On the effect of loading conditions on viscoelastic crack propagation in a thin beam

Crack growth in viscoelastic materials is often assumed in an experimental form known as Gent-Schultz for which the velocity of crack propagation is some power law of the applied strain energy release rate. The power coefficient is often believed to be related to material properties alone, and this gives some bounds to its value. However, we show with a simple Maxwell material model that for a thin Double Cantilever Beam loaded by a shear force that the crack velocity power law depends significantly also on the loading conditions: indeed, for not too large crack sizes, the velocity can be proportional to the power 2.5 of the force (a result already found by Wang et al. for thin beams under concentrated remote moments), or to power 5 for larger forces. For a constant load, a small crack would accelerate passing from one regime to the other, until eventually elastic fracture limit is found, which depends only on the instantaneous elastic modulus, while the speed depends only on viscosity. This may explain why the power law coefficient has experimentally been found to be outside the range of the classical theories of viscoelastic crack propagation.