Effects of finite thickness on crack propagation in viscoelastic materials

Crack propagation in viscoelastic materials is a problem of considerable importance, now relatively well understood after early paradoxical results have been addressed with the use of cohesive models. However, finite size effects have received limited theoretical attention so far. Here, following suggestions of Persson (2017), we derive simple results for a crack propagating in a finite size specimen for a model of a single relaxation time material (but extension to many relaxation times is trivial). We show results for the maximum velocity above which the crack may become unstable and the toughness enhancement reduction with respect to that of the infinite system, which corresponds to the ratio of instantaneous to relaxed elastic moduli. Agreement with the literature is dubious, since de Gennes (1996) predicts instability but same amplification as the infinite system, whereas a more recent theory of Persson (2021) suggests same amplification of that of the infinite system, but without instability. A clarification of these qualitative differences is hoped for the future.