The Resistance of Rubber to Dynamic Forces Part I

1940 ◽  
Vol 13 (1) ◽  
pp. 81-91 ◽  
Author(s):  
R. Ariano
Keyword(s):  
Elastic Recovery ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Joule Effect ◽  
Dynamic Forces ◽  
Widespread Belief ◽  
The Subject ◽  
Service Conditions ◽  
Straight Lines

Abstract The subject of the present paper, which is of great interest on account of the numerous service conditions under which rubber is subjected to dynamic forces, has received little attention, perhaps because of the complexity of the phenomena and the consequent difficulty of coming to any definite and significant conclusions from experimental data. It is a widespread belief, for instance, that in static tension plastic flow takes place and that this is responsible for the Joule effect and that it modifies the shape of the stress-strain curve. By working at high velocities of extension, Williams proved that at room temperature and also at 60° C the stress-strain curves are straight lines and that complete elastic recovery takes place. The importance of verifying such a conclusion as this is obvious. Since, in fact, the elongations for a given load found by Williams were in every case greater when the stress was static, one is led to the conclusion that the deformation brought about by a given load is the sum of two components; one a perfectly elastic component, which obeys Hooke's law and which therefore is applicable to the established science of construction; a second component, which, in contrast to the first, is plastic in character and consequently depends on the duration of application of the load and on the loads previously applied. In brief, the law of deformation should be capable of reduction to the laws of two types of systems, viz., an elastic system and a plastic system. Unfortunately however this assumption could not be confirmed.

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.

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.

Composite Nature of the Stress-Strain Curve of Rubber

1940 ◽  
Vol 13 (1) ◽  
pp. 74-80 ◽  
Author(s):  
Ira Williams ◽  
B. M. Sturgis
Keyword(s):  
Strain Curve ◽  
Load Ratio ◽  
Industrial Applications ◽  
Load Carrying Capacity ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Load Carrying ◽  
High Elongation ◽  
Composite Nature ◽  
Straight Lines

Abstract The stress-strain curve of rubber can be imagined to consist of three curves which tend to approach straight lines. The first curve has a high elongation load ratio and intercepts the second portion at an elongation which depends on the temperature. The second curve is parallel to the elongation axis and represents a condition of flow. The third curve has a low elongation to load ratio and represents rubber with a high load carrying capacity. It is evident that the second curve must be avoided as much as possible in most industrial applications. Most industrial applications require the rubber to work only within the limits of the first curve. The first curve is lengthened when the temperature is increased and the rubber can work efficiently to a higher elongation. No evidence has been found regarding the nature of the change which occurs in rubber during the period of flow. Since the flow is reversible, it must be within the molecule and not between molecules.

The Joule Effect

1940 ◽  
Vol 13 (1) ◽  
pp. 49-49
Author(s):  
W. B. Wiegand ◽  
J. W. Snyder
Keyword(s):  
Internal Energy ◽  
Dynamic Stress ◽  
Strain Curve ◽  
Heat Evolution ◽  
Point Of View ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Joule Effect ◽  
Steel Spring ◽  
Heat Transfers

Abstract With reference to a paper by Gleichentheil and Neumann on “The Gough-Joule Effect in Vulcanizates,” we should like to call attention to the similarity between the results reported in their paper and the earlier work reported by Wiegand and Snyder entitled “The Rubber Pendulum, the Joule Effect and the Dynamic Stress-Strain Curve.” The latter authors analyzed from a thermodynamic point of view the rubber stress-strain curve as affected by temperature. As a result of this analysis the stress-strain curve was divided into three groups, Region A, Region B and Region C. Each region was characterized by different trends as regards the Joule effect and internal energy changes. The following description is taken from the original paper: “Region A, The Steel Spring.—This region, extending to approximately 300 per cent elongation for the conditions in the experiments described, is characterized by the comparative absence of heat transfers . … little or no Joule effect.” “Region B, The Gas (and the Crystal).—In region B the region of the Joule effect . … there is the maximum of heat evolution. It should be noted that Region B extends from approximately 300 per cent elongation to 700 per cent elongation. “Region C, The Friction Member.—This region is characterized by the almost entire absence of reversible effects. The Joule effect has disappeared. There is no evolution of heat….“

