Split Hopkinson Pressure Bar

Determination of the mechanical properties of materials under the combined effects of high-temperatures and high strain-rates has been an important and challenging issue. A strategy has been proposed and evaluated recently towards this purpose in which a heating cell with accurate temperature control is synchronized with the split Hopkinson pressure bar (SHPB) system. This strategy allows pre-heating the specimen to desired temperatures before arrival of the stress wave and provides an experimental technique for the measurement of dynamic mechanical properties of materials at high-temperatures. Since its advent, this method has gained increasing interest in the community of dynamic mechanical testing owing to its ease of manipulation. However, a couple of critical problems should be addressed to validate the experimental results. Among the problems, a crucial one is associated with the temperature change in the heated specimen upon its contact with the relatively cold bars. In this paper, experiments were designed to determine the influence of cold-contact-time (CCT) on the temperature variation within the specimen. The experiments were conducted on Ti700 alloy at strain-rates of w10 4 s À1 and at temperatures from 20 to 800 C. The results show that the CCT does have a strong effect on the experimental results. Based on the experimental results and our analyses, we believe that the data can faithfully reflect the material behavior if CCT is shorter than 50 ms. While in most systems without the heating cell being synchronized with the SHPB system, the typical CCT is about 500 ms, and therefore the experimental data cannot be taken as representing the material behavior.

The split Hopkinson pressure bar (SHPB) technique has been employed to evaluate the dynamic squeeze flow behavior of viscous Newtonian fluids. In this paper, the conditions under which classic Hopkinson bar data analysis is applicable for fluid specimens are discussed in detail. Requirements include the development of a parabolic flow profile and associated pressure distribution across the specimen. The times required for these processes to occur are calculated and compared with the experimental timescale in order to establish a specimen design criterion for valid SHPB testing. To evaluate this design criterion, an isothermal squeeze flow model describing the behavior of a cylindrical fluid specimen which includes inertial forces is used to predict the experimental results for a model Newtonian fluid. Good agreement between the theory and the experiment is obtained for thin specimens (w1.0 mm) across a wide range of shear strain rates (over 10 5 s À1 ). As a result of this study, the conditions under which valid SHPB experimental results may be obtained for a Newtonian fluid specimen are identified.

PBX 9501 contains ~95 wt% HMX and 5 wt% binder system comprised of a 1:1 mixture of Estane5703 and a nitroplasticizer (NP). Prior studies have shown that storage of PBX 9501 in humid environments leads to hydrolysis of the ester linkages in the Estane that reduces its molecular weight. In addition, some nitroplasticizer has been shown to migrate out of the formulation with time. Four lots of PBX 9501 were formulated using new Estane and virtuallyaged Estane which had been exposed to 70°C and 74% relative humidity for 14, 23 and 36 days. To mimic extreme NP migration, two lots of X-0557 were formulated similar to PBX 9501 but with reduced NP/Estane ratios in the binder. Quasi-static and dynamic (split-Hopkinson pressure bar (SHPB)) compression tests were conducted, in addition to quasi-static tension tests, at temperatures between -55 to 50°C. The dynamic compression data show significant differences between the baseline and VA Estane specimens only at -15°C; however, significant differences are observed in the quasi-static compression data at all three temperatures. Reduced NP content strongly increases the strength and modulus of X-0557 versus PBX 9501.

In this paper two types of polymeric foams, namely, cross-linked poly-vinyl chloride (PVC) and polyurethane (PUR) were examined under compression loading at different strain rates. Quasi-static compression tests were performed using a servo-hydraulic material testing system (MTS) at strain rate of 0.001, 0.01, and 0.1 s −1 . Higher strain rate compression tests were performed using a split Hopkinson pressure bar (SHPB) apparatus with polycarbonate bars at strain rate ranging from 130 to 1750 s −1 . PVC foams with three densities and two microstructures, and PUR foams with two densities were considered. All foam specimens were tested in the thickness (rise) direction and the stress-strain responses at different strain rate were established to determine the peak stress and energy absorption. Both peak stress and energy absorption were found to be dependent on foam density, foam microstructure, and strain rate. A power law relationship between the peak stress and foam density revealed that the constants were different at different strain rate. Microstructural examinations of the failed specimens showed that PUR foams disintegrated completely around 1600 s −1 whereas PVC foams densified completely like a solid material.

