John J Harrigan

Inertia effects in uniaxial dynamic compression of a closed cell aluminium alloy foam

Abstract The dynamic compressive characteristics of a closed cell aluminium alloy foam (manufactured by Hydro Aluminium AS, Norway) have been studied experimentally by using a direct impact technique for a range of velocities up to 210 m s–1. Experimental data on the dynamic initial crushing and plateau stresses are compared for two average cell sizes of approximately 4 and 14 mm. The data reveal significant dynamic enhancements of the initial crushing strengths throughout the range of velocities used. The dynamic plateau stresses are insensitive to impact velocity below the values of 50 and 100 m s–1 for the large and small cell foams respectively. Beyond a critical velocity value of ~ 100 m s–1, the crushing wave front propagates through the foam with shock like characteristics. The inertia effects associated with the dynamic localisation of crushing and the microinertia of the cell wall/edge material on the dynamic strength enhancement are discussed. A one-dimensional shock model based on a rate independent, rigid, perfectly plastic locking idealisation of the nominal stress–strain curve for foams is employed to provide a first order understanding of the various parameters involved in the crushing process. The results of the analyses are seen to predict well the dynamic strength enhancements that are measured experimentally. The sources of discrepancies are highlighted and discussed, as are the limitations and shortcomings of the shock model.

Inertia effects in impact energy absorbing materials and structures

Experimental data and numerical/computational models concerning the internal inversion of metal tubes and the dynamic crushing of aluminium honeycombs are presented and discussed as illustrations of impact energy absorbers whose behaviour is strongly influenced by inertial effects.

Transient effects in the quasi-static and dynamic internal inversion and nosing of metal tubes

Abstract The plastic deformation mechanisms of metal tubes during quasi-static nosing and internal inversion are analysed. Rigid-plastic analyses which incorporate an assumption of full conformity between the deforming tube and the forming die predict accurately the nosing load-displacement curve. Details of the deformation processes during internal inversion are examined using the non-linear facilities of the finiteelement code ABAQUS. The early stages of the forced inversion characteristic are more complex than for nosing, with different deformation modes dominating the behaviour at different times. Each of these is also examined using rigid, perfectly plastic models. The quasi-static behaviour is used to provide insight into features of the load pulses generated during dynamic/impact loading of the tubes. The peak impact loads can only be assessed through a full dynamic analysis since inertial effects strongly influence the magnitude of the dynamic loads. It is shown that measured dynamic force pulses for both nosing and internal inversion can be accurately predicted fusing appropriate finite element models and the source of the high dynamic force peaks in inversion is discussed. It has been found both experimentally and numerically that the steady-state inversion force is lower under dynamic loading conditions than under quasi-static loading. A simple analytical model provides an explanation for this and highlights the importance of the ratio of the mass of the striker to that of the inverted portion of the tube in this phenomenon.

A framework for reliability assessment of ship hull damage under ship bow impact

Ship collision analysis outcomes are generally used in computational models to derive damage distributions. However, damage is usually assessed after the collision energy has been fully absorbed by structural members rather than at the onset of outer hull fracture. Furthermore, the deformation behaviour of ship structural members under load depends on uncertainty modelling through material, geometric, and structural considerations, captured in an appropriate reliability framework. To consider these significant missed opportunities in understanding the probability of ship structures meeting their performance targets during collisions, a novel stochastic framework is proposed in this paper. For efficient reliability computations, a plate resistance model is developed for hull damage assessment at the onset of failure. Stochastic modelling capabilities of Python scripting are interfaced with Abaqus® to compute the stochastic response. The reliability computations show that the probability of hull fracture increases as the hull deformation progresses, with maximum values occurring at the onset of outer hull fracture. The framework outcomes are useful in determining optimal ship structural design capabilities.

Probabilistic Considerations in the Damage Analysis of Ship Collisions

Ship collision events are often analyzed by following the approach of internal mechanics and external dynamics. The uncertainties in collision scenario parameters, which are used in the calculation of external dynamics, are usually quantified during ship collision analysis. However, uncertainties in the material and geometric properties are often overlooked during the analysis of internal mechanics. Consequently, it may lead to overestimation or underestimation of ship structural design capacity, which could impact on system performance.

