Relationship of Young's modulus with the macrostructure of polycrystalline graphites

1985 ◽  
Vol 17 (9) ◽  
pp. 1282-1286 ◽  
Author(s):  
A. S. Kotosonov ◽  
I. Ya. Levintovich ◽  
V. Ya. Kotosonova
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Relationship Of

A precise correcting method for the study of the superhard material using nanoindentation tests

2007 ◽  
Vol 22 (5) ◽  
pp. 1255-1264 ◽  
Author(s):  
Yan Ping Cao ◽  
Ming Dao ◽  
Jian Lu
Keyword(s):  
Young’S Modulus ◽  
Half Space ◽  
Young's Modulus ◽  
Elastic Half Space ◽  
Indentation Load ◽  
Superhard Materials ◽  
Element Analysis ◽  
Diamond Indenter ◽  
Load Displacement ◽  
Relationship Of

The accurate description of the indentation load–displacement relationship of an elastic sharp indenter indenting into an elastic half-space is critical for analyzing the nanoindentation data of superhard materials using the procedure proposed by Oliver and Pharr [J. Mater. Res.7, 1564 (1992)]. A further discussion on this issue is made in the present work to reconcile the apparent inconsistencies that have appeared between the experimental results reported by Lim and Chaudhri [Philos. Mag.83, 3427 (2003)] and the analysis performed by Fischer-Cripps [J. Mater. Res.18, 1043 (2003)]. It is found that the indenter size effect is responsible for this large discrepancy. Moreover, according to our analysis, we found that when the deformation of the indenter is significant, besides the errors caused by the Sneddon’s boundary condition as addressed by Hay et al. [J. Mater. Res.14, 2296 (1999)], the errors induced by the application of reduced modulus should be considered at the same time in correcting the modified Sneddon’s solution. In the present work, for the diamond indenter of 70.3° indenting into an elastic half-space with its Poisson’s ratio varying from 0.0 to 0.5 and the ratio of the Young’s modulus of the indented material to that of the diamond indenter, Ematerial/Eindenter, varying from 0 to 1, a set of new correction factors are proposed based on finite element analysis. The results reported here should provide insights into the analysis of the nanoindentation load–displacement data when using a diamond indenter to determine the hardness and Young’s modulus of superhard materials.

Influence of the Process Temperature of Spark Plasma Sintering on Micorsturcture and Nanoindentation Hardness/Young’s Modulus of WC-8wt%Co

2014 ◽  
Vol 616 ◽  
pp. 56-61
Author(s):  
Jian Feng Zhang ◽  
Eberhard Burkel
Keyword(s):  
Young’S Modulus ◽  
Spark Plasma Sintering ◽  
Young's Modulus ◽  
Peak Load ◽  
Fine Grain ◽  
Plasma Sintering ◽  
Spark Plasma ◽  
Nanoindentation Hardness ◽  
Relationship Of ◽  
The Relationship

WC-8wt%Co nanopowder was consolidated by spark plasma sintering at process temperatures (TSPS) from 1100 to 1400 °C. The nanoindentation hardness and Young’s modulus of the consolidated specimens were measured under different peak load levels (Pmax). The hardnesses and modulus of WC-8wt% Co shows a clear dependence on the microstructures and peak load levels. At 1200 and 1300 °C, the hardness and modulus were higher than those at 1100 and 1400 °C due to the higher relative density and fine grain size. The relationship of stiffness (S) and contact depth (hc) of nanoindentation was discussed.

How Structural Features of a Spring-Based Model of Fibrous Collagen Tissue Govern the Overall Young's Modulus

2021 ◽  
Author(s):  
Nathaniel Neubert ◽  
Emily Evans ◽  
John Dallon
Keyword(s):  
Young’S Modulus ◽  
Fiber Length ◽  
Young's Modulus ◽  
Structural Features ◽  
Strain Response ◽  
Stress Strain ◽  
Nodal Density ◽  
Relationship Of ◽  
Fibrous Tissues ◽  
Insight Into

