Tensile Stress—Strain and Stress Relaxation Behavior of Raw Elastomers Using a High Speed Tester

1974 ◽  
Vol 47 (2) ◽  
pp. 307-317 ◽  
Author(s):  
H. H. Bowerman ◽  
E. A. Collins ◽  
N. Nakajima
Keyword(s):  
Stress Relaxation ◽  
High Speed ◽  
Strain Rates ◽  
Time Behavior ◽  
Stress Strain ◽  
Strain Behavior ◽  
Relaxation Measurements ◽  
Ultimate Properties ◽  
Short Time ◽  
Acrylonitrile Copolymers

Abstract A high-speed, tensile-testing device was used to determine the stress—strain behavior of uncompounded butadiene—acrylonitrile copolymers over a range of temperatures and deformation rates. The strain rates were varied from 267 to 26,700 per cent/sec and the temperature was varied from 25 to 97° C. The high-speed tester was also used for stress—relaxation measurements by applying the strain nearly instantly in conformity with theoretical requirements in order to obtain the short time behavior. The WLF equation was obtained from the stress—relaxation data and then used to reduce the ultimate properties to one temperature over four decades of the strain rates. The ultimate properties could be represented by a failure envelope similar to those obtained for vulcanizates.

Viscoelastic Behavior of Butadiene-Acrylonitrile Copolymers at Small and Large Deformations and Their Ultimate Properties

1973 ◽  
Vol 46 (2) ◽  
pp. 417-424 ◽  
Author(s):  
N. Nakajima ◽  
H. H. Bowerman ◽  
E. A. Collins
Keyword(s):  
Shear Rate ◽  
Stress Relaxation ◽  
Tensile Stress ◽  
High Speed ◽  
Capillary Flow ◽  
Viscoelastic Behavior ◽  
Stress Strain ◽  
Flow Measurements ◽  
Acrylonitrile Copolymers ◽  
Good Agreement

Abstract With four samples of butadiene-acrylonitrile copolymers the following viscoelastic measurements have been performed: dynamic mechanical measurements in tension at 110 Hz from −60 to 180° C, tensile stress relaxation measurements with 100 per cent elongation at 25, 54, and 97.5° C, capillary flow measurements at 70, 100, and 125° C, and high-speed tensile stress-strain measurements carried to break at 25, 54, and 97° C. All the data have been treated with the same equation for the time-temperature conversion. The complex viscosity-frequency curves calculated from the dynamic measurements were found to be in good agreement with the capillary viscosity-shear rate curves. From the stress-strain relationship at the yield point the viscosity is estimated; such viscosity as a function of the strain rate is similar to the viscosity-shear rate curve. Good agreement was found with some samples. The elongation to break may be predicted with some samples from the treatment of stress relaxation data together with steady shear flow data.

Understanding Dynamic Recrystallization Behavior through a Delay Differential Equation Approach

2007 ◽  
Vol 558-559 ◽  
pp. 441-448 ◽  
Author(s):  
Jong K. Lee
Keyword(s):  
Differential Equation ◽  
Strain Rate ◽  
Critical Strain ◽  
Strain Curve ◽  
Single Peak ◽  
Strain Rates ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Strain Behavior ◽  
Delay Differential

During hot working, deformation of metals such as copper or austenitic steels involves features of both diffusional flow and dislocation motion. As such, the true stress-true strain relationship depends on the strain rate. At low strain rates (or high temperatures), the stress-strain curve displays an oscillatory behavior with multiple peaks. As the strain rate increases (or as the temperature is reduced), the number of peaks on the stress-strain curve decreases, and at high strain rates, the stress rises to a single peak before settling at a steady-state value. It is understood that dynamic recovery is responsible for the stress-strain behavior with zero or a single peak, whereas dynamic recrystallization causes the oscillatory nature. In the past, most predictive models are based on either modified Johnson-Mehl-Avrami kinetic equations or probabilistic approaches. In this work, a delay differential equation is utilized for modeling such a stress-strain behavior. The approach takes into account for a delay time due to diffusion, which is expressed as the critical strain for nucleation for recrystallization. The solution shows that the oscillatory nature depends on the ratio of the critical strain for nucleation to the critical strain for completion for recrystallization. As the strain ratio increases, the stress-strain curve changes from a monotonic rise to a single peak, then to a multiple peak behavior. The model also predicts transient flow curves resulting from strain rate changes.

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.

