The Elastic Behavior of Vulcanized Rubber

1933 ◽  
Vol 1 (2) ◽  
pp. 45-48
Author(s):  
H. Hencky
Keyword(s):  
Simple Function ◽  
Elastic Behavior ◽  
Stress Strain ◽  
Vulcanized Rubber ◽  
Tension And Compression ◽  
Elastic Coefficients

Abstract Up to extensions of about 270 per cent the elastic behavior of vulcanized rubber can be represented analytically by a very simple function. The stress-strain diagrams for tension and compression are quite different; nevertheless this asymmetrical behavior is satisfactorily taken care of by employing only two elastic coefficients.

Stress Softening in Rubber Vulcanizates. Part I. Use of a Strain Amplification Factor to Describe Elastic Behavior of Filler-Reinforced Vulcanized Rubber

1966 ◽  
Vol 39 (4) ◽  
pp. 799-813 ◽  
Author(s):  
L. Mullins ◽  
N. R. Tobin
Keyword(s):  
Volume Concentration ◽  
Spherical Particles ◽  
Elastic Behavior ◽  
Simple Extension ◽  
Factor X ◽  
Stress Strain ◽  
Vulcanized Rubber ◽  
Stress Strain Relation ◽  
Strain Data ◽  
Volume Swelling

Abstract Measurements of Young's modulus of vulcanized rubbers containing thermal carbon black show the predicted dependence on the volume concentration given by relationships derived for a suspension of spherical particles, for example, that due to Guth, Simha, and Gold which gives E=E0 (1+2.5c+14.1c2). A simple interpretation of the results is that the strain in the rubber is increased by the presence of filler so that the ratio of the average strain to the measured overall strain is given by the factor X=1+2.5c+14.1c2. This factor was used to analyze simple extension stress-strain data obtained at larger extensions. For this purpose the Mooney—Rivlin relation was used to describe the behavior of the rubber phase. Values of C1 independent of the volume concentration and in close accord with measurements of the equilibrium volume swelling of the rubbers were obtained. Values of λ* were also consistent with those of #5#. Analysis of stress—strain data obtained on rubbers containing smaller particle-sized carbon blacks is more complex. For these materials the relation due to Guth, viz., E=E0 (1+2.5c+14.1c2), was chosen. By the choice of suitable values of f, good agreement with the Mooney—Rivlin stress—strain relation was achieved at volume concentrations less than about 0.15.

scholarly journals A General Temperature-Dependent Stress–Strain Constitutive Model for Polymer-Bonded Composite Materials

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1393
Author(s):  
Xiaochang Duan ◽  
Hongwei Yuan ◽  
Wei Tang ◽  
Jingjing He ◽  
Xuefei Guan
Keyword(s):  
Composite Materials ◽  
Constitutive Model ◽  
Model Parameters ◽  
Temperature Dependent ◽  
Stress Strain ◽  
Proposed Model ◽  
Single Temperature ◽  
Testing Data ◽  
Bonded Composite ◽  
Tension And Compression

This study develops a general temperature-dependent stress–strain constitutive model for polymer-bonded composite materials, allowing for the prediction of deformation behaviors under tension and compression in the testing temperature range. Laboratory testing of the material specimens in uniaxial tension and compression at multiple temperatures ranging from −40 ∘C to 75 ∘C is performed. The testing data reveal that the stress–strain response can be divided into two general regimes, namely, a short elastic part followed by the plastic part; therefore, the Ramberg–Osgood relationship is proposed to build the stress–strain constitutive model at a single temperature. By correlating the model parameters with the corresponding temperature using a response surface, a general temperature-dependent stress–strain constitutive model is established. The effectiveness and accuracy of the proposed model are validated using several independent sets of testing data and third-party data. The performance of the proposed model is compared with an existing reference model. The validation and comparison results show that the proposed model has a lower number of parameters and yields smaller relative errors. The proposed constitutive model is further implemented as a user material routine in a finite element package. A simple structural example using the developed user material is presented and its accuracy is verified.

Entropy Elasticity in High Polymers

1967 ◽  
Vol 40 (3) ◽  
pp. 777-785
Author(s):  
Friedrich Linhardt
Keyword(s):  
Present Article ◽  
19Th Century ◽  
Experimental Approach ◽  
Operating Temperature ◽  
Elastic Behavior ◽  
Unusual Property ◽  
Vulcanized Rubber ◽  
Entropy Elasticity ◽  
The 19Th Century ◽  
High Polymers

Abstract Vulcanized rubber has an unusual property, known early in the 19th century, but not understood until 1935: it increases in stiffness with rise in operating temperature. A strip of rubber loaded with a weight and heated does not stretch; on the contrary, it contracts to some extent. Theoretical interpretations of this effect showed deformation of rubber, as well as its softness and high extensibility, to be determined by entropy, among other things. “Entropy elasticity” was looked upon as a peculiarity of rubber. It was thus only logical, when materials were classified as “rubbers” that they should be distinguished from all other materials by using the expression “entropy elastic behavior”. To be sure, one is inclined today to consider entropy elasticity a characteristic of all high polymers, including those not crosslinked. The present article reports an experimental approach to this problem.

