Influence of Large Static Deformation on the Dynamic Properties of Polymers Part II. Influence of Carbon Black Loading

1981 ◽  
Vol 54 (4) ◽  
pp. 857-870 ◽  
Author(s):  
E. A. Meinecke ◽  
S. Maksin
Keyword(s):  
Carbon Black ◽  
Energy Loss ◽  
Amplification Factor ◽  
Complex Modulus ◽  
Dynamic Properties ◽  
Strain Curve ◽  
Static Stress ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Static Modulus

Abstract The influence of carbon black loading on the dynamic properties of statically deformed elastomers has been investigated. The energy loss per cycle was found to increase according to the square of the strain amplification factor as expressed by the Guth-Gold-Einstein equation. The dynamic complex modulus |E*| is approximately equal to the static modulus obtained from the slope of the static stress-strain curve. The influence of carbon black loading on E* can, therefore, be predicted from its influence on the static stress-strain curve which was found to be governed by the first power of the strain amplification factor. The tangent of the loss angle can thus be predicted from |E*| and the energy loss per cycle. It does not only depend upon the dynamic viscosity of the material; it also depends upon the shape of the stress-strain curve as well.

Nonlinearity in the Dynamic Properties of Rubber

1957 ◽  
Vol 30 (1) ◽  
pp. 218-241 ◽  
Author(s):  
A. R. Payne
Keyword(s):  
Second Harmonic ◽  
Dynamic Properties ◽  
Strain Curve ◽  
Resonance Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Positive Displacement ◽  
Static Modulus ◽  
Nonlinear Stress ◽  
Newtonian Liquids

Abstract The first two sections of this paper deal with the necessity for amending the classical Newtonian equations by assuming a nonlinear stress-strain curve in order to account for the presence of a considerable amount of second harmonic of the test frequency in the restoring forces in a rubber, in both forced-vibration and positive-displacement dynamic testers. The nonlinear stress-strain curve is applied also to a damped free-vibration curve of the Yerzley type, and is shown to account for the asymmetry of the envelope of the vibration curve. The latter part of the paper obtains a relationship between the dynamic modulus of loaded rubbers and amplitude of vibration, leading to equations analogous to those used in rheology to deal with rate of shear effects in non-Newtonian liquids, and to explain the effects of fillers on the static modulus and hardness of vulcanized rubbers. A resonance curve from a resonant vibrator is analyzed and the variation of modulus with amplitude is shown to exhibit the typical thixotropic effect associated with loaded rubbers subjected to vibrations. The last section discusses how the decrease of modulus with increasing amplitude can be attributed to two different mechanisms: (1) thixotropic breakdown of filler structure, (2) in compression, nonlinearity of the stress-strain curve.

Reinforcement of Butyl with Carbon Black. II. Thermally vs. Chemically Oxidized Blacks

1964 ◽  
Vol 37 (4) ◽  
pp. 1034-1048 ◽  
Author(s):  
A. M. Gessler
Keyword(s):  
Carbon Black ◽  
Chemical Reactivity ◽  
Preceding Paper ◽  
Strain Curve ◽  
Convincing Evidence ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Carbon Particles ◽  
Vulcanized Rubber ◽  
Oxygen Functionality

Abstract The effect of oxidized blacks on the stress-strain properties and bound-rubber content of butyl and SBR was discussed in the preceding paper. Oxidized blacks, when compared with similar untreated blacks, were shown to have a greatly increased reinforcing capacity in butyl. Oxygen functionality on carbon black, it was therefore concluded, is essential in butyl to produce the chemical reactivity which is required between polymer and black if high-order reinforcement is to be obtained. Oxygen functionality on carbon black, it was also demonstrated, is not only not required for enhanced reinforcement in SBR, but it is in fact a deterrent, because it exerts severe restraining effects on the cure of the resulting vulcanizates as well. These interesting results were proposed to provide qualitative but convincing evidence that carbon-polymer bonding, which we believe is requisite to reinforcement, is achieved by different mechanisms in butyl and SBR. In butyl, the unique sensitivity of the stress-strain curve to reinforcing effects was used to speculate on the disposition of carbon blacks in “filled” and reinforced vulcanizates, respectively. With oxidized blacks, reinforcement effects were pictured as stiffening effects which, starting with the gum vulcanizates, caused the stress-strain curve to be shifted without intrinsic changes in its shape. The resulting “reinforced gum,” it was suggested, derived its physical characteristics from the fact that carbon black was included in the vulcanized rubber network. With untreated blacks, in “filled” systems, carbon black was pictured as being enmeshed or entangled in an independently formed vulcanized rubber network. The stiffening effects in this case were attributed to viscous contributions arising from steric restrictions which the occluded carbon particles were thought to impose on both initial movements and the subsequent orientation of network chains when the sample was extended.

