Tau lag

In Eq. (16), the time constant is called the tau lag it depends on the particular instrument used. Moreover, Eq. (16) follows directly fl om Eqs. (9)-(12) with dTJdt = dTIdt, the latter being the applied thermal rate. The value of the tau lag constant is usually provided with the DSC equipment. However, this time constant can be optimized experimentally by repeating the same measurement... 

The tau lag constant (x ) must therefore be replaced with the x value. Greater details about this topic are given later. The main problem relates to the availability of a standard for the system as a whole. 

I. Calibration of Thermal Lag In the Mettler Toledo DSC to compensate for thermal lags, an adjustment, denoted by Mettler Toledo as tau lag, is used. The DSC tau lag performs two compensations (1) it matches the program temperature to the reference temperature (as noted in Fig. 2.17), and (2) it adjusts for the heating rate as noted in the following equation ... 

Figure 2.17. Temperature-time profile of the Mettler DSC before and after compensation for the thermal lag. In the figure, = furnace temperature, 7 = reference temperature, Ts = sample temperature, = program temperature, = melting point, ATiag = extent that reference temperature lags behind furnace temperature, and tiag = tau lag compensation of the furnace temperature. The tau lag compensation synchronizes the program temperature with the reference and sample temperatures. [From Mettler Toledo (2004) courtesy of Mettler Toledo.]...

Figure 2.18. Melting points or extrapolated onset calibration temperatures for tau lag adjustment factor after compensation as a function of heating rate. The extrapolated onset temperatures (Tinset) are determined from calibration standards note that there is no change with heating rate after the tau lag compensation has been applied. [From Mettler Toledo (2004) courtesy of Mettler Toledo.]...

Process is a first-order lag with time constant tau=IO minute,... 

Determination of Tau and Tfu on the basis of the fibre pull-out load vs. fibre displacement curves requires identification of the characteristic points on the curves, as discussed in Section 3.2.5, using shear lag and frictional shear equations to calculate Tau and Tfu. Laws [15] has pointed out the limitation of such an approach, which requires the use of a value of Gm which is the shear modulus of the matrix in the interfacial zone. Since the matrix in the interfacial zone is different from the bulk matrix (see Chapter 2), the shear modulus of the bulk matrix should not be substituted for Gm-... 

It is interesting to note that when the same results are analysed by different models (Gray s results in Table 3.2), the characteristic values obtained are usually similar. This should not come as a total surprise, since the different models are based on the same concepts shear lag combined with frictional resistance. It should also be noted that tau reflects local adhesional strength calculated on the basis of shear stress concentration profiles derived by various models, whereas zfu is an average value. Therefore the tau values can be quite high, and exceed the tensile strength of the matrix. 

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