High‐Rate Compaction of Aluminium Alloy Foams

The response of aluminium foams to impact can be categorised according to the impact velocity. Tests have been carried out at a range of impact velocities from quasi‐static to velocities approaching the speed of sound in the foam. Various experimental arrangements have been employed including pneumatic launcher tests and plate impact experimants at velocities greater than 1000 m s−1. The quasi‐static compression behaviour was approximately elastic, perfectly‐plastic, locking. For static and dynamic compression at low impact velocities the deformation pattern was through the cumulative multiplication of discrete, non‐contiguous crush bands. Selected impact tests are presented here for which the impact velocity is less than the velocity of sound, but above a certain critical impact velocity so that the plastic compression occurs in a shock‐like manner and the specimens deform by progressive cell crushing. Laboratory X‐ray microtomography has been employed to acquire tomographic datasets of aluminium foams b...

Analytical Description of Stress Waves in Viscoelastic Bars

Strain‐gauged circular rods are used for Split Hopkinson Pressure Bar (SHPB) testing. Strain measurements along the bar are used to determine the stress and displacement histories at the end of the bar. A new wave equation is derived for long polymeric rods. The material properties are modelled as a Maxwell viscoelastic material acting in parallel with an elastic material. Lateral motions of the rod that result from the Poisson effect are accounted for using a new concept called the “effective density.” The effects of both the material properties and the diameter of the bar on dispersion and attenuation coefficients are highlighted. The new wave theory simplifies to Wang et al.’s formula (1994) for one‐dimensional waves in polymer rods if the Poisson ratio is set to zero. The predictions simplify to Love’s equation for stress waves in elastic bars when rate dependency is removed from the material model.

Strength of the aluminium alloy 6082-T6 under high strain-rate conditions

The measurement of shear strength via the use of lateral stress gauges has been shown to be a viable technique in a number of materials. An experimental investigation on the intermediate‐rate behaviour and shock response of the aluminium alloy, 6082‐T6, is reported here. Results obtained using the lateral stress gauge technique show that the shear strength increases with impact stress. The lateral stress behind the shock front is seen to be relatively flat, unlike many other face‐centred cubic metals and alloys, where a decrease in lateral stress indicates an increase in shear strength. This unusal response may be a reflection of the high stacking fault energy of aluminium and its alloys resulting in a reduction of the work hardening (i.e. increases in dislocation and/or twin density). Further plate impact results show that the Hugoniot of 6082‐T6 is in effect identical to that of the more widely known 6061‐T6. Split Hopkinson pressure bar results are used to provide a fuller picture of the rate‐dependant...

Intermediate and High Strain‐Rate Testing of Soft Materials

Strain‐gauged bars are often employed as load cells for direct impact testing of materials and are incorporated within the split Hopkinson pressure bar (SHPB). Low impedance bars (e.g., magnesium or polymer bars) are desirable when testing soft specimens such as various energetic materials and cellular solids. However, due to the rheological properties of polymer bars, wave dispersion and attenuation occurs. For relatively large diameter bars and high frequency waves, geometrical wave dispersion due to radial inertia also occurs. In this paper the spectral finite element method (SFEM) is applied to the SHPB to obtain the stress‐strain curves of specimens under investigation by an inverse analysis. The method presented makes use of a higher‐order rod approximation, applicable to viscoelastic bars, that accounts for wave dispersion. To demonstrate the technique experimental results for balsa wood using both magnesium alloy and PMMA bars are provided.

Inversion of Metal Cylinders

The quasi-static behaviour of inversion tubes can provide insight into features of the load pulses generated during dynamic/impact loading of the tubes. A rigid-plastic analysis of the first stage of forced, internal inversion is provided. The assumption that the tube conforms to the profile of the shaped die is removed. The influence of the interaction surface in plastic deformation is investigated by utilising a three-dimensional Tresca yield criterion for shells.