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.

Further Investigation of the Hydrostatic Bulge Test in a Plasticity Laboratory

2009 ◽  
Vol 37 (2) ◽  
pp. 159-174
Author(s):  
O. Ifedi ◽  
Q. M. Li ◽  
Y. B. Lu
Keyword(s):  
Tensile Test ◽  
Effective Stress ◽  
Strain Curve ◽  
Plasticity Theory ◽  
Loading Path ◽  
Uniaxial Tensile ◽  
Bulge Test ◽  
Uniaxial Tensile Test ◽  
Stress Strain Curve ◽  
Stress Strain

In plasticity theory, the effective stress–strain curve of a metal is independent of the loading path. The simplest loading path to obtain the effective stress–strain curve is a uniaxial tensile test. In order to demonstrate in a plasticity laboratory that the stress–strain curve is independent of the loading path, the hydrostatic bulge test has been used to provide a balanced biaxial tensile stress state. In our plasticity laboratory we compared several different theories for the hydrostatic bulge test for the determination of the effective stress–strain curve for two representative metals, brass and aluminium alloy. Finite element analysis (FEA) was performed based on the uniaxial tension test data. It was shown that the effective stress–strain curve obtained from the biaxial tensile test (hydrostatic bulge test) had a good correlation with that obtained in the uniaxial tensile test and agreed well with the analytical and FEA results. This paper may be used to support an experimental and numerical laboratory in teaching the concepts of effective stress and strain in plasticity theory.

Hardening of the Porcine Thoracic Aorta Subjected to Freezing and Thawing: Experimental Evaluation and Mathematical Modeling

2008 ◽  
Author(s):  
Hiroshi Yamada ◽  
Kousuke Yasuno ◽  
Kensuke Fujisaki ◽  
Hiroshi Ishiguro
Keyword(s):  
Cooling Rate ◽  
Physiological Stress ◽  
Strain Curve ◽  
Fluid Phase ◽  
Collagen Fibers ◽  
Uniaxial Tensile ◽  
Freezing And Thawing ◽  
Loading Test ◽  
Stress Strain ◽  
Collagen Molecules

Identifying changes in the mechanical behavior of blood vessels subjected to freezing and thawing, such as occur with cryopreservation, are of key importance. Excising pairs of fresh ring specimens from identical porcine thoracic aortas (n = 8 for each cooling rate), we carried out uniaxial tensile loading and unloading tests over the physiological stress range (first and second tests) and performed a loading test until the breaking point within the range of a load cell (third test). After the first test, one specimen of the pair was frozen at −80°C at a cooling rate of −1°C or −50°C/min and thawed, while the other was held at 5°C as a control. At both cooling rates, for the specimens subjected to freezing, the ratios of the tangential modulus in the stress-strain curve (between 130 and 150 kPa) in the second test to that in the first test differed significantly (p < 0.01) from the respective ratios of the control specimens. We formulated a mathematical model of the stress–strain relationship considering elastic and collagen fibers and an incompressible fluid phase. We evaluated the working hypothesis that collagen fibers reduce their extensibility either by hardening as a mechanical change or by shortening as a geometric change. We attributed this response to the formation of dehydration-induced cross-linking in collagen molecules at the microscopic level.

Effect of Finite Extensibility on the Viscoelastic Properties of a Styrene-Butadiene Rubber Vulcanizate in Simple Tensile Deformations up to Rupture

1970 ◽  
Vol 43 (4) ◽  
pp. 714-734
Author(s):  
T. L. Smith ◽  
R. A. Dickie
Keyword(s):  
Strain Rate ◽  
Constant Strain Rate ◽  
Shift Factor ◽  
Styrene Butadiene Rubber ◽  
Butadiene Rubber ◽  
Stress Strain ◽  
Temperature Function ◽  
Extension Ratio ◽  
Styrene Butadiene ◽  
Maximum Extensibility

Abstract Stress-strain and rupture data were determined on an unfilled styrene-butadiene vulcanizate at temperatures from −45 to 35° C and at extension rates from 0.0096 to 9.6 min−1. The data were represented by four functions: (1) the well-known temperature function (shift factor) aT; (2) the constant-strain-rate modulus, F (t, T) reduced to temperature T0 and time t/aT, i.e., T0F (t/aT)/T (3) the time-dependent maximum extensibility λm (t/aT); and (4) a function Ω(χ) where χ=(λ−1)λm0/λm, in which λ is the extension ratio and λm0 is the maximum extensibility under equilibrium conditions. The constant-strain-rate modulus characterizes the stress-time response to a constant extension rate at small strains, within the range of linear response; λm is a material parameter needed to represent the response at large λ; and Ω(χ) represents the stress-strain curve of the material in a reference state of unit modulus and λm=λm0. The shift factor aT was found to be sensibly independent of extension. At all values of t/aT for which the maximum extensibility is time-independent, the relaxation rate was also found to be independent of λ. These observations indicate that the monomeric friction coefficient is strain-independent over the ranges of T and λ covered in the present study. It was found that λm0=8.6 and that the largest extension ratio at break (λb)max is 7.3. Thus, rupture always occurs before the network is fully extended.

