A unified formulation for fatigue crack onset and growth via cohesive zone modelling

Abstract

This paper presents a unified cohesive zone formulation for describing the fatigue-driven crack onset and propagation in quasi-brittle materials. This approach is based on formulating a modified traction-displacement law involving linear softening, which accounts for the onset of fatigue failure described by materials S-N curves. The fatigue crack propagation in a steady-state regime is described as a sequence of initiation stages that progressively take place within the process zone ahead of the “zero-stress” fracture tip. It is demonstrated that the damage distribution within the process zone under cyclic load is governed by a non-linear Fredholm integral equation of the second kind, which is solved numerically using an iterative scheme. It is also shown that the Paris-Erdogan law for fatigue crack growth can be directly obtained from engineering S-N curves via the linear traction displacement model introduced here. The Paris-Erdogan propagation regime is attained when the crack propagation rate is much smaller that the length of the process zone. The exponent of the Paris-Erdogan law is equal to half the inverse of that characterising the material S-N curve. The main advantage of the cohesive zone model introduced here is that it does require neither ad-hoc additional parameters nor calibration constant to obtain the Paris-Erdogan law from material S-N data. It is also proved that the cohesive zone length in fatigue depends on the exponent of the S-N curve and it always shorter than its static counterpart. The unified cohesive zone model is validated against experimental data for the specific cases of mode I and mode II fatigue delamination growth in the carbon/epoxy composite material IM7/8552. Finally, an analysis of the role played by size effects is presented, with emphasis on the influence of the laminate thickness on the fatigue damage accumulation within the process zone and the ensuing propagation rates of cohesive cracks.