Measurements are presented of the compressive stress-strain behaviour of polycarbonate (PC) and polyvinylidene difluoride (PVDF) at strain rates from 10 K4 to 10 4 s K1 at room temperature, and temperatures from K50 to C150 8C at 10 3 s K1 . These results, obtained using a split Hopkinson pressure bar and Instron testing machine, are supported by dynamic mechanical analysis (DMA) measurements on the materials. Previous researchers have observed that the yield stress of these materials is bilinearly dependent on the logarithm of strain rate. The data presented here show that the bilinearity is due to the movement of low order transitions in the materials, so that they occur at temperatures above room temperature at the higher strain rates. In particular, these transitions are the b transition in PC, and the glass transition in PVDF. In addition, Appendix A presents measurements of a high strain rate Poisson's ratio of polycarbonate and its evolution with strain. q

The paper describes the quasi-static and dynamic experimental methods used to examine the confined shear strength of an Ultra-High Performance Concrete, with and without the presence of steel fibers in the concrete composition. The experimental setup that employs a hydraulic press allows investigating the concrete shear strength under quasi-static loading regime while dynamic shear strength is characterized by subjecting concrete samples to dynamic loading through a modified Split Hopkinson Pressure Bar set-up. Both methods are based on a so called Punch Through Shear (PTS) test with a well-instrumented aluminum-alloy passive confinement ring that allows measuring the change of radial stress in the shear ligament throughout the test. First, four equally distributed radial notches have been performed on the concrete samples in order to deduce the radial stress in the shear ligament by suppressing self-confinement of the sample peripheral part. However, by analyzing the strain gauge data obtained from the confinement ring, it has been noticed that these were insufficient, especially for fiber-reinforced samples, resulting in subsequently practicing eight radial notches through the peripheral part of the samples. The results obtained from both procedures in addition to post-mortem observations are reported and discussed. It is concluded that the apparent increase of shear strength under dynamic loading compared to the quasi-static response is the consequence of higher radial confinement stresses at high strain-rates that results from an alteration of fracturing in mode I prior to mode II cracking in the ligament.

The 3D image correlation technique is used for full field measurement of strain (and strain rate) in compression and tensile split Hopkinson bar experiments using commercial image correlation software and two digital high-speed cameras that provide a synchronized stereo view of the specimen. Using an array of 128×80 (compression tests) and 258×48 (tensile tests) pixels, the cameras record about 110,000 frames per second. A random dot pattern is applied to the surface of the specimens. The image correlation algorithm uses the dot pattern to define a field of overlapping virtual gage boxes, and the 3-D coordinates of the center of each gage box are determined at each frame. The coordinates are then used for calculating the strains throughout the surface of the specimen. The strains determined with the image correlation method are compared with those determined from analyzing the elastic waves in the bars, and with strains measured with strain gages placed on the specimens. The system is used to study the response of OFE C10100 copper. In compression tests, the image correlation shows a nearly uniform deformation which agrees with the average strain that is determined from the waves in the bars and the strains measured with strain gages that are placed directly on the specimen. In tensile tests, the specimen geometry and properties affect the outcome from the experiment. The full field strain measurement provides means for examining the validity and accuracy of the tests. In tests where the deforming section of the specimen is well defined and the deformation is uniform, the strains measured with the image correlation technique agree with the average strain that is determined from the split Hopkinson bar wave records. If significant deformation is taking place outside the gage section, and when necking develops, the strains determined from the waves are not valid, but the image correlation method provides the accurate full field strain history.

A variety of techniques used to obtain the mechanical properties of materials at high rates of strain (X10 s À1 ) are summarised. These include dropweight machines, split Hopkinson pressure bars, Taylor impact and shock loading by plate impact. High-speed photography, particularly when used in association with optical techniques, is a key area and recent advances and applications to studies of ballistic impact are discussed. More comprehensive bibliographies and a fuller discussion of the history may be found in earlier reviews published by us in 1994, 1998 and 2001 (J Phys IV France 4 (C8) (1994) 3; Review of experimental techniques for high rate deformation studies,

This paper presents first material tests on HDPE and PVC, and subsequently impact tests on plates made of the same materials. Finally, numerical simulations of the plate impact tests are compared with the experimental results. A rather comprehensive series of mechanical material tests were performed to disclose the behaviour of PVC and HDPE in tension and compression. Quasi-static tests were

This report concerns the results of a S.T.I.R. Program carried out between March and November 2005. The general objectives of the program were to demonstrate the feasibility and utility of a novel use of the Split Hopkinson Pressure Bar (SHPB) as a tool for the investigation and development of multi-layered materials for high strain rate applications.

Electronic products are subjected to high G-levels during mechanical shock and vibration. Failure-modes include solder-joint failures, pad cratering, chip-cracking, copper trace fracture, and underfill fillet failures. The second-level interconnects may be experience high-strain rates and accrue damage during repetitive exposure to mechanical shock. Industry migration to leadfree solders has resulted in proliferation of a wide variety of solder alloy compositions. Few of the popular tin-silver-copper alloys include Sn1Ag0.5Cu and Sn3Ag0.5Cu.

For Kolsky bar testing beyond strain-rates of 10,000/s, it is useful to employ bars with diameters of only a few millimeters or less. Furthermore, very small (sub-millimeter) systems are compatible with micron-sized specimens, to be used, for example, for the determination of mesoscale properties. However, at these sizes, traditional strain-gage measurements of the longitudinal waves within the bars become impractical. In this paper we describe the application of optical measurement techniques to two Kolsky bars, with 3.2 and 1.6 mm diameters. A transverse displacement interferometer is used to measure the displacement of the mid-point of the incident bar and provide measurements of the incident and reflected pulses. Similarly, a normal displacement interferometer is used to measure the displacement of the free-end of the transmitter bar and provide a measurement of the transmitted pulse. The new methods are used to characterize the behavior of 6061-T6 aluminum at rates greater than 100,000/s. The feasibility of application to smaller bars is also discussed.

