A history-dependent cohesive zone model in elastic and visco-elastic materials under constant and variable loading. (August 2018) - Hakim, L.
Highlights: Novel non-linear history-dependent generalisation of the Leonov-Panasyuk-Dugdale cohesive zone model of crack propagation. Linearly elastic and visco-elastic materials. CZ history-dependent yield condition used for numerical simulation of the crack propagation under constant and variable loads. After the crack starts, the crack growth rate increases, while the CZ length decreases with time. The time, when the CZ length decreases to zero can be associated with the complete rupture of the body. Unstable crack growth (a jump) at the onset of crack propagation followed by a stable crack growth in some cases. Graphical abstract: Abstract: A history-dependent cohesive zone model approach is used to study the crack behaviour in elastic and visco-elasto materials. The cohesive (yield) stress at the cohesive zone points is related to the nonlinear normalised equivalent stress functional over the stress history at these points, and is expressed in the form of an Abel-type (fractional) integral. We analyse the cohesive zone length evolution in time and the crack tip opening during the stationary crack stage as well as during the propagating crack stage. We consider the external load increasing linearly with time and compare the solution with the case of the constant load. We obtain the solution numerically and analyse the influence of the viscoelasticity by comparing with the case of purely elastic behaviour of the bulk of the material.