Influence of penetration depth and mechanical properties on contact radius determination for spherical indentation

Abstract

International audienceKnowledge of the relationship between the penetration depth and the contact radius is required in order to determine the mechanical properties of a material starting from an instrumented indentation test. The aim of this work is to propose a new penetration depth-contact radius relationship valid for most metals which are deformed plastically by parabolic and spherical indenters. Numerical simulation results of the indentation of an elastic-plastic half-space by a frictionless rigid paraboloid of revolution show that the contact radius-indentation depth relationship can be represented by a power law, which depends on the reduced Young's modulus of the contact, on the strain hardening exponent and on the yield stress of the indented material. In order to use the proposed formulation for experimental spherical indentations, adaptation of the model is performed in the case of a rigid spherical indenter. Compared to the previous formulations, the model proposed in the present study for spherical indentation has the advantage of being accurate in the plastic regime for a large range of contact radii and for materials of well-developed yield stress. Lastly, a simple criterion, depending on the material mechanical properties, is proposed in order to know when piling-up appears for the spherical indentation. (c) 2005 Elsevier Ltd. All rights reserved

Experimental analysis of indentation morphologies after spherical indentation

“…The materials tested have strain-hardening exponents of less than 0.4, a necessary condition for the model proposed by Hernot et al 1 . The following equations described by Hernot et al 1 were therefore used with the mechanical properties obtained in tensile tests:…”

“…The following equations described by Hernot et al 1 were therefore used with the mechanical properties obtained in tensile tests:…”

“…In this context, this manuscript aims to compare the indentation morphologies for different metals calculated using models described by Hernot et al 1 and Cheng and Cheng 13 and to show how they explain the findings in the study by Pintaude et al 7 . Both models are based on numerical simulations.…”

“…Both models are based on numerical simulations. In the case of the paper by Hernot et al 1 , a series of equations were derived, as the amount of pile-up or sink-in depends on the ratio of the maximum indentation depth to ball radius (h/R) and on the mechanical properties (n and Y/E) extracted from tensile tests. Cheng and Cheng 13 make use of dimensional analysis in addition to numerical simulation to obtain the indentation morphology index and present the results graphically for each value of strain-hardening exponent.…”

Numerical study of pile-up in bulk metallic glass during spherical indentation

“…However, in real indentation tests, the deformation during loading and unloading cannot be obtained. To overcome this barrier, finite element analysis (FEA) can be performed [20,30,31] , by which the stress and deformation field can be continuously measured. The present work focuses on the pile-up effect at indentation test of Zr 41.2 Ti 13.8 Cu 12.5 Ni 10 Be 22.5 BMG by using the FE model of spherical indentation.…”