Strain Rate Dependence and Short-Term Relaxation Behavior of a Thermoset Polymer at Elevated Temperature: Experiment and Modeling

2008 ◽  
Author(s):  
A. J. W. McClung ◽  
M. B. Ruggles-Wrenn
Keyword(s):  
Strain Rate ◽  
Strain Curve ◽  
Strain Recovery ◽  
Relaxation Behavior ◽  
Solid Polymer ◽  
Experimental Program ◽  
Model Parameters ◽  
Stress Strain ◽  
Nonlinear Stress ◽  
Thermoset Polymer

The inelastic deformation behavior of PMR-15 neat resin, a high-temperature thermoset polymer, was investigated at 288°C. The experimental program was designed to explore the influence of strain rate changes in the 10−6 to 10−3 s−1 range on tensile loading, unloading, and strain recovery behavior, as well as on the relaxation response of the material. The material exhibits positive, nonlinear strain rate sensitivity in monotonic loading. Nonlinear, “curved” stress-strain behavior during unloading is observed at all strain rates. The strain recovery at zero stress is profoundly affected by prior strain rate. The prior strain rate is also found to have a strong influence on relaxation behavior. The rest stresses measured at the termination of relaxation tests form the relaxation boundary which resembles a nonlinear stress-strain curve. The results suggest that the inelastic behavior of the PMR-15 solid polymer at 288°C can be represented using a unified constitutive model with an overstress dependence of the inelastic rate of deformation. The experimental data are modeled with the viscoplasticity theory based on over-stress (VBO). A systematic procedure for determining model parameters is presented and the model is employed to predict the response of the material under various test histories.

Strain Rate Dependence and Short-Term Relaxation Behavior of a Thermoset Polymer at Elevated Temperature: Experiment and Modeling

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
A. J. W. McClung ◽  
M. B. Ruggles-Wrenn
Keyword(s):  
Strain Rate ◽  
Strain Curve ◽  
Strain Recovery ◽  
Relaxation Behavior ◽  
Solid Polymer ◽  
Experimental Program ◽  
Model Parameters ◽  
Stress Strain ◽  
Nonlinear Stress ◽  
Thermoset Polymer

The inelastic deformation behavior of polymerization of monomeric reactants-15 (PMR-15) neat resin, a high-temperature thermoset polymer, was investigated at 288°C. The experimental program was designed to explore the influence of strain rate changes in the 10−6–10−3 s−1 range on tensile loading, unloading, and strain recovery behavior, as well as on the relaxation response of the material. The material exhibits positive, nonlinear strain rate sensitivity in monotonic loading. Nonlinear, “curved” stress-strain behavior during unloading is observed at all strain rates. The strain recovery at zero stress is profoundly affected by prior strain rate. The prior strain rate is also found to have a strong influence on relaxation behavior. The rest stresses measured at the termination of relaxation tests form the relaxation boundary, which resembles a nonlinear stress-strain curve. The results suggest that the inelastic behavior of the PMR-15 solid polymer at 288°C can be represented using a unified constitutive model with an overstress dependence of the inelastic rate of deformation. The experimental data are modeled with the viscoplasticity theory based on overstress. A systematic procedure for determining model parameters is presented and the model is employed to predict the response of the material under various test histories.

The Rate (Time)–Dependent Mechanical Behavior of the PMR-15 Thermoset Polymer at Temperatures in the 274–316 °C Range: Experiments and Modeling

2011 ◽  
Author(s):  
C. E. C. Ryther ◽  
M. B. Ruggles-Wrenn
Keyword(s):  
Strain Rate ◽  
Mechanical Behavior ◽  
Deformation Behavior ◽  
Inelastic Deformation ◽  
Monotonic Loading ◽  
Relaxation Behavior ◽  
Time Dependent ◽  
Experimental Program ◽  
Model Parameters ◽  
Thermoset Polymer