Abstract While much study has been dedicated to investigating biopolymers' stress-strain response at low strain levels, little research has been done to investigate the linear region of biopolymers' stress-strain response and how the microstructure affects it. We propose a mathematical model of fibrous networks which reproduces qualitative features of collagen gel's stress-strain response and provides insight into the key features which impact the Young's Modulus of similar fibrous tissues. This model analyzes the relationship of the Young's Modulus of the lattice to internodal fiber length, number of connection points or nodes per unit area, and average number of connections to each node. Our results show that fiber length, nodal density, and level of connectivity each uniquely impact the Young's Modulus of the lattice. Furthermore, our model indicates that the Young's Modulus of a lattice can be estimated using the effective resistance of the network, a graph theory technique that measures distances across a network. Our model thus provides insight into how the organization of fibers in a biopolymer impact its linear Young's Modulus.

scholarly journals Analysis of Carbon Nanotubes on the Mechanical Properties at Atomic Scale

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaowen Lei ◽  
Toshiaki Natsuki ◽  
Jinxing Shi ◽  
Qing-Qing Ni
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Mathematic Model ◽  
Deformation Energy ◽  
Atomic Scale ◽  
Graphite Sheet ◽  
Relationship Of ◽  
Walled Carbon Nanotubes

This paper aims at developing a mathematic model to characterize the mechanical properties of single-walled carbon nanotubes (SWCNTs). The carbon-carbon (C–C) bonds between two adjacent atoms are modeled as Euler beams. According to the relationship of Tersoff-Brenner force theory and potential energy acting on C–C bonds, material constants of beam element are determined at the atomic scale. Based on the elastic deformation energy and mechanical equilibrium of a unit in graphite sheet, simply form ED equations of calculating Young's modulus of armchair and zigzag graphite sheets are derived. Following with the geometrical relationship of SWCNTs in cylindrical coordinates and the structure mechanics approach, Young's modulus and Poisson's ratio of armchair and zigzag SWCNTs are also investigated. The results show that the approach to research mechanical properties of SWCNTs is a concise and valid method. We consider that it will be useful technique to progress on this type of investigation.

Mechanical properties of FeAlSi powders prepared by mechanical alloying from different initial feedstock materials

2019 ◽  
Vol 107 (2) ◽  
pp. 207 ◽  
Author(s):  
Jaroslav Čech ◽  
Petr Haušild ◽  
Miroslav Karlík ◽  
Veronika Kadlecová ◽  
Jiří Čapek ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Mechanical Alloying ◽  
Young’S Modulus ◽  
Milling Time ◽  
Young's Modulus ◽  
Element Model ◽  
X Ray Diffraction ◽  
X Ray ◽  
Powder Particles ◽  
Complete Homogenization

FeAl20Si20 (wt.%) powders prepared by mechanical alloying from different initial feedstock materials (Fe, Al, Si, FeAl27) were investigated in this study. Scanning electron microscopy, X-ray diffraction and nanoindentation techniques were used to analyze microstructure, phase composition and mechanical properties (hardness and Young’s modulus). Finite element model was developed to account for the decrease in measured values of mechanical properties of powder particles with increasing penetration depth caused by surrounding soft resin used for embedding powder particles. Progressive homogenization of the powders’ microstructure and an increase of hardness and Young’s modulus with milling time were observed and the time for complete homogenization was estimated.

Degradation of Rocks, Through Cracking Caused by Differential Thermal Expansion, in Relation to Nuclear Waste Repositories

1981 ◽  
Vol 6 ◽  
Author(s):  
J.R. Mclaren ◽  
R.W. Davidge ◽  
I. Titchell ◽  
K. Sincock ◽  
A. Bromley
Keyword(s):  
Thermal Expansion ◽  
Grain Boundary ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Crack Density ◽  
Granitic Rocks ◽  
Multiphase Materials ◽  
Thermal Expansion Behaviour ◽  
Waste Repositories ◽  
Expansion Behaviour

ABSTRACTHeating to temperatures up to 500°C, gives a reduction in Young's modulus and increase in permeability of granitic rocks and it is likely that a major reason is grain boundary cracking. The cracking of grain boundary facets in polycrystalline multiphase materials showing anisotropic thermal expansion behaviour is controlled by several microstructural factors in addition to the intrinsic thermal and elastic properties. Of specific interest are the relative orientations of the two grains meeting at the facet, and the size of the facet; these factors thus introduce two statistical aspects to the problem and these are introduced to give quantitative data on crack density versus temperature. The theory is compared with experimental measurements of Young's modulus and permeability for various rocks as a function of temperature. There is good qualitative agreement, and the additional (mainly microstructural) data required for a quantitative comparison are defined.

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.

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