Shear mechanical measurements

This chapter focuses on the elastic properties of the NEs deduced from shear mechanical measurements. As the comparison between the theoretical descriptions and the experimental results have led to considerable controversies (Martinoty et al. 2004a, b, c Terentjev and Warner 2004 Stenull and Lubensky 2004) it is useful to understand the evolution of the topic in order to make a brief historical presentation of the various static and dynamic theories—conventional linear elastic theory, soft elasticity (original version), soft elasticity (version 2), bifurcation-type theory—which were progressively introduced for describing the elastic properties of these materials. 

Powder Mechanics Measurements As opposed to fluids, powders may withstand applied shear stress similar to a bulk solid due to interparticle friction. As the applied shear stress is increased, the powder will reach a maximum sustainable shear stress T, at which point it yields or flows. This limit of shear stress T increases with increasing applied normal load O, with the functional relationship being referred to as a yield locus. A well-known example is the Mohr-Coulomb yield locus, or... 

Fig. 2. Results of interfacial shear strength measurements of the same fiber/matrix systems using four different micro-mechanical tests during a round-robin program involving 12 different laboratories, (a) Results for untreated, unsized carbon fibers, (b) Results for carbon fibers with the standard level of surface treatment. Redrawn from ref. [13].

It has also been suggested that steady state low shear dynamic measurements in the melt could be a convenient method for the study of particle dispersion in relation to flller properties, which might also correlate with mechanical properties of the composite [48,49]. 

Filler-filler interaction (Payne effect) - The introduction of reinforcing fillers into rubbery matrices strongly modifies the viscoelastic behavior of the materials. In dynamic mechanical measurements, with increasing strain amplitude, reinforced samples display a decrease of the storage shear modulus G. This phenomenon is commonly known as the Payne effect and is due to progressive destruction of the filler-filler interaction [46, 47]. The AG values calculated from the difference in the G values measured at 0.56% strain and at 100% strain in the unvulcanized state are used to quantify the Payne effect. 

The dynamic mechanical measurements were performed with a Rheometrics IV apparatus in a geometrical arrangement of parallel plates. The complex shear modulus G (= G + fG", where G and G", respectively, are the storage and loss moduli) at a constant frequency of 1 Hz was determined [30]. 

The results obtained by the present mechanical measurements are also consistent with the previous experimental results of the dynamic light scattering studies of the collective diffusion coefficient of gels and the rheological studies of the shear modulus of gels. The studies published by different researchers indicate that the concentration dependence of the collective diffusion constant of the polymer networks of gel and that of the elastic modulus are well represented by the following power law relationships [2, 3, 5]... 

When a specimen is gripped, the stress must be transferred from the grip to the specimen. This transfer takes place across the specimen-grip interface by a shear mechanism. Furthermore the stress must diffuse across the entire specimen cross section, before we reach the situations described by the theoretical solutions. We have already discussed the theoretical background to this problem in the previous chapter here we shall be concerned with the practical problems it imposes on real measurements. For isotropic materials it is usual to adopt the convenient rule of thumb that specimens should have an aspect ratio of at least 10. We feel it is useful to illustrate the effect of aspect ratio on modulus for isotropic materials. In Fig. 1 we present the modulus , measured as the... 

Dynamic-Mechanical Measurement. This is a very sensitive tool and has been used intensively by Nielsen (17) and by Takayanagi (18). When the damping curves from a torsion pendulum test are obtained for the parent components and for the polyblend and die results are compared, a compatible polyblend will show a damping maximum between those of the parent polymers whereas the incompatible polyblend gives two damping maxima at temperatures corresponding to those of the parent components. Dynamic mechanical measurement can also give information on the moduli of the parent polymer and the polyblend. It can be shear modulus or tensile modulus. If the modulus-temperature curve of a polyblend locates between those of the two parent polymers, the polyblend is compatible. If the modulus-temperature curve shows multiple transitions, the polyblend is incompatible. 

