High Strain Rate Characterization Research Articles

On the development of a high strain-rate tensile testing method for thin low-impedance materials

This work deals with the high strain-rate characterization of paper under uniaxial tension using a Split Hopkinson test bench. An aluminum bar system featuring a highly sensitive hollow transmission bar was used. Paper tests were performed in a strain-rate range between approximately 60 s−1 and 210 s−1. The experimental tests showed that the breaking strength appears to decrease with increasing strain-rate. To verify these results, a digital twin of both the paper specimen and the entire test rig was created in an explicit Finite Element method environment. The numerical model was then used to perform a parameter study with different types of transmission bars. It was shown that the system is quite sensitive to additional masses caused by the specimen fixtures, as well as to drastic reductions in the cross section of the transmission bar. As a result, the transmitted measuring signal can be distorted and may need to be corrected using the digital twin.

Revisiting the effect of sabot on the incident signals of split-Hopkinson pressure bar

In typical split-Hopkinson pressure bar set-ups, the striker bar is propelled in a barrel of larger diameter. Teflon/brass sabots are used to concentrically-align the striker inside the barrel. The influence of the area mismatch between barrel and striker, length of the sabots and interface condition between sabot and striker are analyzed in detail using finite element simulations. We show that for a given geometry of the sabot, a frictionless interface does not alter the incident signals. In the presence of friction, the incident signals deviate from the classical trapezoidal shape. The magnitude of the deviation depends on the geometry of the sabot. As an alternative to the shrink/press fitted sabot, a stepped striker is used to eliminate some issues faced during the usage of the shrink/press-fitted sabot. The stepped striker has a non-uniform diameter such that at two locations its diameter is that of the barrel, and at other locations it has the same diameter as the incident bar. The influence of the geometry of the stepped striker on the distortion of the incident signal is investigated in detail using the method of characteristics. A parametric study is used to quantify this distortion for various geometric configurations of the stepped striker. Three striker geometries are chosen from these configurations to validate the parametric study using experiments. High strain rate characterization of SS304 is also carried using these strikers to illustrate the effect of the geometry of the stepped striker on the stress versus strain and strain rate versus strain response.

An update on the development of techniques for the determination and modelling of the impact behaviour of adhesives and bonded structures used in the automotive sector

The automotive sector is one of the key users of adhesive bonding, adopting this technology for the manufacture of high performance multi material structures, seeking to reduce vehicle weight and increase overall stiffness. In these industrial applications, the design of bonded structures is supported by numerical models, which require the determination of the mechanical properties of the adhesives and the adherends, taking into account factors such as temperature and strain rate dependence. However, while the design of bonded joints under quasi-static loadings is currently well understood, the design of impact resistant structures is much more complex, since it requires the establishment of accurate models for the strain rate dependent behaviour of the materials used in vehicle construction. This document provides an updated outlook on the research work being performed by the authors in this specific field. Most of the work is devoted to the analysis of the effects of strain rate on the behaviour of adhesives and adhesive joints. This includes high strain rate characterisation of the mechanical behaviour of modern crash resistant adhesives, using both standardised and custom testing procedures. Special experimental equipment has also been developed for impact testing procedures, including high strain rates and mixed mode conditions and full-size specimens.

High strain-rate characterization of shear thickening fluid reinforced with MWCNT nanoparticles using SHPB

In this study, the stress–strain behavior and energy absorption of silica/multi-walled carbon nanotubes shear thickening fluid (SiO2/MWCNT-STF) at different strain rates were studied using a split Hopkinson pressure bar (SHPB) apparatus. The SHPB results revealed that SiO2/MWCNT-STFs have more significant strain rate effects than SiO2-STF upon impact. Furthermore, the addition of MWCNT to SiO2-STF elicited a strain rate effect, wherein both the stress and energy absorption peaks varied proportionally with strain rate. Specifically, at a deformation rate of 5100 s−1, the energy absorption peak of SiO2-STF increased by 168.5 % and 229.1 % with the addition of 0.8 % and 1.2 % MWCNT, respectively.

