13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- potential at the notch root, Mises' equivalent stress concentration factor Kt eq is defined by Eq. (1) where σxN , , τzxN are the stress components of the nominal condition and σxNR, , τzxNR are those of the notch root. Moreover, Eq. (2) that has been rewritten by principal stresses is obtained by dividing Eq. (1) with Kt eq . Then, the principal stresses σiNR (i=1-3) are already not those arising actually at the notch root but those of which nominal values σiN (i=1-3) are expanded to the same potential level as the notch root has. After all, the principal stress of the un-notch condition where the potential is equal to that of the notch root is given by σiNR (i=1-3) in Eq. (3). The difference in the stress path of the nominal condition (magnified by Kt eq ) and the notch root condition is disregarded in the present method. As it is mentioned in the following section 2.3, such disregard does not affect the correspondence between fatigue strength of the notch and un-notch condition. Kt eq = σeqNR σeqN = 1 2 ( ) σxNR − σyNR ( ) 2 + σyNR − σzNR ( ) 2 + σzNR − σxNR ( ) 2 +6 τxyNR 2 + τ yzNR 2 + τ zxNR 2 ( ) 1 2 ( ) σxN − σyN ( ) 2 + σyN − σzN ( ) 2 + σzN − σxN ( ) 2 +6 τxyN 2 + τ yzN 2 + τ zxN 2 ( ) = 1 2 ( ) Kt x σxN − Kt y σyN ( ) 2 + Kt y σyN − Kt z σzN ( ) 2 + Kt z σzN − Kt x σxN ( ) 2 +6 Ktsxy 2 τ xyN 2 + K ts yz 2 τ yzN 2 + K ts zx 2 τ zxN 2 ( ) 1 2 ( ) σxN − σyN ( ) 2 + σyN − σzN ( ) 2 + σzN − σxN ( ) 2 +6 τxyN 2 + τ yzN 2 + τ zxN 2 ( ) (1) 1= σeqNR Kt eq σeqN = 1 2 ( ) σ1NR − σ2NR ( ) 2 + σ2NR − σ3NR ( ) 2 + σ3NR − σ1NR ( ) 2 1 2 ( ) Kt eq σ1N − Kt eq σ2N ( ) 2 + Kt eq σ2N − Kt eq σ3N ( ) 2 + Kt eq σ3N − Kt eq σ1N ( ) 2 (2) ∴ σ1NR = Kt eq σ1N , σ2NR = Kt eq σ2N , σ3NR = Kt eq σ3N (3) One example of the process of the cyclic plastic-adaptation at the notch root of material subject to cyclic torsion is shown in Fig.2, where plane stress is assumed. The segments ab and cd show the stress path of the nominal condition and the expanded one of the un-notch condition of which the potential is equal to the notch root, respectively. The segment ef shows the stress path where the Fig. 2 Illustration of the graphic method of how to estimate REQ and σmeanEQ (cyclic torsion)
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