13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- The simple bar hypothesis was firstly proposed for determining the J integral [4]. Then it was used in the research of relationship between J integral and fracture surface average profile [6]; and relationship between J integral and COD [7] respectively. Results in these researches verified the validity of the proposed simple bar hypothesis. Based on the hypothesis, a new method for determining the applied loads of fractured specimens during the course of failure will be proposed and experiments will be performed to verify it. It is well known that, by means of Mises yield criterion, for the Mode stress field, the boundary Ⅰ of plastic zone around crack tip for plain strain [8] can be expressed as Eq. (1) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + = Ι 2 (1 2 ) 3sin 2 cos 2 ( ) 2 2 2 2 2 θ ν θ πσ θ y K r . (1) where KΙ is the stress intensity factor and ν is the Poisson’s ratio. In plastic zone, the distribution of strain component that perpendicular to fracture surface is ( ) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ′ + + ′ + ′ = Ι 2 3 sin 2 (1 ) (1 )sin 2 cos 2 2 1 ( ) θ θ ν ν θ π ν ε r G K y . (2) where ν ν ′ = and (1 ) ν ν ν ′ = − for plain stress and plain strain respectively, G is shear modulus. Introduction of Eq. (1) into Eq. (2) leads to Eq. (3) ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ′ + + ′ + ′ − + = 2 3 sin 2 (1 ) (1 )sin 2 2 (1 ) (1 2) 3sin ( ) 2 2 θ θ ν ν θ ν ν σ ε G y y , (3) where yσ is the yielding stress. It is clear that, on the boundary of plastic zone, for certain material, ( )y ε is only relative to θ. And for 2 θ π = , ( )y ε can be represented as Eq. (4), ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ′ − + ′ − + = 2 2 3 2 3 ) (1 2 ) 2 (1 ( ) 2 2 ν ν ν σ ε π G y y . (4) Boundary of upper surface Boundary of lower surface Upper surface Lower surface ijδ Fatigue pre-crack Figure 1. Division of plastic deformation on cross-sectional plot
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