Compliance storage

These were calculated using the relationships given in Section (4.6.1). The storage compliance starts from an initial compliance Je given by... 

Note 2 The absolute compliance is related to the storage compliance (5.16) and the loss compliance (Definition 5.17) by the relationship... 

Tan 5, storage compliance, and loss compliance values for these experiments are plotted as a function of time in Figure 8. This transient temperature cycle data illustrates interactions between the dynamic mechanical plasticization and blocking behavior just discussed as well as the epoxy s equilibrium moisture uptake behavior (3), and the temperature behavior of dynamic mechanical properties observed for this epoxy in Figure 2a. Perhaps the easiest comparison to consider involves the relationship between transient temperature cycling data of Figure 8 and the thermal behavior observed for N-5208 epoxy tan 6 data of Figure 2a. 

When the stress is decomposed into two components the ratio of the in-phase stress to the strain amplitude (j/a, maximum strain) is called the storage modulus. This quantity is labeled G (co) in a shear deformation experiment. The ratio of the out-of-phase stress to the strain amplitude is the loss modulus G"(co). Alternatively, if the strain vector is resolved into its components, the ratio of the in-phase strain to the stress amplitude t is the storage compliance J (m), and the ratio of ihe out-of-phase strain to the stress amplitude is the loss compliance J"(wi). G (co) and J ((x>) are associated with the periodic storage and complete release of energy in the sinusoidal deformation process. Tlie loss parameters G" w) and y"(to) on the other hand reflect the nonrecoverable use of applied mechanical energy to cause flow in the specimen. At a specified frequency and temperature, the dynamic response of a polymer can be summarized by any one of the following pairs of parameters G (x>) and G" (x>), J (vd) and or Ta/yb (the absolute modulus G ) and... 

Figure 3.12 (a) Storage compliance ot poIy(n-octyl methacrylate) versus frequency measured at 24 temperatures, given in degrees Celsius, (b) Master curve of J versus reduced frequency (Mj obtained from the data of (a) by time temperature shifting, fc) Temperature-dependence of the shift... 

Owing to the fact that at the glass-rubber relaxation temperature the storage compliance function is an increasing function of temperature, the inequality... 

Let us now proceed with the development of the expressions for the components of the complex compliance function. According to Eqs. (6.23) and (9.11), the storage compliance function is given by... 

Figure 9.3 Double logarithmic plots of the storage compliance function ( ) and the reciprocal of the storage relaxation modulus (O ) for a 40% solution of polystyrene in tri-m-tolyl phosphate.

The approximate value of L(x) can be derived from the storage compliance function J m) following the method outlined to calculate H(x) from G (o)). Thus by taking into account Eq. (9.18), / ((o) can be written as... 

Figure 1 Examples of mechanical spectra of gluten (Olympic x Gabo cross line -jl 7 + 18/-) in water (a) and in deuterium dioxide (b). Temperature 35°C strain amplitude 3%. Filled symbols storage compliance J (co) empty symbols J"(co). The lines represent the fits of the Cole-Cole functions to the high frequency data ...

The compliance can be used instead of the modulus to quantify storage and loss behaviour in viscoelastic solids. The shear storage compliance is defmed as ... 

If, on the other hand, the strain vector is resolved into its components, the ratio of the in-phase strain to stress amplitude (maximum stress) is the storage compliance J (oj) and the ratio of the out-of-phase strain to the stress amplitude is the loss compliance... 

Fig. 7.14 The storage compliance of poly(n-octyl methacrylate) in the glass-transition region plotted against frequency on a logarithmic scale. Left-hand side values obtained at 24 temperatures, ranging from -14.3 °C (bottom curve) to 129.5 °C (top curve) right-hand side the master curve obtained by using appropriate shifts log aj. Note that the horizontal scales differ by a factor of two for the two parts of the figure. (Adapted by permission of Academic Press.)...

In an analogous manner, the steady sinusoidal strain in response to the applied sinusoidal stress of constant frequency is expressed in terms of the (in phase) storage compliance J ico) and the (90° out of phase) loss compliance J co) as... 

Viscoelastic problems can also be considered in terms of the compliance of the system and one can define a storage compliance, =efpos8 (T and a loss compliance, "=e(,sin6/a-j. The energy dissipated per cycle At/ can be determined from... 

The ratio of the stress to the strain is used to define a complex modulus "(iw), the real part of which is the storage modulus and the imaginary part the loss modulus, i.e., E ( )=E+ E. Alternatively, one can define a complex compliance < (iw) as the ratio of the strain to the stress. For this case, real part is the storage compliance and the imaginary part is the negative of the loss compliance (note that E = l/d> ). 

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