Contact Elasticity of Seal Elastomers

1968 ◽  
Vol 90 (2) ◽  
pp. 478-483 ◽  
Author(s):  
R. C. Drutowski
Keyword(s):  
Young’S Modulus ◽  
Experimental Work ◽  
Optical Measurement ◽  
Young's Modulus ◽  
Contact Analysis ◽  
Hertzian Contact ◽  
Depth Of Penetration ◽  
Critical Comparison ◽  
Hardness Tests ◽  
Work Done

The calculation of Young’s modulus of an elastomer is based on the optical measurement of the contact between a transparent spherical indenter and the elastomer. The technique is based on Hertzian contact analysis and agrees with the work done by others on the depth of penetration of indenters. A critical comparison of this method is made with conventional hardness tests. Experimental work establishes the fact that determinations of Young’s modulus based on indentations in thin samples are permissible only if the strains in the elastomer are kept below a calculable limit. The dependence of elastomer modulus on prior strain is described and fluid-elastomer interactions are examined in detail.

Is it necessary to calculate Young’s modulus in AFM nanoindentation experiments regarding biological samples?

2020 ◽  
Vol 12 ◽  
Author(s):  
S.V. Kontomaris ◽  
A. Malamou ◽  
A. Stylianou
Keyword(s):  
Young’S Modulus ◽  
Biological Samples ◽  
Young's Modulus ◽  
Reference Sample ◽  
Nonlinear Behavior ◽  
Accurate Method ◽  
Accurate Solution ◽  
Hertz Model ◽  
Work Done

Background: The determination of the mechanical properties of biological samples using Atomic Force Microscopy (AFM) at the nanoscale is usually performed using basic models arising from the contact mechanics theory. In particular, the Hertz model is the most frequently used theoretical tool for data processing. However, the Hertz model requires several assumptions such as homogeneous and isotropic samples and indenters with perfectly spherical or conical shapes. As it is widely known, none of these requirements are 100 % fulfilled for the case of indentation experiments at the nanoscale. As a result, significant errors arise in the Young’s modulus calculation. At the same time, an analytical model that could account complexities of soft biomaterials, such as nonlinear behavior, anisotropy, and heterogeneity, may be far-reaching. In addition, this hypothetical model would be ‘too difficult’ to be applied in real clinical activities since it would require very heavy workload and highly specialized personnel. Objective: In this paper a simple solution is provided to the aforementioned dead-end. A new approach is introduced in order to provide a simple and accurate method for the mechanical characterization at the nanoscale. Method: The ratio of the work done by the indenter on the sample of interest to the work done by the indenter on a reference sample is introduced as a new physical quantity that does not require homogeneous, isotropic samples or perfect indenters. Results: The proposed approach, not only provides an accurate solution from a physical perspective but also a simpler solution which does not require activities such as the determination of the cantilever’s spring constant and the dimensions of the AFM tip. Conclusion: The proposed, by this opinion paper, solution aims to provide a significant opportunity to overcome the existing limitations provided by Hertzian mechanics and apply AFM techniques in real clinical activities.

Determination of the hardness and young's modulus from the depth of penetration of a pyramidal indentor

1983 ◽  
Vol 15 (11) ◽  
pp. 1624-1628 ◽  
Author(s):  
B. A. Galanov ◽  
O. N. Grigor'ev ◽  
Yu. V. Mil'man ◽  
I. P. Ragozin
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Depth Of Penetration

Estimation of Young's Modulus and of Hardness by Ultra-Low Load Hardness Tests with a Vickers Indenter

1994 ◽  
Vol 22 (4) ◽  
pp. 365 ◽  
Author(s):  
DR Petersen ◽  
AC Trindade ◽  
A Cavaleiro ◽  
JV Fernandes
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Vickers Indenter ◽  
Hardness Tests ◽  
Low Load

scholarly journals Optical Measurement Techniques Determine Young’s Modulus of Sand Core Materials

2016 ◽  
Vol 10 (4) ◽  
pp. 524-530 ◽  
Author(s):  
Benjamin Griebel ◽  
Daniel Brecheisen ◽  
Robert Ramakrishnan ◽  
Wolfram Volk
Keyword(s):  
Young’S Modulus ◽  
Optical Measurement ◽  
Young's Modulus ◽  
Measurement Techniques ◽  
Sand Core ◽  
Core Materials

