An Analysis of the “Durometer” Indentation

1993 ◽  
Vol 66 (5) ◽  
pp. 827-836 ◽  
Author(s):  
Brian J. Briscoe ◽  
K. Savio Sebastian
Keyword(s):  
Elastic Modulus ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Theory Of Elasticity ◽  
Time Dependent ◽  
Shore Hardness ◽  
Hardness Tester ◽  
Hardness Number

Abstract The mechanics of the indentation of elastomers by the “Durometer” (Shore A) hardness tester is analysed using the theory of elasticity to derive an interrelation between the Shore hardness number and the Young's modulus. Experimental compliance curves, for different elastomers, are provided to support the theory. The theoretical interrelationships between the International Rubber Hardness and the Shore A Hardness and the corresponding elastic modulus are also compared. The effects of the time dependent deformations are examined. Finally, the error introduced by computing the Young's modulus using an equivalent punch solution is examined and a means of improving the predictions is provided.

Solution of the inverse elastography problem for parametric classes of inclusions with a posteriori error estimate

2018 ◽  
Vol 26 (4) ◽  
pp. 493-499 ◽  
Author(s):  
Alexander S. Leonov ◽  
Alexander N. Sharov ◽  
Anatoly G. Yagola
Keyword(s):  
Error Estimate ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Posteriori Error ◽  
Theory Of Elasticity ◽  
A Posteriori Error Estimate ◽  
Posteriori Error Estimate ◽  
A Posteriori ◽  
Unknown Parameters ◽  
A Posteriori Error

Abstract This article presents the solution of a special inverse elastography problem: knowing vertical displacements of compressed biological tissue to find a piecewise constant distribution of Young’s modulus in an investigated specimen. Our goal is to detect homogeneous inclusions in the tissue, which can be interpreted as oncological. To this end, we consider the specimen as two-dimensional elastic solid, displacements of which satisfy the differential equations of the linear static theory of elasticity in the plain strain statement. The inclusions to be found are specified by parametric functions with unknown geometric parameters and unknown Young’s modulus. Reducing this inverse problem to the search for all unknown parameters, we solve it applying the modified method of extending compacts by V. K. Ivanov and I. N. Dombrovskaya. A posteriori error estimate is carried out for the obtained approximate solutions.

Residual Properties of the Drawn Steel Wires for Damage-Based Fretting Fatigue Models of the Wire Ropes

2020 ◽  
Vol 1010 ◽  
pp. 71-78
Author(s):  
Maslinda Kamarudin ◽  
Zaini Ahmad ◽  
Mohd Nasir Tamin
Keyword(s):  
Elastic Modulus ◽  
Fatigue Life ◽  
Young’S Modulus ◽  
Prediction Models ◽  
Young's Modulus ◽  
Steel Wire ◽  
Fretting Fatigue ◽  
Wire Ropes ◽  
Residual Properties ◽  
Steel Wires

This paper presents the residual properties and parameters of the damage-based fatigue life prediction models of the steel wire ropes under fretting fatigue conditions. The damage mechanics-based approach is employed to develop the predictive method for the reliability of the steel wire ropes. The elastic modulus is dependent on the fatigue load condition and the accumulated number of the load cycles. The characteristic degradation of the Young’s modulus of drawn steel wires is established through the phenomenological presentation of the interrupted fatigue test data. The samples are given a quasi-static loading followed by a block cyclic loading with various stress amplitudes and ratios. The residual Young’s modulus is calculated after each block of cycles. The effect of the different loading condition with the amplitude and mean stress on the measured fatigue life of a single wire is presented using the life parameter, χ. The residual Young’s modulus data are presented in terms of normalized quantities. Significant reduction in the elastic modulus due to fatigue is exhibited after enduring 70% of the fatigue life of the material. The fitting constants are obtained, and the fitted equation is used to describe the degradation of Young’s modulus at N number of cycles. Subsequently, the data can be applied to predict the fatigue-life of steel wire ropes and assess its reliability through fretting-induced damage models.

Evaluation of Physicomechanical Properties of Ti-45Nb Specimens Obtained by Selective Laser Melting

2017 ◽  
Vol 743 ◽  
pp. 9-12
Author(s):  
Zhanna G. Kovalevskaya ◽  
Margarita A. Khimich ◽  
Andrey V. Belyakov
Keyword(s):  
Young’S Modulus ◽  
Selective Laser Melting ◽  
Laser Power ◽  
Young's Modulus ◽  
Scanning Speed ◽  
Physicomechanical Properties ◽  
Optical Methods ◽  
Laser Melting ◽  
Average Value ◽  
Hardness Tester

Porosity, values of nanohardness and Young’s modulus of the specimens obtained with the method of selective laser melting were measured with optical methods, scanning electron microscopy and Nano Hardness Tester NHT-S-AX-000X device for measuring physicomechanical properties. Ti-45wt%Nb powder obtained with mechanical alloying was used for selective laser melting. The results have shown that increased heat input due to the laser power growth up to 80 W and scanning speed decrease down to 40 mm/s decreases the porosity of the specimen. The nanohardness average value is not sensitive to the changes of scanning modes in the investigated range. The Young’s modulus decreases with energy input increase.

