The Relation between the Friction and Viscoelastic Properties of Rubber

1964 ◽  
Vol 37 (2) ◽  
pp. 386-403 ◽  
Author(s):  
K. A. Grosch
Keyword(s):  
Viscoelastic Properties ◽  
Master Curve ◽  
Frictional Heating ◽  
Fine Powder ◽  
Molecular Adhesion ◽  
Jump Distance ◽  
Wide Range ◽  
Rubber Surface ◽  
Single Master Curve ◽  
Two Peaks

Abstract This paper describes a study of the friction of several types of rubber against hard surfaces over a wide range of temperatures and sliding velocities. The highest velocity did not exceed a few centimeters per second so that frictional heating was negligible. The results show that the friction increases with the sliding velocity to a maximum value and then falls. The application of the Williams, Landel and Ferry transform shows that the frictional behavior of a rubber sliding at various velocities and temperatures on a given surface can entirely be described by a single master curve and the glass transition temperature of the material. The master curve on a rough abrasive track shows, in general, two peaks—one of these occurs at a velocity related to the frequency with which the track asperities deform the rubber surface. This maximum is absent on a smooth track and thus reflects the deformation losses produced by the passage of the asperities over the rubber surface. The other peak occurs in general at much lower velocities; it coincides in position with the single maximum obtained on a smooth surface. Introduction of a fine powder (MgO) into the interface between the rubber and track eliminates this peak on both smooth and rough surfaces; it is therefore attributed to molecular adhesion. Comparison with the relaxation spectrum of the rubber gives a fundamental jump distance of the order of 60 A. It appears, therefore, that friction arises from adhesion and deformation losses, and that both are directly related to the viscoelastic properties of the rubber.

The relation between the friction and visco-elastic properties of rubber

1963 ◽  
Vol 274 (1356) ◽  
pp. 21-39 ◽  
Keyword(s):  
Elastic Properties ◽  
Master Curve ◽  
Frictional Heating ◽  
Fine Powder ◽  
Molecular Adhesion ◽  
Jump Distance ◽  
Wide Range ◽  
Rubber Surface ◽  
Single Master Curve ◽  
Two Peaks

This paper describes a study of the friction of several types of rubber against hard surfaces over a wide range of temperatures and sliding velocities. The highest velocity did not exceed a few centimetres per second so that frictional heating was negligible. The results show that the friction increases with the sliding velocity to a maximum value and then falls. The application of the Williams, Landel & Ferry (1955) transform shows that the frictional behaviour of a rubber sliding at various velocities and temperatures on a given surface can entirely be described by a single ‘master curve’ and the glass transition temperature of the material. The master curve on a rough abrasive track shows, in general, two peaks—one of these occurs at a velocity related to the frequency with which the track asperities deform the rubber surface. This maximum is absent on a smooth track and thus reflects the deformation losses produced by the passage of the asperities over the rubber surface. The other peak occurs in general at much lower velocities; it coincides in position with the single maximum obtained on a smooth surface. Introduction of a fine powder (MgO) into the interface between the rubber and track eliminates this peak on both smooth and rough surfaces; it is therefore attributed to molecular adhesion. Comparison with the relaxation spectrum of the rubber gives a fundamental jump distance of the order of 60 Å. It appears therefore that friction arises from adhesion and deformation losses, and that both are directly related to the visco-elastic properties of the rubber.

Cold Rolling of Foil

1992 ◽  
Vol 206 (2) ◽  
pp. 119-131 ◽  
Author(s):  
N A Fleck ◽  
K L Johnson ◽  
M E Mear ◽  
L C Zhang
Keyword(s):  
Cold Rolling ◽  
Constant Coefficient ◽  
Coulomb Friction ◽  
Master Curve ◽  
Critical Value ◽  
Neutral Zone ◽  
Entry And Exit ◽  
Wide Range ◽  
Dimensional Parameters ◽  
Single Master Curve

A theory of cold rolling of thin gauge strip is presented which, within the idealizations of homogeneous deformation and a constant coefficient of Coulomb friction, rigorously models the elastic deformation of the rolls and the frictional traction at the interface. In contrast with classical theories (3) it is shown that, for gauges less than a critical value, plastic reduction takes place in two zones, at entry and exit, which are separated by a neutral zone in which the rolls are compressed fiat and there is no slip between the rolls and the strip. Roll load and torque are governed by five independent non-dimensional parameters which express the influence of gauge, reduction, friction and front and back tensions. Values of load and torque have been computed (for zero front and back tensions) for a wide range of thickness, reduction and friction and have been found to collapse approximately on to a single master curve.

