Biaxial strain ratio

This is why opinions about the procedure of considering OP loadings as if they were IP are so different. Finally, Fig. 9.20c shows an OP cycles so called diamond shaped. The IP or OP cycles can be classified on the base of the so called biaxial strain ratio Ay/As or NP factor One such method to evaluate the factor of... 

The use of a thin layer of standard lubricant in a consistent fashion reduces scatter in test results, simulates production conditions more closely, reduces tooling damage, and simplifies specimen preparation. However, the use of lubrication makes the strain ratio at fracture more biaxial. This is undesirable for production simulation because production failures mostly occur in the plane-strain region or in a less biaxial manner. Specimens of different widths are used to control the strain ratio at fracture. This method has been modified further into the limiting dome height (LDH) test. 

The experimental mechanical techniques most commonly used for network characterization are uniaxial extension and compression,and also biaxial strain.A sketch of a rubber sample under extension is shown in Figure 10(a). The nominal stress a is defined as the ratio of the force/to the cross-sectional area Aq of the undeformed specimen, and the strain e as the ratio of the length change AL to the original length Lq. These definitions are given in equations (67) and (68). The deformation is also often expressed in terms of the extension ratio X defined in equation (69). The cross-sectional area of the specimen varies with deformation. A true stress, defined as the ratio of the force to the real deformed area, is also frequently used. 

Note that the ratio of the ratio of the hoop stress (pR/h) to the axial stress (pR/lh) is only 2. From the data in this question the hoop stress will be 8.12 MN/m. A plastic cylinder or pipe is an interesting situation in that it is an example of creep under biaxial stresses. The material is being stretched in the hoop direction by a stress of 8.12 MN/m but the strain in this direction is restricted by the perpendicular axial stress of 0.5(8.12) MN/m. Reference to any solid mechanics text will show that this situation is normally dealt with by calculating an equivalent stress, Og. For a cylinder under pressure Og is given by 0.5hoop stress. This would permit the above question to be solved using the method outlined earlier. 

Since more trenches are being used in double FML landfills, the impact of waste settlement along such trenches should be considered. Figure 26.17 is a simple evaluation of the impact of waste settlement along trenches on the FML. Settlements along trenches will cause strain in the membrane, even if the trench is a very minor ditch. Knowing that when biaxial tension is applied to HDPE, the material fails at a 16-17% strain, it is possible that the membrane will fail at a moderate settlement ratio. 

Sharma (90) has examined the fracture behavior of aluminum-filled elastomers using the biaxial hollow cylinder test mentioned earlier (Figure 26). Biaxial tension and tension-compression tests showed considerable stress-induced anisotropy, and comparison of fracture data with various failure theories showed no generally applicable criterion at the strain rates and stress ratios studied. Sharma and Lim (91) conducted fracture studies of an unfilled binder material for five uniaxial and biaxial stress fields at four values of stress rate. Fracture behavior was characterized by a failure envelope obtained by plotting the octahedral shear stress against octahedral shear strain at fracture. This material exhibited neo-Hookean behavior in uniaxial tension, but it is highly unlikely that such behavior would carry over into filled systems. 

The biaxial extensional viscosity ( b) was defined as the ratio of the normal stress difference and the radial extension rate assumed to be half the strain rate ... 

A power law strain-energy function expressed in terms of circumferential, longitudinal and transmural extension ratios (A,i, A.2, and k ) was used [111] to describe the biaxial properties of sheep myocardium 2 weeks after experimental myocardial infarction, in the scarred infarct region ... 

We note that for specific modes of deformation, such as uniaxial extension, biaxial stretch, plane-strain compression, and pure shear, the extension ratios... 

In Fig. 23a, the hysteresis energies (I/hys) calculated from the cycles in Fig. 22a are plotted against the maximum strain in terms of uniaxial (/Imax) and biaxial (Abiax nax) extension ratios. All C/bys data collapse onto a single curve hence, the hysteresis energy only depends on the maximum extension of the polymer chains. 

Note that approximate Eq. 6.1.20] defines the strain dependence of the equilibrium swell ratio of the elastomer in a liquid medium under conditions of biaxial symmetric material extension. 

It is of interest to note that experimental values of the parameter d characterizing the strain dependence of equilibrium swelling ratio for elastomers subjected to uniform biaxial extension closely approximate the theoretical values. It will be recalled that this parameter is specified by Eq. [6.1.21]. Moreover, the Flory theory defines it as d = 2/9 = 0.22(2),... 

New methods have been proposed, which allow one to estimate the concentration dependence of liquid diffusion in elastomer and strain dependence of equilibrium swelling ratio under conditions of symmetric biaxial elastomer extension in terms of kinetic and strain curves of swelling. 

Biaxial tests were carried out to study the tensile behavior of the flax fabric. The results showing the biaxial behaviour of the fabric in the weft direction are presented for the plain weave fabric in Figure 5.11 for different values of the parameter kt. The parameter kt = e e is defined as the ratio between the strain in the weft direction (e ) over... 

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