Stress Distribution on the Boundary of a Circular Hole in a Large Plate Due to an Air Shock Wave Traveling Along an Edge of the Plate

Abstract

In the research program reported in this paper an experimental solution was obtained for the stress distribution around a circular hole in a large plate during passage of a pressure wave. The pressure wave was generated by passing an air shock wave of fast rise and slow decay along an edge of the plate with a shock tube. The experimental method used for the study was dynamic photoelasticity complemented with the moire method of strain analysis. A transparent, low-modulus, birefringent, urethane rubber was used as the model material. Transient free-field stresses were determined in the plate, at the hole location, prior to machining the hole. These stresses were introduced in the classical Kirsch solution to obtain what is referred to as a static stress distribution around the boundary of the hole. This stress distribution was compared with the dynamic stress distribution obtained directly from photoelastic data. The free-field stresses were also introduced in the theoretical solution by Baron and Matthews to obtain the maximum tangential stress on the boundary of the hole. The theoretical results are in good agreement with the experimentally determined maximum tangential stress. The results also indicate that the dynamic stress-concentration factor is initially lower than the static one, exceeds is at a later time, and finally approaches it asymptotically.