Anisotropy
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Anisotropy Alexander Brosius1 and Dorel Banabic2 1 Institute of Manufacturing Science and Engineering, TU Dresden, Chair of Forming and Machining Technology, Dresden, Germany 2 CERTETA-Research Center in Sheet Metal Forming, Technical University of Cluj Napoca, Romania, Cluj Napoca, Romania
Synonyms Orthotropy
Definition As the opposite of isotropy, the term anisotropy defines the dependency between the material response for a defined loading level and the loading direction.
forming, the anisotropic behavior comes more and more into picture and is also limited to the orthotropic type. The elastic region is assumed as isotropic usually because the influence on the forming process itself is negligible. Because anisotropic behavior plays a very important role in sheet metal forming, in the following, only this type of semifinished products and the related application in theory and application will be mentioned. As mentioned before, anisotropic behavior in sheets is an orthotropic system, sometimes also called as “orthorhombic” symmetrical system. That means along the symmetry planes, equality between left and right is taken place (Lange 1990). In general, an orthotropic material can be identified by the attribute of uncoupling between normal and shear components – the coupling coefficients of C (e.g., C 14) in the following equation are equal to zero: s¼Ce
Theory and Application Introduction One can distinguish between a “general” anisotropic and an orthotropic material behavior. In sheet metal forming, one can usually assume orthotropic behavior in the elastic-plastic behavior due to the production process of the semifinished part by means of rolling. For bulk metal
(1)
To describe this kind of anisotropic material behavior precisely, the yield surface is needed. For quite simple but well-known and established yield surfaces, the so-called r-values are used to describe this behavior. The r-value (normal anisotropy) is defined by the ratio of width to thickness strain (measured as true strains). The index indicates the angle between drawing and
# CIRP 2016 The International Academy for Production Engineering et al. (eds.), CIRP Encyclopedia of Production Engineering, DOI 10.1007/978-3-642-35950-7_6679-3
2
Anisotropy
rolling direction of the material. Usually, the r-values are determined in 0 , 45 , and 90 . The mean normal anisotropy is defined as 1 r ¼ ðr 0 þ 2r 45 þ r 90 Þ 4
(2)
and can be used to evaluate the formability in deep drawing. The next defined indicator is the planar anisotropy Dr as Dr ¼ ðr r 45 Þ
(3)
regarding the tendency to earing during deep drawing. Because most of modern high-strength materials show great differences in the biaxial stress point, a biaxial anisotropic coefficient is defined as rb ¼
er et
For the case of an isotropic metallic material, the well-known von Mises yield criterion is often sufficient to describe yielding. This is, however, not true for anisotropic materials, especially aluminum sheet metals. In order to take into account anisotropy, the classical yield criterio
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