Changes in the Microhardness and Young's Modulus in 2 MeV C+ Ion-Irradiated IG-110 Nuclear Graphite

2005 ◽  
Vol 475-479 ◽  
pp. 1471-1474 ◽  
Author(s):  
Se Hwan Chi ◽  
Gen-Chan Kim ◽  
Jun Hwa Hong ◽  
Sang Chul Kwon ◽  
Jong Hwa Chang
Keyword(s):  
Elastic Modulus ◽  
Young’S Modulus ◽  
Indentation Depth ◽  
Young's Modulus ◽  
Microhardness Test ◽  
Surface Distortion ◽  
Nuclear Graphite

The changes in the microhardness and Young’s modulus of the 2 MeV C+ ion–irradiated IG-110 isotropic nuclear graphite were evaluated by a dynamic ultra-microhardness test. Indentation depth and load dependency of the hardness and elastic modulus were observed possibly due to the formation of a range. Both the hardness and Young’s modulus (E) – dpa curves have shown an incubation dose for about ı 0.3 mdpa. After the incubation dose, both the hardness and E showed a rapid increase with the dose. The doses that corresponds to these rapid increases in the hardness and E coincides with the dose that corresponds to the beginning of the irradiationinduced surface distortion, and the loss of the graphite crystallinity (amorphization).

On the Relation between Indentation Hardness and Young's Modulus

1958 ◽  
Vol 31 (4) ◽  
pp. 896-906 ◽  
Author(s):  
A. N. Gent
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Empirical Relation ◽  
Rigid Sphere ◽  
Indentation Hardness ◽  
Shore Hardness ◽  
Theoretical Relation ◽  
Classical Elasticity ◽  
British Standard ◽  
Classical Elasticity Theory

Abstract A relation between British Standard and International rubber hardness and Young's modulus is derived from classical elasticity theory, and compared with the empirical relation given in B.S.903:1950. An experimental examination of the load-indentation relationship for a rigid sphere pressed into a flat rubber pad is described ; it indicates that the theoretical relation is more appropriate than the empirical one for small indentations, corresponding to hardnesses exceeding about 60° B.S. & I.R.H., and equally valid for hardnesses between about 40° and 60°. Moreover, the numerical constants are not subject to experimental uncertainty. If reduced major loads are stipulated for determining the hardness of rubbers of less than 35° to 40° B.S. & I.R.H., the theoretical relation should apply over the entire useful range. An approximate relation between Shore hardness and Young's modulus is derived similarly. The approximate equivalence of the British Standard and International rubber hardness and Shore hardness scales over the major part of the hardness range is confirmed.

Hardness and Elastic Modulus Measurements in CdTe and ZnTe Thin Film and Bulk Samples and ZnTe-CdTe Superlattices

1988 ◽  
Vol 130 ◽  
Author(s):  
L. J. Farthing ◽  
T. P. Weihs ◽  
D. W. Kisker ◽  
J. J. Krajewski ◽  
M. F. Tang ◽  
...  
Keyword(s):  
Thin Film ◽  
Elastic Modulus ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Superlattice Structure ◽  
Alloying Effects

AbstractHardness and modulus values of bulk and epilayer ZnTe and CdTe samples and of ZnTe-CdTe superlattices are reported. Both hardness and Young's modulus values increase with increasing ZnTe content in the ZnCdTe samples. Alloying effects and strains in the superlattice structure are proposed to explain the strengthening.

scholarly journals Dependence of ultrasonic contact impedance hardness on Young’s modulus of elasticity of creep-resistant steels

ACTA IMEKO ◽  
2017 ◽  
Vol 6 (1) ◽  
pp. 27 ◽  
Author(s):  
Michal Junek ◽  
Jiri Janovec ◽  
Petr Duchacek
Keyword(s):  
Young’S Modulus ◽  
Power Unit ◽  
Modulus Of Elasticity ◽  
Young's Modulus ◽  
Contact Impedance ◽  
Hardness Tester ◽  
Experimental Part ◽  
Young’S Modulus Of Elasticity ◽  
Creep Resistant Steels ◽  
Hardness Values

<p class="Abstract"><span lang="EN-US">The paper deals with the hardness measurements by mobile UCI hardness testers as a means of determining the residual operation life of power unit components. It aims to answer questions regarding the level of dependence of UCI hardness on Young's modulus of creep-resistant steels and determining the conditions of a UCI hardness tester calibration. The experimental part describes comparative measurements of hardness values obtained using stationary hardness testers and UCI hardness testers.</span></p>

scholarly journals Loading-Rate Dependency of Young’s Modulus for Class I and Class II Rocks

