Verification of crack opening criterion deduced by newly derived micro-crack evolution equation

Abstract The author proposed a criterion of micro-crack nucleation, which was deduced theoretically by shock wave theory, and derived new micro-crack evolution equations. The new micro-crack evolution equation suggested that the strain gradients play an important role in the fracture mechanism. In this paper, based on the crack opening criterion deduced by the new micro-crack evolution equation and the stresses, strains and strain gradients substituted by the stress intensity factor the fracture mechanisms of metallic and ceramic materials are examined using those well-known data, i.e. fracture toughness and so forth, to verify the crack opening criterion. Moreover, the fracture toughness of the plane stress condition is estimated and becomes almost 1.2–1.8 times as much as the plane-strain fracture toughness generally so called “fracture toughness”. Even though the two-dimensional analytical version is adopted, the crack opening criterion gives the useful information that is verified by comparisons of the estimated yielding stress of metallic materials, the estimated bending facture strength of ceramic materials and the critical time from yielding stress/bending fracture strength loading to crack opening with those of well-known data of both materials. Therefore, it is expected that the micro-crack evolution equation and the crack opening criterion would give the useful tool to examine the fracture mechanism.