Representation of Hashin–Shtrikman Bounds in Terms of Texture Coefficients for Arbitrarily Anisotropic Polycrystalline Materials

Journal of Elasticity - Tập 134 Số 1 - Trang 1-38 - 2019
Mauricio Fernández1, Thomas Böhlke2
1EMMA—Efficient Methods for Mechanical Analysis, Institute of Applied Mechanics (CE), University of Stuttgart, Stuttgart, Germany
2Chair for Continuum Mechanics, Institute of Engineering Mechanics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

Tóm tắt

Từ khóa


Tài liệu tham khảo

Adams, B.L., Boehler, J., Guidi, M., Onat, E.: Group theory and representation of microstructure and mechanical behavior of polycrystals. J. Mech. Phys. Solids 40(4), 723–737 (1992)

Adams, B.L., Kalidindi, S.R., Fullwood, D.T.: Microstructure Sensitive Design for Performance Optimization. Butterworth-Heinemann, Waltham (2013). https://doi.org/10.1016/B978-0-12-396989-7.00001-0

Böhlke, T.: Application of the maximum entropy method in texture analysis. Comput. Mater. Sci. 32(3–4), 276–283 (2005). https://doi.org/10.1016/j.commatsci.2004.09.041

Böhlke, T.: Texture simulation based on tensorial Fourier coefficients. Comput. Struct. 84(17–18), 1086–1094 (2006). https://doi.org/10.1016/j.compstruc.2006.01.006

Böhlke, T., Haus, U.U., Schulze, V.: Crystallographic texture approximation by quadratic programming. Acta Mater. 54(5), 1359–1368 (2006). https://doi.org/10.1016/j.actamat.2005.11.009

Böhlke, T., Lobos, M.: Representation of Hashin–Shtrikman bounds of cubic crystal aggregates in terms of texture coefficients with application in materials design. Acta Mater. 67, 324–334 (2014). https://doi.org/10.1016/j.actamat.2013.11.003

Bröcker, T., tom Dieck, T.: Representations of Compact Lie Groups. Springer, Berlin, Heidelberg (1985)

Bunge, H.J.: Texture Analysis in Materials Science: Mathematical Methods. Butterworth, London (1982)

Cheng, L., Assary, R.S., Qu, X., Jain, A., Ong, S.P., Rajput, N.N., Persson, K., Curtiss, L.A.: Accelerating electrolyte discovery for energy storage with high-throughput screening. J. Phys. Chem. Lett. 6(2), 283–291 (2015). https://doi.org/10.1021/jz502319n

Eschner, T., Fundenberger, J.J.: Application of anisotropic texture components. Textures Microstruct. 28(C), 181–195 (1997)

Forte, S., Vianello, M.: Symmetry classes for elasticity tensors. J. Elast. 43(2), 81–108 (1996). https://doi.org/10.1007/BF00042505

Forte, S., Vianello, M.: Symmetry classes and harmonic decomposition for photoelasticity tensors. Int. J. Eng. Sci. 35(14), 1317–1326 (1997). https://doi.org/10.1016/S0020-7225(97)00036-0

Fullwood, D.T., Niezgoda, S.R., Adams, B.L., Kalidindi, S.R.: Microstructure sensitive design for performance optimization. Prog. Mater. Sci. 55(6), 477–562 (2010). https://doi.org/10.1016/j.pmatsci.2009.08.002

Gel’fand, I.M., Minlos, R., Shapiro, Z.: Representations of the Rotation and Lorentz Groups and Their Applications. Pergamon Press, Oxford (1963)

Guidi, M., Adams, B.L., Onat, E.T.: Tensorial representation of the orientation distribution function in cubic polycrystals. Textures Microstruct. 19(3), 147–167 (1992). https://doi.org/10.1155/TSM.19.147

Hashin, Z., Shtrikman, S.: A variational approach to the theory of the elastic behaviour of polycrystals. J. Mech. Phys. Solids 10(4), 343–352 (1962). https://doi.org/10.1016/0022-5096(62)90005-4

Hashin, Z., Shtrikman, S.: On some variational principles in anisotropic and nonhomogeneous elasticity. J. Mech. Phys. Solids 10(4), 335–342 (1962)

