An Experimental Evaluation of the Constant β Relating the Contact Stiffness to the Contact Area in Nanoindentation

2004 ◽  
Vol 841 ◽  
Author(s):  
Jeremy H. Strader ◽  
Sanghoon Shim ◽  
Hongbin Bei ◽  
W. C. Oliver ◽  
G. M. Pharr
Keyword(s):  
Mechanical Properties ◽  
Contact Area ◽  
Contact Stiffness ◽  
Experimental Measurements ◽  
Berkovich Indenter ◽  
Cube Corner ◽  
Fused Quartz ◽  
The Relationship ◽  
Theoretical Analyses ◽  
Scanning Electron

ABSTRACTMeasurements of mechanical properties by nanoindentation with triangular pyramidal indenters like the Berkovich rely heavily upon the relationship between the contact stiffness, S, the contact area, A, and the reduced elastic modulus, Er. This relationship is often written in the form S = 2βEr(A/π)1/2, where β is a constant that depends on the geometry of the indenter. Although the most common values for β used in experimental measurements are 1.000 and 1.034, various theoretical analyses have yielded values as small as 1.00 or as large as 1.2, depending on the assumptions made to model the deformation. Here, we explore the most appropriate value of β by performing careful experiments in fused quartz with thin gold coatings applied to the surface to reveal the actual contact area when observed in the scanning electron microscope. Experiments were performed not only with the Berkovich indenter, but with five other three-sided pyramidal indenters with centerline-to-face angles ranging from 35.3° (cube corner) to 85°. Results are discussed as they apply to obtaining accurate measurements of mechanical properties by nanoindentation.

scholarly journals A Calculation Theory of Earth Pressure Considering Microstructure of Porous Materials

2018 ◽  
Vol 142 ◽  
pp. 02010
Author(s):  
Jun-hu Li ◽  
Chao Zhang ◽  
Wei Xue ◽  
Wen-chao Zhang ◽  
Ri-qing Xu
Keyword(s):  
Contact Area ◽  
Soft Clay ◽  
Stress Transfer ◽  
Earth Pressure ◽  
Transfer Principle ◽  
Lateral Stress ◽  
Microstructure Characteristics ◽  
Pressure Calculation ◽  
The Relationship ◽  
Scanning Electron

To explore a more reasonable earth pressure calculation theory, microstructure characteristics of soft clay in Hangzhou, Ningbo and Wenzhou had been observed using scanning electron microscope (SEM) and were quantitatively analysed using Image-Pro Plus (IPP) software. The relationship between porosity and contact area of soft clay was got by considering the microstructure. Combining soil lateral stress transfer principle, a calculation theory of earth pressure considering soil contact area was got. The possible reason of the differences between earth pressure and the actual monitoring earth pressure was analysis by the case.

On the generality of the relationship among contact stiffness, contact area, and elastic modulus during indentation

1992 ◽  
Vol 7 (3) ◽  
pp. 613-617 ◽  
Author(s):  
G.M. Pharr ◽  
W.C. Oliver ◽  
F.R. Brotzen
Keyword(s):  
Elastic Modulus ◽  
Contact Area ◽  
Contact Stiffness ◽  
Elastic Half Space ◽  
Elastic Contact ◽  
Simple Relationship ◽  
Depth Sensing ◽  
Force Microscopy ◽  
Atomic Force ◽  
The Relationship

Results of Sneddon's analysis for the elastic contact between a rigid, axisymmetric punch and an elastic half space are used to show that a simple relationship exists among the contact stiffness, the contact area, and the elastic modulus that is not dependent on the geometry of the punch. The generality of the relationship has important implications for the measurement of mechanical properties using load and depth sensing indentation techniques and in the measurement of small contact areas such as those encountered in atomic force microscopy.

Dispersion technology on mechanical properties of carbon nanomaterials reinforced epoxy nanocomposites

2020 ◽  
Vol 34 (07n09) ◽  
pp. 2040019
Author(s):  
Chin-Lung Chiang ◽  
Chien-Wei Hsu ◽  
Hsiu-Ming Wu ◽  
Ming-Yuan Shen
Keyword(s):  
Mechanical Properties ◽  
Contact Area ◽  
Carbon Nanomaterials ◽  
Flexural Modulus ◽  
Stress Transfer ◽  
Phonon Transport ◽  
Epoxy Nanocomposites ◽  
Constant Area ◽  
Surface Contact Area ◽  
Scanning Electron

