scholarly journals Uniaxial Extension and Compression in Stress-Strain Relations of Rubber

1978 ◽  
Vol 51 (4) ◽  
pp. 840-851 ◽  
Author(s):  
Lawrence A. Wood
Keyword(s):  
Experimental Data ◽  
Tensile Deformation ◽  
Uniaxial Extension ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Stress Strain ◽  
General Applicability ◽  
Empirical Constant ◽  
Strain Data ◽  
Theoretical Predictions

Abstract A comprehensive literature survey shows the general applicability of the generalized normalized Martin, Roth and Stiehler equation to uniaxial stress-strain data in extension and compression on rubber vulcanizates. The equation can be expressed as F/M=(L−1−L−2) expA (L−L−1) where F is the stress on the undeformed section and L the ratio of stressed to unstressed length. The equation contains two constants—M, Young's Modulus, the slope of the stress-strain curve at L=1, and A an empirical constant. The conformity of stress-strain data to the equation can readily be determined by a plot of logF/(L−1−L−2) against (L−L−1). In almost every case a straight line is obtained, from the slope and intercept of which both the constants can be determined. The range of validity of the equation usually begins near L=0.5 (in the compression region) and continuing through the region of low deformations often extends to the region of rupture in extension. If uniaxial compression data are available the modulus can thus be obtained by interpolation through the region of low deformations, where experimental data are often somewhat unreliable. The value of the modulus M varies with the nature of the rubber, the extent of vulcanization, and the time and temperature of creep or stress relaxation. The value of the constant A is near 0.4 for pure-gum vulcanizates, increasing to values near 1.0 with increasing filler content, and showing an abrupt increase when crystallization occurs. Direct experimental observations where the deformation of a single specimen is varied continuously from compressive to tensile deformation, are cited to show that M, defined as the limit of the ratio of stress to strain, is independent of the direction of approach to the limit at L=0.5. The normalized Mooney-Rivlin plots show F/[2M (L−L−2)] against L−1. These graphs have only limited regions of linearity corresponding to constant values of the coefficients C1 and C2. Since these regions do not include the undeformed state the Mooney-Rivlin equation cannot be used at low elongations or in compression. The values of C1 and C2 show very wide fluctuations for the Mooney-Rivlin plots of experimental data, which are themselves usually well represented by the Martin, Roth, and Stiehler equation with different values of the constant A. In view of all these considerations the conclusion of the present study confirms that of Treloar in his recent publications in failing to find much utility in making Mooney-Rivlin plots. The failure to represent the experimental data at low elongations and the inability to correlate the constants with theoretical predictions based on strain energy or statistical theory considerations are the most serious objections.

Elastomer Behavior IV. Loop Structure of Elastomer Networks

1966 ◽  
Vol 39 (5) ◽  
pp. 1489-1495
Author(s):  
L. C. Case ◽  
R. V. Wargin
Keyword(s):  
Experimental Data ◽  
Crosslink Density ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Polymer Chains ◽  
Theoretical Treatment ◽  
Loop Structure ◽  
Stress Strain ◽  
Strain Behavior ◽  
Selection Of

Abstract A new theoretical treatment strongly indicates that an elastomer network actually consists of a system of fused, closed, interpenetrating loops of polymer chains. This interpenetrating loop structure restricts the movement of the chains and thereby affects the stress-strain behavior of the elastomer. Methods have been developed to enable the calculation of the number of effective crosslinks caused by loop interpenetrations (virtual crosslinks). The uniaxial stress-strain behavior of an elastomer predicted using our methods can be fitted almost perfectly to published experimental data by proper selection of chain parameters. Previous theoretical treatments gave only a qualitative fit to the experimental data for the stress-strain behavior of elastomers and were not capable of predicting the correct shape of the experimental stress-strain curve. The present treatment gives a nearly perfect fit for both stress as a function of strain at constant crosslink density, and stress as a function of crosslink density at constant strain, and thus represents a vast improvement.

Inverse Calculation of Uniaxial Stress-Strain Curves From Bending Test Data

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
G. S. Schajer ◽  
Y. An
Keyword(s):  
A Priori ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Inverse Solution ◽  
Surface Strain ◽  
Bending Test ◽  
Stress Strain ◽  
Strain Data ◽  
Tension And Compression ◽  
Priori Information

Uniaxial tension and compression stress-strain curves are simultaneously evaluated from load and surface strain data measured during a bending test. The required calculations for the uniaxial results are expressed as integral equations and solved in that form using inverse methods. This approach is taken to reduce the extreme numerical sensitivity of calculations based on equations expressed in differential form. The inverse solution method presented addresses the numerical sensitivity issue by using Tikhonov regularization. The use of a priori information is explored as a means of further stabilizing the stress-strain curve evaluation. The characteristics of the inverse solution are investigated using experimental data from bending and uniaxial tests.

