Elastomer Behavior IV. Loop Structure of Elastomer Networks

1966 ◽  
Vol 39 (5) ◽  
pp. 1489-1495
Author(s):  
L. C. Case ◽  
R. V. Wargin
Keyword(s):  
Experimental Data ◽  
Crosslink Density ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Polymer Chains ◽  
Theoretical Treatment ◽  
Loop Structure ◽  
Stress Strain ◽  
Strain Behavior ◽  
Selection Of

Abstract A new theoretical treatment strongly indicates that an elastomer network actually consists of a system of fused, closed, interpenetrating loops of polymer chains. This interpenetrating loop structure restricts the movement of the chains and thereby affects the stress-strain behavior of the elastomer. Methods have been developed to enable the calculation of the number of effective crosslinks caused by loop interpenetrations (virtual crosslinks). The uniaxial stress-strain behavior of an elastomer predicted using our methods can be fitted almost perfectly to published experimental data by proper selection of chain parameters. Previous theoretical treatments gave only a qualitative fit to the experimental data for the stress-strain behavior of elastomers and were not capable of predicting the correct shape of the experimental stress-strain curve. The present treatment gives a nearly perfect fit for both stress as a function of strain at constant crosslink density, and stress as a function of crosslink density at constant strain, and thus represents a vast improvement.

scholarly journals Uniaxial Extension and Compression in Stress-Strain Relations of Rubber

1978 ◽  
Vol 51 (4) ◽  
pp. 840-851 ◽  
Author(s):  
Lawrence A. Wood
Keyword(s):  
Experimental Data ◽  
Tensile Deformation ◽  
Uniaxial Extension ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Stress Strain ◽  
General Applicability ◽  
Empirical Constant ◽  
Strain Data ◽  
Theoretical Predictions

Abstract A comprehensive literature survey shows the general applicability of the generalized normalized Martin, Roth and Stiehler equation to uniaxial stress-strain data in extension and compression on rubber vulcanizates. The equation can be expressed as F/M=(L−1−L−2) expA (L−L−1) where F is the stress on the undeformed section and L the ratio of stressed to unstressed length. The equation contains two constants—M, Young's Modulus, the slope of the stress-strain curve at L=1, and A an empirical constant. The conformity of stress-strain data to the equation can readily be determined by a plot of logF/(L−1−L−2) against (L−L−1). In almost every case a straight line is obtained, from the slope and intercept of which both the constants can be determined. The range of validity of the equation usually begins near L=0.5 (in the compression region) and continuing through the region of low deformations often extends to the region of rupture in extension. If uniaxial compression data are available the modulus can thus be obtained by interpolation through the region of low deformations, where experimental data are often somewhat unreliable. The value of the modulus M varies with the nature of the rubber, the extent of vulcanization, and the time and temperature of creep or stress relaxation. The value of the constant A is near 0.4 for pure-gum vulcanizates, increasing to values near 1.0 with increasing filler content, and showing an abrupt increase when crystallization occurs. Direct experimental observations where the deformation of a single specimen is varied continuously from compressive to tensile deformation, are cited to show that M, defined as the limit of the ratio of stress to strain, is independent of the direction of approach to the limit at L=0.5. The normalized Mooney-Rivlin plots show F/[2M (L−L−2)] against L−1. These graphs have only limited regions of linearity corresponding to constant values of the coefficients C1 and C2. Since these regions do not include the undeformed state the Mooney-Rivlin equation cannot be used at low elongations or in compression. The values of C1 and C2 show very wide fluctuations for the Mooney-Rivlin plots of experimental data, which are themselves usually well represented by the Martin, Roth, and Stiehler equation with different values of the constant A. In view of all these considerations the conclusion of the present study confirms that of Treloar in his recent publications in failing to find much utility in making Mooney-Rivlin plots. The failure to represent the experimental data at low elongations and the inability to correlate the constants with theoretical predictions based on strain energy or statistical theory considerations are the most serious objections.

Global Stress-Strain Behavior of Perforated Plate

1980 ◽  
Vol 102 (2) ◽  
pp. 255-263 ◽  
Author(s):  
F. P. J. Rimrott ◽  
A. Singh
Keyword(s):  
Plastic Material ◽  
Perforated Plate ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Elastic Behavior ◽  
Theoretical Interpretation ◽  
Stress Strain ◽  
Strain Behavior ◽  
Perfectly Plastic ◽  
Lower Limits

The present paper establishes and interprets the global uniaxial stress-strain behavior of regularly perforated plate, throughout the elastic, partly plastic, and fully plastic regimes up to fracture, as function of hole size and number. The elastic part of the stress-strain curve is described by means of an effective modulus of elasticity which is obtained by using the strain energy stored in the plate. During the partly plastic range, perforated plate response has been found to be governed essentially by the remaining elastic portion and consequently appears as part of the elastic behavior. Beyond global yield point, the material is nearly perfectly plastic for a large range of strains and upper and lower limits of collapse load are calculated by using upper and lower-bound techniques for a perfectly plastic material. Experiments were conducted and serve as the basis for the theoretical interpretation.

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.

