The Resolution of Elastomer Blend Properties by Stress-Strain Modelling. An Extension of the Model to Carbon-Black-Loaded Elastomers

1990 ◽  
Vol 63 (5) ◽  
pp. 779-791 ◽  
Author(s):  
R. F. Bauer ◽  
A. H. Crossland
Keyword(s):  
Carbon Black ◽  
Full Range ◽  
Filler Particle ◽  
Particle Surface ◽  
Practical Method ◽  
Particulate Phase ◽  
Stress Strain ◽  
Strain Behavior ◽  
Strain Relationship ◽  
Elastomer Blend

Abstract The unique stress-strain behavior of a carbon-black-loaded elastomer is due to the presence of a rigid, particulate phase, but also to the interaction of the elastomer chains with the filler. It is postulated that this interaction takes the form of adsorption on the filler-particle surface, which results in trapped entanglements. Upon deformation, the trapped chains are aligned parallel to the axis of stress. Thus, a practical stress-strain relationship could be developed which is capable to model the stress-strain behavior of compounds over the full range of extensions up to break. The analysis of a highly prestrained carbon-black-loaded NR compound in which the entanglement effect had been mechanically destroyed, demonstrated that the “sea-island” (SIP) coupling arrangement is most suitable for accounting for the interaction effect of the elastomer and carbon black. For moderately prestrained carbon-black-loaded NR and BR compounds a good fit of theory to experiment is obtained for a combination of the SIP coupling arrangement and the specially derived stress-strain relationship. Thus, a practical method is available for describing the deformation of carbon-black-loaded elastomers and for the modelling of carbon-black-loaded elastomer blends.

A Method to Resolve the Properties of Individual Phases in Carbon-Black-Loaded Elastomer Blends

1991 ◽  
Vol 64 (2) ◽  
pp. 234-242
Author(s):  
R. F. Bauer ◽  
A. H. Crossland
Keyword(s):  
Carbon Black ◽  
Large Deformation ◽  
Polymer Phase ◽  
Stress Strain ◽  
Strain Behavior ◽  
Stress Behavior ◽  
Strain Relationship ◽  
Deformation Stress ◽  
The Individual ◽  
Vulcanization Process

Abstract Properties of the individual phases in a 70/30 carbon-black-loaded BR/NR blend could be successfully resolved using large deformation stress-strain modelling. Since the dispersed NR phase of the example had a lower modulus than the continuous BR phase, the interaction between the blend phases could be modelled by a simple parallel coupling arrangement. The stress behavior of each individual carbon-black-loaded polymer phase was then determined with respect to strain using a specially derived stress-strain relationship. The blend components also have to be characterized with respect to state-of-cure by empirically establishing how the parameters in the stress-strain relationship vary with respect to cure. The properties of the phases in the blend are then determined by finding the combination of component parameters which precisely reproduce the stress-strain behavior of the blend. In the demonstration example of this paper, there was evidence of a significant amount of curative migration between phases during the vulcanization process.

Expression of a Generic Full-Range True Stress-True Strain Model for Pipeline Steels Using the Product-Log (Omega) Function

2017 ◽  
Author(s):  
Onyekachi Ndubuaku ◽  
Michael Martens ◽  
J. J. Roger Cheng ◽  
Samer Adeeb
Keyword(s):  
True Strain ◽  
Full Range ◽  
True Stress ◽  
Stress Strain ◽  
Pipeline Steels ◽  
Strain Behavior ◽  
Proposed Model ◽  
Strain Relationship ◽  
Strain Model

Steel pipelines are subjected to a variety of complex, and sometimes difficult to predict, loading schemes during the fabrication, installation and operation phases of their lifecycles. Consequently, the mechanical behavior of steel pipelines is not only influenced by the steel grade but also by the loading history of the pipe segments. Due to the resultant intricacies of the nonlinear load-deformation behavior of pipelines, adequate numerical analysis techniques are usually required for simulation of pipelines under different loading schemes. The validity of such numerical simulations is largely influenced by the accuracy of the true stress-true strain characterization of the pipeline steels. However, existing stress-strain mathematical expressions, developed for the characterization of metallic materials over the full-range of the stress-strain relationship, have been observed to either loose predictive accuracy beyond a limited strain range or, for the more accurate full-range models, are cumbersome due to their requirement of a large number of constituent parameters. This paper presents a relatively accurate and simple true stress-true strain model which is capable of accurately predicting the stress-strain behavior of pipeline steels over the full range of strains. The proposed stress-strain model is characteristically unlike existing stress-strain models as it is essentially defined by a Product-Log function using two proposed parameters, and is capable of capturing a reasonable approximation of the yield plateau in the stress-strain curve. To validate the proposed model, curve-fitting techniques are employed for comparison to experimental data of the stress-strain behavior of different pipeline steel grades (X52 – X100). Excellent agreements are observed between the proposed model and the different pipeline steels over the full-range of the true stress-true strain relationship. Furthermore, the applicability of the proposed model is validated by means of a proposed parametric procedure for predicting the ultimate compressive strength of shell elements.

