Calculation of macroscopic fracture parameters from given microstructural properties represents a fundamental problem of micromechanics of brittle and quasibrittle materials. As proposed before, the macroscopic fracture energy can be obtained according to the size effect method. The method can also be used to determine the dependence of the mean macro-fracture energy on the microscopic properties, such as the coefficient of variation of the microstrength of the interparticle links, and the microductility of these links.
The size effect method can further be used to determine the effective process zone size of a particle system and its dependence on the aforementioned microscopic properties.
The ratio of macro-fracture energy to the fracture energy of idealized square lattice of particles for straight-line fracture parallel to a lattice line varies approximately from 1 to 3. The effective process zone size varies approximately from 0.5 to 2 times the average interparticle distance.
At constant average microstrength and microductility, the macro-fracture energy is proportional to the average particle spacing. It decreases with increasing coefficient of variation of microstrength (or micro-fracture energy) and increases with increasing microductility. The latter increase however weakens with increasing coefficient of variation of microstrength. It follows that in order to manufacture a quasibrittle material of high fracture energy, the material properties should be as uniform as possible and the size of inhomogeneities as large as possible while at the same time the microductility should be maximized (e.g., by inhibiting sudden formation of large microcracks).
An efficient solution algorithm for the response of the particle system is required. Using a bilinear force-displacement diagram for each link, such an algorithm is obtained by (1) using variable loading step from one change of status of interparticle link to another, and (2) replacing changes of the stiffness matrix due to particle link breaks by inelastic forces, which makes it possible to use the initial elastic stiffness matrix.
The particle simulation should be helpful especially for materials such as sea ice plates in which the dominant inhomogeneity spacing is so large that it would require specimens larger than feasible for laboratory tests.
Please send me an email if you wish to receive the complete paper.