## 5 Conclusions and Way Ahead
### Way Ahead  
From these results, it can be concluded that the velocity on its own is insufficient to reliably quantify the grain size or the phase fraction, especially given the impact of small temperature or sample thickness variations. The attenuation is a more promising metric for quantification of grain size and/or phase fraction. Note that in case of phase fraction, the impact of grain size variation has not been taken into account, but that plays an important role as well in actual measurements. In the simulations the impact of grain size and phase fraction have been studied individually. Further research might focus on the use of a combination of velocity and attenuation, in order to be able to determine grain size and phase fraction within a sample at the same time.  
In the previous analysis, the velocity was determined based on an observed time delay and the measured sample thickness. Especially this latter parameter requires a very accurate measurement, often in the order of micrometers. Since this is challenging, especially with local thickness variations, an alternative approach might be considered, such as the ratio of the pressure and shear wave velocities. The theoretical values of these velocities, derived from the elasticity matrices and densities, are shown in Figure 19a,b, and their ratios are shown in Figure 19c, again for the five samples and four temperatures. The advantage of this velocity ratio is that the thickness (and its inherent measurement error) drops out the equations, and hence the method does not require highly accurate thickness measurements.  
Future investigations will be directed towards a simultaneous estimation of grain size and phase fraction, and/or texture. The challenge in this is that the setup for estimation of grain size might differ from the setup for estimation of phase fraction or texture. The current simulations have been performed with a relatively large source (laser spot) diameter, which is dedicated to grain size measurements. This setup generates pure pressure waves and hardly any shear waves. However, for texture and phase fraction measurements, the source diameter can be reduced, leading to the generation of shear waves as well. Alternatively, with a completely different setup (e.g., using piezo transducers) it is feasible to measure both pressure and shear waves simultaneously.  
**Author Contributions:** Conceptualization, A.D., A.V. and F.V.d.B.; Data curation, F.V.d.B. and C.C.-C.: Formal analysis, A.D; Funding acquisition, F.V.d.B.; Investigation, A.D., A.V. and F.B; Methodology, A.D. and A.V.; Project administration, A.V. and F.V.d.B.; Resources, A.D., A.V., F.V.d.B. and C.C.-C.; Software, A.D. and A.V.; Supervision, A.V. and F.V.d.B.; Validation, A.D. and A.V.; Visualization, A.D.; Writing--original draft, A.D.; Writing--review & editing, A.D., A.V., F.V.d.B. and C.C.-C. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work has been financed by European Union's Research Fund for Coal and Steel (RFCS) research program under grant agreement no. RFCS-2018-847296.  
**Acknowledgments:** GLUS(r) data (Section 2.3) has been provided by [PERSON] (data curation, investigation), [PERSON] (investigation), and [PERSON] (investigation), all affiliated with Swerim AB, 164 40 Kista, Sweden.  
**Conflicts of Interest:** The authors declare no conflict of interest.