Capillary Rheometry of Carbon-Black-Filled Butadiene—Acrylonitrile Copolymers

1975 ◽  
Vol 48 (4) ◽  
pp. 615-622 ◽  
Author(s):  
N. Nakajima ◽  
E. A. Collins
Keyword(s):  
Shear Rate ◽  
Carbon Black ◽  
Tensile Stress ◽  
Capillary Flow ◽  
Complex Viscosity ◽  
Appreciable Effect ◽  
Stress Strain ◽  
Capillary Rheometry ◽  
Strain Behavior ◽  
Acrylonitrile Copolymers

Abstract Capillary rheometry of carbon-black-filled butadiene—acrylonitrile copolymers at 125°C was performed over a wide shear rate range. The data were corrected for pressure loss in the barrel and at the capillary entrance, and for the non-Newtonian velocity profile (Rabinowitsch correction). No appreciable effect of pressure on viscosity was observed. The die swell values were very small, 1.1–1.4. This fact and the shape of the plots of shear stress vs. shear rate imply the presence of a particulate structure, which is probably built by carbon black surrounded with bound rubber. Unlike the behavior of raw amorphous elastomers, the steady-shear viscosity, the dynamic complex viscosity, and the viscosity calculated from tensile stress-strain behavior were significantly different from each other. That is, the capillary flow data indicated an alteration of the structure towards strain softening, and the tensile stress-strain behavior showed strain hardening, indicating retention of the structure up to the yield point. In the dynamic measurement, being conducted at very small strain, the structure is least disturbed. With unfilled elastomers essentially the same deformational mechanism was believed to be responsible in these three measurements, because the results can be expressed by a single master curve.

Determination of Full Range Stress-Strain Behavior of Pipeline Steels Using Tensile Characteristics

2010 ◽  
Author(s):  
Stijn Hertele´ ◽  
Wim De Waele ◽  
Rudi Denys
Keyword(s):  
Full Range ◽  
Tensile Tests ◽  
Proof Stress ◽  
Stress Strain ◽  
Pipeline Steels ◽  
Strain Behavior ◽  
Parameter Values ◽  
Near Future ◽  
Strain Model

It is standard practice to approximate the post-yield behavior of pipeline steels by means of the Ramberg-Osgood equation. However, the Ramberg-Osgood equation is often unable to accurately describe the stress-strain behavior of contemporary pipeline steels with a high Y/T ratio. This is due to the occurrence of two distinct, independent stages of strain hardening. To address this problem, the authors recently developed a new ‘UGent’ stress-strain model which provides a better description of those steels. This paper elaborates a methodology to estimate suited parameter values for the UGent model, starting from a set of tensile characteristics. Using the proposed methodology, good approximations have been obtained for a preliminary series of eight investigated stress-strain curves. Next to all common tensile characteristics, the 1% proof stress is needed. The authors therefore encourage the future acquisition of this stress level during tensile tests. Currently, the authors perform a further in-depth validation which will be reported in the near future.

Studies on the Stress-Strain Relationship Bovine Cortical Bone Based on Ramberg–Osgood Equation

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
N. K. Sharma ◽  
M. D. Sarker ◽  
Saman Naghieh ◽  
Daniel X. B. Chen
Keyword(s):  
Cortical Bone ◽  
Linear Regression Analysis ◽  
Tensile Tests ◽  
Uniaxial Tensile ◽  
Loading Conditions ◽  
Stress Strain ◽  
Strain Behavior ◽  
Nonlinear Stress ◽  
Strain Relationship ◽  
Relationship Of

Bone is a complex material that exhibits an amount of plasticity before bone fracture takes place, where the nonlinear relationship between stress and strain is of importance to understand the mechanism behind the fracture. This brief presents our study on the examination of the stress–strain relationship of bovine femoral cortical bone and the relationship representation by employing the Ramberg–Osgood (R–O) equation. Samples were taken and prepared from different locations (upper, middle, and lower) of bone diaphysis and were then subjected to the uniaxial tensile tests under longitudinal and transverse loading conditions, respectively. The stress–strain curves obtained from tests were analyzed via linear regression analysis based on the R–O equation. Our results illustrated that the R–O equation is appropriate to describe the nonlinear stress–strain behavior of cortical bone, while the values of equation parameters vary with the sample locations (upper, middle, and lower) and loading conditions (longitudinal and transverse).

