Variable Material Length Scale Associated with Nanoindentation Experiments
Publication: Journal of Engineering Mechanics
Volume 135, Issue 3
Abstract
Material length scale that can be used in nonlocal gradient theories is obtained in this work based on experimental observations for two metals using nanoindentation experiments. The materials are cold rolled 1018 steel and oxygen free high conductivity copper. A fixed value of the material length scale is not always realistic and different problems under various conditions could require different values. Therefore, two models are proposed for a dynamic length scale that depends on strain rates and temperature. First the model is physically based, with parameters related to dislocation densities. This model introduces strain rate and temperature dependency in a coupled form. The second model is a phenomenological one that is based on hardness tests. Both models show that length scale decreases with increasing equivalent strain rate. The temperature effects are not studied in this work.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abed, F. H., and Voyiadjis, G. Z. (2007). “Thermodynamic consistent formulations of viscoplastic deformations in FCC metals.” J. Eng. Mech., 133(1), 76–86.
Abu Al-Rub, R. K., and Voyiadjis, G. Z. (2004). “Analytical and experimental determination of the material intrinsic length scale of strain gradient plasticity theory from micro- and nano-indentation experiments.” Int. J. Plast., 20(6), 1139–1182.
Aifantis, E. C. (1992). “On the role of gradients in the localization of deformation and fracture.” Int. J. Eng. Sci., 30, 1279–1299.
Almasri, A. H., and Voyiadjis, G. Z. (2007a). “Constitutive modeling of BCC metals: Application to ingot iron.” Proc., McMat2007 Conf., Univ. of Texas at Austin, Austin, Tex.
Almasri, A. H., and Voyiadjis, G. Z. (2007b). “The effect of strain rate on the dynamic hardness in metals.” J. Eng. Mater. Technol., 129(4), 505–512.
Almasri, A. H., and Voyiadjis, G. Z. (2008). “A physically based constitutive model for BCC metals with applications to iron.” J. Eng. Mech., 134(7), 521–529.
Arsenlis, A., and Parks, D. M. (1999). “Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density.” Acta Mater., 47, 1597–1611.
Ascheron, C., Huse, C., Kuhn, G., and Neumann, H. (1989). “Microhardness of Sn-doped In P.” Cryst. Res. Technol., 24(2), 33–35.
Bammann, D. J., Mosher, D., Hughes, D. A., Moody, N. R., and Dawson, P. R. (1999). “Using spatial gradients to model localization phenomena.” Sandia National Laboratories Rep. No. SAND99-8588, Albuquerque, N.M.
Begley, M. R., and Hutchinson, J. W. (1998). “The mechanics of size dependent indentation.” J. Mech. Phys. Solids, 35(9), 2049–2068.
Benallal, A., Fudoli, C. A., and Venturini, W. S. (2002). “An implicit BEM formulation for gradient plasticity and localization phenomena.” Int. J. Numer. Methods Eng., 53, 1853–1869.
Berthier, L., et al. (2005). “Direct experimental evidence of a growing length scale accompanying the glass transition.” Science, 310(5755), 1797–1800.
Boria, R. I. (2002). “Finite element simulation of strain localization with large deformation: Capturing strong discontinuity using a Petrov-Galerkin multiscale formulation.” Comput. Methods Appl. Mech. Eng., 191, 2949–2978.
Chong, A. C. M., and Lam, D. C. C. (1999). “Strain gradient plasticity effect in indentation hardness of polymers.” J. Mater. Res., 14(10), 4103–4110.
Das, S. P. (2000). “Dynamic length scales and feedback from long-time structural relaxation in a simple liquid.” J. Phys.: Condens. Matter, 12, 6423–6430.
de Borst, R., and Mühlhaus, H. B. (1992). “Gradient-dependent plasticity formulation and algorithmic aspects.” Int. J. Numer. Methods Eng., 35, 521–539.
Elmustafa, A. A., and Stone, D. S. (2003). “Nanoindentation and the indentation size effect: Kinetics of deformation and strain gradient plasticity.” J. Mech. Phys. Solids, 51, 357–381.
Fleck, N. A., and Hutchinson, J. W. (1997). “Strain gradient plasticity.” Adv. Appl. Mech., 33, 295–361.
Gao, H., Huang, Y., Nix, W. D., and Hutchinson, J. W. (1999). “Mechanism-based strain gradient plasticity. I: Theory.” J. Mech. Phys. Solids, 47, 1239–1263.
Gracio, J. J. (1994). “The double effect of grain size on the work-hardening behavior of polycrystalline copper.” Scr. Metall. Mater., 31, 487–489.
Guille, J., and Sieskind, M. (1991). “Microindentation studies on BaFCl single crystals.” J. Mater. Sci., 26(4), 899–903.
Haque, M. A., and Saif, M. T. A. (2003). “A review on micro and nano-mechanical testing with MEMS.” Exp. Mech., 43(3), 1–8.
Hay, J. L., and Pharr, G. M. (2000). “Instrumented indentation testing.” ASM handbook, Mechanical testing and evaluation, Vol. 8, H. Kuhn and D. Medlin, eds., ASM, Materials Park, Ohio, 232–243.
Hendrix, B. C. (1995). “The use of shape correction factors for elastic indentation measurements.” J. Mater. Res., 110(2), 255–257.
