An alternative point of view with regard to understanding the mechanism of energy transfer involved to create new surface is considered in this study. A combination of transport equation and cohesive element is presented. A practical demonstration in 1-D is presented to simulate the mechanism of energy transfer in a damage zone model for both elastic and elastic-plastic materials. The combination of transport and cohesion element shows the extent elastic energy plays to supply the energy required for crack growth. Meanwhile, plastic energy dissipation for an elastic-plastic material is shown to be well described by the transport approach. The cohesive zone model is one of many alternative approaches used to simulate fatigue crack growth. The model incorporates a relationship between cohesive traction and separation in the zone ahead of a crack tip. The model introduces irreversibility into the constitutive relationships by means of damage accumulation with cyclic loading. The traction-separation relationship underpinning the cohesive zone model is not required to follow a predetermined path, but is dependent on irreversibility introduced by decreasing a critical cohesive traction parameter. The approach can simulate fatigue crack growth without the need for re-meshing and caters for constant amplitude loading and single overloading. This study shows the retardation phenomenon occurring in elastic plastic-materials due to single overloading. Plastic materials can generate a significant plastic zone at the crack which is shown to be well captured by the cohesive zone model approach.In a cohesive zone model, fatigue crack growth involves the dissipation of separation energy released per cycle. The crack advance is defined by the total energy separation dissipated term equal to the critical energy release rate or toughness. The effect of varying toughness with the assumption that the critical traction remains fixed is investigated here. This study reveals that varying toughness does not significantly affect the stress distribution along the crack path. However, plastic energy dissipation can significantly increase with toughness. A new methodology called the fast-track method is introduced to accelerate the simulation of fatigue crack growth. The method adopts an artificial material toughness. The basic idea of the proposed method is to decrease the number of cycle for computation by reducing the toughness. By establishing a functional relationship between the number of cycles and variable artificial toughness, the real number of cycles can be predicted. The proposed method is shown to be an excellent agreement with the numerical results for both constant amplitude loading and single overloading. A new approach to predict fatigue crack growth curves is presented. The approach combines the fast-track method and an extrapolation methodology. The basic concept is to establish a function relationship using the curve fitting technique applied to data obtained from preliminary calculation of fast-track methodology. It is shown in this thesis that the new methodology provides excellent agreement with an empirical model. The methodology is limited to constant amplitude loading and small scale yielding conditions. It is shown in the thesis that fatigue crack growth curves for variable amplitude loading can be predicted by using the data set for fatigue crack growth rate for constant amplitude loading. A retardation parameter can be deduced from the number of cycles delayed using the cohesive zone model. The retardation parameter is established by performing calculation for different toughness. This methodology is shown to give good agreement with results from empirical models for different variable amplitude loading conditions.