The Strain Dependence of Rubber Viscoelasticity. II. The Influence of Carbon Black

1962 ◽  
Vol 35 (4) ◽  
pp. 918-926 ◽  
Author(s):  
P. Mason
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Particle Diameter ◽  
Viscoelastic Behavior ◽  
Spherical Particles ◽  
Rubber Compound ◽  
Similar Treatment ◽  
Linear Relations ◽  
The Individual ◽  
Individual Particles

Abstract In Part I of this series it was shown how variations in the dynamic Young's modulus with extension could be represented by linear relations for gum rubbers in the region of 0 to 100% extension. The present work uses a similar treatment to examine how the viscoelastic behavior of natural rubber within this extension region is affected by the incorporation of two carbon blacks of widely differing colloidal activity. One of these materials, MT black, consists substantially of spherical particles with a mean diameter of about 0.4 microns: electron microscopy of cut surfaces of the black-rubber compound showed that the individual particles were well-dispersed. The finer material, HAF black, has a mean particle diameter of about 0.04 microns but exists in the rubber compound in a flocculated condition with aggregates up to about 0.3 microns in diameter. The rubber containing the coarse, MT black yielded linear strain relations enabling a direct comparison to be made with the behavior of the gum: the HAF material did not give linear relations for either the dynamic or the equilibrium Young's modulus. To facilitate discussion of this behavior it is desirable to set out more explicitly than in Part I the model underlying the analysis.

The Effect of Design Changes on Sound Transmission through a Building

1996 ◽  
Vol 3 (3) ◽  
pp. 145-185
Author(s):  
Robert J.M. Craik
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Sound Transmission ◽  
Poisson's Ratio ◽  
Analysis Model ◽  
Room Size ◽  
Design Changes ◽  
Small Change ◽  
The Individual

A statistical energy analysis model of a building was used to assess the effect of design changes on sound transmission. Systematic changes were made to the material properties (density, Young's modulus, Poisson's ratio and internal loss factor) and to the dimensions (thickness and room size). These changes resulted in a redistribution of the energy throughout the building causing the noise level to go up in some rooms and to go down in others. For each case examined it was found that the effect of several changes could be estimated from the sum of the individual changes. Thus a change of 20% in the density resulted in approximately double the change in DnTw that was obtained from a 10% change in density. The same additive effect was also found to apply if more than one variable was changed at the same time. Thus the change in DnTw resulting from a small change in Young's modulus for the floors and a small change in the density of the walls can be estimated from the sum of the two individual effects. Changes to the thickness and density of the walls and floors have the greatest effect on sound transmission whilst changes to Young's modulus and Poisson's ratio have a much smaller effect. Damping can also have a significant effect on transmission particularly far from the source.

Young’s modulus measurements of SiC coatings on spherical particles by using nanoindentation

2009 ◽  
Vol 393 (1) ◽  
pp. 22-29 ◽  
Author(s):  
J. Tan ◽  
P.J. Meadows ◽  
D. Zhang ◽  
Xi Chen ◽  
E. López-Honorato ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Spherical Particles ◽  
Sic Coatings

scholarly journals Viscoelasticity in simple indentation-cycle experiments: a computational study

2020 ◽  
Author(s):  
Yu.M. Efremov ◽  
S.L. Kotova ◽  
P.S. Timashev
Keyword(s):  
Young’S Modulus ◽  
Relaxation Function ◽  
Young's Modulus ◽  
Computational Study ◽  
Viscoelastic Behavior ◽  
Elastic Model ◽  
Experimental Conditions ◽  
Relaxation Functions ◽  
Force Curves ◽  
Linear Viscoelastic Theory

Instrumented indentation has become an indispensable tool for quantitative analysis of the mechanical properties of soft polymers and biological samples at different length scales. These types of samples are known for their prominent viscoelastic behavior, and attempts to calculate such properties from the indentation data are constantly made. The simplest indentation experiment presents a cycle of approach (deepening into the sample) and retraction of the indenter, with the output of the force and indentation depth as functions of time and a force versus indentation dependency (force curve). The linear viscoelastic theory based on the elastic-viscoelastic correspondence principle might predict the shape of force curves based on the experimental conditions and underlying relaxation function of the sample. Here, we conducted a computational analysis based on this theory and studied how the force curves were affected by the indenter geometry, type of indentation (triangular or sinusoidal ramp), and the relaxation functions. The relaxation functions of both traditional and fractional viscoelastic models were considered. The curves obtained from the analytical solutions, numerical algorithm and finite element simulations matched each other well. Common trends for the curve-related parameters (apparent Young’s modulus, normalized hysteresis area, and curve exponent) were revealed. Importantly, the apparent Young’s modulus, obtained by fitting the approach curve to the elastic model, demonstrated a direct relation to the relaxation function for all the tested cases. The study will help researchers to verify which model is more appropriate for the sample description without extensive calculations from the basic curve parameters and their dependency on the indentation rate.

