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A Comparison of Tensile Stress-Strain Data from Dumbbell, Ring, and Oval Specimens
Abstract
This paper reports the study comparing tensile stress strain data taken on elastomeric materials using three different specimen geometries: a standard tensile bar or dumbbell, a ring, and an oval. It is shown that the tensile bar or dumbbell gives higher values for failure stress and strain than does either the ring or oval specimen. The ring, oval, and tensile bar show agreement for values of stress and strain above 100 per cent strain but below failure. For soft, low modulus stocks the ring and oval agree at low strains. For stock with tensile modulus values above 1000 psi, the beinding stress and strain, required to straighten the ring to its in-test configuration, significantly affect the data. Yielding, as defined in this paper, can be related to hysteresis effects and hence to the phenomenon known as cyclic softening. The stress as 300 per cent strain and the stress and strain at failure are not sufficient to characterize stress-strain behavior, particularly for thermoplastic elastomers.
... The tensile test of the rubber composites was carried out on a universal testing machine (UTM) and provided direct information about the mechanical properties of the samples. The tensile properties of the vulcanized samples were measured by using a Zwick tensile tester (Model Z1.0/TH1S, ZwickRoell, Kennesaw, GA, USA) according to ISO 37. The specimens were cut into a dumbbell shape [33] from approximately 2 mm thick vulcanized sheets, and the tests were carried out at a crosshead speed of 500 mm/min with a pretension of 0.1 N. An average of five dumbbells was used for the analysis, and the mechanical properties discussed are the tensile strength and elongation at break [34]. ...
... As explained earlier, the lower compatibility of BR with silica can influence the filler dispersion and, thus, also cause a slight shift of the percolation threshold F c . Also, no significant dependence of the percolation threshold on temperature is observed, as reported earlier for other rubber compounds [33]. Comparing the tiny ∆G ′ values for rubber composites with low silica contents (F << F c ), one observes near-room-temperature trends similar to those found in RPA measurements on uncured samples. ...
... As explained earlier, the lower compatibility of BR with silica influence the filler dispersion and, thus, also cause a slight shift of the percola threshold Fc. Also, no significant dependence of the percolation threshold on tempera is observed, as reported earlier for other rubber compounds [33]. Comparing the tiny values for rubber composites with low silica contents (F << Fc), one observes near-ro temperature trends similar to those found in RPA measurements on uncured sam The ′ values are highest for SSBR 3402 and lowest for the BR matrices. ...
Active fillers such as carbon black and silica are added to rubber to improve its mechanical and viscoelastic properties. These fillers cause reinforcement in rubber compounds through physical and/or chemical interactions. Consequently, the compounds’ rheological, mechanical, and viscoelastic behavior are affected. Changing the filler loading influences these properties due to the different interactions (filler-filler and filler-polymer) taking place in the compounds. In addition, rubbers with varying microstructures can interact differently with fillers, and the presence of polymer functionalization to enhance interactions with fillers can further add to the complexity of the network. In this work, the effects of different loadings (0–108 phr/0–25 vol. %) of a highly dispersible grade of silica with three types of solution styrene-butadiene rubbers (SSBR) and one butadiene rubber (BR) on their rheological, mechanical, and viscoelastic properties were investigated. It was observed that the Mooney viscosity and hardness of the compounds increased with an increasing filler loading due to the increasing stiffness of the compounds. Payne effect measurements on uncured compounds provided information about the breakdown of the filler-filler network and the extent of the percolation threshold (15–17.5 vol. %) in all the compounds. At high filler loadings, the properties for BR compounds worsened as compared to SSBR compounds due to weak polymer-filler interaction (strong filler-filler interaction and the lower compatibility of BR with silica). The quasi-static mechanical properties increased with the filler loading and then decreased, thus indicating an optimum filler loading. In strain sweeps on cured rubber compounds by dynamic shear measurements, it was observed that the type of rubber, the filler loading, and the temperature had significant influences on the number of glassy rubber bridges in the filler network and, thus, a consequential effect on the load-bearing capacity and energy dissipation of the rubber compounds.
