Modulus data

Free- Vibration Methods. Free-vibration instmments subject a specimen to a displacement and allow it to vibrate freely. The oscillations are monitored for frequency and damping characteristics as they disappear. The displacement is repeated again and again as the specimen is heated or cooled. The results are used to calculate storage and loss modulus data. The torsional pendulum and torsional braid analy2er (TBA) are examples of free-vibration instmments. 

Although sealant manufacturer s Hterature commonly reports modulus values, these values must be interpreted carefully. Specimen sizes, test rate, cure conditions, and the time a sealant has been allowed to cure when tested can all have a significant effect on modulus. Therefore, for a tme comparison, sealants should be evaluated by a standard test that examines all sealants by the same procedure. In general, the longer a sealant has been allowed to cure, the more reaUstic the modulus data. 

Stress-relaxation measurements, where stress decay is measured as a function of time at a constant strain, have also been used extensively to predict the long-term behavior of styrene-based plastics (9,12). These tests have also been adapted to measurements in aggressive environments (13). Stress-relaxation measurements are further used to obtain modulus data over a wide temperature range (14). 

Data are for fully crystalline material apart from electrical data for PEEKK It may be noted that the amorphous SG of PEEK is 1.265. The modulus data is flexural for PEEK and tensile for PEEKK. 

After some early uncertainty in the literature about the nature of the pressure sensitive bond, Dahlquist [5,6] related modulus data to tack-temperature studies and observed that the compression modulus of the adhesive had to be less than about 3 X 10 dyne/cm (3 x lO Pa) before any adhesive tack was observed. This was explained as the highest modulus that still allowed the adhesive to be sufficiently compliant to wet out or come into molecular contact with the substrate and form dispersive bonds. As other investigators [7-9] accepted this requirement it was termed the Dahlquist Criterion . 

The tensile modulus is an important property that provides the designer with information for a comparative evaluation of plastic material and also provides a basis for predicting the short-term behavior of a loaded product. Care must be used in applying the tensile modulus data to short-term loads to be sure that the conditions of the test are comparable to those in use. The longer-term modulus is treated under the creep test (Chapter 2). 

Data in Table 30.1 clearly show that, whatever the position of the test sample along the compounding line, there is a substantial difference between run 1 and run 2 data, particularly in what the linear modulus data are concerned. However, G is an extrapolated value and quite unrealistic values are obtained on certain samples, e.g., TR and AA, and it might be safer to consider modulus variations along the compounding line by using the (recalculated) complex modulus at 10% strain (Figure 30.13). 

TABLE 3 Modulus Data and Spreading Speed, U, for the Silicone Elastomer... 

For effective demulsification of a water-in-oil emulsion, both shear viscosity as well as dynamic tension gradient of the water-oil interface have to be lowered. The interfacial dilational modulus data indicate that the interfacial relaxation process occurs faster with an effective demulsifier. The electron spin resonance with labeled demulsifiers suggests that demulsifiers form clusters in the bulk oil. The unclustering and rearrangement of the demulsifier at the interface may affect the interfacial relaxation process. 

Figure 6.2 shows yield stress versus shear modulus data for face-centered cubic metals at about 78 K. The yield stresses were derived from Brinell Hardness Numbers (Gilman, 1960). The slope of the correlation line is tb = G/333, in good agreement with the theoretical estimate of the previous paragraph. 

Distributions of relaxation or retardation times are useful and important both theoretically and practicably, because // can be calculated from /.. (and vice versa) and because from such distributions other types of viscoelastic properties can be calculated. For example, dynamic modulus data can be calculated from experimentally measured stress relaxation data via the resulting // spectrum, or H can be inverted to L, from which creep can be calculated. Alternatively, rather than going from one measured property function to the spectrum to a desired property function [e.g., Eft) — // In Schwarzl has presented a series of easy-to-use approximate equations, including estimated error limits, for converting from one property function to another (11). 

