Fracture energy master curves

Fracture energy master curves were determind as a function of nearly equivalent ranges of reduced crack velocity (King and Andrews), and extension rate (Swetlin). In both cases, T was used as the reference temperature. King and Andrews master curves were obtained using the WLF Equation and the universal constants, while Swetlin s master curves were determined via numerical best-fit shifting. 

It was found that both normalizations yielded tear energy master curves over all the test temperatures investigated for all but the most highly crosslinked 828/DDS network. The fact that master curves can be generated over the entire range of test temperatures shows the important role that M,. plays in the rubbery fracture of these highly crosslinked epoxies. 

Fig. 1. Master curve of fracture energy G against reduced test rate (daj) for SBR and for adhesion bonds between SBR and various pol3mer substrates. After Andrews and Kinloch ...

For a rubber adhesive, Gent found that he could use the WLF equation to obtain a master curve of breaking stress (see Viscoelasticity - time-temperature superposition). He used a Fracture mechanics analysis to link the breaking stress to critical strain energy density. 

Mazich et al. utilized the pure shear fracture test to generate master curves of threshold fracture energy for polydimethylsiloxane polymers as a function of crosslink density [40]. Their data compared well with recent data from Gent and Tobias [39]. 

After superposition, the results form a master curve, Fig. 32, giving the fracture energy at any desired temperature (in this case Tg) as a function of the equivalent rate of peeling at that... 

Firstly, the values of at calculated from the WLF equation yield a good master curve for data measured over a wide range of temperatures and rates. Secondly, at lower temperatures and higher rates than those shown in Fig. 7.17 the adhesive becomes glassy and the hysteresis and the fracture energy fall -the value of Gc typically being 100 to 1000 J/m. Thirdly, the rate-temperature dependence of the fracture energy may be modelled by Equation 7.8, namely ... 

Figure 7.17 Master relationship for adhesive fracture energy, Gc, versus effective rate, aax, of crack propagation. The points for each curve represent data from various test rates and temperatures [16] O, Gc for cohesive fracture of crosslinked SBR , Gc for fracture of crosslinked SBR/etched fluorinated ethylene-propylene copolymer joint , Gc for fracture of crosslinked SBR/treated fluorinated ethylene-propylene copolymer joint T, Gc for fracture of crosslinked SBR/poly(ethylene terephthalate) joint. 

Figure 7.18 Master relationship for the adhesive fracture energy, Gc, against effective rate of crack growth, aaT, for an uncrosslinked SBR/poly(ethylene terephthalate) joint. The different symbols represent different test temperatures from -35 to + 60 Broken curves denote the extreme values when unstable, stick-slip peeling occurred [138].

Figure 22 Fracture energy versus annealing time measured on notched samples forthe three polymers of Figure 21 that differ in molecular weight, and the master curves constructed thereof. In shifting the curves, the activation energy of Figure 21 is used.

---