Virtual machine concept applied to uncertainties estimation in instrumented indentation testing
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Virtual machine concept applied to uncertainties estimation in instrumented indentation testing Thierry Coorevits1, Stephania Kossman1,a) Alex Montagne1, Alain Iost1
, Didier Chicot2, François Hennebelle3,
1
Mécanique, Surface, Matériaux et Procédés, MSMP-EA7350, Arts et Métiers ParisTech, F-59800 Lille, France Laboratoire de Génie Civil et géo-Environnement, LGCgE-EA4515, Université de Lille, Villeneuve d’Ascq F-59650, France 3 Université Bourgogne Franche-Comté, F-21000 Dijon, France a) Address all correspondence to this author. e-mail: [email protected] 2
Received: 17 March 2019; accepted: 29 May 2019
The basis of the virtual machine concept, which is commonly used in coordinate measuring machines, was implemented to determine more realistic uncertainties on the estimation of the elastic modulus obtained from nanoindentation tests. The methodology is based on a mathematical model applied to simulate the testing process and to evaluate the uncertainties through Monte Carlo simulations whose application depends on the studied system (instrument, material, scale, etc.). The methodology was applied to the study of fused silica (FQ) and steel samples tested in a nanoindentation system. The results revealed that the most relevant sources of uncertainty are related to the calibration procedure, particularly to the elastic modulus of the calibration material, and to the contact depth estimation; however, the relevance of the uncertainties is system dependent. This work represents a first insight for a deeper consideration of the uncertainties in instrumented indentation testing.
Introduction Instrumented indentation testing (IIT) is a useful technique in materials science and engineering due to the straightforwardness of the testing method, which allows to determine the mechanical properties, such as elastic modulus and hardness. The technique involves the penetration of an indenter of known properties and geometry into a material of unknown properties; during the penetration and withdrawal of the indenter, force and penetration depth are continuously recorded, leading to the so-called load–displacement curve. Like many mechanical systems, instrumented indentation devices are affected by several sources of uncertainty, which have an influence on the estimation of the mechanical properties. The sources of uncertainty are related to different factors, such as the instrument, sample, indenter, test parameters, processing, environment, and calculation methods. The study of these uncertainties has been carried out by several authors, typically by an analytical approach, using the law of propagation of uncertainties [Eq. (1)] [1, 2, 3, 4] described in
ª Materials Research Society 2019
the guide to the expression of uncertainty measurement (GUM) [5]. uc 2 ð yÞ ¼
N X @f 2 i¼1
@xi
u2 ðxi Þ ;
ð1Þ
where f is a specific function, u(xi) is a standard uncertainty, and N is the number of uncertainty sources. The combined standard uncertainty uc(y) is an estimated standard deviation and characterizes the dispersi
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