Graphene nanoplatelets (GNPs) are platelet-liked graphite nanocrystals with multigraphene layers. In general, a high contact area between polymer and nanofiller maximizes stress transfer from the polymer matrix to nanofillers. Therefore, GNPs can be expected to exhibit better reinforcement than CNTs in polymer composites, because of their ultrahigh aspect ratio (600–10,000) and higher surface constant area. The GNPs planar structure provides a 2D path for phonon transport, and the ultrahigh surface area allows a large surface contact area with polymer resulting in the enhancement of the composite thermal conductivity. In this study, simple and efficient planetary mixing methods were used to enable the GNPs to disperse uniformly throughout the epoxy solution (i.e. 0, 0.1, 0.25, 0.5, 0.75, and 1.0 wt%) and then to prepare GNPs/epoxy nanocomposites. Mechanical properties of the nanocomposite, including ultimate tensile, flexural strength and flexural modulus, were investigated. Finally, the fracture surface of the specimen was investigated using scanning electron microscopy (SEM) to determine the dispersion of the GNPs in the composites.

scholarly journals Joining Alumina and Sapphire by Growing Aluminium Borate Whiskers In-Situ, and the Whiskers’ Orientation Relationship with the Sapphire Substrate

Materials ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 175 ◽  
Author(s):  
Chun Li ◽  
Xiaoqing Si ◽  
Shuang Wu ◽  
Junlei Qi ◽  
Yongxian Huang ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Orientation Relationship ◽  
Sapphire Substrate ◽  
Great Influence ◽  
The Other ◽  
Aluminium Borate ◽  
Random Growth ◽  
The Relationship ◽  
Scanning Electron

Bonding between polycrystal alumina and sapphire with (0001), (10 1 ¯ 0), (11 2 ¯ 0), (1 1 ¯ 02) orientations is successfully achieved by growing aluminium borate whiskers in the joint. The morphology of the whiskers in the joint is characterised by (Scanning Electron Microscopy) SEM. The relationship between the growing direction of the aluminium borate whiskers and the orientation of the sapphire substrate is investigated. The effect of the growing direction of the aluminium borate whiskers on the mechanical properties of the joint is discussed. The results show that the whiskers on the sapphire with (10 1 ¯ 0) orientation grow perpendicular to the surface of the substrate while the whiskers show a random growth on the other substrates. It is found that there is an orientation relationship between the whiskers (220) and sapphire (10 1 ¯ 0) and the morphology of the whiskers has great influence on the mechanical properties of the joint. The joint between polycrystal alumina and sapphire with (10 1 ¯ 0) orientation exhibits the highest strength, which reaches 26 MPa.

Fundamental relations used in nanoindentation: Critical examination based on experimental measurements

2002 ◽  
Vol 17 (9) ◽  
pp. 2227-2234 ◽  
Author(s):  
M. Martin ◽  
M. Troyon
Keyword(s):  
Elastic Modulus ◽  
Correction Factor ◽  
Contact Stiffness ◽  
Elastic Half Space ◽  
Critical Examination ◽  
Experimental Measurements ◽  
Contact Depth ◽  
Power Law Exponent ◽  
Fused Quartz ◽  
Measured Hardness

The fundamental relations used in the analysis of nanoindentation load–displacement data to determine elastic modulus and hardness are based on Sneddon's solution for indentation of an elastic half-space by rigid axisymmetric indenters. It has been recently emphasized that several features that have important implications for nanoindentation measurements are generally ignored. The first one concerns the measurement of the contact depth, which is actually determined by using a constant value ε = 0.75 for the geometry of a Berkovich indenter and for any kind of material, whereas the reality is that ε is a function of the power law exponent deduced from the analysis of the unloading curve. The second feature concerns the relation between contact stiffness, elastic modulus, and contact area, in which a correction factor γ larger than unity is usually ignored leading to a systematic overestimation of the area function and thus to errors in the measured hardness and modulus. Experimental measurements on fused quartz are presented that show the variation of ε with the geometry of the tip–sample contact; that is to say with the contact depth, as well as the existence of the correction factor γ, as predicted in some recent articles. Effects of both ε and γ on harness and modulus measurements are also shown.

Comparison of Particle Size Analyses from FEG-SEM and TEM Images

2000 ◽  
Vol 6 (S2) ◽  
pp. 380-381
Author(s):  
S. Lanteri ◽  
D. Gendt ◽  
P. Barges ◽  
G. Petitgand
Keyword(s):  
Electron Microscopy ◽  
Experimental Data ◽  
Mechanical Properties ◽  
Size Range ◽  
Experimental Measurements ◽  
Mechanical Processing ◽  
Size Distributions ◽  
Heat Treated ◽  
Steel Properties ◽  
Scanning Electron

Much effort has recently been employed in modeling steel behavior as a function of chemical composition and thermo-mechanical processing. In order for the models to be predictive, experimental data are needed to first calibrate and then validate the calculated results. Since many steel properties are conditioned in part by the state of precipitation, this study was undertaken to provide experimental measurements of precipitates in terms of their size distributions. Due to the size range (2-100 nm) of particles which exert the greatest influence on the mechanical properties, electron microscopy is practically the only technique available for obtaining images of the precipitates.Two types of micrographs were used for image analysis in order to determine the size distribution of NbC particles present in a ternary alloy (Fe-Nb-C) heat treated at 800°C for 1000 mn. Polished surfaces lightly etched with a solution of 2% HNO3 and 98% ethanol were prepared for observations in a LEO 1550 scanning electron microscope equipped with a field emission gun.

