INDENTATION OF FLAT-ENDED AND TAPERED INDENTERS WITH POLYGONAL CROSS-SECTIONS

Qiang Li, Valentin L. Popov

DOI Number
10.22190/FUME1603241L
First page
241
Last page
249

Abstract

Using the Boundary Element Method, we numerically study the indentation of prismatic and tapered indenters with polygonal cross-sections. The contact stiffness of punches with flat bases in the form of a triangle and a square as well as a number of higher-order polygons is determined. In particular, the classical results of King (1987) for indenters with triangle and square base shapes are revised and more precise numerical results are provided. For tapered indenters, the equivalent transformed profile used in the Method of Dimensionality Reduction (MDR) is determined. It is shown that the MDR-transformed profile of polygon-based indenters with power function side is given by the power function with the same power; it differs from the 3D profile only by a constant coefficient. These coefficients are listed in the paper for various types of indenters, in particular for pyramidal and paraboloid ones. The determined MDR-transformed profiles can be used for study of other contact problems such as tangential contact, normal contact with elastomers, and, in an approximate way, to adhesive contacts.

Keywords

Indentation, Contact Stiffness, Polygonal Indenter, Boundary Element Method, MDR Transformed Profile

Full Text:

PDF

References

Oliver, W.C., Pharr, G.M., 2011, Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology, Journal of Materials Research, 19(1), pp. 3–20.

Fischer-Cripps, A.C., 2000, A review of analysis methods for sub-micron indentation testing, Vacuum, 58(4), pp.569-585.

Hay, J., Agee, P., Herbert, E., 2010, Continuous stiffness measurement during instrumented indentation testing, Experimental Techniques, 34, pp. 86–94.

Swadener, J.G., George, E.P., Pharr, G.M., 2002, The correlation of the indentation size effect measured with indenters of various shapes, Journal of the Mechanics and Physics of Solids, 50(4), pp. 681-694.

King, R.B., 1987, Elastic analysis of some punch problems for a layered medium, International Journal of Solids and Structures, 23(12), pp. 1657-1664.

Galin, L.A., 1961, Contact Problems in the Theory of Elasticity, North Carolina State College, USA

Sneddon, I.N., 1965, The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile, International Journal of Engineering Science, 23(12), pp. 1657-1664.

Oliver, W.C., Pharr, G.M., 1992, An Improved Technique for Determining Hardness and Elastic-Modulus Using Load and Displacement Sensing Indentation Experiments, Journal of Materials Research, 7(6), pp. 1564-1583.

Pharr, G.M., Oliver, W.C., Brotzen, F.R., 2011, On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation, Journal of Materials Research, 7(3), pp. 613–617.

Popov V.L., 2010, Contact mechanics and friction: Physical principles and foundations, Springer, Berlin.

Pohrt, R., Li, Q., 2014, Complete boundary element formulation for normal and tangential contact problems, Physical Mesomechanics, 17(4), pp. 334-340.

Pohrt, R., Popov, V.L., 2015, Adhesive contact simulation of elastic solids using local mesh-dependent detachment criterion in Boundary Elements Method, Facta Universitatis series: Mechanical Engineering, 13(1), pp. 3-10

Argatov, I., 2010, Frictionless and adhesive nanoindentation: Asymptotic modeling of size effects, Mechanics of Materials, 42(8), pp. 807–815.

Popov, V.L., Heß, M., 2015, Method of dimensionality reduction in contact mechanics and friction, Springer, Berlin.

Argatov, I., Heß, M., Pohrt, R., Popov, V.L., 2016, The extension of the method of dimensionality reduction to non-compact and non-axisymmetric contact, Journal of Applied Mathematics and Mechanics (ZAMM), 96(10), pp. 1144-1155.

Popov, V.L., Pohrt, R., Heß, M., 2016, General procedure for solution of contact problems under dynamic normal and tangential loading based on the known solution of normal contact problem, Journal of Strain Analysis for Engineering Design, 51(4), pp. 247-255.




DOI: http://dx.doi.org/10.22190/FUME1603241L

Refbacks

  • There are currently no refbacks.


ISSN: 0354-2025 (Print)

ISSN: 2335-0164 (Online)

COBISS.SR-ID 98732551

ZDB-ID: 2766459-4