A MATHEMATICAL TREATMENT OF A THEORY OF RUBBER STRUCTURE

1934 ◽  
Vol 10 (5) ◽  
pp. 486-520 ◽  
Author(s):  
T. R. Griffith
Keyword(s):  
Average Length ◽  
Average Distance ◽  
Strain Curve ◽  
Molecular Chain ◽  
Mathematical Work ◽  
Mathematical Treatment ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Starting Point ◽  
Junction Points

The theory that the elasticity of rubber is due to the heat vibrations of very long chain molecules, bound to one another at occasional points along their length, but able to move freely relatively to one another at all other points, is susceptible of mathematical treatment. In the present treatment it is assumed that the rubber molecule has a restricted rotation about the axis formed by joining two adjacent junction points.A stress-strain curve has been developed mathematically on this assumption, and this curve, which is a reasonably close approximation to the curve obtained experimentally, serves as a standard with which to compare the rubber stress-strain curve and as a starting point for further mathematical work on the structure of rubber. The discrepancy between the mathematical and the experimental curve is explained on the very probable assumption that there is a wave motion or other vibration along the length of the rotating chain, as well as a rotation of the chain as a whole.An explanation of the peculiar S-shape of the beginning of the experimental stress-strain curve develops automatically from the mathematically deduced relation between stress and strain, and it is also shown why the S-shape appears to vanish when the calculation of the stress is based on the actual cross section of the stretched rubber.In addition, the following values, calculated from the above assumption and X-ray data, of certain constants, were obtained:(i) The average distance between junction points.(ii) The average length of molecular chain between junction points and, incidentally, the ratio between the number of freely swinging carbon atoms and those bound at junction points. This gives the number of freely swinging carbon atoms on the molecular chain between junction points and an idea of the length of the rubber molecule.(iii) The quantity of kinetic energy per cubic centimetre causing the elastic effect in rubber.(iv) The percentage of sulphur necessary to form the junction points in vulcanized rubber and, consequently, the minimum quantity of sulphur needed for vulcanization, both for hard and soft rubber. This minimum agrees closely with practical experiment.

A Mathematical Treatment of a Theory of Rubber Structure

1935 ◽  
Vol 8 (1) ◽  
pp. 23-38
Author(s):  
T. R. Griffith
Keyword(s):  
Elastic Modulus ◽  
Plastic Flow ◽  
Strain Curve ◽  
The Other ◽  
Stress Axis ◽  
Mathematical Treatment ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Joule Effect ◽  
Vulcanized Rubber

Abstract A brief consideration of the work that has been done on the structure of rubber convinces, one that the elasticity is wholly or at least mainly explained by a consideration of the kinetics involved. The fact that when a strip of stretched rubber, one end of which is free, contracts when it is warmed, contrary to the behavior of most bodies, and that it becomes warmed on stretching, commonly known as the Gough-Joule effect, pp. 453–461, would lead one to suspect .that there is a connection between the kinetic energy of the rubber molecule and its elasticity. Lundal, Bouasse, Hyde, Somerville and Cope, Partenheimer and Whitby and Katz have reported observations, principally stress-strain curves, which show that vulcanized rubber has a lower modulus of elasticity at higher temperatures, i. e., it becomes easier to stretch as the temperature is raised. On the other hand, Schmulewitsch, Stevens, and Williams found that the elastic modulus increases with the temperature. Williams shows that the softening of vulcanized rubber with rise of temperature is due to an increase of plasticity. In order to get rid of plastic flow, he first stretches the specimen several times to within about 50 per cent of its breaking elongation, and then obtains an autographic stress-strain curve of the rubber stretched very quickly. He finds that in this case the rubber actually becomes stiffer with rise of temperature, increasing temperatures causing the stress-strain curves to lean progressively more and more toward the stress axis. He concludes that rise of temperature has two effects, one a softening due to increase of plasticity, rendering plastic flow more easy, the other an actual stiffening of the rubber due to rise of temperature. It is not easy to explain the latter effect on any theory which does not take kinetics into account.

A modified version of MATLAB application window for predicting the weld bead profile and stress–strain plot of AA5052 CMT weldment using ER4043

SIMULATION ◽  
2021 ◽  
pp. 003754972110315
Author(s):  
B Girinath ◽  
N Siva Shanmugam
Keyword(s):  
Strain Curve ◽  
Weld Bead ◽  
Welding Parameters ◽  
Bead Geometry ◽  
Hybrid Technique ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Weld Bead Geometry ◽  
Inference System ◽  
Engineering Stress