A Master Curve for Amorphous Elastomers Derived from Small and Large Deformations Using Various Instruments

1975 ◽  
Vol 48 (1) ◽  
pp. 69-78 ◽  
Author(s):  
N. Nakajima ◽  
E. A. Collins
Keyword(s):  
Steady State ◽  
Viscoelastic Properties ◽  
High Speed ◽  
Master Curve ◽  
Large Deformations ◽  
Stress Strain ◽  
Strain Measurements ◽  
Mechanical Measurements ◽  
Single Master Curve ◽  
Butadiene Styrene

Abstract Dynamic mechanical measurements, stress—strain measurements, and steady-shear measurements made over a range of temperatures and frequencies or deformation rates are used to characterize the viscoelastic properties of raw elastomers. The measurements involve both small and large deformations. It is shown that the results on either butadiene—acrylonitrile (NBR) or butadiene—styrene (SBR) can be reduced to a single master curve. The instruments and ranges covered included Instron stress—strain (0.2–20 in./min; 25–75°C), Instron capillary (100−104sec −1; 100°C), Rheovibron (110 Hz; 23–156°C), Rheometrics (4×10−2−2.6×102 sec−1; 100°C), MTS high speed tester (267-26 700%/sec; 25–97°C), steady-state Mooney (0.05–20 rpm; 25–150°C) and transient Mooney (0.05 rpm; 25–150°C).

scholarly journals Astral hydrogels mimic tissue mechanics by aster-aster interpenetration

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qingqiao Xie ◽  
Yuandi Zhuang ◽  
Gaojun Ye ◽  
Tiankuo Wang ◽  
Yi Cao ◽  
...  
Keyword(s):  
Common Core ◽  
Self Assembly ◽  
Master Curve ◽  
Soft Tissues ◽  
Tissue Mechanics ◽  
Fresh Perspective ◽  
Single Master Curve ◽  
Unique Mechanism ◽  
Gel Network

AbstractMany soft tissues are compression-stiffening and extension-softening in response to axial strains, but common hydrogels are either inert (for ideal chains) or tissue-opposite (for semiflexible polymers). Herein, we report a class of astral hydrogels that are structurally distinct from tissues but mechanically tissue-like. Specifically, hierarchical self-assembly of amphiphilic gemini molecules produces radial asters with a common core and divergently growing, semiflexible ribbons; adjacent asters moderately interpenetrate each other via interlacement of their peripheral ribbons to form a gel network. Resembling tissues, the astral gels stiffen in compression and soften in extension with all the experimental data across different gel compositions collapsing onto a single master curve. We put forward a minimal model to reproduce the master curve quantitatively, underlying the determinant role of aster-aster interpenetration. Compression significantly expands the interpenetration region, during which the number of effective crosslinks is increased and the network strengthened, while extension does the opposite. Looking forward, we expect this unique mechanism of interpenetration to provide a fresh perspective for designing and constructing mechanically tissue-like materials.

