Norman Jones

University of Liverpool | UoL · School of Engineering

This paper discusses the energy-absorbing effectiveness factor which provides a ratio between the energy absorbed in a structural system with the total potentially available elastic and plastic strain energies in all the materials used in the construction. Experimental and numerical predictions for the factor are expressed in terms of the solidity...

Accidental loads often cause failure to tubular structures on offshore platforms and subsea pipelines due to, for instance, dropped objects and collisions. Thus, the dynamic behavior of pipes subjected to lateral impact loadings should be investigated in order to ensure safe operations. An experimental programme is used in this paper to study the d...

Theoretical predictions are developed for the deformation and denting of fibre-metal laminates when subjected to low-velocity impact loads, or uniform blast loadings, and compared with available experimental test results. The rigid plastic material approximation with modifications to reflect the actual cross-section of a fibre-metal laminate is use...

This paper presents a study on the potential offered by lightweight energy-absorbing foam structures reinforced with aluminium and steel cylindrical tubes subjected to compressive crushing. Initially, attention was focused on establishing the influence of the length as well as the diameter to thickness ratio of the metal tubes on the specific energ...

Shakedown occurs when a structure responds steadily under cyclic loadings within appropriate limits after one or a few cycles of loading. This study proposes a new method for assessing the shakedown limit state associated with the breakage of a ship's hull girder, considering the buckling effects seen under the cyclic hull girder actions of hogging...

This note reports on simple equations that can be used to interpret the behaviour of structural members struck by impact loads as used in a simple undergraduate laboratory exercise. The application of these equations is illustrated for some test results on a long vertical thin-walled top-hat section struck axially by a large mass at one end and sup...

The pseudo-shakedown phenomenon for the repeated and identical mass impact loadings on circular and rectangular plates, is studied using a rigid-plastic method of analysis. Comparisons are made with experimental data which has been published on the response of circular and square plates subjected to repeated mass impacts. Previous studies have expl...

The perforation of mild steel, stainless steel and high-strength steel plates subjected to impacts characterised as low-velocity (up to about 20 m/s) and moderate-velocity (20–300 m/s, approximately) are examined in this paper, wherein recent experimental data and some empirical equations have been compared. The threshold velocity for the normal pe...

It is the purpose of this article to present design equations which can be used to predict the damage of ductile plating when subjected to mass impact, dynamic pressure or impulsive loadings. The external loadings are sufficiently severe to produce inelastic material behaviour and produce finite transverse displacement, or geometry change, effects....

A study was published recently by ASME which contain the views of experienced numerical analysts on the credibility of numerical calculations in engineering design. Various important issues were raised so this paper is an attempt to examine some of these concerns from the narrower perspective of the response of structures subjected to large dynamic...

This article derives bending moment-axial force (M-P) interaction curves for mild steel by considering elastic-plastic and strain hardening idealisations with linear and parabolic strain hardening characteristics.

In many industries, rigid-plastic methods of analysis are a useful design aid for safety calculations, hazard assessments, security studies and forensic investigations of ductile structures, which are subjected to large dynamic loads producing an inelastic response. This paper examines the behaviour of a rectangular plate struck at the centre by a...

The perforation of aluminium alloy plates subjected to impacts characterised as low-velocity (up to about 20 m/s) and moderate-velocity (20–300 m/s, approximately) are examined in this paper, wherein recent experimental data and some empirical equations have been compared. The threshold velocity for the normal perforation of metal plates focuses on...

This article focuses on the energy absorption of structural systems and components subjected to extreme loadings which can arise from impact, explosion and various other dynamic events. The dynamic properties of high-strength steels are discussed briefly because they have been proposed for energy-absorbing systems and other components in place of t...

This article provides a broad overview of the contributions that relatively simple methods of analysis can make to the design of structural systems for the protection of the public and the security of industrial plant against extreme dynamic loading events which involve explosive blast pressures or impact loadings from fragments and projectiles. It...

A study is reported on the energy-absorbing effectiveness factor which was introduced recently. The factor is defined as the quotient of the total energy, which can be absorbed in a system, to the maximum energy up to failure in a normal tensile specimen, which is made from the same volume of material. This dimensionless parameter allows comparison...

