Cellular structures are of growing interest for industry, and are of particular importance for lightweight applications. In this paper, a special case of metal matrix composite foams (MMCs) is investigated. The investigated foams are composed of austenitic steel exhibiting transformation induced plasticity (TRIP) and magnesia partially stabilized zirconia (Mg-PSZ). Both components exhibit martensitic phase transformation during deformation, thus generating the potential for improved mechanical properties such as strength, ductility, and energy absorption capability. The aim of these investigations was to show that stress-assisted phase transformations within the ceramic reinforcement correspond to strong local deformation, and to determine whether they can trigger martensitic phase transformations in the steel matrix. To this end, in situ interrupted compression experiments were performed in an X-ray computed tomography device (XCT). By using a recently developed registration algorithm, local deformation could be calculated and regions of interest could be defined. Corresponding cross sections were prepared and used to analyze the local phase composition by electron backscatter diffraction (EBSD). The results show a strong correlation between local deformation and phase transformation

The mechanical properties of a metal-matrix composite foam are investigated by interrupted in-situ compressive deformation experiments within an X-ray computed tomography device (XCT). Each in-situ experiment generates a sequence of reconstructed 3D images of the foam microstructure. From these data, the deformation field is estimated by registring the images corresponding to three consecutive steps. To this end, the generic registration framework of the itk software suite is exploited and combined with several image preprocessing steps. Both segmented (binary) images having just two grey values for foreground (strut structure) and background (pore space) and the result of the Euclidean distance transform (EDT) on pore space and solid phase are used. The estimation quality is evaluated based on a sequence of synthetic data sets, where the foam's microstructure is modelled by a random Laguerre tessellation. For large deformations, a combination of non-rigid registration for the EDT images and partwise-rigid registration on strongly deformed regions of the binary images, yields surprisingly small estimation errors.

Intensity inhomogeneities in images cause problems in gray-value based image segmentation since the varying intensity often dominates over gray-value differences of the image structures. In this paper we propose a novel biconvex variational model that includes the intensity inhomogeneities to tackle this task. We combine a total variation approach for multi class segmentation with a multiplicative model to handle the inhomogeneities. In our model we assume that the image intensity is the product of a smoothly varying part and a component which resembles important image structures such as edges. Therefore, we penalize in addition to the total variation of the label assignment matrix a quadratic difference term to cope with the smoothly varying factor. A critical point of the resulting biconvex functional is computed by a modified proximal alternating linearized minimization method (PALM). We show that the assumptions for the convergence of the algorithm are fulfilled. Various numerical examples demonstrate the very good performance of our method. Particular attention is paid to the segmentation of 3D FIB tomographical images serving as a motivation for our work.

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