scholarly journals Stress-strain curve of concretes with recycled concrete aggregates: analysis of the NBR 8522 methodology

2017 ◽  
Vol 10 (3) ◽  
pp. 547-567 ◽  
Author(s):  
D. A. GUJEL ◽  
C. S. KAZMIERCZAK ◽  
J. R. MASUERO
Keyword(s):  
Test Procedure ◽  
Strain Curve ◽  
Recycled Concrete ◽  
Load Test ◽  
Recycled Aggregates ◽  
Elastic Behavior ◽  
It Use ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Brazilian Standard

ABSTRACT This work analyses the methodology "A" (item A.4) employed by the Brazilian Standard ABNT 8522 (ABNT, 2008) for determining the stress-strain behavior of cylindrical specimens of concrete, presenting considerations about possible enhancements aiming it use for concretes with recycled aggregates with automatic test equipment. The methodology specified by the Brazilian Standard presents methodological issues that brings distortions in obtaining the stress-strain curve, as the use of a very limited number of sampling points and by inducing micro cracks and fluency in the elastic behavior of the material due to the use of steady stress levels in the test. The use of a base stress of 0.5 MPa is too low for modern high load test machines designed do high strength concrete test. The work presents a discussion over these subjects, and a proposal of a modified test procedure to avoid such situations.

The Oil Resistance of Rubber. I Study of the Swelling of Vulcanized Rubber

1936 ◽  
Vol 9 (1) ◽  
pp. 70-73
Author(s):  
Yoshio Tanaka ◽  
Shû Kambara ◽  
Jirô Noto
Keyword(s):  
Molecular Structure ◽  
Elastic Properties ◽  
Mixed Solvents ◽  
Experimental Results ◽  
Stress Strain ◽  
Oil Resistance ◽  
Effect Of Solvents ◽  
Vulcanized Rubber

Abstract To study the effect of solvents on the elastic properties of vulcanized rubber, the following three points were investigated. 1. The swelling maximum obtained by various mixed solvents. 2. The stress-strain curves of rubber swollen to different degrees. 3. Time-swelling and time-deswelling curves. The spiral theory of molecular structure of rubber proposed by Fikentscher and Mark is utilized to explain the experimental results.

The Behavior of Raw Rubber When Stretched Isothermally

1938 ◽  
Vol 11 (4) ◽  
pp. 647-652 ◽  
Author(s):  
H. Hintenberger ◽  
W. Neumann
Keyword(s):  
Room Temperature ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Steep Ascent ◽  
Flow Effect ◽  
Vulcanized Rubber ◽  
Flow Phenomena ◽  
Entropy Effect ◽  
The Subject

Abstract The S-shaped form of the stress-strain curve of rubber is today explained in a quite satisfactory way. In the first part of the curve, i. e., the gradual ascent, work must be expended because of the van der Waals forces of attraction of the molecules; in the second part, i. e., the steep ascent, the elasticity is chiefly an entropy effect, which is finally exceeded by crystallization phenomena. The phenomenon of crystallization itself has been the subject of extensive investigations, but in most cases vulcanized rubber has been employed, and because of the various accelerators and fillers which the rubber has contained, the products have been rather ill-defined. It is evident that the phenomena involved in crystallization would be much more clearly defined if the substance under investigation were to be in a higher state of purity. If experiments are carried out with raw rubber, a flow effect is added to the various other phenomena. As a result of this flow effect, Rosbaud and Schmidt, and Hauser and Rosbaud as well, found that the stress-strain curve depends on the rate of elongation at very low extensions, with a greater stiffness at high rates of elongation. As found recently by Kirsch, there is no evidence of any flow phenomena in vulcanized rubber at room temperature. Most investigations have been so carried out that the stress has been measured at a definite elongation. It was therefore of interest to determine the elongation at constant stress, and the changes in this relation with time and with temperature, of various types of raw rubber.

