13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- ( ) ( ) 2 2 2 2 4 1 1 2 1 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + − = I p I I s c E ν σ γ E π r σ ν ε π . (18) The square-root factor in Eq. (18) replaces the exponent of plastic strain in the modified Griffith criterion used previously [2-14]. As before, it is intended to account for the reduction in crack driving force due to plastic dissipation in the matrix. The difference is that in the case of Eq. (18) the effect is not only dependent on the plastic strain but also on stress triaxiality via the ratio between the maximum plastic strain and the maximum stress. 2.4. FE model The developed LA has been applied to an FE model of Pre-Cracked Charpy-V (PCCV) specimens used in the tests [21]. These were 30 mm thick, 200 mm long and 25.4 mm deep. Here, this is modelled in 2D under plane strain conditions. Crack depth was 12.7 mm representing high constraint conditions. Rigid loading rollers were positioned with a total span of 180 mm (i.e. 10 mm from the specimen edge) and at the crack back-face. The FE model, with account for symmetry, was created and analysed with ABAQUS 6.11 [24]. The crack tip region was modelled as a fine blunt notch with a radius of 25 μm for use in large strain analyses. The crack tip elements were 5 μm long and 0.6 μm wide. In total 34,000 CPE8R elements were used. Model illustration is given in Fig. 1. Figure 1. FE Model of 3PB specimen We considered a range of temperatures in un-irradiated and irradiated states, spaced between approximately ±60oC of the un-irradiated T0 in a maximum of 10 oC increments. Power-law stress-strain relation was used to describe material behaviour at each temperature, such that ε = σ /E for σ < σ0, and ε = ( σ0 /E) ( σ / σ0) n for σ > σ 0, where E was determined from Eq. (6) and σ0 was determined from Eqns. (7) or (8). The power law exponent, n, was found using the Considère’s rule describing the stress-strain condition at the point of loss of stability, represented by σu. Loading was applied by displacing the bottom loading pin into the specimen whilst preventing the top pin from moving. It was also necessary to apply boundary conditions to the loading pins to prevent free rotation and unwanted displacement. Standard contact was used with a small adjustment of 0.015 mm to the mesh around the rigid surface of the loading pins to ensure correct transference of the load. The contact was also modelled as having no separation, ensuring contact throughout the analyses. Large strain analyses were performed in all cases.
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