This work presents an investigation on the effects of adiabatic heating and strain rate on the dynamic compressive response of titanium, iron, copper, and tin. The high strain rate tests were carried out with a Split Hopkinson Pressure Bar (SHPB) and the low strain rate tests with a servohydraulic testing machine. The temperature increase of the specimens during deformation was measured with high speed infrared thermography (IRT). The results show that all the investigated materials have positive strain rate sensitivity and temperature increases of up to 65 • C were observed in the high strain rate experiments (500-3100 s − 1). Adiabatic heating in all investigated materials increased with strain rate. The temperature increase at the strain rate of 1 s − 1 clearly diminished the strain hardening rate of iron and titanium but was seemingly insufficient to impact the mechanical behavior of copper and tin. The Taylor-Quinney coefficients (β int and β diff) were found to be strain and strain rate dependent. At higher strain rates (1200-3100 s − 1), the integral β int was smaller in the beginning of the test (0.2 to 0.7) and increased to approximately 0.8-0.9 at larger plastic strains. The differential β diff comprised gaussian curves as a function of strain whose maximum values were from 0.9 to 1.2 for the investigated materials. Tin had lower β int and β diff with higher strain hardening rates, while copper had a higher β int and β diff with a low strain hardening rate throughout the high strain rate tests. These results indicate that copper had a more stable microstructure during deformation and converted most of the applied plastic work into heat, while tin had a faster evolving microstructure which stored more plastic work in its microstructure during plastic deformation. Furthermore, this suggests that β int and β diff can be used as parameters to investigate the stability and the microstructural evolution of materials under high strain rate plastic deformation. β diff is more appropriate to describe the instantaneous thermomechanical behavior of a material and β int is more appropriate for applications which benefit from a single parameter to characterize how efficiently a material converts plastic work into heat up to a given strain level.

This work presents a new design for a split Hopkinson tensile bar (SHTB) and generated representative experimental results. The new design uses a U shaped striker bar as projectile and addresses several shortcomings of classical SHTB designs using hollow striker bars. The results presented show that the non-symmetrical striker bar is capable of generating a clean and virtually oscillation free square pulse signal five times longer than typically achieved by classical striker tubes, whilst at the same time offering superior signal quality. Due to the longer stress pulse duration, the new SHTB design allows for the characterisation of materials at strain rates that were difficult to achieve for hydraulic testing machines and classical striker tube based SHTB designs. In addition, the developed SHTB is based on a simple and modular design and allows for a wide range of pulse shaping methodologies to be applied. Therefore, materials requiring different input stress pulse shapes, such as square (ductile), trapezoid or triangular (brittle), can be experimentally characterised at a large range of strain rates.

During automotive related accidents, PVB plays an important role in both pedestrian and passenger protection as an interlayer of automotive windshield. In this paper, dynamic constitutive behavior of PVB material is thoroughly studied. Firstly, a set of dynamic compression impact experiments on PVB specimens using SHPB (Split Hopkinson Pressure Bar) method are conducted at strain rates from 700/s to 4500/s. Details of the constitutive response is analyzed based on the validation of experiment data. Stress-strain curve of PVB is then divided into two parts, i.e., "Compaction Stage" and "Hardening Stage". Dislocations and entanglements among molecules are major reasons for the two-stage phenomena. Constitutive behaviors are different in low and high speed impacts, leading to three times more energy absorption ability of PVB in high speed impact scenario. Further, data fitting models based on both MooneyeRivlin and Ogden Model are studied and then compared. MooneyeRivlin Model is found to be more appropriate to describe PVB material. Moreover, PVB is proved to be a rate-dependent material with the failure strength intensify factor b z 4. PVB material shows little viscoelasticity after comparison of the both models with and without the viscoelasticity part. Results offer critical experimental data, constitutive models and analysis of PVB material to further study of automotive crashworthiness and pedestrian/passenger protection.

The mixed system composed by a Sensing block system and a Hopkinson bar is a new method to investigate mechanical properties of materials under high strain rates. In practice, however, wave dispersion distorts pulse shape and may limit the accuracy of results. Using finite element simulat ion, it is shown in this work that a half sinusoidal pulse decreases wave dispersion. Moreover, it is also demonstrated that the higher the rise time the lower the wave dispersion. It is known that a half s inusoidal pulse with a great rise time may be obtained by inserting a deformable disk (pad) between the incident bar and the sensing block. This fact is verified in this work using an appropriate constitutive suitable for the rise time. Optimu m characteris tics are found for the sensing block, the most suitable material and dimensions. The use of deformable pad is also impo rtant when brittle materials are tested; this is because the increase in pulse rise time allo ws a gradual stress application .