High Strain-Rate Compressive Behavior and Constitutive Modeling of Selected Polymers Using Modified Ramberg-Osgood Equation

2014 ◽  
Vol 566 ◽  
pp. 80-85
Author(s):  
Kenji Nakai ◽  
Takashi Yokoyama
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Compressive Stress ◽  
Constitutive Modeling ◽  
High Strain ◽  
Strain Rates ◽  
Stress Strain ◽  
Strain Behavior ◽  
Least Squares Fit ◽  
Wide Range

The present paper is concerned with constitutive modeling of the compressive stress-strain behavior of selected polymers at strain rates from 10-3 to 103/s using a modified Ramberg-Osgood equation. High strain-rate compressive stress-strain curves up to strains of nearly 0.08 for four different commercially available extruded polymers were determined on the standard split Hopkinson pressure bar (SHPB). The low and intermediate strain-rate compressive stress-strain relations were measured in an Instron testing machine. Six parameters in the modified Ramberg-Osgood equation were determined by fitting to the experimental stress-strain data using a least-squares fit. It was shown that the monotonic compressive stress-strain behavior over a wide range of strain rates can successfully be described by the modified Ramberg-Osgood constitutive model. The limitations of the model were discussed.

Master Curve for Tensile Stress—Strain Behavior of Amorphous Elastomers at Small and Large Deformations

1974 ◽  
Vol 47 (2) ◽  
pp. 318-332 ◽  
Author(s):  
N. Nakajima ◽  
E. A. Collins ◽  
H. H. Bowerman
Keyword(s):  
Tensile Stress ◽  
Master Curve ◽  
Large Deformations ◽  
Strain Rates ◽  
Stress Strain ◽  
Strain Behavior

Abstract A master curve scheme for small and large deformations was developed for tensile stress-strain behavior of butadiene—acrylonitrile uncrosslinked elastomers. Measurements were carried out at strain rates of 267 to 26,700 per cent/sec at temperatures of 25 to 97° C.

Time and Temperature Dependence of the Ultimate Properties of an SBR Rubber at Constant Elongations

1961 ◽  
Vol 34 (3) ◽  
pp. 897-909
Author(s):  
Thor L. Smith ◽  
Paul J. Stedry
Keyword(s):  
Tensile Strength ◽  
Strain Rate ◽  
Temperature Dependence ◽  
Rate Dependence ◽  
Strain Rates ◽  
Type Specimens ◽  
Stress Strain ◽  
Ultimate Elongation ◽  
Tensile Tester ◽  
Ultimate Properties

Abstract A study was made previously of the temperature and strain rate dependence of the stress at break (tensile strength) and the ultimate elongation of an unfilled SBR rubber. In that study, stress-strain curves to the point of rupture were measured with an Instron tensile tester on ring type specimens at 14 temperatures between −67.8° and 93.3° C, and at 11 strain rates between 0.158×10−3 and 0.158 sec−1 at most temperatures. The tensile strength was found to increase with both increasing strain rate and decreasing temperature. At all temperatures above −34.4° C, the ultimate elongation was likewise found to increase with increasing strain rate and decreasing temperature but at lower temperatures the opposite dependence on rate was observed; at −34.4° C, the ultimate elongation passed through a maximum with increasing rate.

One-Dimensional Dynamic Compressive Behavior of EPDM Rubber

2003 ◽  
Vol 125 (3) ◽  
pp. 294-301 ◽  
Author(s):  
B. Song ◽  
W. Chen
Keyword(s):  
Strain Rate ◽  
High Speed ◽  
Dynamic Stress ◽  
Split Hopkinson Pressure Bar ◽  
Constant Strain Rate ◽  
Strain Rates ◽  
Hopkinson Pressure Bar ◽  
Stress Strain ◽  
Epdm Rubber ◽  
One Dimensional

Dynamic compressive stress-strain curves at various strain rates of an Ethylene-Propylene-Diene Monomer Copolymer (EPDM) rubber have been determined with a modified split Hopkinson pressure bar (SHPB). The use of a pulse-shaping technique ensures that the specimen deforms at a nearly constant strain rate under dynamically equilibrated stress. The validity of the experiments was monitored by a high-speed digital camera for specimen edge deformation, and by piezoelectric force transducers for dynamic stress equilibrium. The resulting dynamic stress-strain curves for the EPDM indicate that the material is sensitive to strain rates and that the strain-rate sensitivity depends on the value of strain. Based on a strain energy function theory, a one-dimensional dynamic constitutive equation for this rubber was modified to describe the high strain-rate experimental results within the ranges of strain and strain rates presented in this paper.

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