Exploring the Effect of Dispersed Phase on the High Strain Rate Mechanical Response of Nanosilica Dispersions

Shear Thickening Fluids (STFs) constitute a special class of materials which exhibit phase transition from low to high viscosity state when exposed to shearing forces, particularly, when the applied shear rate exceeds a critical value. The last decade has witnessed a mutual symbiotic relationship between STF and high-performance fabrics such as Kevlar®, Dyneema®, Ultra High Molecular Weight Polyethylene (UHMWPE) etc., to produce new light weight and flexible protective materials systems with enhanced knife, stab and ballistic resistant properties than the existing ones. In this study, we explore the effect of particle shape and size on the high strain rate dynamic response of nanosilica dispersions. Shear thickening fluid (STF) was synthesized using fumed silica and spherical nanosilica particles, comprising the dispersed phase, whereas PPG400 (Polypropylene Glycol) was used as the dispersion medium. Ultrasonic homogenization technique was used for the synthesis of STF. The low strain rate rheological characterization was conducted on MCR302 rheometer at 25°C, whereas the high strain rate characterization was performed on inhouse designed and developed SHPB (Split Hopkinson Pressure Bar) apparatus. Fumed silica (FS) particles possess high specific surface area owing to their fractal structure. Therefore, their low molecular weight dispersions exhibit shear thickening behavior thus making them potential candidates for liquid body armour applications. On the other hand, spherical silica dispersions exhibit shear thickening behavior in high phase volume concentrations. Experimental studies showed that spherical silica based STF dispersions exhibited enhanced shear thickening in the low strain rate domain, as well as better mechanical response in terms of higher peak stress under high strain rate compressive loading conditions, during SHPB testing, in comparison to their fumed silica counterpart. Thus, it can be inferred that the mechanical response of nano-silica dispersions is influenced by the shape of the particles constituting the dispersed phase.

Correction to: High strain rate characterisation of soda-lime-silica glass and the effect of residual stresses

Correction to: High strain rate characterisation of soda-lime-silica glass and the effect of residual stresses

High strain rate characterisation of soda-lime-silica glass and the effect of residual stresses

A ring-on-ring test configuration for the equibiaxial flexural testing of flat samples was integrated into a novel modified split-Hopkinson pressure bar (SHPB) setup. The established modifications enabled high-speed cameras for fracture assessment and non-contact optical deflection measurements using stereo digital image correlation (stereo-DIC). In the present paper, this setup was utilised to characterise the flexural surface strength and stiffness (Young’s modulus) of circular, as-received soda-lime-silica glass samples at high strain rates. The effect of residual stresses was also studied by including thermally tempered glass samples divided into four residual stress groups. Despite the frequent application of glass products in the built environment, often post-processed into tempered or laminated glass, these investigations are still rare and thus highly demanded when designing for extreme events such as extreme weather, ballistic impacts, or blast loads. A total of 315 samples were tested at a quasi-static and a dynamic loading rate ranging from 2.0 to \(4.3\cdot 10^6\,\hbox {MPa}\,\hbox {s}^{-1}\). It was found that the flexural strength of the glass across residual stress groups was strongly dependent on the applied dynamic loading rate, while the residual stresses themselves showed no significant effect on the loading rate dependence. At the dynamic loading, the strength increased between 60 and 86%. Within the two tested loading rates, strength increased expectedly with compressive surface stress. From the stereo-DIC deflection measurements, no change in Young’s modulus with loading rate was observed.

A Microstructure-Based Mechanistic Model for Bone Sawing: Part 1—Cutting Force Predictions