The scope of this study is to numerically simulate the behaviour of Brazilian disc specimens as observed in laboratory during dynamic, high-strain rate, indirect tensile tests using an innovative combined finite-discrete element method (FEM/DEM) research code. Laboratory experiments using a split Hopkinson pressure bar (SHPB) apparatus were conducted by the authors and the measured indirect tensile strength values were used to verify the FEM/DEM models. In the models the applied boundary conditions, related to the loading rate of the specimen, were matched with the experimental observations. The results of the numerical simulations, including tensile strength and failure time, are in agreement with the laboratory findings. The main failure mechanisms, i.e. tensile splitting along loading axis and shear failure close to loading platens are captured by the numerical model. A linear relationship between tensile strength and loading rate is found for the range of dynamic strain rates tested and simulated. The simulation results are in good agreement with laboratory observations and demonstrate the potential for using FEM/ DEM to realistically model dynamic response of rocks.

This paper describes the experimental procedure to identify the predominant frequencies of the high speed testing machine by conducting modal analysis. The effects due to the predominant frequencies of the system and loading rate on the magnitude of system ringing and the flow stress were analyzed by using a single degree-of-freedom (SDOF) spring-mass-damper model. The system was then used to study the dynamic tensile behavior of two engineering materials, i.e., polyethylene (PE) fabric-cement composite and Alkaline Resistant (AR) glass fabrics at an intermediate strain rate. The stress oscillations in the response of these materials due to system ringing were addressed. The failure behavior of each material was studied by examining high speed digital camera images of specimens during the test. The validity of the dynamic tensile tests was investigated by examining the condition of dynamic stress equilibrium—a criterion used in split Hopkinson pressure bar (SHPB) tests. The results ...

The split Hopkinson pressure bar (SHPB) technique is implemented to evaluate the transient response of a colloidal suspension exhibiting shear thickening at strain rates and timescales never before explored in a laboratory instrument. These suspensions are shown to exhibit a discontinuous transition from fluid-like (shear thinning) to solid-like (shear thickening) behavior when evaluated using rotational rheometry. The effect of loading rate on this transition time is studied for a particle volume fraction of 0.54 using the SHPB technique. It is shown that the time required for transition to occur decreases logarithmically with loading rate. From these results, we conclude that transition is not triggered by a characteristic shear rate, but rather a critical shear strain is required. Results from SHPB experiments performed up to Peclet numbers of order 10 7 are presented and discussed for 0.50, 0.52, and 0.54 particle volume fraction suspensions.

Sandwich composites are widely used in many structural applications due to their superior bending stiffness, low weight and excellent thermal insulation, etc. Many innovative improvements have been made in the construction of sandwich composites in recent years to improve their impact resistance. Evaluation of dynamic properties of such laminates is of vital importance to the designer. In the current study, foam filled 3D integrated core sandwich composite laminates with and without additional face sheets were fabricated using vacuum assisted resin infusion molding process in multiple steps. For additional facing, plain weave S2-glass and twill weave carbon fabrics were used on top and bottom sides of the panels in four different monolithic (S2-glass only, carbon only) and hybrid (glass + carbon, one with S2-glass layer outside and other with carbon layer outside) combinations. High strain rate (HSR) response of integrated core sandwich composites was determined using a split Hopkinson pressure bar setup (SHPB) under compression loading at strain rates ranging from 742 to 1546 s −1 . Dynamic response of different types of samples was compared in terms of the peak stress, modulus, strain at peak stress and failure modes.

In general, the shear localization process involves initiation and growth. Initiation is expected to be a stochastic process in material space where anisotropy in the elastic-plastic behavior of single crystals and inter-crystalline interactions serve to form natural perturbations to the materialÕs local stability. A hat-shaped sample geometry was used to study shear localization growth. It is an axisymmetric sample with an upper ''hat'' portion and a lower ''brim'' portion with the shear zone located between the hat and brim. The shear zone length is 870-890 lm with deformation imposed through a split-Hopkinson pressure bar system at maximum top-to-bottom velocity in the range of 8-25 m/s. We present experimental results of the deformation response of tantalum and 316L stainless steel samples. The tantalum samples did not form shear bands but the stainless steel sample formed a late stage shear band. We have also modeled these experiments using both conductive and adiabatic continuum models. An anisotropic elasto-viscoplastic constitutive model with damage evolution was used within the finite element code EPIC. A Mie-Gruneisen equation of state and the rate and temperature sensitive MTS flow stress model together with a Gurson flow surface were employed. The models performed well in predicting the experimental data. The numerical results for tantalum suggested a maximum equivalent strain rate on the order of 7 · 10 4 s À1 in the gage section for an imposed top surface displacement rate of 17.5 m/s. The models also suggested that for an initial temperature of 298 K a temperature in the neighborhood of 900 K was reached within the 0749-6419/$ -see front matter Ó (C.A. Bronkhorst).

