13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Numerical Investigation of the Fracture Behavior of Tungsten at the Micro Scale Christoph Bohnert1,2*, Sabine M. Weygand1, Nicola J. Schmitt2, Ruth Schwaiger2, Oliver Kraft2 1 Faculty of Mechanical Engineering and Mechatronics (MMT), Karlsruhe University of Applied Sciences, Moltkestr. 30, 76133 Karlsruhe (Germany) 2 Institute for Applied Materials (IAM), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany) * Corresponding author: christoph.bohnert2@hs-karlsruhe.de Abstract Due to its high melting point tungsten has the potential to be used as a structural material in future energy applications. However, one of the challenges is to deal with the brittleness of tungsten at room temperature, where the fracture behavior of polycrystalline tungsten is strongly influenced by the grain structure and texture as well as sample dimensions. The aim of the present work is to numerically analyze the stress field at a notch in a single crystal tungsten micro cantilever. A three dimensional finite element model is presented representing the microstructure of the cantilever which is deflected by a nanoindentation device. The study addresses experimental shortcomings as, for instance, in the experimental setup pure mode I cannot be realized. Due to friction between indenter and microbeam, lateral forces arise and have an impact directly on the stress field at the notch. The FE model is used to study the influence of the friction coefficient on the lateral forces and on the stress intensity factor. The simulations reveal that with rising friction coefficient the lateral force increasing linearly and the stress intensity factor decreases. Keywords Micro Cantilever, Single Tungsten Crystal, Fracture Toughness, FE Model, Crystal Plasticity 1. Introduction Tungsten – a material with many outstanding advantages and features – has been mainly used in the light engineering industry as a functional material. Owing to its high melting point, tungsten may be used in the future as a significant structural-material in energy applications. Improvement of the fracture toughness represents one of the challenges due to the brittle-to-ductile transition of tungsten above the room temperature. Several fracture studies have been already performed on macro specimens. Rupp et al. [1] as well as Gludovatz et al. [2] found a strong influence of the microstructure on the fracture morphology and toughness as well as on the brittle-to-ductile transition temperature in polycrystalline tungsten. The grain structure and texture has namely a decisive influence on the dominating failure mechanisms and on the resulting fracture toughness. In order to consider ways of increasing the fracture toughness, it is therefore necessary to understand the entire complexness of the mechanisms. Gumbsch et al. [3] investigated the fracture toughness of tungsten single crystals with different crystal orientation. They identified fracture toughness values varying from 6.2 to 20.2 MPa m1/2 for the {100} and {110} cleavage planes at different crack front directions. However, fracture studies using micro specimens are very rare. Wurster et. al. [4-5] performed fracture experiments on tungsten single crystal notched micrometer-sized cantilevers. In the present work the fracture behavior of single tungsten crystals is numerically analyzed for micro scale samples. This is related to an ongoing experimental study on single crystal tungsten microbeams with the focus on crack initiation and crack growth performed by N. Schmitt [6]. In the experimental work notched cantilevers with a height of 55 μm and a width of 28 μm are manufactured and bend by a nanoindenter. Experimental shortcomings are for instance the deviation from ASTM standard geometry and the deviation from the pure mode I. To support and complement the experiments a finite element model of the microbending test is presented in the present paper. It is applied to compute the stress intensity factor K for the present nonstandard specimen geometry. Furthermore, it is used to analyze the influence of lateral forces (due to friction between indenter and microbeam) on the stress intensity factor and to evaluate different nanoindenter geometries.
RkJQdWJsaXNoZXIy MjM0NDE=