Mound morphology and growth dynamic of the wedding-cake interfaces

Crack diffusion in failure process of composite materials

“…However the calculation of the crack correlation function in the failure process in composite materials exhibits an avalanche decrease with temperature near a temperature value T = 400 (see figure 6). This avalanche phenomenon is also observed in the breaking process of the composite materials subject not only to a single load but to its all intact fibers [2,3,9].…”

“…The presence of the thermal noise will affect the lifetime for a constant applied stress controlled by the temperature T of the system [2,9]. So, the actual stress arising δl i of fiber i is written as:…”

“…It's characterized by clear-cut rules for stress, caused by a failed element, which is redistributed in undamaged fibers. This model has been studied extensively since it can be analyzed to an extent that is not possible for more complex materials [1][2][3][4][5][6]. The statistical distribution of the magnitude of avalanche phenomenon in fiber bundles is well studied [7][8][9], and the failure dynamics under constant load has been investigated through recursion relations which appears in a phase transitions and associated critical behavior in this model [10].…”

“…For an undamaged material with intact fibers on which we applied an external force f, the material resists to the applied load, but under a threshold time value t r where the elongation of some fibers becomes greater than their critical ones, micro cracks appear in the system and grow rapidly in time until the final crack of the material through an avalanche process [2,3] However, the situation differs totally if one creates the initial applied load localized at an arbitrarily chosen central site in a local load-sharing fiber bundle model. So, initially, no load is applied on any fiber except (for) the one at the central site.…”