Breaking stress and strain

One of the unique characteristics of AA-PEA hbers is their elastomeric mechanical behavior, similar to Spandex and natural rubber materials, enabling them to be stretched to several times their length. Figure 11.5 shows the breaking stress and strain of one type of Phe-based PEA monohl-ament hbers, which support their elastomeric behavior. The AA-PEA-based... 

The time dependence of the breaking stress and strain measured at different temperatures often follows the time-temperature superposition principle (9> 12), to give a single conrposite curve. Typically, the rupture stress superposes more smoothly than the rupture strain. When the reduction is carried out for Galcit the breaking... 

The elasticity of a fiber describes its abiUty to return to original dimensions upon release of a deforming stress, and is quantitatively described by the stress or tenacity at the yield point. The final fiber quaUty factor is its toughness, which describes its abiUty to absorb work. Toughness may be quantitatively designated by the work required to mpture the fiber, which may be evaluated from the area under the total stress-strain curve. The usual textile unit for this property is mass pet unit linear density. The toughness index, defined as one-half the product of the stress and strain at break also in units of mass pet unit linear density, is frequentiy used as an approximation of the work required to mpture a fiber. The stress-strain curves of some typical textile fibers ate shown in Figure 5. 

This linear relationship between stress and strain is a very handy one when calculating the response of a solid to stress, but it must be remembered that most solids are elastic only to very small strains up to about 0.001. Beyond that some break and some become plastic - and this we will discuss in later chapters. A few solids like rubber are elastic up to very much larger strains of order 4 or 5, but they cease to be linearly elastic (that is the stress is no longer proportional to the strain) after a strain of about 0.01. 

The mechanical properties can be studied by stretching a polymer specimen at constant rate and monitoring the stress produced. The Young (elastic) modulus is determined from the initial linear portion of the stress-strain curve, and other mechanical parameters of interest include the yield and break stresses and the corresponding strain (draw ratio) values. Some of these parameters will be reported in the following paragraphs, referred to as results on thermotropic polybibenzoates with different spacers. The stress-strain plots were obtained at various drawing temperatures and rates. 

Ultimate stress and strain, or stress and strain at break, are the values corresponding to the breaking of the samples. 

An edible film should have good water vapor barrier properties (low or no water permeation and diffusion through film), which should not increase or increase very little with increasing relative vapor pressure (Lawton, 1996). Films should withstand mechanical stress and strain to such an extent that they do not break easily under a decent mechanical force (Talja et al, 2008). Thus, composition of starch-based films is an important factor influencing its barrier and mechanical properties. Also, starch-based edible films may have an impact on the sensory and textural characteristics of the food. 

Landel and Fedors (53, 54) have recently explored the usefulness of extreme value statistics applied to the statistical distribution of rupture in various unfilled polymer specimens. Both breaking stress and breaking strain of natural rubber (47) and styrene butadiene elastomers (53, 54) may be described by the double exponential distribution... 

The uniaxial failure envelope developed by Smith (95) is one of the most useful devices for the simple failure characterization of many viscoelastic materials. This envelope normally consists of a log-log plot of temperature-reduced failure stress vs. the strain at break. Figure 22 is a schematic of the Smith failure envelope. Such curves may be generated by plotting the rupture stress and strain values from tests conducted over a range of temperatures and strain rates. The rupture locus moves counterclockwise around the envelope as the temperature is lowered or the strain rate is increased. Constant strain, constant strain rate, and constant load tests on amorphous unfilled polymers (96) have shown the general path independence of the failure envelope. Studies by Smith (97) and Fishman (29) have shown a path dependence of the rupture envelope, however, for solid propellants. 

As has been mentioned previously, rings present more of a problem because of non-uniformity of stress and strain. ISO 37 calculates strength at break from force divided by twice the cross-sectional area but this is not the true strength (see Section 5.1). The elongation at break is calculated on the increase in internal circumference on the assumption that failure starts at the internal, most highly stressed, surface. To be precise, a small correction... 

The fracture properties of thermosets are often very difficult to measure the brittleness of these materials. If a thermoset is tested in uniaxial tensile mode, the stress and strain at break, strain rate, e = df/dt, and also on the sample dimensions (length and cross section). Thus, the parameters intrinsic values of the materials because they depend on the... 

Because of its higher rigidity at warm temperatures, sand Thermopave formulations are not as flexible as asphalt concrete mixes. A typical sand Thermopave mix (6 wt % asphalt 12 wt % sulfur) exhibits a flexural strain at break of 0.004 cm/cm under the same test conditions as indicated in Table IV. Although this is below the strain values for asphalt concrete, lower flexibility in Thermopave can be tolerated as the tensile stresses and strains developed at the underside of the pavement are lower than for an asphalt pavement of equivalent thickness and subjected to the same loading. Performance of test pavements to date, some over six years old, have not indicated flexibility to be a problem as yet. 

For any given load W there will be some stress a and a corresponding tensile or compressive strain. Provided the load is not great enough to break the glass the ratio of these two values will be a constant. This connection between stress and strain is known as Hooke s law, and the constant ratio as Young s modulus ... 

Stress and Strain at Break for Hyflon lon-FM Membranes and Other... 

In practice, large deformation properties are far more useful, and determination of the full relation between stress and strain gives the best information. Materials vary widely in their linear region, i.e., the strain range over which stress and strain remain proportional. Deforming it much farther, the material may eventually break. Relevant parameters then are fracture stress or strength, fracture strain or shortness, and work of fracture or toughness. The correlation between fracture parameters and the modulus is often poor. Since many soft solids exhibit viscoelastic behavior, the values of these parameters can depend, often markedly, on the strain rate. 

Placentas. The placentas of mares grazing E+ tall fescue are thickened, reddish colored, and heavier, with an increased rate of retention than for E— mares (Monroe et al., 1988). Using an Ingstrom meter to measure stress and strain, these E+ placentas appeared to be more resistant to force that would tear them, which partially explains why some foals are unable to break through the thickened placentas (Monroe et al., 1988). Frequently, the foal is presented normally but encased in a tough, thickened chorioallantois membrane, which it cannot break through, and it therefore suffocates unless an attendant is present to cut the chorioallantois immediately. 

Tensile Tests. Tensile tests were done on an Instron tensile tester un er ambient coi dition at strain rates, , ranging from 1.0 X 10 to 5.5 x 10 sec. Experiments were done in triplicate at each strain rate. Stress, a, and strain, , at yield (not shown) were determined using tSe 0.2% offset method (5). Stress,, and strain, , at break and the work to break, W, (the area under the stress-strain curve) were also calculated. The latter was evaluated via a computer program using a Simpson s Rule method. 

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