Abstract This two-part paper is aimed at developing a microstructure-based mechanistic modeling framework to predict the cutting forces and acoustic emissions (AEs) generated during bone sawing. The modeling framework is aimed at the sub-radius cutting condition that dominates chip-formation mechanics during the bone sawing process. Part 1 of this paper deals specifically with the sawing experiments and modeling of the cutting/thrust forces. The model explicitly accounts for key microstructural constituents of the bovine bone (viz., osteon, interstitial matrix, lamellar bone, and woven bone). The cutting and thrust forces are decomposed into their shearing and ploughing components. Microstructure-specific shear stress values critical to the model calculations are estimated using micro-scale orthogonal cutting tests. This approach of estimating the microstructure-specific shear stress overcomes a critical shortcoming in the literature related to high-strain rate characterization of natural composites, where the separation of the individual constituents is difficult. The six model coefficients are calibrated over a range of clinically relevant depth-of-cuts (DOCs) using pure haversian regions (comprising of osteon and interstitial matrix), and pure plexiform regions (comprising of lamellar bone and woven bone). The calibrated model is then used to make predictions in the transition region between the Haversian and plexiform bone, which is characterized by gradient structures involving varying percentages of osteon, interstitial matrix, lamellar bone, and woven bone. The mean absolute percentage error in the force predictions is under 10% for both the cutting and thrust forces. The reality of spatially varied properties in the cortical bone limits the universal use of microstructure-specific shear stress values reported here. Fundamental advancements in the literature associated with both high-strain rate bone mechanics and machining are needed to address this critical limitation.

Mechanical characterisation and modelling of a thermoreversible superamolecular polyurethane over a wide range of rates

Understanding the mechanical response of thermo-recoverable elastomers to applied deformation at different strain rates and temperatures is crucial for more effective exploitation of these reusable materials in industrial applications. The research presented in this paper aims to understand the thermal and mechanical responses of a healable, elastomeric supramolecular polyurethane, examining morphology, rheology and mechanical responses from low to high strain rates. In particular, measurement of the high strain rate response of low modulus, or low strength, materials is challenging, and the current paper addresses this by incorporating a modelling framework based on low-rate characterization. To support this research, significant characterization experiments have been performed, which also show, for the first time, the excellent reusability of the polymer. The structure of specimens with different thermal histories was characterized using nuclear magnetic resonance spectroscopy, gel permeation chromatography and small angle X-ray scattering. Differential scanning calorimetry and Rheometry were used to investigate thermomechanical performance during heating and cooling cycles, whilst large strain compression characterization was performed on a commercial screw-driven test frame, a hydraulic loading system and a split-Hopkinson pressure bar. To describe the mechanical response of the polymer, a viscoelastic softening model was developed and characterized. The model incorporates data from rheometry and dynamic mechanical analysis using the principle of time-temperature superposition in a Prony series, combined with a non-linear large strain response, and recovery. The model was able to describe low strain rate behaviour under monotonic and cyclic loading, as well as predicting the response to monotonic loading at medium-to-high strain rates from 40 to 1220 s−1. The paper therefore demonstrates the effectiveness of using the viscoelastic theory and its analytical model to calibrate and further predict the mechanical behaviour of polymers at different strain rates: this is particularly useful for low modulus materials for which high strain rate characterization is challenging.

Numerical simulation of AA7075 under high strain rate with different shape of striker of split Hopkinson Pressure bar

The high strain rate characterization of materials have always remained an essential to know the exact behaviour in dynamic conditions, such as blasts, earthquakes, projectile penetrations, crashworthiness of vehicles, bullet proof armours. These high strain rate characterizations can be done using experimental technique such as Split Hopkinson Pressure Bar (SHPB) Test. These experimental techniques are very costly and difficult to conduct. However, the behaviour of materials under dynamic loading can be performed under high strain rate using finite element simulation of SHPB Test. The numerical simulations of AA7075 under different shape and velocity of striker in dynamic conditions are performed utilizing ABAQUS/Explicit 6.14. To understand the effect of shape, striker bar’s shape is varying from circular to square while its length is kept constant as 200 mm. Furthermore, impact velocity is also varied from 20 to 50 m/s to see the effect of velocity under large strain rates. The test specimen’s shapes are also of varying cross-section to understand the effect of shape of specimen under dynamic conditions. Results stated that the wave’s amplitude and duration are dependent to the striker parameters. Specimen shape also affects the flow behaviour of specimen.

