13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- 7. The non-zero relative rotations between P0 and principal particles were twists as expected from Eq. (12) and the magnitude shown in Fig. 7 is the twist of the particle in direction X1. It is seen that this is 3-4 orders of magnitude smaller that the relative rotations between P0 and octahedral particles. The latter were found to be bend-type rotations only, conforming to Eq. (12), and suggesting that the only moment springs activated are the bending springs in the octahedral direction with stiffness Kb o. The magnitudes of the bend-rotations of octahedral particles were found nearly independent of particle size. These results suggest that for the case of pure twist, the elastic strain energy is accumulated in the shear and bending springs in the octahedral direction only, and one can calibrate a linear combination of Ks o and Kb o, which should depend on the cell to particle size ratio. From this perspective the results support the analytical derivations in [16], where pure twists do not contribute to the elastic energy. From here, it can be speculated that the torsion springs in the principal directions could be omitted from the site-bond model, i.e. Kt p = 0. This should be supported by considering other cases with curvature-free displacement fields which introduce twists of principal particles according to the theory. Figure 7. Relative rotation vs size ratio under pure twist The cell energy dependence on for the case of pure bending is shown in Fig. 8. The effect of particle size is smaller than in the case of pure twist, but not negligible. The relative displacements between P0 and the octahedral particles were non-zero axial and tangential, conforming to Eq. (13). The relative displacements between P0 and the principal particles also conform to theory with non-zero axial for particles in X2, non-zero tangential for particles in X1 and zero displacements of particles in X3. This means that the activated linear springs in the site-bond model would be axial and shear springs in all octahedral directions with stiffness coefficients Kn o and Ks o, and axial and shear springs in two principal directions with stiffness coefficients Kn p and Ks p. The calculated relative rotations of the particles are shown in Fig. 9. The only non-zero relative rotation of principal particles was found to be the bend-type rotation of the particles in X1, conforming to Eq. (14). However, this relative rotation was found at least an order of magnitude 1.E‐07 1.E‐06 1.E‐05 1.E‐04 1.E‐03 1.E‐02 0 5 10 15 Magnitude of relative rotations Cell size / Particle size Principal Octahedral
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