Modulus determination

The main purpose of DMA is to make measurements as a function of temperature. This invariably results in a compromise between optimum modulus determination and the best use of the DMA stiffhess range, as discussed in Section 4.3.2. Three-point bending and tension geometry are the best modes for accurate modulus determination. 

Three-point (or simply supported) bending is free of such clamping errors and therefore the measured moduli are correct. In fact, testing an accurately machined steel sample (ordinary steel, not stainless) is certainly the best way of verifying a DMA s modulus measuring accuracy. 

The clamping error is difficult to correct since this error depends upon the sample stiffness, its modulus and its aspect ratio. By the time the sample reaches the rubbery condition this error is insignificant, due to the low sample stiffiiess. 

Since the error is a constant value which adds to the length, it can be mitigated by ensuring that stiff samples are run with long free lengths, at least 10 mm. Fortunately, such samples tend to show the least drop in modulus at 7, especially fibre reinforced composites, and therefore measurement of the minimum modulus value is not an issue with such samples. Alternatively thinner samples can be produced, which therefore have a lower sample stiffness. 

Remember that doubling the length decreases the sample stiffness by 8 times, as does halving the sample thickness. Doing both reduces the stiffness by 16 times. 

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Hardness measures the resistance of a material to a permanent change of shape. That is, the resistance to shear deformation (not the resistance to a volume change). The precursor to a permanent shape change is a temporary elastic shape change, and a shear modulus determines this. Therefore, the first necessity for high hardness is a high shear modulus. 

The tensile test is typically destructive that is, the sample is extended until it plasticly deforms or breaks, though this need not be the case if only elastic modulus determinations are desired. As described in the previous section, ductile materials past their yield point undergo plastic deformation and, in doing so, exhibit a reduction in the cross-sectional area in a phenomenon known as necking. 

The stress strain curve is recorded and the modulus determined at a shear strain of 25 %. For the quadruple test piece, the shear strain is half the measured deformation divided by the thickness of one rubber block. The shear stress is the applied force divided by twice the area of a bonded face of one block. 

E = storage modulus determined in a dynamic mechanical test, GPa... 

The measurement of the sound speed in filaments and yams requires special techniques, viz. by means of a magnetostrictive oscillator (see Ballou et al. 1944/1949). The dynamic modulus, determined in this way is considerably larger than the Young modulus from stress-strain experiments Edyn 1-5 Estat-... 

There are a couple of things about this relationship. First of all it is only an approximation. We ll get back to that in a while. Second, we have only considered simple elongation so far. There is a modulus associated with shear and also a bulk modulus. The most important point, however, is that the modulus determined this way, dividing stress by strain, is a material property and independent of the shape of an object. It is what we mean when we talk about the stiffness of a material. Stiffness is crucial in many engineering applications. If a strain of just 1.6% were allowed in an aircraft s wing spar booms, for example, it would look something like Figure 13-8. 

Fig. 25. Axial Young modulus, determined at 0.1 % maximum strain at 21 °C, versus maximum steady draw ratio for PP copolymer die drawn at a nominal temperahire of 110 °C,(0,R-n = 15.5 mm die ...

The Time-Temperature Superposition Principle. For viscoelastic materials, the time-temperature superposition principle states that time and temperature are equivalent to the extent that data at one temperature can be superimposed upon data at another temperature by shifting the curves horizontally along the log time or log frequency axis. This is illustrated in Figure 8. While the relaxation modulus is illustrated (Young s modulus determined in the relaxation mode), any modulus or compliance measure may be substituted. 

Willems G, Celis JP, Lambrechts P, Braem M, Vanherle G Hardness and Young s modulus determined by nanoindentation technique of filler particles of dental restorative materials compared with human enamel. J Biomed Mater Res 1993 27 747-755. 

Table 7.37 shows lower values for flexural modulus determined by using 3-pt load compared to 4-pt load. On average, the difference is 9 + 7% in favor of third-point load compared to center-point load in terms of flexural modulus test values. The difference is very close to that (9 + 3%) for flexural strength values (see above). 

The test method can be used for testing materials with thickness up to 0.55 in. (14 mm). The apparatus recommended for ASTM D 5083 procedure is similar in kind to that in ASTM D 638. Test specimens shall be in the form of a rectangular prism, with the preferred overall length more than 10 in., width of 1.0 in., and thickness between 0.08 in. (2 mm) and 0.55 in. (14 mm). The recommended standard speed of testing shall be 0.2 in. (5 mm)/min for stress testing and 0.08 in. (2 mm)/ min for tensile modulus determinations. 

Fig. 6.17 Dilational elasticity modulus determined from longitudinal wave damping experiments,BSA(B), lysozyme(D) according to Graham Phillips (19S0a)...

Fig. 3.1 Variation of 1 /E as a function of f Mc) curve], where E is the Young s tensile modulus determined with a 1 mm min strain rate, and Me [g mol ] is the average mass between two crosslinks.

This modulus determines the velocity of ultrasonic stress pulses through a solid. 

R. Lucklum, P. Hauptmann, Thin Film Shear Modulus Determination with Quartz Crystal Resonators A Review, IEEE International Frequency Control Symposium, (2001) 408-17. 

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 concentration effect was demonstrated in the viscoelastic behaviour of SELP-47K hydrogels, cured for 4 hours at 37 °C. The storage modulus determined by dynamic mechanical analysis (DMA) was 75.4 kPa for SELP-47K at 4 wt%, whereas a greater value of 1600 kPa was obtained for 12 wt%. Macroscopically, the 4 wt% hydrogels showed to be translucent, soft and easily deformable, while the 12 wt% hydrogels were opaque and firm [54]. 

Figure 4. Stress-strain data at 24"C for modulus determination shown in Figure 3...

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