Q.M. Li

About the dynamic strength enhancement of concrete-like materials in a split Hopkinson pressure bar test

Split Hopkinson pressure bar (SHPB) technique has been used widely to measure the dynamic strength enhancement of concrete-like materials at high strain-rate between 101 and 103 s−1. Although SHPB technique has been verified for metallic materials, the validity and accuracy of SHPB results for non-metallic materials have not been thoroughly studied. The present paper examines the application of SHPB to determine the dynamic strength of concrete-like materials whose compressive strength is hydrostatic-stress-dependent. It shows that the apparent dynamic strength enhancement beyond the strain-rate of 102 s−1 is strongly influenced by the hydrostatic stress effect due to the lateral inertia confinement in a SHPB test. This apparent dynamic strength enhancement has been wrongly interpreted as strain-rate effect and has been adopted in both dynamic structural design and concrete-like material models for analytical and numerical simulations, which may lead to over-prediction on the dynamic strength of concrete-like materials. The SHPB test is simulated in the present paper using FE method and Drucker–Prager model to investigate how the hydrostatic stress affects the SHPB test results of concrete-like materials. A rate-insensitive material model is used in order to examine this pseudo-strain-rate sensitive phenomenon. A collection of SHPB test results of concrete-like materials are compared with simulation results, which confirms quantitatively that the apparent dynamic strength enhancement of concrete-like materials in a SHPB test is caused by the lateral inertia confinement instead of the strain-rate sensitivity of the tested material.

An SHPB set-up with reduced time-shift and pressure bar length

A modification of split Hopkinson pressure bar (SHPB) set-up based on wave separation technique is proposed in the present paper, which may be used to reduce the time-shifting distance and the pressure bar length in an SHPB test. Incident and reflected strains are separated through two-point strain measurement and the associated iterative formulas. A general error analysis is conducted for the iterative algorithm. The proposed modification of SHPB set-up is examined by using both FE-based numerical simulation and actual SHPB test.

Appraisal of Pulse-Shaping Technique in Split Hopkinson Pressure Bar Tests for Brittle Materials

Split Hopkinson pressure bar (SHPB) technique has been frequently used to measure the uniaxial compressive stress–strain relation of brittle materials at intermediate strain-rates where pulse-shaping technique is employed to improve the stress uniformity and maintain a nearly constant strain-rate in the specimen during the effective loading period. This paper appraises the functions of the pulse-shaping technique in SHPB tests of brittle samples based on numerical simulations of SHPB tests. It is shown that a proper pulse-shaper can attenuate high frequency oscillations of the incident pulse and increase the rise-time of the pulse, resulting in the improvement of stress equilibrium and uniformity along the axial direction of an SHPB specimen. However, it is found that the inertia-induced confinement in the radial direction of a brittle specimen is still significant even though the shaped incident stress pulse can generate a nearly flat plateau in the reflected pulse in the SHPB test. It implies that the achievement of a nearly constant strain-rate represented by a nearly flat plateau in the reflected pulse in an SHPB test may not give a true nearly constant strain-rate in the SHPB specimen. It is concluded that the application of the pulse-shaping technique in SHPB tests on brittle materials may not change the nature of the observed transition strain-rate, which represents the transition of the stress state from a uniaxial-compressive-stress-dominated state to a confined compressive stress state, rather than the start of significant strain-rate effect. Therefore, inertia-induced radial confinement effect needs to be considered in the interpretation of any SHPB results for brittle materials even though a pulse-shaper is used.

Perforation of a thick plate by rigid projectiles

Perforation of a thick plate by rigid projectiles with various geometrical characteristics is studied in the present paper. The rigid projectile is subjected to the resistant force from the surrounding medium, which is formulated by the dynamic cavity expansion theory. Two perforation mechanisms, i.e., the hole enlargement for a sharp projectile nose and the plugging formation for a blunt projectile nose, are considered in the proposed analytical model. Simple and explicit formulae are obtained to predict the ballistic limit and residual velocity for the perforation of thick metallic plates, which agree with available experimental results with satisfactory accuracy.

