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The effect of two singularity fields.the HRR solution and a modified form of Rices solution for anti-plane shear, are investigated in the present study to discuss a former fatigue crack growth (FCG) model based on energy balance during growth of the crack.A function which can demonstrates the effect of different types singularity fields is included in the crack propagation model which can predicts the stage-Ⅰ and stage-Ⅱ FCG behavior independently from the basic low cycle fatigue properties.Good agreement between experimental and theoretical results is obtained.