Non-direct estimations of adhesive and elastic properties of materials by depth-sensing indentation

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 464, Issue 2098, 2008, Pages 2759-2776

  Borodich, Feodor M ^a   Galanov, Boris A ^a,b  

^a CARDIFF UNIVERSITY   (United Kingdom)

^b FRANTSEVICH INSTITUTE FOR PROBLEMS OF MATERIALS SCIENCE   (Ukraine)

Author keywords

Adhesion of solids; Contact mechanics; Depth sensing indentation

Indexed keywords

ADHESION; ELASTICITY; ESTIMATION; EXPERIMENTS; EXTRACTION; MATHEMATICAL TECHNIQUES; MEASUREMENT ERRORS; MECHANICS; SPEED;

ADHESION OF SOLIDS; ADHESIVE CONTACTS; ADHESIVE PROPERTIES; CONTACT MECHANICS; CONTACTING MATERIALS; DEPTH-SENSING INDENTATION; DIRECT APPROACH; DIRECT DETERMINATION; DIRECT METHODS; ELASTIC CHARACTERISTICS; ELASTIC PROPERTIES; EXPERIMENTAL DATA; FORCE-DISPLACEMENT CURVES; FORCE-DISPLACEMENT DIAGRAMS; ILL-POSED PROBLEMS; MOLECULAR ADHESION; PULL-OFF FORCES; SPHERICAL INDENTERS; TENSILE FORCES; WORK OF ADHESION;

MATERIALS PROPERTIES;

EID: 49749096429     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2008.0044     Document Type: Article

References (41)