A modified model for the penetration into moderately thick plates by a rigid, sharp-nosed projectile

The deep penetration model based on cavity expansion analysis (Int. J. Impact Eng. 27 (2002) 619) is modified to take account of the increase of the contact area between the projectile nose and the target medium before the projectile nose fully penetrates into the target. The modified penetration model is applicable to those penetration problems where the length of the projectile nose is comparable to the penetration depth. The predicted results are in good agreement with experimental results from Diskshit and Sundararajan (Int. J. Impact Eng. 12(3) (1992) 373) and Diskshit et al. (Int. J. Impact Eng. 16(2) (1995) 293).

Penetration resistance of aluminium foam

The resistance of aluminium foam against projectile penetration has been studied experimentally and analytically and the results are presented in this paper. The penetration depth of a rigid, flat-nosed projectile into an aluminium foam target was measured at various impact velocities between 20 m/s and 120 m/s. An analytical model based on crushing stress shock enhancement theory is presented to offer estimation for the penetration depth into aluminium foam target by such a projectile.

In Situ Investigation and Image-Based Modelling of Aluminium Foam Compression Using Micro X-Ray Computed Tomography

Our understanding of the compressive behaviour of foams can be improved by combining micro X-ray computed tomography (CT) and finite element modelling based on realistic image-based geometries. In this study, the cell structure of an aluminium foam (AlporasTM) specimen and its deformation during continuous low-strain-rate compressive loading are recorded by ‘fast’ CT imaging. The original 3D meso-structure is used to construct a 3D finite element model (FEM) for simulation. It is observed that local collapse can occur in cells with a wide variety of shapes and sizes, and the compressive strength is determined by the formation and development of the localised deformation bands. The FE prediction of the stress–strain relationship and cell deformation process has reasonable agreement with the experimental observation, especially for the cell-wall collapse corresponding to the plateau in the stress–strain curve. The simulation also indicates that local yielding actually occurs in cell walls well before the plateau regime. The experimental and image-based modelling methods demonstrated here for foams have potential across a very wide range of applications.

Internal resonance of vibrational modes in single-walled carbon nanotubes

We show, by molecular dynamics simulations, that 2:1 internal resonance may occur between a radial breathing mode (RBM) and a circumferential flexural mode (CFM) in single-walled carbon nanotubes (SWCNTs). When the RBM vibration amplitude is greater than a critical value, automatic transformations between the RBM and CFM with approximately half RBM-frequency are observed. This discovery in the discrete SWCNT atom assembly is similar to the 2:1 internal resonance mechanism observed in continuum shells. A non-local continuum shell model is employed to determine the critical conditions for the occurrence of observed 2:1 internal resonance between the RBM and CFMs based on two non-dimensional parameters and the Mathieu stability diagram.

A correction methodology to determine the strain-rate effect on the compressive strength of brittle materials based on SHPB testing

Strain-rate effect on the compressive strength of brittle materials is normally characterized using split Hopkinson pressure bar (SHPB) technique. It has been found recently that the transition strain-rate observed in SHPB tests on concrete-like and other brittle materials represents the start of significant influence of lateral confinement effect, which has been widely misinterpreted as real strain-rate effect. This paper proposes a correction methodology to determine the real strain-rate effect for brittle materials in actual SHPB tests. The proposed method is verified using hybrid numerical simulations and experimental data. A complete procedure to conduct the correction is recommended.

Investigation of the Structural Failure of Penetration Projectiles

Structural failure of penetration projectiles is investigated in this paper. Normal and oblique penetration tests of small-scale projectiles into concrete targets are performed at impact velocities in the range of 620∼820 m/s. Three main failure modes, i.e. compressive, tensile and bending failures, are observed, based on which, analytical models are proposed to guide the design of the penetration projectile. Penetration resistance from a rigid projectile analysis is employed to estimate the forces applied on the projectile during penetration. Projectile nose erosion and the projectile tail attachment failure are also discussed. The proposed model leads to an improved classification of penetration regimes and a more accurate determination of the valid range of the rigid projectile assumption. Analytical models are validated by experimental results.