The biaxial bulge test is a material test for sheet metals to evaluate formability and determine the flow stress diagram. Due to the biaxial state of stress induced in this test, the maximum achievable strain before fracture is much larger than in the uniaxial tensile test. A new dynamic bulge testing technique is simulated and analyzed in this study which can be performed on a conventional split Hopkinson pressure bar (SHPB) system to evaluate the strain-rate dependent strength of material at high impact velocities. Polyurethane rubber as pressure carrying medium is used to bulge the OFHC copper sheet. The use of hyperelastic rubber instead of fluid as a pressure medium makes the bulge test simple and easy to perform. The input bar of SHPB is used to apply and measure the bulging pressure. The finite element simulation using ABAQUS/explicit and analytical analysis are compared and show good correlation with each other. The results clearly show that as the strain-rate increases, the strength of the OFHC copper increases. From the study, a robust method to determine the material behavior under dynamically biaxial deformation conditions has been developed.

Fibre reinforced polymers (FRP) are finding increasing use in structures subjected to
high rate loading such as blast or impact. Proper design of such structures requires
thorough characterisation of the material behaviour over a range of loading rates from
quasi-static to impact. This thesis investigated the quasi-static and impact response
of Glass Fibre Polypropylene (GFPP) in compression, bending and delamination. The
bending and delamination response of Fibre Metal Laminates (FMLs) based on GFPP
and aluminium was also investigated at quasi-static and impact rates.
High strain rate (5 × 10 2 − 10 3 /s) compression tests were conducted on GFPP using
a compressive Split Hopkinson Pressure Bar (SHPB) and a Direct Impact Hopkinson
Pressure Bar (DIHPB), in the through-thickness and in-plane directions. In both load-
ing directions, the peak stress of GFPP increased linearly with the logarithm of strain
rate. For in-plane loading, the failure modes were dominated by localised fibre buck-
ling and kink bands, leading to delamination. The through thickness loading produced
macroscopic shear and spreading failure modes. However, both of these failure modes
are linked to in-ply fibre failures, due to through thickness compression causing trans-
verse tensile strain. Previous studies of similar materials have not explicitly stated the
link between through thickness compression and fibre failure associated with trans-
verse tensile strain.
A novel test rig was developed for Three Point bend testing at impact rates. The
specimen was supported at the outer points on a rigid impacter and accelerated to-
wards a single output Hopkinson Pressure Bar (HPB), which impacted the specimen
at its midspan. Previous impact bend test rigs based on HPBs were limited to testing
specimens with deflections to failure up to approximately 1 mm, whereas the rig imple-
mented herein measured deflections up to approximately 10 mm. This configuration
permits the output HPB to be chosen purely on the magnitude of the expected im-
pact force, which resulted in superior force resolution to configurations used in other
studies. The HPB Impact Bend rig was used to test GFPP and aluminium-GFPP FML
specimens, at impact velocities ranging from 5 to 12 m/s. The flexural strength of GFPP
increased with strain rate, while the flexural response of the FML specimens was rela-
tively insensitive to strain rate.
vSeveral candidate delamination test geometries were investigated at quasi-static
displacement rates (1 mm/min), and the Single Leg Bend (SLB) test was identified as
suitable for adaptation to higher rate testing. Single Leg Bend delamination tests of
both GFPP and FML specimens were performed using the HPB Impact Bend rig, at
impact velocities of 6 to 8 m/s. The shape of the force displacement response for the
high rate testswas markedly different from the quasi-static tests, for both the GFPP and
FML specimens. Finite element (FE) simulation of the quasi-static and impact rate SLB
tests on GFPP indicated that the difference was probably due to the interaction of flex-
ural vibrations and stress waves in the specimen and the impacter cross member. The
experimental results and FE analysis suggest that the delamination fracture toughness
of GFPP decreases slightly as strain rate increases. High rate delamination tests on
FML specimens resulted in unstable crack growth.

This report concerns the results of a S.T.I.R. Program carried out between March and November 2005. The general objectives of the program were to demonstrate the feasibility and utility of a novel use of the Split Hopkinson Pressure Bar (SHPB) as a tool for the investigation and development of multi-layered materials for high strain rate applications.

The development of an innovative apparatus, based on Hopkinson bar techniques, for performing large scale dynamic tests is presented and discussed. The activity is centered at the recently upgraded HOPLAB facility, which is basically a split Hopkinson bar with a total length of approximately 200 m, with bar diameters of 72 mm and where force pulses up to 2 MN and 40 ms duration can be generated and strain rates up to 50 s −1 can be achieved. Several modifications in the basic configuration have been introduced: twin incident and transmitter bars have been installed with strong steel plates at their ends where large specimens can be placed. A series of calibration and quan-tification tests has been conducted in order to prove the reliability of the experimental technique proposed. Moreover , real tests on concrete cylindrical samples of 200 mm diameter and of up to 400 mm length have been performed. Analyses of recorded signals indicate proper Hopkinson bar testing conditions and reliable functioning of the facility.

The split Hopkinson bar test is the most commonly used method for determining material properties at high rates of strain. The theory governing the specifics of Hopkinson bar testing has been around for decades. It has only been the last decade or so, however, that significant data processing advancements have been made. It is the intent of this thesis to offer the insight of its author towards new advancements.

