Pergamon PII : S0020-7403 (96) 00063-X Int. J. Mech. Sci. Vol. 39, No. 5, pp. 575 583, 1997 Copyright ,t" 1997 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0020 7403/97 $17.00 + 0.00 EXPERIMENTAL EVALUATION OF THE STRAIN FIELD HISTORY DURING PLASTIC PROGRESSIVE FOLDING OF ALUMINIUM CIRCULAR TUBES MASSIMILIANO AVALLE and GIOVANNI BELINGARDI Dipartimento di Meccanica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy (Received 11 October 1995; and in revisedjbrm 9 April 1996) Abstract--The axisymmetric collapse by plastic progressive folding of a circular tube submitted to axial loading is considered by an experimental approach. The strain field history is measured by means of electric strain gages properly placed on the external surface of the tube so that more than one fold is covered and both axial and circumferential strains are measured. The measured strains are examined both as time-histories and as a deformation field. The formation and development of circumferential plastic hinges are pointed out. The strain histories, reported as a function of the displacement of the testing machine cross-head, are then correlated with the crushing force diagram, leading to a better understanding of the folding mechanics. In particular, the formation of each fold develops through three subsequent phases: the initialization at the closure of the previous fold, the flattening of the upper conical surface, and the flattening of the lower conical surface. While most of the tube wall is pushed outwards of the original cylindrical surface, a portion is pushed inwards of that surface. Moreover, there is a small portion of the wall that is pulled inward during the fold initialization and then pushed outward during the fold closure. The analysis of these histories lead to the validation of the basic assumption of our and other recent kinematical models of the plastic progressive folding. Copyright © 1997 Elsevier Science Ltd. Keywords: structural collapse, plasticity, experimental tests, strain measurement, progressive folding. 1. INTRODUCTION The use of axially crushing thin-walled structures as energy absorbers [1] for safety applications mainly in the transportation industry (in particular in the automotive industry) has been extensively investigated in recent years both from experimental and theoretical points of view. Theoretical simplified models have been proposed [2 4]. Special interest is devoted to axial collapse of tubes with circular cross-section since this type of structure exhibits the highest values of specific energy absorption (energy per unit of material volume). The collapse develops according to two different deformation modes: one is axisymmetric and is generally referred to as a concertina mode and the other is not axisymmetric and is generally referred to as a diamond mode. In the case of the concertina mode of deformation the collapse develops by the subsequent formation of a regular sequence of folds. The theoretical models are based on the assumption of kinematics, i.e. the description of the displacement field, and from this assumption, information on the material strains, on the sustained forces and on the energy needed for the deformation is derived. The kinematics include the formation of some plastic hinges, either fixed or moveable. These mathematical models depict rather well the global behavior, and good correspondence is found with some experimentally measured geometrical values such as the fold length. However experimental crush tests were mainly accomplished on a global basis, i.e. measuring only global force and displacement during the test. Unfortunately an estimate of strains and stresses from force-displacement values is not possible due to geometrical non-linearity (large displacements due to the formation of folds). This paper deals with the experimental measurements of material deformation by application of electric strain gages during the plastic progressive folding of tubes according to the concertina mode. Strain measurements in the folding zone during tube collapse allow the analysis of the crushing mechanics of the tube both in the initialization phase, in the development phase and in the final closure of the fold. Some of these results have already been presented in a previous paper [5]. The analysis that was briefly outlined is now developed in more detail. 575