Investigation of Crystalline and Amorphous Forms of Aluminum and Its Alloys: Computational Modeling and Experiment

NANO ◽  
2018 ◽  
Vol 13 (03) ◽  
pp. 1850026
Author(s):  
Sergey Shityakov ◽  
Norbert Roewer ◽  
Carola Y. Förster ◽  
Hai T. Tran ◽  
Wenjun Cai ◽  
...  
Keyword(s):  
Metal Structure ◽  
Dislocation Nucleation ◽  
Al Alloys ◽  
Atomic Scale ◽  
Face Centered Cubic ◽  
Stress Strain ◽  
The Face ◽  
Tension And Compression ◽  
Face Centered ◽  
Dynamics Simulations

The purpose of this study is to investigate polycrystalline lattices of aluminum (Al) under the stress–strain conditions in all-atom molecular dynamics simulations and Al alloys using X-ray diffraction. Isothermal uniaxial tension and compression of these polycrystalline lattices showed no dislocation nucleation peaks, which correspond only to the Al monocrystal form. The best tensile and compressive resistance characteristics were observed for a material with the highest grain number ([Formula: see text]) due to the significant reduction of the face-centered cubic lattice in the metal structure. This process is mainly driven by the gradual elevation of the system’s kinetic energy. In the experiment, the amorphous Al alloys with higher manganese composition (20.5%) were investigated, matching the simulated amorphous structures. Overall, the results suggest that the increase in number of grains in Al lattices diminishes the stress–strain impact due to a more disordered atomic-scale (amorphous) metal composition.

scholarly journals On the behavior of slackline webbings under dynamic loads and the simulation of leash falls

2018 ◽  
Vol 233 (1) ◽  
pp. 75-85
Author(s):  
Panos J Athanasiadis
Keyword(s):  
Standardized Test ◽  
Strain Curve ◽  
Effective Modulus ◽  
Dynamic Loads ◽  
Elastic Response ◽  
Elastic Behavior ◽  
Stress Strain ◽  
Different Types ◽  
The Impact ◽  
Minimal Research

Slackline is a new and rapidly expanding sport, which has had minimal research published on it in terms of sport physics and engineering. Slackline dynamics strongly depend upon the elastic response of used webbing, typically made of polyester or nylon. Depending on the stress and strain rates applied, polymers are known to exhibit a visco-elastic behavior characterized by hysteresis effects. Through a series of carefully executed experiments, this study examined the behavior of slackline webbing under dynamic loads to determine the departures from the respective static response (stress–strain curves). Such knowledge is fundamental for the accurate simulation of slackline dynamics, so as to predict peak forces and aid safe rigging. The results demonstrate that the effective modulus during leash falls was significantly higher than the slope of the respective stress–strain curve, indicating a stiffer response. Also, the effective modulus increased with the applied pretension. Using the moduli determined experimentally for the rigged slacklines with different types of webbing, the respective leash falls were simulated numerically with high accuracy. A standardized test is proposed, to be adopted by the International Slackline Association and slackline webbing manufacturers, is proposed in order to provide key information on the response of each webbing available in the market under typical dynamic loads, similar to the “impact force” test designed for dynamic ropes by the International Climbing and Mountaineering Federation.

Stress-Strain Equations for Some Near-Eutectic Tin-Lead Solders

1991 ◽  
Vol 113 (4) ◽  
pp. 475-484 ◽  
Author(s):  
K. P. Jen ◽  
J. N. Majerus
Keyword(s):  
Strain Rate ◽  
Printed Circuit Boards ◽  
Volume Fraction ◽  
Total Error ◽  
Tensile Tests ◽  
Elastic Behavior ◽  
Plastic Behavior ◽  
Strain Rates ◽  
Stress Strain ◽  
Engineering Strain

This paper presents the evaluation of the stress-strain behavior, as a function of strain-rate, for three tin-lead solders at room temperature. This behavior is critically needed for reliability analysis of printed circuit boards (PCB) since handbooks list minimal mechanical properties for the eutectic solder used in PCBs. Furthermore, most handbook data are for stable eutectic microstructure whereas PCB solder has a metastable microstructure. All three materials were purchased as “eutectics.” However, chemical analysis, volume fraction determination, and microhardness tests show some major variations between the three materials. Two of the materials have a eutectic composition, and one does not. The true stress-strain equations of one eutectic and the one noneutectic material are determined from compressive tests at engineering strain-rates between 0.0002/s and 0.2/s. The second eutectic material is evaluated using tensile tests with strain-rates between 0.00017/s and 0.042/s. The materials appear to exhibit linear elastic behavior only at extremely small strains, i.e., less than 0.0005. However, this “elastic” behavior showed considerable variation, and depended upon the strain rate. In both tension and compression the eutectic alloy exhibits nonlinear plastic behavior, i.e., strain-softening followed by strain-hardening, which depends upon the strain rate. A quadratic equation σy = σy(ε˚/ε˚0) + A(ε˚/ε˚0)ε + B(ε˚/ε˚0)ε2 fit to the data gives correlation coefficients R2 > 0.91. The coefficients σy(ε˚/ε˚0), A(ε˚/ε˚0), B(ε˚/ε˚0) are fitted functions of the normalized engineering strain rate ε˚/ε˚0. Replicated experiments are used at each strain-rate so that a measure of the statistical variation could be estimated. Measures of error associated with the regression analysis are also obtained so that an estimate of the total error in the stress-strain relations can be made.

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