Tensile strain, practical

Division of the total tensile strain under conditions of F = const into several components 25,6R,69) produced interesting results (see Fig. 8). It has been found that the behavior of molten low-density polyethylene (Fig. 8a) is qualitatively different from polyisobutylene (Fig. 8 b) the extension of which was performed under temperature conditions where the high-elasticity modulus, relaxation time, and initial Newtonian viscosity practically coincided (in the linear range) in the compared polymers. Flow curves in the investigated range of strain velocities were also very close to one another (Fig. 21). It can be seen from the comparison of dependencies given in Fig. 8a,... 

In practice, up to 90% of polyurethanes are used in compression, a few percent in torsion, and very little in tension. There is considerable data on the tensile stress against tensile strain (elongation) for polyurethanes. Most polyurethane specification sheets provide this data. Figure 7.3 and Figure 7.4 show typical stress-strain curves for both polyester and polyether polyurethanes. 

A few rheometers are available for measurement of equi-biaxial and planar extensional properties polymer melts [62,65,66]. The additional experimental challenges associated with these more complicated flows often preclude their use. In practice, these melt rheological properties are often first estimated from decomposing a shear flow curve into a relaxation spectrum and predicting the properties with a constitutive model appropriate for the extensional flow [54-57]. Predictions may be improved at higher strains with damping factors estimated from either a simple shear or uniaxial extensional flow. The limiting tensile strain or stress at the melt break point are not well predicted by this simple approach. 

In practice growth stresses are not measured directly (Archer, 1987). It is easier to release the stress and measure the strain relief (e), together with the elastic modulus or stiffness, E. The growth stress (a) is calculated assuming simple elastic theory, E = o/e. Where growth stresses are severe the longitudinal tensile strain at... 

A key result of the early crack growth studies was the "critical stress" effect, i.e., no crack growth occurs unless a specific stress value is exceeded. In practical terms these stress values correspond to threshold tensile strains of 3-5%, depending on stiffness. It has been found that critical stress values are largely unchanged by temperature, plasticization, and ozone concentration. Polychloroprene has a higher critical stress value than other diene rubbers, consistent with its reduced reactivity to ozone. 

Characterization of stress-strain behavior of poly(ether ester)s is of a great interest from both practical and fundamental point of view. Poly(ether ester)s exhibit a high tensile strains comparable to chemically crosslinked rubbers ranging from 500 to 800 %, while their tensile stress is higher than that of vulcanized rubbers, i.e. 20 to 50 MPa... 

For simplicity, the condition considers the conservative case where the pipe acts simply as support. The normal practice is to solve all these equations simultaneously, then determine the minimum wall thickness that has strains equal to or less than the allowable design strain. Thus, the minimum structural wall thickness dictated as longitudinal tensile strain is ... 

In most treatises,"- 3 the strain tensor is defined with all components smaller by a factor of 2 than inequation 3, so that 711 = dui/dxi and 721 = du2/bx + bui/bx ). However, such a definition makes discussion of shear or shear flow somewhat clumsy either a practical shear strain and practical shear rate must be introduced which are twice 721 and 721 respectively, or else a factor of 2 must be carried in the constitutive equations. Since most of the discussion in this book is concerned with shear deformations, we use the definition of equation 3 which follows Bird and his school" and Lodge. - This does cause a slight inconvenience in the discussion of compressive and tensile strain, where a practical measure of strain is subsequently introduced (Section F below). In older treatises on elasticity, strains are defined without the factor of 2 appearing in the diagonal components of equation 3, but with the other components the same. 

If the practical tensile strain is defined as e = L/Lo 1. where L and Lq are the stretched and unstretched lengths respectively, the practical tensile strain rate is (1 /Lo)dL/dt (cf. equation 60 of Chapter 3), and a constant e can be achieved by pulling the clamps apart at a constant rate. However, if the elongational strain rate is defined as the ratio of the velocity of a material point to its displacement, this quantity, denoted ci, is ( /L)dL/dt and it will remain constant only if the clamps are pulled apart at a rate which increases exponentially with time. Several instruments which accomplish this have been described. oo-io2a Qf... 

The state of strain in large deformations is commonly described either by the principal extension ratios, Xi, X2, X3, deflned in the notation of Chapter 1 as X,- = 1 + Uilxi, with the coordinate axes suitably oriented, or by three strain invariants whose values are independent of the coordinate system. In simple extension, Xi = 1 + e, where e is the (practical) tensile strain U jx cf. equation 8 above), not to be confused with the e in equations 3,4 and 6. Most of this section is concerned with simple extension. 

Til 1 3 cule tensile strain (twice the practical tensile strain e)... 

The theoretical maximum tensile strain, or elongation, of a SWCNT is almost 20 % [48, 49], but in practice, only 6 % [50] has been achieved at room temperatures. However, at high temperatures (estimated at 2,000 K might be too high with respect to Ref. [24]), individual SWCNTs can undergo a superplastic deformation, becoming nearly 280 % longer and 15 times thinner, from 12 to 0.8 nm, before tensile failure [51]. 

Kelly and Zweben [20] indicated that although Eq. 3.20 may predict a compressive normal stress due to the Poisson effect, this may not occur in some special cases, in which fibres are being pulled out of a matrix (i.e. a pull-out test, or fibres bridging across a crack in the composite). In these instances, the tensile strain in the fibre as it enters the matrix is high, while that of the matrix is low. At the cracked composite surface (or at the matrix surface in the pull-out test) the matrix is practically stress-free. Therefore, in these regions the normal stress across the... 

Designers of most structures specify material stresses and strains well within the pro-portional/elastic limit. Where required (with no or limited experience on a particular type product materialwise and/or process-wise) this practice builds in a margin of safety to accommodate the effects of improper material processing conditions and/or unforeseen loads and environmental factors. This practice also allows the designer to use design equations based on the assumptions of small deformation and purely elastic material behavior. Other properties derived from stress-strain data that are used include modulus of elasticity and tensile strength. 

More or less implicit in the theory of materials of this type is the assumption that all the fibers are straight and unstressed or that the initial stresses in the individual fibers are essentially equal. In practice this is quite unlikely to be true. It is expected, therefore, that as the load is increased some fibers will reach their breaking points first. As they fail, their loads will be transferred to other as yet unbroken fibers, so that the successive breaking of fibers rather than the simultaneous breaking of all of them will cause failure. As reviewed in Chapter 2 (SHORT TERM LOAD BEHAVIOR, Tensile Stress-Strain, Modulus of elasticity) the result is usually the development of two or three moduli. 

The continuous chain model includes a description of the yielding phenomenon that occurs in the tensile curve of polymer fibres between a strain of 0.005 and 0.025 [ 1 ]. Up to the yield point the fibre extension is practically elastic. For larger strains, the extension is composed of an elastic, viscoelastic and plastic contribution. The yield of the tensile curve is explained by a simple yield mechanism based on Schmid s law for shear deformation of the domains. This law states that, for an anisotropic material, plastic deformation starts at a critical value of the resolved shear stress, ry =/g, along a slip plane. It has been... 

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