A procedure for estimating Young’s modulus of textured polycrystalline materials Masayuki Kamaya * Institute of Nuclear Safety System, Inc., 64 Sata, Mihama-cho, Mikata-gun, Fukui 919-1205, Japan article info Article history: Received 24 September 2008 Received in revised form 13 February 2009 Available online 28 February 2009 Keywords: Young’s modulus Elastic moduli Polycrystalline aggregate Anisotropic elasticity Finite element analysis Stainless steel EBSD abstract In this study, a procedure for estimating Young’s modulus of textured and non-textured polycrystalline materials was examined based on finite element analyses, which were performed using three-dimen- sional polycrystalline finite element models of a random structure, generated using the Voronoi tessel- lation. Firstly, the local stress/strain distribution and its influence on macroscopic elastic properties were evaluated. Then, the statistical relationship between Young’s modulus obtained from the finite element analyses and averaged Young’s modulus of all grains evaluated based on Voigt’s or Reuss’ model was investigated. It was revealed that the local stress/strain in the polycrystalline body is affected by crystal orientation and deformation constraint caused by adjacent grains, whereas only the crystal orientation affects Young’s modulus of the polycrystalline body when the number of grains is large enough. It was also shown that Young’s modulus correlates well with the averaged Young’s modulus of all grains, in which the size of grains is considered in the averaging. Finally, a procedure for estimating Young’s modulus of textured and non-textured materials was proposed. Young’s modu- lus of various materials can be estimated from the elastic constants of single crystal and the distribu- tion of crystal orientation and size of grains, which can be obtained by using electron backscatter diffraction (EBSD). Æ 2009 Elsevier Ltd. All rights reserved. 1. Introduction Since a polycrystalline material is an aggregate of crystal grains of various sizes and shapes, its macroscopic properties are affected by the properties of individual grains. The elastic deformation of a sin- gle crystal exhibits anisotropy in most materials and depends on the orientation of the crystal. However, the macroscopic behavior of polycrystalline materials can be regarded as isotropic and homoge- neous in terms of elastic deformation when the materials have ran- dom crystallographic and morphologic texture. The influence of the crystal orientation of individual grains on the elasticity of the aggre- gate is minor. Therefore, for engineering structural materials, we consider not the properties of individual grains but those of their aggregate, such as Young’s modulus and Poisson’s ratio. However, this assumption may not be true when the material does not consist of a sufficient number of grains. Young’s modulus of a micro-structure consisting of a small number of grains is depen- dent on the crystal orientations of individual grains in addition to the elasticity of a single crystal (Mullen et al., 1997; Nygårds, 2003). Even if the number of grains is large enough, Young’s modulus is influ- enced by the crystal orientation of each grain for the textured mate- rial. In order to estimate Young’s modulus of such structures, it is important to identify local properties, which are the elasticity and crystal orientation of each grain. Although it is difficult to identify the crystal orientations of all grains, a statistical distribution of crys- tal orientation can be obtained by using X-ray diffraction or electron backscatter diffraction (EBSD). Once the crystal orientation of each grain or its statistical distri- bution is identified, Young’s modulus of the aggregate can be eval- uated by averaging Young’s modulus of each grain (hereafter, local Young’s modulus) based on a geometrical assumption. However, as explained in detail later, the geometrical condition (uniform local strain or stress) in a polycrystal is not obvious due to the complex- ity of the geometrical structure of a crystal grain. Furthermore, the complex geometry causes nonuniform stress at the microstructural level even under a uniform remote stress condition (Hashimoto and Margolin, 1983; Nichols et al., 1991; Sarma et al., 1998; Schroeter and McDowell, 2003; Kanit et al., 2003; Kamaya et al., 2007). The deformation constraint caused by neighboring grains as well as the variation in local Young’s modulus induces large stress (or strain) near the grain boundary (Barbe et al., 2001; Diard et al., 2005; Kamaya, 2009). Such nonuniform stress may affect the macroscopic Young’s modulus. In order to quantify the effect of complex geometry and the local stress distribution in the polycrystalline material, it is necessary to use a numerical approach such as the finite element method. It has been shown that the local stress and strain distribution can be solved by using a reconstructed model of the grain structure and crystal orientations (Sumigawa et al., 2004; Zhao and Tryon, 2004; Lewis et al., 2005; Musienko et al., 2007; St-Pierre et al., 2008). Several attempts have been made to evaluate Young’s 0020-7683/$ - see front matter Æ 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijsolstr.2009.02.013 * Tel.: +81 770 379114; fax: +81 770 372009. E-mail address: kamaya@inss.co.jp International Journal of Solids and Structures 46 (2009) 2642–2649 Contents lists available at ScienceDirect International Journal of Solids and Structures journal homepage: www.elsevier.com/locate/ijsolstr