Continuous measurements of load-penetration curves with spherical microindenters and the estimation of mechanical properties

1998 ◽  
Vol 13 (5) ◽  
pp. 1390-1400 ◽  
Author(s):  
J. Alcalá ◽  
A. E. Giannakopoulos ◽  
S. Suresh
Keyword(s):  
Young’S Modulus ◽  
Large Scale ◽  
Young's Modulus ◽  
Accurate Determination ◽  
Elastic Response ◽  
Small Scale ◽  
Depth Of Penetration ◽  
Plastic Properties ◽  
Continuous Measurements ◽  
Contact Response

Elastic and plastic properties of metals and Young's modulus of ceramics are determined in the microindentation regime by continuous measurements of load versus depth of penetration with spherical indenters. Calibration procedures, usually applied in nanoindentation experiments, are not needed in the microregime where spherical indenters (rather than sharp indenters with microscopical spherical tips) can be manufactured. As indenters of larger diameters are used, the elastic response of the specimen can be probed during the loading stage of the indentation tests (and not only during unloading, as is the case with nanoindenters). Hence, an accurate determination of Young's modulus can be achieved without a prior knowledge of possible “piling up” or “sinking in” which may occur at the perimeter of the contact area. The contact response of materials is shown to undergo four distinct regions: (i) pre-Hertzian regime, (ii) Hertzian regime, (iii) small-scale plasticity, and (iv) large-scale plasticity. A general methodology for estimation of yield strength and hardening exponent of metals is proposed in the last regime.

scholarly journals Structure and Elastic Modulii of Silicon Nanotubes

2008 ◽  
Vol 2 ◽  
pp. 85-90 ◽  
Author(s):  
Veena Verma ◽  
Keya Dharamvir ◽  
V.K. Jindal
Keyword(s):  
Mechanical Properties ◽  
Shear Modulus ◽  
Young’S Modulus ◽  
Experimental Work ◽  
Cohesive Energy ◽  
Young's Modulus ◽  
Young Modulus ◽  
Bulk Silicon ◽  
Silicon Nanotubes

Based on the assumption that sp3 hybridization is more stable in bulk silicon, this study is a step forward in understanding the structures and mechanical properties of silicon nanotubes (SiNT). Using the well tested form of Tersoff potential we have calculated cohesive energy and other parameters for SiNT of various diameters and chiralities. Using this potential, the results obtained for bulk silicon are satisfactory, so we expect that the same potential would work well with SiNT as well. We calculated Young’ modulus and shear modulus for SiNT. Young’s modulus lies in the range of 100- 200 GPa which is about 10-20 times lower than CNT and shear modulus lies between 200-300 GPa. This work shall motivate further theoretical and experimental work in the field of nanostructures.

The Indentation and Puncture Properties of Rubber Vulcanizates

1961 ◽  
Vol 34 (3) ◽  
pp. 937-952 ◽  
Author(s):  
G. S. Yeh ◽  
D. I. Livingston
Keyword(s):  
Young’S Modulus ◽  
Satisfactory Agreement ◽  
Young's Modulus ◽  
Rubber Compound ◽  
Depth Of Penetration ◽  
Characteristic Relation ◽  
Puncture Strength

Abstract A detailed study has been made of the indentation and puncture properties of a number of rubber vulcanizates by a puncture method. It is shown that the characteristic relation between the force and depth of penetration, i.e., the two regions of linearity observed in a former study on a log-log plot, can be represented by two equations. The first region, in which the indenter penetrates into the rubber to a depth approximately equal to twice its diameter, can be generally described by Timoshenko's classical relation, FI=2.67 Erd In the second region, an empirically derived equation FII=1.34 Er0.5d1.5 holds. For a given rubber compound, Young's modulus calculated from the second equation is in satisfactory agreement with the modulus obtained from the first. The puncture strength and the puncture depth are both shown to be dependent upon the compounding variations and they provide useful information about the vulcanizates such as stiffness and cure. Valuable information relating to rubber abrasion and road wear may also result from studies of these two puncture properties.

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