The dynamic plastic response of a simply supported circular plate is analysed. Emphasis is given to the plate behaviour after it has broken free from the supports due to a local material failure. The theoretical rigid plastic analysis predicts various features of the response such as the time to failure, residual kinetic energy and the critical vel...

Experimental tests are reported on steel pipelines which have been struck by a relatively large rigid wedge-shaped mass travelling up to 10.4m/s. A pipeline is supported across a span, is fully clamped at both ends and is struck at the mid-span and at the one-quarter span positions. Most of the pipelines are pressurised with a nitrogen gas. The ini...

The influence of elastic shear deformation on the transverse shear response of a fully clamped beam is investigated in the present paper. The beam is made from a rigid, perfectly plastic material and subjected to a uniformly distributed pressure pulse loading. The elastic shear deformation is idealized by an elastic, perfectly plastic spring with a...

This article discusses the role of the plastic methods of analysis in the design process for the protection and safety of structural systems subjected to extreme impact, explosive and dynamic loadings. These potential hazards would cause large deformations and large inelastic strains in structural components and rupture and failure of the material...

This article studies the perforation of mild steel circular plates struck normally by cylindrical projectiles having blunt, hemispherical, and conical impact faces. Experimental results are obtained using a drop hammer rig for the perforation of 2-8 mm thick plates struck by projectiles weighing between 1.75 kg and 176 kg and traveling up to about...

This article studies the perforation of mild steel square and rectangular plates struck normally by cylindrical projectiles having blunt, hemispherical, and conical impact faces. Experimental results are obtained in a drop hammer rig for the perforation of 4 mm and 8 mm thick plates struck by relatively heavy projectiles weighing between 11.9 kg an...

Experimental results are reported for the perforation of geometrically similar fully clamped circular and square mild steel plates struck transversely by cylindrical projectiles having blunt, conical, and hemispherical noses. The striking masses are much heavier than the corresponding plate mass and travel with initial impact velocities up to about...

In a recent experimental and analytical study for the axial progressive collapse of some thin-walled structural sections, no consistent reliability could be obtained for the prediction of crush parameters for different geometries and materials with an analytical approach that relied on a yield hinge model. Square and spot-welded top-hat sections we...

The common features of the deformation of long circular tubes made from different aluminium alloys and subjected to various axial impact loadings are established and used to develop simplified structural models for global bending collapse and progressive buckling. A two-phase deformation model for axially loaded structural elements is proposed, whi...

Experimental tests are reported on steel pipelines that have been struck by a relatively large rigid wedge-shaped mass travelling up to 10.4 m/s. A pipeline is supported across a span, is fully clamped at both ends and is struck at the mid-span and at the one quarter span positions. Most of the pipelines are pressurised with a nitrogen gas. The ini...

This paper provides an overview of the contributions that plastic methods of analysis can make to the protection of the public and the security of industrial plant against extreme dynamic loading events which involve explosive blast pressures or impact loadings from various projectiles. It is possible, by careful design, to absorb the external dyna...

This paper analyses the response of a clamped rigid, perfectly plastic beam subjected to an impulsive velocity loading throughout the span. A critical velocity is determined using a damage mechanics model, beyond which a beam fails at the supports. Attention is focused on the dynamics of the beam after failure. A transient phase of deformation deve...

This article examines some recent experimental test data on the perforation of mild steel plates having thicknesses 2 ≤ H ≤ 8 mm and struck by relatively heavy masses travelling up to about 13 m/s. The plates are fully clamped around circular, square and rectangular boundaries and struck by projectiles having blunt, conical and hemispherical impact...

A previous study presented a lower bound estimate of the limit torque for a regular polygonal shaft having any number of equal sides. The given equation has been derived for a shaft made from a ductile material having perfectly plastic characteristics. The present work presents an upper bound value for the same problem so that the exact collapse to...

This article contains a brief review of some recent developments on the response of structures subjected to large dynamic loads, which produce large inelastic strains. It is focussed on topics which are of interest in the design of naval architecture and ocean engineering structures. In particular, comments are offered on the strain rate sensitive...

