For the industry of pipe-laying, the propagation of a crack can finally lead to failure of the structural components. This may cause catastrophic consequences for environment, economy and even lives of people. Therefore, the mechanical assessment of crack-like defects is of great importance in engineering practice. For non-linear problems, application of cohesive zone models (CZM), as an alternative approach, has become more and more popular over the past two decades or more. From different respective to fracture mechanics, the concept of CZM regards the fatigue crack process as a result of material deterioration with damage concentrated at the cohesive zone. As a essential part of the CZM, several Traction-Separation Law (TSL) has been developed. Needleman proposed an exponential TSL in 1990 to describe micro damage. This model has been applied for parameter calibration for metals such aluminium [and stainless steel. There application for pipeline steel, specifically X65 is yet to be explored. From literature, similar simulation has given suggestions for the cohesive parameter calibration for structural steel. The commercial software ABAQUS has provided a triangle-shaped TSL. It is interesting to study about the feasibility of the provided triangle TSL in simulation of crack propagation in pipeline steel under monotonic and fatigue loading. Will the cohesive parameters calibrated depend on the choice of TSL? If yes, to what level will the difference be and what is the reason for this? On the other hand, through a series of parametric study and comparison with experimental data, it is necessary to have a deeper understanding on the influences of the cohesive parameters on the crack propagation applying the triangle-shaped TSL. Also there is a debate on whether the initial stiffness will place an effect on the simulation on the crack propagation and this issue is also addressed in this project. Meanwhile, in recent two decades, cohesive zone model has also been adapted for fatigue simulations, referred to as the cyclic cohesive zone model. Specifically, Silitonga et al applied a cyclic cohesive zone with a certain damage accumulation model to simulate the fatigue crack propagation in Aluminum specimens via a Subroutine UEL. Also they managed to show the potential of cyclic CZM in predicting overload effect by looking into the decreasing interface separation. However, this model considered only separation with positive values and so as the applied load. While the plasticity induced crack closure effect could have an impact on the fatigue crack propagation, a numerical simulation accounting for this effect involves a separate implementation of a contact algorithm for loading cases with overclosure of the crack interfaces. In this project, a variety of load cases including compression is considered while implementing the user element in to the ABAQUS code.