Rheology of Unmasticated and Masticated Smoked Sheet

1954 ◽  
Vol 27 (1) ◽  
pp. 20-35 ◽  
Author(s):  
R. W. Whorlow
Keyword(s):  
Strain Rate ◽  
Elevated Temperatures ◽  
Test Methods ◽  
High Rate ◽  
Rate Curve ◽  
Stress Axis ◽  
Plastic Behavior ◽  
Stress Strain ◽  
High Shear Rates ◽  
Internal Mixer

Abstract Extensive tests on unmasticated and masticated smoked sheet samples in the shearing-cone and Williams plastometers are reported. These constitute a preliminary survey of the behavior of these materials during shearing at various rates and for various periods at elevated temperatures. Masticated rubber shows a temporary stiffening when kept at normal or elevated temperature; to eliminate this, and so obtain reproducible plasticity measurements, the rubber must be sheared at a high rate. Since normal Mooney and Williams tests do not involve high shear rates, the influence of this stiffening as a possible source of error needs examining. In tests at 100° C, the logarithmic stress/strain-rate curve is convex to the log stress axis. The most important difference observed between samples prepared by masticating one batch of smoked sheet in various ways was in the slope of the curve (log stress plotted horizontally), the curves for cold-milled samples being steeper than for samples prepared by hot milling or by mastication in an internal mixer. Curves for samples plasticized in the same way for different periods do not cross. There is evidence that the results of other types of plasticity test can be predicted from the stress/strain-rate curve for the sample. These last two observations, if confirmed by more extensive tests, indicate that for control of normal mastication processes a compression test such as the Williams can be satisfactory, provided the mastication method remains basically the same, that is, using the same type of machine (mill or internal mixer) and similar temperature conditions. The method of mastication appears to be more important than the properties of the raw rubber used as starting material in determining the properties of masticated rubber. Tests on unmasticated smoked sheet showed that many samples stiffen during shearing or during very light mastication; this effect persists longer, under continued shearing, when stiffness is measured at a high strain rate than when measured at a low rate; in other words, the stress/strain-rate curve becomes much less steep and crosses the curve for very lightly sheared rubber. This latter behavior, apparently not previously observed, is shown to be consistent with certain other observations that have been reported. The complex changes produced by short milling treatments, and which vary from one rubber to another, may be the cause of inconsistencies in Mooney tests on unmasticated rubbers, which are usually prepared for testing by a few passages through a mill. The fact that such treatments may alter the stiffness in different directions according as this is measured at high or low strain rate is doubtless one reason why Mooney and Williams tests on unmasticated rubbers do not correlate closely. In contrast to this complex and variable behavior, rubbers that have been subjected to a normal mastication treatment give stress/strain-rate curves that do not cross, so tests at one strain rate give a valid indication of their relative behavior at other strain rates. This observation supports the view already held in some quarters that in classifying natural rubbers by a plasticity test they should first be given a standard mastication or shearing treatment. Many of these conclusions must be regarded as tentative until confirmed on a larger number of rubber samples; with this reservation they form a more complete picture than has hitherto been available of the plastic behavior of unvulcanized raw rubber, which must form the basis for improving control test methods.

Stress-Strain Equations for Some Near-Eutectic Tin-Lead Solders

1991 ◽  
Vol 113 (4) ◽  
pp. 475-484 ◽  
Author(s):  
K. P. Jen ◽  
J. N. Majerus
Keyword(s):  
Strain Rate ◽  
Printed Circuit Boards ◽  
Volume Fraction ◽  
Total Error ◽  
Tensile Tests ◽  
Elastic Behavior ◽  
Plastic Behavior ◽  
Strain Rates ◽  
Stress Strain ◽  
Engineering Strain

This paper presents the evaluation of the stress-strain behavior, as a function of strain-rate, for three tin-lead solders at room temperature. This behavior is critically needed for reliability analysis of printed circuit boards (PCB) since handbooks list minimal mechanical properties for the eutectic solder used in PCBs. Furthermore, most handbook data are for stable eutectic microstructure whereas PCB solder has a metastable microstructure. All three materials were purchased as “eutectics.” However, chemical analysis, volume fraction determination, and microhardness tests show some major variations between the three materials. Two of the materials have a eutectic composition, and one does not. The true stress-strain equations of one eutectic and the one noneutectic material are determined from compressive tests at engineering strain-rates between 0.0002/s and 0.2/s. The second eutectic material is evaluated using tensile tests with strain-rates between 0.00017/s and 0.042/s. The materials appear to exhibit linear elastic behavior only at extremely small strains, i.e., less than 0.0005. However, this “elastic” behavior showed considerable variation, and depended upon the strain rate. In both tension and compression the eutectic alloy exhibits nonlinear plastic behavior, i.e., strain-softening followed by strain-hardening, which depends upon the strain rate. A quadratic equation σy = σy(ε˚/ε˚0) + A(ε˚/ε˚0)ε + B(ε˚/ε˚0)ε2 fit to the data gives correlation coefficients R2 > 0.91. The coefficients σy(ε˚/ε˚0), A(ε˚/ε˚0), B(ε˚/ε˚0) are fitted functions of the normalized engineering strain rate ε˚/ε˚0. Replicated experiments are used at each strain-rate so that a measure of the statistical variation could be estimated. Measures of error associated with the regression analysis are also obtained so that an estimate of the total error in the stress-strain relations can be made.