Universality of fractal aggregates as probed by light scattering

1989 ◽  
Vol 423 (1864) ◽  
pp. 71-87 ◽  
Keyword(s):  
Light Scattering ◽  
Dynamic Light Scattering ◽  
Master Curve ◽  
Rotational Diffusion ◽  
Fractal Dimensions ◽  
Scattering Data ◽  
Diffusion Limited ◽  
Single Master Curve ◽  
Using Data ◽  
Dynamic Light Scattering Data

Fractal colloid aggregates are studied with both static and dynamic light scattering. The dynamic light scattering data are scaled onto a single master curve, whose shape is sensitive to the structure of the aggregates and their mass distribution. By using the structure factor determined from computer-simulated aggregates, and including the effects of rotational diffusion, we predict the shape of the master curve for different cluster distributions. Excellent agreement is found between our predictions and the data for the two limiting régimes, diffusion-limited and reaction-limited colloid aggregation. Furthermore, using data from several completely different colloids, we find that the shapes of the master curves are identical for each régime. In addition, the cluster fractal dimensions and the aggregation kinetics are identical in each régime. This provides convincing experimental evidence of the universality of these two régimes of colloid aggregation.

scholarly journals QUARK SPECTRUM ABOVE THE CRITICAL TEMPERATURE FROM SCHWINGER–DYSON EQUATION

2007 ◽  
Vol 16 (07n08) ◽  
pp. 2282-2288
Author(s):  
MASAYASU HARADA ◽  
YUKIO NEMOTO ◽  
SHUNJI YOSHIMOTO
Keyword(s):  
Critical Temperature ◽  
Weak Coupling ◽  
Gauge Coupling ◽  
Dyson Equation ◽  
Coupling Region ◽  
Chiral Phase ◽  
Loop Approximation ◽  
Wide Range ◽  
Region Temperature ◽  
Two Peaks

We investigate a spectrum of a fermion, which we call a quark, above the critical temperature of the chiral phase transition in a gauge theory using the Schwinger–Dyson (SD) equation. The SD equation enables us to study the spectrum over a wide range of the gauge coupling. It is shown that the quark spectrum has two sharp peaks which correspond to the normal quasi-quark and the plasmino and is consistent with that obtained in the hard thermal loop approximation in the weak coupling region, while it has also two peaks but with smaller thermal masses and broader widths in the strong coupling region. Temperature-dependence of the quark spectrum is also discussed.

Effect of Extending Oil on Viscoelastic Behavior of Elastomers

1983 ◽  
Vol 56 (4) ◽  
pp. 784-807 ◽  
Author(s):  
N. Nakajima ◽  
E. R. Harrell
Keyword(s):  
Molecular Weight ◽  
Viscoelastic Properties ◽  
Polymer Concentration ◽  
Viscoelastic Behavior ◽  
Chain Structure ◽  
Frequency Range ◽  
Molecular Weight Polymer ◽  
Wide Range ◽  
Two Samples ◽  
Superposition Principles

Abstract For a number of years, oil-extended elastomers have been in commercial use. The obvious advantage is to dilute elastomers with less expensive oil. In addition, oil improves the processability of the elastomer. This enables the use of a higher-molecular-weight polymer, which, in turn, yields mechanical properties comparable or superior to those of a lower-molecular-weight polymer without oil extension. The viscoelastic properties of the oil-elastomer mixtures at a wide range of concentration and temperature offer information useful for understanding elastomer processability. The viscoelastic properties of such systems are also most sensitive manifestations of the polymer chain structure and, therefore, they represent fundamental characteristics of a given elastomer sample. In this work, two samples of ethylene-propylene copolymer differing in chain structure were selected. The oil-elastomer mixtures were prepared for polymer concentration in the range of 2.5–100%. The viscoelastic properties have been measured in the temperature range of 30–150°C. The frequency range was 10−1–102 rad/s and in some cases −2–102 rad/ s. The superposition principles have been examined with these data for both the temperature and concentration dependence.

scholarly journals Photosynthetic characteristics of the freshwater red alga Batrachospermum delicatulum (Skuja) Necchi & Entwisle

2005 ◽  
Vol 19 (1) ◽  
pp. 125-137 ◽  
Author(s):  
Orlando Necchi Júnior ◽  
Abner H.S. Alves
Keyword(s):  
Inorganic Carbon ◽  
Photosynthetic Apparatus ◽  
High Capacity ◽  
Temporal Distribution ◽  
Red Alga ◽  
Photosynthetic Characteristics ◽  
Photosynthetic Parameters ◽  
Wide Range ◽  
Freshwater Red Algae ◽  
Two Peaks

