Ultimate Tensile Properties of Elastomers. IV. Dependence of the Failure Envelope, Maximum Extensibility, and Equilibrium Stress‐Strain Curve on Network Characteristics

1965 ◽  
Vol 36 (10) ◽  
pp. 2996-3005 ◽  
Author(s):  
Thor L. Smith ◽  
J. E. Frederick
Keyword(s):  
Tensile Properties ◽  
Strain Curve ◽  
Failure Envelope ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Equilibrium Stress ◽  
Network Characteristics ◽  
Maximum Extensibility

Ultimate Tensile Properties of Elastomers. IV. Dependence of the Failure Envelope, Maximum Extensibility, and Equilibrium Stress Strain Curve on Network Characteristics

1967 ◽  
Vol 40 (3) ◽  
pp. 694-709
Author(s):  
Thor L. Smith ◽  
J. E. Frederick
Keyword(s):  
Tensile Properties ◽  
Strain Curve ◽  
Network Models ◽  
Uniaxial Tensile ◽  
Failure Envelope ◽  
Stress Strain ◽  
Equilibrium Stress ◽  
Maximum Extension ◽  
Extension Ratio ◽  
Maximum Extensibility

Abstract Uniaxial tensile data from tests at different rates of extension over a wide temperature range are considered for butyl, silicone, Viton B, SBR, and natural rubber vulcanizates (series A) and for six Viton A-HV vulcanizates (series B) of differing crosslink densities. For series A and for A-6 in series B, equilibrium stress-strain data were obtained at large deformations by an indirect method. The ultimate tensile properties of all vulcanizates were previously characterized by a time- and temperature-independent failure envelope. The failure envelope's maximum extension ratio, (λb)max, to be equal to or less than (λ∞)max, the maximum extension ratio (hypothetical) in the absence of rupture and also the maximum extension ratio of network models. Failure and equilibrium data for series A vulcanizates are represented by a specific function of the equilibrium modulus and the maximum extensibility; except for SBR and possibly Viton B, equilibrium and failure data are sensibly identical; thus, (λb)max≅ (λ∞)max. For series B vulcanizates, qualitative considerations indicate that (λ∞)max/(λb)max is greater than unity and possibly dependent on crosslink density. Consideration of network models suggests that (λ∞)max should be directly proportional to Mc1/2 and inversely proportional to (〈r2〉0/M)1/2. For series A, no correlation between (λb)max and (〈r2〉0/M)1/2 was found. For series B, it that (λb)max ∝ Mcβ, where β is a constant in the neighborhood of 0.7. For all vulcanizates, (σb)max≅ 104 (λb)max−1, where (σb)max is the stress in psi (based on the undeformed cross section) at (λb)max.

The Effect of Nitrogen and Inoculation on the Tensile Properties and Microstructure of Cast Iron with Lamellar Graphite

2010 ◽  
Vol 457 ◽  
pp. 114-119 ◽  
Author(s):  
Fredrik Wilberfors ◽  
Ingvar L. Svensson
Keyword(s):  
Cast Iron ◽  
Plastic Strain ◽  
Tensile Properties ◽  
Cell Size ◽  
Deformation Behaviour ◽  
Strain Curve ◽  
Eutectic Cell ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Lamellar Graphite

The main purpose with this paper is to show the effect of nitrogen and inoculation on the tensile properties and microstructure of cast iron with lamellar graphite. Casting experiments were performed with the main composition: 3.4 % C, 2.0 % Si, 0.7 % Mn, 0.5 % Cu. The nitrogen content was varied between 90-180 ppm and inoculant was added as 0, 0.2 or 0.4 % by weight. The addition of inoculant changed the graphite structure from distribution D/B/A to distribution A, according to ISO 945. The eutectic cell size decreased significantly. The addition of inoculant had no influence on the hardness. The addition of nitrogen shortened the graphite flakes and increased the hardness. The influence on the eutectic cell size was low and there was no significant effect on the graphite distribution. Tensile test samples were analysed by true stress – true plastic strain in terms of the flow relationships proposed by Hollomon, , and Ludwigson, . The stress-strain curves were fitted to polynomial functions of the 6:th to 8:th order before evaluating the constants in order to eliminate noise from the measurements. This approach also enabled the slope of the stress-strain curve to be evaluated at zero stress (Young’s modulus), resulting in plastic strain from stress levels close to zero. The Hollomon flow relationship failed to describe the deformation behaviour for the whole range of the stress-strain curve. The correction terms in the Ludwigson flow relationship resulted in a better fit. The addition of inoculant mainly affected the strength coefficient, . The addition of nitrogen also affected the constant. The main reason for this was that the addition of inoculant influenced the last part of the stress-strain curve while the addition of nitrogen had an effect over the whole range of the curve. The addition of nitrogen and inoculant increased the tensile strength from 288 MPa to 393 MPa and the total elongation at fracture from 0.8 % to 1.6 %.

