Norman Jones

Dynamic Progressive Buckling of Circular and Square Tubes

Abstract A series of over 120 axial crushing tests were conducted on circular and square steel tubes loaded either statically or dynamically. Approximate theoretical predictions for static and dynamic progressive buckling are developed. Fair agreement with the experimental results is achieved provided the effective crushing distance is taken into account and the infuence of material strain rate sensitivity is retained for dynamic loads.

Dynamic axial crushing of square tubes

Abstract Eighty-four dynamic tests on thin-walled square steel tubes having two different cross-sections with c/h = 30.25 and c/h = 32.18 and various lengths were crushed axially on a drop hammer rig. Approximate theoretical predictions were developed for the axial progressive crushing of square box columns using a kinematically admissible method of analysis. This theoretical study predicts four deformation modes which govern the behaviour for different ranges of the parameter c/h. New asymmetric deformation modes were predicted theoretically and confirmed in the experimental tests. These asymmetric modes cause an inclination of a column which could lead to collapse in the sense of Euler even for relatively short columns. The effective crushing distance is considered in the approximate theoretical analysis together with the influence of material strain rate sensitivity, which is important for steel even when the loadings are quasi-static. The simple equations presented herein for the design of axially crushed spuare box columns give reasonable agreement with the corresponding experimental results.

Dynamic axial crushing of circular tubes

Abstract A series of axial crushing tests on steel circular cylindrical shells loaded either statically or dynamically is reported and compared with various theoretical predictions and empirical relations. A modified version of Alexanders theoretical analysis for axisymmetric, or concertina, deformations gives good agreement with the experimental results when the effective crushing distance is considered and provided that the influence of material strain rate sensitivity is retained in the dynamic crushing case.

A THEORETICAL STUDY OF THE DYNAMIC PLASTIC BEHAVIOR OF BEAMS AND PLATES WITH FINITE - DEFLECTIONS,

Abstract An approximate theoretical procedure is developed herein in order to estimate the permanent transverse deflections of beams and arbitrarily shaped plates which are subjected to large dynamic loads. The influence of finite-deflections or geometry changes is retained in the analysis but elastic effects are disregarded. The particular case of a fully clamped rectangular plate acted on by a uniformly distributed dynamic pressure pulse is studied in some detail. It is observed that reasonable agreement between the theoretical predictions and the experimental results has been obtained for beams (β = 0) and rectangular plates (β = 0.593) which were made from a strain-rate insensitive material.

Recent Studies on the Dynamic Plastic Behavior of Structures

This article contains a review of the literature, which has been published recently, on the dynamic plastic behavior of simple structures. The dynamic loads cause large plastic strains which dominate material elastic effects. Thus, the accuracy of various refinements of simple rigid-plastic methods are discussed, together with the phenomena of pseudoshakedown under repeated loads, dynamic plastic buckling, and progressive buckling. Recent studies are also reported on similitude under large impact loads, and on the ductile-brittle fracture transition due to the changes in the physical dimensions of a structure.

Impulsive loading of fully clamped beams with finite plastic deflections and strain-rate sensitivity

Abstract : A review is given of earlier work on the plastic response to impulsive loading of a beam clamped against end rotation and axial displacements, taking account of small finite transverse displacements and ofstrain rate dependence of the yield stress. New solutions are derived from rigid-plastic analysis which include both effects in simple approximate ways. Deflections are compared as obtained from these formulas, from experiments described here on mild steel beams, and from finite-difference numerical solutions using the M. I. T. rod model with elastic-plastic strain rate sensitive behavior. The significance of agreements observed is discussed. (Author)

The dynamic plastic behavior of fully clamped rectangular plates

Abstract An experimental investigation was undertaken in order to study the behavior of fully-clamped rectangular plates when subjected to uniformly distributed impulsive velocities. The total energy of the dynamic loads was sufficiently large to cause plastic flow of the plate material and maximum permanent deflections from 0.2 to nearly seven times the corresponding plate thicknesses. All the rectangular plates had the same aspect ratio (B/L = 0.593) but various thicknesses (H), and were made from either hot-rolled mild steel or aluminum 6061-T6. The permanent deformed profiles of the plates are similar to the shape of the velocity field used by Wood [11] for calculating the minimum upper bound to the collapse pressure of a fully-clamped rectangular plate loaded with a uniformly distributed time-independent pressure. It is observed that a modification of the bending only prediction of Martin [13] provides adequate engineering estimates of the maximum permanent deflections up to the order of one-half of the corresponding plate thickness. For larger deflections, it is necessary to include the influence of geometry changes; and in the case of mild steel, material strain-rate sensitivity as well.

Dynamic response and failure of fully clamped circular plates under impulsive loading

Abstract An approximate theoretical analysis is presented which examines the dynamic plastic response and three failure modes of fully clamped circular plates subjected to uniformly distributed transverse impulsive loads. The rigid-plastic analysis employs an interaction yield surface which combines the bending moments, membrane force and the transverse shear force required for plastic flow and uses the Cowper-Symonds constitutive equation to cater for material strain rate effects. Good agreement is obtained between the theoretical predictions for permanent transverse deflections (failure mode 1) and the corresponding experimental results of Bodner and Symonds, and Teeling-Smith and Nurick recorded on strain rate sensitive plates. Correlation of a theoretical critical impulse to rupture with the corresponding experimental values of Teeling-Smith and Nurick was poor, possibly because the boundary conditions in the experiments were not ideally clamped, as assumed in the theory. Further experimental results are required which pay particular attention to the details of the clamped boundary conditions in the experimental tests when failure occurs due to tensile tearing (failure mode 2) or transverse shear (failure mode 3) at the supports.

A failure criterion for beams under impulsive loading

Summary An energy criterion is suggested in this paper for predicting the inelastic failure modes of beams subjected to large dynamic loadings. The experimental results of Menkes and Opat on the failure of impulsively loaded beams may be interpreted to show that the length of a plastic hinge varies with the ratio of the plastic shear work to the total plastic work dissipated at a hard point or other region of intense localized plastic strain. The variation of this parameter is obtained from a theoretical analysis for the impulsive loading of a rigid, perfectly plastic clamped beam with plastic yielding governed by an interaction yield surface which combines the influences of bending, shear and membrane tension. The Cowper-Symonds dynamic constitutive relation is used to study the influence of material strain rate sensitivity.

Dynamic elastic–plastic buckling of circular cylindrical shells under axial impact

Abstract Dynamic axisymmetric buckling of circular cylindrical shells struck axially by a mass is studied in order to clarify the initiation of buckling and to provide some insight into the buckling mechanism as a transient process. It is assumed that the material is elastic–plastic with linear strain hardening and displaying the Bauschinger effect. The deformation process is analysed by a numerical simulation using a discrete model. Particular attention is paid to the influence of stress wave propagation on the initiation of buckling. It is found that the development of the buckling shape depends strongly on the inertia properties of the striker and on the geometry of the shell. The theoretical method is used to clarify some experimental data and good agreement is obtained with results on aluminium alloy tubes.