The evolution of the dynamic viscosity rp (co, x) or of the dynamic shear complex modulus G (co.x) as a function of conversion, x, can be followed by dynamic mechanical measurements using oscillatory shear deformation between two parallel plates at constant angular frequency, co = 2irf (f = frequency in Hz). In addition, the frequency sweep at certain time intervals during a slow reaction (x constant) allows determination of the frequency dependence of elastic quantities at the particular conversion. During such experiments, storage G (co), and loss G"(co) shear moduli and their ratio, the loss factor tan8(co), are obtained ... 

Figure 35. Mechanical properties of carbon-carbon epoxy-resin hybrid composites, compared with the properties of the composite skeletons before resin impregnation (61,62). The composite skeletons were prepared from Sigrafil HM 3 PAN based fiber, rigidized with a phenolic resin, and densified by four cycles with coal-tar pitch plus sulfur the carbonization temperature was 1000 C. (b) Flexural strength. (c) Interlaminar shear stress, measured with two sample thicknesses.

Here are the components of the stress tensor as defined in rheology Tn—T22 is the first normal stress difference and T21 the shear stress, equal to Nt and rxsh, respectively. Hence, from dynamic mechanical measurements it is possible to determine the zero shear first normal stress coefficient Fq0 and zero shear viscosity y0. 

Dynamic mechanical measurements, 407 Dynamic modulus, 451,508 Dynamic network of blobs, 279 Dynamic or absolute system of units, 53 Dynamic shear viscosity, 410 Dynamictensile viscosity, 410 Dynamic transitions, 418... 

A variety of rheological tests can be used to evaluate the nature and properties of different network structures in foods. The strength of bonds in a fat crystal network can be evaluated by stress relaxation and by the decrease in elastic recovery in creep tests as a function of loading time (deMan et al. 1985). Van Kleef et al. (1978) have reported on the determination of the number of crosslinks in a protein gel from its mechanical and swelling properties. Oakenfull (1984) used shear modulus measurements to estimate the size and thermodynamic stability of junction zones in noncovalently cross-linked gels. 

The electrical response of a liquid-loaded TSM resonator can be related to the shear mechanical impedance, Z, at the device surface. This mechanical impedance serves as a quantitative measure of the strength of the interaction between the solid and a contacting liquid. 

The TICA specimen preparation procedure has been described elsewhere (4). The mechanical measurements were made with the Rheometrics Mechanical Spectrometer (RMS) which measures the in-phase and out-of-phase stress response (a and b component respectively) of a specimen being subjected to a sinusoidal shear strain. The instrumental set-up was reported by Lee (6). The frequency of the strain function was kept constant at 1.6 Hz (10 rad/sec). All temperature scan experiments were scanned at 2 C/min rate. The temperature was scanned down at the same rate when the maximum temperature was reached. 

Arheopectic pigmented bleach (alkali metal hypochlorite) hard surface cleaner formulated with bentonite clay is disclosed in U.S. Patent 5,688,435. Examples of time-dependent shear effects determined from constant shear rate measurements at 1, 10, 50, and 100 sec-1 are provided in the patent and shown in Figure 4.2 and Figure 4.3. The viscosity data show evidence of shear thickening as a function of time at constant shear rates of 1 and 10 sec-1 and thixotropy occurs at 50 and 100 sec-1. The formulation is rheopectic at 10 sec-1. Dynamic mechanical data are also contained in the patent and the storage and loss modulus as a function of strain amplitude is shown in Figure 4.4, for one patent example. 

The dynamic shear storage modulus (G1) and loss modulus (G") were measured from -150° to 50°C using the forced torsion fixture on a Rheometric Mechanical Spectrometer (RMS). When the storage modulus dropped below 10 Pa. this fixture became insensitive. For moduli less than 10 Pa, the parallel plate fixture with serrated disks was used. The parallel plate fixture was used to extend the dynamic mechanical measurements to high temperatures. Degradation above about 250°C dictated this temperature as an upper limit for RMS measurements. Further discussion of equations and use of these fixtures are given elsewhere (2,8). 

The compatibility of the polymers in solutions was determined by dynamic viscosity measurements using a rotational viscometer at 293 K and shear rate 1312 s. The morphology of the film cast from a solution was examined with a polarization-interference microscope by differential method, at magnification of 250x. Dynamic mechanical measurements were made using direct reading visco-elastometer, the Rheovibron. The temperature was scanned... 

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