The modulus data are then used to estimate the total signal amount by means of various algorithms. The simplest one uses the average of the modulus over a pre-defined data-array window. 

Fig. 2.5. Modulus data as a function of distance from the fiber surface of a carbon fiber-epoxy matrix composite which are measured from nanoindentation experiments. After Williams et al. (1990).

The modulus data were fitted with a second degree polynomial equation, and these functions were used in the calculations of the thermal stresses from Equations 1 through 3. The polynomial coefficients and the correlation coefficient for each sample are given in Table III. 

Young s modulus of the block copolymer fibers compared favorably with that of the physical blends as shown in Table 6, and in general they follow the linear rule of mixtures. The modulus data suggested that one does not need very large PBZT molecules to have the reinforcing efficiency. From the tensile data, one clear trend is that the tensile strength of the block copolymer system is much... 

Modulus data on crosslinked systems would seem to offer the most direct method for studying entanglement effects. Certainly, from the standpoint of molecular modeling, the advantages of equilibrium properties are clear. However, the structural characterization of networks has proven to be very difficult, and without such characterization it is almost impossible to separate entanglement contributions from those of the chemical crosslinks alone. Recent work suggests, however, that these problems are not insurmountable, and some quantitative results are beginning to appear. 

Fig. 7.1. Plot of modulus data on poly(dimethyl siloxane) networks to determine g and Me by Langley s method [Eq.(7.26)] (292)...

E modulus data for Norton hardness grades (after Moser, 1980)... 

The following table gives the bulk modulus data(K) for several HE s and wax at temps of 25-30° as detd by Cramer(Ref 5,p7) ... 

Analysis of the modulus data by Maxwells equation suggests that at the higher rubber concentrations, both the epoxy and rubber phases are continuous (7), with the epoxy phase slightly predominant. 

The dynamic mechanical response of a material can be characterised through the loss modulus, the loss tangent, tan S, or the loss compliance, However, as already mentioned for Ar-Al-PA (Sect. 6), the loss compliance can be considered the most relevant parameter for quantitatively comparing different materials, at least for additive purposes. For this reason, the semi-quantitative analysis and the comparison of viscoelastic data determined for different systems have been performed [63] in terms of /", whereas the determination of activation energies and entropies are based on loss modulus data. 

Figure 12.7 Plot of yield stress and modulus data according to Kitagawa s equation (T0 = 22°C) for different epoxy formulations (see Table 12.1 for abbreviations). (Reprinted from Cook et al., 1998, Copyright 2001, with permission from Elsevier Science.)... 

Figure 1.36 presents some creep modulus data for polystyrene at various temperatures [11], Create a master curve at 109.8°C by graphically sliding the curves at some temperatures horizontally until they line up. 

A Models to describe microparticles with a core/shell structure. Diametrical compression has been used to measure the mechanical response of many biological materials. A particular application has been cells, which may be considered to have a core/shell structure. However, until recently testing did not fully integrate experimental results and appropriate numerical models. Initial attempts to extract elastic modulus data from compression testing were based on measuring the contact area between the surface and the cell, the applied force and the principal radii of curvature at the point of contact (Cole, 1932 Hiramoto, 1963). From this it was possible to obtain elastic modulus and surface tension data. The major difficulty with this method was obtaining accurate measurements of the contact area. 

Figure 8 presents the storage and loss-modulus master curves obtained on all five samples of interest. The dashed lines indicate extensions of the master curves, using appropriately reduced data from the Rheovibron experiments in tension. Storage-modulus data in the rubbery plateau region vary systematically with composition, i.e., the... 

Again, reliable creep modulus data have to be available in order to apply the deflection equations. Tables 25.2 and 25.3 (see also Fig. 25.3) give the expressions for the deflections and torsional deformations of bars. By means of these equations the modulus of engineering materials may be determined from deflection and torsion experiments. The reader is also referred to, e.g. Ferry (1980), McCrum et al. (1997), Whorlow (1992) and Te Nijenhuis (1980, 2007). 

---