Analysis of the Mechanic Behavior and Rutting of Asphalt Concrete Using a Sand Model

1999 ◽  
Vol 15 (4) ◽  
pp. 177-184
Author(s):  
Ming-Lou Liu
Keyword(s):  
Asphalt Concrete ◽  
Stress Path ◽  
Plasticity Model ◽  
Test Results ◽  
Research Subjects ◽  
Stress Strain ◽  
Strain Behavior ◽  
Strain Relationship ◽  
Concrete Materials ◽  
Relationship Of

AbstractThe stress-strain relationship of the sand and asphalt concrete materials is one of the most important research subjects in the past, and many conctitutive laws for these materials have been proposed in the last two decades. In this study, the Vermeer plasticity model is modified and used to predict the behavior of the sand and asphalt concrete materials under different stress path conditions. The results show that the predictions and test results agree well under different stress path conditions. However, the orignal Vermeer model can not predict the stress-strain behavior of the asphalt concrete. Finally, the modified Vermeer plasticity model is incorporated with the pavement rutting model to predict the rut depth of pavement structure under traffic loadings.

Rubber–Filler Interactions and Network Structure in Relation to Stress–Strain Behavior of Vulcanized, Carbon Black Filled EPDM

2011 ◽  
Vol 44 (12) ◽  
pp. 4887-4900 ◽  
Author(s):  
V. M. Litvinov ◽  
R. A. Orza ◽  
M. Klüppel ◽  
M. van Duin ◽  
P. C. M. M. Magusin
Keyword(s):  
Carbon Black ◽  
Network Structure ◽  
Stress Strain ◽  
Strain Behavior ◽  
Rubber Filler

Mechanism of the Modulus Increase of Carbon-Black-Filled Rubber at Small Extension

2011 ◽  
Vol 284-286 ◽  
pp. 1969-1973
Author(s):  
Xiao Ling Hu ◽  
Yong Ouyang ◽  
Xiong Zhou ◽  
Wen Bo Luo
Keyword(s):  
Carbon Black ◽  
Tensile Stress ◽  
Volume Fraction ◽  
Tensile Modulus ◽  
Homogenization Method ◽  
Stress Strain ◽  
Filled Rubber ◽  
Strain Relationship ◽  
Filled Rubbers ◽  
Relationship Of

The tensile stress-strain relationship of rubbers is fairly linear and can be used for obtaining tensile modulusE. In this work we analyzed the tensile stress-strain relationship of filled rubber experimentally and employed the extended 2D homogenization method to compute the modulus of the carbon black (CB) filled rubbers with various CB volume fractions ranging from 5% to 25%. The results reveal that the modulus of CB-filled rubbers increased with the increase in CB volume fraction and in CB aggregation.

Normalized Stress-Strain Behavior of Yingkou Clay

2013 ◽  
Vol 838-841 ◽  
pp. 47-52
Author(s):  
Fu Yi ◽  
Hong Yu Wang
Keyword(s):  
Strain Hardening ◽  
Principal Stress ◽  
Soft Soil ◽  
Confining Pressure ◽  
Stress Strain ◽  
Strain Behavior ◽  
Strain Relationship ◽  
Relationship Of ◽  
Is Strain

In order to systemic study the normalized stress-strain relationship behavior of Yingkou clay. By the consolidated undrained triaxial sherar test of Yingkou clay, obtaining that stress-strain relationship is strain hardening under different confining pressures.A kind of cementation structure in the soil directly affects soft soil strength.And the paper contrast four kinds of normalized factors to study stress-strain characteristics,which are confining pressurethe average consolidation pressureand the ultimate value of principal stress.The results indicate that the normalized degree is more accurate when used value of principal stress and as normalized factor. Meanwhile the normalized stress-strain relationship of Yingkou clay under consolidated undrained condition is established,which can well predict the stress-strain relationship under different confining pressure.

scholarly journals Effect of Initial Backfill Temperature on the Deformation Behavior of Early Age Cemented Paste Backfill That Contains Sodium Silicate

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Aixiang Wu ◽  
Yong Wang ◽  
Bo Zhou ◽  
Jiahua Shen
Keyword(s):  
Modulus Of Elasticity ◽  
Deformation Behavior ◽  
Initial Temperature ◽  
Cemented Paste Backfill ◽  
Stress Strain ◽  
Degree Of Hydration ◽  
Strain Behavior ◽  
Paste Backfill ◽  
Strain Relationship ◽  
The Relationship

Enhancing the knowledge on the deformation behavior of cemented paste backfill (CPB) in terms of stress-strain relations and modulus of elasticity is significant for economic and safety reasons. In this paper, the effect of the initial backfill temperature on the CPB’s stress-strain behavior and modulus of elasticity is investigated. Results show that the stress-strain relationship and the modulus of elasticity behavior of CPB are significantly affected by the curing time and initial temperature of CPB. Additionally, the relationship between the modulus of elasticity and unconfined compressive strength (UCS) and the degree of hydration was evaluated and discussed. The increase of UCS and hydration degree leads to an increase in the modulus of elasticity, which is not significantly affected by the initial temperature.

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