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Model for instrumented indentation of brittle open-cell foam

Published online by Cambridge University Press:  23 July 2018

Robert F. Cook Open the ORCID record for Robert F. Cook [Opens in a new window]
Robert F. Cook*
Affiliation:
Materials Measurement Science Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
*
Address all correspondence to Robert F. Cook at robert.cook@nist.gov
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Abstract

A model is developed and implemented for load-controlled instrumented conical indentation of a brittle open-cell foam on a dense substrate. A survey of observations suggests that such indentations are typified by displacement excursions at small indentation loads, load-displacement variability, localized crushing, and a discrete to continuum transition at intermediate loads. The model includes all these effects as well as stiffening at large loads as the substrate is encountered. Direct quantitative comparison is made with measurements of a silica foam on a soda-lime glass substrate, strongly supporting the physical basis of the model.

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Type
Research Letters
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MRS Communications , Volume 8 , Issue 3 , September 2018 , pp. 1267 - 1273
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Copyright © Materials Research Society 2018 

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References

1.Schaefer, D.W. (ed.): Engineered Porous Materials [Section]. MRS Bulletin 19, 14–53.Google Scholar
2.Gibson, L.J. (ed.): Cellular Solids [Section]. MRS Bulletin 28, 270–300.Google Scholar
3.Erlebacher, J. and Seshadri, R. (ed.): Hard Materials with Tunable Porosity. MRS Bulletin 34, 561–601.Google Scholar
4.Gibson, L.J. and Ashby, M.F.: Cellular Solids, 2nd ed. (Cambridge University Press, Cambridge, England, 1997).Google Scholar
5.Ashby, M.F., Evans, A., Fleck, N.A., Gibson, L.J., Hutchinson, J.W., and Wadley, H.N.G.: Metal Foams (Elsevier, Oxford, UK, 2000).Google Scholar
6.Shaw, M.C. and Sata, T.: The plastic behavior of cellular materials. Int. J. Mech. Sci. 8, 469 (1966).Google Scholar
7.Wilsea, M., Johnson, K.L., and Ashby, M.F.: Indentation of foamed plastics. Int. J. Mech. Sci. 17, 457 (1975).Google Scholar
8.Ashby, M.F., Palmer, A.C., Thouless, M., Goodman, D.J., Howard, M., Hallam, S.D., Murrell, S.A.F., Jones, N., Sanderson, T.J.O., and Ponter, A.R.S.: Nonsimultaneous failure and ice loads on Arctic structures. Proc. Offshore Technology Conference, pp 399 (1986).Google Scholar
9.Krommenhoek, M., Shamma, M., and Morsi, K.: Processing, characterization, and properties of aluminum–carbon nanotube open-cell foams. J. Mater. Sci. 52, 3927 (2017).Google Scholar
10.Sarkar, N., Lee, K.S., Park, L.G., Mazumder, S., Aneziris, C.G., and Kim, I.J.: Mechanical and thermal properties of highly porous Al2TiO5-mullite ceramics. Ceram. Int. 42, 3548 (2016).Google Scholar
11.Olurin, O.B., Fleck, N.A., and Ashby, M.F.: Indentation resistance of an aluminum foam. Scripta Mater. 43, 983 (2000).Google Scholar
12.Sudheer Kumar, P., Ramachandra, S., and Ramamurty, U.: Effect of displacement-rate on the indentation behavior of an aluminum foam. Mater. Sci. Eng. A347, 330 (2003).Google Scholar
13.Latella, B.A., O'Connor, B.H., Padture, N.P., and Lawn, B.R.: Hertzian contact damage in porous alumina ceramics. J. Am. Ceram. Soc. 80, 1027 (1997).Google Scholar
14.Staub, D., Meille, S., Le Corre, V., Rouleau, L., and Chevalier, J.: Identification of a damage criterion of a highly porous alumina ceramic. Acta Mater. 107, 261 (2016).Google Scholar
15.Huang, D. and Lee, J.H.: Mechanical properties of snow using indentation tests: size effects. J. Glaciol. 59, 35 (2013).Google Scholar
16.Bouterf, A., Adrien, J., Maire, E., Bajer, X., Hild, F., and Roux, S.: Identification of the crushing behavior of brittle foam: from indentation to odoemetric tests. J. Mech. Phys. Solids 98, 181 (2017).Google Scholar
17.Bouterf, A., Maire, E., Roux, S., Hild, F., Bajer, X., Gouillart, E., and Boller, E.: Analysis of compaction in brittle foam with multiscale indentation tests. Mechanics Mater. 118, 22 (2018).Google Scholar
18.Clément, P., Meille, S., Chevalier, J., and Olognon, C.: Mechanical characterization of highly porous inorganic solids materials by instrumented micro-indentation. Acta Mater. 61, 6649 (2013).Google Scholar
19.Kitamura, M. and Hirose, T.: Strength determination of rocks by using indentation tests with a spherical indenter. J. Structural Geol. 98, 1 (2017).Google Scholar
20.Hodge, A.M., Biener, J., Hayes, J.R., Bythrow, P.M., Volkert, C.A., and Hamza, A.V.: Scaling equation for yield strength of nanoporous open-cell foams. Acta Mater. 55, 1343 (2007).Google Scholar
