approaches solidus. The critical strain rate asymptotically approaches zero around solidus, meaning inevitable hot tearing, which is not physically real. This suggests the critical strain rate should be looked for around temperatures where the fraction of the solid phase is approximately 0.9, not around soli- dus temperature. Strain rate is the highest in the
mold preheated to 392F (200C) and drops down with increasing preheat temperature. Te main feature is a distinct difference in strain rates in the casting when molds preheated to 626F (330C) and 644F (340C). Strain rates next to the spherical ends were even slightly negative around solidus temperature when the mold was preheated to 644F (340C). It is interesting that, except in the shortest rod next to the riser, strain rates were higher if the mold was preheated further to 698F (370C). Experiments were performed up to around 707F (375C) for this alloy, and no hot tearing was reported. Hence, we can assume strain rate developed when the mold was pre- heated to 698F (370C). It is reasonable to expect that the thin liquid films between solid grains need higher cavitation threshold due to lack in cavitation nuclei, like gas bubbles and dis- solved gases. The ratio of cooling rates between mold and casting also has been examined. The underlying
The effect of the shrinkage
mismatch should
be well captured by the strain rate.
hypothesis is that hot tearing may be avoided if thermal expansion and shrinkage of the mold and casting occur simultaneously. If the mold is preheated to an insufficiently high temperature, it still will expand while the casting is shrinking. This increases stress buildup in the cast- ing, which leads to cracking in the final stages of solidification, when the material starts to gain mechani- cal strength. To estimate the difference in
shrinkage, it would be ideal to compare a variation in the length between characteristic points in the mold with the variation of uncon- strained length in the casting. Te latter is, however, very hard to deter- mine. For that reason, the cooling rates at adjacent points in the mold and in the casting are compared. As shown in Fig. 2, this result does not give a conclusive proof of hot tearing. Te ratio is positive, meaning both casting and mold shrink at these points when the casting is around solidus tempera- ture. Also, the distance between the
control points in the mold decreases when the casting is below 932F (500C). Even if the mold shrinks, it can impose significant constraint if the unconstrained casting would have shrunk at the faster rate. In any case, the effect of the
shrinkage mismatch should be well captured by the strain rate. One expects these two are in direct proportion. The ratio of cooling rates is
slightly negative at the beginning of cooling, indicating its expansion, but in all cases the ratio reaches positive values when the casting is at around 932F (500C). Therefore, according to the simulation, mold expands while castings shrink when the fraction of the solid phase is around 0.75, when the danger of hot tearing is not so great. There are occasional large negative peaks that show up and disappear within 50F to 59F (10C to 15C) before the ratio turns to positive values. Occurrence of these peaks does not depend on the preheating temperature. In conclusion, the effect of the shrink- age mismatch could not be clearly evidenced in this simulation. Simulated stresses show only neg- ligible plastic deformations in short rods during a very small temperature range below solidus temperature, and only in the mold preheated to 392F (200C). So, the simulation would show no danger of hot tearing if this result was used as a prediction.
Fig. 2. These graphs show the (a) ratio of cooling rates of the mold and the casting in the longest rod at the joint with the sprue/riser and (b) at the joint with the spherical end.
40 | MODERN CASTING October 2014
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