Quasi-static and high strain rate response of Kevlar reinforced thermoplastics

The present study deals with the quasi-static and high strain rate characterization of Kevlar-129 based thermoplastic composites. Two different thermoplastic matrices, namely, Polypropylene (PP) and Polyetherimide (PEI) were used to manufacture composite laminates. Quasi-static compression tests were performed at strain rates of 0.041 s−1 and 0.045 s−1. High strain rate tests were performed using a split Hopkinson pressure bar apparatus within the strain rates ranging from 2548 s−1 to 4379 s−1. Stress-strain relations reveals the rate-sensitive behaviour of composites. Kevlar/PP (K-PP) showed higher peak stress under quasi-static loading as compared to the high strain rate test. Comparable peak stresses were revealed under quasi-static and high strain rate loading for Kevlar/PEI (K-PEI) composite. Also, high strain rate compression properties such as peak stress, peak strain and toughness of K-PP were 25%, 27% and 6% higher than that of the K-PEI composite. The failure mechanisms of both the composites were characterized through macroscopic and scanning electron microscopy. K-PP failed majorly due to matrix crush and fibre failure while K-PEI failed due to shear cracking. Damage study reveals that a single fibre based composite system can be tailored to act as an energy-absorbing or dissipating material system by varying the thermoplastic matrix materials.

Characterization of Sandstone for Application in Blast Analysis of Tunnel

Abstract The present work aims to gain an understanding of the stress-strain response of sandstone, a sedimentary rock, under high loading rate and further determine the appropriate specimen dimension of sandstone for dynamic testing. The high strain rate characterization of sandstone is done for two different diameters and five different slenderness ratios of sandstone specimens using a 76-mm–diameter split Hopkinson pressure bar (SHPB) device. The stress-strain response of sandstone is studied by systematically varying the length of the striker bars and gas gun pressure of the SHPB device. The petrological and static characterizations of the sandstone rock are also carried out. Finally, the appropriate specimen size of sandstone for SHPB testing is proposed by checking the strength gain of the rock and amount of energy absorbed during the tests. Further, finite element (FE) analysis of the SHPB test on sandstone is performed using the strain rate–dependent Johnson-Holmquist (JH-2) model available in the FE software, LS-DYNA. The simulation results are compared with the experimental data in order to determine the parameters of the JH-2 model for sandstone. A parameter database is thus prepared for sandstone. The determined parameters are then used in the blast analysis of tunnels for a 20-kg trinitrotoluene (TNT) explosion and the tunnel response is studied.

High strain rate characterisation of intralaminar fracture toughness of GFRPs for longitudinal tension and compression failure

The elastic parameters, strengths, and intralaminar fracture toughness are determined for an E-Glass polymer composite material system, statically and at high strain rate, adapting methodologies previously developed by the authors for different carbon composites. Dynamic experiments are conducted using tension and compression Split-Hopkinson Bars (SHBs). A unique set of experimental parameters is obtained, and reported together with the experimental set-up, in order to ensure reproducibility. While in-plane elastic and strength properties were obtained by testing one specimen geometry, intralaminar fracture properties required the testing of different sized notched specimens with scaled geometries. This allowed the use of the size-effect method for the determination of the dynamic R-curve. When comparing these results with those previously obtained for a carbon/epoxy material system, it is observed that the dynamic fracture toughness exhibits a much more significant increase in both tension and compression. The obtained results permit the identification of the softening law at different strain rates, allowing its use in any analytical or numerical strength predictive method.

Dynamic Characterisation of Gneiss

The present work aims to understand the stress–strain response of a metamorphic rock, and gneiss under high loading rate for different specimen diameters and slenderness ratios through detailed tests. The high strain rate characterisation of gneiss rock is done for two different diameters and five different slenderness ratios of the rock specimens using a 76 mm-diameter split Hopkinson pressure bar (SHPB) device in an effort to understand the standard specimen dimension for gneiss in SHPB test. The stress–strain response of the rock specimens is studied by varying the length of the striker bars and the gas gun pressure values, systematically. The petrological and static characterisation of the gneiss rock is also carried out to assess the response of the rock specimens. Finally, a methodology is proposed to characterize gneiss rock specimens under high loading rate. Furthermore, numerical simulation of SHPB test on gneiss rock is performed using strain rate-dependent Johnson–Holmquist (JH-2) model available in the finite-element software package, LS-DYNA. The simulation results are compared with the experimental data, and thus, the parameters of JH-2 model for gneiss rock are determined.

