PSI - Issue 37

L.V. Stepanova et al. / Procedia Structural Integrity 37 (2022) 908–919 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

914

7

( ) , rr r   at

component 1 p M = and

0  = has discontinuity whereas for the cases of pure mode I and pure mode II loadings when

0 p M = are valid the radial stress component is continuous at 0  = . Numerical analysis carried out previously for mixed-mode crack problem under plane strain conditions leads to the continuous angular distributions of the radial stress component ( ) , rr r   at 0  = (Stepanova and Yakovleva (2015), Stepanova and Yakovleva (2016)). Thus, one can compute the whole set of eigenvalues for plane stress conditions from the continuity requirements of the radial stress components on the line extending the crack. In accordance with the procedure proposed the spectrum of the eigenvalues  is numerically obtained. Results of computations are shown in Tables 5,6 where the new eigenvalues  computed and the values of the functions ( 0) f   = , ( 0) f   = , ( ) f    = − ( ) f    = − numerically obtained for the different values of the mixity parameter p M and the creep exponent n are given. The angular distributions of the stress components for different values of creep exponent n and for all values of the mixity parameter p M are shown in Fig. 3-5. The method proposed has been applied to nonlinear eigenvalue problems arising from the problem of the determining the near crack-tip fields in the damaged materials.

Fig. 3 . Circumferential distributions of the stress components in the vicinity of mixed mode crack tip (plane stress conditions).

Fig. 4. Circumferential distributions of the stress components in the vicinity of mixed mode crack tip (plane stress conditions).