Low-Cycle Fatigue Evaluation Using the Weld Master S-N Curve

2006 ◽  
Author(s):  
P. Dong ◽  
Z. Cao ◽  
J. K. Hong
Keyword(s):  
Test Data ◽  
Low Cycle Fatigue ◽  
Strain Curve ◽  
Cyclic Stress ◽  
Structural Stress ◽  
Stress Strain ◽  
Strain Behavior ◽  
Scale Test ◽  
Stress Estimation ◽  
Fatigue Evaluation

In the context of fatigue evaluation in the low-cycle regime, the use of the master S-N curve in conjunction with elastic FE-based structural stress calculations is presented. An elastic pseudo structural stress estimation is introduced by assuming that Neuber’s rule applies in relating structural stress and strain concentration at a weld to the material’s cyclic stress-strain behavior. With the pseudo structural stress procedure, recent sources of recent full scale test data on pipe and vessel welds were analyzed as a validation of the proposed procedure. The estimated fatigue lives versus actual test lives show a reasonable agreement. Finally, the feasibility of using monotonic stress-strain curves as a first approximation is also examined for applications when cyclic stress-strain curve may not be readily found. The analysis results indicate that the life estimations using monotonic stress-strain curves are reasonable, with the recent test data falling within mean ± 2σ, where σ represents the standard deviation of the master S-N curve.

Buckling of Rectangular Cross-Ply Laminated Plates With Nonlinear Stress-Strain Behavior

1979 ◽  
Vol 46 (3) ◽  
pp. 637-643 ◽  
Author(s):  
Harold S. Morgan ◽  
Robert M. Jones
Keyword(s):  
Strain Curve ◽  
Material Model ◽  
Laminated Plates ◽  
Nonlinear Material ◽  
Stress Strain ◽  
Buckling Loads ◽  
Strain Behavior ◽  
Reinforced Composite ◽  
Nonlinear Stress ◽  
Behavior Characteristic

The Jones-Nelson-Morgan nonlinear material model is used in the derivation of a buckling criterion for laminated plates with nonlinear stress-strain behavior characteristic of many fiber-reinforced composite materials. A search procedure is developed to solve this buckling criterion which is transcendental because of interdependence of the buckling load and the coefficients relating the variations in laminate forces and moments to the variations in strains and curvatures. The effect of stress-strain curve nonlinearities on laminate buckling loads is illustrated by comparing solutions of the buckling criterion to buckling loads for laminates with linear stress-strain behavior.

scholarly journals Stress-Strain Behavior of Cementitious Materials with Different Sizes

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Jikai Zhou ◽  
Pingping Qian ◽  
Xudong Chen
Keyword(s):  
Flexural Strength ◽  
Size Effect ◽  
Cement Mortar ◽  
Strain Curve ◽  
Cementitious Materials ◽  
Test Results ◽  
Stress Strain ◽  
Strain Behavior ◽  
Modified Equation ◽  
Good Agreement

The size dependence of flexural properties of cement mortar and concrete beams is investigated. Bazant’s size effect law and modified size effect law by Kim and Eo give a very good fit to the flexural strength of both cement mortar and concrete. As observed in the test results, a strong size effect in flexural strength is found in cement mortar than in concrete. A modification has been suggested to Li’s equation for describing the stress-strain curve of cement mortar and concrete by incorporating two different correction factors, the factors contained in the modified equation being established empirically as a function of specimen size. A comparison of the predictions of this equation with test data generated in this study shows good agreement.

Predictive Stress-Strain Models for High Strength Concrete Subjected to Uniaxial Compression

2014 ◽  
Vol 567 ◽  
pp. 476-481
Author(s):  
Nasir Shafiq ◽  
Tehmina Ayub ◽  
Muhd Fadhil Nuruddin
Keyword(s):  
Predictive Models ◽  
High Strength Concrete ◽  
Cement Content ◽  
Strain Curve ◽  
High Strength ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Strength Concrete ◽  
Strain Behavior ◽  
Four Cylinders

To date, various predictive models for high strength concrete (HSC) have been proposed that are capable of generating complete stress-strain curves. These models were validated for HSC prepared with and without silica fume. In this paper, an investigation on these predictive models has been presented by applying them on two different series of HSC. The first series of HSC was prepared by utilizing 100% cement content, while second series was prepared by utilizing 90% cement and 10% Metakaolin. The compressive strength of the concrete was ranged from 71-87 MPa. For each series of HSC, total four cylinders of the size 100×200mm were cast to obtain the stress-strain curves at 28 days.It has been found that the pattern of the stress-strain curve of each cylinder among four cylinders of each series was different from other, in spite of preparing from the similar batch. When predictive models were applied to these cylinders using their test data then it was found that all models more or less deficient to accurately predict the stress-strain behavior.

Stress Strain Testing of the Strand of E-Glass Fibers

2008 ◽  
Vol 39-40 ◽  
pp. 165-168
Author(s):  
Mária Chromčíková ◽  
Marek Liška
Keyword(s):  
Experimental Data ◽  
Fiber Strength ◽  
Glass Fibers ◽  
Length Distribution ◽  
Continuous Distribution ◽  
Strain Curve ◽  
Young Modulus ◽  
Strength Distribution ◽  
Stress Strain ◽  
Strain Testing

The mathematical model of the stress-strain curve of the strand of glass fibers was proposed and applied on the experimental data obtained for E glass fibers. The model reflects the lognormal continuous distribution of the unstrained lengths of glass fibers and the Weibull distribution of the fibers strength. The regression treatment of experimental data provided the statistically robust estimates of the parameters of the lognormal length distribution, of the Young modulus, and of the parameters of the Weibull glass fibers strength distribution. It was shown that neglecting of the continuous unstrained length distribution leads to serious errors in estimates of the fiber strength distribution.

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