Break strain

A common feature of the three PTEB samples is that the yield stress decreases as the drawing temperature increases (Table 2), whereas it does not change significantly with the strain rate. The Young modulus does not change with the strain rate but it decreases and the break strain increases as the drawing temperature increases. The main conclusion is that the behavior of PTEB-RT is intermediate between the other two samples, with the advantage of a considerable increase in the modulus in relation to sample PTEB-Q and without much decrease in the break strain (Table 2). 

Resin Modulus (Mpa) Strength (Mpa) Break strain (%) Permanent set (%) (°C)... 

Although the uniaxial test has traditionally received the most attention, such tests alone may be insufficient to characterize adequately the mechanical capability of solid propellants. This is especially true for ultimate property determinations where a change in load application from one axis to several at once may strongly affect the relative ranking of propellants according to their breaking strains. Since the conditions usually encountered in solid rocket motors lead to the development of multiaxial stress fields, tests which attempt to simulate these stress fields may be expected to represent more closely the true capability of the material. 

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... 

Sources of strength loss in such fibers are mainly surface damage due to contamination and, possibly, the presence of microcracks (e.g. bubbles, etc.). Polymer surface coalings are used to minimize the damage. Fibers are also proof tested to breaking strains in the range of 0.5-1%. 

Wall thickness uniformity is often compromised when fabricating near the material break point. Thinner walls are expected in the most stretched regions, but only if the melt is not allowed to recoil after cessation of flow. Often fabrication conditions are selected to be well away from the break point to minimize these issues. Key break point metrics for the startup of data illustra-trated in Figure 13.5 are the time /b and tensile stress coefficient rj (e,ti,) at break. Both quantities may be multiplied by the strain rate e to estimate the Hencky break strain (sb = tb s) and the break stress (tTb = kr (s, t)). Similar metrics can be defined for other startup extensional flows. 

Fibers have high initial moduli which are usually in the range 0.5 x 10 to 2 X 10 psi (3 X 10 to 14 X 10 MN/m ). Their extensibilities at break are often lower than 20%. If a fiber is stretched below its breaking strain and then allowed to relax, part of the deformation will be recovered immediately and some, but not all, of the remainder will be permanent (Fig. l-3b). Mechanical properties of commercial synthetic fibers do not change much in the temperature range between —50 and about I50°C (otherwise they would not be used as fibers). 

Plastics generally have intermediate tensile moduli, usually 0.5 x 1O to 4 x 1O psi (3.5 X 10 to 3 X 10 MN/m ), and Iheir breaking strain varies from a few percent for brittle materials like polystyrene to about 400% for tough, semicrystalline polyethylene. Their strain recovery behavior is variable, but the elastic component is generally much less significant than in the case of fibers (Fig. I-3c). Increased temperatures result in lower stiffness and greater elongation at break. 

Fig. 3.14. Computer simulation data for stress (a) - strain (e) in fractured triangular network with bond-bending forces (with / = 0.1) for two different linear sizes L of the sample. The bond breaking strain distribution is assumed to be uniform (a = 0) (Sahimi and Arbabi 1993).

Initial) Extension Break Strain at Peak at Peak Peak Mass xy Dimensional... 

Highly drawn crystalline fibres produce abundant radicals at strains exceeding about 8% and rising to the breaking strain of, say, 15 to 20%. Such fibres of course have already undergone draw ratios of 500% or more from the isotropic condition. 

Figure 3. Spontaneous strains and elastic properties at the 422 < i> 222 transition in Te02. (a) Spontaneous strain data extracted from the lattice-parameter data of Worlton and Beyerlein (1975). The linear pressure dependence of (e - (filled circles) is consistent with second-order character for the transition. Other data are for non-symmetiy-breaking strains (e + 62) (open circles), 63 (crosses), (b) Variation of the symmetry-adapted elastic constant (Cn - Cu) at room temperature (after Peercy et al. 1975). The ratio of slopes above and below Po is 3 1 and deviates from 2 1 due to the contribution of the non-symmetry-breaking strains. (After Carpenter and Salje 1998).

SYMMETRY-ADAPTED STRAIN, SYMMETRY-BREAKING STRAIN, NON-SYMMETRY-BREAKING STRAIN AND SOME TENSOR FORMALITIES... 

Both the order parameter and the spontaneous strain for a phase transition have symmetry properties. The relationship between them is therefore also constrained by symmetry. Only in the case of proper ferroelastic transitions is the symmetry-breaking strain itself the order parameter. For most transitions, the order parameter relates to some... 

Thus, typically, Ssb Q applies when the symmetry-breaking strain has the same symmetry as the order parameter and e applies in all other cases. The volume strain should also scale as qc Q, therefore. Experimental data for the lattice parameters of stishovite as a function of pressure are shown in Figure 6. The symmetry-breaking strain... 

Figure 7. A linear variation of the sqnare of the symmetry breaking strain with pressnre implies second order character for the tetragonal orthorhombic transition in stishovite. Circles represent strains calcnlated nsing flo = (abf and the data of Andranlt et al. (1998) crosses represent strains calcnlated nsing the alternative variation of Oq shown by crosses in Fignre 6. Open sqnares are from single crystal X-ray diffraction data of Mao et al. (1994) D designates measnrements of the orthorhombic phase made dnring decompression.

The next step is to define the relationship between the unit-cells of the trigonal and monoclinic phases. By inspection of Figure A2 it can be seen that for lead phosphate, in the absence of symmetry-breaking strains, the unit-cell parameters of the monoclinic phase are ... 

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