The inelastic deformation behavior of the PMR-15 neat resin, a high-temperature thermoset polymer, was investigated at temperatures in the 274–316 °C range. The experimental program was designed to explore the influence of strain rate on monotonic loading at various temperatures. In addition, the effects of prior strain rate on relaxation response and on creep behavior following strain controlled loading were examined at temperatures in the range of interest. Positive, nonlinear strain rate sensitivity is observed in monotonic loading at all temperatures investigated. Both relaxation behavior and creep are profoundly influenced by prior strain rate at all temperatures. The time-dependent mechanical behavior of the PMR-15 polymer is also strongly affected by temperature. The elastic modulus decreases and the departure from quasi-linear behavior is accelerated with increasing temperature. Stress levels in the region of inelastic flow decrease as the temperature increases. The relaxation behavior as well as the creep response is strongly influenced by temperature. The viscoplasticity theory based on overstress (VBO) is augmented to model the effects of temperature on the inelastic deformation behavior of PMR-15. VBO is a unified state variable theory with growth laws for three state variables: the equilibrium stress, the kinematic stress and the isotropic stress. Based on experimental findings several VBO model parameters are developed as functions of temperature. The augmented model is employed to predict the response of the material under both strain- and stress-controlled loading histories at temperatures in the range of interest. Comparison with experimental data demonstrates that the augmented VBO successfully predicts the inelastic deformation behavior of PMR-15 polymer under various loading histories at temperatures between 274 and 316 °C.

The Rate (Time)-Dependent Mechanical Behavior of the PMR-15 Thermoset Polymer at Temperatures in the 274–316 °C Range: Experiments and Modeling

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
C. E. C. Ryther ◽  
M. B. Ruggles-Wrenn
Keyword(s):  
Strain Rate ◽  
Mechanical Behavior ◽  
Deformation Behavior ◽  
Inelastic Deformation ◽  
Monotonic Loading ◽  
Relaxation Behavior ◽  
Time Dependent ◽  
Experimental Program ◽  
Model Parameters ◽  
Thermoset Polymer

The inelastic deformation behavior of the PMR-15 neat resin, a high-temperature thermoset polymer, was investigated at temperatures in the 274–316 °C range. The experimental program was designed to explore the influence of strain rate on monotonic loading at various temperatures. In addition, the effects of prior strain rate on relaxation response and on creep behavior following strain-controlled loading were examined at temperatures in the range of interest. Positive, nonlinear strain rate sensitivity is observed in monotonic loading at all temperatures investigated. Both relaxation behavior and creep are profoundly influenced by prior strain rate at all temperatures. The time-dependent mechanical behavior of the PMR-15 polymer is also strongly affected by temperature. The elastic modulus decreases and the departure from quasi-linear behavior is accelerated with increasing temperature. Stress levels in the region of inelastic flow decrease as the temperature increases. The relaxation behavior as well as the creep response is strongly influenced by temperature. The viscoplasticity theory based on overstress for polymers (VBOP) is augmented to model the effects of temperature on the inelastic deformation behavior of PMR-15. VBOP is a unified state variable theory with growth laws for three state variables: the equilibrium stress, the kinematic stress, and the isotropic stress. Based on the experimental findings several VBOP model parameters are developed as functions of temperature. The augmented model is employed to predict the response of the material under both strain- and stress-controlled loading histories at temperatures in the range of interest. Comparison with experimental data demonstrates that the augmented VBOP successfully predicts the inelastic deformation behavior of PMR-15 polymer under various loading histories at temperatures between 274 and 316 °C.

Effect of Pre-Stress on the Dynamic Tensile Behavior of the TMJ Disc

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
J. Lomakin ◽  
P. A. Sprouse ◽  
M. S. Detamore ◽  
S. H. Gehrke
Keyword(s):  
Mechanical Properties ◽  
Strain Rate ◽  
Strain Curve ◽  
Dynamic Mechanical Properties ◽  
Polymer Materials ◽  
Stress Strain ◽  
Dynamic Mechanical ◽  
Highly Nonlinear ◽  
Nonlinear Stress ◽  
Tmj Disc

