William-Landel-Ferry Transform

There are several analytical tools that provide methods of extrapolating test data. One of these tools is the Williams, Landel, Ferry (WLF) transformation.14 This method uses the principle that the work expended in deforming a flexible adhesive is a major component of the overall practical work of adhesion. The materials used as flexible adhesives are usually viscoelastic polymers. As such, the force of separation is highly dependent on their viscoelastic nature and is, therefore, rate- and temperature-dependent. Test data, taken as a function of rate and temperature, can be expressed in the form of master curves obtained by WLF transformation. This offers the possibility of studying adhesive behavior over a sufficient range of temperatures and rates for most practical applications. Fligh rates of strain may be simulated by testing at lower rates of strain and lower temperatures. 

Initially, a line was constructed for each graph that passed through the points. For analysis of the data, the form of the curve drawn is not important as the Williams Landel Ferry (WLF) transform uses the data points and the parameters for the Arrhenius plot are extracted from the graphs manually, when the best fit can be estimated by eye. 

Adhesion is not an intrinsic property of a materials system, but is dependent on many factors. By now it should come as no surprise that the measurement of adhesion is sensitive to both rate and temperature as all of the other mechanical properties have been. In fact, adhesion can often be transformed by the WLF (Williams, Landel, Ferry) equation or Arrhenius transformation in the same maimer as modulus and other properties. Figure 11.7 shows the transformation of isothermal peel data transformed into a master curve along with the polyester adhesive s shear and tensile strength properties. In another study investigating the effect of temperature and surface treatment on the adhesion of carbon fiber/epoxy systan, five epoxy systems were found to fit an overall master curve when corrected for the material T. This result is quite remarkable and is shown in Fignre 11.8. 

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