Section 6: Material modelling in solid mechanics - GAMM 2012

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6 Section 6: Material modelling in solid mechanics kinematics at the continuum scale. As a result the total energy becomes non-convex, thus giving rise to the development of microstructure. To guarantee the existence of minimizers an exact quasi-convex envelope of the corresponding energy functional is derived. As a result microstructure occurs in both the displacement and micro-rotation field. The corresponding relaxed energy is then used for finding the minimizers of the two field minimization problem corresponding to a Cosserat continuum. Finite element formulation and numerical simulations are presented. Analytical and numerical results are discussed. About the Microstructural Effects of Polycrystalline Materials and their Macroscopic Representation at Finite Deformation Eva Lehmann, Stefan Loehnert, Peter Wriggers (Universität Hannover) In the sheet bulk metal forming field, the strict geometrical requirements of the workpieces result in a need of a precise prediction of the material behaviour. The simulation of such forming processes requires a valid material model, performing well for a huge variety of different geometrical characteristics and finite deformation. Because of the crystalline nature of metals, anisotropies have to be taken into account. Macroscopically observable plastic deformation is traced back to dislocations within considered slip systems in the crystals causing plastic anisotropy on the microscopic and the macroscopic level. A finite crystal plasticity model is used to model polycrystalline materials in representative volume elements (RVEs) of the microstructure. A multiplicative decomposition of the deformation gradient into elastic and plastic parts is performed, as well as a volumetric-deviatoric split of the elastic contribution. In order to circumvent singularities stemming from the linear dependency of the slip system vectors, a viscoplastic power-law is introduced providing the evolution of the plastic slips and slip resistances. The model is validated with experimental microstructural data under deformation. The validation on the macroscopic scale is performed through the reproduction of the experimentally calculated initial yield surface. Additionally, homogenised stress-strain curves from the microstructure build the outcome for a suitable effective material model. Through optimisation techniques, effective material parameters can be determined and compared to results from real forming processes. A rheological model for arbitrary symmetric distortion of the yield surface A.V. Shutov, J. Ihlemann (TU Chemnitz) A new rheological model is presented, which provides insight into phenomenological modelling of combined nonlinear kinematic and distortional hardening. The model is constructed by coupling idealized two-dimensional rheological elements like Hooke-body, Newton-body, and modified St. Venant element [1,2]. The symmetric distortion of the yield surface and its orientation depending on the recent loading path are captured by the rheological model in a vivid way. We emphasize the flexibility of the proposed approach since it can be used to capture any smooth convex saturated form of the yield surface observed experimentally, if the yield surface is symmetric with respect to the recent loading direction. In particular, an arbitrary sharpening of the saturated yield locus in the loading direction combined with a flattening on the opposite side can be taken into account [2]. Moreover, the yield locus evolves smoothly and its convexity is ensured at each hardening stage. The rheological model serves as a guideline for construction of new constitutive relations. The kinematic assumptions, the ansatz for the free energy and for the yield function are motivated by the rheological model. Additionally to kinematic and distortional hardening, a nonlinear isotropic hardening is introduced as well. Normality flow rule is considered, and a rigorous proof of ther-
Section 6: Material modelling in solid mechanics 7 modynamic consistency is provided. Finally, the predictive capabilities of the resulting material model are verified using the experimental data for a very high work hardening annealed aluminum alloy 1100 Al. [1] A.V. Shutov, S. Panhans, R. Kreißig, A phenomenological model of finite strain viscoplasticity with distortional hardening, ZAMM, 8, 653 - 680. [2] A.V. Shutov, J. Ihlemann, A viscoplasticity model with an enhanced control of the yield surface distortion, Submitted to International Journal of Plasticity. Towards the simulation of Internal Traverse Grinding – from mesoscale modelling to process simulations Raphael Holtermann (TU Dortmund), Andreas Menzel (TU Dortmund / Lund University) The present work aims at the modelling and simulation of Internal Traverse Grinding of hardened 100Cr6/AISI 52100 using electro plated cBN grinding wheels. We focus on the thermomechanical behaviour resulting from the interaction of tool and workpiece in the process zone on a mesoscale. Based on topology analyses of the grinding wheel surface, two-dimensional single- and multigrain representative numerical experiments are performed to investigate the resulting loaddisplacement-behaviour as well as the specific heat generation due to friction and plastic dissipation. A thermoelastic-viscoplastic constitutive model is used to capture thermal softening of the material taken into account. Based on previous work [1,2], an adaptive remeshing scheme which uses a combination of error estimation and indicator methods, is applied to overcome mesh dependence. In consequence, the formulation allows to resolve the complex deformation patterns and to predict a realistic thermomechanical state of the resulting workpiece surface [3]. As a future goal, we aim at coupling the above cutting zone model to a process scale simulation to model the thermomechanical behaviour of the entire three-dimensional workpiece. [1] C. Hortig and B. Svendsen, Simulation of chip formation during high-speed cutting, J. Mat. Processing Technology 186, 66–76 (2007) [2] C. Hortig and B. Svendsen, Adaptive modeling and simulation of shear banding and high speed cutting, Proc. 10th ESAFORM Conference on Material Forming CP907, 721–726 (2007) [3] D. Biermann, A. Menzel, T. Bartel, F. Höhne, R. Holtermann, R. Ostwald, B. Sieben, M. Tiffe, A. Zabel, Experimental and computational investigation of machining processes for functionally graded materials, Procedia Engineering, accepted for publication, 2011 Multiscale crystal plasticity based on continuum theory of dislocation mechanics: an extension to ductile fracture. Mubeen Shahid, Klaus Hackl (Universität Bochum) The presentation focuses on the modelling of phenomena associated with plastic deformations in crystalline materials. The plastic deformation in crystalline materials strongly depends on aggregate behaviour of dislocations. However there is no universal constitutive frame-work which directly relates all the attributes of dislocations at microscale to the macroscale deformations, both qualitatively and quantitatively.
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