Multilayer materials consisting of ceramic and glass/epoxy composites have been subjected to high strain rate compression testing using the Split Hopkinson Pressure Bar. The samples were extensively strain gaged so that dynamic data were generated directly from the samples during testing. Output data from the experiments were compared with numerical simulations of the same experiments and good agreement was noted. It was found that the stress distribution within samples was quite inhomogeneous and that stresses were highest in the region of the bar-sample interface. The presence of a rubber interlayer between the ceramic and glass/epoxy decreased the stress in both components but dramatically increased the degree of stress inhomogeneity.

In order to face the grand challenge of characterizing soft and light armour material system shaving polymers and shear thickening fluids under impacts at high strain rates lead to design and development of this particular SHPB set up. The developed set up is designed for a maximum firing pressure of 300 bar of nitrogen gas and it comprises automated gas filling and firing, striker bar velocity recording and data acquisition system. Pressure bars are made of titanium alloy due to its high yield strength and reasonably lower density which could protect plastic deformation, wave dispersion and reduces impedance mismatch with the intended soft specimens, unlike maraging steel bars. The maximum stresses on the critical parts of the setup are crosschecked with simulation results and compared with corresponding yield strengths. Velocitypressure calibration of the developed setup shows higher velocities can be achieved at any particular pressure, when it is compared with the existing publi...

The mechanical behaviour of a 7 series high-strength aluminium alloy that is mainly used by the aerospace industry is under investigation. Aluminium alloy AA7449-T7651 is mechanically tested at high strain rates (SRs), from 1000 to 10,000 s −1 and from room temperature up to elevated temperatures (80, 140, 200, and 300 • C). The mechanical characterisation is performed in compression by means of an experimental Split Hopkinson Pressure Bar facility. The material's flow stress (σ n) and maximum stress are significantly affected by both temperature and SR Nowadays, where the numerical simulation of several mechanical applications and processes that involve high deformation rates is a requirement the mechanical behaviour of the material should be described accordingly. The experimental data are utilised to calculate the SR hardening coefficients of two commonly used material models: Cowper Symonds and Johnson-Cook.

The paper presents results on dynamic mechanical properties of jute, and kenaf fibre reinforced composites at various strain rates using compression Split Hopkinson Pressure Bar technique. The stress-strain curves for both pultruded natural fibre reinforced composites at strain rates of nearly 1400 s À1 are illustrated and then compared with statically determines stress-strain curve (1.0 Â 10 À3 s À1 ). Results show that the strain rate does affect the value of dynamic compressive properties of both pultruded natural fibre composites. Higher dynamic compression modulus and 2.5% flow stress were recorded for higher strain rates as compared to lower strain rate over the range of strain rates investigated. Under dynamic loading, jute fibre reinforced composites recorded the highest value of dynamic response in terms of compression modulus, 2.5% flow stress and compressive strength than that of kenaf fibre reinforced composites. In addition, kenaf fibre reinforced composites is more severely damaged as compared to jute fibre reinforced composites for all tested strain rate.

A modified miniaturized version of the Direct Impact Compression Test (DICT) technique is described in this paper. The method permits determination of the rate-sensitive plastic properties of materials up to strain rate ∼10 5 s −1. Miniaturization of the experimental setup with specimen dimensions: diameter d S =2.0 mm and thickness l S =1.0 mm, Hopkinson bar diameter 5.2 mm, with application of a novel optical arrangement in measurement of specimen strain, makes possible compression tests at strain rates from ∼10 3 s −1 to ∼10 5 s −1. In order to estimate the rate sensitivity of a low-alloy construction steel, quasi-static, Split Hopkinson Pressure Bar (SHPB) and DICT tests have been performed at room temperature within the rate spectrum ranging from 5*10 −4 s −1 to 5*10 4 s −1. Adiabatic heating and friction effects are analyzed and the final true stress versus true strain curves at different strain rates are corrected to a constant temperature and zero friction. The results have been analyzed in the form of true stress versus the logarithm of strain rate and they show two regions of a constant rate sensitivity β ¼ Δσ. log " Á " : relatively low up to the strain rate threshold ∼50 s −1 , and relatively high above the threshold, up to strain rate ∼4.5*10 4 s −1 .

In this paper two types of polymeric foams, namely, cross-linked poly-vinyl chloride (PVC) and polyurethane (PUR) were examined under compression loading at different strain rates. Quasi-static compression tests were performed using a servo-hydraulic material testing system (MTS) at strain rate of 0.001, 0.01, and 0.1 s −1 . Higher strain rate compression tests were performed using a split Hopkinson pressure bar (SHPB) apparatus with polycarbonate bars at strain rate ranging from 130 to 1750 s −1 . PVC foams with three densities and two microstructures, and PUR foams with two densities were considered. All foam specimens were tested in the thickness (rise) direction and the stress-strain responses at different strain rate were established to determine the peak stress and energy absorption. Both peak stress and energy absorption were found to be dependent on foam density, foam microstructure, and strain rate. A power law relationship between the peak stress and foam density revealed that the constants were different at different strain rate. Microstructural examinations of the failed specimens showed that PUR foams disintegrated completely around 1600 s −1 whereas PVC foams densified completely like a solid material.

