Review of experimental techniques for high rate deformation and shock studies

Classic Split-Hopkinson Pressure Bar Testing

This study of the dynamic compressive strength properties of metal foams is in two parts. Part I presents data from an extensive experimental study of closed-cell Hydro/Cymat aluminium foam, which elucidates a number of key issues and phenomena. Part II focuses on modelling issues. The dynamic compressive response of the foam was investigated using a direct-impact technique for a range of velocities from 10 to 210 ms - 1 . Elastic wave dispersion and attenuation in the pressure bar was corrected using a deconvolution technique. A new method of locating the point of densification in the nominal stress–strain curves of the foam is proposed, which provides a consistent framework for the definition of the plateau stress and the densification strain, both essential parameters of the ‘shock’ model in Part II. Data for the uniaxial, plastic collapse and plateau stresses are presented for two different average cell sizes of approximately 4 and 14 mm. They show that the plastic collapse strength of the foam changes significantly with compression rate. This phenomenon is discussed, and the distinctive roles of microinertia and ‘shock’ formation are described. The effects of compression rates on the initiation, development and distribution of cell crushing are also examined. Tests were carried out to examine the effects of density gradient and specimen gauge length at different rates of compression and the results are discussed. The origin of the conflicting conclusions in the literature on the correlation between nominal strain rate ɛ ˙ (ratio of the impact velocity V i to the initial gauge length l o of the specimen) and the dynamic strength of aluminium alloy foams is identified and explained.

Dynamic compressive strength properties of aluminium foams. Part I—experimental data and observations

The mechanical properties of polymers are becoming increasingly important as they are used in structural applications, both on their own and as matrix materials for composites. It has long been known that these mechanical properties are dependent on strain rate, temperature, and pressure. In this paper, the methods for dynamic loading of polymers will be briefly reviewed. The high strain rate mechanical properties of several classes of polymers, i.e. glassy and rubbery amorphous polymers and semi-crystalline polymers will be reviewed. Additionally, time–temperature superposition for rate dependent large strain properties and pressure dependence in polymers will be discussed. Constitutive modeling and shock properties of polymers will not be discussed in this review.

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High Strain Rate Mechanics of Polymers: A Review

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 −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.

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

An experimental method is developed to perform Hopkinson tests by means of viscoelastic bars by considering the wave propagation attenuation and dispersion due to the material rheological properties and the bar radial inertia (geometric effect). A propagation coefficient, representative of the wave dispersion and attenuation, is evaluated experimentally. Thus, the Pochhammer and Chree frequency equation is not necessary. Any bar cross-section shapes can be employed, and the knowledge of the bar mechanical properties is useless. The propagation coefficients for two PMMA bars with different diameters and for an elastic aluminum alloy bar are evaluated. These coefficients are used to determine the normal forces at the free end of a bar and at the ends of two bars held in contact. As an application, the mechanical impedance of an accelerometer is evaluated.

An experimental method for considering dispersion and attenuation in a viscoelastic Hopkinson bar

The paper presents a method to determine dynamic fracture toughness using a notched three-point bend specimen. With dynamic loading of a specimen there is a complex relation between the stress-intensity factor and the force applied to the specimen. This is due to effects of inertia, which have to be accounted for to evaluate a correct value of the stress-intensity factor. However, the stress-intensity factor is proportional to the load-point displacement if the fundamental mode of vibration is predominant in the specimen. The proportionality constant depends only on the geometry and stiffness of the specimen. In the present method we have measured the applied force and load-point displacement by a modified Hopkinson pressure bar, where two-point strain measurement has been used to evaluate force and displacement for times greater than the transit time for elastic waves in the Hopkinson bar. We have compared the method with the stress-intensity factor derived from strain measurement near the notch tip and good agreement was obtained. The method is well suited for high-temperature testing and results from fracture toughness tests of brittle materials at ambient and elevated temperatures are presented.

Dynamic fracture toughness determined from load-point displacement

A freely oscillating torsional pendulum was designed and built for measuring the in-plane shear modulus of film materials. To make the work easier for the experimenter, an online computer application was also developed with the help of numeric tools (Fourier and Hillbert transforms) for data acquisition and processing. The experimental part was performed on various materials. Experiments on a brass foil (isotropic material) validated measurements achieved with this experimental device. Experiments on orthotropic materials (base papers with different basis weights) gave prominence to the good reproducibility of measurements and to the ability for using this torsional pendulum. For this kind of material (large basis weight base paper), the in-plane shear modulus seemed independent of the fiber orientation.

Conception of an experimental device for measuring the in-plane shear modulus of film materials

This paper studies the effects of a microwave excitation on the transverse vibrations of viscoelastic bars placed inside unconventional electromagnetic waveguides Its purpose is to present a general approach that can be applied to analyze and to interpret the physical phenomena risen during the heating process These phenomena were not predicted either by conventional experiments or by existing theoretical models To measure the bar transverse deformations, an opening line and a hole have been made respectively on one of the small transverse sides of the waveguides The comparison between the spectra of the experimental transverse velocities measured with these two waveguides has pointed out some differences Theoretical and finite element (FE) simulations of the experiments have been firstly applied to figure out the nature of these variations The analysis is conducted by a parameterized approach that takes into account the effects of the opening line made along the waveguide on both the propagation of the electromagnetic power density and the temperature rise distribution inside the sample Good agreements between the models and the experimental data are demonstrated Furthermore, the method has also shown a sudden asymmetric temperature distribution that leads to the generation of new flexural modes These last modes are specific to the experiment used to apply the microwave induce acoustic technique

C. Bacon

Papers

An experimental method for considering dispersion and attenuation in a viscoelastic Hopkinson bar

Dynamic fracture toughness determined from load-point displacement

Conception of an experimental device for measuring the in-plane shear modulus of film materials

Transverse Vibrations of Viscoelastic Bars Subjected to an Asymmetric Temperature Distribution Induced by a Microwave Source