Dynamic Behavior of a Clamped Plastic Beam With Cracks at Supporting Ends Under Impact

Abstract

This paper examines a projectile impact on a rigid-plastic beam with cracks at the fully clamped ends. By assuming the cracked sections yield immediately after impact, a three-hinge/two-hinge mechanism for the response process is constructed so that a complete solution considering the interaction between bending moment M and axial force N is derived. The key of the formulation is to find a complementary equation concerning the axial force N . To predict accurately the stability of the initial cracks, the J -integral criterion is extended to involve the contribution of the axial force. All the governing equations are nondimensionalized and rearranged, ready for Runge-Kutta integration procedure. The numerical results demonstrate that the mass ratio and the axial force have significant influence on the final deformation, energy partition, and the value of J -integral near the crack tip. The J -integral is not very sensitive to the depth of the initial cracks, but the presence of initial cracks in a beam may alter the failure behavior of the beam after impact, that is, from a strength-type failure to a fracture-type failure.