Grain-Scale Modeling Approaches for Polycrystalline Aggregates

In polycrystalline aggregates microstructure plays an important role in the evolution of stresses and strains and consequently development of damage processes such as for example evolution of microstructurally small cracks and fatigue. Random grain shapes and sizes, combined with different crystallographic orientations, inclusions, voids and other microstructural features result in locally anisotropic behavior of the microstructure with direct influence on the damage initialization and evolution (Hussain, 1997; Hussain et al., 1993; King et al., 2008a; Miller, 1987). To account for these effects grain-scale or meso-scale models of polycrystalline aggregates are being developed and are increasingly being used. In this chapter we present some of the most often used approaches to modeling polycrystalline aggregates, starting from more simplistic approaches and up to the most state-of-the art approaches that draw on the as-measured properties of the microstructure. The models are usually based on the finite element approach and differ by a) the level to which they account for the complex geometry of polycrystalline aggregates and b) the sophistication of the used constitutive model. In some approaches two dimensional models are used with grains approximated using simple geometrical shapes like rectangles (Bennett & McDowell, 2003; Potirniche & Daniewicz, 2003) and hexagons (Sauzay, 2007; Shabir et al., 2011). More advanced approaches employ analytical geometrical models like Voronoi tessellation in 2D (Simonovski & Cizelj, 2007; Watanabe et al., 1998) and 3D (Cailletaud et al., 2003; Diard et al., 2005; Kamaya & Itakura, 2009; Simonovski & Cizelj, 2011a). In the most advanced approaches, however, grain geometry is based on experimentally obtained geometry (Lewis & Geltmacher, 2006; Qidwai et al., 2009; Simonovski & Cizelj, 2011b) using methods such as serial sectioning or X-ray diffraction contrast tomography (DCT) (Johnson et al., 2008; Ludwig et al., 2008). These approaches are often referred to as "image-based computational modeling" and can also embed in the model measured properties such as crystallographic orientations. The acquired information is of immense value for advancing our understanding of materials and for developing advanced multiscale computational models. The rather high level of available details may render extremely complex geometries, resulting in highly challenging preparation of finite element (FE) models (Simonovski & Cizelj, 2011a) and computationally extremely demanding simulations. These two constraints have so far limited the development and use 2 Polycrystalline Materials of the image-based models. Steps aimed at obtaining a ’reasonable’ size model in the terms of computational times are presented. The term ’reasonable’ should be taken in relative terms as these models may still run for several days on today’s high performance clusters.

SIMONOVSKI Igor;  CIZELJ Leon; 

2012-02-14

InTech

JRC66780

978-953-307-934-9,