13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- 3.2. Primary equations at the onset of formulation and their modification (Domain II) The fatigue strength diagram is formulated first for the prototype notch of the domain II ( ρt ≥ L0 ), where the notch size effect is not taken into consideration. In the following section 3.3, the equation is developed into a general form including the short-crack-like notch of the domain IV ( ρt < L0 ), where the notch size effect is taken into consideration. Primary equations that become a starting point of formulation are as follows, where Eq. (9) is quoted from Ref. [8]; ΔσNR ( ) w1 =C1 1− REQ ( ) γ , (Fatigue strength σw1) (9) ΔσNR ( ) w2 =C2 1− REQ ( ) . (Fatigue strength σw2 ) (10) Eq. (10) is rewritten by using the conversion expression of Eq. (8), as follows; σmaxN ( ) w2 =C2 . (Fatigue strength σw2 ) (11) Eq. (12) is adopted as an asymptotic equation of Eq. (9) on σw1, so that the ultimate strength of material SU may be gradually approached with an increase of the value REQ; σmaxN ( ) w1 = SU i.e. ΔσNR ( ) w1 = SU 1− REQ ( ). (12) Solving Eqs. (9) and (12) about 1− REQ ( ) and susequently transposing those algebraic sum to new 1− REQ ( ), Eq. (13) can be expressed; ΔσNR ( ) w1 =C1 1− REQ − ΔσNR ( ) w1 SU ⎧ ⎨ ⎪ ⎩⎪ ⎫ ⎬ ⎪ ⎭⎪ γ . (Fatigue strength σw1) (13) Eq. (13) is a very important as the expression which not only improves the precision for calculating the fatigue strength σw1 but also explains how the tensile strength of material SU relates quantatively with σw1. The equation expresses that the SCF-criterion ( Kt -criterion) is materialized for σw1 by using the equivalent cyclic stres ratio REQ. On the otherhand, for the fatigue strength σw2 , Eq. (10) and (11) is used in a form as it is. It should be noted that, at this stage, γ, C1 and C2 are not material constants but variables. Strictly speaking, C1 includes free boundary correction and C2 includes a function of the notch depth t . 3.3. The equations generalized by incorporation of notch-size effects (Domain IV) The factor of a notch size effect is incorporated into the euations derived in the foregoing paragraph. The judgement whether it is necessary to take the notch size effect into consideration or not is performed according to the value of a notch size ρt . In the present study, the value of ρt = L0 is selected as the critical value as shown in Fig. 5. As it is mentioned in the foregoing section 3.1, the fatigue strength σw1 depends on the notch size ρt and the fatigue strength σw2 does on the notch depth t . Therefore, the size factors FS1 and FS2 are introduced in the forms of the functions of ρt and t , respectively;
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