TY - GEN
T1 - Contact problems and nanoindentation tests for indenters of non-ideal shapes and effects of molecular adhesion
AU - Borodich, Feodor M.
AU - Galanov, Boris A.
AU - Keer, Leon M.
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2005
Y1 - 2005
N2 - Depth-sensing nanoindentation, when the displacement the indenter is continuously monitored is widely used for analysis and estimations of mechanical properties of materials. Starting from pioneering papers by Bulychev, Alekhin, Shorshorov and their co-workers, nanoindentation tests are connected with Hertzian contact problems and the frictionless BASh relation is commonly used for evaluation of elastic modulus of materials. We discuss further the connections between Hertz type contact problems and nanoindentation tests and derive fundamental relations for depth-sensing nanoindentation for indenters of various shapes and for various boundary conditions within the contact region. For the loading branch, relations are derived among depth of indentation, size of the contact region, load, hardness, and contact area, using authors' scaling formulae. The relations are valid for indenters of non-ideal shapes, whose shape function is a monomial function an arbitrary degree d, in particular for blunted pyramidal indenters when 1 < d < 2. We show that some uncertainties in nanoindentation measurements, which are sometimes attributed to properties of the material, can be explained and quantitatively described by properly accounting for geometric deviation of the indenter tip from its nominal geometry. Then relation is derived for the slope of the unloading branch of adhesive (no-slip) indentation, The relation is analogous the frictionless BASh relation and it is independent of the geometry of the indenter. Further, the JKR theory of contact the presence of forces of molecular adhesion is extended to describe contact between a monomial indenter of an arbitrary degree d and an elastic sample. Finally, some exact formulae are obtained for adhesive contact (both the no-slip contact and the contact in the presence of molecular adhesive forces) between indenters and isotropic, linear elastic materials. In particular, it is shown that the BASh formula is still valid for contact between a flat punch and a soft elastic sample in the presence of molecular adhesive forces (the Boussinesq-Kendall problem).
AB - Depth-sensing nanoindentation, when the displacement the indenter is continuously monitored is widely used for analysis and estimations of mechanical properties of materials. Starting from pioneering papers by Bulychev, Alekhin, Shorshorov and their co-workers, nanoindentation tests are connected with Hertzian contact problems and the frictionless BASh relation is commonly used for evaluation of elastic modulus of materials. We discuss further the connections between Hertz type contact problems and nanoindentation tests and derive fundamental relations for depth-sensing nanoindentation for indenters of various shapes and for various boundary conditions within the contact region. For the loading branch, relations are derived among depth of indentation, size of the contact region, load, hardness, and contact area, using authors' scaling formulae. The relations are valid for indenters of non-ideal shapes, whose shape function is a monomial function an arbitrary degree d, in particular for blunted pyramidal indenters when 1 < d < 2. We show that some uncertainties in nanoindentation measurements, which are sometimes attributed to properties of the material, can be explained and quantitatively described by properly accounting for geometric deviation of the indenter tip from its nominal geometry. Then relation is derived for the slope of the unloading branch of adhesive (no-slip) indentation, The relation is analogous the frictionless BASh relation and it is independent of the geometry of the indenter. Further, the JKR theory of contact the presence of forces of molecular adhesion is extended to describe contact between a monomial indenter of an arbitrary degree d and an elastic sample. Finally, some exact formulae are obtained for adhesive contact (both the no-slip contact and the contact in the presence of molecular adhesive forces) between indenters and isotropic, linear elastic materials. In particular, it is shown that the BASh formula is still valid for contact between a flat punch and a soft elastic sample in the presence of molecular adhesive forces (the Boussinesq-Kendall problem).
UR - http://www.scopus.com/inward/record.url?scp=32844475802&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=32844475802&partnerID=8YFLogxK
U2 - 10.1115/wtc2005-63912
DO - 10.1115/wtc2005-63912
M3 - Conference contribution
AN - SCOPUS:32844475802
SN - 0791842010
SN - 9780791842010
T3 - Proceedings of the World Tribology Congress III - 2005
SP - 371
EP - 372
BT - Proceedings of the World Tribology Congress III - 2005
PB - American Society of Mechanical Engineers
T2 - 2005 World Tribology Congress III
Y2 - 12 September 2005 through 16 September 2005
ER -