Modulus variation with angle

Figure 8.15 Comparison of the observed variation in modulus Eo with angle 0 to draw direction and the theoretical relation (i.e. full curve) calculated from Eo, E4S and Ego for low-density polyethylene sheet drawn to a draw ratio of 4.65. (Reproduced from Raumann, G. and Saunders, D.W. (1961) Ehe anisotropy of Young s modulus in drawn polyethylene. Proc. Phys. Soc., 77, 1028. Copyright (1961).)...

Figure 3.17 Variation of Young s modulus with angle 0 to draw direction for LDPE sheet drawn...

Fig. 6. Variation of Young s modulus (-) and shear modulus (—), with cord angle 9 for one-ply nylon—mbber system (88).

The torsional pendulum principle, via a braid sample, was used to measure the variation of shear modulus with temperature, and the loss angle, and hence to derive the glass transition temperature. This gave for the gelled but uncured material Tg 80°C, and for the material which had been kept at 70°C for 120 h, and could therefore be regarded as fully crosslinked, Tg -60°C. 

A part of this peculiar variation in the stress-strain phase angle difference comes from the variation of elastic modulus with the phase angle. Therefore, to determine the phase angle difference which is caused by the nonelastic contribution, it is necessary to determine and to subtract the contribution from the variation of elastic modulus as a function of the strain. 

The above analysis shows that the nonlinear dynamic viscoelastic behavior of polymers can be resolved into three components the nonlinear elasticity resulting from the variation of modulus with the phase angle or strain during the cycle nonlinear internal friction resulting from strain and strain-rate dependence and eflFects associated with the reversible, strain-induced structural changes. 

Table 7 Variation of lattice constant ao(A), bulk modulus Ko(GPa), rhombohedral distortion angle Ay( ), charge q(e), and spin moments h jib), in MnO with both composition of the hybrid functional and magnetic state ...

The variation of the isochronous modulus at 100 s with the magnitude of the creep strain at 100 s for strains in the region OT-10% in samples cut at various angles to the fibre axis is shown in Fig. 3. The data were obtained using the isochronous stress-strain procedure, previously referred to, on LDPE drawn at 20 C so as to produce fibre symmetry with a draw ratio of 4-2. In this figure horizontal straight lines would indicate linear viscoelastic behaviour. The strain at which significant deviation firom... 

The tensile creep behaviour of oriented high-density polyethylene has been studied by McCrum and coworkers " and by Ward and co-workers. " No creep curves as such are given, but the variation of isochronous modulus with temperature for specimens cut at various angles... 

Rheological studies show some similarities with chemical relaxation studies. For instance, a rectangular shear rate is applied and the relaxation of the stress is monitored. This directly yields the stress relaxation time(s). One can also apply a sinusoidal deformation or strain of angular frequency 0). The response of the system is a two-component sinusoidal shear stress. The first component is in phase with the strain and corresponds to the elastic (storage) properties of the system. The second component is out of phase with the strain with a phase angle 5, and corresponds to the viscous loss in the system. These quantities give access to the storage (elastic) modulus G (co) and to the loss (viscous) modulus G"(o)), with G" ((o)/G (co) = tg5. As in the case of chemical relaxation methods with harmonic perturbation, the variations of G (w) and G" (co) with co yield the relaxation time(s) of the system. 

---