An orthotropic polymeric foam with transverse isotropy (Divinycell H250) used in composite sandwich structures was characterized at various strain rates. Uniaxial experiments were conducted along principal material axes as well as along off-axis directions under tension, compression, and shear to determine engineering constants, such as Young's and shear moduli. Uniaxial strain experiments were conducted to determine mathematical stiffness constants, i. e., C ij . An optimum specimen aspect ratio for these tests was selected by means of finite element analysis. Quasi-static and intermediate strain rate tests were conducted in a servo-hydraulic testing machine. High strain rate tests were conducted using a split Hopkinson Pressure Bar system built for the purpose using polymeric (polycarbonate) bars. The polycarbonate material has an impedance that is closer to that of foam than metals and results in lower noise to signal ratios and longer loading pulses. It was determined by analysis and verified experimentally that the loading pulses applied, propagated along the polycarbonate rods at nearly constant phase velocity with very low attenuation and dispersion. Material properties of the foam were obtained at three strain rates, quasi-static (10 −4 s −1 ), intermediate (1 s −1 ), and high (10 3 s −1 ) strain rates. A simple model proposed for the Young's modulus of the foam was in very good agreement with the present and published experimental results.

In the present work, dynamic tests have been performed on AISI 1018 CR steel specimens by means of a split Hopkinson pressure bar (SHPB). The standard SHPB arrangement has been modified in order to allow running tensile tests avoiding spurious and misleading effects due to wave dispersion, specimen inertia and mechanical impedance mismatch in the clamping region. However, engineering stress-strain curves obtained from experimental tests are far from representing true material properties because of several phenomena that must be taken into account: the strain rate is not constant during the test, the specimen undergoes remarkable necking, so stress and strain distributions are largely non-uniform, and the temperature increases because of plastic work. Experimental data have been post-processed using a finite element-based optimization procedure where the specimen dynamic deformation is reproduced. Optimal sets of material constants for different constitutive models (Johnson-Cook, Zerilli-Armstrong and others) have been computed by fitting, in a least mean square sense, the numerical and experimental load-displacement curves.

This paper presents the experimental measurements of a highly magnetoelastic material (Galfenol) under impact loading. A Split-Hopkinson Pressure Bar was used to generate compressive stress up to 275 MPa at strain rates of either 20/s or 33/s while measuring the stress-strain response and change in magnetic flux density due to magnetoelastic coupling. The average Young's modulus (44.85 GPa) was invariant to strain rate, with instantaneous stiffness ranging from 25 to 55 GPa. A lumped parameters model simulated the measured pickup coil voltages in response to an applied stress pulse. Fitting the model to the experimental data provided the average piezomagnetic coefficient and relative permeability as functions of field strength. The model suggests magnetoelastic coupling is primarily insensitive to strain rates as high as 33/s. Additionally, the lumped parameters model was used to investigate magnetoelastic transducers as potential pulsed power sources. Results show that Galfenol can generate large quantities of instantaneous power (80 MW/m3 ), comparable to explosively driven ferromagnetic pulse generators (500 MW/m3 ). However, this process is much more efficient and can be cyclically carried out in the linear elastic range of the material, in stark contrast with explosively driven pulsed power generators.

Crash simulations with Finite Element human body models would be better predictors of injury than with dummy models. During dynamic loading, human body soft tissues are exposed to varying strain rates. To characterize them, the conventional Split Hopkinson Pressure Bar (SHPB) is modified in order to test soft tissues. Experimentally determined engineering stress vs engineering strain curves for erector spinae, hamstring and gluteus max muscles are reported in the strain rate range of from 250/s to 1000/s. The loading curves exhibit multi linear behavior with increasing strain rate shifting the transition points between the slopes.

In general, the shear localization process involves initiation and growth. Initiation is expected to be a stochastic process in material space where anisotropy in the elastic-plastic behavior of single crystals and inter-crystalline interactions serve to form natural perturbations to the materialÕs local stability. A hat-shaped sample geometry was used to study shear localization growth. It is an axisymmetric sample with an upper ''hat'' portion and a lower ''brim'' portion with the shear zone located between the hat and brim. The shear zone length is 870-890 lm with deformation imposed through a split-Hopkinson pressure bar system at maximum top-to-bottom velocity in the range of 8-25 m/s. We present experimental results of the deformation response of tantalum and 316L stainless steel samples. The tantalum samples did not form shear bands but the stainless steel sample formed a late stage shear band. We have also modeled these experiments using both conductive and adiabatic continuum models. An anisotropic elasto-viscoplastic constitutive model with damage evolution was used within the finite element code EPIC. A Mie-Gruneisen equation of state and the rate and temperature sensitive MTS flow stress model together with a Gurson flow surface were employed. The models performed well in predicting the experimental data. The numerical results for tantalum suggested a maximum equivalent strain rate on the order of 7 • 10 4 s À1 in the gage section for an imposed top surface displacement rate of 17.5 m/s. The models also suggested that for an initial temperature of 298 K a temperature in the neighborhood of 900 K was reached within the

