13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- Figure 2. Elliptical crack model used by Shin and Cai [6] The fitting of the results provides a three-parametrical expression which is defined as a function of the coefficients Mijk for tension with free sample ends [11], i.e., unrestrained bending during tension, i j k 2 7 2 ijk 0 0 0 i j k a a x Y M b D h (3) and the coefficients Nijk for bending [11], i j k 2 6 2 ijk 0 0 0 i j k a a x Y N b D h (4) 2.3. Dimensionless Compliance Experimentally the geometrical evolution of the crack front in a cylindrical bar can be observed post mortem (once fractured) and there are several techniques to mark the front according to the material studied. It is possible to relate the crack front geometry with compliance, one of the few characteristics which can be measured during the crack propagation [15]. If tensile load is applied, it is obtained that the local displacement u is related to the applied force F through compliance as follows: u λF (5) If bending is applied, in this case the angle φ is related to the applied moment M through compliance as follows: φ λM (6) The strain energy U can be expressed taking into account the equivalence between the energy release rate G and the stress intensity factor in plane strain K, 2 2 (1 ) d d d K ν U G A A E (7) where v is the Poisson coefficient and dA the differential of the cracked area. On the other hand, the strain energy for a cracked bar subjected to tensile load is, introducing the value du from eq. (5), 2 1 1 d d d 2 2 U F u F λ (8)
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