Huang, Y., Xue, Z., Gao, H., and Xia, Z. C. (2000). “A study of micro-indentation hardness tests by mechanism-based strain gradient plasticity.” J. Mater. Res., 15, 1786–1796.
LeMonds, J., and Needleman, A. (1986). “Finite element analysis of shear localization in rate and temperature dependent solids.” Mech. Mater., 5, 339–361.
Lim, Y. Y., and Chaudhri, Y. Y. (1999). “The effect of the indenter load on the nanohardness of ductile metals: An experimental study of polycrystalline work-hardened and annealed oxygen-free copper.” Philos. Mag. A, 79(12), 2979–3000.
Ma, Q., and Clarke, D. R. (1995). “Size dependent hardness of silver single crystals.” J. Mater. Res., 10, 853–863.
Needleman, A. (1988). “Material rate dependent and mesh sensitivity in localization problems.” Comput. Methods Appl. Mech. Eng., 67, 68–85.
Nix, W. D., and Gao, H. (1998). “Indentation size effects in crystalline materials: A law for strain gradient plasticity.” J. Mech. Phys. Solids, 46(3), 411–425.
Oliver, W. C., and Pharr, G. M. (1992). “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments.” J. Mater. Res., 7(6), 1564–1583.
Perzyna, P. (1966). “Fundamental problems visco-plasticity.” Adv. Appl. Mech., 9, 243–377.
Pijaudier-Cabot, T. G. P., and Bazant, Z. P. (1987). “Nonlocal damage theory.” J. Eng. Mech., 113(10), 1512–1533.
Sneddon, I. N. (1965). “The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile.” Int. J. Eng. Sci., 3, 47–57.
Stelmashenko, N. A., Walls, M. G., Brown, L. M., and Milman, Y. V. (1993). “Microindentations on W and Mo oriented single crystals: An STM study.” Acta Metall. Mater., 41, 2855–2865.
Tickoo, R., Tandon, R. P., Bamzai, K. K., and Kotru, P. N. (2003). “Microindentation studies on samarium-modified lead titanate ceramics.” Mater. Chem. Phys., 80(2), 446–451.
Vengatesan, B., Kanniah, H., and Ramasvamy, P. (1986). “Microhardness and crack patterns of CVT grown CdGa2S4 single crystals.” J. Mater. Sci. Lett., 5(10), 987–988.
Voyiadjis, G. Z., and Abed, F. H. (2005). “Microstructural based models for BCC and FCC metals with temperature and strain rate dependency.” Mech. Mater., 37(2–3), 355–378.
Voyiadjis, G. Z., and Abed, F. H. (2006). “A coupled temperature and strain rate dependent yield function for dynamic deformations of BCC metals.” Int. J. Plast., 22(8), 1398–1431.
Voyiadjis, G. Z., and Abu Al-Rub, R. K. (2002). “Length scales in gradient plasticity.” Proc., IUTAM Symp. on Multiscale Modeling and Characterization of Elastic-Inelastic Behavior of Engineering Materials, S. Ahzi, M. Cherkaoui, M. A. Khaleel, H. M. Zbib, M. A. Zikry, and B. LaMatina, eds., Kluwer Academic, Dordrecht, The Netherlands, 167–174.
Voyiadjis, G. Z., and Abu Al-Rub, R. K. (2005). “Gradient plasticity theory with a variable length scale parameter.” Int. J. Solids Struct., 42(14), 3998–4029.
Voyiadjis, G. Z., Abu Al-Rub, R. K., and Palazotto, A. N. (2003). “Non-local coupling of viscoplasticity and anisotropic viscodamage for impact problems using the gradient theory.” Arch. Mech., 55(1), 39–89.
Voyiadjis, G. Z., Abu Al-Rub, R. K., and Palazotto, A. N. (2004). “Thermodynamic framework for coupling of non-local viscoplasticity and non-local anisotropic viscodamage for dynamic localization problems using gradient methods.” Int. J. Plasticity, 20(6), 981–1038 (Special issue in recent advances in multiscale modeling of plasticity).
Voyiadjis, G. Z., and Almasri, A. H. (2008). “A physically based constitutive model for FCC metals with applications to dynamic hardness.” Mech. Mater.
Voyiadjis, G. Z., and Deliktas, B. (2000). “Multi-scale analysis of multiple damage mechanics coupled with inelastic behavior of composite materials.” Mech. Res. Commun., 27(3), 295–300.
Voyiadjis, G. Z., Deliktas, B., and Aifantis, E. C. (2001). “Multi-scale analysis of multiple damage mechanics coupled with inelastic behavior of composite materials.” J. Eng. Mech., 127(7), 636–645.
Voyiadjis, G. Z., and Dorgan, R. J. (2001). “Gradient formulation in coupled damage-plasticity.” Arch. Mech., 53(4–5), 565–597.
Wang, W., Huang, Y., Hsia, K. J., Hu, K. X., and Chandra, A. (2003). “A study of microbend test by strain gradient plasticity.” Int. J. Plast., 19, 365–382.
Zbib, H. M., and Aifantis, E. C. (1992). “On the gradient-dependent theory of plasticity and shear bending.” Acta Mech., 92, 209–225.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 3 • March 2009
Pages: 139 - 148
Copyright
© 2009 ASCE.
History
Received: May 1, 2008
Accepted: May 2, 2008
Published online: Mar 1, 2009
Published in print: Mar 2009
Notes
Note. Associate Editor: Richard A. Regueiro
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.