Split Hopkinson Pressure Bar Technique Research Articles

An improvement of the Lagrangian analysis method based on particle velocity profiles

In general, techniques used in studies on dynamic behaviour of materials could be classified into two categories, namely the split Hopkinson pressure bar technique (SHPB) and the wave propagation technique (WPT). Lagrangian analysis method is one of the most famous methods in WPT. The traditional Lagrangian analysis based on the particle velocity wave-profiles measurements should consider a boundary condition, because it involves integral operations. However, the boundary stress data in some cases cannot be detected or determined by the experimental measures. To tackle this situation, this paper presents a modified Lagrangian analysis method which does not involve the boundary stress computation. Starting from the path-lines method and utilizing the zero-initial condition, the material constitutive stress-strain curves under high strain-rates is deduced from only observing the particle velocity curve measurements. The dynamic stress/strain wave-profiles of the PMMA material, as a paradigm, are numerically studied using the proposed method, which are well in agreement with the theoretical result using the method of characteristics, which confirms the reliability and validity of the presented method.

Additively manufactured penetrating warheads

Penetrating warheads have to both defeat thick and high strength targets and have high blast effects. Lattice structures could help to enhance blast effect and reduce the weight of the penetrators. Additive manufacture provides a method to produce this concept. This paper details a programme to evaluate the perforation performance of such a penetrator. This study implemented an approach based on the integration of virtual and physical tests. A mesoscale numerical approach based on explicit high order finite element (HOFEM) was first developed to optimize the lattice pattern. The dynamic behaviour of this material was then determined using the Split Hopkinson Pressure Bar (SHPB) technique and this was then used to fit a constitutive model in Impetus Afea Solver®. The modelling of the concrete penetration of small scale warhead was based on the advanced meshless approach coupled with HOFEM. The models developed enabled the determination, simultaneously, of the homogenised behaviour of the lattice material and also the global behaviour of the penetrators during and after the penetration. Seven ballistic tests against concrete targets were performed at Thiot Ingenierie to investigate the penetration capabilities of the additively manufactured penetrating warhead concept and especially when using a lattice pattern.

Compressive behavior of Sulcata Tortoise’s carapace at high rate of deformation

This paper presents the dynamic compressive response of tortoise carapace at high rate of deformation. Disk specimens are cut from carapace and compressed using Split-Hopkinson Pressure Bar (SHPB) technique. The steel bar system together with a copper pulse shaper generate an incident wave that can achieve a constant rate of deformation within the specimens. The results show increasing compressive modulus and compressive strength compared to the quasi-static data of carapace. The strain waves on the incident and the transmission bars from finite element analysis based on the experimental setup agree with the test data.

Experimental characterization of dynamic crack growth behavior in CFRP adhesive interface

The dynamic crack growth behavior of adhesively bonded joints under mode I and mixed mode (I + II) loading were investigated. The split Hopkinson pressure bar (SHPB) apparatus and the digital image correlation (DIC) technique were employed to determine the mode I fracture toughness of the adhesively bonded joints during crack propagation under impact loading. The dynamic crack growth behavior for carbon fiber reinforced plastics (CFRP) adhesively bonded joints under mode I loading was studied using this method. In order to verify the proposed method, the dynamic crack growth behavior of titanium alloy adhesively bonded joints was also studied. Moreover, the crack growth behavior of CFRP adhesively bonded joints under mixed mode loading was studied using the SHPB technique. For the considered CFRP adhesively bonded joints, the fracture toughness decreased under both mode I and mixed mode loading as the loading rate increased. Microscope observation showed that a shift in the crack location occurred in the high loading tests.

Method for determining the strain rate sensitivity factor for the Johnson-Cook model in Charpy tests

Abstract The basis for the study was the necessity to design a supporting structure of the road infrastructure subjected to high strain rates occurring during vehicle accidents. Mathematical models of hardening due to the high strain rates are reviewed. Commonly used methods for determining constants for one of the models, i. e., Johnson-Cook model are characterized. The main section of the study presents a proposed method for determining the strain rate sensitivity of the material. It is a hybrid method which requires Charpy tests using unnotched specimens and a series of calculations using the finite element method to simulate the tests. Several variants of strain measurement of specimen subjected to failure in Charpy tests, as required for the proposed method are analyzed. Using the suggested method, a strain rate sensitivity factor was obtained with a value similar to the value obtained using the split Hopkinson pressure bar technique. The advantages of the suggested method compared to the existing me...

