13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- was reported in [24, 26, 38]. It is also worth mentioning that the moment stress µ23 in Mode I crack has the sign opposite to the sign of KI. Thus for the conventional Mode I crack the moment stress is negative: the flexure cracks grow in the direction of propagation of the main crack, Figs. 2a, 3a. In the case of anti-crack the direction of flexure crack growth is opposite to the direction of propagation of the main crack, Figs. 2a, 3b. We emphasise that the role of flexure cracks is to initiate the breakage of the cement bonds between the particles, while the ultimate fracture propagation is produced by further particle rotations and particle detachment form the bulk of the material. The beginning of flexure crack propagation and the resulting bond breakage are controlled by microscopic tensile stress on the edge of the bond, which is caused by moment stress µ23. The value of the microscopic tensile stress is determined by the Cosserat continuum stresses σ22 and µ23 acting at a point r=lm of the continuum. In other words this is a superposition of the tensile stress generated by bending (moment stress µ23) and the normal stress σ22. The latter is positive for Mode I cracks and negative for anti-cracks, Fig. 3. It was shown in [29] for Mode II crack that the microscopic tensile stress created by bending can be an order of magnitude higher than the conventional stress applied to the bond. This makes the mechanism based on moment stress the main fracture growth mechanism. µ23! x3 x2 x1 σ22 >0, µ23 <0 σ22! s11 µ23! x3 x2 x1 σ22 <0, µ23 >0 σ22! s11 (a) (b) Figure 3. The directions of flexure crack propagation controlled by the sign of moment stress µ23: (a) Mode I crack; (b) anti-crack.
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