Effect of Axial Force on Dynamic Fracture of a Beam or Plate in Pure Bending

The dynamic fracture response of a long beam of brittle elastic material subjected to pure bending is studied. If the magnitude of the applied bending moment is increased to a critical value, a crack will propagate from the tensile side of the beam. As an extension of previous work, a dynamically induced axial force which is generated during the fracture process is included in the analysis. Thus an improved formulation is presented by means of which the crack length, crack tip velocity, bending moment, and axial force at the fracturing section are determined as functions of time after crack initiation. It is found that the effect of the axial force becomes significant after the crack travels about one third of the beam thickness, and better agreement with experimental data is achieved. The results also apply for plane strain fracture of a plate in pure bending provided that the value of the elastic modulus is appropriately modified.