Fatigue in Rubber. Part II

1939 ◽  
Vol 12 (2) ◽  
pp. 332-343 ◽  
Author(s):  
W. J. S. Naunton ◽  
J. R. S. Waring
Keyword(s):  
Carbon Black ◽  
Internal Friction ◽  
High Frequency ◽  
Strain Curve ◽  
Power Input ◽  
Viscous Resistance ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Wide Range ◽  
Rubber Part

Abstract 1. An apparatus is described for measuring the modulus and resilience of rubber over a wide range of frequencies. 2. These measurements can be made at any point in the stress-strain curve of the sample. 3. By increasing the power input, the same apparatus can be used to induce high frequency fatigue in the sample. 4. The earlier work with the torsion head apparatus has been confirmed, namely, that internal friction is greatest near zero strain. 5. High frequency resilience is more independent of degree of vulcanization than tripsometer resilience. 6. Modulus tends to increase with frequency. The effect is least with a rubber gum stock and is greater with compounds containing gas black. 7. Resilience decreases with frequency both in gum and gas black compounds. The decrease is more rapid in the gum compounds. 8. Viscous resistance decreases with frequency and becomes constant at higher frequencies. 9. The modulus of both rubber and Neoprene carbon black compounds decreases with fatigue. 10. The change in modulus with frequency in fatigued stocks is exactly analogous to the change before fatigue in rubber, but there is a slight divergence in the case of Neoprene.

Effect of Carbon-Black Loading and Crosslink Density on the Heat Build-Up in Elastomers

1991 ◽  
Vol 64 (2) ◽  
pp. 269-284 ◽  
Author(s):  
Eberhard Meinecke
Keyword(s):  
Carbon Black ◽  
Energy Loss ◽  
Heat Generation ◽  
Amplification Factor ◽  
Position Control ◽  
Dynamic Properties ◽  
Filler Loading ◽  
Load Control ◽  
Local Overheating ◽  
In Series

Abstract It has been shown that it is possible to predict the viscoelastic response of elastomers and elastomeric engineering components under both load- and position-control conditions if one assumes: a) that the modulus of the materials increases with the strain amplification factor as given by the Guth and Gold equation, b) that the occluded rubber is taken into account when using this equation, and c) that the energy loss per cycle and unit volume of material is increasing with the square of the strain-amplification factor. These calculations were applied to an assembly where one unfilled section is in series with a filled one. The overall filler loading was kept constant, and it was found that the equations derived show completely different heat-generation rates for load- and position-control conditions. While the losses are the same in both sections and equal to that of the assembly as a whole under position-control conditions, they are quite different under load-control conditions. They increase with both filler loading and values of α and abnormally high local overheating in the unfilled section occurs. These considerations indicate that a uniform mixing quality is important for compounds which will be used in dynamically deformed engineering components. Under position-control conditions, poor filler dispersion will give rise to a decrease in the dynamic modulus and the energy loss per cycle, i.e., variations in the quality of the mix will cause variability of the dynamic properties. Under load-control conditions, the situation is even worse, since the energy dissipation increases with poor mixing, and local overheating of the sections containing less than the average amount of carbon black takes place. The model is obviously too oversimplified for qualitative predictions. But it still gives good qualitative indications regarding the heat-generation rate in structures made from two elastomers having different filler loadings or for imperfectly mixed compounds.

