Stress Distribution on the Boundary of a Circular Hole in a Large Plate during Passage of a Stress Pulse of Short Duration

Abstract

A solution to the problem of the stress distribution on the boundary of a circular hole in a large plate during passage of a stress pulse of short duration is presented. The solution was experimentally obtained by using a low-modulus urethane rubber model in a combined photoelasticity, moiré, and grid analysis. The stress pulse of short duration was generated by detonating a small charge of lead azide on an edge of the plate. The hole was placed at a location in the plate where both dilatational and distortional waves would be felt. It was also located in such a way that a symmetric point was available in the free field for making free-field stress determinations. The short-duration pulse at the free-field symmetric point had a length of approximately 25 hole diameters; the portion associated with the pulse front (rise from zero to peak) was approximately 5 hole diameters.

The results of the study indicate that the stress of greatest magnitude is a compressive stress which develops on the hole boundary as the front of the stress pulse passes the hole. The maximum tensile stress which develops much later is only about half as large. As the end of the stress pulse passes the hole, the tensile and compressive stresses on the hole boundary are essentially equal in magnitude. The isochromatic fringe pattern during this period indicates that the hole is located in a stress field of pure shear. The orientation of the pattern indicates that the stress pulse is primarily a distortional wave at this time. The maximum dynamic compressive stresses on the boundary of the hole can be computed to a first approximation by applying the Kirsch solution for a hole in an infinite plate, considering the biaxial stress field and assuming an average value of stress over the hole diameter. The free-field biaxial stresses as computed from photoelasticity and moiré data were used in making this check. The maximum dynamic tensile stresses on the hole boundary were always smaller than the values computed using the same procedure.