Abstract
The process of plastic flow localization in a composite material consisting of welded steel and copper plates under shear strain is considered. The mathematical model of this physical process is formulated. A new numerical algorithm based on the Courant–Isaacson–Rees scheme is proposed. The algorithm is verified using three test problems. The algorithm efficiency and performance are proved by the test simulations. The proposed algorithm is used for numerical simulation of plastic strain localization on composite materials. The influence of boundary conditions, the initial plastic strain rate, and the width of the materials forming the composite bar on the localization process is studied. It is demonstrated that at the initial stage, the shear velocity for the material layers varies. Theoretical estimates of the oscillation frequency and period are proposed; the calculations using these estimates agree completely with the numerical experiments. It is established that the deformation is localized in the copper part of the composite. One or two localization regions situated at a typical distance from the boundaries are formed, depending on the width of the steel and copper parts, as well as the initial plastic strain rate and the chosen boundary conditions. The dependence of this distance on the initial plastic strain rate is demonstrated and corresponding estimates for boundary conditions of two types are obtained. It is established that in the case of two localization regions, the temperature and deformation in one of them increase much faster than in the other, while at the initial stage these quantities are nearly equal in both regions.
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References
Schneider, J. and Nunes, J.A., Characterization of plastic flow and resulting microtextures in a friction stir weld, Metall. Mater. Trans. B., 2004, vol. 35, pp. 777–783.
Seidel, T. and Reynolds, A., Visualization of the material flow in aa2195 friction stir welds using a marker insert technique, Metall. Mater. Trans., 2001, vol. 32A, pp. 2879–2884.
Moss, G., Shear strains, strain rates, temperature changes in adiabatic shear bands, in Waves and High Strain Rate Phenomena in Metals, Meyers, L. and MurrShock, L., Eds., Springer, 1981.
Rogers, H.C., Adiabatic plastic deformation, Annu. Rev. Mater. Sci., 1979, vol. 9.
Bai, Y. and Dodd, B., Adiabatic Shear Localization, Pergamon Press, Oxford, 1992.
Lee, W.S., Liu, C.Y., and Chen, T.C., Adiabatic shearing bends havior of different steels under extreme high shear loading, J. Nuclear Mater., 2008, vol. 374, pp. 313–319.
Gupta, G., Was, G.S., and Alexandreanu, B., Grain boundary engineering of ferritiction martensitic alloy T91, Metall. Mater. Trans. A, 2004, vol. 35, pp. 717–719.
Rittel, D., Adiabatic shear failure of a syntactic polymeric foam, Mater. Lett., 2005, vol. 59, pp. 723–732.
Shockey, D.A., et al., Shear failure of inconel 718 under dynamic loads, Exp. Mech., 2007, vol. 47, pp. 723–732.
Wright, T.W., The Physics and Mathematics of Adiabatic Shear Bands, Cambridge University Press, 2002.
Marchand, A. and Duffy, J., An experimental study of the formation process of adiabatic shear bands in a structural steel, J. Mech. Phys. Solids, 1988, vol. 36, pp. 251–283.
Kolsky, H., An investigation of the mechanical properties of materials at very. High rates of loading, Proc. Phys. Soc., 1949, vol. 62-B, p. 676.
Nesterenko, V.F. and Bondar, M.P., Investigation of deformation localization by the ‘thick-walled cylinder’ method, DYMAT J., 1994, vol. 1, pp. 245–251.
Zhou, F., Wright, T.W., and Ramesh, K.T., A numerical methodology for investigating the formation of adiabatic shear bands, J. Mech. Phys. Solids, 2006, vol. 54, pp. 904–926.
Zhou, F., Wright, T.W., and Ramesh, K.T., The formation of multiple adiabatic shear bands, J. Mech. Phys. Solids, 2006, vol. 54, pp. 1376–1400.
Batra, R.C. and Wei, Z.G., Shear bands due to heat flux prescribed at boundaries, Int. J. Plast., 2006, vol. 22, pp. 1–15.
Kudryashov, N.A., Ryabov, P.N., and Zakharchenko, A.S., Self-organization of adiabatic shear bands in OFHC copper and HY-100 steel, J. Mech. Phys. Solids, 2015, vol. 76, pp. 180–192.
Walter, J.W., Numerical experiments on adiabatic shear band formation in one dimension, Int. J. Plast., 1992, vol. 8, pp. 657–693.
Rozhdestvenskii, B.L. and Yanenko, N.N., Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike (Systems of Quasilinear Equations and Their Applications to Gas Dynamics), Moscow: Nauka, 1978.
Koshkin, V.I., Kudryashov, N.A., and Ryabov, P.N., Numerical simulation of the formation of adiabatic shear bands under deformations, Yad. Fiz. Inzh., 2010, vol. 1, pp. 465–474.
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Original Russian Text © N.A. Kudryashov, R.V. Muratov, P.N. Ryabov, 2016, published in Modelirovanie i Analiz Informatsionnykh Sistem, 2016, Vol. 23, No. 3, pp. 298–308.
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Kudryashov, N.A., Muratov, R.V. & Ryabov, P.N. Numerical Simulation of Adiabatic Shear-Band Formation in Composites. Aut. Control Comp. Sci. 51, 614–620 (2017). https://doi.org/10.3103/S0146411617070136
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DOI: https://doi.org/10.3103/S0146411617070136