Modeling of Fracture in Polycrystalline Materials
Predicting the behaviour of fracture processes within polycrystalline microstructures will help to develop more accurate mesoscale material models and will give insight to effects which can only be measured ex-situ. Therefore a non-local damage model is i
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Abstract Predicting the behaviour of fracture processes within polycrystalline microstructures will help to develop more accurate mesoscale material models and will give insight to effects which can only be measured ex-situ. Therefore a non-local damage model is introduced and coupled to finite deformation crystal plasticity. Cracks are represented sharply by using the extended finite element method in combination with level set techniques. As damage evolves cracks start to propagate. A new crack propagation algorithm is presented and studied by academic examples.
1 Introduction In industrial forming processes metals are subjected to large plastic deformations. Related to the plastic deformation within the material microstructure pores start to grow, merge and finally lead to microcracks within the material. Macroscopically this is recognised as a loss of stiffness of the structural behaviour and a reduced strength. This effect is usually modelled with continuum damage mechanics as done by Tvergaard and Needleman in [29]. In the context of finite elements, during the last decades several theories were established to circumvent the mesh dependent localization. Most of them, see e.g. [10, 23] or [26], are based on the introduction of a new degree of freedom for the thermodynamic driving force of the damage. This contributions follows the work of Reusch et al. [26] who determinate the new degree of freedom by solving an additional scalar balance equation. Nevertheless, if damage evolves and is used to predict the initiation or propagation of cracks the global stiffness matrix becomes ill-conditioned. Furthermore cracks are just represented in a smeared way and their dimension is related to the mesh size and some artificial internal length parameter.
S. Beese () • S. Loehnert • P. Wriggers Institute of Continuum Mechanics, Leibniz Universität Hannover, Appelstraße 11, Hannover, Germany e-mail: [email protected]; [email protected]; [email protected] © Springer International Publishing Switzerland 2016 G. Ventura, E. Benvenuti (eds.), Advances in Discretization Methods, SEMA SIMAI Springer Series 12, DOI 10.1007/978-3-319-41246-7_4
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To overcome this drawback the damage is transferred to discrete cracks if it exceeds a material depended threshold value. The representation of fracture is modeled with the eXtended Finite Element Method (XFEM) according to [4]. In combination with the level set techniques [5] this numerical tool enables a nearly mesh independent crack representation. The position of the crack is described implicitly by level set functions, and the discontinuity within the displacement field is captured using enrichment functions and additional degrees of freedom. Since classical crack propagation criteria lose their validity in a finite deformations context and for inelastic material behaviour an alternative approach is described. The argumentation for the chosen damage based criterion is that once the crack is initiated it will propagate if the pore
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