## 3 Results
### Multiphase  
A set of simulations has been performed on samples with various ratios of austenite and martensite as material. This is the series marked with 'C' in Table 2. The grain diameters are the same in all five samples: 10.0 \(\upmu\)m for martensite and 15.0 \(\upmu\)m for austenite. For each of those samples, simulations have again been performed at four different temperatures (27 \({}^{\circ}\)C, 300 \({}^{\circ}\)C, 550 \({}^{\circ}\)C, and 900 \({}^{\circ}\)C). These temperatures were used in the simulations to study a large temperature domain. Note that again the phase transition temperature has not been taken into account and that this multiphase steel might not actually exist at all four simulated temperatures. The elasticity coefficients (based on the polycrystalline Voigt-Reuss-Hill average) of the sample are shown in Figure 16, as well as the isotropy. As can be seen, all samples are nearly isotropic, and the coefficients show a (nearly) linear relation with the phase ratio (in terms of percentage martensite). The given values are for a temperature of 550 \({}^{\circ}\)C, but other temperatures show the same trends. The observed wave velocities for the five samples and four temperatures are shown in Figure 17, which show linear trends as function of the phase ratio. Although the grain size of the individual phases is kept invariant in all simulations, the average grain size of the total sample increases with the amount of austenite. However, since the scattering is only of minor impact on the wave velocity (cf. Figure 12), the underlying elasticity matrices are expected to be the dominant determining factor for the wave velocity. The resulting relation is linear with the phase ratio. However, the relation with temperature (Figure 17b) depends on the underlying material properties, which reveals its non-linearity. Differences in wave velocity are relatively small (in the order of 3.7 m/s difference for each percent in phase ratio difference (50% martensite at 300 \({}^{\circ}\)C, Figure 17a). Measurement of such small differences (5 m/s means a change in the order of 0.1% of the total velocity) means the sample thickness has to be measured at least as accurate (order of micrometers), which is very challenging. At the same time, the temperature has to be known accurately as well, since a 4 \({}^{\circ}\)C temperature increase can also lead to a 4 m/s velocity decrease (50% martensite at 300 \({}^{\circ}\)C, Figure 17b). As in the previous case of grain sizes, the propagation wave velocity measurement is also not a viable method for phase ratio characterization. Results of the attenuation analysis are shown in Figure 18. As a reference, the sample with 50% martensite and 50% austenite is taken in subplot a) and the sample with a temperature of 300 \({}^{\circ}\)C in subplot b). With only five different ratios, the curves appear not very smooth, although a trend is visible. Given this limited set of simulations, it is hard to derive a reliable quantitative relationship. Figure 16: All polycrystal (Voigt-Reuss-Hill averaged) coefficients plotted as function of the phase ratio (in percentage of martensite, with the other phase being austenite). The bottom right curve shows the isotropy \(\mathcal{Z}\) (cf. Equation (1)) in all five samples for a temperature of 550 \({}^{\circ}\)C.  
The curves appear to be depending on both phase ratio and temperature, as expected, although not in a linear fashion. A phase ratio change of 1% leads to an attenuation change of 0.002 (50% austenite at 300 \({}^{\circ}\)C, Figure 18a). A temperature change of 10 \({}^{\circ}\)C causes an attenuation change in the order of 0.003 (again 50% austenite at 300 \({}^{\circ}\)C, Figure 18b), which is of the same magnitude order. This shows that the effect of temperature is significant and cannot be ignored. Thus, assuming that the temperature can be measured on the order of 10 \({}^{\circ}\)C, the phase ratio can be estimated on the order of a percent.