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 %.

Elastic-Plastic Stress Distribution in a Compressed Ring

1968 ◽  
Vol 90 (4) ◽  
pp. 435-440
Author(s):  
K. T. Chang ◽  
P. M. Leopold
Keyword(s):  
Stress Distribution ◽  
Strain Curve ◽  
Experimental Results ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Strain Gages ◽  
Stress Strain ◽  
Theoretical Predictions ◽  
Strain Relationship ◽  
Plastic Stress

This investigation was conducted to define the plastic stress distribution at a section 90 degrees from the point of load application on a ring. The elastic and plastic stress distribution was determined experimentally by using postyield strain gages and the stress-strain relationship obtained from a uniaxial tensile test. The experimental results in the elastic range were found to agree with presently available theoretical predictions. A theoretical plasticity analysis of the ring was made by assuming that it deforms to the shape of an ellipse and that plane sections remain plane. The strains determined in this manner were used to calculate stresses off the tensile stress-strain curve. The experimental results indicated that this initial analysis gave a good approximation of the stress distribution for large deflections of the ring.

Effect of Temperatures on Tensile of Aluminium Thin Films

2012 ◽  
Vol 528 ◽  
pp. 135-139 ◽  
Author(s):  
Qiao Neng Guo ◽  
Shi E Yang ◽  
Qiang Sun ◽  
Yu Jia ◽  
Yu Ping Huo
Keyword(s):  
Thin Films ◽  
Molecular Dynamics ◽  
Maximum Stress ◽  
Tensile Deformation ◽  
Uniaxial Extension ◽  
Strain Curve ◽  
Local Maximum ◽  
Temperature Curve ◽  
Uniaxial Tensile ◽  
Stress Strain

The mechanical process of single-crystal aluminium thin films under uniaxial tensile strain was simulated with molecular dynamics method at different temperature. The stress–strain curve and potential energy–strain curve of thin aluminium film under uniaxial tensile deformation were obtained by molecular dynamics simulations. With the changes of sample temperatures in uniaxial extension, the variation characteristics of stress–strain curves are alike at the elastic stage and different at the plastic one below and above 370 K, respectively. From the stress–strain curves, we gained the first local maximum stress-temperature curve and the strain at the first local maximum stress-temperature curve, and found that the strange temperature dependence of first local maximum stress: when the temperature is above 370 K, the stress goes down quickly with temperature, and when below 370 K, it descends slowly. With increasing temperature, the difference between two strain values corresponding to two maximal potential energies changes slowly below and above 370K but it goes up quickly about 370K. By these dependences, we have identified the critical temperature （370K） for the transition of plastic flow mechanism.

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.

scholarly journals Mechanical Properties of Compact Bone Defined by the Stress-Strain Curve Measured Using Uniaxial Tensile Test: A Concise Review and Practical Guide

Materials ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4224
Author(s):  
Che-Yu Lin ◽  
Jiunn-Horng Kang
Keyword(s):  
Mechanical Properties ◽  
Tissue Engineering ◽  
Tensile Test ◽  
Bone Tissue Engineering ◽  
Strain Curve ◽  
Compact Bone ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Stress Strain Curve ◽  
Stress Strain

Mechanical properties are crucial parameters for scaffold design for bone tissue engineering; therefore, it is important to understand the definitions of the mechanical properties of bones and relevant analysis methods, such that tissue engineers can use this information to properly design the mechanical properties of scaffolds for bone tissue engineering. The main purpose of this article is to provide a review and practical guide to understand and analyze the mechanical properties of compact bone that can be defined and extracted from the stress–strain curve measured using uniaxial tensile test until failure. The typical stress–strain curve of compact bone measured using uniaxial tensile test until failure is a bilinear, monotonically increasing curve. The associated mechanical properties can be obtained by analyzing this bilinear stress–strain curve. In this article, a computer programming code for analyzing the bilinear stress–strain curve of compact bone for quantifying the associated mechanical properties is provided, such that the readers can use this computer code to perform the analysis directly. In addition to being applied to compact bone, the information provided by this article can also be applied to quantify the mechanical properties of any material having a bilinear stress–strain curve, such as a whole bone, some metals and biomaterials. The information provided by this article can be applied by tissue engineers, such that they can have a reference to properly design the mechanical properties of scaffolds for bone tissue engineering. The information can also be applied by researchers in biomechanics and orthopedics to compare the mechanical properties of bones in different physiological or pathological conditions.

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