**Deformation Regimes for Sphere-Plane Contact: Revisiting Tabor's Criteria for Differential Hardness** Deformation Regimes for Sphere-Plane Contact: Revisiting Tabor's Criteria for Differential Hardness

DOI: 10.5772/intechopen.72642

Giuseppe Pintaude Giuseppe Pintaude

[14] Caron A. Quantitative hardness measurement by instrumented AFM-indentation. Jour-

[15] Caron A, Bennewitz R. Lower nanometer-scale size limit for the deformation of a metallic glass by shear transformations revealed by quantitative AFM indentation. Beilstein Jour-

[16] Meyer E, Hug HJ, Bennewitz R. Scanning Probe Microscopy: The Lab on a Tip. Berlin,

[17] Nonnenmacher M, Greschner J, Wolter O, Kassing R. Journal of Vacuum Science and

[18] Butt H-J, Jaschke M. Calculation of thermal noise in atomic force microscopy. Nanotech-

[19] Cook SM, Schaeffer TE, Chynoweth KM, Wigton M, Simmonds RW, Lang KM. Practical implementation of dynamics methods for measuring atomic force microscope cantilever

[20] Voihtlaender B. Scanning Probe Microscopy: Atomic Force Microscopy and Scanning

[21] Schroers J, Johnson WL. Ductile bulk metallic glass. Physical Review Letters. 2004;93:

[22] Giessibl FA. Direct method to calculate tip-sample forces from frequency shifts in frequency-modulation atomic force microscopy. J. Applied Physics Letters. 2001;78:123

[23] Cannara RJ, Brukman MJ, Carpick RW. Cantilever tilt compensation for variable-load atomic force microscopy. The Review of Scientific Instruments. 2005;76:053706

[26] Bennewitz R. Friction force microscopy. In: Gnecco E, Meyer E, editors. Fundamentals of

[27] Meyer E, Luethi R, Howald R, Bammerlin M, Guggisberg M, Guentherodt H-J. Sitespecific friction force spectroscopy. Journal of Vacuum Science and Technology B. 1996;

[28] Johnson KL, Kendall K, Roberts AD. Proceedings of the Royal Society of London. Series A.

[30] Li Q, Dong Y, Martini A, Carpick RW. Atomic friction modulation on the reconstructed

[29] Johnson KL. Contact Mechanics. Cambridge, UK: Cambridge University Press; 1985

Tunneling Microscopy. Berlin, Heidelberg, Germany: Springer; 2015

[25] Fischer-Cripps A, Nanoindentation C. 2nd ed. Springer: New York; 2004

Friction and Wear. Berlin, Heidelberg, Germany: Springer; 2007

Au(111) surface. Tribology Letters. 2011;43:369-378

nal of Visualized Experiments. 2016;117:e54706

spring constants. Nanotechnology. 2006;17:2135-2145

nal of Nanotechnology. 2015;6:1721-1732

Heidelberg, Germany: Springer; 2004

Technology B. 1991;9:1358

nology. 1995;6:1-7

44 Contact and Fracture Mechanics

[24] http://www.gwyddion.net

14:1285-1288

1971;324:301-313

255506

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.72642

#### Abstract

This chapter presents an update of theories involving the differential hardness problem, starting from the hypothesis made by Tabor for the contact between a sphere and a plane. In this way, the reader interested in problems affected directly by these formulations, such as contact area and contact fatigue, can take part of a fundamental theoretical basis to perform investigations in this field.

Keywords: differential hardness, sphere-plane contact, deformation regimes
