13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- Table 1. The mixity parameter and crack orientation α, º 0 5 10,5 18 27 Me 1 0,75 0,5 0,25 0 Determination of KI, KII, Txx, Tzz The evaluation of the stress intensity factor (SIF) is based on the well-known approach that includes the calculating of the SIF in a number of points (at varied r) using relations obtained from Eq. (1): ( ) ( ) π θ π θ π θ π θ θ σ σ π σ σ σ π =+ =− =+ =− = − = − − = | | 8 , | | | 2 2 0 xx xx II xx xx xx I r K r K , (3) and extrapolation of the obtained values of the SIFs to the point r=0. The computational procedure considers the nodes of the finite element mesh as the calculation points, but the nodes are located at some small distance from the crack front. To obtain the distribution of the SIF along the crack front, this procedure is used for a number of planes (x0y) orthogonal to the crack front. Their location is characterized by local coordinate s along the front and starts from the center of the crack front. To assess the accuracy of the values of SIF, the comparison of magnitudes of the J-integral, calculated as contour integral (Eq. 4a) and based on the known relationship (Eq. 4b), has been done. ∫ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − = Г i j ij ds dy du J W x y dx nσ ( , ) (4a) ( ) [ ] III II I K K K E J υ υ + + + − = 1 1 (4b) The calculation of the Txx- and Tzz-stress is performed using the stresses in the points on the crack surface: [ ] [ ] π θ π θ π θ π θ σ σ σ σ =+ =− =+ =− + = + = zz zz zz xx xx xx T T 2 1 2 1 (5) The determination of Txx Tzz is similar to the procedure for SIF including extrapolation to the point r=0. The special macros that carry out the automatic computation of the SIF, J-integral and T-stresses (on referred above relations) along the crack front are created in ANSYS environment. Estimation of the accuracy of the numerical model and computational procedures is based on comparison of the calculated values of the SIF and the T-stresses with one presented in [7] for the СССВ-specimen in case of R=50 mm, b=0,8, l=1/3. Comparison of the results shows that there is good coincidence and only in some cases the relative difference is close to 10%.
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