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Hailong Zhang ◽  
Seisuke Okubo ◽  
Cancan Chen ◽  
Yang Tang ◽  
Jiang Xu
Keyword(s):  
Young’S Modulus ◽  
Loading Rate ◽  
Young's Modulus ◽  
Underlying Mechanism ◽  
Time Dependent ◽  
Rate Dependency ◽  
Underground Structures ◽  
Dependent Behavior ◽  
Rate Of Increase ◽  
Variable Compliance

Understanding the time-dependent behavior of rocks is important for ensuring the long-term stability of underground structures. Aspects of such a time-dependent behavior include the loading-rate dependency of Young’s modulus, strength, creep, and relaxation. In particular, the loading-rate dependency of Young’s modulus of rocks has not been fully clarified. In this study, four different types of rocks were tested, and the results were used to analyze the loading-rate dependency of Young’s modulus and explain the underlying mechanism. For all four rocks, Young’s modulus increased linearly with a tenfold increase in the loading rate. The rocks showed the same loading-rate dependency of Young’s modulus. A variable-compliance constitutive equation was proposed for the loading-rate dependency of Young’s modulus, and the calculated results agreed well with measured values. Irrecoverable and recoverable strains were separated by loading-unloading-reloading tests at preset stress levels. The constitutive equations showed that the rate of increase in Young’s modulus increased with the irrecoverable strain and decreased with increasing stress. The increase in the irrecoverable strain was delayed at high loading rates, which was concluded to be the main reason for the increase in Young’s modulus with an increasing loading rate.

scholarly journals Theoretical and experimental investigation of MWCNT dispersion effect on the elastic modulus of flexible PDMS/MWCNT nanocomposites

2021 ◽  
Vol 11 (1) ◽  
pp. 55-64
Author(s):  
Pardis Ghahramani ◽  
Kamran Behdinan ◽  
Rasool Moradi-Dastjerdi ◽  
Hani E. Naguib
Keyword(s):  
Elastic Modulus ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Testing Machine ◽  
Experimental Tests ◽  
Weight Fraction ◽  
Experimental Results ◽  
Multiwalled Carbon ◽  
Displacement Mode ◽  
Theoretical Predictions

Abstract In this article, Young’s modulus of a flexible piezoresistive nanocomposite made of a certain amount of multiwalled carbon nanotube (MWCNT) contents dispersed in polydimethylsiloxane (PDMS) has been investigated using theoretical and experimental approaches. The PDMS/MWCNT nanocomposites with the governing factor of MWCNT weight fraction (e.g., 0.1, 0.25, and 0.5 wt%) were synthesized by the solution casting fabrication method. The nanocomposite samples were subjected to a standard compression test to measure their elastic modulus using Instron Universal testing machine under force control displacement mode. Due to the costs and limitations of experimental tests, theoretical predictions on the elasticity modulus of such flexible nanocomposites have also been performed using Eshelby–Mori–Tanaka (EMT) and Halpin–Tsai (HT) approaches. The theoretical results showed that HT’s approach at lower MWCNT contents and EMT’s approach at higher MWCNT contents have a better agreement to experimental results in predicting the elastic modulus of PDMS/MWCNT nanocomposites. The experimental results indicated that the inclusion of MWCNT in the PDMS matrix resulted in a noticeable improvement in Young’s modulus of PDMS/MWCNT nanocomposite at small values of MWCNT contents (up to w f = 0.25%); however, exceeding this nanofiller content did not elevate Young’s modulus due to the emergence of MWCNT agglomerations in the nanocomposite structure.

Young’s Modulus Measurement of Electroplated Nickel Using AFM

2006 ◽  
Author(s):  
Sang-Hyun Kim ◽  
James G. Boyd
Keyword(s):  
Elastic Modulus ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Beam Theory ◽  
Spring Constant ◽  
Time Step ◽  
Simple Method ◽  
Atomic Force ◽  
Silicon Cantilever ◽  
Afm Cantilever

This paper addresses a relatively simple method of measuring Young's modulus of electroplated nickel using Atomic Force Microscope. Thin layer of nickel to be measured is electroplated onto the tip side of AFM silicon cantilever, whose Young's modulus and the geometric dimensions are defined from manufacturer. The resonant frequency and the quality factor of the electroplated AFM cantilever are measured by the tapping mode of AFM and its spring constant is calculated using Sader's method. The spring constant of the electroplated cantilever is also calculated by using the laminar composite beam theory. Comparing two spring constants, Young's modulus of the electroplated nickel is determined. The measured elastic modulus of nickel in each time step is in the range of between and the average elastic modulus is with relative uncertainty of less than 5%

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