Abstract
The material microstructural interfaces have a profound impact on the scale-dependent yield strength and strain hardening when the surface-to-volume ratio of the medium increases such as in micro and nanosystems. In this paper, the framework of higher-order strain gradient plasticity with interfacial energy effect is used to investigate the coupling of thermal and mechanical responses of materials in small scales and fast transient processes. In addition to the nonlocal yield condition for the material bulk, a temperature and rate dependent microscopic yield condition for the interface is presented, which determines the stress at which the interface begins to deform plastically and harden. In order to address the strengthening and hardening mechanisms, the theory is developed based on the decomposition of the mechanical state variables into energetic and dissipative counterparts. This, consecutively, provides the constitutive equations to have both energetic and dissipative gradient length scales \(\ell _{en}\) and \(\ell _{dis}\) respectively. Hence four material length scales are introduced: two for the bulk and the other two for the interface. In addition, the effect of temperature on the yield strength and hardening of the interface is included in the formulation by postulating that the interfacial energy decreases as temperature increases. Finally the developed framework is solved numerically to investigate the size effect of unaxial loading of a film substrate system.
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Abu Al-Rub, R.K., Faruk, A.N.M.: Coupled interfacial energy and temperature effects on size-dependent yield strength and strain hardening of small metallic volumes. J. Eng. Mater. Technol. Trans. ASME 133(1), (2011). doi:Artn 011017, Doi 10.1115/1.4002651
Aifantis, E.C.: On the role of gradients in the localization of deformation and fracture. Int. J. Eng. Sci. 30(10), 1279–1299 (1992)
Aifantis, K.E., Soer, W.A., De Hosson, J.T.M., Willis, J.R.: Interfaces within strain gradient plasticity: theory and experiments. Acta Materialia 54(19), 5077–5085 (2006). doi:10.1016/j.actamat.2006.06.040
Brorson, S.D., Kazeroonian, A., Moodera, J.S., Face, D.W., Cheng, T.K., Ippen, E.P., Dresselhaus, M.S., Dresselhaus, G.: Femtosecond room-temperature measurement of the electron-phonon coupling constant-lambda in metallic superconductors. Phys. Rev. Lett. 64(18), 2172–2175 (1990)
Cahn, J.W.: Free energy of a nonuniform system. 2. Thermodynamic basis. J. Chem. Phys. 30(5), 1121–1124 (1959)
Cahn, J.W., Hilliard, J.E.: Free energy of a nonuniform system. 1. Interfacial free energy. J. Chem. Phys. 28(2), 258–267 (1958)
Chung, Y.-w.: Introduction to Materials Science and Engineering. CRC, Boca Raton (2007)
De Hosson, J.T.M., Aifantis, K.E., Soer, W.A., Willis, J.R.: Interfaces within strain gradient plasticity: theory and experiments. Acta Materialia 54(19), 5077–5085 (2006). doi:10.1016/j.actamat.2006.06.040
Elsayed-Ali, H.E., Juhasz, T., Smith, G.O., Bron, W.E.: Femtosecond thermoreflectivity and thermotransmissivity of polycrystalline and single-crystalline gold-films. Phys. Rev. B 43(5), 4488–4491 (1991)
Espinosa, H.D., Prorok, B.C., Peng, B.: Plasticity size effects in free-standing submicron polycrystalline FCC films subjected to pure tension. J. Mech. Phys. Solids 52(3), 667–689 (2004). doi:10.1016/j.jmps.2003.07.001
Faghihi, D., Voyiadjis, G.Z.: Determination of nanoindentation size effects and variable material intrinsic length scale for body-centered cubic metals. Mech. Mater. (2011, in press, corrected proof). doi:10.1016/j.mechmat.2011.07.002
Fleck, N.A., Willis, J.R.: A mathematical basis for strain-gradient plasticity theory—part I: scalar plastic multiplier. J. Mech. Phys. Solids 57(1), 161–177 (2009a). doi:10.1016/j.jmps.2008.09.010
Fleck, N.A., Willis, J.R.: A mathematical basis for strain-gradient plasticity theory. Part II: tensorial plastic multiplier. J. Mech. Phys. Solids 57(7), 1045–1057 (2009). doi:10.1016/j.jmps.2009.03.007
Forest, S., Aifantis, E.C.: Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua. Int. J. Solids Struct. 47(25–26), 3367–3376 (2010). doi:10.1016/j.ijsolstr.2010.07.009
