## 6 Concluding Remarks and Further Research  
We have described and explained a continuous research effort made over more than twenty years to model a welded material microstructure for ultrasonic testing simulation. All the steps proposed in the introductory figure (Figure 1) have now been investigated in detail, and complete solutions are available for industrial applications. Research advances are here discussed to continue to improve the quality of simulation predictions or to enlarge the field of applications for existing solutions. Three axes for further research can be identified. The first axis is aiming at improving the prediction of the wave attenuation. The second axis for further research is the optimisation of the grain map. The third axis is obtaining the real weld geometry instead of a simplified geometry. The question of wave attenuation is not discussed in details. Wave attenuation is very difficult to take into account both for the modelling part and for the experimental part. The intrinsic attenuation of a material is a mechanism very difficult to quantify. In many situations, the diagnosis to validate material knowledge is based on velocity measurements and thus based on time of flight values. It requires precise wave path prediction, which is why very good material description is mandatory. The use of wave amplitude is more difficult, both experimentally and in simulation, as attenuation also has an anisotropic behaviour and data are scarce in the literature on the subject, mainly because precise measurements require strong efforts to eliminate all transducer effects (definition, position, etc.). In combination with the study of \(C_{ijkl}\), we have taken into account this question in many previous papers, and more specifically, we have used attenuation measurements made during several specific studies [73]. [PERSON] and al. [74] developed dedicated experimental studies based on the decomposition of the beam into a plane wave angular spectrum and on the calculation of transmission coefficients in the k-space domain. Solving [PERSON]'s equation at the corresponding boundary conditions makes it possible to calculate transmission coefficients. The material symmetry should be chosen in the monoclinic case. It is difficult to align the material internal symmetry axis with the symmetry axis of the ultrasonic measurement setup. If there is a difference between these two axes, the material exhibits a monoclinic behaviour. The experimental results obtained are in accordance with theoretical behaviours predicted by [PERSON]'s theory [75] and [PERSON]'s work [76]. These values are considered now as reference values in several codes for austenitic weld materials (ATHENA or CIVA codes). Attenuation properties (or the imaginary part of \(C_{ijkl}\)) should be properly taken into account in any inverse problem that uses amplitude measurements to investigate welds using ultrasonic images. In the MUSCAD project, it is mentioned that there is a bigger uncertainty of the imaginary part of the \(C_{ijkl}\), which is very difficult to evaluate. It may produce significant differences between simulated and real attenuation [72]. Attenuation is also closely related to the shape and the distribution of the grains. Studies about microstructure noise also play a part in the necessary understanding of the attenuation mechanisms. Such studies are not discussed here; important work on the subject is presented in [PERSON]'s work [76]. Finite element modelling has been used to evaluate the effect of various grain distributions on the ultrasonic noise. Three dimensional simulations are now possible [77]. It still requires heavy computational workflow; hopefully this drawback can be reduced in years to come. To reduce the attenuation impact and to limit the beam-splitting phenomenon in dissimilar welded material, [PERSON] et al. [78], propose to apply phased arrays to enlarge the ultrasonic energy, thereby improving the potential to detect cracks.