Dynamic Bond Stress in a Composite Structure Subjected to a Sudden Pressure Rise

The model studied in this paper is that of a composite structure represented by two elastic rods, of uniform cross section, which are bonded together along their generators. The rods are semi-infinite in length and are suddenly loaded by a pressure step applied over the end of the structure. The resulting elastic waves which are generated in each of the rods cause a dynamic bond shearing stress which is proportional to the difference between the two rod displacements. An integral solution is obtained for the bond stress and is evaluated numerically. The bond stress is composed of a static and a dynamic part and it is found that the peak bond stress, which occurs at the loaded end, is dominated by the static stress. Results are shown graphically for a particular rod configuration as well as the parametric dependence of the peak bond stress on the rod composite-stiffness ratio. Several limiting cases for the stiffness parameter and elastic wave-speed ratio parameter are investigated analytically and some asymptotic formulas are given which describe the small and large time behavior of the dynamic-bond stress.