G. Gary

On the use of SHPB techniques to determine the dynamic behavior of materials in the range of small strains

The classical Split Hopkinson Pressure Bar technique is re-examined in order to optimize its accuracy, especially in the range of small strains. For many nonmetallic materials such as concrete, rocks, ceramics and polymers, the most important aspects of their behavior can be located in the range of small strains. The accuracy of the basic measurements of forces and velocities at both sample faces is discussed concerning the early stage of the loading. This accuracy depends on data processing which consists mostly of an accurate dispersion correction and of exact delays setting. A more precise wave dispersion correction and a new method to set exact origins of waves are then proposed. The validity of the average stress-strain curve obtained from measured forces and velocities is analysed using an one-dimensional numerical transient simulation of the tests. A fictitious specimen with a rate sensitive behavior described by a Sokolovsky-Malvern type constitutive model is used for this simulation. For the case where the classical SHPB analyses do not give acceptable results, an identification technique based on an inverse calculation method is presented. It relates material properties to forces and particle velocities measured at both faces of the specimen without using the assumption of axial uniformity of stresses and strains.

On the use of a viscoelastic split hopkinson pressure bar

To test weak materials such as foams at high strain rates, the use of a Split Hopkinson Pressure Bar (SHPB) setup made of low impedance bars, which are mostly viscoelastic, is indispensable. In this paper a detailed study of the technical problems of such a viscoelastic setup related to the measurement and to the loading conditions is offered. On the basis of the three-dimensional (3D) Fourier stationary harmonic wave analysis, the wave shifting technique is developed. It is shown that the effect of geometrical dispersion in a viscoelastic setup is generally non-negligible. The case of loading with a viscoelastic projectile is also analysed, showing that the impact of a viscoelastic projectile creates an incident wave with a significant time extension.

A three dimensional analytical solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar. Application to experimental techniques

This paper presents an original three dimensional (3D) analytical general solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar and its applications to some experimental methods of material behaviour testing to improve their accuracy. One application is to take into account the wave dispersion effects in the split Hopkinson pressure bar (SHPB) setup composed of viscoelastic bars. Another is to eliminate the geometrical effects in an impulse test in which the linear viscoelastic material properties can be deduced from the change in the wave shape due to the propagation between two points of measurement in a specimen bar.

A new method for the separation of waves. Application to the SHPB technique for an unlimited duration of measurement

The measuring duration of an SHPB (Split Hopkinson Pressure bar) set-up is limited by the length of the bars so that there is a limitation of maximum measurable strains in material testing applications. This paper presents a new two-gauge measurement method which takes account of the correction for wave dispersion effects, which cannot be ignored for long time measurements. Using bars of equal dimensions, it allows a quasi-unlimited measuring duration which can be up to 100 times longer than the classical one. Analyses of the sensitivity of results to the imprecision of experimental data show that the method is robust and reliable. It is applied to the testing of soft materials like foam (metallic or polymeric) in the complete range of their response (nominal strains up to 80%) not only at high strain rates but also at medium strain rates (5 s−1 < e < 50 s−1), with a measuring accuracy comparable with that of the SHPB. It is also successfully used to perform large displacement tests such as crushing of metallic tubes.

An optimisation method for separating and rebuilding one-dimensional dispersive waves from multi-point measurements. Application to elastic or viscoelastic bars

When using a classical SHPB (split Hopkinson pressure bar) set-up, the useful measuring time is limited by the length of the bars, so that the maximum strain which can be measured in material testing applications is also limited. In this paper, a new method with no time limits is presented for measuring the force and displacement at any station on a bar from strain or velocity measurements performed at various places on the bar. The method takes the wave dispersion into account, as must inevitably be done when making long time measurements. It can be applied to one-dimensional and single-mode waves of all kinds propagating through a medium (flexural waves in beams, acoustic waves in wave guides, etc.). With bars of usual sizes, the measuring time can be up to 50 times longer than the time available with classical methods. An analysis of the sensitivity of the results to the accuracy of the experimental data and to the quality of the wave propagation modelling was also carried out. Experimental results are given which show the efficiency of the method.

Behaviour characterisation of polymeric foams over a large range of strain rates

The testing and modelling of the mechanical behaviour of some polymeric foams involved in the automotive industry are presented. A variety of current experimental arrangements over a large range of strain rates have been reviewed. Recent improvements of a particularly useful technique for impact loading – the split Hopkinson bar - are presented. A phenomenological model is developed to describe experimental data. Difficulties for 3-dimensional testing and modelling are also discussed.

The testing and behaviour modelling of sheet metals at strain rates from 10−4 to 104 s−1

Abstract Uniaxial quasi-static tests and dynamic compression tests at high strain rates have been performed to determine the mechanical behaviour of sheet metals widely used in the automotive industry. The quality of experimental data at high strain rates obtained with a split Hopkinson pressure bar (SHPB) depended on signals processing. Improvements in this field are discussed: the wave dispersion correction, an exact delay setting in the shifting of the waves and the use of an inverse calculation technique. A constitutive elastic-plastic model for strain rates in the range 10 −4 –10 4 s −1 is then proposed for sheet metals. The thermal softening due to the adiabatic conditions of the dynamic test was taken into account in creating this model.

Identification de la relation de dispersion dans les barres

Dispersion and attenuation of longitudinal waves in elastic or weakly viscoelastic rods are measured by analysing the resonant frequencies present in the strain spectrum due to an unknown loading. The method takes the finite measuring time of the test into account. It is applied to an aluminium bar, in which the dispersion relation is identified very accurately at frequencies up to 60 kHz.

Dynamic buckling of an elastoplastic column

Abstract Dynamic buckling of columns under axial step loading which produces plastic behaviour is investigated. An experimental study is described and an elastoplastic model is developed in order to analyse the buckling process. Good agreement is obtained between the theoretical predictions and experimental results which justifies the main assumptions underlying the model.

An experimental investigation of compressive failure strength of fibre-reinforced polymermatrix composite plates under impact loading

This paper presents an experimental investigation on the compressive failure strength of fibre-reinforced polymer-matrix composite plates under impact loading. A new viscoelastic split Hopkinson pressure bar (SHPB) is used to measure those properties. Experimental problems such as dispersion corrections in viscoelastic bars are analysed. Significant increases of the compressive failure strength with the strain rate are found. It is also observed that the failure strength is sensitively higher when the loading is in the fibre direction. It is then in agreement with theoretical and experimental results under quasi-static loading.