Section 6: Material modelling in solid mechanics - GAMM 2012

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8 Section 6: Material modelling in solid mechanics First the macroscale constitutive model based on the continuum theory of dislocations [1,2] is discussed. The plastic deformation and crack growth during ductile fracture mutually effect each other, where dislocations’ movement shape the crack growth, and the latter effects the dislocations density [3]. We discuss the numerical implementation of the proposed crystal viscoelastoplasticity model coupled with modern dislocation measures [1,2] and present an example where the mechanisms of crystal plasticity are linked to the ductile fracture. The results focus the effect of severe plastic deformation on dislocations evolution and crack growth behaviour, following the approach of Cherepanov [3]. [1] T. Hochrainer, M. Zaiser, P. Gumbsch, A three-dimensional continuum theory of dislocation systems: kinematics and mean-field formulation, Philosophical Magazine, 87:8-9 (2007), 1261-1282. [2] S. Sandfeld, T. Hochrainer, P. Gumbsch, M. Zaiser, Numerical implementation of a 3D continuum theory of dislocation: dynamics and application to micro-bending, Philosophical Magazine, 90:27-28 (2010), 3697-3728. [3] G.P. Cherepanov et al., Dislocation generation and crack growth under monotonic loading, J. Appl. Phys., 78(10) (1995), 6249-6264. Multiscale modelling and simulation of micro machining of titan Richard Lohkamp, Ralf Müller (TU Kaiserslautern) The topology of micro machined surfaces depends strongly on the underlying heterogeneous microstructure of the material. The crystal structure influences the deformation and separation characteristics. In the case of α-titanium the deformation is dictated by the hcp crystal structure with its specific slip systems. In the crystal plastic deformation it is essential to take self and latent hardening into account. Furthermore to capture the rate dependent behavior a visco-plastic evolution law is used. This setting serves as a framework for more complex constitutive laws, such as the one given in [1]. As a first attempt to model the cutting process, the fracture mechanisms in a crystalline αtitanium are analysed within the concept of configurational forces. To this end the theory of configurational forces is presented for a standard dissipative medium and is specialized to the crystal plasticity setting. The numerical implementation of the material law and the configurational forces is done in a consistent way within the finite element method. The application of configurational forces in the crystal plasticity setting is discussed and demonstrated by illustrative examples. S6.4: Polymers and Elastomers II Tue, 16:00–18:00 Chair: Alexander Lion, Joachim Schmitt S1|01–A1 How to approximate the inverse Langevin function? Mikhail Itskov, Roozbeh Dargazany, Karl Hörnes (RWTH Aachen) The inverse Langevin function directly results from the non-Gaussian theory of rubber elasticity as the chain force and represents an indispensable ingredient of full-network rubber elasticity models. However, the inverse Langevin function cannot be represented in a closed-form and requires an approximation as for example a Padé approximation. The Padé approximations can be given
Section 6: Material modelling in solid mechanics 9 in a relatively simple form and are able to describe the asymptotic behavior of the inverse Langevin function in the vicinity of the maximum chain extensibility. Far away from the asymptotic area the approximation error can be, however, relatively large. In the present contribution we compare various Padé approximants with the Taylor power series representation of the inverse Langevin function. To this end, a simple recursive procedure calculating power series coefficients of the inverse function is proposed. The procedure can be applied to any function which can be expanded into Taylor series. Within the convergence radius the resulting series of the inversed Langevin function demonstrates better agreement with the analytical solution than the Padé approximations. Phenomenological modeling of a polymeric composite Sebastian Borsch, Albrecht Bertram (Universität Magdeburg) A composite material consisting of a polymeric matrix material and metallic filler particles is modeled in a phenomenological way. The isotropic viscoplastic constitutive model is formulated within the theory of finite deformations. The flow rule is a superposition of two terms. This approach enables us to simulate the strong backflow behavior during unloading, which can be observed in various polymeric materials. A quasi-static finite-element simulation has been performed to compare the model with cyclic tension tests as well as a relaxation test. Modelling of nanoindentation of polymers with effects of surface roughness and parameters identification Zhaoyu Chen, Stefan Diebels (Universität des Saarlandes) Since the nanoindentation testing technique can measure the properties of extremely small volumes with sub-m and sub-N resolution from the continuously sensed force-displacement curves, it also became one of the primary testing techniques for polymeric materials and biological tissues. The analysis of individual indentation tests using the conventionally applied Oliver & Pharr method has limitations to capture the hyperelastic and rate-dependent properties of polymers. Therefore, an inverse method with respect to the experimental testing, based on finite element simulation and numerical optimisation has been used and evolved. However, nanoindentation is composed of various error contributions, e. g. friction, adhesion, surface roughness and indentation process associated factors. These contributions forming the systematic errors between the numerical model and the experiments will often lead to large errors in the parameters identification. Therefore, basic investigations and quantification of these influences are indispensable to characterise the materials accurately from nanoindentation based on the inverse method. In the present contribution, the characterisation of polymers through nanoindentation with effects of the surface roughness based on inverse method will be investigated numerically. The boundary value problems of nanoindentation of polymers are modelled with the FE code ABAQUS R○ . In contrast to the traditional inverse method, virtual experimental data calculated by numerical simulations with chosen parameters replace the real experimental measurements. Such a procedure is called parameter re-identification. In this sense, the finite element code ABAQUS R○ is used as our virtual laboratory. The model parameters are identified using an evolution strategy based on the concept of numerical optimisation. The surface roughness effects are investigated numerically based on the approach utilizing the phenomenological concepts. The surface roughness is chosen to have a simple representation considering only one-level of roughness profile described by a sine function. The influence of the surface roughness is quantified associated to the sine curve parameters as well as to the indentation parameters. Moreover, the real surface topography is
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Section 6: Material modelling in solid mechanics - GAMM 2012

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