Effect of Temperatures on Tensile of Aluminium Thin Films

2012 ◽  
Vol 528 ◽  
pp. 135-139 ◽  
Author(s):  
Qiao Neng Guo ◽  
Shi E Yang ◽  
Qiang Sun ◽  
Yu Jia ◽  
Yu Ping Huo
Keyword(s):  
Thin Films ◽  
Molecular Dynamics ◽  
Maximum Stress ◽  
Tensile Deformation ◽  
Uniaxial Extension ◽  
Strain Curve ◽  
Local Maximum ◽  
Temperature Curve ◽  
Uniaxial Tensile ◽  
Stress Strain

The mechanical process of single-crystal aluminium thin films under uniaxial tensile strain was simulated with molecular dynamics method at different temperature. The stress–strain curve and potential energy–strain curve of thin aluminium film under uniaxial tensile deformation were obtained by molecular dynamics simulations. With the changes of sample temperatures in uniaxial extension, the variation characteristics of stress–strain curves are alike at the elastic stage and different at the plastic one below and above 370 K, respectively. From the stress–strain curves, we gained the first local maximum stress-temperature curve and the strain at the first local maximum stress-temperature curve, and found that the strange temperature dependence of first local maximum stress: when the temperature is above 370 K, the stress goes down quickly with temperature, and when below 370 K, it descends slowly. With increasing temperature, the difference between two strain values corresponding to two maximal potential energies changes slowly below and above 370K but it goes up quickly about 370K. By these dependences, we have identified the critical temperature （370K） for the transition of plastic flow mechanism.

Stress-Strain Relation in Rubber Blocks under Compression. I

1959 ◽  
Vol 32 (2) ◽  
pp. 409-419
Author(s):  
Géza Schay ◽  
Péter Ször
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Cross Section ◽  
Experimental Error ◽  
Stress Strain ◽  
General Applicability ◽  
Empirical Constant ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Good Agreement

Abstract For the stress-strain relation of differently shaped rubber blocks submitted to compression, an equation of general applicability is deduced, starting from the idea that compression work must be done also against the tension arising through the increase of the free surface. In this equation the stress is not a function of the compression ratio only, but of the ratio of the fixed to the free surface as well. Besides the shear modulus of the block's substance, this equation involves a single empirical constant which changes only slightly with the shape of the block's cross section. The validity of the equation obtained was tested by measurements performed by the authors on cylinders as well as by data on quadratic prisms published in previous literature. The calculated values are in good agreement with the experimental data within the limits of experimental error.

Compression Stress Strain of Rubber

1933 ◽  
Vol 6 (1) ◽  
pp. 126-150 ◽  
Author(s):  
J. R. Sheppard ◽  
W. J. Clapson
Keyword(s):  
Hollow Sphere ◽  
Compressive Force ◽  
Strain Curve ◽  
The Other ◽  
One Dimension ◽  
Compression Stress ◽  
Stress Strain ◽  
Strain Data ◽  
Tensile Forces ◽  
Strain Axis

Abstract 1. A relation of simple form between compressive force and equivalent two-way tensile forces is developed. 2. Based on this relation, a new method for determining the compression stress strain of rubber is outlined, which avoids difficulties and errors inherent in direct compression. It consists in applying tensile forces simultaneously in two directions, and, from these and the strained dimensions, in computing the compressive force that would have produced the same deformation. 3. The mode of applying the two-way tensiles is to inflate a hollow sphere of rubber; the experimental data required to determine the compression stress strain are pressure of gas in, and dimensions of, the inflating hollow sphere. 4. The method has been applied to cold-cured pure-gum rubber in the form of toy balloons which, in its ordinary elongation stress strain, shows a breaking elongation of about 650 to 700 per cent and a tensile of 30 to 40 kg. per square centimeter. While the numerical values obtained on this stock have no special significance, as they will vary from stock to stock, the following are examples: breaking compression, about 97.3 per cent; breaking compressive force, 6000 to 9000 kg. per square centimeter (on original cross section); hysteresis, 29 to 35 per cent of work of compression to near rupture. 5. As a common measuring stick by which to gage degree of strain in deformations of different types—e. g., increasing one dimension (and diminishing the other two) as against diminishing one dimension (and increasing the other two)—energy seems the best. Energy at break for ordinary elongation stress strain was 50 to 70 kg. cm. per cubic centimeter, and for compression stress strain was 89 to 103 kg. cm. per cubic centimeter. 6. The compression stress-strain data may, if desired, be expressed in terms of two-way tensiles vs. two-way elongations. Energy of compression may be computed either as twice the area subtended between such a curve and the strain axis, or as the area between the compression stress strain and the strain axis. 7. It is strongly indicated that the compression stress strain of rubber is continuous with the ordinary elongation stress strain when both are plotted in the same units, and that the complete stress strain should accordingly be considered as a single continuous curve having an elongation branch and a compression branch with the origin as dividing point. 8. The analytic features of the complete stress strain are described. 9. Granting the observed concavity of the upper part of the elongation stress strain, and the thesis of continuity between elongation and compression, a point of inflection is bound to exist theoretically. 10. Implications of the thesis of continuity are: (1) An equation for the stress-strain curve must fit the complete curve; it is not sufficient that it fit the elongation branch only. (2) It is impossible to compute the compression stress strain from the ordinary (one-way) elongation stress-strain data. The two sets of data are related empirically. 11. When compressive force and equivalent two-way tensiles are based on actual cross sections, stress conditions at a point are expressed and we have the simple rule: Pressure at a point is numerically equal to the transverse tensions which, substituted therefor, will maintain the same strain.