Characterisation of the behaviour of welded aluminium structures under dynamic loading

The presence and quality of welds in metallic structures has the ability to influence their likelihood of failure under dynamic loading. This investigation focused on characterising the behaviour of a welded aluminium structure. Samples were taken from the parent metal, heat affected zone (HAZ) and the weld bead and high strain rate characterisation testing was performed to determine the Johnson-Cook (JC) strength and failure model parameters for each material. However, significant scatter was found in the data for the weld bead due to porosity within the samples. Additional tensile tests were performed using a rotating fly wheel machine with four larger samples, which were machined from the welded aluminium structure and contained HAZs on either side of the weld bead, located in the centre of the specimen. Three of the four samples had the weld bead ground flush to the level of the base plate. Digital image correlation was used to determine the surface strain within each region of the sample and identified significant strain localisation at the interface between the weld metal and the HAZ, as well as within the weld bead. Comparisons between the ground welded specimens and those with the weld reinforcement showed a different failure mode between the two specimens. For the ground specimens, the strain localisation in the weld bead initiated failure prior to the strain localisation occurring at the interface between the weld bead and HAZ. Sectioning of the welds indicated that the strain localisation in the weld bead may have been caused by significant levels of porosity within the weld bead. Preliminary numerical simulations of the ground specimens indicated that the force-time history could be well captured. However, as the strain localisation due to porosity is not captured using a JC model, in addition to the scatter in the characterisation data for the weld bead, failure was not accurately predicted numerically.

Investigating the strength of materials at very high strain rates using electro-magnetically driven expanding cylinders

Most metallic materials exhibit a noticeable strain rate sensitivity in the range of 103–104 s−1 due to changes in dislocation dynamics in this regime. For applications that are sensitive to the material behavior at very high strain rates, there is a true need to measure the material strength at strain rates exceeding 104 s−1 and calibrate a reliable model that accounts for their strain rate hardening.Various experimental methods are reported in the literature for measuring strength at very high strain rates such as explosively driven expanding ring tests (ERT), various plate impact techniques and Rayleigh-Taylor instability growth tests. While the attainable strain rates can be very high, the interpretation of these tests can be somewhat controversial, as coupled effects such as pressure hardening and thermal softening, together with the effects of high strain rates, do not enable a unique determination of the contribution of the high strain rate to the actual measured strength.We present here a new methodology to measure the strength of materials at very high strain rates, up to 7.5⋅104 s−1, using magnetically driven expanding cylinder experiments. We use a pulse current generator (PCG) to apply magnetic forces on hollow cylindrical specimens and measure the expanding motion using velocity interferometery. To investigate the dynamic behavior of the specimens and their strength, we use numerical simulations. 2D hydrodynamic simulations were conducted for the design of the specimens, and 1D MHD simulations for simulating the actual tests. In this work, we present results for nine EM driven OFHC cylinders, reaching strain rates up to 7.5⋅104 s−1. We report a significant strain rate hardening for the OFHC copper and provide a calibrated Modified Johnson Cook (MJC) constitutive model for our data in the regime ranging from 103 s−1 (Kolsky bar tests) up to 105 s−1, from the PCG tests. It is believed that the methodology that is presented here will open the way for very high strain-rate characterization of metallic materials.

High strain rate characterization of shear thickening fluids using Split Hopkinson Pressure Bar technique

