Spherical shells in inelastic collision with a rigid wall—tentative analysis and recent quasi-static testing

Abstract

This paper considers the crushing which occurs in a spherical shell made of ductile material on striking a rigid wall. A static analysis is developed which allows for strain hardening, while for relatively low impact velocities, such as to permit the effect of inertia to be neglected, strain rate sensitivity is allowed for in an empirical manner.

The analysis presented is applicable to spherical shells with a mean radius to thickness ratio exceeding seven, constructed in ductile material obeying a simple power law work hardening relationship. The deformation is assumed to occur in two phases. In the first phase a local flattening of the shell in contact with the rigid wall occurs, while in the second, an axisymmetric dimpling of the previously flattened portion takes place.

Other workers have discovered that at radius to thickness ratios exceeding one hundred, a third mode of behaviour takes place when a number of non-axisymmetric nodes can be formed. The analysis in this paper, however, is only applicable to lower ratios when the crushing deformation, although reaching a value of half the radius, remains axisymmetric, as is borne out in all the experimental results examined for correlation.

A number of assumptions and simplifications are made, all of which are clearly stated below. Reference is made to earlier papers on this subject and a comparison is made of correlations by such earlier work and by the present analysis in respect of a group of quasi-static tests carried out by the Civil Engineering Department of the Queen's University of Belfast under a Leverhulme Trust fellowship funding: this is described in detail in Appendix 1.

The result of a moderate velocity impact test on a spherical shell of 625 mm diameter is utilized to examine the correlation given by the present analysis taking strain rate effect into account.

Note: the first author was mainly concerned with the analysis, while the co-authors carried out the experimental work detailed in Appendix 1.

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