Empirical Equations for Describing the Strain-Hardening Characteristics of Metals Subjected to Moderate Strains

1974 ◽  
Vol 96 (2) ◽  
pp. 123-126 ◽  
Author(s):  
C. Adams ◽  
J. G. Beese
Keyword(s):  
Strain Hardening ◽  
Elastic Recovery ◽  
Strain Curve ◽  
Stress And Strain ◽  
Accurate Assessment ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Initial Portion ◽  
Design Problems ◽  
Work Hardening Exponent

The strain-hardening characteristics of a metal have often been described by a power function which employs a work-hardening exponent, “n.” Usually the material is assumed to be rigid to the yield point and therefore the possibility of any elastic recovery is denied. The authors show that, particularly for the initial portion of a stress-strain curve, n is not a constant and therefore the curve cannot be described by one power law alone. A method is proposed for fitting equations to experimental stress-strain curves up to strain values of 0.05. The equations take into account possible elastic recovery. The equations should facilitate more accurate assessment of underload stress and strain distributions in various design problems.

Some Practical Aspects of Rubber Evaluation

1929 ◽  
Vol 2 (3) ◽  
pp. 406-408 ◽  
Author(s):  
R. P. Dinsmore
Keyword(s):  
Reliable Method ◽  
Strain Curve ◽  
Standard Test ◽  
Testing Methods ◽  
Substantial Agreement ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
The Past ◽  
The Subject ◽  
Curing Agents

Abstract In various papers, published in the past three years, E. C. Zimmerman and the writer have made references to the variability of crude rubber as determined by the properties of vulcanized compounds of various types. We were, I believe, the first to point out the chief stumbling block in the way of establishing a standard test formula for evaluating crude rubber, namely the variation in both quality and rate of cure produced by curing the same rubber with different curing agents. At the outset we were confronted with difficulties which resulted from a deplorable lack of standardization of rubber testing methods, and more specifically from a lack of agreement as to the proper way to select comparable cures. Indeed, it is obvious that these drawbacks have been among the major causes for lack of correlation of available data on the subject. We have stressed the importance of considering those properties of the vulcanizate which are reflected in the performance of the finished product, and have stated our objections to many of the popular criteria, such as “slope,” tensile product, tensile, and coefficient of vulcanization. We had concluded that aging should be the chief criterion of best technical cure. Accelerated age tests cannot be relied upon for comparison of different mixes, but experience has shown that for lightly loaded mixes hand tear is a reliable method of fixing the best aging cure. With this as a means of selecting the time of cure, the quality was studied by comparing the stiffness of the stress-strain curve at best cure. Later, in a paper on acceleration classification, if was shown that these conclusions might properly be modified when dealing with loaded mixes. Here the cures, as selected by hand tear and by maximum, tensile product, were in substantial agreement, except in the case of non-accelerated stocks.

The Bending of Some Common Beam Sections into the Plastic Range

1953 ◽  
Vol 57 (506) ◽  
pp. 110-115 ◽  
Author(s):  
Anthony J. Barrett
Keyword(s):  
Cross Sections ◽  
Strain Curve ◽  
Bending Moment ◽  
Mathematical Form ◽  
Military Aircraft ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Actual Material ◽  
The Subject ◽  
Axis Of Symmetry

SummaryThere is already in existence a fair volume of work on the subject of bending beyond the limit of proportionality, most of which requires the use of actual material stress-strain curves. This note aims to examine the problem in a more general way by using an accurate mathematical form for the stress-strain curve, strain and bending moments being expressed as functions of the ratios of various properties of the material.The value of maximum permissible fibre stress is considered in relation to current requirements for military aircraft stressing and a guide is presented for the maximum permissible bending moment in some of the more familiar beam cross sections bending about an axis of symmetry.

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.

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