This article investigates the compressive strength of cemented paste backfill (CPB) under dynamic loading. To accommodate the low impedance CPB, a modified split Hopkinson pressure bar (SHPB) system is adopted. In contrast to traditional solid steel transmitted bar, a hollow aluminum transmitted bar is introduced to reduce the impedance. With this system, the dynamic stress equilibrium is achieved, which guarantees the valid dynamic material testing condition. The dynamic tests are conducted for CPB with different cement contents and curing time. It is observed that: (1) for CPB with the same curing time and cement content, the dynamic strength increases with the strain rate, (2) for CPB with the same cement content, the dynamic strength increases with the curing time, and (3) for CPB with the same curing time and tested under similar strain rate, the dynamic strength increases with the percentage of cement. This observation can be understood by considering the hydration process of cements.

Low velocity impacts on energetic materials induce plastic deformations and sliding friction which can lead to ignition. If some ignition criteria have been proposed, the remaining difficulty is to characterize the mechanical behavior of the material when submitted to the corresponding solicitations (high pressure and high strain rate). Thus, a technique based on the Split Hopkinson Pressure Bars system is proposed to carry out a triaxial compression test. A cylindrical specimen is placed into a confining ring and is compressed by the system of bars. The ring prevents the radial extension of the specimen and creates a lateral confining pressure. The material and dimensions chosen for the ring maintain a constant radial pressure during the test. Some tests were carried out on an inert aggregate material and proved the validity of this experimental device. The experimental data processing shows the influence of both the pressure and the strain rate. The shear stresses, which contribute to thermal dissipation and then to the ignition threshold, increase according to the pressure.

Finite element analysis is used to study experiments with the torsional split Hopkinson bar technique in which strain rates on the order of 10 4 s À1 are reached by using specimens with a very short gage length. Time-dependent analysis with a viscoplastic constitutive model for the specimen material is used to analyze the whole apparatus (elastic bars and specimen). Results from modeling tests with 1100-O aluminum show that the waves in the elastic bars can be modeled accurately when a significant increase is the flow stress at strain rates of 10 4 s À1 is assumed in the constitutive model of the material. The calculated stresses, strain rates, and strains in the specimen's gage section show that the state is not exactly of pure and homogeneous shear as assumed when the experimental stress strain curve is determined from the measured waves on the elastic bars, and that the plastic zone extends beyond the gage length. Even with these discrepancies the results show that the experimental curve provides a good estimation to the true material response. A time-independent analysis with rate-dependent material model is also used to analyze only the specimen and a short section of the adjacent flanges. The results show that this analysis can also be used to determine the validity of the assumed constitutive model of the material.

The split Hopkinson pressure bar (SHPB) technique has been used widely for the impact testing of materials in the strain-rate range from 10 2 to 10 4 s-1. However, some specific problems still remain mainly concerning the effects of radial inertia and end friction in a cylindrical specimen on the accurate determination of dynamic stress-strain curves of materials. In this study, the basic principle of the SHPB technique is revisited based on energy conservation and some modifications are made considering radial momentum conservation. It is pointed out that the radial inertia and end friction effects are coupled to each other in the SHPB specimen. Computational simulations using the commercial finite element (FE) code ABAQUS/Explicit ver. 6.8 are conducted to check the validity of the modifications for ductile pure aluminum specimens. Both rate-independent and rate-dependent models are adopted for the test material. Simulations are performed by varying two different control parameters: a friction coefficient between the specimen and the pressure bars and a slenderness ratio of the specimen (or thickness to diameter ratio).

The paper presents results on dynamic mechanical properties of jute, and kenaf fibre reinforced composites at various strain rates using compression Split Hopkinson Pressure Bar technique. The stress-strain curves for both pultruded natural fibre reinforced composites at strain rates of nearly 1400 s À1 are illustrated and then compared with statically determines stress-strain curve (1.0 Â 10 À3 s À1 ). Results show that the strain rate does affect the value of dynamic compressive properties of both pultruded natural fibre composites. Higher dynamic compression modulus and 2.5% flow stress were recorded for higher strain rates as compared to lower strain rate over the range of strain rates investigated. Under dynamic loading, jute fibre reinforced composites recorded the highest value of dynamic response in terms of compression modulus, 2.5% flow stress and compressive strength than that of kenaf fibre reinforced composites. In addition, kenaf fibre reinforced composites is more severely damaged as compared to jute fibre reinforced composites for all tested strain rate.

High strain rate bulge test technique which is introduced in this paper adopts a rubber-pad as pressure carrying medium to bulge a sheet metal at high velocity using split Hopkinson pressure bar (SHPB) system. The experimental set-up is based on conventional hydraulic bulge test which is modified to mount on SHPB. The thickness thinning of the sheet metal during the test will be considered as a measure of true strain of the bulged sheet. The theoretical approach is developed in this study to attain pressure-strain curves of sheet metals during high strain rate bulge forming process. This approach is followed by a finite element simulation of the process in ABAQUS/Explicit software. To verify the developed method, analytical and finite element methods are compared with experiments.