13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- W = We (1) where W, We are the energy of formation of new surfaces (shear cracks) and elastic energy gone to it of the layer, weakened (destroyed) by the cracks net arised, respectively. Somewhat roughenning the real situation, we assume that the fracture pattern is axially periodic Fig. 4 Fig. 5 [24, p. 326] (Fig. 4) and is built of n «petals", each seen from the center of the cavity at an angle 2φn and formed by a couple of cracks emanating from the surface of the cavity at an angle of 450 and directed to each other 2φn = 2π/n, φn = π/n (2) The energy of formation of new surfaces (shear cracks) W = γL = γ·2nΛ (3) where γ is corresponding effective (specific) surface fracture energy (or more precisely, the specific energy of cracking, since there are two surfaces but one crack), L – total length of all the cracks, n – number of petals-sectors formed (2n cracks), Λ – the length of a crack. Taking that fracture occurs along the slip lines and the cracks grid forms a regular pattern like Fig. 4, calculate the total length of cracks ∫ π ϕ= ϕ= = Λ= ⋅ ⋅ n dS L n n 0 2 2 (4) where n is the number of pieces (wedges), cut out by the cracks, φ – polar coordinate, dS – differential of arc length along the crack. As is known, the direction of the maximum shear stresses divides the angles between the principal axes of the stress tensor in two [25, p. 265]. Circular cavity considered is a special case of a tube with an infinite outer radius. The principal stresses in the cross section of the tube are directed radially and circumferentially, the slip lines being inclined to these directions at an angle 450 (Fig.
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