Hashin, Z., Shtrikman, S.: A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11(2), 127–140 (1963)

Helming, K.: Some applications of the texture component model. Mater. Sci. Forum 157(162), 363–368 (1994). https://doi.org/10.4028/www.scientific.net/MSF.157-162.363

Hill, R.: Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 11(5), 357–372 (1963)

Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge Univ. Press, Cambridge (1990)

Huang, M., Man, C.S.: Explicit bounds of effective stiffness tensors for textured aggregates of cubic crystallites. Math. Mech. Solids 13(5), 408–430 (2007). https://doi.org/10.1177/1081286507078299

Jain, A., Ong, S.P., Hautier, G., Chen, W., Richards, W.D., Dacek, S., Cholia, S., Gunter, D., Skinner, D., Ceder, G., Persson, K.A.: Commentary: the materials project: a materials genome approach to accelerating materials innovation. APL Mater. 1(1), 011002 (2013). https://doi.org/10.1063/1.4812323

de Jong, M., Chen, W., Angsten, T., Jain, A., Notestine, R., Gamst, A., Sluiter, M., Krishna Ande, C., van der Zwaag, S., Plata, J.J., Toher, C., Curtarolo, S., Ceder, G., Persson, K.A., Asta, M.: Charting the complete elastic properties of inorganic crystalline compounds. Sci. Data 2, 1–13 (2015). https://doi.org/10.1038/sdata.2015.9

Kalidindi, S.R., Knezevic, M., Niezgoda, S., Shaffer, J.: Representation of the orientation distribution function and computation of first-order elastic properties closures using discrete Fourier transforms. Acta Mater. 57(13), 3916–3923 (2009). https://doi.org/10.1016/j.actamat.2009.04.055

Kröner, E.: Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls. Z. Phys. 151(4), 504–518 (1958)

Kröner, E.: Bounds for effective elastic moduli of disordered materials. J. Mech. Phys. Solids 25(2), 137–155 (1977). https://doi.org/10.1016/0022-5096(77)90009-6

Kröner, E.: Self-consistent scheme and graded disorder in polycrystal elasticity. J. Phys. F, Met. Phys. 8, 2261–2267 (1978)

Lobos, M., Böhlke, T.: Materials design for the anisotropic linear elastic properties of textured cubic crystal aggregates using zeroth-, first- and second-order bounds. Int. J. Mech. Mater. Des. 11(1), 59–78 (2015). https://doi.org/10.1007/s10999-014-9272-z

Lobos, M., Böhlke, T.: On optimal zeroth-order bounds of linear elastic properties of multiphase materials and application in materials design. Int. J. Solids Struct. 84, 40–48 (2016). https://doi.org/10.1016/j.ijsolstr.2015.12.015

Lobos, M., Yuzbasioglu, T., Böhlke, T.: Homogenization and materials design of anisotropic multiphase linear elastic materials using central model functions. J. Elast. 128(1), 17–60 (2017). https://doi.org/10.1007/s10659-016-9615-0

Lobos Fernández, M.: Homogenization and materials design of mechanical properties of textured materials based on zeroth-, first- and second-order bounds of linear behavior. Doctoral thesis, Karlsruhe Institute of Technology, Karlsruhe, Germany (2018, in press)

Man, C.S.: On the constitutive equations of some weakly-textured materials. Arch. Ration. Mech. Anal. 143, 77–103 (1998)

Man, C.S., Huang, M.: A simple explicit formula for the Voigt–Reuss–Hill average of elastic polycrystals with arbitrary crystal and texture symmetries. J. Elast. 105(1–2), 29–48 (2011). https://doi.org/10.1007/s10659-011-9312-y

Man, C.S., Huang, M.: A representation theorem for material tensors of weakly-textured polycrystals and its applications in elasticity. J. Elast. 106(1), 1–42 (2012). https://doi.org/10.1007/s10659-010-9284-3

Mardia, K.V., Jupp, P.E.: Directional Statistics. Wiley, London (2008)

Matthies, S., Muller, J., Vinel, G.: On the normal distribution in the orientation space. Textures Microstruct. 10(1), 77–96 (1988)

Mehrabadi, M.M., Cowin, S.C.: Eigentensors of linear anisotropic elastic materials. Q. J. Mech. Appl. Math. 43(1), 15–41 (1990). https://doi.org/10.1093/qjmam/43.1.15

