References
- R.N. Gunn, Duplex Stainless Steels – Microstructure, Properties and Applications, Woodhead Publishing Ltd., 1997.
- International Molybdenum Association, Practical Guidelines for the Fabrication of Duplex Stainless Steel, International Molybdenum Association, 2014.
- J.O. Nilsson, Super duplex stainless steels, Mater. Sci. Technol. 8 (1992), pp. 685–700. doi: 10.1179/mst.1992.8.8.685
- M. Mola, Numerische Legierungsentwicklung eines nickelreduzierten Duplex-Stahls, Europ. Univ.-Verlag, 2005.
- F. Feyel and J.L. Chaboche, FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials, Comput. Methods. Appl. Mech. Eng. 183 (2000), pp. 309–330. Available at https://doi.org/10.1016/s0045-7825(99)00224-8
- H. Moulinec and P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput. Methods. Appl. Mech. Eng. 157 (1998), pp. 69–94. Available at https://doi.org/10.1016/s0045-7825(97)00218-1
- J. Schröder, D. Balzani and D. Brands, Approximation of random microstructures by periodic statistically similar representative volume elements based on lineal-path functions, Archive Appl. Mech.81 (2010), pp. 975–997. Available at https://doi.org/10.1007/s00419-010-0462-3
- J. Michel and P. Suquet, Nonuniform transformation field analysis, Int. J. Solids. Struct. 40 (2003), pp. 6937–6955. Available at https://doi.org/10.1016/s0020-7683(03)00346-9
- W. Voigt, Ueber die Beziehung zwischen den beiden Elasticitätsconstanten isotroper Körper, Ann. Phys. 274 (1889), pp. 573–587. Available at https://doi.org/10.1002/andp.18892741206
- A. Reuss, Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle., ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik 9 (1929), pp. 49–58. Available at https://doi.org/10.1002/zamm.19290090104
- Z. Hashin and S. Shtrikman, A variational approach to the theory of the elastic behaviour of polycrystals, J. Mech. Phys. Solids. 10 (1962), pp. 343–352. Available at https://doi.org/10.1016/0022-5096(62)90005-4
- J. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. Lond. A. Math. Phys. Sci. 241 (1957), pp. 376–396. Available at https://doi.org/10.1098/rspa.1957.0133
- E. Kröner, Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls, Zeitschrift für Physik 151 (1958), pp. 504–518. Available at https://doi.org/10.1007/bf01337948
- T. Mori and K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica 21 (1973), pp. 571–574. Available at https://doi.org/10.1016/0001-6160(73)90064-3
- G. Lielens, Micro-Macro Modeling of Structured Materials, Universite Catholique de Louvain, 1999.
- O. Pierard, C. Friebel and I. Doghri, Mean-field homogenization of multi-phase thermo-elastic composites: a general framework and its validation, Compos. Sci. Technol. 64 (2004), pp. 1587–1603. Available at https://doi.org/10.1016/j.compscitech.2003.11.009
- N. Simon, H. Erdle, S. Walzer, J. Gibmeier, T. Böhlke and M. Liewald, Phase-specific residual stresses induced by deep drawing of lean duplex steel: measurement vs. simulation, Product. Engin. 13 (2019), pp. 227–237. Available at https://doi.org/10.1007/s11740-019-00877-4
- J. Chaboche, Unified cyclic viscoplastic constitutive equations: development, capabilities, and thermodynamic framework, in Unified Constitutive Laws of Plastic Deformation, Elsevier, 1996, pp. 1–68. Available at https://doi.org/10.1016/b978-012425970-6/50002-3.
- V. Glavas, Micromechanical Modeling and Simulation of Forming Processes, Kontinuumsmechanik im Maschinenbau Vol. 8, KIT Scientific Publishing, 2016. Available at https://doi.org/10.5445/ksp/1000061958.
- R. Hill, The elastic behaviour of a crystalline aggregate, Proc. Phys. Soc. Sect. A 65 (1952), pp. 349–354. Available at https://doi.org/10.1088/0370-1298/65/5/307
- S. Nemat-Nasser and M. Hori, Micromechanics: Overall Properties of Heterogeneous Materials (North-Holland Series in Applied Mathematics and Mechanics), North Holland, 1999.