Dynamic behavior and constitutive modeling of magnesium alloys AZ91D and AZ31B under high strain rate compressive loading

2014 ◽  
Vol 28 (08) ◽  
pp. 1450063 ◽  
Author(s):  
Jing Xiao ◽  
Iram Raza Ahmad ◽  
D. W. Shu
Keyword(s):  
Strain Rate ◽  
Magnesium Alloys ◽  
Dynamic Stress ◽  
Elevated Temperatures ◽  
High Strain ◽  
Compressive Loading ◽  
Strain Rates ◽  
High Strain Rates ◽  
Stress Strain ◽  
Cook Model

The dynamic stress–strain characteristics of magnesium alloys have not been sufficiently studied experimentally. Thus, the present work investigated compressive dynamic stress–strain characteristics of two representative magnesium alloys: AZ91D and AZ31B at high strain rates and elevated temperatures. In order to use the stress–strain characteristics in numerical simulations to predict the impact response of components, the stress–strain characteristics must be modeled. The most common approach is to use accepted constitutive laws. The results from the experimental study of the response of magnesium alloys AZ91D and AZ31B under dynamic compressive loading, at different strain rates and elevated temperatures are presented here. Johnson–Cook model was used to best fit the experimental data. The material parameters required by the model were obtained and the resultant stress–strain curves of the two alloys for each testing condition were plotted. It is found that the dynamic stress–strain relationship of both magnesium alloys are strain rate and temperature dependent and can be described reasonably well at high strain rates and room temperature by Johnson–Cook model except at very low strains. This might be due to the fact that the strain rate is not strictly constant in the early stage of deformation.

DYNAMIC TENSILE AND COMPRESSIVE STRESS-STRAIN CHARACTERISTICS OF MAGNESIUM ALLOYS AT ELEVATED TEMPERATURES

2008 ◽  
Vol 22 (09n11) ◽  
pp. 1135-1140 ◽  
Author(s):  
TEPPEI ARAMOTO ◽  
HIROSHI TACHIYA ◽  
AKIYOSHI HORI ◽  
AKIHIRO HOJO ◽  
YUSUKE MIYAZAKI
Keyword(s):  
Strain Rate ◽  
Magnesium Alloys ◽  
Dynamic Stress ◽  
Elevated Temperatures ◽  
Compressive Load ◽  
Tensile Load ◽  
Strain Rate Range ◽  
Stress Strain ◽  
Rate Range ◽  
Temperature Ranges

The dynamic stress-strain characteristics of magnesium alloys have not been clarified sufficiently. Thus, the study investigated both the compressive and tensile dynamic stress-strain characteristics of representative magnesium alloys: AZ61A-F, ZK60A-T5 and AZ31B-F at wide strain rate and temperature ranges. About the strain rate dependency, the dynamic stresses are higher than the static ones under both compressive and tensile loads at elevated temperatures; however the dynamic stress-strain relations change slightly in the dynamic strain rate range. Thus, the magnesium alloys has little strain rate dependence. However, the elongation of the dynamic stress-strain relations under tensile load tends to be larger than that of static one. About the temperature dependency, the yield and flow stresses of the investigated magnesium alloys under compressive load decrease abruptly at temperatures higher than about 600 K in the wide strain rate range. Meanwhile, the ones under tensile load decrease with the temperature more gently. Totally, the magnesium alloys exhibit low temperature dependence. Furthermore, as well known, the yield stresses caused under the tensile load exhibit about twice as high as those under compressive load. This study verified that such a characteristic can be observed over a wide strain rate and temperature ranges.

The Dynamic Stress-Strain Behavior in Torsion of 1100-0 Aluminum Subjected to a Sharp Increase in Strain Rate

1972 ◽  
Vol 39 (4) ◽  
pp. 939-945 ◽  
Author(s):  
R. A. Frantz ◽  
J. Duffy
Keyword(s):  
Strain Rate ◽  
Strain Curve ◽  
Initial Response ◽  
Material Behavior ◽  
High Rate ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Strain Behavior ◽  
Split Hopkinson ◽  
Explosive Charges

A modification of the torsional split Hopkinson bar is described which superimposes a high rate of shear strain on a slower “static” rate. The static rate of 5 × 10−5 sec−1 is increased to 850 sec−1 at a predetermined value of plastic strain by the detonation of small explosive charges; the rise time of the strain-rate increment is about 10 microsec. During deformation at the dynamic rate, direct measurement is made of the excess stress above the maximum static stress attained. Results for 1100-O aluminum show that the initial response to the strain rate increment is elastic, followed by yielding behavior reminiscent in appearance to an upper yield point. The incremental stress-strain curve always lies beneath the stress-strain curve obtained entirely at the higher strain rate but approaches it asymptotically with increasing strain. It is concluded that the material behavior is a function of strain, strain rate, and strain rate history.

