Fracture and Stress Waves in Glass and Polymer Plates Under Transverse Dynamic Loadings

摘要

The dynamic contact stresses between an axisymmetric projectile and elastic half-space are obtained by solving three-dimensional equations of motion. These stresses are written as sums of the Hertz contact stresses and wave-effect integrals. In terms of contact radius, the Hertz impact theory is shown to be a good approximation in determining total applied force. However, to calculate maximum radial surface stress at the maximum contact radius, the Hertz theory applies only when the contact time is longer than about 40 microseconds. The impact of spheres on elastic plates of finite thickness overlying a rigid foundation is studied. A general calculation method is described to account for the effect of plate thickness on stresses in plate and contact time between the plate and sphere. Experiments are conducted to measure contact times and fracture velocities for steel balls impinging on glass plates of various thicknesses overlying a large steel block. It is shown both theoretically and experimentally that for sufficiently large steel balls the contact time decreases with decreasing plate thickness, and good agreement between theory and experiment is obtained. The measured fracture velocities are smaller for a thin glass plate than for a thick glass plate. This is due to stress magnification around the contact circle. The problem of a penny-shaped crack located at the center of a plate of finite thickness is considered. (Author)