Forest, S., Amestoy, M.: Hypertemperature in thermoelastic solids. Comptes Rendus Mecanique 336(4), 347–353 (2008). doi:10.1016/j.crme.2008.01.007
Fredriksson, P., Gudmundson, P.: Size-dependent yield strength and surface energies of thin films. Mater. Sci. Eng. Struct. Mater. Prop. Microstruct. Process. 400, 448–450 (2005). doi:10.1016/j.msea.2005.02.090
Fredriksson, P., Gudmundson, P.: Competition between interface and bulk dominated plastic deformation in strain gradient plasticity. Model. Simul. Mater. Sci. Eng. 15(1), S61–S69 (2007). doi:10.1088/0965-0393/15/1/S06
Fujimoto, J.G., Liu, J.M., Ippen, E.P., Bloembergen, N.: Femtosecond laser interaction with metallic tungsten and nonequilibrium electron and lattice temperatures. Phys. Rev. Lett. 53(19), 1837–1840 (1984)
Gurtin, M.E.: Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance. Physica D 92(3–4), 178–192 (1996)
Gurtin, M.E., Anand, L.: Thermodynamics applied to gradient theories involving the accumulated plastic strain: the theories of Aifantis and Fleck and Hutchinson and their generalization. J. Mech. Phys. Solids 57(3), 405–421 (2009). doi:10.1016/j.jmps.2008.12.002
Gurtin, M.E., Fried, E., Anand, L.: The Mechanics and Thermodynamics of Continua. Cambridge University Press, New York (2010)
Joshi, A.A., Majumdar, A.: Transient ballistic and diffusive phonon heat-transport in thin-films. J. Appl. Phys. 74(1), 31–39 (1993)
Meyers, M.A., Chawla, K.K.: Mechanical Behavior of Materials, 2nd edn. Cambridge University Press, Cambridge (2009)
Narayan, J., Godbole, V.P., White, C.W.: Laser method for synthesis and processing of continuous diamond films on nondiamond substrates. Science 252(5004), 416–418 (1991)
Niordson, C.F., Hutchinson, J.W.: Non-uniform plastic deformation of micron scale objects. Int. J. Numer. Methods Eng. 56(7), 961–975 (2003). doi:10.1002/Nme.593
Polizzotto, C.: A nonlocal strain gradient plasticity theory for finite deformations. Int. J. Plast. 25(7), 1280–1300 (2009). doi:10.1016/j.ijplas.2008.09.009
Soer, W.A., Aifantis, K.E., De Hosson, J.T.M.: Incipient plasticity during nanoindentation at grain boundaries in body-centered cubic metals. Acta Materialia 53(17), 4665–4676 (2005). doi:10.1016/j.actamat.2005.07.001
Stolken, J.S., Evans, A.G.: A microbend test method for measuring the plasticity length scale. Acta Materialia 46(14), 5109–5115 (1998)
Sze, S.M., Ng, K.K.: Physics of Semiconductor Devices, 3rd edn. Wiley-Interscience, Hoboken (2007)
Tzou, D.Y.: Experimental support for the lagging behavior in heat propagation. J. Thermophys. Heat Transf. 9(4), 686–693 (1995a)
Tzou, D.Y.: The generalized lagging response in small-scale and high-rate heating. Int. J. Heat Mass Transf. 38(17), 3231–3240 (1995b)
Tzou, D.Y., Zhang, Y.S.: An analytical study on the fast-transient process in small scales. Int. J. Eng. Sci. 33(10), 1449–1463 (1995)
Voyiadjis, G.Z., Deliktas, B.: Formulation of strain gradient plasticity with interface energy in a consistent thermodynamic framework. Int. J. Plast. 25(10), 1997–2024 (2009a). doi:10.1016/j.ijplas.2008.12.014
Voyiadjis, G.Z., Deliktas, B.: Mechanics of strain gradient plasticity with particular reference to decomposition of the state variables into energetic and dissipative components. Int. J. Eng. Sci. 47(11–12), 1405–1423 (2009). doi:10.1016/j.ijengsci.2009.05.013
Voyiadjis, G.Z., Faghihi, D.: Thermo-mechanical strain gradient plasticity with energetic and dissipative length scales. Int. J. Plast. (2011a) doi:10.1016/j.ijplas.2011.10.007
Voyiadjis, G.Z., Faghihi, D.: Variable (intrinsic) material length scale for face-centred cubic metals using nano-indentation. Proc. Inst. Mech. Eng. Part N J. Nanoeng. Nanosyst. (2011b). doi:10.1177/1740349911413647
Zhang, J., Zhao, J.J.: Unconditionally stable finite difference scheme and iterative solution of 2D microscale heat transport equation. J. Comput. Phys. 170(1), 261–275 (2001)
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Voyiadjis, G., Faghihi, D. (2013). The Effect of Temperature on Interfacial Gradient Plasticity in Metallic Thin Films. In: Altenbach, H., Kruch, S. (eds) Advanced Materials Modelling for Structures. Advanced Structured Materials, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35167-9_31
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