ICF13B

13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- 2. Statement of the problem 2.1. Main equations Let us consider the polar coordinate system (r, φ) associated with the tip of inclined crack (Fig. 1). The equilibrium equations and the Cauchy relations in the polar coordinate system for the plane strain or stress conditions are [1-3]: 0, 1         r r r rr r rr        0. 2 1        r r r r r        (1) , r ur rr     , 1         u r r ur , 1 2 r u r u u r r r             (2) The constitutive equations for an incompressible material with a power creep law have the following form [1-2]: ij n e ij B s 1 (3 2)     (3) where ij is the strain rate tensor, ij kk ij ij s    (13)   is the deviator of ij  stress tensor, ij ij e s s (3 2)   is the equivalent stress, B is the material constant, n is the index of nonlinearity. The equivalent stress е for the plane stress and the plane strain is calculated as 2 2 2 3          r rr rr e     , 2 2) 3 (3 4)(       r rr e    (4) The strain compatibility equation in polar coordinates, resulting from Eq. (2), has the following form [1-3]: ) 0. ( 2 1 1 ) ( 1 2 2 2 2 2 2                       r rr rr r r r r r r r r r (5) Taking into account Eq. (1), Eq. (3) and Eq. (4), the strain compatibility Eq. (5) can be rewritten in the stress terms for the plane stress (a) and the plane stain (b) conditions as the follows:                                            2 1 1 2 1 1 1 2 2 2 1 2 2 rr n e rr n e r r r r   0 3 2 1 1 1 2 1                                       r n e rr n e r r r r r , (6a)                            rr n e rr n e r r r r 1 2 2 2 1 2 2 1 1       0 4 1 1 2 1                           r n e rr n e r r r r r , (6b)

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