STRAIN AT BREAK

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. 

Table 2 Average Values of the Modulus, Yield Stress, Yield Strain, and Strain at Break for Three Samples of PTEB Stretched at Different Temperatures and Deformation Rates...

As shown in Figure 18.1, in the stress-strain curve of the real unfilled SBR vulcanizate, the stress upturn does not appear and as a result, tensile strength and strain at break are only about 2 MPa and 400%-500%, respectively. Nevertheless, the stress-strain curve of the SBR vulcanizate filled with carbon black shows the clear stress upturn and its tensile stress becomes 30 MPa. This discrepancy between both vulcanizates is actually the essential point to understand the mechanism and mechanics of the carbon black reinforcement of mbber. 

Figure 18.17 shows that the characteristics of the stress-strain curve depend mainly on the value of n the smaller the n value, the more rapid the upturn. Anyway, this non-Gaussian treatment indicates that if the rubber has the idealized molecular network strucmre in the system, the stress-strain relation will show the inverse S shape. However, the real mbber vulcanizate (SBR) that does not crystallize under extension at room temperature and other mbbers (NR, IR, and BR at high temperature) do not show the stress upturn at all, and as a result, their tensile strength and strain at break are all 2-3 MPa and 400%-500%. It means that the stress-strain relation of the real (noncrystallizing) rubber vulcanizate obeys the Gaussian rather than the non-Gaussian theory. 

Figure 5. True stress-at-break plotted on doubly logarithmic coordinates against the strain-at-break. Conditions 30°C extension rates from 9.4 X 103 to 9.4 min 1. Quantity A introduced for clarity.

Composition Tensile Strength (MPa) % Strain At Break Elastic Modulus (MPa) Fracture p Energy (J/m3)... 

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

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. 

Tour et al. (2) prepared polystyrene having an Mn of 60,000 Da reinforced with nanotubes and observed that composites displayed an enhancement in their tensile modulus without a large reduction in their strain-at-break properties. 

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... 

Many responses have such one-sided limitations tensile strength, strain at break, shock toughness, etc. One can see this in Example 2.2 where for all given responses the limitation yu>ymin is valid. The other form of limitations yuspecific weight, content of valuable ingredients, etc. Double-sided desirability limitation is shown in Fig. 2.7. 

A convenient wav of measuring Tgn is to determine the ultimate strain(at break and the yield ot a specimen as a function of temperature. The intersection of the two curves defines TBq. 

An important mechanical property is the strength, which is the stress at which the material breaks. Besides, the strain at break is of relevance, since this indicates whether the material is brittle or tough. Figure 7.16 gives a survey of both properties for a number of polymeric materials in comparison with other ones. 

Figure 7.16. Tensile strength and strain at break of various materials.

Contrary to particulate-filled composites, fibres induce an increase in strength. Again on the basis of data from technical brochures, it can be concluded that the tensile strength is raised by a factor between 1.5 and 3.5 at 20 vol % glass fibres. Apparently the fibres play such an important load-carrying role, that the polymer itself is considerably less stressed. The strain at break, however, strongly decreases. 

A very important diagram for fibres and yams is the stress—strain diagram, where the specific stress is plotted as a function of the elongation (extensional strain) in %. The curve starts at an elongation of zero and ends in the breaking point at the ultimate specific stress (=tensile strength or tenacity) and the ultimate elongation (=strain at break). 

Material Yield stress (MPa) Tensile strength (MPa) Strain at break (%) Young s modulus (MPa) Specific wear rate lO"8 (mm3/Nm)... 

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