The improvements in vehicle crashworthiness observed in recent years have been closely linked to advanced high-strength steels that are currently being produced or in process of development. Amongst these, Dual-Phase and TRIP (Transformation Induced Plasticity) steels have presented excellent properties for use in crashworthy structures. For these...

The theoretical foundation of Youngdahl's correlation parameters, which have been used to eliminate pulse shape effects in the dynamic plastic response of two-dimensional structural members, is studied in the present paper with the aid of bounds obtained for a rigid-plastic material. It is shown that Youngdahl's empirical estimate for the structura...

The dynamic energy imparted to structures can cause material failure. The present investigation considers such a failure for a simply supported beam which is subjected to a blast loading idealised as an initial velocity distributed uniformly throughout the span. The theoretical solutions are developed using a rigid, perfectly plastic idealization a...

An experimental programme is reported which examines the progressive collapse behaviour of some thin-walled closed-section structural sections made from high-strength steels under quasi- static and impact axial loads. A comparison is made with theoretical formulae, which have been used successfully for predicting the behaviour of mild steel thin-wa...

Dynamic elastic–plastic buckling of thin-walled square tubes is studied from the viewpoint of elastic–plastic stress wave propagation, which originates from an axial impact loading. The influence of the impact velocity and the striking mass on the development of the buckling shape is discussed when considering the transient deformation process. It...

An experimental investigation was carried out to study the behaviour of circular thin-walled aluminium alloy 6063T6 extrusions subjected to large axial impact loadings. The specimens, having an external diameter of 51 mm, were 1.5 mm thick, giving a 2R/H ratio of 33, approximately. Eighteen quasi-static and thirty-seven dynamic tests were performed...

The post-failure motion of a simply supported beam subject to a blast loading, which causes failure at the supports, is investigated analytically. The theoretical solution adopts a rigid, perfectly plastic idealisation and is exact in the sense that it satisfies the requirement of the upper and lower bound theorems of dynamic plasticity. Attention...

Structural effectiveness differences have been observed in a recent study on the progressive axial collapse of thin-walled structural sections when made from different classes of steels (mild steel, interstitial-free rephosphorized high-strength steel and high-strength low-alloyed steel). A higher effectiveness was observed for spot-welded top-hat...

This article discusses the dynamic plastic instability of various basic structural members, subjected to large axial impact loads, which is relevant to the fields of structural impact and structural crashworthiness. In particular, studies on the dynamic axial response of idealised elastic–plastic models, rods, cylindrical shells and square tubes, i...

This paper examines the response of circular and square plates struck by a rigid mass at the plate centre with a sufficient initial kinetic energy to produce large inelastic deformations. A simplified analysis, which retains finite-deflection effects and assumes that the plates are made of a rigid, perfectly plastic material, provides a relatively...

Some characteristic features of the dynamic inelastic buckling behaviour of cylindrical shells subjected to axial impact loads are discussed. It is shown that the material properties and their approximations in the plastic range influence the initial instability pattern and the final buckling shape of a shell having a given geometry. The phenomena...

The analytical model developed in Part I (Int J Impact Eng 2002;27(8):837–61) using continuum damage mechanics is used in this paper to predict the displacement to failure of beams subjected to static or dynamic loads producing large plastic strains. The beams, which were made of a ductile, strain rate sensitive material, were loaded at different p...

A simple theoretical method, which is based on ductile damage mechanics and which retains strain rate effects, is presented for predicting the failure of beams made from a perfectly plastic material and subjected to impact loads. For this class of materials, the strains can be estimated by defining a hinge length. The definition adopted here leads...

Experimental results are reported for the response and failure of a notched double-shear (DS) beam made from BS970/En24 medium carbon steel alloy when subjected to a mass impact loading. Mechanical properties and constitutive equations were obtained from quasi-static, dynamic and temperature tests on the beam material. Response and failure features...

The effect of loading rate on the interfacial fracture toughness of a glass-fiber/polyamide fiber-metal laminates (FMLs) was studied. Impact testing was conducted at 3 m/s using a drop weight impact machine with a striker of mass 2.6 kg. Overall, although the results and differences in failure mode suggest a viscoelastic response in the film adhesi...

