Tensile strain, defined

The reaction of a material to a tensile stress is to stretch or elongate. This is measured as tensile strain, defined as the elongation or increased length per initial length. Strain is a dimensionless unit that is usually expressed as a percent (percent elongation). 

We can now define the elastic moduli. They are defined through Hooke s Law, which is merely a description of the experimental observation that, when strams are small, the strain is very nearly proportional to the stress that is, they are linear-elastic. The nominal tensile strain, for example, is proportional to the tensile stress for simple tension... 

One final point. We earlier defined Poisson s ratio as the negative of the lateral shrinkage strain to the tensile strain. This quantity, Poisson s ratio, is also an elastic constant, so we have four elastic constants E, G, K and v. In a moment when we give data for the elastic constants we list data only for . For many materials it is useful to know that... 

Generally our material will be compressible and zxx zyyj2 = ezz/2 and we have to introduce another material parameter, Poisson s ratio, v. Poisson s ratio is defined as the ratio of the contractile to the tensile strain, i.e. v = zyy exx. Equation (2.4) now becomes ... 

We have written Eq. (5.4) with variables grouped as they are in order to define two very important quantities. The first quantity in parentheses is called the modulus—or in this case, the tensile modulus, E, since a tensile force is being applied. The tensile modulus is sometimes called Young s modulus, elastic modulus, or modulus of elasticity, since it describes the elastic, or recoverable, response to the applied force, as represented by the springs. The second set of parentheses in Eq. (5.4) represents the tensile strain, which is indicated by the Greek lowercase epsilon, e. The strain is defined as the displacement, r — rp, relative to the initial position, rp, so that it is an indication of relative displacement and not absolute displacement. This allows comparisons to be made between tensile test performed at a variety of length scales. Equation (5.4) thus becomes... 

One of the simplest criteria specific to the internal port cracking failure mode is based on the uniaxial strain capability in simple tension. Since the material properties are known to be strain rate- and temperature-dependent, tests are conducted under various conditions, and a failure strain boundary is generated. Strain at rupture is plotted against a variable such as reduced time, and any strain requirement which falls outside of the boundary will lead to rupture, and any condition inside will be considered safe. Ad hoc criteria have been proposed, such as that of Landel (55) in which the failure strain eL is defined as the ratio of the maximum true stress to the initial modulus, where the true stress is defined as the product of the extension ratio and the engineering stress —i.e., breaks down at low strain rates and higher temperatures. Milloway and Wiegand (68) suggested that motor strain should be less than half of the uniaxial tensile strain at failure at 0.74 min.-1. This criterion was based on 41 small motor tests. 

Recoverable strain can also be defined as the tensile strain needed to pull a fully swollen extrudate until its diameter is that of the capillary (22).5 Assuming constant density nD-iL/A = kDqLq/A, or Lq/L = SR = (D/Dq)2. At 0.1 cm past the capillary exit SR = 0.81 (D/Dq)2, and at 3 cm, it is (D/Dq)2. Therefore, at 0.1 cm, 19% of the recoverable tensile strain that the extradate is capable of undergoing is still present. In other words, if no further swelling were allowed, 0.19(D/Dq)2 would he the value of the average frozen-in strain in the extradate. 

The diagonal elements of Eq. 10.3 are the stretches or tensile strains. The nondiagonal elements are the shear strains. The variation of the displacement vector, u, with the position vector, d, for a point in the solid is used to define the nine tensor components in Eq. 10.3, as follows ... 

A standard set of reference axes and equations to describe spontaneous strains is now well established (Schlenker et al. 1978, Redfern and Salje 1987, Carpenter et al. 1998a). The orthogonal reference axes, X, Y and Z, are selected so that Y is parallel to the crystallographic y-axis, Z is parallel to the normal to the (001) plane (i.e. parallel to c ) and X is perpendicular to both. The +X direction is chosen to conform to a right-handed coordinate system. Strain is a second rank tensor three linear components, cn, 622 and 33 are tensile strain parallel to X, Y and Z respectively and co, 623, eu are shear strains in the XZ, YZ and XY planes, respectively. The general equations of Schlenker et al. (1978) define the strains in terms of the lattice parameters of a crystal (a, b, c, a, P, y, where P is the reciprocal lattice angle) with respect to the reference state for the crystal ( , bo, Co, cto, Po,Yo) ... 

The bulk modulus K is defined as the reciprocal of the isothermal compressibility, and Young s modulus E is defined as the ratio of longitudinal tensile stress and longitudinal tensile strain ... 

Analyses have been carried out assuming a cavitated particle, that is, the particle is replaced by a void (see the section Cavitation of the Rubber Particles ). The analysis is applied to an annulus of epoxy resin. The volume fraction of the void is 20%. The elastic material properties used for the epoxy matrix are shown in Table I. The elastic-plastic material properties used are shown in Figure 4. Nonlinear geometric effects were included to take account of large deformations. Final failure of the cell was defined (23) to be the applied strain required for the maximum linear tensile strain in the resin to attain the value of 20%. 

The application of a tensile stress to a real body will result in a corresponding extensional deformation as illustrated in Figure 2-la. The fractional extension is defined as the tensile strain. Thus, s, the tensile strain resulting from the application of a uniaxial stress, is given as... 

The homogeneous longitudinal tensile strain of a solid, of a metal bar, for example (Fig. 4.8), is defined as the expansion per unit length of the undeformed... 

The strain that is found on application of a load to a rod is equal to the elongation of the rod. The increment in tensile strain experienced, A e, when a rod is extended, is defined as the ratio of the increase in length, A I, to the total length ... 

Tensile stress at v% strain the stress at which the strain reaches the specified value. v expressed in percentage. It may be measured, for example, if the stress-strain curve does not exhibit a yield point. In this case. v must be defined either in the relevant product standard or agreed upon by the interested parties Tensile strain the increase in length per unit original length of the gauge. It is used for strains up to the yield point for strains beyond this limit see nominal tensile strain below... 

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)... 

In extensional flows, the velocity increases (fibre melt spinning) or decreases (radial flow from the sprue in an injection mould) along the streamlines, but there is no velocity gradient in the perpendicular direction. Figure 5.5 shows fibre melt spinning where the velocity increases with distance x from the spinneret, as the result of a tensile stress along the fibre. The tensile strain rate 6x is defined by... 

The only way to generate data for this type of unsteady biaxial tensile flow is to instrument a blown film machine. The tensile viscosity, defined by Eq. (5.16), hardly changes with the tensile strain rate. Figure 5.15 shows data for the uniaxial stretching of an LDPE and an HDPE. The apparent tensile viscosity increases with strain rate for the more elastic LDPE, in contrast with the non-Newtonian reduction in viscosity in shear flows. 

The general equation defining the fatigue life in terms of tensile strain, as a criterion, is as follows ... 

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