ( ) ( ) = −ρ ∂ Δ ∂ −ρ The heat transfer and fluid flow equations were solved for the complete workpiece. For the region inside the keyhole, the coefficients and source terms in the equations were adjusted to obtain boiling point temperature and zero fluid velocities. A 3D Cartesian coordinate system is used in the calculation. Only half of the workpiece is considered since the weld is symmetrical about the weld centerline. At the bottom of the weld pool, Marangoni force-driven fluid velocity boundary conditions are assumed for complete-joint-penetration welding. A 187 × 77 × 26 grid system is used in the calculation and the corresponding calculation domain dimensions are 522 mm in length, 36 mm in half-width, and 4.8 mm in depth. The interactions between laser and arc as well as the heat transfer and fluid flow within the weld pool are affected by the separation distance between laser and arc. In the numerical model, the effect of arc energy on the formation of the keyhole and the energy transportation from the keyhole wall to the liquid weld pool are calculated. However, the laser-arc interaction, which has been characterized experimentally with optical emission spectroscopy (Ref. 37), is not rigorously simulated here. During laser-GMA hybrid welding, the rates of heat, mass, and momentum transport are often enhanced because of the presence of fluctuating velocities in the weld pool. The contribution of the fluctuating velocities is considered by the incorporation of a turbulence model that provides a systematic framework for calculating effective viscosity and thermal conductivity (Refs. 32, 33). The values of these properties vary with the location in the weld pool and depend on the local fluid flow characteristics. In this work, a turbulence model based on Prandtl’s mixing length hypothesis (Ref. 32) is used to estimate the turbulent viscosity. Calculation of Heat Transfer from GMA Metal Droplets The hot molten metal droplets produced by the GMAW process impinge into the weld pool at high velocities and carry a significant amount of heat into the liquid weld pool (Refs. 34–36, 38, 39). The heat transfer from the metal droplets was simulated by considering a cylindrical heat source with a time-averaged uniform power density (Sv). The use of a cylindrical volumetric heat source assumes the spray transfer mode of the droplets, which is consistent with the welding conditions in the present study. In order to calculate Sv, the radius of the heat source, its effective height, and the total sensible heat input by the droplets are required. The radius of the volumetric heat source is assumed to be twice that of the droplet radius, and the effective height, d, is calculated from the following equation (Refs. 34, 38, 39): d = hv – xv + Dd (7) where hv is the estimated height of the cavity caused by the impact of metal droplets, xv is the distance traveled by the center of the two successive impinging droplets, and Dd is the droplet diameter. The total sensible heat input from the metal droplets, Qd, is given as (Ref. 34) Qd = prwrw 2wfCp(Td – Tl) (8) where rw is the density of the electrode wire, rw is the radius of the wire, wf is the wire feeding rate, Td is the droplet temperature, and Tl is the liquid temperature. The values of hv and xv in Equation 7 are calculated based on an energy balance as (Ref. 39): f T T T T T T T T T T T L L S L S S L S = > − − ≤ ≤ < ⎧ ⎨ ⎪⎪ ⎩ 1 0 (4) h t u ,h x x k C h x i S i i p i +ρ ∂ ∂ = ∂ ∂ ∂ ∂ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + S H t u H x U h x U H x h i i i i ∂ Δ ∂ −ρ ∂ ∂ −ρ ∂Δ ∂ (6) h D g D g D v v 6g d d ρ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ (9) 2 2 Fig. 10 — Calculated CCT diagrams with the cooling curves superimposed. Cooling rates are taken at the top center of welds with 1 mm laser arc separation distance and 20 and 30 mm/s welding speed (welds 1 and 2, respectively). Cooling rates are taken at 1 mm from the bottom surface of welds with 40 mm/s welding speed and 1 and 5 mm laser arc separation (welds 3 and 4, respectively). The symbols , W, and a represent allotriomorphic, Widmanstätten, and acicular ferrite, respectively. Ms is the starting temperature for martensite formation. Fig. 11 — Variation of the volume fractions of allotriomorphic ferrite, Widmanstätten ferrite, acicular ferrite, and martensite with different cooling rates.
Welding Journal | April 2015
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