Abstract
We show that the Persson-Brener theory of crack propagation in viscoelastic solids gives a viscoelastic fracture energy factor G/G_0 = 1+f which is nearly the same as the viscoelastic factor obtained using the cohesive-zone model. We also discuss finite size effects and comment on the use of crack propagation theories for “solids” with a viscoelastic modulus that vanishes at zero frequency.Graphical
Highlights
Crack propagation in viscoelastic solids, or at the interface between a viscoelastic solid and a counter surface, have many important applications, e.g., for rubber wear [1], or in adhesion and friction involving rubber-like materials [2,3,4,5,6,7,8,9,10]
In Ref. [17, 18], it was stated that the Persson–Brener theory gives nearly the same result for the viscoelastic factor G∕G0 = 1 + f (v) as the cohesive-zone model
The discussions of finite size effects presented above has assumed that at the onset of pull-off, the viscoelastic solid far from the crack tip is in a fully relaxed state characterized by the low frequency modulus E0
Summary
Crack propagation in viscoelastic solids, or at the interface between a viscoelastic solid and a counter surface, have many important applications, e.g., for rubber wear [1], or in adhesion and friction involving rubber-like materials [2,3,4,5,6,7,8,9,10]. The numerical results for G∕G0 obtained by Greenwood and by Hui et al for the three-element viscoelastic model (see Fig. 1) is nearly the same as predicted by the Persson–Brener theory if one chooses 0 to get the best possible overlap between the two curves (which means using 0 ≈ 3 c ), see Fig. 2 (see Appendix B for the equations used in the calculations) Shifting like this is the only meaningful way to compare the factor G∕G0 between the two theories, because the velocity normalization factor in the cohesive-zone approach depends on the cut-off stress 0 which differ from c (see Appendix A). The adiabatic crack tip radius a0 could in principle be measured using, e.g., an electron microscope
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