Strain tensile, definition

Extension ratios are most often used in cases of large strains or large deformations and can be found by examining the basic tensile strain definition as follows. 

It should be noted that the stresses usually used are engineering stresses calculated from the ratio of force and original cross section area whereas true stress is the ratio of the force and the actual cross sectional area at that deformation. Clearly, the relationship between stress and strain depends on the definition of stress used and taking the case of tensile strain, for example, the true stress is equal to the engineering stress multiplied by the extension ratio. 

If the strain derived is entirely due to craze matter production, there will be no significant change in the cross-sectional area A of the part during such (dilational) flow. Then, by definition, the imposed tensile strain rate e must be... 

Nominal tensile strain at the tensile strength the nominal temsile strain at the tensile strength, if the specimen breaks after yielding Modulus of elasticity in tension the ratio of stress difference to the corresponding strain difference. These strains are defined in the standard as being 0.05% and 0.25%. Also known as Young s modulus. This definition is not applicable to films (or rubber as noted earlier)... 

It is worth noting the definitions for tensile strain and nominal tensile strain. This distinction was not made in previous editions of the standard. 

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. 

A closely related phenomenon appears when application of a tensile strain increases the volume under circumstances where Poisson s ratio pi is substantially less than —i.e near or below the glass transition temperature. In accordance with. the definition of n in connection witli equation 50 of Chapter 1, the volume increase accompanying longitudinal extension is given by... 

The test control and data acquisition were achieved using Instron Series 9 software. The material parameters for tensile properties, such as tensile strengtii (a ), tensile strain at tensile strength (Em), stress at break ((7 ), and strain at break (Eq), were obtained according to the definitions in ASTM D 638 and ISO Determination of tensile properties (ISO 527-1, 2 1993 (E)). The Young s modulus, E, was calculated according to the definition in ISO 527-1, which gives... 

By analogy with Eq. (3.1), we seek a description for the relationship between stress and strain. The former is the shearing force per unit area, which we symbolize as as in Chap. 2. For shear strain we use the symbol y it is the rate of change of 7 that is involved in the definition of viscosity in Eq. (2.2). As in the analysis of tensile deformation, we write the strain AL/L, but this time AL is in the direction of the force, while L is at right angles to it. These quantities are shown in Fig. 3.6. It is convenient to describe the sample deformation in terms of the angle 6, also shown in Fig. 3.6. For distortion which is independent of time we continue to consider only the equilibrium behavior-stress and strain are proportional with proportionality constant G ... 

The maximum in the curve denotes the stress at yield av and the elongation at yield v. The end of the curve denotes the failure of the material, which is characterized by the tensile strength a and the ultimate strain or elon gation to break. These values are determined from a stress-strain curve while the actual experimental values are generally reported as load-deformation curves. Thus (he experimental curves require a transformation of scales to obtain the desired stress-strain curves. This is accomplished by the following definitions. For tensile tests ... 

Tyres are very definitely fatigued during use and, as mentioned for fabric/rubber adhesion above, it is very important to carry out dynamic tests to assess bond efficiency. Methods have not apparently been standardised but a variety of procedures have been reported71 79 Some workers have used the same or a similar test piece as in static tests and applied a cyclic tensile stress or strain, whilst others have used some form of fatigue tester operating in compression/shear to repeatedly stress or strain cord/rubber composite, or even to flex samples in the form of a belt. Khromov and Lazareva80 describe a method using test pieces cut from tyres. 

In the above considerations, a sinusoidal shear strain is applied to the sample. It should be clear that a sinusoidal shear stress could also be applied resulting in corresponding compliance functions J and J". The former results from the deformation in phase with the stress, while the latter corresponds to the out-of-phase deformation. The value of tan 5 remains the same, as can be seen from the curves in Figure 2-13, where we can easily imagine the stress as the applied variable and strain as the measured variable. Tensile stress is equally applicable and definitions of E (co), E" (o), D"(co), D co), etc. are completely analogous to the derived shear parameters. At a given frequency, the value of tan 8 is always the same for any of these quantities, i.e., tan 8 = E"/E = D"/D . 

Tensile properties that are related to fiber stiffness can be used to measure the T of almost all fibers. The elastic modulus, that is, the sl pe of the Hookean region of the fiber stress-strain curve, is a measure of the fiber stiffness and can be used for T determination since, by definition, a glass is stlffer than rubber (Figure 6). Since the transition from a glassy to a rubbery state Involves a reduction in stiffness, the temperature at which the modulus is abruptly lowered is taken as... 

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