Shear thickening fluids (STFs) are a special class of field responsive fluids which exhibit change of phase from liquid to solid when subjected to imposed shear. This remarkable characteristic of STFs has led to their application in soft body armor technologies, leading the development of concept of Liquid Body Armors (LBAs). LBAs extensively rely upon the symbiotic relationship between STF and high strength FRP (Fiber Reinforced Polymer) composites comprising of high tenacity fibers such as Kevlar, UHMWPE (Ultra High Molecular Weight Poly Ethylene) etc. Although in the past, STFs have been widely characterized by rheometers at low strain rates (≤103 s−1), but in actual practical scenarios, body armours encounter much higher strain rates (of the order of 105–107 s−1) under a ballistic impact. The main objective of this study is to capture the dynamics of STFs at such high strain rates by employing Split Hopkinson Pressure Bar (SHPB) technique. The STF sample was synthesized by dispersing 67.5wt.% of 100nm silica powder in Poly Propylene Glycol (PPG) and ethanol, using ultrasonic homogenization method. The mechanical response of STF was studied at high strain rates in terms of the stress-strain behavior and variation of the impact toughness with the loading rate of the fluid specimen. It was observed that the impact toughness of STF increased progressively with the specimen loading rate. The peak stress and peak strain rate attained in the SHPB tests were 147MPa and 22,100 s−1, respectively. The characteristic transition time of STF was found to be in the range of 13–25 µs.

High Strain Rate Characterization of Himalayan Dolomite

This paper presents the static and dynamic experimental characterization of dolomite subjected to static unconfined compressive strength test and dynamic split Hopkinson pressure bar (SHPB) tests. The dynamic compression tests on rock samples are performed at strain rates from 500/sec to 1500/sec. It is observed from the results that the rocks exhibit significant strain rate sensitive behaviour and the peak stress increases with increasing strain rate. In the present work, the force equilibrium at the incident and transmission bar ends of the rock samples has been studied. Dynamic increase factor (DIF), i.e. the ratio of the dynamic to static peak stress has been calculated at different strain rates. Based on the calculated DIF values, an empirical correlation equation has been proposed for the DIF of the rock with the strain rate induced.

Influence of particle size on the low and high strain rate behavior of dense colloidal dispersions of nanosilica

Shear thickening is a non-Newtonian flow behavior characterized by the increase in apparent viscosity with the increase in applied shear rate, particularly when the shear rate exceeds a critical value termed as the critical shear rate (CSR). Due to this remarkable property of shear-thickening fluids (STFs), they are extensively used in hip protection pads, protective gear for athletes, and more recently in body armor. The use of STFs in body armor has led to the development of the concept of liquid body armor. In this study, the effect of particle size is explored on the low and high strain rate behavior of nanosilica dispersions, so as to predict the efficacy of STF-aided personal protection systems (PPS), specifically for ballistic applications. The low strain rate study was conducted on cone and plate rheometer, whereas the high strain rate characterization of STF was conducted on in-house fabricated split Hopkinson pressure bar (SHPB) system. Spherical nanosilica particles of three different sizes (100, 300, and 500 nm) as well as fumed silica particles of four different specific surface areas (Aerosil A-90, A-130, A-150, and A-200), respectively, were used in this study. The test samples were prepared by dispersing nanosilica particles in polypropylene glycol (PPG) using ultrasonic homogenization method. The low strain rate studies aided in determining the CSR of the synthesized STF dispersions, whereas the high strain rate studies explored the impact-resisting ability of STFs in terms of the impact toughness and the peak stress attained during the impact loading of STF in SHPB testing.

Development of a Hopkinson Bar Apparatus for Testing Soft Materials: Application to a Closed-Cell Aluminum Foam.

An increasing interest in lightweight metallic foams for automotive, aerospace, and other applications has been observed in recent years. This is mainly due to the weight reduction that can be achieved using foams and for their mechanical energy absorption and acoustic damping capabilities. An accurate knowledge of the mechanical behavior of these materials, especially under dynamic loadings, is thus necessary. Unfortunately, metal foams and in general “soft” materials exhibit a series of peculiarities that make difficult the adoption of standard testing techniques for their high strain-rate characterization. This paper presents an innovative apparatus, where high strain-rate tests of metal foams or other soft materials can be performed by exploiting the operating principle of the Hopkinson bar methods. Using the pre-stress method to generate directly a long compression pulse (compared with traditional SHPB), a displacement of about 20 mm can be applied to the specimen with a single propagating wave, suitable for evaluating the whole stress-strain curve of medium-sized cell foams (pores of about 1–2 mm). The potential of this testing rig is shown in the characterization of a closed-cell aluminum foam, where all the above features are amply demonstrated.