Six populations of the freshwater red alga Batrachospermum delicatulum (Skuja) Necchi & Entwisle, including gametophyte and 'Chantransia' stage, were analysed in culture and natural conditions applying chlorophyll fluorescence and oxygen evolution. Parameters derived from the photosynthesis-irradiance curves indicated adaptation to low irradiance for all populations, which was characterized by photoinhibition, low values of Ik and Ic and high values of a. Data from both techniques revealed significant differences among populations and phases for most photosynthetic parameters. Similarly, photosynthesis responded differently to variations in temperature in each population with similar rates under a wide range of temperature. No consistent pattern was found when the same population or phase was tested, suggesting high capacity to adjust the photosynthetic apparatus to distinct conditions of irradiance and temperature. pH experiments showed a decreasing trend towards higher pH or higher rates at pH 6.5, suggesting, respectively, higher affinity to inorganic carbon as CO2 or indistinct use of bicarbonate and CO2. The diurnal pattern of photosynthesis essentially agree with that for seaweeds and freshwater red algae, consisting of two peaks: a first (generally higher) during the morning and a second (typically lower) in the afternoon. Photosynthetic characteristics of B. delicatulum (Skuja) Necchi & Entwisleexhibited a wide range of responses to irradiance, temperature and pH/inorganic carbon, reflecting its wide tolerance to these variables, which probably contributes to its wide spatial and temporal distribution.

scholarly journals Computational Experiments to Evaluate the Approaches to the Modeling of Viscoelastic Plates Motion Based on Various Theories

2018 ◽  
pp. 15-33
Author(s):  
B. A. Khudayarov
Keyword(s):  
Differential Equations ◽  
Mathematical Models ◽  
Viscoelastic Properties ◽  
Numerical Solutions ◽  
Aircraft Design ◽  
Panel Flutter ◽  
Scientific Problem ◽  
Wide Range ◽  
Hereditary Theory ◽  
Theory Of Viscoelasticity

Mathematical and computer modeling of the flutter of elements and units of the aircraft design is an actual scientific problem; its study is stimulated by the failure of aircraft elements, parts of space and jet engines. In view of the complexity of the flutter phenomenon of aircraft elements, simplifying assumptions are used in many studies. However, these assumptions, as a rule, turn out to be so restrictive that the mathematical model ceases to reflect the real conditions with sufficient accuracy. Therefore, results of theoretical and experimental studies are in bad agreement.At present, the problem of panel flutter is very relevant. Improvement of characteristics of military and civil aircraft inevitably requires reducing their weight, and consequently, the rigidity of paneling, which increases the possibility of a panel flutter. The concept of creating the aircraft with a variable shape, which would inevitably lead to a reduction in paneling thickness are actively discussed. Finally, the use of new materials and, in particular, composites, changes physical properties of the panels and can also lead to a flutter.The above-mentioned scientific problem gives grounds to assert that the development of adequate mathematical models, numerical methods and algorithms for solving nonlinear integral-differential equations of dynamic problems of the hereditary theory of viscoelasticity is actual.In connection with this, the development of mathematical models of individual elements of aircraft made of composite material is becoming very important.Generalized mathematical models of non-linear problems of the flutter of viscoelastic isotropic plates, streamlined by a supersonic gas flow, are constructed in the paper on the basis of integral models. To study oscillation processes in plates, a numerical algorithm is proposed for solving nonlinear integro-differential equations with singular kernels. Based on the developed computational algorithm, a package of applied programs is created. The effect of the singularity parameter in heredity kernels on the vibrations of structures with viscoelastic properties is numerically investigated. In a wide range of changes in plate parameters, critical flutter velocities are determined. Numerical solutions of the problem of viscoelastic plate flutter are compared for different models. It is shown that the most adequate theory for investigating a wide class of problems of the hereditary theory of viscoelasticity is the geometric nonlinear Kirchhoff-Love theory with consideration of elastic waves propagation. It is established that an account of viscoelastic properties of plate material leads to 40-60% decrease in the critical flutter velocity.

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