Softening of Rubber by Deformation

1969 ◽  
Vol 42 (1) ◽  
pp. 339-362 ◽  
Author(s):  
L. Mullins
Keyword(s):  
Steady State ◽  
Strain Curve ◽  
Hardness Test ◽  
Simple Extension ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Equilibrium Stress ◽  
Softening Behavior ◽  
Reinforcing Fillers ◽  
Conventional Test

Abstract It has been known for many years that deformation results in softening of rubber and that the initial stress-strain curve determined during the first deformation is unique and cannot be retraced. Further the effect of repeated deformation is to cause rubber asymptotically to approach a steady state with a constant or equilibrium stress-strain curve. Softening in this way occurs in vulcanizates either with or without fillers although the effect appears to be much more pronounced in vulcanizates containing high proportions of reinforcing fillers. After the hardness test the simple extension stress-strain test is the test most widely used by rubber technologists. The conventional stress-strain curve is obtained on samples which have not been previously deformed and for design purpose the unique value of stiffness given by this curve may be of little significance. Thus it appears that the values of stress—strain properties determined after “conditioning” cycles of deformation would be of more practical use than the unique value obtained in the conventional test. In recent years much interest has been shown in the factors responsible for this softening behavior particularly in regard to the implications of the loss of the stiffening action of reinforcing fillers on the mechanism of reinforcement.

Joint Inclination Effect on Strength, Stress-Strain Curve and Strain Localization of Rock in Plane Strain Compression

2005 ◽  
Vol 495-497 ◽  
pp. 69-76 ◽  
Author(s):  
X.B. Wang
Keyword(s):  
Plane Strain ◽  
Strain Softening ◽  
Strain Curve ◽  
Plane Strain Compression ◽  
Peak Strength ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Softening Behavior ◽  
Ideal Plastic ◽  
Joint Inclination

Peak strength, mechanical behavior, and shear band (SB) of anisotropic jointed rock (JR) were modeled by Fast Lagrangian Analysis of Continua (FLAC). The failure criterion of rock was a composite Mohr-Coulomb criterion with tension cut-off and the post-peak constitutive relation was linear strain-softening. An inclined joint was treated as square elements of ideal plastic material beyond the peak strength. A FISH function was written to find automatically elements in the joint. For the lower or higher joint inclination (JI), the higher peak strength and more apparent strain-softening behavior are observed; the failure of JR is due to the slip along the joint and the new generated SBs initiated at joint’s two ends. For the lower JI, the slope of softening branch of stress-strain curve is not concerned with JI since the new and longer SBs’s inclination is not dependent on JI, as can be qualitatively explained by previous analytical solution of post-peak slope of stress-strain curve for rock specimen subjected to shear failure in uniaxial compression based on gradient-dependent plasticity. For the higher JI, the post-peak stress-strain curve becomes steeper as JI increases since the contribution of the new SBs undergoing strain-softening behavior to axial strain of JR increases with JI. For the moderate JI, the lower strength and ideal plastic behavior beyond the elastic stage are found, reflecting that the inclined joint governs the deformation of JR. The present numerical prediction on anisotropic peak strength in plane strain compression qualitatively agrees with triaxial experimental tests of many kinds of rocks. Comparison of the present numerical prediction on JI corresponding to the minimum peak strength of JR and the oversimplified theoretical result by Jaeger shows that Jaeger’s formula has overestimated the value of JI.

Deformation of Adaptive Heterophase Crystal

1994 ◽  
Vol 360 ◽  
Author(s):  
Alexander L. Roytburd ◽  
Julia Slutsker
Keyword(s):  
Strain Curve ◽  
Negative Slope ◽  
Product Phase ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Equilibrium Stress ◽  
Stress Control ◽  
Plane Parallel ◽  
Loading And Unloading ◽  
Calculated Equilibrium

AbstractA crystal which can be in two possible phase states is considered. During tensile extension the crystal is deformed elastically. After a certain amount of elastic strain a phase transformation begins. For each fixed level of strain an equilibrium mesostructure is established, which corresponds to a minimum in the free energy of the crystal. The equilibrium mesostructure consists of plane, parallel layers of a product phase separated by layers of an initial phase. The product phase itself consists of two or more different domains (twins) forming plane, parallel alternations. The volume fractions of the phases and of different twin components in the product phase are functions of strain and temperature. Above a critical temperature the product phase is a single domain (untwinned). The stress-strain curve which reflects the evolution of the equilibrium mesostructure is calculated. For deformation under a strain control the calculated equilibrium stress-strain curve has a section with negative slope that corresponds to a negative Young's modulus. If deformation proceeds under stress control, hysteretic stress-strain curves on loading and unloading will result from a section with negative slope.

Thermodynamics of Stressed Vulcanized Rubber

1930 ◽  
Vol 3 (2) ◽  
pp. 304-314 ◽  
Author(s):  
Roscoe H. Gerke
Keyword(s):  
Modulus Of Elasticity ◽  
Strain Curve ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Equilibrium Stress ◽  
Permanent Set ◽  
Vulcanized Rubber ◽  
Laws Of Thermodynamics

Abstract The first and second laws of thermodynamics are applied to the stretching of vulcanized gum rubber stocks. Equilibrium stress-strain curves without appreciable hysteresis are described. The modulus of elasticity of vulcanized rubber for higher elongations obtained from the equilibrium stress-strain curve is capable of giving agreement with predictions of the second law of thermodynamics and the Joule heat effect. The modulus of elasticity from the equilibrium stress-strain curve is practically independent of the time of cure for a range of cures for elongations less than 600 per cent. The customary stress-strain curves show the rubber to be stiffer with increased cure. These facts are additional evidence that the important effect caused by vulcanization is a greater resistance to plastic flow or permanent set.

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
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