Table 2 Summary of energy barriers for different fracture toughening events

Observed fracture toughening events	Energy barrier
Crack by-pass	\({{\alpha }_{{CB}}\rho }_{{CB}}{\Delta }_{{CB}1}{G}_{f0}\)
Crack cut-through	\({{\alpha }_{{CB}}\rho }_{{CB}}{\Delta }_{{CB}2}{P}_{{CB}2}{G}_{f0}\)
Crack deflection	\({\alpha }_{{CD}}{{\Delta }_{{CD}}{l}_{f}G}_{f0}\)
Shielded crack	\({\alpha }_{S}{{\Delta }_{S}G}_{f0}\)
Shielded deflection	\({{{\alpha }_{S}P}_{{SD}}\Delta }_{{SD}}{G}_{f0}\)
Bridged deflection	\({\alpha }_{B1}{{\Delta }_{{CD}}{O}_{{BD}}G}_{f0}\)
Bridged cut-through	\({\alpha }_{B2}{{\Delta }_{{CB}2}{O}_{{BC}}G}_{f0}\)
Bridged crack	\({\alpha }_{B3}{{\Delta }_{B}{A}_{B}{S}_{B}G}_{f0}\)

\({\alpha }_{{CB}},\,{\alpha }_{{CD}},\,{\alpha }_{S},\,{\alpha }_{B1},\,{\alpha }_{B2}\), and \({\alpha }_{B3}\) are the geometrical scaling factor related to the sizes of test specimens for the additional fracture energies caused by crack bowing, crack deflection, shielded crack, bridged deflection, bridged cut-through, and bridged crack, respectively. \({\rho }_{{CB}}\) is the density of crack bowing (CB) phase. \({\Delta }_{{CB}1},\,{\Delta }_{{CB}2},\,{\Delta }_{{CD}},\,{\Delta }_{S},\,{\Delta }_{SD},\,{\Delta }_{B}\) are the fraction of energy increment for crack by-pass, crack cut-through, crack deflection, shielded crack, shielded deflection, and bridged crack, respectively. \({G}_{f0}\) represent the required fracture energy for propagating through a base cell. \({P}_{{CB}2}\) and \({P}_{{CB}2}\) are the scaled possibility of the cut-through event and the potential function of the shielded deflection, respectively. l_f is the actual length of the deflected fracture path. O_BD and O_BC are the occurrences of the bridged deflection and bridged cut-through, respectively. A_B is the statistical result of the bridging area per length of the bridging fibers. S_B represents the size of the bridging fiber.

Quick links

Search