Experimental Study on Full Stress-Strain Curve of SFRC in Axial Tension

2012 ◽  
Vol 238 ◽  
pp. 41-45
Author(s):  
Hong Yuan Huo ◽  
Chen Jie Cao ◽  
Li Sun ◽  
Li Sha Song ◽  
Tong Xing
Keyword(s):  
Tensile Properties ◽  
Cement Paste ◽  
Steel Fiber ◽  
Strain Curve ◽  
Fiber Reinforced Concrete ◽  
Steel Fibers ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Axial Tension ◽  
Axial Tensile

The tests were carried out to study the effects of the fraction of steel fiber by volume and the thickness of cement paste wrapping steel fibers on the axial tensile properties of steel fiber reinforced concrete (SFRC). The strength grade of SFRC was CF40 with the fraction of steel fiber by volume varying from 0.5% to 2.0%, and the thickness of cement paste wrapping steel fibers varying from 0.8mm to 1.2mm. The tests were conducted by WAW-600 electric-hydraulic servo-type test machine. The results show that the axial tensile properties such as the axial tensile strength, the fullness of stress-strain curve, the tensile energy and the axial tensile toughness ratio are all improved obviously by the adding of steel fiber in concrete. The reasonable thickness of cement paste wrapping steel fibers is 1.0mm. The formulas for stress-strain relationship of SFRC in axial tension are proposed.

Deformation of Adaptive Heterophase Crystal

1994 ◽  
Vol 360 ◽  
Author(s):  
Alexander L. Roytburd ◽  
Julia Slutsker
Keyword(s):  
Strain Curve ◽  
Negative Slope ◽  
Product Phase ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Equilibrium Stress ◽  
Stress Control ◽  
Plane Parallel ◽  
Loading And Unloading ◽  
Calculated Equilibrium

AbstractA crystal which can be in two possible phase states is considered. During tensile extension the crystal is deformed elastically. After a certain amount of elastic strain a phase transformation begins. For each fixed level of strain an equilibrium mesostructure is established, which corresponds to a minimum in the free energy of the crystal. The equilibrium mesostructure consists of plane, parallel layers of a product phase separated by layers of an initial phase. The product phase itself consists of two or more different domains (twins) forming plane, parallel alternations. The volume fractions of the phases and of different twin components in the product phase are functions of strain and temperature. Above a critical temperature the product phase is a single domain (untwinned). The stress-strain curve which reflects the evolution of the equilibrium mesostructure is calculated. For deformation under a strain control the calculated equilibrium stress-strain curve has a section with negative slope that corresponds to a negative Young's modulus. If deformation proceeds under stress control, hysteretic stress-strain curves on loading and unloading will result from a section with negative slope.

Thermodynamics of Stressed Vulcanized Rubber

1930 ◽  
Vol 3 (2) ◽  
pp. 304-314 ◽  
Author(s):  
Roscoe H. Gerke
Keyword(s):  
Modulus Of Elasticity ◽  
Strain Curve ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Equilibrium Stress ◽  
Permanent Set ◽  
Vulcanized Rubber ◽  
Laws Of Thermodynamics

Abstract The first and second laws of thermodynamics are applied to the stretching of vulcanized gum rubber stocks. Equilibrium stress-strain curves without appreciable hysteresis are described. The modulus of elasticity of vulcanized rubber for higher elongations obtained from the equilibrium stress-strain curve is capable of giving agreement with predictions of the second law of thermodynamics and the Joule heat effect. The modulus of elasticity from the equilibrium stress-strain curve is practically independent of the time of cure for a range of cures for elongations less than 600 per cent. The customary stress-strain curves show the rubber to be stiffer with increased cure. These facts are additional evidence that the important effect caused by vulcanization is a greater resistance to plastic flow or permanent set.

scholarly journals Crimp in Wool: Cortical Segmentation and Tensile Properties of Well-Crimped and Abnormally Crimped Fibres of Merino Wool

1965 ◽  
Vol 18 (3) ◽  
pp. 689 ◽  
Author(s):  
RE Chapman
Keyword(s):  
Mechanical Properties ◽  
Tensile Properties ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Deficient Diet ◽  
Outer Root Sheath ◽  
Merino Wool ◽  
Root Sheath ◽  
Breaking Points

Poorly crimped (or doggy) fibres, produced by follicles with hyperplasia of the outer root sheath tissue, have greater proportions of paracortex than adjacent well-crimped fibres. Associated with this increase in paracortex is an increase in strength, as indicated by significant increases in the stresses in wet poorly crimped fibres at the turnover and breaking points on the stress-strain curve. Use of the stronger mechanical properties of doggy fibres as a means of distinguishing such fibres from the poorly crimped fibres in steely wool, produced by sheep on a copper-deficient diet, is proposed.

Softening of Rubber by Deformation

1969 ◽  
Vol 42 (1) ◽  
pp. 339-362 ◽  
Author(s):  
L. Mullins
Keyword(s):  
Steady State ◽  
Strain Curve ◽  
Hardness Test ◽  
Simple Extension ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Equilibrium Stress ◽  
Softening Behavior ◽  
Reinforcing Fillers ◽  
Conventional Test

Abstract It has been known for many years that deformation results in softening of rubber and that the initial stress-strain curve determined during the first deformation is unique and cannot be retraced. Further the effect of repeated deformation is to cause rubber asymptotically to approach a steady state with a constant or equilibrium stress-strain curve. Softening in this way occurs in vulcanizates either with or without fillers although the effect appears to be much more pronounced in vulcanizates containing high proportions of reinforcing fillers. After the hardness test the simple extension stress-strain test is the test most widely used by rubber technologists. The conventional stress-strain curve is obtained on samples which have not been previously deformed and for design purpose the unique value of stiffness given by this curve may be of little significance. Thus it appears that the values of stress—strain properties determined after “conditioning” cycles of deformation would be of more practical use than the unique value obtained in the conventional test. In recent years much interest has been shown in the factors responsible for this softening behavior particularly in regard to the implications of the loss of the stiffening action of reinforcing fillers on the mechanism of reinforcement.

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