The Influence of the Grain Structure Size on Microstructurally Short Cracks

The dominant processes in the initialization and propagation of microstructurally short cracks include microstructural features such as crystallographic orientations of grains, grain boundaries, inclusions, voids, material phases, etc. The influence of the microstructural features is expected to vanish with distance from the crack tip. Also, the influence of the nearby microstructural features is expected to be smaller for a long than for a small crack. Finally, a crack of sufficient length can be modeled using classical fracture mechanic methods. In this paper the approach to estimate the crack length with vanishing influence from the microstructural feature is proposed. To achieve this, a model containing a large number of randomly sized, shaped, and oriented grains is employed. The random grain structure is modeled using a Voronoi tessellation. A series of cracks of lengths from about 1 to 7 grain lengths is inserted into the model, extending from a grain at the surface toward the interior of the model. The crack tip opening displacements are estimated and statistically analyzed for a series of random crystallographic orientation sets assigned to the grains adjacent to the crack. Anisotropic elasticity and crystal plasticity constitutive models are employed at the grain size scale. It is shown that the standard deviation of the crack tip opening displacement decreases from about 20% for a short surface crack embedded within a single grain to about 7% for a surface crack extending through seven grains. From the engineering point of view, a crack extending through less than about ten grain sizes is therefore considered to strongly depend on the neighboring microstructural features.