Analysis of the Dynamic Stress Intensity Factor of an Impacted Freely Supported Bend Specimen Based on Modified Timoshenko's Beam Theory

摘要

A freely supported bending specimen momentarily disengages from the anvils during the impact bending tests, which will be called one-point bending. 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 which is freely supported. The mode shape functions and the natural frequency equations of the cracked beam in freely supported boundary conditions are derived from modified Timoshenko beam equations, in which the rotary inertia caused by the shear deformation of the beam is considered, by treating the crack as a discontinuity in the moment of inertia. The transverse beam deflection is derived by the mode superposition method employing the orthogonality conditions of the vibration normal mode function when a point-load excitation is applied at the midspan. Assuming the dynamic stress intensity factor is proportional to the difference between the displacement of the specimen at the midspan and that at the end, a simple formula is employed for calculating the time history of the dynamic stress intensity factor for a dynamic one-point bending test. It is shown that the natural frequency and the dynamic stress intensity factor are reduced due to the shear deformation of the beam based on the Timoshenko beam theory comparing to the results based on the Euler-Bernoulli beam theory, and the effect of the rotary inertia caused by the shear deformation is evident when the frequency is high based on the modified Timoshenko beam theory.