The influence of loading rate on the interfacial fracture toughness of a polypropylene-based fiber-metal laminate was studied. Interfacial fracture tests were conducted under static and impact loading using a single cantilever beam (SCB) specimen. The study showed no significant effect in interfacial fracture toughness. An increase in the load requ...

An experimental investigation is reported on the impact loading of fully clamped mild steel beams and circular plates struck by relatively heavy masses. The impact energies are sufficient in some tests to cause material failure and, thus, to provide the threshold conditions for cracking and severance for impact velocities up to 6.74m/s for beams an...

Twenty-five quasi-static and forty-three dynamic axial crushing tests have been performed on square and circular stainless steel type 304 specimens in order to investigate the transitions between dynamic progressive buckling and global bending of thin-walled tubes. The columns consisted of three different circular (mean diameter/ thickness, 2R/H ≈...

The crushing behaviour of aluminium and steel cylindrical shells, when subjected to an axial impact, is examined using a numerical simulation. The influence of the material properties, shell geometry, boundary conditions and loading techniques on the energy absorbed and the buckling shapes is explored. Various shell response characteristics, such a...

This study examines the conditions of the transition from progressive plastic buckling to dynamic plastic buckling on thin-walled circular tube with an increase in the impact velocity. This report deals with the discussion of numerical analysis for buckling modes. Their buckling modes are progressive plastic buckling, dynamic plastic buckling and f...

The axisymmetric buckling of elastic–plastic cylindrical shells subjected to axial impact are studied using a finite element analysis. This study reveals that shells, subjected to axial impact, are both velocity and mass sensitive, so that larger energies can be absorbed by a shell for high-velocity impacts when decreasing the striking mass. It is...

The formation of a transverse shear localization (shear hinge) in a beam element made from a ductile material and subjected to transverse dynamic loads is studied in the present paper. Dimensional analysis and a finite-element simulation are used to describe the formation and structure of a transverse shear hinge. It is shown that the beam response...

To measure accurately the elastic modulus of a metal, E, can be a difficult task when a specimen undergoes plastic strains. Moreover, some failure criteria, such as those associated with Continuum Damage Mechanics, require the change of elastic modulus with strain to define a measure of damage, D, in a material or structure. Thus, it is important t...

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 def...

This article examines some aspects of the dynamic material properties of ductile metals which are required for the design of energy absorbing systems and structural crashworthiness problems. Some lacunae in our knowledge are revealed, particularly on the dynamic inelastic failure of structures and components.

An analytical model is proposed for studying the material failure in shear hinges which develop during the dynamic plastic response of beams under impulsive pressure loadings. The structural response outside a shear hinge is modelled using a rigid, perfectly plastic theory. However, within the shear hinge, strain hardening, strain rate and temperat...

To investigate the role of the hydrostatic stress on failure, some static and dynamic tensile tests on mild steel axisymmetric notched specimens are described in this paper. Finite–Element results and experimental data indicate that the failure site, for specimens having a small notch radius, occurs in regions of low triaxiality. Comparisons are ma...

This article examines the dynamic axial crushing of thin-walled sections made from ductile metals and uses these solutions to explore several important phenomena in the structural crashworthiness field. In particular, the range of validity of quasi-static behaviour is explored, and the transitions to dynamic plastic buckling and global bending are...

This presentation examines the dynamic axial crushing of thin-walled sections made from ductile metals and uses these solutions to explore several important phenomena in the structural crashworthiness field. In particular, the range of validity of quasi-static behaviour is explored, and the transitions to dynamic plastic buckling and global bending...

This article focuses on the behaviour of structures which are subjected to dynamic loads (impact, blast, pulse) which produce large inelastic strains and material failure. Particular attention is given to the elementary and strain energy density failure criteria and some recent experimental results on the dynamic inelastic failure of structural mem...

The experimental results for clamped mild steel beams under impact loading reported by Yu and Jones (Yu, J. L. and Jones, N. (1991) Further experimental investigations on the failure of clamped beams under impact loads. International Journal of Solids and Structures27, 1113–1137) are simulated numerically using the finite-element code ABAQUS with p...

