Composites: General considerations, relationship of the microstructure and effective properties, application of composites in development of the materials with specific properties. III. Relationship of the microstructure and effective properties of materials using Young's modulus as an example

1993 ◽  
Vol 32 (6) ◽  
pp. 555-560 ◽  
Author(s):  
G. Ondracek ◽  
I. A. Kravchenko
Keyword(s):  
Young’S Modulus ◽  
Effective Properties ◽  
Young's Modulus ◽  
Properties Of Materials ◽  
Relationship Of

Effective properties of composite materials containing voids

1993 ◽  
Vol 440 (1909) ◽  
pp. 461-473 ◽  
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Effective Properties ◽  
Young's Modulus ◽  
Matrix Material ◽  
Practical Importance ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Two Dimensional ◽  
Isotropic Composite

Recent results of theoretical and practical importance prove that the two-dimensional (in-plane) effective (average) Young’s modulus for an isotropic elastic material containing voids is independent of the Poisson’s ratio of the matrix material. This result is true regardless of the shape and morphology of the voids so long as isotropy is maintained. The present work uses this proof to obtain explicit analytical forms for the effective Young’s modulus property, forms which simplify greatly because of this characteristic. In some cases, the optimal morphology for the voids can be identified, giving the shapes of the voids, at fixed volume, that maximize the effective Young’s modulus in the two-dimensional situation. Recognizing that two-dimensional isotropy is a subset of three-dimensional transversely isotropic media, it is shown in this more general case that three of the five properties are independent of Poisson’s ratio, leaving only two that depend upon it. For three-dimensionally isotropic composite media containing voids, it is shown that a somewhat comparable situation exists whereby the three-dimensional Young’s modulus is insensitive to variations in Poisson’s ratio, v m , over the range 0 ≤ v m ≤ ½, although the same is not true for negative values of v m . This further extends the practical usefulness of the two-dimensional result to three-dimensional conditions for realistic values of v m .

scholarly journals Measurement of Young’s Modulus in Noodles and Bucatini

2019 ◽  
Vol 01 (02) ◽  
pp. 1950010
Author(s):  
Vladimir Vargas-Calderón ◽  
A. F. Guerrero-González ◽  
F. Fajardo
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Low Cost ◽  
Small Deformation ◽  
The Other ◽  
Experimental Setup ◽  
Mechanical Hysteresis ◽  
Elastic Curves ◽  
Properties Of Materials ◽  
Basic Concepts

The mechanical behavior of two types of pasta (noodles and bucatini) was studied in a cantilever-loaded-at-the-end experimental setup. One end of each pasta was fixed while the other end was submitted to forces perpendicular to the line determined by the pasta when undeflected. Elastic curves were studied, resulting in values of [Formula: see text][Formula: see text]GPa and [Formula: see text][Formula: see text]GPa for the Young’s modulus of bucatini and noodles respectively. The relation coming from small slopes approximation between the free end’s displacement and the load was analyzed, resulting in values of [Formula: see text][Formula: see text]GPa and [Formula: see text][Formula: see text]GPa for the Young’s modulus of bucatini and noodles respectively. Mechanical hysteresis was found in the pasta, resulting in a small deformation. The experiment that we propose illustrates elastic properties of materials, and shows students how to perform measurements of Young’s modulus in cantilevers of different geometries. Furthermore, the experiment can be done with low cost materials, so that it is reproducible in basic mechanics laboratories and it is a good first introduction to some basic concepts of elasticity like mechanical hysteresis.

scholarly journals Displacement Approach to Determine the Effective Tensile and Torsional Modulus of Nanowires

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Lin Fang ◽  
Quan Yuan ◽  
Bin Wu ◽  
Honglin Li ◽  
Mengyang Huang
Keyword(s):  
Young’S Modulus ◽  
Effective Properties ◽  
Young's Modulus ◽  
Axial Strain ◽  
Surface Elasticity ◽  
Volume Ratio ◽  
Field Equations ◽  
Surface Residual Stresses ◽  
Residual Strains ◽  
Displacement Approach

Surface elasticity and residual stress have a strong influence on the effective properties of nanowire (NW) due to its excessively large surface area-to-volume ratio. Here, the classical displacement method is used to solve the field equations of the core-surface layer model subjected to tension and torsion. The effective Young’s modulus is defined as the ratio of normal stress to axial strain, which decreases with the increase in NW radius and gradually reaches the bulk value. The positive or negative surface residual stresses will increase or decrease Young’s modulus and shear modulus due to the surface residual strains. Nonzero radial and circumferential strains enhance the influence of surface moduli on the effective modulus.

Study on the Electrometric Method to Measure the Young’s Modulus of Metal Materials

2013 ◽  
Vol 652-654 ◽  
pp. 1319-1334
Author(s):  
Li Feng Xiao ◽  
Ran Duan ◽  
Xin Guang Chen
Keyword(s):  
Young’S Modulus ◽  
Strain Gauge ◽  
Young's Modulus ◽  
Key Factors ◽  
Electrometric Method ◽  
Measurement Results ◽  
Engineering Significance ◽  
Properties Of Materials ◽  
Metal Materials

Young's modulus is one of the basic mechanical properties of materials, so its accurate measurement has great engineering significance. Electrometric method is one of the commonly used method. Proceeding from experimental techniques, this paper studies the key factors which affect the result of the experimental measurement, including the influence of the uneven load, the pre-stretching, the hardening time of the strain gauge binder, and sticking quality of strain gauge; comprehensively provides the experimental measures to improve the measurement accuracy. Then through the uncertainty evaluations of the results with different measures, this paper from a point of quantitative view proves that taking these measures can reduce the dispersion of the measurement results and significantly improve the accuracy of experimental results.

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.

Sensing Mechanical Properties of Solid Materials with Bimorph Piezotransducers

2013 ◽  
Vol 543 ◽  
pp. 289-292
Author(s):  
Yung Cheng Wang ◽  
Chih Chin Ko ◽  
Tien Shu Chang
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Material Properties ◽  
Young's Modulus ◽  
Viscoelastic Damping ◽  
Base Excitation ◽  
Solid Materials ◽  
Resonant Frequencies ◽  
Linear Viscoelastic ◽  
Properties Of Materials

Mechanical properties of materials, such as Young's modulus, shear modulus andlinear viscoelastic damping, are experimentally measured with a thin- lm cantilever shaker. Theexperimental apparatus consists of a bimorph piezoelectric transducer acting as an actuator togenerate base excitation to the cantilever, which is analogous to earthquake causing buildingvibration. The motion of the cantilever is monitored by a pair of ber optics to measure thedisplacements of the xed end and the sample. Linear viscoelastic properties of the materialare measured from the resonant frequencies of the vibrating cantilever. Young's modulus andshear modulus are measured from bending and torsion resonant peaks, respectively. For highloss materials, loss tangent of the materials is obtained from the Lorenzian curve t around theresonant peak. Material properties at various frequencies are measured by changing the lengthof the specimens. Furthermore, by introducing crack-like defects, the measured resonances,which may be viewed as a measure of e ective moduli, are able to be adopted to locate thecrack via the method of system identi cation.

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.

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