A B S T R A C T To better understand the crack closure and propagation, an analytical model is established. The residual stress effect on fatigue crack growth equations has been considered using the residual stress intensity factor (SIF) (K res ). The joint geometries, residual stress distributions (s res ) and residual stress ratio (R res ) were considered also. K res are calculated using the analytical weight function (WF) method and different residual stress distributions. It is to be emphasized that the current approach is little investigated. This is because the WF has already been developed to calculate SIF for an existing crack. The current approach calculates K res for the crack that initiates and propagates until failure. Different stress distributions have been used, and R res is defined. The validity of using the WF has been shown. SIF due to applied load (K app ) and applied stress ratio (R app ) have been considered. Fatigue crack growth rate was investigated in accordance with the current approach. The results have been verified and benchmarked. a = Crack length a i = Initial crack length a f = Final crack length A 0 , A 1 and A 2 = Polynomial function of weld size A 0,n , A 1,n , A 2,n , and A 3,n = Polynomial coefficient in Newman's equation BSI = British Standard Institution C ESA , C th = Materials depends constant (NASGRO Equation) da/dN = Crack growth rate f = Newman's effective stress ratio f(a/t) = Geometrical function (crack length/thickness) FAT = Fatigue strength at two million cycles (FAT95%) FAT char , (FAT50%) = The fatigue strength corresponding to 95% survival probability FAT mean , (FAT95%) = The fatigue strength corresponding to 50% survival probability FCG = Fatigue crack growth FEM = Finite element method FNK = Forman, Newman and de Konig IIW = International Institute of Welding K = Linear elastic stress intensity factor (SIF) K app = Applied stress intensity factor K c = Critical stress intensity factor K eff = Effective stress intensity factor K mat (K IC ) = Fracture toughness K max or K max,app = Stress intensity factor due to maximum applied load Correspondence: A. M. Al-Mukhtar.