5 s t E y K σ δ ⋅ Δ Δ = 2 2 2 2 (9) 2 2 2 2 2 2 2 2 λ σ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⋅ Δ = × × s pv eff E y K B v dN da , ) ( /m cycle , ( 0) = mσ (10) Here for s σ σ< ，and under the symmetrical cyclic loading ( 1 / max min =− = δ δ δR )， pv s eff eff v E K B ⎟⎟ × ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⋅ = − 2 2 2 2 2 λ σ (11) But for 1 / max min ≠− = σ σ σR (or 1 / max min ≠− = δ δ δR ), for 1=β , the parameters mδ in equations (6) should be also changed as follow forms, pv c s eff eff v K K K E K B × ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + × − ⋅ = − 2 2 1 2 1min 2 1max 2 2 2 1 2 2 λ σ (12) c th eff K K K1 ≈ or c eff K K 1 (0.25 ~ 0.55) ≈ (13) Where eff K is an effective stress intensity factor, th K is threshold stress intensity factor. 1max K and 1min K are respectively the Maximums and minimums value of stress intensity factor. Eis a modulus of elasticity. In fact the (12) is consistent with (6). (2) The calculation methods used by the stress σ For this method, the comprehensive material constant eff B2 and the crack tip open displacement tδΔ range in the crack propagation rate equation are all to use the stress to express. Here the crack tip open displacement tδ and tδΔ are as below [10] ( / ) / ,( ) 2 2 2 a E m y t s s σ σ πσ δ = (14) Under cyclic loading, and for stress ratio 1 / max min =− = δ δ δR , the crack tip open displacement
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