13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- In the plane stress (b) and plane strain (c) cases, the development of the main crack follows very different patterns. The parallel increase of normal to the first loading axis and octahedral surfaces in plane stress, Fig. 5(b), seems to be responsible for the immediate development of damage-induced anisotropy, which after that appears to be moderated by the development of surfaces normal to the second loading axis. The constraint in plane strain, Fig. 5(c), leads to a delayed but rapid increase of surfaces normal to the first loading axis together with a lower rate of creation of octahedral surfaces. This appears to delay substantially the development of cracked surfaces normal to the second loading axis and results in significantly higher anisotropy. It should be noted that the structure-damage relations reported here were found qualitatively independent of the random assignment of pores in the lattice model as well as of the shape parameter of the pore distribution. This has been confirmed by a number of simulations with different shape of distribution and random assignments. One parameter that may affect the outcomes is the shear to normal strength ratio; this is a subject of ongoing work. It is further understood that the outcomes reported here are principally related to the selected lattice connectivity. However, the detail to which the surface topography can be studied is higher than the detail allowed by models based on cubic lattices. One unknown in the analysis is whether the crack development in the lattice is energetically equivalent to the development of continuum cracks. This question remains to be addressed in a future work. The current observations suggest that a common, constraint independent, damage evolution law might not be feasible to achieve. In such case it seems that a lattice-based analysis might be necessary as a sub-modelling approach to inform the behaviour of finite elements in a continuum model. The last question of interest in this work is related to the use of the weakest-link statistics for global failure predictions. It was suggested in [16] that weakest-link should be applied to the population of micro-cracks in the system. However, from the simulations performed here it is evident that a single crack, the maximal connected component of the cracked surface, becomes rapidly dominating the behaviour, Fig. 4(b), with few much smaller components disconnected from the main crack. This does not allow for invoking the weakest-link as a descriptor of final failure. Figure 6. Probability density of pore sizes in the lattice (a) and in the maximal component at failure for three loading cases (b)-(d). Results obtain with the same distribution given by (a).
RkJQdWJsaXNoZXIy MjM0NDE=