# Research

## Martensite Formation in Nanostructured NiTi Shape Memory Alloys

Nanostructured NiTi Shape Memory Alloys exhibit superior fatigue properties compared to their coarse-grained counterpart. Grain sizes in the order of fractions of a micrometer can be achieved by severe plastic deformation and subsequent annealing. The martensite morphology that appears after transformation is widely influenced by the grain size as can be proven by evaluating the total energy input into the system including interface energy contributions as well as the strain energy, the latter being evaluated numerically for various 3D configurations, see the attached figure. The energy-minimizing configuration is then compared with HRTEM experiments performed by T. Waitz, Physics of Nanostructured Materials, Department of Physics, University of Vienna.

## Transformation Induced Plasticity

The phenomenon of Transformation Induced Plasticity (TRIP) is studied on the example of a maraging steel by the brand name Marval X12 which has thoroughly been investigated in a series of experiments carried out at the Tokyo Metropolitan Institute of Technology. Our goal is to develop a constitutive model that eventually allows the reliable prediction of residual stresses in structural components. In the particular case of martensitic transformation the selection of variant favorably oriented relative to the stress direction gives rise to what is referred to as orientation effect which, in turn, leads to transformation related backstress effects similar to what is known in classical plasticity of kinematically hardening materials. Eventually the constitutive model should be able to reproduce the experimentally determined strain response given arbitrary external thermo-mechanical loading conditions, see the attached figure.

Schematic sketch representing the dissipative processes during diffusive phase transformations.

## Diffusive phase transformations

The microstructural changes connected with phase transformations determine the properties of the evolving materials. A basic understanding of the transformation kinetics is required to obtain the desired microstructure and to design functionally oriented materials. The transformation kinetics depends on diffusion of components in the bulk materials and on the rearrangement of the lattice characterized by the interface mobility [1-3]. In addition diffusion processes in the interface frequently influence the kinetics of solid/solid phase transformations. The evolution equations for all variables describing the system are derived from the principle of maximum dissipation [4].

[1] E. Gamsjäger: Pure and Applied Chemistry 83 (2011), 1105-1112.
[2] J. Svoboda, E. Gamsjäger: Int. J. Mater. Res. 102 (2011), 666-673.
[3] E. Gamsjäger: Acta Mater. 55 (2007) 4823-4833.
[4] J. Svoboda, I. Turek, F. D. Fischer: Phil. Mag. 85 (2005) 3699-3707.

## Finite Element Modeling of the Cyclic Wetting Mechanism in Wheat Awns

Awns and appendages on the seed dispersal unit play an important role in dispersing the seed to the germination site. The seed unit of the wild wheat plants (Triticum turgidum ssp. dicoccoides) is assembled of two pronounced awns that stabilize the dispersal fall off from the mother plant. Although consisting only of dead tissue, wheat awns work like muscles, being able to propel seeds several millimeters into the soil. The cross-section of the awn consists macroscopically of an active part, an intermediate gap and a resistance part, all of them consisting of hollow cylindrical cells. The active part is responsible for the awn bending with changing ambient humidity. It is built of cylindrical cells containing layers with parallel cellulose fibrils embedded in a soft hygroscopic matrix. It was shown that the active and resistance part expand differently at varying humidity, pushing the awns together with increasing moisture and pulling them apart while drying. In the present study, a single cylindrical cell of the active part is modeled as plywood architecture with the finite elements, especially focusing on the specific microscopic features. Based on earlier experimental findings the cell wall is modeled as a multilayered cylindrical tube with alternating cellulose fiber orientation in successive layers. It is shown that swelling upon hydration leads to the formation of gaps between neighboring layers, which could act as nanometer-sized valves, thus enabling the entry of humidity into the cell wall. This finding supports the hypothesis that the plywood-like arrangement of cellulose fibrils enhances the effect of ambient humidity by accelerating water or vapor diffusion along gaps. The model shows that a certain distribution of fibers with tangential and axial orientation is necessary to enable an opening of the gaps between cell wall layers.

Circumferential stress $\tilde{\sigma}_{\theta} \left(\tilde{r}\right)$ distributions across the grown tissue as a function of radius, $\tilde{r}$. Tissue grows into the centre of the pore $\tilde{r} = 0$ from right $\tilde{r} = 1-\delta$ to left. Dotted lines indicate position of inner pore boundary for the different times ( $\tilde{\tau} = 7,8,9,10,11$ ).

## Tissue growth

Research in this field is focussed on thermodynamically consistent modelling of tissue growth in living materials such as bone, and the activities are carried out in cooperation with the department of Biomaterials of Max-Planck-Institute in Golm (Director: Prof. P. Fratzl) within the research group of Dr. Dunlop. It is a goal to derive evolution equations so that the experimentally observed coupling between the growth of new material and the local deformation or stress state can be mapped in an according way. Theory has been applied to model tissue growth in a simple geometrical setting, namely tissue growth confined inside a circular hole [1]. The results of the calculations can be compared with experimental findings [2]. However, in case of growth on convex surfaces the predicted exponential growth behaviour is in contrast to experimental results where no growth, apart from the formation of a thin monolayer of cells, is observed. There is experimental evidence that actin fibers can act as “contractile” elements. This is considered in a more advanced model by introducing a surface stress term [3] so that both inward and outward growth can be modelled in a realistic way.

