Dynamic behavior of a clamped plastic beam with cracks at supporting ends under impact

This paper examines a projectile impact on a rigid-plastic beam with cracks at the fully clamped ends. By assuming the cracked sections yield immediat ely after impact, a three-hinge/two-hinge mechanism for the response proces s is constructed so that a complete solution considering the interaction be tween bending moment M and axial force N is derived. The key of the formula tion is to find a complementary equation concerning the axial force N. To p redict accurately the stability of the initial cracks, the J-integral crite rion is extended to involve the contribution of the axial force. All the go verning equations are nondimensionalized and rearranged, ready for Runge-Ku tta integration procedure. The numerical results demonstrate that the mass ratio and the axial force have significant influence on the final deformati on, energy partition, and the value of J-integral near the crack tip. The J -integral is nob very sensitive to the depth of the initial cracks, bur 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-typ e failure.