The present study deals with the extended version of our previous research work. In this article, for predicting the entire weld bead geometry and engineering stress–strain curve of the cold metal transfer (CMT) weldment, a MATLAB based application window (second version) is developed with certain modifications. In the first version, for predicting the entire weld bead geometry, apart from weld bead characteristics, x and y coordinates (24 from each) of the extracted points are considered. Finally, in the first version, 53 output values (five for weld bead characteristics and 48 for x and y coordinates) are predicted using both multiple regression analysis (MRA) and adaptive neuro fuzzy inference system (ANFIS) technique to get an idea related to the complete weld bead geometry without performing the actual welding process. The obtained weld bead shapes using both the techniques are compared with the experimentally obtained bead shapes. Based on the results obtained from the first version and the knowledge acquired from literature, the complete shape of weld bead obtained using ANFIS is in good agreement with the experimentally obtained weld bead shape. This motivated us to adopt a hybrid technique known as ANFIS (combined artificial neural network and fuzzy features) alone in this paper for predicting the weld bead shape and engineering stress–strain curve of the welded joint. In the present study, an attempt is made to evaluate the accuracy of the prediction when the number of trials is reduced to half and increasing the number of data points from the macrograph to twice. Complete weld bead geometry and the engineering stress–strain curves were predicted against the input welding parameters (welding current and welding speed), fed by the user in the MATLAB application window. Finally, the entire weld bead geometries were predicted by both the first and the second version are compared and validated with the experimentally obtained weld bead shapes. The similar procedure was followed for predicting the engineering stress–strain curve to compare with experimental outcomes.

Stress-strain curve of paper revisited

2012 ◽  
Vol 27 (2) ◽  
pp. 318-328 ◽  
Author(s):  
Svetlana Borodulina ◽  
Artem Kulachenko ◽  
Mikael Nygårds ◽  
Sylvain Galland
Keyword(s):  
Three Dimensional ◽  
Strain Curve ◽  
Failure Behavior ◽  
Three Dimensional Model ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Fiber Network ◽  
Bonding Parameters ◽  
Particle Level ◽  
The Impact

Abstract We have investigated a relation between micromechanical processes and the stress-strain curve of a dry fiber network during tensile loading. By using a detailed particle-level simulation tool we investigate, among other things, the impact of “non-traditional” bonding parameters, such as compliance of bonding regions, work of separation and the actual number of effective bonds. This is probably the first three-dimensional model which is capable of simulating the fracture process of paper accounting for nonlinearities at the fiber level and bond failures. The failure behavior of the network considered in the study could be changed significantly by relatively small changes in bond strength, as compared to the scatter in bonding data found in the literature. We have identified that compliance of the bonding regions has a significant impact on network strength. By comparing networks with weak and strong bonds, we concluded that large local strains are the precursors of bond failures and not the other way around.

Definition of the yield point in plasticity and its effect on the shape of the yield locus

1966 ◽  
Vol 1 (4) ◽  
pp. 331-338 ◽  
Author(s):  
T C Hsu
Keyword(s):  
Yield Point ◽  
Experimental Work ◽  
Strain Curve ◽  
Yield Locus ◽  
Experimental Results ◽  
Stress Strain Curve ◽  
Proportional Limit ◽  
Stress Strain ◽  
Small Section ◽  
Definition Of

Three different definitions of the yield point have been used in experimental work on the yield locus: proportional limit, proof strain and the ‘yield point’ by backward extrapolation. The theoretical implications of the ‘yield point’ by backward extrapolation are examined in an analysis of the loading and re-loading stress paths. It is shown, in connection with experimental results by Miastkowski and Szczepinski, that the proportional limit found by inspection is in fact a point located by backward extrapolation based on a small section of the stress-strain curve, near the elastic portion of the curve. The effect of different definitions of the yield point on the shape of the yield locus and some considerations for the choice between them are discussed.

Identification of post-necking stress–strain curve for sheet metals by inverse method

2016 ◽  
Vol 92 ◽  
pp. 107-118 ◽  
Author(s):  
Kunmin Zhao ◽  
Limin Wang ◽  
Ying Chang ◽  
Jianwen Yan
Keyword(s):  
Inverse Method ◽  
Strain Curve ◽  
Sheet Metals ◽  
Stress Strain Curve ◽  
Stress Strain

Behavior and modeling of post-heated circular concrete specimens repaired with fiber-reinforced polymer composites

2021 ◽  
pp. 136943322110585
Author(s):  
Seyed Mehrdad Elhamnike ◽  
Rasoul Abbaszadeh ◽  
Vahid Razavinasab ◽  
Hadi Ziaadiny
Keyword(s):  
Strain Curve ◽  
Concrete Columns ◽  
Fiber Reinforced Polymer ◽  
Fiber Reinforced ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Concrete Members ◽  
Frp Composites ◽  
Reinforced Polymer ◽  
Fiber Reinforced Polymer Composites

Exposure of buildings to fire is one of the unexpected events during the life of the structure. The heat from the fire can reduce the strength of structural members, and these damaged members need to be strengthened. Repair and strengthening of concrete members by fiber-reinforced polymer (FRP) composites has been one of the most popular methods in recent years and can be used in fire-damaged concrete members. In this paper, in order to provide further data and information about the behavior of post-heated circular concrete columns confined with FRP composites, 30 cylindrical concrete specimens were prepared and subjected under four exposure temperatures of 300, 500, 700, and 900. Then, specimens were repaired by carbon fiber reinforced polymer composites and tested under axial compression. Results indicate that heating causes the color change, cracks, and weight loss of concrete. Also, with the increase of heating temperature, the shape of stress–strain curve of FRP-retrofitted specimens will change. Therefore, the main parts of the stress–strain curve such as ultimate stress and strain and the elastic modulus will change. Thus, a new stress–strain model is proposed for post-heated circular concrete columns confined by FRP composites. Results indicate that the proposed model is in a good agreement with the experimental data.

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.

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