Shear modulus composition dependence

These parameters were also shown to depend on the system variables such as composition and temperature. The elastic modulus at high frequency is equivalent in these systems to the shear modulus and depends on the interfacial tension, droplet radius and volume fraction in the way predicted by eqn. (11.1) within... 

Fig. Z4 (a) Temperature ramp at a frequency a> = lOrads (strain amplitude A = 2%) for a nearly symmetric PEP-PEE diblock with Mn = 8.1 X 104gmol l, heating from the lamellar phase into the disordered phase. The order-disorder transition occurs at 291 1 °C, the grey band indicates the experimental uncertainty on the ODT (Rosedale and Bates 1990). (b) Dynamic elastic shear modulus as a function of reduced frequency (here aT is the time-temperature superposition shift factor) for a nearly symmetric PEP-PEE diblock with Mn = 5.0 X 1O g mol A Shift factors were determined by concurrently superimposing G and G"for w > and w > " respectively. The filled and open symbols correspond to the ordered and disordered states respectively. The temperature dependence of G (m < oi c) for 96 < T/°C 135 derives from the effects of composition fluctuations in the disordered state (Rosedale and Bates 1990). (c) G vs. G"for a PS-PI diblock with /PS = 0.83 (forming a BCC phase) (O) 110°C (A) 115°C ( ) 120°C (V) 125°C ( ) 130°C (A) 135°C ( ) 140°C ( ) 145°C. The ODT occurs at about 130°C (Han et at. 1995).

To complete the illustration of the dependence of the real part of the effective shear modulus p of the fractal structure composite on the ratio of the real parts of the shear modulii of the phases p /p j = x-> the results of calculations of the... 

As the model studied constitutes a self-similar, chaotic system of clusters of various sizes, on the jth scale level, each cluster will have its own resonance parameters—that is, its own characteristic frequency, which produces the system of peaks (characteristic frequencies) in the dependence of the effective shear modulus p on the parameters of the composite. 

Fig. 18. Temperature dependencies of the real ((. ) and imaginary (( .") component of the shear modulus measured at the deformation frequency of lOrad/s for the pure and tapered triblock copolymers pMMA-b-pBA-b-pMMA and p(MMA-grad-BA)-b-pBA-b- p(MMA-grad-BA) of approximately the same overall composition, MW and polydispersity DSC traces are shown to help localize the glass transition temperatures (T ) of the microphases. Reprinted with permission from [94]. Copyright (2000) John Wiley Sons, Inc.

Figure 16.10. Composition dependence of modulus, E, and yield stress, o, for blends of recycled PS/PO blends. The phase inversion concentration depends on the relative shear viscosity at the processing stress [Morrow et al., 1994].

Smith, J. R., Smith, T. L., and Tschoegl, N. W. (1970). Rheological properties of wheat flour doughs. III. Dynamic shear modulus and its dependence on amplitude, frequency and dough composition. Rheol. Acta 9, 239-252. 

Figure 2.6 Dependencies of mechanical properties of angle interlock reinforced composite on parameters of the reinforcement (normalised values) (a) Young s modulus in the warp direction, Ff = 58% (b) Young s modulus in the weft direction, Ff = 58% (c) shear modulus, Ff=58% (d) Young s moduli versus fibre volume fraction, PSl and PS2 refer to two values of the weft spacing.

Shear Modulus. The shear modulus determined from torsion measurements exhibits some dependence on temperature. For the Kevlar composite, the increase was 1.5, and for carbon fiber composite it was 1.2, from 293 to 4.2 K. Of course, both the damping and storage shear moduli represent tensorial quantities, and this must be included in the analysis. For anisotropic fibers, both the tensorial quantities of the fibers and those of the composite are involved. Here, only one tensor element, which was expected to be sensitive to temperature, was considered. 

The elastomer-filler composite is partly destroyed during deformation, then partly restored. This results in a change in the stress-strain curve and depends on the prestressing level. Relaxation leaves a residual deformation. Under dynamic load applications, the shear modulus depends on the stress amplitude [14, 15]. 

The results of the Eshelby inclusion model of Chow (1978) are summarized in Figs. 4.4 and 4.5 for a prominent application in which the heterogeneities are much stiffer than the matrix and the results are evaluated for the special system of glass fiber or disks in an epoxy-resin polymer matrix where the shear modulus and bulk modulus of the glass are 30.6 GPa and 44.4 GPa, respectively, and those of the epoxy-resin matrix are 1.30 GPa and 3.90 GPa, respectively. For this system the dependence on volume fraction (p of filler of the normalized shear modulus of the heterogeneous composite is given in Fig. 4.4, with p being either the transverse shear modulus p 2 axial-radial shear modulus of the com-... 

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