Stress Strain Testing of the Strand of E-Glass Fibers

2008 ◽  
Vol 39-40 ◽  
pp. 165-168
Author(s):  
Mária Chromčíková ◽  
Marek Liška
Keyword(s):  
Experimental Data ◽  
Fiber Strength ◽  
Glass Fibers ◽  
Length Distribution ◽  
Continuous Distribution ◽  
Strain Curve ◽  
Young Modulus ◽  
Strength Distribution ◽  
Stress Strain ◽  
Strain Testing

The mathematical model of the stress-strain curve of the strand of glass fibers was proposed and applied on the experimental data obtained for E glass fibers. The model reflects the lognormal continuous distribution of the unstrained lengths of glass fibers and the Weibull distribution of the fibers strength. The regression treatment of experimental data provided the statistically robust estimates of the parameters of the lognormal length distribution, of the Young modulus, and of the parameters of the Weibull glass fibers strength distribution. It was shown that neglecting of the continuous unstrained length distribution leads to serious errors in estimates of the fiber strength distribution.

Interpretation of Experimental Data is Substantial for Constitutive Characterization of Arterial Tissue

2021 ◽  
Author(s):  
Ondrej Lisický ◽  
Anna Hrubanová ◽  
Jiri Bursa
Keyword(s):  
Experimental Data ◽  
Soft Tissues ◽  
Constitutive Models ◽  
Uniaxial Stress ◽  
Mechanical Tests ◽  
Data Sets ◽  
Stress Strain ◽  
Rigorous Approach ◽  
Carotid Wall

Abstract The paper aims at evaluation of mechanical tests of soft tissues and creation of their representative stress-strain responses and respective constitutive models. Interpretation of sets of experimental results depends highly on the approach to the data analysis. Their common representation through mean and standard deviation may be misleading and give non-realistic results. In the paper, raw data of 7 studies consisting of 11 experimental data sets (concerning carotid wall and atheroma tissues) are re-analysed to show the importance of their rigorous analysis. The sets of individual uniaxial stress-strain curves are evaluated using three different protocols: stress-based, stretch-based and constant-based, and the population-representative response is created by their mean or median values. Except for nearly linear responses, there are substantial differences between the resulting curves, being mostly the highest for constant-based evaluation. But also the stretch-based evaluation may change the character of the response significantly. Finally, medians of the stress-based responses are recommended as the most rigorous approach for arterial and other soft tissues with significant strain stiffening.

Mechanical Behavior of Materials under Tensile Loads

2004 ◽  
pp. 13-31
Keyword(s):  
Tensile Test ◽  
Mechanical Behavior ◽  
Tensile Deformation ◽  
True Strain ◽  
Strain Curve ◽  
Tensile Specimen ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Mathematical Expressions ◽  
Reduction In Area

Abstract This chapter focuses on mechanical behavior under conditions of uniaxial tension during tensile testing. It begins with a discussion on the parameters that are used to describe the engineering stress-strain curve of a metal, namely, tensile strength, yield strength or yield point, percent elongation, and reduction in area. This is followed by a section describing the parameters determined from the true stress-true strain curve. The chapter then presents the mathematical expressions for the flow curve. Next, it reviews the effect of strain rate and temperature on the stress-strain curve. The chapter then describes the instability in tensile deformation and stress distribution at the neck in the tensile specimen. It discusses the processes involved in ductility measurement and notch tensile test in tensile specimens. The parameter that is commonly used to characterize the anisotropy of sheet metal is covered. Finally, the chapter covers the characterization of fractures in tensile test specimens.

A Three Dimensional Graphical Aid for Fatigue Data Analysis

2011 ◽  
Vol 488-489 ◽  
pp. 755-758 ◽  
Author(s):  
Bruno Atzori ◽  
Giovanni Meneghetti ◽  
Mauro Ricotta
Keyword(s):  
Experimental Data ◽  
Data Analysis ◽  
Three Dimensional ◽  
Strain Curve ◽  
Fatigue Behaviour ◽  
Fatigue Tests ◽  
Compatibility Conditions ◽  
Stress Strain ◽  
Fatigue Data ◽  
Best Fitting

The fatigue behaviour of materials is usually synthesised in terms of stress-life (S-N) curve or in terms of strain-life (e-N) curve, the latter being described by the so-called Manson-Coffin equation. It is known that the assumption of equality of the plastic and elastic components between the Manson-Coffin and the stabilised stress-strain curves leads to the so-called compatibility conditions which connect the equations theoretically. The material constants of the Manson-Coffin and of the stabilised stress-strain curve are commonly determined by best fitting separately the experimental data obtained from strain-controlled fatigue tests. As a consequence the compatibility conditions may not be fulfilled. In this paper a method for fatigue data analysis that ensures the compatibility conditions is proposed and validated against experimental data.

Sign in / Sign up

Export Citation Format

Share Document