1. Becky, J. V. & Woodburyz, K. A. 1998 Inverse problems and parameter estimation: integration of measurements and analysis. Meas. Sci. Technol. 9, 839-847. (doi:10.1088/0957-0233/9/6/001)
2. Bolzon, G., Maier, G. & Pánico, M. 2004 Material model calibration by indentation, imprint mapping and inverse analysis. Int. J. Solids Struct. 41, 2957-.2975. (doi:10.1016/j.ijsolstr.2004.01.025)
3. Borodich, F. M. 1983 Similarity in the problem of contact between elastic bodies. J. Appl. Math. Mech. 47, 519-521. (doi:10.1016/0021- 8928(83)90077-1)
4. Borodich, F. M. 1989 Hertz contact problems for an anisotropic physically nonlinear elastic medium. Strength Mater. 21, 1668 1676. (doi:10.1007/BF01533408)
5. Borodich, F. M. 1998 Similarity methods in Hertz contact problems and their relations with the Meyer hardness test. Glasgow Caledonian University, Technical report TR/MAT/FMB/98-98, 1-45.
6. Borodich, F. M. & Galanov, B. A. 2002 Self-similar problems of elastic contact for non-convex punches. J. Mech. Phys. Solids 50, 2441-2461. (doi:10.1016/S0022-5096(02)00031-5)
7. Borodich, F. M. & Keer, L. M. 2004a Evaluation of elastic modulus of materials by adhesive (no-slip) nanoindentation. Proc. R. Soc. A 460, 507 514. (doi:10.1098/rspa.2003.1224)
8. Borodich, F. M. & Keer, L. M. 2004b Contact problems and depth-sensing nanoindentation for frictionless and frictional boundary conditions. Int. J. Solids Struct. 41, 2479-2499. (doi:10.1016/j.ijsolstr.2003.12.012)
9. Borodich, F. M., Keer, L. M. & Korach, C. S. 2003 Analytical study of fundamental nanoindentation test relations for indenters of non-ideal shapes. Nanotechnology 14, 803-808. (doi:10.1088/0957-4484/14/7/319)
10. Bradley, R. S. 1932 The cohesive force between solid surfaces and the surface energy of solids. Phil. Mag. 13, 853-862.
11. Bulychev, S. I., Alekhin, V. P., Shorshorov, M. Kh., Ternovskii, A. P. & Shnyrev, G. D. 1975 Determination of Young's modulus according to indentation diagram. Indust. Lab. 41, 1409-1412.
12. Cao, Y. P. & Lu, J. 2004 Depth sensing instrumented indentation with dual sharp indenters: stability analysis and corresponding regularization schemes. Acta Mater. 52, 1143-1153, (doi:10.1016/j.actamat.2003. 11.001)
13. Carpick, R. W., Ogletree, D. F. & Salmeron, M. 1999 A general equation for fitting contact area and friction vs load measurements. J. Colloid, Interface Sci. 211, 395-400. (doi:10.1006/jcis.1998.6027)
14. Chaudhri, M. M. & Lim, Y. Y. 2007 Nanoindentation techniques: a critical assessment of the current methods of data analysis. Key Eng. Mater. 345-346, 1107-1114.
15. Dao, M., Chollacoop, N., Van Vliet, K. J., Venkatesh, T. A. & Suresh, S. 2001 Computational modeling of the forward and reverse problems in instrumented sharp indentation. Acta Mater. 49, 3899-3918. (doi:10.1016/S1359-6454(01)00295-6)
16. Davidenkov, N. N. 1943 Extracting the tension diagram on the basis of hardness tests. Zhur. Tekh. Fiz. 13, 389-393. [In Russian.]
17. Derjaguin, B. V. 1934 Untersuchungen über die Reibung und Adhäsion, IV. Theorie des Anhaftens kleiner Teilchen. Kolloid Z. 69, 155-164. (doi:10.1007/BF01433225)
18. Derjaguin, B. V., Muller, V. M. & Toporov, Y. P. 1975 Effect of contact deformations on adhesion of particles. J. Colloid. Interface Sci. 53, 314-326. (doi:10.1016/0021-9797(75)90018-1)
19. Ebenstein, D. M. & Wahl, K. J. 2006 A comparison of JKR-based methods to analyze quasi-static and dynamic indentation force curves. J. Colloid. Interface Sci. 298, 652-662. (doi:10.1016/j.jcis.2005.12.062)
20. Fischer-Cripps, A. C. 2006 Review of analysis and interpretation of nanoindentation test data. Surf. Coat. Technol. 200, 4153-4165. (doi:10.1016/j.surfcoat.2005.03.018)
21. Galanov, B. A. 1981a Approximate solution to some problems of elastic contact of two bodies. Mech. Solids 16, 61-67.
22. Galanov, B. A. 1981b Approximate solution of some contact problems with an unknown contact area under conditions of power law of material hardening. Dokl. AN Ukrain. SSR, A, no. 6, 36-41. [In Russian and Ukrainian.]
23. Hansen, P. C. & O'leary, D. P. 1993 The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput. 14, 1487-1503. (doi:10.1137/0914086)
24. Huber, N., Nix, W. D. & Gao, H. 2002 Identification of elastic-plastic material parameters from pyramidal indentation of thin films. Proc. R. Soc. A 458, 1593 1620. (doi:10.1098/rspa.2001.0927)
25. Johnson, K. L., Kendall, K. & Roberts, A. D. 1971 Surface energy and the contact of elastic solids. Proc. R Soc. A 324, 301-310. (doi:10.1098/rspa.1971.0141)
26. Johnston, P. R. & Gulrajani, R. M. 1997 A new method for regularization parameter determination in the inverse problem of electrocardiography. IEEE Trans. Biomed. Eng. 44, 19-39. (doi:10.1109/10.553710)
27. Kalei, G. N. 1967 Studies of methods of determination of microhardness by measurements of sizes of imprints by diagonal and by depth. PhD thesis, Blagonravov State Scientific and Research Institute of Machine Science, Moscow. [In Russian.]
28. Kalei, G. N. 1968 Some results of microhardness test using the depth of impression. Mashinovedenie 4, 105-107. [In Russian.]
29. Kendall, K. 2001 Molecular adhesion and its applications. New York, NY: Kluwer Academic/ Plenum Publishers.
30. Lan, H. Z. & Venkatesh, T. A. 2007 Determination of the elastic and plastic properties of materials through instrumented indentation with reduced sensitivity. Acta Mater. 55, 2025-2041. (doi:10.1016/j.actamat. 2006.11.012)
31. Maugis, D. 2000 Contact, adhesion and rupture of elastic solids. Berlin, Germany: Springer.
32. Maugis, D. & Barquins, M. 1978 Fracture mechanics and the adherence of viscoelastic bodies. J. Phys. D: Appl. Phys. 11, 1989-2023. (doi:10.1088/0022-3727/11/14/011)
33. Muller, V. M., Yushchenko, V. S. & Derjaguin, B. V. 1980 On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane. J. Colloid, Interface Sci, 77, 91-101. (doi:10.1016/0021-9797(80)90419-1)
34. Pethica, J. B. & Oliver, W. C. 1987 Tip surface interactions in STM and AFM. Phys. Ser. T19A, 61-66. (doi:10.1088/0031-8949/1987/T19A/ 010)
35. Tabor, D. 1977 Surface forces and surface interactions. J. Colloid. Interface Sci. 58, 2 13. (doi:10.1016/0021-9797(77)90366-6)
36. Tarantola, A. 2004 Inverse problem theory and methods for model parameter estimation. Philadelphia, PA: SIAM.
37. Tikhonov, A. N. & Arsenin, V. Y. 1977 Solutions of ill-posed problems. New York, NY: Wiley.
38. Wach, P., Modre, R., Tilg, B. & Fischer, G. 2001 An iterative linearized optimization technique for non-linear ill-posed problems applied to cardiac activation time imaging. COMPEL:Int. J. Comp. Math. Elect. Electr. Eng. 20, 676-688. (doi:10.1108/03321640110393644)
39. Wahl, K. J., Asif, S. A. S., Greenwood, J. A. & Johnson, K. L. 2006 Oscillating adhesive contacts between micron-scale tips and compliant polymers. J. Colloid. Interface Sci. 296, 178-188. (doi:10.1016/j.jcis.2005. 08.028)
40. Zabaras, N. & Ganapathysubramanian, B. 2008 A scalable framework for the solution of stochastic inverse problems using a sparse grid collocation approach. J. Comput. Phys. 227, 4697-4735. (doi:10.1016/j.jcp. 2008.01.019)
41. Zimon, A. D. 1988 Adhesion. In Physical encyclopedia, vol. 1, Moscow, Russia: Soviet Encyclopedia.