A Simple Formula for the Dynamic Stress Intensity Factor of an Impacted Freely-Supported Bend Specimen

The time history of the dynamic stress intensity factor is analyzed for a dynamic one-point bending test in which an edge-cracked specimen is impacted at the midspan without supports. A simple formula is derived for calculating the dynamic stress intensity factor with the specimen modeled as a cracked Euler-Bernoulli beam. Numerical examples are presented to demonstrate the practical applicability of the formula. It is shown that a reasonable accuracy is obtained by the present formula as compared with a finite element computation, and the CPU time is about 1% of the finite element method. Another numerical analysis is also performed for a steel 1PB specimen impacted by a falling cylinder. The contact force between the specimen and the impactor is estimated by applying Hertz's theory to the local deformation near the contact point. It is found that both ends of the 1PB specimen bounce up in an early stage and then the specimen flies off flexing vibrationally; the value of the dynamic stress intensity factor reaches its maximum at the instant when the specimen bends most sharply.