[1] W.C. Dunlop, F. D. Fischer, E. Gamsjäger and P. Fratzl, Journal of the Mechanics and Physics of Solids (2010) 58(8), 1073-1087.
[2] M. Rumpler, A. Woesz, J. W. C. Dunlop, J. T. van Dongen, P. Fratzl, (2008), Journal of the Royal Society Interface 5(27): 1173-1180.
[3] E. Gamsjäger, J. W.C. Dunlop, F. D. Fischer, C. Bidan and P. Fratzl: "The role of surface stress on the kinetics of tissue growth in confined geometries", (in preparation for Acta Biomaterialia).

## Behavior of Railway Crossings

Turnouts are a critical part of the railway track system. They consist of a switch and a crossing panel. It is of crucial interest for the development of new and optimized turnouts to know the distinct loading of the components. A main part of a turnout represents the crossing nose where in facing direction a vertical impact of the wheel occur on the crossing nose or, in the opposite direction coming from the crossing nose on the wing rail. These areas are highly dynamically loaded and at the same time a slip between the wheel and the crossing parts occurs. This is the reason why crossing parts sometimes feature high wear and high damage. Crossings thus have a big influence on the maintenance costs of the tracks. For the necessary service time or the replacement of crossings in the track, there are only small time intervals available. This is another reason for the importance of increasing the service/reparation time and the lifetime of the crossing parts.

## Fundamental research on damage in the wheel rail contact

Metallurgical investigations of rolling sliding contact report the very common fact that a layer, very close to the surface of the contacting bodies, is heavily deformed. For the investigation of the plastic straining processes very close to the surface (within 100 microns depth) one needs to consider the surface roughness on a micrometer length scale but also the unevenness of the wheel and rail on a millimeter length scale. Numerical micro-models indicate a crack initiation at asperities. It will be investigated if these cracks must be either related to wear or cracks growing into the depth and their relation to head checks. The main aim is the prediction of growth rate and path of shear cracks which remains an open task in material research. Shear cracks are one of the most important damage mechanisms regarding rolling contact fatigue of rails and crossings. Another aim will be the detection of mechanisms of crack initiation in rolling sliding contacts given arbitrary external thermo-mechanical loading conditions. The aim of a new physically justified wear law is based on preceding numerical and metallurgical investigations.

## Mechanics of Structures

• Stress, deformation state and life time of structures, like storage tanks and vessels during earthquake excitation Partners: ESI Leoben, Kolednik
• Analysis Micromechanics of forming tools during thermomechanical treatment, development of defects and irreversible shape changes Partners: MC Leoben, R. Ebner et al.
• Stress and deformation state in biological structures, swelling and shrinking mechanisms during life time Partners: MPI Colloids & Interfaces, Potsdam/Golm, Fratzl et al.
• Dynamics of the railway wheel/rail or wheel/switch contact process. Deformation, stress and wear state in the wheel and the rail or switch Partners: MC Leoben, Daves; VA Schienen GmbH Leoben; VAE Zeltweg

## Mechanics and Thermodynamics of Materials

• Elementary principles to develop evolution equations for dissipative processes Partners: Czech Acad Sci, Brno, Svoboda; RU Bochum Inst. Mech. Hackl; Polish Acad Sci, Warszaw, Petryk
• Martensitic and displacive phase transformations in metals and intermetallics Partners: Paris Materials Centre, Evry, Cailletaud et al.; Polish Acad Sci, Warszwa, Petryk et al.; U. Wien, Waitz; MUL, Clemens et al.; ESI Leoben, Dehm et al.
• Phase transformation in nanoparticles and thin layers Partners: Nanoconsulting, Karlsruhe, Vollath; MUL, P. Mayrhofer; ESI Leoben, Dehm et al.
• Thermodynamics of moving interfaces in metals, intermetallics and minerals, phase boundaries in particles and crystals Partners: Czech Acad Sci, Brno Svoboda; U Jena, Rettenmayr; FU Berlin, Abart; MPI Colloids & Interfaces, Potsdam/Golm, Fratzl; MUL, Clemens et al.; U Wien, Waitz; FWF Wien, Liu
• Prediction of the microstructure of alloys and compounds, diffusive processes in multicomponent, multiparticle systems, application to development of steels with specific properties profile Partners: Czech Acad Sci, Brno, Svoboda; TU Graz, Cerjak et al; TU Wien, Kozeschnik et al; Böhler Uddeholm, Kapfenberg

## Defects and Cracks

• Design tools for inhomogeneous materials with cracks, the concept of configurational forces Partners: ESI Leoben, Kolednik; U Marburg, Gubeljak et al.; U. Minnesota, Simha
• Multicrack systems in ceramics and biological materials, design of fracture-resistant structures Partners: ESI Leoben, Kolednik; MPI Colloids & Interfaces, Potsdam/Golm, Fratzl et al.; MUL, Danzer

## Appendices:

ZAMM – Integral

Int. J. Solids and Structures – Supplementary Materials

Scripta Mater - Supplementary Material