Elastic modulus as a function

The response of a plastic to an applied stress depends on the temperature and the time at that temperature to a much greater extent than does that of a metal or ceramic. The variation of an amorphous TP over an extended temperature range can be exemplified by the behavior of its elastic modulus as a function of temperature. 

Tensile Modulus. Tensile samples were cut from the 0.125 in. plates of the compositions according to Standard ASTM D638-68, into the dogbone shape. Samples were tested on an Instron table model TM-S 1130 with environmental chamber. Samples were tested at temperatures of -30°C, 0°C. 22°C, 50°C, 80°C, 100°C and 130°C. Samples were held at test temperature for 20 minutes, clamped into the Instron grips and tested at a strain rate of 0.02 in./min. until failure. The elastic modulus was determined by ASTM D638-68. Second order polynomial equations were fitted to the data to obtain the elastic modulus as a function of temperature for each of the compositions. 

Figure 5.22 Hardness and elastic modulus as a function of indentation depth at various peak loads for Si(lOO). Reprinted, by permission, from X. Li and B. Bhushan, Materials Characterization, Vol. 48, p. 14. Copyright 2002 by Elsevier Science, Inc.

Figure 5. Left stress—strain behavior of MEA based on NR111 membrane tested at 25°C and with different RH levels right calculated elastic modulus as a function of RH [reprinted with permission from reference 34].34...

The established concepts predict some features of the Payne effect, that are independent of the specific types of filler. These features are in good agreement with experimental studies. For example, the Kraus-exponent m of the G drop with increasing deformation is entirely determined by the structure of the cluster network [58, 59]. Another example is the scaling relation at Eq. (70) predicting a specific power law behavior of the elastic modulus as a function of the filler volume fraction. The exponent reflects the characteristic structure of the fractal heterogeneity of the CCA-cluster network. 

Fig. 5. Schematic illustration of the fluid-to-gel transition observed for colloidal silica inks. The bottom graph is a plot of zeta potential as a function of pH for PEl-coated silica and bare silica microspheres suspended in water. The upper graph is a log-log plot of shear elastic modulus as a function of shear stress for concentrated silica gels of varying strength (o) denotes weak gel pH = 9.5 and ( ) denotes strong gel pH = 9.75 (Ref. 36).

FIGURE 5.28 Elastic modulus as a function of PECVD-TEOS coating time [86],... 

Fig. 6 (A) A representative load-displacement curve of an indentation made at 3mN peak indentation load and (B) the hardness and elastic modulus as a function of indentation contact depth for the AI74 gCoig 9Ni8.4 quasicrystal. (Li, X. Zhang, L. Gao, H. Micro/nanomechanical characterization of a single decagonal AlCoNi quasicrystal. J. Phys. D Appl. Phys. 2004, 37, 753-757.)...

Figure 2a Variation of elastic modulus as a function of lateral strain...

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. 

As mentioned earlier, the DMTA technique measures molecular motion in adhesives, and not heat changes as with DSC. Many adhesives exhibit time-dependent, reversible viscoelastic properties in deformation. Hence a viscoelactic material can be characterized by measuring its elastic modulus as a function of temperature. The modulus depends both on the method and the time of measurement. Dynamic mechanical tests are characterized by application of a small stress in a time-varying periodic or sinusoidal fashion. For viscoelastic materials when a sinusoidal deformation is applied, the stress is not in phase with displacement. A complex tensile modulus E ) or shear modulus (G ) can be obtained ... 

Figure 6 Elastic modulus as a function of shear stress for the system described in Fig. 5. Aging time was varied from 2-24 h and the shear stress was fixed in 1 mPa.

Figure 8 Elastic modulus as a function of frequency obtained from oscillatory shear dynamic rheometry (see text) performed at the oil-water interface. The proportions of oleic and aqueous phase are the same as described for Fig. 5. Concentrations of 0.25, 0.75, and 1.5% (w/v) B6 asphaltenes were dissolved in the oleic phase (50% yh toluene in heptane) before adsorption. Samples were aged for 8 or 24 h. Shear stress was held constant at 1 mPa.

FIGURE 14. Elastic modulus as a function oftemperature for 10-YSZ/aluminaparticulatecomposites with different alumina contents, determined by the impulse excitation method. ZAO to ZA30 in the figure indicate respective alumina mol% (e.g., ZAO = 0 mol%). 

Figure 3 shovre the nanoindentation data of elastic modulus as a function of maximum indentation depth relative to film thickness ratio (i.e. hmaxAf) of films after sintering at 900-1200 °C. Further data analysis will be discussed afterwards. 

It is evident to find from the table that the elastic modulus increased dramatically with sintering temperature as further densification took place at higher temperamres. For example, the elastic modulus rose nearly fourfold across the whole range of sintering temperatures. Figure 9 further shows the measured elastic modulus as a function of porosity for the as-sintered films. 

FIGURE 36.1. Filler particles with hard core relative increase of the elastic modulus as a function of filler volume fraction for different values of the ratio shell modulus to matrix modulus The ratio between shell (total) and core radius is taken as 4/3. 

Numerical evaluation of kinetic curves was performed using values of Em and Ep appropriate for the para-toluene sulphonate monomer (TS) (20) Ihe effects of lattice mismatch. Fig. 5, and blocking defect concentration on kinetics are similar. Fig. 5. Other parameters calculated were polymer chain length and effective polymer chain elastic modulus as a function of conversion. The values of Y(X),... 

Once highly swollen multiple emulsions have reached pseudo equilibrium between salted droplets and the continuous aqueous phase is achieved, as detailed in Section 2.1, the amount of work W, needed to strain the multiple emulsion is the amount of work needed to increase the surface of both droplets and globules (Michaut et al., 2004b). The elastic modulus as a function of frequency is displayed in Figure 2.6. 

The mechanical properties of elastomeric networks are described within the theory of rubber elasticity, which accounts for the behavior of a network—in fact, its elastic modulus—as a function of its molecular parameters (number of elastic... 

A full description of the mechanical properties of the solution requires a study of its complex elastic modulus as a function of frequency. Such a description has been made in detail for polymer melts in the classic book by Ferry (see also Volume 2, Chapter 8 of this work). We limit our discussion here to the macroscopic viscosity. 

Elongation at break(eA),tensilestrength (cr ), and elastic modulus ( ) as a function of the glass-transition temperature of plasticized poly(lactic acid) (PLA). Plasticizer ( ) poly(ethylene glycol) (PEG) 400 (O) PEG 1.5K (A) PEG 10K ( ) acetyl tri-n-butyl citrate (ATBC) (Baiardo eta ., 2003). 

Fig. 4.25 a Tensile strength and tensile modulus versus diameter and b variations of measured elastic modulus as a function of diameter for poly (2-acrylamido-2-methyl-l-propanesulfonic acid) (PAMPS) nanofibre. Reproduced from Refs. [251, 252], respectively... 

The increase in the elastic modulus as a function of increasing temperature and cross-link density is due to changes in entropy. When the temperature of a... 

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