Longitudinal strain, relationship

In the [ 45]j tensile test (ASTM D 3518,1991) shown in Fig 3.22, a uniaxial tension is applied to a ( 45°) laminate symmetric about the mid-plane to measure the strains in the longitudinal and transverse directions, and Ey. This can be accomplished by instrumenting the specimen with longitudinal and transverse element strain gauges. Therefore, the shear stress-strain relationships can be calculated from the tabulated values of and Ey, corresponding to particular values of longitudinal load, (or stress relations derived from laminated plate theory (Petit, 1969 Rosen, 1972) ... 

Gibson, A.G. at al. (1978). Dynamic mechanical behaviour and longitudinal crystal thickness measurements on ultra-high modulus linear polyethylene a quantitative model for the elastic modulus. Polymer, Vol. 19 (1978), pp. 683-693 Hong, K. et al. (2004). A model treating tensile deformation of semi-crystalline polymers Quasi-static stress-strain relationship and viscous stress determined for a sample of... 

Figure 3.20. Relationship between volume strain A F/Fand longitudinal strain AL/L for creep of HiPS and blends of HiPS with PPO (from 12.5 to 50% ABS) (Bucknall et u/., 1972a). Note that the fraction of deformation due to crazing as opposed to shear drops from about 100 % in the case of HiPS alone to about 60% for a 50-50 blend with PPO. It is interesting that the HiPS, itself a craze-prone polymer, promotes shear yielding in the somewhat ductile PPO.

Figure 3.21. Relationship between volume strain AF/F and longitudinal strain for creep of a high-impact ABS resin, showing mechanism of creep as a function of strain at five different stresses. (Bucknall and Drink water, 1973.)...

Steady-propagating plastic waves [20]-[22] also give some useful information on the micromechanics of high-rate plastic deformation. Of particular interest is the universality of the dependence of total strain rate on peak longitudinal stress [21]. This can also be expressed in terms of a relationship between maximum shear stress and average plastic shear strain rate in the plastic wave... 

In solids of cubic symmetry or in isotropic, homogeneous polycrystalline solids, the lateral component of stress is related to the longitudinal component of stress through appropriate elastic constants. A representation of these uniaxial strain, hydrostatic (isotropic) and shear stress states is depicted in Fig. 2.4. Such relationships are thought to apply to many solids, but exceptions are certainly possible as in the case of vitreous silica [88C02]. 

The electrostrictive behavior of P(VDF-CTFE) copolymers was investigated (Li et al. 2004 Li et al. 2006). A high electromechanical response was obtained in these copolymer films. As other PVDF-based polymers, the processing condition plays a very critical role on its properties. For a well-stretched and annealed P (VDF-CTFE) 88/12 copolymer film, a longitudinal electrostrictive strain as much as 5.5 % was obtained. A linear relationship between the strain response and the was observed, which indicates the electrostrictive nature of the electromechanical response in P(VDF-CTFE) copolymers. The corresponding electric field-related electrostrictive coefficient for the copolymer film is obtained as Mss = —1.23 0.02 X 10 (m /V ) (Li et al. 2006). 

When forces are applied normally to a thin sheet with large lateral dimensions, as illustrated in Figure 1(d), the lateral strains will be negligible. The ratio of stress to strain ((Tzz/ zz) is the longitudinal modulus L. The relationship to the moduli K and G is... 

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