A much more meaningful use of the |

A much more meaningful use of the |dT/d(fS1/2)| near (fS)1/2 = 1 as the crack susceptibility index than calculating a K-shaped curve is to predict the crack susceptibility of an alloy even just qualitatively. Fig. 7a shows the curves of T vs. (fS)1/2 for commercial Al casting alloys A206 and A356. Their chemical compositions are shown in Table 1 [34]. Alloy A206 has a significantly higher steepness |dT/d(fS1/2)| near (fS)1/2 = 1 than A356. This can be seen, for instance, in the range of 0.87 < fS < 0.94 (0.933 < (fS)1/2 < 0.970). Thus, Fig. 7a predicts the significantly higher crack susceptibility of alloy A206 than A356. This prediction is consistent with the known high crack susceptibility of A206 and low crack susceptibility of A356 in casting practice [35–37], which can also be seen in the results of the constrained-rod casting in Fig. 7b [38]. It is worth mentioning that with a change in the height/width aspect ratio of the T (fS)1/2 plot, the same curves of A206 and A356 in Fig. 7a were shown previously in Fig. 5 to help reveal the shapes of grains near (fS)1/2 = 1.