## 6 Concluding Remarks and Further Research
Welded material is not always described at a very thin scale (a millimetre one) but over larger areas [79] using macrographic examination on representative welds to propose welded material definition. The material description is based on an averaged grain orientation. Further development for MINA modelling could consist of proposing an automatic definition of this kind of zone of interest by automatically clustering material meshes in larger areas. Advances in various artificial intelligence algorithms clearly make this research way possible, even if it would require more available macrograph data to cover as many welding cases as possible. The best situation to develop a weld-related algorithm would be to have the initial welding notebook. That is a real difficulty in many cases, specifically when nondestructive inspection should be applied to help to assess the structural integrity of aged welded structures. However, a major drawback is the risk of obtaining not-so-accurate ultrasound paths. When few hypotheses are possible in weld manufacturing, it is still possible to reconstruct welded material without using solidification laws in detail. Algorithms are developed by considering the material locally, and of course by trying to obtain the local grain orientation. A number of studies can be found in the literature that take the benefit of multiple array measurements. As indicated, reconstruction is performed using time of flight data. [PERSON] et al. [80] proposed a forward model to simulate the wave front propagation in an anisotropic medium. It is combined with the reversible-jump Markov chain Monte Carlo approach to modify grain orientations. Significant improvement across multiple metrics developed to characterise flaws is shown. Methods like the total focusing method (TFM) have the potential to reconstruct welded material thanks to image optimisation. More recently, [PERSON] et al. [81] developed an algorithm for homogeneous austenitic material. Ultrasonic image enhancement is searched for in unknown anisotropic steels. An optimisation algorithm modifies the unknown variables to optimise the quality of TFM images. Experiments are performed on two industrial components. The potential of neural networks is also investigated to help describe welded material. A framework is proposed that uses deep neural networks (DNNs) in combination with a dedicated experimental setup with full aperture, pitch-catch and pulse-echo transducer configurations to reconstruct material maps of grain orientation [82]. The objective is to obtain real-time imaging to unlock a large range of applications for ultrasonic testing, making in-process inspection during manufacturing possible. Among the possible improvements to make to all these methods developed to define welded material considering the weld geometry definition, indeed, a first typical input is the geometry of the weld, often a V-shaped weld. But it is known that during the welding processes, residual stresses and distortions occur. Numerical process simulation provides the evolution of physical quantities such as temperature, strains and stresses at each point in the welded component. Three-dimensional simulations are needed to accurately predict weld distortions in the case of multipass welding. In their work, [PERSON] et al. [83] made a three-dimensional finite element simulation of the multipass welding of a stainless steel pipe with thirteen passes. Computed distortions and residual stresses are calculated. Experimental measurements show that the chamfer presents a distortion of several millimetres after five passes. It is observed regularly that the largest differences between modelled orientations and those measured on the macrograph are near the weld chamfers. This is the result of a MINA model simplification, as a parabolic shape of the pass is used, and there is no specific refined part to fill the potential remaining volume between the passes and the initial chamfer geometry.