A B C D established without interference from the liquid, and the cracking resistance is generally good. (The presence of surface-active elements that modify the solid/liquid surface energy and promote extensive wetting of the boundaries by the liquid at even small liquid fractions can alter this general trend.) As the fraction of terminal eutectic liquid increases, the liquid more extensively wets the boundaries, thus interfering with the formation of solid-solid boundaries and causing an increase in the cracking susceptibility. At considerably higher fractions of liquid, backfilling of cracks can occur by the liquid and heal the cracks as they form. This phenomenon is similar to liquid feeding by risers used to control solidification shrinkage defects in castings. With this background in mind, the influence of Gd concentration on the cracking susceptibility, amount of terminal eutectic constituent, and solidification temperature range are summarized in Fig. 27. The lines in the bottom two figures represent the fraction eutectic and solidification temperature range, respectively, calculated with the equations above, and there is good agreement between the calculated and measured values. This supports the use of a pseudo binary analog for modeling the solidification behavior of these alloys. More importantly, the results provide a basis for developing a detailed understanding of the weldability results. At low Gd concentrations, the solidification temperature range is high, but the fraction of terminal eutectic liquid is very low. Thus, the cracking susceptibility is low. As the Gd concentration increases, there is only a slight decrease in the solidification temperature range, but a rather significant increase in the fraction of terminal eutectic liquid. This leads to the increase in cracking susceptibility shown in Fig. 27 that reaches a maximum at ~ 1 wt- % Gd. With still increasing amounts of Gd, the amount of terminal liquid increases to the point where cracking susceptibility decreases due to backfilling of solidification cracks. The reduction in the solidification temperature range with increasing Gd concentration also assists in decreasing the cracking susceptibility. The amount of terminal liquid required to promote backfilling has been suggested to be in the range of 7–10 vol-% (Ref. 48). The results in Fig. 27 support this, where the cracking susceptibility is observed to decrease when the fraction of terminal eutectic reaches this range. This occurs when the Gd concentration reaches ~1.5 wt-%. This phenomenon is also supported by direct observation of backfilling that became appreciable when the Gd reached 1.5 wt- %, as shown in Fig. 25. These effects can be evaluated in more quantitative detail by combining solidification theory with simple heat flow equations for determining both the size of the crack-susceptible region of the solid + liquid mushy zone and variation in fraction liquid with distance within the mushy region. The well-known Scheil equation can also be used to calculate the fraction of liquid (fL) as a function of temperature via (5) f 1 1 T T o o L L T T where, as before, To is the melting point of the Ni-Cr-Mo solvent and TL is the liquidus temperature of the alloy (as affected by Gd concentration). T is the actual temperature. Noting that k for Gd is 0, Equation 6 reduces simply to (6) − − T T T T o L o = L k 0 The variation in temperature within the solid + liquid region can be estimated using the Rosenthal heat flow solution (Ref. 49) which, for three-dimensional heat flow, is given by ( ) = +⎛⎝ ⎜ ⎡− − η π α (7) ⎞⎠ ⎟ ⎣ ⎢ where T is the actual temperature, Tp is the preheat temperature, η is the heat source transfer efficiency, P is the arc power, h is the thermal conductivity of the base metal, α is the thermal diffusivity of the base metal, S is the heat source travel speed, r is the radial distance from the heat source, and x is the distance behind the heat source. The weld centerline is of the most interest here because this is the location where the temperature gradient is the lowest and, as a result, where the crack-susceptible solid + liquid region is the largest. This accounts for the experimental observation of the maximum crack length occurring in the weld centerline region. At the weld centerline, r = x and Equation 7 reduces t k = − − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥− f for = T T p hr S r x 2 exp p 2 ⎤ ⎦ ⎥ FEBRUARY 2014, VOL. 93 42-s WELDING RESEARCH Fig. 25 — Microstructures of the Varestraint samples from Alloy C-4 alloyed with various concentrations of Gd. A — 1.01 wt-% Gd; B — 1.49 wt-% Gd; C — 1.90 wt-% Gd; D — 2.45 wt-% Gd. Fig. 26 — Pseudo-binary solidification diagram developed for Gd-enriched Alloy C-4.
Welding Journal | February 2014
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