Milton, G.W.: The Theory of Composites, vol. 6. Cambridge University Press, Cambridge (2002). https://doi.org/10.1017/CBO9780511613357

Müller, V., Böhlke, T.: Prediction of effective elastic properties of fiber reinforced composites using fiber orientation tensors. Compos. Sci. Technol. 130, 36–45 (2016). https://doi.org/10.1016/j.compscitech.2016.04.009

Nadeau, J., Ferrari, M.: On optimal zeroth-order bounds with application to Hashin–Shtrikman bounds and anisotropy parameters. Int. J. Solids Struct. 38(44–45), 7945–7965 (2001). https://doi.org/10.1016/S0020-7683(00)00393-0

Niezgoda, S.R., Kanjarla, A.K., Kalidindi, S.R.: Novel microstructure quantification framework for databasing, visualization, and analysis of microstructure data. Integr. Mater. Manuf. Innov. 2(1), 3 (2013). https://doi.org/10.1186/2193-9772-2-3

Nomura, S., Kawai, H., Kimura, I., Kagiyama, M.: General description of orientation factors in terms of expansion of orientation distribution function in a series of spherical harmonics. J. Polym. Sci., Part A-2, Polym. Phys. 8(3), 383–400 (1970). https://doi.org/10.1002/pol.1970.160080305

Ponte Castañeda, P., Suquet, P.: Nonlinear composites. Adv. Appl. Mech. 34, 171–302 (1997)

Reuss, A.: Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle Z. Angew. Math. Mech. 9(1), 49–58 (1929)

Roe, R.J.: Description of crystallite orientation in polycrystalline materials. III. General solution to pole figure inversion. J. Appl. Phys. 36(6), 2024 (1965). https://doi.org/10.1063/1.1714396

Schaeben, H.: Texture approximation or texture modelling with components represented by the von Mises-Fisher matrix distribution on SO(3) and the Bingham distribution on S4+. J. Appl. Crystallogr. 29(5), 516–525 (1996). https://doi.org/10.1107/S0021889896002804

Schaeben, H., van den Boogaart, K.G.: Spherical harmonics in texture analysis. Tectonophysics 370(1), 253–268 (2003). https://doi.org/10.1016/S0040-1951(03)00190-2

Schouten, J.A.: Der Ricci-Kalkül. Springer, Berlin (1924). https://doi.org/10.1007/978-3-662-06545-7

Torquato, S.: Random Heterogeneous Materials: Microstructure and Macroscopic Properties. Springer, New York (2002)

Varshalovich, D., Moskalev, A.N., Khersonskii, V.K.: Quantum Theory of Angular Momentum. World Scientific, Singapore (1988)

Voigt, W.: Lehrbuch der Kristallphysik (mit Ausschluss der Kristalloptik). Teubner, Leipzig (1910)

Walpole, L.J.: On bounds for the overall elastic moduli of inhomogeneous systems—I. J. Mech. Phys. Solids 14(3), 151–162 (1966)

Wassermann, G., Grewen, J.: Texturen metallischer Werkstoffe, 2nd edn. Springer, Berlin, Heidelberg (1962). https://doi.org/10.1007/978-3-662-13128-2

Wigner, E.P.: Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektrum. Vieweg+Teuber, Wiesbaden (1931)

Willis, J.R.: Bounds and self-consistent estimates for the overall properties of anisotropic composites. J. Mech. Phys. Solids 25(3), 185–202 (1977). https://doi.org/10.1016/0022-5096(77)90022-9

Willis, J.R.: Variational and related methods for the overall properties of composites. Adv. Appl. Mech. 21, 1–78 (1981)

Yabansu, Y.C., Kalidindi, S.R.: Representation and calibration of elastic localization kernels for a broad class of cubic polycrystals. Acta Mater. 94, 26–35 (2015). https://doi.org/10.1016/j.actamat.2015.04.049

Zheng, Q.S., Fu, Y.B.: Orientation distribution functions for microstructures of heterogeneous m materials (II)—crystal distribution functions and irreducible tensors restricted by various material symmetries. Appl. Math. Mech. 22(8), 885–902 (2001)