Ultimate Tensile Properties of Elastomers. I. Characterization by a Time and Temperature Independent Failure Envelope

1964 ◽  
Vol 37 (4) ◽  
pp. 777-791 ◽  
Author(s):  
Thor L. Smith
Keyword(s):  
Strain Rate ◽  
Tensile Properties ◽  
Elevated Temperatures ◽  
Constant Strain Rate ◽  
Test Methods ◽  
Constant Stress ◽  
Test Method ◽  
Failure Envelope ◽  
Polymeric Network ◽  
Time To Rupture

Abstract The tensile stress at break (σb) and the associated ultimate strain (εb) of an elastomer depend on (1) the chemical and topological characteristics of the polymeric network, and (2) the test conditions under which rupture is observed. To separate these effects, the ultimate tensile properties can often be characterized by a “failure envelope” defined by values of σb and εb determined at various strain rates over a wide temperature range. Provided time—temperature superposition is applicable, such data superpose on a plot of log σbT0/T versus log εb, where T is the test temperature (absolute) and T0 is an arbitrarily selected reference temperature. The resulting failure envelope is independent of time (strain rate) and temperature and thus it depends only on basic characteristics of the polymeric network. To illustrate the characterization method, data on two styrene-butadiene gum vulcanizates, SBR-I and SBR-II, were analyzed. For SBR-I, values of σb and εb obtained over extensive ranges of strain rate and temperature superposed to give a failure envelope. Data at elevated temperatures also gave a reliable value for the equilibrium modulus. For SBR-II, data obtained at various temperatures under conditions of constant strain and constant strain rate yielded identical failure envelopes; this strongly suggests that the failure envelope is independent of the test method. A theoretical consideration of the time-to-rupture associated with different test methods showed that for given values of σb and εb the time-to-rupture from the following types of tests should increase in the order: constant strain < constant stress < constant strain rate < constant stress rate.

Research on Flow Behavior of Advanced High Strength Steel at Elevated Temperature

2013 ◽  
Vol 749 ◽  
pp. 498-503
Author(s):  
Cheng Xi Lei ◽  
Jun Jia Cui ◽  
Zhong Wen Xing ◽  
Hao Zhao
Keyword(s):  
Strain Rate ◽  
Linear Equation ◽  
High Strength Steel ◽  
Elevated Temperatures ◽  
Flow Behavior ◽  
Peak Stress ◽  
High Strength ◽  
Test Machine ◽  
Advanced High Strength Steel ◽  
Stress Strain

Tensile experiments were carried out on advanced high strength steel (AHSS) by the test machine Gleeble3500, under the temperature ranging from 650 to 850 and the strain rate of 0.1/s~5/s, and the corresponding stress-strain curves were obtained. The peak stress level decreases with the increasing of deformation temperature or the decreasing of strain rate, which can be represented by a ZenerHollomon parameter in a linear equation. A revised model describing the relationships between the peak stress, strain rate and temperature of advanced high strength steel at elevated temperatures was proposed by compensation of strain and strain rate. The comparison of the predicted and experimental results of stressstrain curve can prove the good predictive power of the model, the Adj. R-Square between the peak stress and the linear equation was reached to 0.97.

Constitutive Modeling of Flow Behaviour of AISI 4340 Steel under Hot Working Conditions

2012 ◽  
Vol 249-250 ◽  
pp. 863-869
Author(s):  
Apichat Sanrutsadakorn ◽  
Vitoon Uthaisangsuk ◽  
Surasak Suranuntchai ◽  
Borpit Thossatheppitak
Keyword(s):  
Strain Rate ◽  
Working Conditions ◽  
Elevated Temperatures ◽  
Flow Behavior ◽  
Type Equation ◽  
Hot Working ◽  
Stress Strain ◽  
Hollomon Parameter ◽  
Steel Aisi ◽  
Aisi 4340

Using compression test on a thermo-mechanical simulator/dilatometer, hot deformation behavior of steel AISI 4340 was studied in the temperature range of 850-1150°C and strain rate range of 0.01-10 s-1. The resulted true stress-strain curves exhibited a peak stress at low strain values, after which the flow stresses decreased monotonically until higher strains, representing the dynamic flow softening. The stress level decreased with increasing deformation temperature and decreasing strain rate. The material flow behavior at elevated temperatures was described using a Zener-Hollomon parameter with an exponent-type equation. Additionally, the model was modified by compensating strain rate parameter. The stress-strain responses for the investigated steel predicted by the proposed model agreed well with the experimental results. It was confirmed that the modified constitutive equations provided a more accurate prediction of the flow stress under hot working conditions for steel AISI 4340.

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