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A B S T R A C T The maximum crack opening displacement is introduced to investigate the effect of compressive loads on crack opening stress in tension-compression loading cycles. Based on elastic-plastic finite element analysis of centre cracked finite plate and accounting for the effects of crack geometry size, Young's modulus, yield stress and strain hardening, the explicit expression of crack opening stress versus maximum crack opening displacement is presented. This model considers the effect of compressive loads on crack opening stress and avoids adopting fracture parameters around crack tip. Besides, it could be applied in a wide range of materials and load conditions. Further studies show that experimental results of da/dN À ΔK curves with negative stress ratios could be condensed to a single curve using this crack opening stress model.Keywords compressive load effect; crack opening stress; finite element analysis; maximum crack opening displacement; tension-compression loading. N O M E N C L A T U R Ea = initial half crack length E = Young's modulus k = slope K max = maximum stress intensity factor K op = crack opening stress intensity factor L = half-length of plate L e = the smallest element size in crack tip n = strain-hardening exponent of material R = stress ratio, R = σ min /σ max r y = crack-tip plastic zone size r p = crack-tip forward plastic zone size u max = maximum crack opening displacement corresponding to σ max (MCOD) u min = maxmum crack opening displacement corresponding to σ min W = half-width of plate ΔK eff = effective stress intensity factor range ΔK = stress intensity factor range Δu = variable quantity of maximum crack opening displacement (VMCOD) σ op = crack opening stress (COS) σ s = yield stress σ max = maximum stress in the cyclic tensile load, which is positive σ min = minimum stress in the cyclic tensile load, which is negative σ op_0 = crack opening stress when the remote applied minimum stress is zero ν = Poisson's ratioCorrespondence: Y. Huang.