Section 6: Material modelling in solid mechanics - GAMM 2012

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12 Section 6: Material modelling in solid mechanics 1992 Deformation induced martensite transformation in a cold-worked forming process of austenitic stainless steel Tim Dally, Kerstin Weinberg (Universität Siegen) Within the last years the goal of industrial manufacturing processes - such as tube forming - has shifted towards an optimization of technological as well as mechanical properties of the manufactured structures. For example, during the forming procedure of sheets made of austenitic stainless steel X5CrNi18-10, the content of strain-induced martensite needs to be controlled. In order to achieve optimal structural properties of the manufactured tube with respect to very high-cycle fatigue (VHCF), a martensite ratio of approximately 25% needs to be obtained. On the basis of experimental investigations our contribution deals with the numerical simulation of the forming process with special consideration of the martensite ratio c as a function of temperature and deformation field: c = c(T, ε p ). In particular, we study the interaction of processing temperature, friction, plastic deformation and stress state during forming. We will further present different approaches of modelling the martensite evolution as well as the extension of an existing martensite model on polyaxial states of stress and compare experimental results and numerical simulations for the modified model. Additionally a facility to calculate the hardening due to martensitic phase transformation will be presented. Finally, we will propose a strategy to control the martensite evolution during the tube-forming process that enables us to achieve the optimal c mentioned above. Micromechanical modeling of bainitic phase transformation A. Schneidt, R. Mahnken (Universität Paderborn), T. Antretter (Montanuniversität Leoben) We develop a micromechanical material model for phase transformation from austenite to bainite for a polycrystalline low alloys steel. In this material (e.g. 51CrV4) the phase changes from austenite to perlite-ferrite, bainite or martensite, respectively. This work is concerned with phase transformation between austenite and n-bainite variants in different orientated grains. Characteristic of bainite are the combination of time-dependent transformation kinetics and lattice shearing in the microstructure. These effects are considered on the microscale and by means of homogenisation scale in the polycrystalline macroscale with stochastically orientated grains. Furthermore, the numerical implementation of our model with a Newton projection algorithm into a finite-element program is presented, based on the algorithm in [1]. [1] R. Mahnken and S. Wilmanns, A projected Newton algorithm for simulation of multivariant textured polycrystalline shape memory alloys. Computational Materials Science 50, 25352548, 2011. Effects of heat treatment on phase transformation in powder metallurgical multifunctional coating Reza Kebriaei, Jan Frischkorn, Stefanie Reese (RWTH Aachen)
Section 6: Material modelling in solid mechanics 13 Heat treatment is an indispensable part of the manufacturing of metallic products, especially in powder coating process. It provides an efficient way to manipulate the properties of the metal as e.g. hardness, yield stress and tensile stress by controlling the rate of diffusion and the rate of cooling within the microstructure. The process-integrated powder coating by radial axial rolling of rings is a new hybrid production technique which is introduced in [1]. It takes advantage of the high temperatures and high forces of the ring rolling process not only to increase the rings diameter, but also to integrate the application and compaction of powder metallurgical multi-functional coatings to the solid substrate rings within the same process [2]. The applied temperatures in hot rolling are within the range of austenitizing temperatures for the investigated steels. Therefore, controlled cooling can be conducted directly from process heat subsequent to the deformation process. The talk is concerned with the finite element (FE) simulation of the process-integrated powder coating by radial axial rolling of rings and the integration of heat treatment of the rolled ring into the subsequent cooling process. Finally parameter studies are performed to analyse the temperature profile and phase transformation in the rings cross-section. [1] J. Frischkorn, S. Reese, Modelling and Simulation of Process-integrated Powder Coating by Radial Axial Rolling of Rings, Archive of Applied Mechanics 81 (2011) [2] R. Kebriaei, J. Frischkorn, S. Reese, Influence of Geometric Parameters on Residual Porosity in Process-integrated Powder Coating by Radial Axial Rolling of Rings, Steel Research International 163 (2011) Simulation of phase-transformations based on numerical minimization of intersecting Gibbs energy potentials Richard Ostwald, Thorsten Bartel (TU Dortmund), Andreas Menzel (U Dortmund / Lund University) We present a novel approach for the simulation of solid to solid phase-transformations in polycrystalline materials. To facilitate the utilization of a non-affine micro-sphere formulation with volumetric-deviatoric split, we introduce Helmholtz free energy functions depending on volumetric and deviatoric strain measures for the underlying scalar-valued phase-transformation model. As an extension of affine micro-sphere models [3], the non-affine micro-sphere formulation with volumetric-deviatoric split allows to capture different Young’s moduli and Poisson’s ratios on the macro-scale [1]. As a consequence, the temperature-dependent free energy assigned to each individual phase takes the form of an elliptic paraboloid in volumetric-deviatoric strain space, where the energy landscape of the overall material is obtained from the contributions of the individual constituents. For the evolution of volume fractions, we use an approach based on statistical physics—taking into account actual Gibbs energy barriers and transformation probabilities [2]. The computation of individual energy barriers between the phases considered is enabled by numerical minimization of parametric intersection curves of elliptic Gibbs energy paraboloids. The framework provided facilitates to take into account an arbitrary number of solid phases of the underlying material, though we restrict ourselves to the simulation of three phases, namely an austenitic parent phase and a martensitic tension and compression phase. It is shown that the model presented nicely reflects the temperature-dependent effects of pseudo-elasticity and pseudo-plasticity, and thus captures experimentally observed behaviour at different temperatures.
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