## 4 Results and Discussion
### Attenuation Behavior of Ferrous Alloys
These steel samples were water-quenched and had high hardness for respective C levels (estimated to be 0.2, 0.25, and 0.3%C), with the initial Vickers hardness values being 206, 311, and 576 (from Vickers tests at 1 kg load; tests F4, F19, and F24). These showed high \(\alpha\) values at 1 MHz of 91.1, 81.6, and 99.3 dB/m, respectively. With tempering, the Vickers hardness gradually decreased to 114, 180, and 196, while \(\alpha\) values at 1 MHz also dropped to 18.8, 14.3, and 12.3 dB/m, respectively. These changes are shown in Figure 13, along with the data for brass, which showed a similar decrease with annealing (to be discussed in the next section). For most cases of steel tempering (or annealing of brass), the linear frequency dependence was retained. Tempering of low- to medium-carbon steels results from carbide precipitation and the loss of dislocations from displacive phase transformation [77; 80]. It appears that high attenuation in acicular ferrite and martensite from water quenching arises from high dislocation densities in these fine microstructures. As tempering progresses, dislocation densities gradually decrease, causing the loss of dislocation-induced damping. Simultaneously, fine carbide precipitation reduces the dislocation mobility, contributing to reduced damping. This is similar to the type-p CW effect discussed above. When C levels were higher in hardness calibration blocks (tests F73-F77), hardened conditions with Vickers hardness values of 434 to 695 produced only moderate attenuation of \(\alpha\) values at 1 MHz of 25 to 37 dB/m. These blocks are typically heat-treated into tempered martensite for increased stability in hardness, which is likely to lead to C segregation at dislocations, unlike in the as-quenched hypooutectoid steels discussed above. Such segregation suppresses dislocation damping. In the present study, this aspect was explored further using 4142 steel samples (tests F46-F48). Water quenching (WQ) caused increased hardness (Vickers 529) and a higher \(\alpha\) value (49.6 dB/m), followed reduction of these values upon tempering at 200 \({}^{\circ}\)C (test F47) and 400 \({}^{\circ}\)C (test F48). However, changes were smaller than in lower C steels discussed above. On the other hand, when the same 4142 steel sample was oil-quenched (OQ), its hardness increased moderately to a Vickers value of 327 (test F49), but its \(\alpha\) value was reduced to a level not measurable using 19-mm thick samples (only maximum level of \(\alpha\) estimated as 3 dB/m). Tempering at 400 \({}^{\circ}\)C hardly affected the \(\alpha\) value, but tempering at 700 \({}^{\circ}\)C increased it to 13.2 dB/m, which is comparable to the range of \(\alpha\) values of annealed structural steels (tests F50 and F51). The different responses to quenching speed are expected to arise from the transformation products--martensite for fast WQ and bainite for moderate OQ [77]. High dislocation densities remain in martensite, together with super-saturation of C interstitials, while fine carbide distributions were formed in bainite with lower dislocation densities, stabilized by C interstitials [80]. Low attenuation of medium- to high-C steels (4150 and 52100) was observed in earlier works [81; 82]. For 1% C bearing steel (52100), [PERSON] found \(\alpha\) values at 5 MHz (the lowest frequency used) of 5 to 9 dB/m [81]. In most of his plots, \(\alpha\) values did not decrease much below 10 MHz in contrast to the high slope with frequencies above 10 MHz. [PERSON] study on 4150 steel [82] reported 11.9 dB/m at 1.8 MHz for a ferritic-pearlitic microstructure, again showing a flattened frequency dependence below 10 MHz. For bainite, the \(\alpha\) value was 6.8 dB/m at 14 MHz (the lowest frequency used for hardened 4150 steel samples). These results are consistent with \(\alpha\) values found in the present study.