- E. Kröner, Statistical Continuum Mechanics, Springer, Vienna, 1971. Available at https://doi.org/10.1007/978-3-7091-2862-6.
- P.P. Castañeda and P. Suquet, Nonlinear composites, in Advances in Applied Mechanics, Elsevier, 1997, pp. 171–302. Available at https://doi.org/10.1016/s0065-2156(08)70321-1.
- A. Bertram, Elasticity and Plasticity of Large Deformations, 3rd ed., Springer, Berlin, Heidelberg, 2012. Available at https://doi.org/10.1007/978-3-642-24615-9.
- Simulia, Abaqus Theory Manual, Dassault Systèmes, 2011.
- F. Meissonnier, E. Busso and N. O'Dowd, Finite element implementation of a generalised non-local rate-dependent crystallographic formulation for finite strains, Inter. J. Plasticity 17 (2001), pp. 601–640. Available at https://doi.org/10.1016/s0749-6419(00)00064-4
- W. Ji, A.M. Waas and Z.P. Bazant, On the importance of work-conjugacy and objective stress rates in finite deformation incremental finite element analysis, J. Appl. Mech.80 (2013), pp. 041024. Available at https://doi.org/10.1115/1.4007828
- T. Böhlke, G. Bondár, Y. Estrin and M. Lebyodkin, Geometrically non-linear modeling of the Portevin–Le Chatelier effect, Comput. Mater. Sci. 44 (2009), pp. 1076–1088. Available at https://doi.org/10.1016/j.commatsci.2008.07.036
- P.M. Pinsky, M. Ortiz and K.S. Pister, Numerical integration of rate constitutive equations in finite deformation analysis, Comput. Methods. Appl. Mech. Eng. 40 (1983), pp. 137–158. Available at https://doi.org/10.1016/0045-7825(83)90087-7
- C. Miehe, D. Rosato and I. Frankenreiter, Fast estimates of evolving orientation microstructures in textured bcc polycrystals at finite plastic strains, Acta. Mater. 58 (2010), pp. 4911–4922. Available at https://doi.org/10.1016/j.actamat.2010.05.004
- G.H. Golub and C.F. Van Loan, Matrix Computations, 4th ed., John Hopkins Studies in the Mathematical Sciences, John Hopkins University Press, 2012.
- T. Mente, Numerische Simulation der wasserstoffunterstützten Rissbildung in austenitisch-ferritischen Duplexstählen, BAM-Dissertationsreihe Vol. 129, BAM Bundesanstalt für Materialforschung und -prüfung, 2015.
- S. Pulvermacher, J. Gibmeier, J. Saroun, J.R. Kornmeier, F. Vollert and T. Pirling, Neutron Strain Scanning of Duplex Steel Subjected to 4-Point-Bending with Particular Regard to the Strain Free Lattice Parameter D0, in Residual Stresses 2018, Sep. Materials Research Forum LLC, 2018. Available at https://doi.org/10.21741/9781945291890-3.
- Iron and Steels Standard Committee, Open die steel forgings for general engineering purposes – part 4: stainless steels (DIN EN 10250-4:2018-10), 2018.
- L. Moreira, G. Ferron and G. Ferran, Experimental and numerical analysis of the cup drawing test for orthotropic metal sheets, J. Mater. Process. Technol. 108 (2000), pp. 78–86. Available at https://doi.org/10.1016/s0924-0136(00)00660-9
- A. Niku-Lari, J. Lu and J. Flavenot, Measurement of residual-stress distribution by the incremental hole-drilling method, J. Mech. Working Technol. 11 (1985), pp. 167–188. Available at https://doi.org/10.1016/0378-3804(85)90023-3
- I. Gil, J. Mendiguren, L. Galdos, E. Mugarra and E.S. de Argandoña, Influence of the pressure dependent coefficient of friction on deep drawing springback predictions, Tribol. Int. 103 (2016), pp. 266–273. Available at https://doi.org/10.1016/j.triboint.2016.07.004