Metals are made of small crystals - i.e., atoms are arranged in a particular geometric arrangement, which are typically in the range of a few 10s of microns (0.01 mm). The arrangement of these crystals greatly affects the performance of the metal and hence the performance of components where metals are used - such as in aeroplanes, gas turbine engines, cars, etc. The manner in which such materials deform, crack and fail under a variety of conditions is an important area in terms of cost and safety. When a metal is made - i.e., the liquid is cooled down and it becomes a solid material - crystals start forming within the liquid, which grow during cooling until they come in contact with each other, where they form crystal boundaries. Hence, we have formed a polycrystalline material, in which all the different crystals might have different orientations. As metals are typically used for load-bearing applications, it is imperative to understand the mechanical performance of such materials. Initially, metals deform in a fully elastic (fully reversable) manner but once the elastic limit has been exceeded, they deform plastically, which means any additional strain is irreversible - i.e., permanent. Such plastic deformation can lead to failure of the material. At a crystal level, the plastic strain - or shearing - happens along particular planes associated with the crystal. Hence, the plasticity in a crystal is not random but can only happen along particular directions. However, as the material is made up of many crystals, and they all have different orientations, the deformation process of a polycrystalline material is highly complex.

For the proposed PhD project, experimental data are already available that bring together maps of orientations of such crystals together with the deformation pattern generated during mechanical loading of such samples. The focus of the PhD project will be to use machine learning techniques to better understand the interplay between the crystal orientations and deformation patterns in a polycrystalline material during plastic deformation in order to eventually predict the manner in which materials deform and fail.

As a first step, we wish to infer a distribution of the directions of deformation displacement and the length of such deformations (or displacements).

As later steps, we will then look at time series data (or movies of images) and also at out-of-plane 3-dimensional deformations.

This will enable us to better understand deformation - with a view to anticipation, remedy and possibly prevention.

The PhD project is a collaboration between the Faculties of IT and Engineering with the student being based in the Faculty of IT.

#### URLs/references

Chen, Z. & Daly, S. H. Active Slip System Identification in Polycrystalline Metals by Digital Image Correlation (DIC). *Exp Mech* 57, 115–127 (2017).

Comley, Joshua W. and D.L. Dowe (2005). ``Minimum Message Length and Generalized Bayesian Nets with Asymmetric Languages'', Chapter 11 (pp265-294) in P. Gru:nwald, I. J. Myung and M. A. Pitt (eds.), Advances in Minimum Description Length: Theory and Applications, M.I.T. Press (MIT Press), April 2005, ISBN 0-262-07262-9. [Final camera ready copy was submitted in October 2003.]

Dowe, D.L., J.J. Oliver and C.S. Wallace (1996). MML estimation of the parameters of the spherical Fisher Distribution. In S. Arikawa and A. K. Sharma (eds.), Proc. 7th International Workshop on Algorithmic Learning Theory (ALT'96), Lecture Notes in Artificial Intelligence (LNAI) **1160**, pp213-227, Sydney, Australia, 23-25 October 1996. [pp213-219, pp220-227; p213, p214, p215, p216, p217, p218, p219, p220, p221, p222, p223, p224, p225, p226, p227] http://dx.doi.org./10.1007/3-540-61863-5_48

Gioacchino, F. D. & Fonseca, J. Q. da. An experimental study of the polycrystalline plasticity of austenitic stainless steel. *Int J Plasticity* 74, 92–109 (2015).

Gioacchino, F. D. & Fonseca, J. Q. da. Plastic Strain Mapping with Sub-micron Resolution Using Digital Image Correlation. *Exp Mech* 53, 743–754 (2013).

Lunt, D. *et al.* Comparison of sub-grain scale digital image correlation calculated using commercial and open-source software packages. *Mater Charact* 163, 110271 (2020).

Wallace, C.S. (2005), ``Statistical and Inductive Inference by Minimum Message Length'', Springer (Link to the preface [and p vi, also here])

Wallace, C.S. and D.L. Dowe (1994b), Intrinsic classification by MML - the Snob program. Proc. 7th Australian Joint Conf. on Artificial Intelligence, UNE, Armidale, Australia, November 1994, pp37-44

Wallace, C.S. and D.L. Dowe (1999a). Minimum Message Length and Kolmogorov Complexity, Computer Journal (special issue on Kolmogorov complexity), Vol. 42, No. 4, pp270-283

Wallace, C.S. and D.L. Dowe (2000). MML clustering of multi-state, Poisson, von Mises circular and Gaussian distributions, Statistics and Computing, Vol. 10, No. 1, Jan. 2000, pp73-83

#### Required knowledge

The PhD project is a collaboration between the Faculties of IT and Engineering with the student being based in FIT. The project does not require any prior understanding of materials science – although an interest in materials science (and strains and material deformation) would not hurt. The project requires a focus in at least one of statistics, machine learning, mathematics and data science, so the student should have at least an undergraduate degree or graduate diploma with a focus on at least one of these. The student should also have studied mathematics at least to 1st year undergraduate level, ideally further. The student should also be able to program. One modelling approach which we expect to at least consider will be the Bayesian information-theoretic minimum message length (MML) principle. We anticipate that knowledge of angular distributions - such as the von Mises circular distribution (as an example, consider compass readings or hospital arrival times on a 24-hour clock) and possibly also the von Mises-Fisher spherical distribution – might assist in analysing the various actions in various orientations.