ICAMS / Interdisciplinary Centre for Advanced Materials Simulation

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Modelling size effect on fracture toughness in semi-brittle crystals by dislocation dynamics

Date: 01.09.2008
Place: Materials Science and Engineering 2008, Nürnberg

Xiaohui Zeng
Alexander Hartmaier

A two-dimensional combined dislocation dynamics / cohesive zone model is employed to analyze the competition between inter- and intra-granular fracture in tungsten polycrystals with pre-existing sharp and blunted cracks at ambient temperature. The study relies on quantifying the influence of grain size and blunting radius on the fracture toughness for a wide range of loading rates. Plasticity is modeled based on the nucleation and motion of individual dislocations in the complex stress field of the material containing a crack. The resulting boundary value problem for the pre-existing crack and the cohesive zones is solved by the method of virtual dislocations. Grain boundaries are introduced as impenetrable obstacles to dislocation motion, against which dislocations may pile up. The density of dislocations in the pile-up is influenced by the stress field and thus by the blunting radius. This dislocation pile-up causes decohesion forces across the grain boundary. Depending on the characteristics of the pile-up and the cohesive strength of the grain boundary, this can result in the generation of new cracks at grain boundaries. The different fracture mechanisms are analyzed for a wide range of grain sizes and blunting radii. A quantitative scaling behavior of fracture toughness with the two length scales is discussed in detail.

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