Improved method for calculating strain energy release rate based on beam theory

Abstract

The Timoshenko beam theory was used to model cracked beams and to calculate the total strain-energy release rate. The root rotations of the beam segments at the crack tip were estimated based on an approximate two-dimensional elasticity solution. By including the strain energy released due to the root rotations of the beams during crack extension, the strain-energy release rate obtained using beam theory agrees very well with the two-dimensional finite element solution. Numerical examples were given for various beam geometries and loading conditions. Comparisons with existing beam models were also given.