Previous dynamic analyses of the temporomandibular joint (TMJ) disc have not included a true preload, i.e., a step stress or strain beyond the initial tare load. However, due to the highly nonlinear stress-strain response of the TMJ disc, we hypothesized that the dynamic mechanical properties would greatly depend on the preload, which could then, in part, account for the large variation in the tensile stiffnesses reported for the TMJ disc in the literature. This study is the first to report the dynamic mechanical properties as a function of prestress. As hypothesized, the storage modulus (E′) of the disc varied by a factor of 25 in the mediolateral direction and a factor of 200 in the anteroposterior direction, depending on the prestress. Multiple constant strain rate sweeps were extracted and superimposed via strain-rate frequency superposition (SRFS), which demonstrated that the strain rate amplitude and strain rate were both important factors in determining the TMJ disc material properties, which is an effect not typically seen with synthetic materials. The presented analysis demonstrated, for the first time, the applicability of viscoelastic models, previously applied to synthetic polymer materials, to a complex hierarchical biomaterial such as the TMJ disc, providing a uniquely comprehensive way to capture the viscoelastic response of biological materials. Finally, we emphasize that the use of a preload, preferably which falls within the linear region of the stress-strain curve, is critical to provide reproducible results for tensile analysis of musculoskeletal tissues. Therefore, we recommend that future dynamic mechanical analyses of the TMJ disc be performed at a controlled prestress corresponding to a strain range of 5–10%.

scholarly journals Transformation of Test Data for the Specification of a Viscoelastic Marlow Model

Solids ◽  
2020 ◽  
Vol 1 (1) ◽  
pp. 2-15
Author(s):  
Olaf Hesebeck
Keyword(s):  
Tensile Test ◽  
Strain Rate ◽  
Finite Strain ◽  
Strain Curve ◽  
Model Parameters ◽  
Strain Rates ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Material Response ◽  
Rate Dependent

The combination of hyperelastic material models with viscoelasticity allows researchers to model the strain-rate-dependent large-strain response of elastomers. Model parameters can be identified using a uniaxial tensile test at a single strain rate and a relaxation test. They enable the prediction of the stress–strain behavior at different strain rates and other loadings like compression or shear. The Marlow model differs from most hyperelastic models by the concept not to use a small number of model parameters but a scalar function to define the mechanical properties. It can be defined conveniently by providing the stress–strain curve of a tensile test without need for parameter optimization. The uniaxial response of the model reproduces this curve exactly. The coupling of the Marlow model and viscoelasticity is an approach to create a strain-rate-dependent hyperelastic model which has good accuracy and is convenient to use. Unfortunately, in this combination, the Marlow model requires to specify the stress–strain curve for the instantaneous material response, while experimental data can be obtained only at finite strain rates. In this paper, a transformation of the finite strain rate data to the instantaneous material response is derived and numerically verified. Its implementation enables us to specify hyperelastic materials considering strain-rate dependence easily.

scholarly journals Black rubber and the non-linear elastic response of scale invariant solids

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Matteo Baggioli ◽  
Víctor Cáncer Castillo ◽  
Oriol Pujolàs
Keyword(s):  
Strain Curve ◽  
Effective Field ◽  
Elastic Response ◽  
Elastic Behaviour ◽  
Scale Invariant ◽  
Stress Strain ◽  
Nonlinear Stress ◽  
Hyper Elastic ◽  
Simple Class ◽  
Nonlinear Elastic

Abstract We discuss the nonlinear elastic response in scale invariant solids. Following previous work, we split the analysis into two basic options: according to whether scale invariance (SI) is a manifest or a spontaneously broken symmetry. In the latter case, one can employ effective field theory methods, whereas in the former we use holographic methods. We focus on a simple class of holographic models that exhibit elastic behaviour, and obtain their nonlinear stress-strain curves as well as an estimate of the elasticity bounds — the maximum possible deformation in the elastic (reversible) regime. The bounds differ substantially in the manifest or spontaneously broken SI cases, even when the same stress- strain curve is assumed in both cases. Additionally, the hyper-elastic subset of models (that allow for large deformations) is found to have stress-strain curves akin to natural rubber. The holographic instances in this category, which we dub black rubber, display richer stress- strain curves — with two different power-law regimes at different magnitudes of the strain.