The structural and mechanical properties of gels formed from biopolymers are discussed both in terms of the techniques used to characterise these systems, and in terms of the systems themselves. The techniques included are spectroscopic, chiroptical and scattering methods, optical and electron microscopy, thermodynamic and kinetic methods and rheological characterisation. The systems considered are presented in order of increasing complexity of secondary, tertiary and quaternary structure, starting with gels which arise from essentially ‘disordered’ biopolymers via formation of ‘quasicrystalline’ junction zones (e.g. gelatin, carrageenans, agarose, alginates etc.), and extending to networks derived from globular and rod-like species (fibrin, globular proteins, caseins, myosin) by a variety of crosslinking mechanisms. Throughout the text, efforts are made to pursue the link (both from experiment and from theory) between the structural methods and mechanical measurements. As far as we are aware this is the first major Review of this area since that of J. D. Ferry in 1948 — The interest shown by polymer physicists in more complex biochemical systems, and the multi-disciplinary approaches now being applied in this area, make the format adopted here, in our opinion, the most logical and appropriate.
The purpose of this chapter is to introduce the subject of physical testing of rubber in terms of its rationale, methods, trends, and limitations. As the name implies, physical testing
involves measurement and evaluation of
physical prop erties. This could include a wide diversity of characteristics, but, by experience, certain categories of tests have emerged as being satisfactory adjuncts to economical development, production, and acceptance of rubber products.
This paper is essentially a review of past work, including structural and rheological studies on gelatin gels and progress made in the last decade or so. Now many aspects of gelatin gelation are unchallenged. For example, it seems clear that the helical junction zones do not have a large cross-sectional radius of gyration, and both the gel modulus, and the absolute optical rotation appear to increase slowly, but without limit, even when plotted on a log time axis. The implications of such work are summarized. Other topics of current interest include the nature of gelatin gels at very long times (creep vs. dynamic measurements), large deformation measurements, mixed chemically and physically cross-linked samples, and also the future of bovine gelatin and the development of novel sources following the BSE crisis. These topics are discussed in terms of the author's view of recent progress in, and future prospects for, gelatin research.
Although rheological measurements are still not familiar to all workers on gels and networks, a recent definition of the gel state is based upon rheological criteria. Small deformation time, strain and frequency sweeps enable the investigation of gelling properties on a curing system. These experiments have been improved by recent technical advances such as ‘multi-wave’ experiments, in which the simple sine wave history is replaced by superimposed harmonics, or more complex oscillatory deformations. Large deformation rheometry involves testing a gel sample either in tension/compression or in shear, up to and sometimes past the yield or failure point. Strain, temperature and concentration effects can be investigated using Smith's failure envelope.
Ultimate tensile measurements were performed on the model system of glass filled gelatin gels. By using a range of sizes of glass ballotini, and also shape sorted fragments of fractured ballotini (denoted ‘cubes’) at varying phase volume of filler, the effect of size, shape and phase volume on the ultimate tensile properties of the filled gel samples was investigated. By constructing a force-extension failure envelope, a relationship was developed which enabled all the fracture data for the samples to be simply related, and this empirical relation was within experimental error identical to previously derived theoretical treatments of the dependence of small deformation modulus on phase volume.
Various methods of probing the tensile failure characteristics of both extensible and brittle gels using the Instron machine were evaluated. The true strain of the gels at failure determined from high speed video camera recording and the corresponding true stress were used as the reference. When the ratio of the test length to the length of the end-pieces of a dumbbell shaped specimen exceeds 10:1, the effect of the end-pieces was negligible and the measured stress and strain at failure by the Instron machine represent the true values in the test sector of the gel. Experimental data from tensile testing using the above method suggest that both extensive and brittle gels were weaker in tension than in compression.
Mechanical properties, including an extensional modulus, penetration modulus and cut force, of an aerated confectionery nougat were measured instrumentally as a function of nougat density in the range 0.66–1.12 g/mL. Despite the fact that the material was not a true cellular solid, the properties were adequately modeled by the expression C1(ρ-ρc)n with n = 3 as befits a closed-cell foam. The critical density, ρc, appeared to correspond to the density at random close packing for spherical air cells, i.e., an air cell fraction of ≈ 0.6.
For many years, scientists interested in describing the stress-strain properties of elastomers have successfully employed empirical non-linear strain functions of various types. One of these, the Seth measure of strain, has been found to fit accurately the stress-strain properties of several crosslinked elastomers up to moderate elongations. By using a memory integral formulation, the Seth strain is here applied to uncrosslinked polyethylene melts to demonstrate that the rheological effects of long chain branching can be described by a dramatic increase in the strain-hardening parameter,n, of the Seth function. The experimental result that is particularly sensitive to this parameter is elongational viscosity, but the slope of the viscosity and the first normal-stress difference functions in the power-law region and the presence of a second normal-stress difference are also determined byn.
