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Many properties of commonly used materials are driven by their microstructure, which can be influenced by the composition and manufacturing processes. To optimise future materials, understanding the microstructure is critically important. Here, we present two novel approaches based on artificial intelligence that allow the segmentation of the phases of a microstructure for which simple numerical approaches, such as thresholding, are not applicable: One is based on the nnU-Net neural network, and the other on generative adversarial networks (GAN). Using large panoramic scanning electron microscopy images of dual-phase steels as a case study, we demonstrate how both methods effectively segment intricate microstructural details, including martensite, ferrite, and damage sites, for subsequent analysis. Either method shows substantial generalizability across a range of image sizes and conditions, including heat-treated microstructures with different phase configurations. The nnU-Net excels in mapping large image areas. Conversely, the GAN-based method performs reliably on smaller images, providing greater step-by-step control and flexibility over the segmentation process. This study highlights the benefits of segmented microstructural data for various purposes, such as calculating phase fractions, modelling material behaviour through finite element simulation, and conducting geometrical analyses of damage sites and the local properties of their surrounding microstructure., Comment: 37 pages, 24 figures

High performance sheet metals with a multi-phase microstructure suffer from deformation induced damage formation during forming in the constituent phases but importantly also where these intersect. To capture damage in terms of the physical processes in three dimensions (3D) and its stochastic nature during deformation, two challenges remain to be tackled: First, bridging high resolution analysis towards large scales to consider statistical data and, second, characterising in 3D with a resolution appropriate for sub-micron sized voids at a large scale. Here, we present how this can be achieved using panoramic scanning electron microscopy (SEM), metallographic serial sectioning, and deep-learning assisted automatic image analysis. This brings together the 3D evolution of active damage mechanisms with volumetric and environmental information for thousands of individual damage sites. We also assess potential surface preparation artefacts in 2D analyses. Overall, we find that for the material considered here, a dual phase (DP800) steel, martensite cracking is the dominant but not sole origin of deformation induced damage and that for a quantitative comparison of damage density, metallographic preparation can induce additional surface damage density far exceeding what is commonly induced between uniaxial straining steps.

In this paper, we study the herding phenomena in financial markets arising from the combined effect of (1) non-coordinated collective interactions between the market players and (2) concurrent reactions of market players to dynamic market signals. By interpreting the expected rate of return of an asset and the favorability on that asset as position and velocity in phase space, we construct an agent-based particle model for herding behavior in finance. We then define two types of herding functionals using this model, and show that they satisfy a Gronwall type estimate and a LaSalle type invariance property respectively, leading to the herding behavior of the market players. Various numerical tests are presented to numerically verify these results., Comment: 31 pages