WELDING RESEARCH A B Fig. 12 — Comparison of the experimental and calculated microstructure volume fractions of the weld metal for weld 1 with welding speed of 20.0 mm/s, laser arc separation distance of 1 mm; weld 2 with welding speed of 30.0 mm/s, laser arc separation distance of 1 mm; 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. The symbols , W, and a represent allotriomorphic, Widmanstätten, = + γ 1/2 where is the surface tension of the molten metal, r is the density, g is acceleration due to gravity, vd is the droplet impingement velocity, and Dt is the time interval between two successive drops, which is the inverse of the droplet transfer frequency. As shown in Equations 9 and 10, calculation of the dimensions of the volumetric heat source requires the knowledge of the droplet transfer frequency, radius, and impingement velocity, which can be determined from literature (Refs. 34, 38, 39). From the calculated values of Qd, Dd, and d, the time-averaged power density of the volumetric heat source, Sv, is calculated as follows (Ref .34) Equation 11 is only valid for grid points within the cylindrical heat source, and the power density is zero outside the cylinder. Free surface calculation of the weld top and bottom surface is not considered in the current model, and the simplification of flat pool surfaces is not expected to affect the calculated weld shape and microstructure significantly (Ref. 40). Phase Transformation Calculation In the weld fusion zone of low-alloy steels, allotriomorphic ferrite is the first phase to form and it nucleates heterogeneously at the boundaries of the columnar austenite grains during cooling. It is a reconstructive transformation b ( ) τ = × Δ × ⎛⎝ ⎜ 140-s WELDING JOURNAL / APRIL 2015, VOL. 94 involving diffusion (Ref. 26). As temperature decreases, diffusion becomes sluggish and gives way to a displacive transformation. At relatively low undercoolings, plates of Widmanstätten ferrite form by a displacive mechanism. At further undercoolings, bainite nucleates and grows in the form of sheaves of small platelets. Acicular ferrite nucleates intragranularly around inclusions inside the austenite (Ref. 26). The diffusionless martensite transformation may take place if the cooling rate is high enough. The isothermal time-temperaturetransformation (TTT) and continuous cooling-transformation (CCT) diagrams together with various transformation starting temperatures are calculated using the phase transformation model based on thermodynamics and phase transformation kinetics with weld deposit compositions as input variables (Refs. 22–24). The incubation times for both reconstructive and displacive transformations are calculated by Russell’s expression: where t is the incubation time for a transformation, T is the temperature, DGmax is the maximum driving force for nucleation, and a, b, c, and d are constants. The details of calculation of DGmax and determination of a, b, c, and d are given in the literature (Ref. 22). The CCT diagrams are calculated from the corresponding TTT diagrams S Q D d v d d 2 = π (11) x h D g cos g h t v v d v ρ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ Δ ⎡ ⎣ ⎢⎢ ⎤ ⎦ ⎥⎥ ⎧⎨ ⎪ ⎩⎪ ⎫⎬ ⎪ ⎭⎪ 2 1 (10) T G exp c T a d max ⎞⎠ ⎟ × (12) and acicular ferrite, respectively. Fig. 13 — Computed volume fractions of allotriomorphic, Widmanstätten, and acicular ferrite, and martensite with corresponding cooling rates from 1073 to 773 K of the fusion zone lower center as a function of laser arc separation distance and welding speed by different laser powers. A — Laser power = 4.0 kW, arc current = 232 A, arc voltage = 31 V; B — laser power = 5.0 kW, arc current = 232 A, arc voltage = 31 V; C — laser power = 6.0 kW, arc current = 232 A, arc voltage = 31 V. The symbols , W, a, and M represent allotriomorphic, Widmanstätten, and acicular ferrite, and martensite, respectively. A B C
Welding Journal | April 2015
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