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.

scholarly journals Evolution of specimen strain rate in split Hopkinson bar test

2019 ◽  
Vol 233 (13) ◽  
pp. 4667-4687 ◽  
Author(s):  
Hyunho Shin ◽  
Jong-Bong Kim
Keyword(s):  
Strain Rate ◽  
Rate Equation ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Hopkinson Bar ◽  
Stress Strain ◽  
Split Hopkinson Bar ◽  
Specimen Diameter ◽  
Strain And Strain Rate ◽  
Split Hopkinson

The specimen strain rate in the split Hopkinson bar (SHB) test has been formulated based on a one-dimensional assumption. The strain rate is found to be controlled by the stress and strain of the deforming specimen, geometry (the length and diameter) of specimen, impedance of bar, and impact velocity. The specimen strain rate evolves as a result of the competition between the rate-increasing and rate-decreasing factors. Unless the two factors are balanced, the specimen strain rate generally varies (decreases or increases) with strain (specimen deformation), which is the physical origin of the varying nature of the specimen strain rate in the SHB test. According to the formulated strain rate equation, the curves of stress–strain and strain rate–strain are mutually correlated. Based on the correlation of these curves, the strain rate equation is verified through a numerical simulation and experiment. The formulated equation can be used as a tool for verifying the measured strain rate–strain curve simultaneously with the measured stress–strain curve. A practical method for predicting the specimen strain rate before carrying out the SHB test has also been presented. The method simultaneously solves the formulated strain rate equation and a reasonably estimated constitutive equation of specimen to generate the anticipated curves of strain rate–strain and stress–strain in the SHB test. An Excel® program to solve the two equations is provided. The strain rate equation also indicates that the increase in specimen stress during deformation (e.g., work hardening) plays a role in decreasing the slope of the strain rate–strain curve in the plastic regime. However, according to the strain rate equation, the slope of the strain rate–strain curve in the plastic deformation regime can be tailored by controlling the specimen diameter. Two practical methods for determining the specimen diameter to achieve a nearly constant strain rate are presented.

scholarly journals Constant Strain-Rate Tensile Testing of Natural Snow

1980 ◽  
Vol 26 (94) ◽  
pp. 519 ◽  
Author(s):  
H. Singh ◽  
F.W. Smith
Keyword(s):  
Strain Rate ◽  
Strain Gage ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Strain Rates ◽  
Strain Gages ◽  
Compression Tests ◽  
Snow Sample ◽  
Stress Strain ◽  
Natural Snow

Abstract In conducting tension and compression tests on snow samples, strains and strain-rates are usually determined from the displacements of the ends of the samples. In this work, a strain-gage which mounts directly onto the snow sample during testing, was developed and was found to give accurate and direct measurements of strain and strain-rates. A commercially available 0-28 pF variable capacitor was modified to perform the required strain measurements. It is a polished metallic plunger sliding inside a metal-coated glass tube. The plunger and tube were each soldered to the end of a spring-steel wire arm. To the other end of these arms were soldered to 10 mm square pads made of thin brass shim stock. The whole device weighs 2.5 g and the low coefficient of friction in the capacitor resulted in a very low actuation force. To mount the strain gage, the pads are wetted and frozen onto the snow sample. A high degree of sensitivity was achieved through the use of “phase-lock-loop” electronic circuitry. The capacitance change caused by the strain in the sample, changes the frequency of output signal from an oscillator and thus causes the change in output from the system. In the locked state, to which the system is constantly driven by a feed-back loop, the system output is almost ripple free. The strain gages were calibrated in the field in order to take into account the effects of very low field temperatures. The calibration curves were almost linear over the travel of 15 mm, the maximum limit. The sensitivity of the system is 4 mV per strain unit, but this could be increased by an order of magnitude by minor adjustments in the circuit. Constant strain-rate tensile tests were performed on natural snow at Berthoud Pass, Colorado, U.S.A., in the density range of 140-290 kg m-3. Four strain gages were mounted onto the samples to sense any non-uniform deformation which otherwise would have gone unnoticed or caused scatter in the data. The average indication of these gages was used to construct stress—strain curves for various types of snow at different strain-rates. The effect of strain-rate on the behavior of snow was studied. “Ratcheting” in the stress-strain curve in the region where the snow becomes plastic was observed first by Kinosita in his compression tests. A similar phenomenon was observed in these tension tests. It was found that directly measured strain is quite different from that which would be calculated from sample end movement. Strain softening was not observed in these tests up to total strains of 8%. The strain-rate effects found were comparable to the results of other investigators.

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