W. Johnson

Impact loading of plates and shells by free-flying projectiles: A review

Abstract This paper reviews recent research into the penetration and perforation of plates and cylinders by free-flying projectiles travelling at sub-ordnance velocities. It is shown that over the last few years there has been a significant amount of experimental research into a wide range of projectile-target configurations. Although most of this research has been concerned with the normal impact of monolithic metallic plates by non-deformable projectiles, valuable work has also been carried out on non-normal impact, impact by deformable projectiles, impact of non-homogeneous metallic and non-metallic targets (including laminated targets) and impact of pipes and tubes. Recent analytical developments that enable the important characteristics of the penetration and perforation process to be modelled are reviewed. These include models that predict local deformations and failure, global deformations or both. It is shown that for some impact situations fairly simple analytical models are capable of predicting target response reasonably accurately, but for others, particularly when both local and global mechanisms contribute significantly to overall target response, more complicated models are required. The development of numerical codes that predict target response to projectile impact is briefly reviewed and the capabilities and limitations of current codes are discussed. The review also includes a section on the impact of soils and reinforced concrete structures.

Extensible plastic collapse of thin-wall frusta as energy absorbers

Abstract The crumpling of thin-walled frusta, under axial compression, in the ‘concertina’ mode is studied. The energy expended in bending at the plastic hinges and in stretching the metal between the hinges is minimized for the total decrease in height due to collapse. The thinning of the cross-section due to stretching is neglected. A theoretical model has been developed and numerical results are obtained that show the effect of slenderness, t/ D , and the semi-apical angle of the frusta. Good qualitative agreement in trends is exhibited when comparison with available experimental results is made.

The buckling of annular plates in relation to the deep-drawing process

Abstract Based on a two-dimensional buckling model of an elastic-plastic annular plate and the well-known energy method, the critical conditions for the elastic buckling and the plastic buckling of the flange of a circular blank during the deep-drawing process are obtained to improve upon previously given results[1, 4]. The influence of a blankholder upon buckling and on the number of waves generated can also be quantitatively predicted.

Spread and flow patterns in ring rolling

Abstract Tellurium lead and aluminium alloy rings were rolled on an experimental radial ring rolling mill to reductions as great as 70% to determine the spread when taking into account the various ring rolling factors. Both plain and profiled rings were rolled. In the case of the profile ring rolling, a T-shaped section was formed from an initially rectangular cross-section, the undriven mandrel being grooved and the main roll plain. The mode of deformation for plain and profiled rings was also examined and is reported.

The crumpling of steel thin-walled tubes and frusta under axial compression at elevated strain-rates: Some experimental results

Abstract Uniformly thin circular cylinders and frusta (truncated circular cones) of low carbon steel were subjected to axial loading at elevated strain-rates. Their initial axial length and the outside diameter of the cylinders and frusta (the larger top end) were kept constant whilst their uniform wall thickness was varied. The load-deformation or compression behaviour of the cylinders and frusta for the two semi-apical angles used, 5° and 10°, were recorded and the modes of collapse were observed and are discussed. Initial axisymmetric rings (‘ring’, ‘bellows’ or ‘concertina’ buckling) developed into non-symmetric ‘diamond’ patterns (elliptic, triangular and square, etc.) as loading progressed and initially non-symmetric diamond buckle patterns were observed to characterise the modes of frustum collapse.

Long stroke energy dissipation in splitting tubes

Abstract A passive crashworthy system that dissipates impact energy by fracture and plastic deformation of metal tubes is analysed. The energy dissipating component is a square tube that is pressed axially against a die where it splits at the corners and curls outward. Experiments on the effect of die radius have shown that a remarkably constant force causes this rate-independent deformation in a dural tube. Tubes which both split and curl can be designed for energy absorbing systems requiring large stroke to length ratio and good specific energy absorption.

Influence of axial force on the elastic-plastic bending and springback of a beam

Abstract In the industrial forming of metal sheet or plate components by means of a bending operation, a constant problem is the change of shape, or “springback”, of the formed part under the elastic stresses that are released when the forming pressure is removed. For the close-tolerance forming of such components, an accurate means of calculating the springback is of great value, as this enables a corrective allowance to be made when designing and performing the forming operation itself. In the present paper, the influence of axial force on the elastic-plastic bending and springback of a beam is examined. After obtaining the fundamental relationship between the curvature of the beam and the load for the case of pure bending, both the elastic-plastic bending of a cantilever subjected to a concentrated force at its tip and the springback are considered. It is shown that the analysis can be applied to the press-brake bending of strips and the equibiaxial bending of plates.

On the inextensional axial collapse of thin PVC conical shells

Abstract Inextensional collapse mechanisms are presented for the axial crumpling of thin-walled circular cones and frusta (truncated circular cones). Shortening of the (thin) shell height is achieved by folding in a non-symmetric diamond mode about stationary circumferential and inclined plastic hinges; collapse proceeds progressively from the narrower end of the conical shell during the passage of a travelling hinge. Expressions for the various mean crushing loads, when collapsing frusta of rigid-perfectly-plastic material, are developed. Theoretical collapse modes and predicted loads are compared with those obtained experimentally by collapsing rigid PVC conical shells of constant axial length, of various wall-thicknesses and semi-apical angles, as well as metal (aluminium alloy and low-carbon steel) conical shells of similar geometry; agreement is found to be good.

Large deformations of thin-walled circular tubes under transverse loading—III: Further experiments on the bending of simply supported tubes

Abstract Further experimental results are presented concerning the transverse loading of simply supported tubes supplementing those given in ref. (1). Surface stresses are examined by means of the brittle laquer technique and strain gauges. The influence of the geometrical parameters on the modes of deformation of the tubes is discussed in general terms.

Springback after the biaxial elastic-plastic pure bending of a rectangular plate—I

Abstract The elastic springback undergone by a rectangular plate after submitting it to biaxial elastic-plastic pure bending is determined. The analysis is first based on non-proportional loading using the Tresca criterion and then on proportional loading for both the Mises and Tresca criteria. Some numerical results and examples are given.