An Experimental Investigation of Elastic-Plastic Pulse Propagation in Aluminum Rods

1967 ◽  
Vol 34 (1) ◽  
pp. 91-99 ◽  
Author(s):  
S. R. Bodner ◽  
R. J. Clifton
Keyword(s):  
Room Temperature ◽  
Elevated Temperatures ◽  
Strain Curve ◽  
Static Stress ◽  
Stress Strain Curve ◽  
Proportional Limit ◽  
Stress Strain ◽  
Elastic Plastic ◽  
Time Profiles ◽  
The Impact

Experiments are reported involving elastic-plastic pulses due to explosive loading at one end of long, annealed, commercially pure, aluminum rods at room temperature and at elevated temperatures up to 750 deg F. The stress waves were detected by a condenser microphone at the far end of the rod and, in some cases, by strain gages at a cross section distant from the impact end. The essential features of the recorded velocity-time profiles and strain-time profiles are found to be in agreement with the predictions of rate independent elastic-plastic theory which takes a Bauschinger effect into account. At room temperature, the reference dynamic stress-strain curve does not differ appreciably from the quasi-static stress-strain curve whereas at elevated temperatures there appears to be a marked difference between the dynamic and quasi-static stress-strain curves. The experiments also serve to determine the dynamic proportional limit which is found to be fairly insensitive to temperature. Since the maximum plastic strains are small at cross sections remote from the impact end, the measurements, and consequently the conclusions, are limited to small strains beyond the proportional limit.

Reinforcement of Butyl with Carbon Black. I. Effect of Oxidized Blacks on Stress-Strain Properties and Bound Rubber

1964 ◽  
Vol 37 (4) ◽  
pp. 1013-1033 ◽  
Author(s):  
A. M. Gessler
Keyword(s):  
Carbon Black ◽  
Chemical Properties ◽  
Strain Curve ◽  
Critical Factor ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Bound Rubber ◽  
Oxygen Functionality ◽  
Physical And Chemical ◽  
Initial Movement

Abstract The increased reinforcing capacity of oxidized blacks in butyl is illustrated, and the results are discussed in terms of the relationships which exist between polymer and black. Oxygen functionality on the black, it is shown, is the critical factor controlling the extent to which butyl is reinforced by the black. The lesser effects of decreased aggregate structure in the black are also demonstrated. These results are obtained using blacks which, though similar to attrited blacks, derive both their physical and chemical properties without the use of comminution. A much more unambiguous approach to the questions of black structure and oxygen content is therefore provided. In butyl, the unique sensitivity of the stress-strain curve to reinforcing effects is attributed to low unsaturation in the polymer. This sensitivity is used to qualify the nature of the reinforcement which is obtained. With oxidized blacks, true reinforcement is pictured as a stiffening effect which, starting with the gum vulcanizate, shifts the stress-strain curve without essentially changing its shape. The result is a “reinforced gum” which, it is suggested, derives its physical characteristics through the bonding of carbon black in the rubber network. With untreated black, carbon black is pictured as being enmeshed or entangled in an independently formed rubber network. Changes in the shape of the stress-strain curve are therefore attributed to steric restrictions which this arrangement imposes on the initial movement and subsequent orientation of network chains when the sample is extended.

Assessment of the Influence of Multiple Cyclic Loading on the Static Modulus of Elasticity of Hardened Concrete

2017 ◽  
Vol 259 ◽  
pp. 21-24
Author(s):  
Petr Misák ◽  
Petr Daněk ◽  
Dalibor Kocáb ◽  
Michaela Potočková ◽  
Bronislava Moravcová ◽  
...  
Keyword(s):  
Cyclic Loading ◽  
Modulus Of Elasticity ◽  
Strain Curve ◽  
Elastic Region ◽  
Hardened Concrete ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Static Modulus ◽  
Static Modulus Of Elasticity

This paper deals with determining the dependence of the value of the static modulus of elasticity of concrete in compression on the number of loading cycles. The deformation of specimens during multiple cyclic loading was measured in the elastic region of the stress-strain curve for concrete. The specimens were subjected to up to 1500 loading cycles. The main goal of the experiment was to ascertain whether the multiple cyclic loading causes significant changes in the static modulus of elasticity.

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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