scholarly journals Material Properties of the Mandibular Trabecular Bone

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Éva Lakatos ◽  
Lóránt Magyar ◽  
Imre Bojtár
Keyword(s):  
Numerical Simulation ◽  
Trabecular Bone ◽  
Young’S Modulus ◽  
Material Properties ◽  
Young's Modulus ◽  
Element Model ◽  
Cortical Layer ◽  
Compression Tests ◽  
The Individual ◽  
And Storage

The present paper introduces a numerical simulation aided, experimental method for the measurement of Young’s modulus of the trabecular substance in the human mandible. Compression tests were performed on fresh cadaveric samples containing trabecular bone covered with cortical layer, thus avoiding the destruction caused by the sterilization, preservation, and storage and the underestimation of the stiffness resulting from the individual failure of the trabeculae cut on the surfaces. The elastic modulus of the spongiosa was determined by the numerical simulation of each compression test using a specimen specific finite element model of each sample. The received mandibular trabecular bone Young’s modulus values ranged from 6.9 to 199.5 MPa.

scholarly journals The scattering of light by the individual particles in smokes

1926 ◽  
Vol 113 (764) ◽  
pp. 312-322 ◽  
Keyword(s):  
Multiple Scattering ◽  
Wave Length ◽  
Practical Investigations ◽  
Spherical Particles ◽  
Scattering Of Light ◽  
Inhomogeneous Systems ◽  
Theoretical Investigations ◽  
Size Of Particles ◽  
The Individual ◽  
Individual Particles

Theoretical investigations made by Rayleigh on the scattering of light have shown that for indefinitely small spherical particles the intensity of the light scattered by individuals should be proportional to the sixth power of the radius. These investigations have been extended by Mie to spherical particles whose diameter is comparable with the wave-length of light, and he has found that, although Rayleigh’s Law should hold good for particles whose diameter is less than about one-tenth of the wave-length of light, for larger particles the power of the radius will gradually decrease with increase of size to less than two, and will then increase, becoming two again when the particle is sufficiently large to act as a true reflector. These calculations can only be applied accurately to individual particles or to dilute systems, as otherwise the calculations may be invalidated by multiple scattering. No practical investigations have hitherto been made on individual particles. The few experiments which have been carried out have always been concerned with the average scattering per unit volume of comparatively condensed and inhomogeneous systems of particles, and it is doubtful whether the results are free from the complicating effect of multiple scattering. Thus, Tyndallmeter experiments have been made by Tolman and his colleagues on smokes, but the results he obtained could not be expressed in terms of any simple law of scattering or reflexion. Mecklenberg has carried out similar experiments on sulphur solutions which he believed to be homogeneous, and these indicate that Rayleigh’s Law is obeyed for the size of particles investigated.

The Stiffest Wire

1995 ◽  
Vol 62 (4) ◽  
pp. 947-951 ◽  
Author(s):  
K. Schulgasser
Keyword(s):  
Young’S Modulus ◽  
Elastic Constants ◽  
Upper Bound ◽  
Principal Axis ◽  
Young's Modulus ◽  
Maximum Modulus ◽  
Axial Direction ◽  
The Individual ◽  
Oriented Parallel ◽  
Individual Crystallite

We consider a polycrystal constituted from orthorhombic single crystals for which one particular principal axis of the crystallites is always oriented parallel to a particular direction; in the plane perpendicular to this direction the crystallites are randomly oriented. Bounds are found for the Young’s modulus in the axial direction. The lower bound on the Young’s modulus, which is realizable, is found to be that of the individual crystallite in the aligned direction. The upper bound determined is necessarily realizable when the single crystal elastic constants satisfy a certain condition. When this condition is not satisfied a bound is found; whether or not this bound is realizable must be examined using the specific elastic constants of the crystal being considered. For all physical examples considered the upper bound was indeed found to be realizable. Thus, generally speaking, a wire constituted as above, with the stiffest direction of the individual crystallites being along the wire, will have a higher Young’s modulus than the maximum modulus of the individual crystallites of which it is composed.

scholarly journals Solvation-Assisted Young’s Modulus Control of Single-Crystal Fullerene Nanowhiskers

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Tokushi Kizuka ◽  
Kun'ichi Miyazawa ◽  
Takayuki Tokumine
Keyword(s):  
Electron Microscopy ◽  
Single Crystal ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Precipitation Method ◽  
Force Measurements ◽  
Transmission Electron ◽  
Bending Behavior ◽  
The Individual

Single-crystal nanowhiskers (NWs) composed of fullerene C70molecules were synthesized by the liquid-liquid interfacial precipitation method that usedm-xylene as a saturated solution of C70molecules. Bending behavior of the individual NWs was observed byin situtransmission electron microscopy equipped with nanonewton force measurements using an optical deflection method. The Young’s modulus of the NWs was estimated to be 0.3–1.9 GPa, which was 2–7% of the moduli of fullerene NWs with similar diameters synthesized using other solvents, that is, toluene and pyridine. The influence of the solvent used in the precipitation method on Young’s modulus is discussed.

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.

Sign in / Sign up

Export Citation Format

Share Document