Review of experimental techniques for high rate deformation and shock studies

Classic Split-Hopkinson Pressure Bar Testing

http://www-mech.eng.cam.ac.uk/profiles/fleck/papers/191.pdf

The uniaxial stress versus strain response of pig skin and silicone rubber at low and high strain rates

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

An experimental method for dynamic tensile testing of concrete by spalling

The dispersion curves for guided waves have been of constant interest in the last decades, because they constitute the starting point for NDE ultrasonic applications. This paper presents an evolution of the semianalytical finite element method, and gives examples that illustrate new improvements and their importance for studying the propagation of waves along periodic structures of infinite width. Periodic boundary conditions are in fact used to model the infinite periodicity of the geometry in the direction normal to the direction of propagation. This method allows a complete investigation of the dispersion curves and of displacement ∕ stress fields for guided modes in anisotropic and absorbing periodic structures. Among other examples, that of a grooved aluminum plate is theoretically and experimentally investigated, indicating the presence of specific and original guided modes.

Wave propagation along transversely periodic structures

In this paper, constitutive relations are solved in the Fourier domain using a finite-element-based commercial software. The dynamic responses of viscoelastic bars or plates to either thermal or mechanical loads are predicted by considering complex moduli (Young, Poisson, stiffness moduli) as input data. These moduli are measured in the same frequency domain as that which is chosen for modeling the wave propagation. This approach is simpler since it suppresses the necessity of establishing a rheological model. Specific output processing then allows the numerical predictions to be compared to analytical solutions, in the absence of scatterers. The performances of this technique and its potential for simulating more complicated problems like diffraction of waves or for solving inverse problems are finally discussed.

Finite element predictions for the dynamic response of thermo-viscoelastic material structures

A single-sided, air-coupled ultrasonic NDT system based on the generation and reception of the A0 Lamb mode is used for detecting defects in plates. Transmitting and receiving transducers, being oriented at the appropriate coincidence angle for the generation and detection of the mode, are scanned along a line from one side to the other over the surface of the sample, passing the area with the defect. This contact-less NDT system is modelled in three dimensions with a Finite Element -based method. The air-coupled transmitter is modelled by the normal pressure that it locally applies on the surface of the plate, and the air-coupled receiver by integrating normal displacements over a finite area of appropriate position on the surface of the plate. In this way, beam spreading of both incident and scattered fields is considered. Numerical predictions have successfully been compared with experimental data for a through-thickness hole in an Aluminium plate and also for an impact damage in a composite sample.

3D finite element simulations of an air-coupled ultrasonic NDT system

Separation of waves propagating in an elastic or viscoelastic Hopkinson pressure bar with three-dimensional effects

This paper describes the implementation of equations of dynamic equilibrium in a finite element (FE) code for modeling, in axisymmetry, the propagation of torsional wave modes along metallic pipes coupled to solid elements. Materials constituting either pipes and/or surrounding elements can be absorbing media, the absorption being caused by either their viscoelasticity or scattering on their internal structure (or both). Complex moduli are used as input data to equations of dynamic equilibrium, which are solved in the frequency domain rather than in the temporal domain. Their real and imaginary parts represent material elasticity and damping, respectively. A new definition of efficient and easy-to-implement absorbing regions that suppress undesired reflections from boundaries is proposed. The resolution of equations in the frequency domain, together with the use of absorbing regions, lead to significant reductions in the number of mesh elements and also in the number of iterations required for describing problems of propagation and scattering. Through two examples, the model is validated by successful comparisons of numerical predictions with experimental data. Then, a third example is presented to illustrate the importance of properly modeling waves damping when using FE models for setting-up or optimizing NDT techniques.

Christophe Bacon

Papers

Wave propagation along transversely periodic structures

Finite element predictions for the dynamic response of thermo-viscoelastic material structures

3D finite element simulations of an air-coupled ultrasonic NDT system

Separation of waves propagating in an elastic or viscoelastic Hopkinson pressure bar with three-dimensional effects

Finite element modeling of torsional wave modes along pipes with absorbing materials