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Title:Anisotropic elastic properties of crystals | Prof. Rajesh Prasad, IIT Delhi | Dept. MEMS, IIT Bombay
Duration:02:01:12
Viewed:45
Published:30-07-2021
Source:Youtube

Abstract of the talk

Crystalline materials are inherently anisotropic in their physical and mechanical properties. In this talk, we will focus on the anisotropy of Young’s modulus, Poisson’s ratio and biaxial modulus. An introduction to handle this anisotropy in tensor formalism will be given. It will be shown that Young’s modulus of any crystal, including cubic crystals, depend upon the direction of the applied stress. Similarly, the Poisson’s ratio depends upon both the loading and transverse directions and can be negative as well as greater than 0.5. Thin films and coatings generally develop a state of biaxial strain during or after the deposition process. Thus, the biaxial modulus (M) is also an important anisotropic elastic property. For polycrystalline thin films and coatings, the effective biaxial moduli such as the Voigt and Reuss bounds are widely used. The coincidence of the Voigt and Reuss bounds of the effective moduli gives exact relations between the moduli of the polycrystal and single crystal. Prior to our work, it was believed that only planes normal to three-, four- and six- fold axes have coinciding bounds. The present study reports that planes without symmetry can also have coinciding bounds. For a general fiber-textured thin film, with the free surface boundary conditions, it is shown that the Voigt assumption of identical strain states in each grain cannot be made, as has been done in previous studies. Under these conditions, a new method to estimate the polycrystalline average of the biaxial modulus under equibiaxial strain is proposed. Novel three-dimensional surfaces representing the averages of the biaxial moduli as functions of the orientation of the fiber axis are illustrated. Although generally anisotropic, it is well known that the biaxial modulus is isotropic along planes with three-, four- and six- fold symmetry. However, here we demonstrate the existence of isotropy in planes without symmetry

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