21.Toivola, Y., Stein, A., and Cook, R.F.: Depth-sensing indentation response of ordered silica foam. J. Mater. Res. 19, 260 (2004).Google Scholar
22.Jauffrès, D., Yacou, C., Verdier, M., Dendievel, R., and Ayral, A.: Mechanical properties of hierarchical porous silica thin films: experimental characterization by nanoindentation and fine element modeling. Microporous Mesoporous Mater. 140, 120 (2011).Google Scholar
23.Tulliani, J.-M., Montanaro, L., Bell, T.J., and Swain, M.V.: Semiclosed-cell mullite foams: preparation and macro- and micromechanical characterization. J. Am. Ceram. Soc. 82, 961 (1999).Google Scholar
24.Kucheyev, S.O., Hamza, A.V., Satcher, J.H. Jr, and Worsley, M.A.: Depth-sensing indentation of low-density brittle nanoporous solids. Acta Mater. 57, 3472 (2009).Google Scholar
25.Han, Y., Hong, S.-H., and Xu, K.W.: Porous nanocrystalline titania films by plasma electrolytic oxidation. Surface Coatings Technol. 154, 314 (2002).Google Scholar
26.Ling, Z., Wang, X., and Ma, J.: The response of porous Al2O3 probed to nanoindentation. Mater. Sci. Eng. A483–484, 285 (2008).Google Scholar
27.Chintapalli, R.K., Jimenez-Pique, E., Marro, F.G., Yan, H., Reece, M., and Anglada, M.: Spherical instrumented indentation of porous nanocrystalline zirconia. J. Eur. Ceram. Soc. 32, 123 (2012).Google Scholar
28.Chen, Z., Wang, X., Bhakhri, V., Giuliani, F., and Atkinson, A.: Nanoindentation of porous bulk and thin films of La0.6Sr0.4Co0.2Fe0.8O3-δ. Acta mater. 61, 5720 (2013).Google Scholar
29.Chen, Z., Wang, X., Giuliani, F., and Atkinson, A.: Surface quality improvement of porous thin films suitable for nanoindentation. Ceram. Int. 40, 3913 (2014).Google Scholar
30.Chen, Z., Wang, X., Atkinson, A., and Brandon, N.: Spherical indentation of porous ceramics: elasticity and hardness. J. Eur. Ceram. Soc. 36, 1435 (2016).Google Scholar
31.Chen, Z., Wang, X., Atkinson, A., and Brandon, N.: Spherical indentation of porous ceramics: cracking and toughness. J. Eur. Ceram. Soc. 36, 3473 (2016).Google Scholar
32.Chen, Z., Wang, X., Brandon, N., and Atkinson, A.: Spherical indentation of bilayer ceramic structures: dense layer on porous substrate. J. Eur. Ceram. Soc. 37, 4763 (2017).Google Scholar
33.Chen, Z., Wang, X., Brandon, N., and Atkinson, A.: Analysis of spherical indentation of porous ceramic films. J. Eur. Ceram. Soc. 37, 1031 (2017).Google Scholar
34.Brezny, R., Green, D.J., and Dam, C.Q.: Evaluation of strut strength in open-cell ceramics. J. Am. Ceram. Soc. 72, 885 (1989).Google Scholar
35.Brezny, R., and Green, D.J.: Fracture behavior of open-cell ceramics. J. Am. Ceram. Soc. 72, 1145 (1989).Google Scholar
36.Dam, C.Q., Brezny, R., and Green, D.J.: Compressive behavior and deformation-mode map of an open cell alumina. J. Mater. Res. 5, 163 (1990).Google Scholar
37.Brezny, R., and Green, D.J.: Uniaxial strength behavior of brittle cellular materials. J. Am. Ceram. Soc. 76, 2185 (1993).Google Scholar
38.Acchar, W., Souza, F.B.M., Ramalho, E.G., and Torquato, W.L.: Mechanical characterization of cellular ceramics. Mater. Sci. Eng. A513–514, 340 (2009).Google Scholar
39.Vekinis, G., Ashby, M.F., and Beaumont, P.W.R.: Plaster of Paris as a model material for brittle porous solids. J. Mater. Sci. 28, 3221 (1993).Google Scholar
40.Tallon, C., Chuanuwatanakul, C., Dunstan, D.E., and Franks, G.V.: Mechanical strength and damage tolerance of highly porous alumina ceramics produced from sintered particle stabilized foams. Ceram. Int. 42, 8478 (2016).Google Scholar
41.Meille, S., Lombardi, M., Chevalier, J., and Montanaro, L.: Mechanical properties of porous ceramics in compression: on the transition between elastic, brittle, and cellular behavior. J. Eur. Ceram. Soc. 32, 3959 (2012).Google Scholar
42.Gold, L.W.: Brittle to ductile transition during indentation of ice. Can. J. Civ. Eng. 18, 182 (1991).Google Scholar
43.Fleck, N.A., Otoyo, H., and Needleman, A.: Indentation of porous solids. Int. J. Solids Structures 29, 1613 (1992).Google Scholar
44.Miller, R.E.: A continuum plasticity model for the constitutive and indentation behavior of foamed metals. Int. J. Mech. Sci. 42, 729 (2000).Google Scholar
45.Nakamura, T., Qian, G., and Berndt, C.C.: Effects of pores on mechanical properties of plasma-sprayed ceramic coating. J. Am. Ceram. Soc. 83, 578 (2000).Google Scholar
46.Hård af Segerstad, P., Toll, S., and Larsson, R.: Computational modelling of dissipative open-cell cellular solids at finite deformations. Int. J. Plasticity 25, 802 (2009).Google Scholar
47.Tekoğlu, G., Gibson, L.J., Pardoen, T., and Onck, P.R.: Size effects in foams: experiments and modeling. Prog. Mater. Sci. 56, 109 (2011).Google Scholar
48.Cook, R.F.: A flexible model for instrumented indentation of viscoelastic-plastic materials. MRS. Commun. (2018) online, doi: 10.1557/mrc.2018.32.Google Scholar
49.Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).Google Scholar