A low density polyethylene (MI = 2) and a high density polyethylene (MI = 0.2) were selected such that their shear viscosities were identical at 150°C and 170°C respectively. Extensional viscosities over the rate range 0.001 to 1.0 s−1 and dynamic viscosities over the frequency range 0.01 to 40 rad s−1 were also measured. Fits to these data using the Seth strainfunction formulation results in the above conclusion concerning the strain-hardening nature of low density polyethylene melts.
The texture of gelatin:high-methoxyl pectin gummy gels was quantified by instrumental and sensory techniques and their microstrucuture examined by light and transmission electron microscopy. Gelatin:HM pectin confectionery gels (33.4% sucrose and 29.8% 42 DE corn syrup solids) with 3.0, 4.5, or 6.0% gelatin and 0.0, 0.5, 1.0, or 1.5% HM pectin were formed into oval-shaped samples and fractured in tension. Descriptive sensory evaluation was done on seven of these gels in duplicate by 10 experienced panelists using free choice profiling. The addition of pectin reduced the strain at fracture of gelatin gels. Stress at fracture could be described by upper and lower bound behavior. Microstructural analysis suggested that at high total polymer or pectin concentration, increased phase viscosity and rate of gelation influenced structure by preventing coalescence of the dispersed gelatin-rich phase. Micrographs suggested that gelatin in the pectin-rich phase was concentrated enough to gel and contributed to mixed gel properties. Gels were described variously as soft to firm and brittle to rubbery. Mixed gels were more fruity, sweet, and tart than pure gelatin gels. Gels with a high degree of coalescence of the dispersed phase were described as pulpy. Sensory texture first principal component values correlated with strain at fracture (r=0.90), log [stress at fracture] (r=0.87), and flavor first principal component values (r=0.83).
Biphasic, mixed gels of agarose and gelatin were prepared, and their mechanical behaviour in tensile tests was determined, up to failure, utilising four decades of (constant) strain rate. The behaviour of pure agarose and pure gelatin in such tests has been determined previously. Suitable ‘blending-laws’ relating the small deformation shear modulus of the composite to the moduli of the component phases have also been discussed elsewhere. This report extends the latter treatment to the more aggressive large deformation regime, deriving bounds for modulus and break stress which closely model observed behaviour.
The large deformation and ultimate properties of gelatin and agarose gels were investigated, in simple tension, as a necessary preliminary to an examination of mixed bipolymer gel systems. The underlying structure of these systems is sufficiently similar in certain respects to that of a ‘rubber-like’ network, to suggest that an analysis along these lines might be fruitful. It is found that under tensile test conditions, the factorization of strain and time dependence appears to be valid over all experimental conditions encountered. Modulus values from the initial slope of stress/strain curves confirm previously derived modulus/concentration relationships. Doubly logarithmic plots of stress at break against strain at break (‘failure envelopes’) provide a means of comparing ultimate properties as a function of polymer concentration. Since both break stress and break strain exhibit strong dependence on strain rate, minimum observed values of these quantities have been chosen to characterize the failure process.
Different gel structures formed by β-lactoglobulin dissolved in distilled water (12% w/w) at pH 3.0–7.5 have been investigated using tensile measurements at large deformations. Gels formed at pH 4–6 were opaque, whereas at pH values below or above this range they were transparent. The fracture properties showed large variations over the pH range studied. Gels formed at low pH were brittle with low strain and stress at fracture, as opposed to those formed at high pH, which were rubber-like with high strain and stress at fracture. Gels formed at intermediate pH (pH 4–6) had an intermediate, near-constant, strain at fracture. The fracture stress was, however, higher at pH 5.5–6.0 than at pH 4.0–5.2. The specific fracture energy resembled the stress at fracture, with a maximum of 6 J/m2 at pH 6.0. Gels formed at pH 4.5, 5.5, 6.5 and 7.5 were all notch-sensitive. The opaque gels were defined as aggregate gels and the transparent gels were defined as fine-stranded gels. The fracture properties clearly showed there are differences between the fine-stranded gels formed at high pH and those formed at low pH. The fracture stress demonstrated that there are structural differences within the pH range in which the aggregate gels are formed. The non-linearity of the stress-strain curve was the same for all fine-stranded gels, which had r-shaped stress-strain curves. The stress-strain curves of the aggregate gels were almost linear. The non-linearity did not influence the fracture properties. Young's modulus showed two peaks, at pH 3.5 and 6.0, coinciding with the range where the structure changes between aggregated and fine-stranded. The stress at fracture also has a maximum at pH 6.0. The high elasticity and fracture stress may depend on strong, elastic areas in the network structure. Apart from the two peaks, Young's modulus shows the same behaviour as the storage modulus, G′, measured at small deformations, but Young's modulus is slightly larger than 3G′.
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