Normal Contact Stiffness on Unit Area of a Mechanical Joint Surface Considering Perfectly Elastic Elliptical Asperities

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
J. P. Shi ◽  
K. Ma ◽  
Z. Q. Liu
Keyword(s):  
Contact Area ◽  
Unit Area ◽  
Rough Surfaces ◽  
Contact Stiffness ◽  
Unit Length ◽  
Joint Surface ◽  
Normal Contact ◽  
Mechanical Joint ◽  
Normal Contact Stiffness ◽  
The Relationship

Based on the Greenwood and Williamson theory, an assumption about the contact-area size of asperities on rough surfaces is proposed under the premise that the height of these asperities on rough surfaces is a Gaussian distribution. A formula has been derived to measure the number of asperities on 2D surfaces. The contact stiffness on a unit length of a 1D outline and that on a unit area of 2D surfaces are presented based on a formula for determining the number of asperities. The relationship between macro parameters, such as contact stiffness and micro parameters on the joint surface, is established.

scholarly journals Modelling the mechanical response of urushi lacquer subject to a change in relative humidity

2012 ◽  
Vol 468 (2147) ◽  
pp. 3533-3551 ◽  
Author(s):  
X. Liu ◽  
R. D. Wildman ◽  
I. A. Ashcroft ◽  
A. E. Elmahdy ◽  
P. D. Ruiz
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Relative Humidity ◽  
Moisture Content ◽  
Thin Layer ◽  
Mechanical Response ◽  
Experimental Measurements ◽  
Environmental Conditioning ◽  
The Relationship ◽  
Good Agreement

A hygromechanical model has been developed to simulate the in-service behaviour of the natural lacquer urushi , using a phenomenological description of viscoelasticity. The material and mechanical properties were determined as a function of the relative humidity (RH), and the relationship between RH and moisture content was determined. These properties served as inputs to a finite-element-based model that was then tested against experimental measurements of the depth-averaged stresses in a thin layer of urushi deposited on a substrate and exposed to changes in the environmental conditions. Good agreement was seen between the predicted and measured behaviour. The validated model was used to investigate the spatial and temperature variation of stress in urushi films subjected to cyclic environmental conditioning.

Effect of Trace Strontium Addition on Microstructure and Room Temperature Fracture Toughness of Nb-12Si-22Ti Alloys

2016 ◽  
Vol 849 ◽  
pp. 603-608 ◽  
Author(s):  
Mei Ling Wu ◽  
Feng Wei Guo ◽  
Ming Li ◽  
Ya Fang Han
Keyword(s):  
Mechanical Properties ◽  
Fracture Toughness ◽  
Electron Microscope ◽  
Scanning Electron Microscope ◽  
Room Temperature ◽  
X Ray Diffraction ◽  
X Ray ◽  
Temperature Fracture ◽  
The Relationship ◽  
Scanning Electron

The effect of strontium (Sr) addition (0.2 at.%) on the microstructure and mechanical properties of Nb-12Si-22Ti alloys were studied. Microstructure of the alloys was observed by scanning electron microscope, and their phase compositions were analyzed with X-ray diffraction and Electro-Probe Microanalyzer. The room temperature fracture toughness was measured. The results indicated that the phases of Nbss and Nb3Si were presented in Nb-12Si-22Ti alloys. However, with the Al and Sr addition, the alloys were composed of Nbss and β-Nb5Si3. Compared with the Nb-12Si-22Ti alloys, the value of room temperature fracture toughness increased about 46% and 73% with the addition of Al and Sr alloy, respectively. The relationship between the microstructure and the mechanical properties was discussed.

Effect of Silk Reeling Velocity on the Aggregation Structure of Raw Silk

2011 ◽  
Vol 175-176 ◽  
pp. 496-499
Author(s):  
Li Na Li ◽  
Shi Qi Bai ◽  
Ya Qin Fu
Keyword(s):  
Electron Microscopy ◽  
Mechanical Properties ◽  
Scanning Electron Microscopy ◽  
Sonic Velocity ◽  
X Ray Diffraction ◽  
Orientation Degree ◽  
X Ray ◽  
Aggregation Structure ◽  
The Relationship ◽  
Scanning Electron

The aggregation structure of raw silk which influences the mechanical properties of raw silk directly is not only determined by the properties of cocoon but also affected by silk reeling velocity. In this study, the relationship between aggregation structure of raw silk and silk reeling velocity was studied by means of sonic velocity method, X-ray diffraction (XRD) and scanning electron microscopy (SEM). The study showed that orientation degree, crystallinity and mechanical properties of raw silk were remarkably influenced by silk reeling velocity, and the mechanical properties of raw silk would be improved through the reasonable silk reeling velocity.

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