An experimental study is reported on the ductile deformation and perforation of plates struck at the center by solid cylindrical projectiles having the longitudinal axis normal to the plate surface. The plates, which are made from 4 to 8-mm-thick mild steel sheet, are fully clamped around a circular boundary and are struck, by projectiles having bl...

An experimental study into the ductile deformations and static and impact perforation of mild steel plates is reported in Part 1. These results are discussed in this article and compared with other experimental data reported in the literature. The accuracy of various empirical formulas for the impact perforation of plates is also examined.

The topic of structural impact is concerned with the response of structures subjected to dynamic loadings producing large inelastic strains and permanent deformations. This is relevant to safety calculations and energy absorption estimates for structural crashworthiness studies. The rigid-plastic method of analysis is introduced and used to examine...

This article contains a brief review of the literature, published since the previous Applied Mechanics Reviews article in 1989 [1], on the dynamic plastic response of basic structural members made from ductile metallic type materials. The external dynamic loads cause large inelastic strains in the structural members which dominate material elastic...

A theoretical rigid-plastic analysis for the dynamic shear failure of beams under impulsive loading is presented when using a travelling plastic shear hinge model which takes into account material strain hardening. The maximum dynamic shear strain and shear strain-rate can be predicted in addition to the permanent transverse deflections and other p...

A theoretical analysis is presented for the dynamic plastic behavior of a fully clamped rigid, perfectly plastic circular plate struck transversely by a rigid mass at the center. It is shown that the maximum permanent transverse deformation predicted by a theoretical solution, with combined transverse shear and bending, is similar to that from a be...

This article is concerned with the response of structural members which are subjected to impact loads causing large inelastic deformations and material failure. The literature published on the dynamic inelastic failure of structural members is reviewed from which a need for additional theoretical and experimental studies emerges clearly. Some exper...

An elastic-plastic beam bending model has been developed to simulate the post-upper skin failure energy absorption behaviour of polymer composite sandwich beams under three-point bending. The beam skins consist of woven and chopped strand glass, while the core is a resin impregnated non-woven polyester material known as Coremat. A polyester resin w...

The dynamic behaviour of a simple plate structure subjected to an axial impact is studied using an elastic-plastic model which takes into account inertia effects and the influence of material strain-rate sensitivity. The entire time-dependent deformation process, including elastic unloading and plastic reloading is obtained. The predictions for the...

The dynamic response of a “short” cylindrical shell, which is made from a rigid, perfectly plastic material, is investigated in this paper. The plastic behaviour of the material is controlled by a cubic yield condition which retains the transverse shear force as well as the circumferential membrane force and the longitudinal bending moment. Theoret...

A theoretical analysis is presented for a fully clamped beam made from a rigid, perfectly plastic material, which is subjected to a uniformly distributed blast loading with a magnitude that decreases with time. The influence of the transverse shear force as well as the bending moment is retained in the yield condition. It is observed that when the...

This article explores the accuracy of quasi-static methods of analysis for predicting the inelastic behaviour of structural impact problems.The quasi-static behaviour of fully clamped beams when struck at the mid-span by a rigid mass, which produces either infinitesimal displacements or finite transverse displacements for sufficiently large impact...

The dynamic response of a fully clamped circular plate, which is made from a rigid, perfectly plastic material, is investigated with the aid of the extended Johansen yield criterion which retains the influence of the transverse shear force as well as the bending moments. Theoretical solutions are obtained for a general blast loading distributed uni...

An experimental investigation is reported on the dynamic response of a clamped circular plate struck transversely by a mass at any point along a radial line. A study is made of the variation of the failure mode with a change of striker diameter-plate thickness ratio, together with an assessment of transverse shear effects and the energy-absorbing c...

A theoretical analysis is presented which examines the dynamic response of a rigid-perfectly plastic clamped beam struck transversely by a mass at any point on the span. The analysis employs an interaction yield surface which combines the bending moment, membrane force and transverse shear force required for plastic flow. Material strain rate sensi...

An approximate theoretical analysis is presented in this paper for the dynamic plastic response of a clamped beam grillage when struck transversely by a mass at the centre which produces large transverse displacements. The theoretical rigid-plastic predictions are compared with some recent experimental results on grillages struck by large masses an...