Influence of the end cap deformation of a hollow transmission bar on the hollow split Hopkinson pressure bar test results

The deformation of an end cap was found when analyzing a hollow transmission bar with an end cap. The deformation may cause errors in hollow split Hopkinson pressure bar (SHPB) test results. Therefore, the influence of the end cap deformation on hollow SHPB test results was analyzed to guide researchers to avoid these mistakes. It is known that the hollow split Hopkinson pressure bar technique using a hollow transmission bar with an end cap is a material dynamic property testing technology, which is used to increase the amplitude of the transmitted signal by reducing the transmission bar cross-sectional area. The relation between the end cap deformation and the test results was derived. And the natural frequency of an end cap was also calculated to compare with the frequency of the interferences in test results. Several simulations and hollow SHPB experiments using hollow transmission bars with end caps in different thickness were undertaken to analyze the influence of the end cap deformation on Hopkinson bar test results. A high-frequency interference was found in a transmitted wave when the end cap was vibrating which also conform the analyzed relation between them. High-frequency interferences were also found in the experiments. The frequency of the interference in a transmitted wave (in both simulations and experiments) was similar to the natural frequency of the end cap. The vibration and the interference became weak and the interference frequency became high when the thickness of an end cap increased. When the thickness of an end cap was larger than half external diameter of the hollow transmission bar, both the vibration and the interference disappeared, however the transmitted wave introduced another kind of distortion.

A new method to measure volume resistivity during tension for strain rate sensitivity in deformation and transformation behavior of Fe-28Mn-6Si-5Cr shape memory alloy

This paper is concerned with the measurement method of volume resistivity in Fe-based shape memory alloy (Fe-SMA) during tensile tests using the circuit with a higher precision based on the Kelvin double bridge. In order to evaluate an amount of martensite associated with shape memory effect (SME), especially at higher deformation rate, it is convenient to capture the change in volume resistivity, which has a correlation with the amount of martensite. On the other hand, it is necessary to consider rate sensitivity of martensitic transformation behavior which is the key of SME as well as deformation behavior in Fe-SMA because the alloy is unavoidable to deform at higher strain rate. In this study, at first, a circuit with a higher precision based on the Kelvin double bridge is assembled. Then, tensile tests of Fe-28Mn-6Si-5Cr alloy at different strain rates are conducted by using two different testing apparatuses such as the conventional material testing machine and impact testing machine based on the split Hopkinson pressure bar technique. The rate sensitivity of the volume resistivity in Fe-SMA is experimentally captured by using the assembled circuit during the tensile testing at various strain rates. Shape recovery strain due to SME is measured by heating the specimens deformed quasi-statically at various strain rates up to above reverse transformation temperature.

Performance of Anchors in Concrete Controlled by Splitting Failure under Dynamic Push-In Loadings

Anchors in concrete are widely used to transfer any given load combination into a concrete member. The dynamic behavior of post-installed rebar anchors has been experimentally investigated in this study. The attention was focused on anchors controlled by concrete splitting failure, the case that may occur with anchors and fastenings located close to an edge or to a corner. In this regard, Split Hopkinson Pressure Bar (SHPB) technique has been employed to test the anchorage systems under dynamic push-in loads. The effect of loading rates, concrete compressive strengths, and embedment depths on ultimate splitting load has been studied. The results showed the loading rates had a pronounced effect on the anchor ultimate loads and total absorbed energy by the anchors. Whereas the variation of concrete compressive strength influenced the ultimate load, the increase in embedment depth had no noticeable effect on ultimate load.

High-strain-rate plastic deformation and fracture behaviour of Ti-5Al-5Mo-5V-1Cr-1Fe titanium alloy at room temperature

To study the plastic deformation and fracture behaviour of Ti-5Al-5Mo-5V-1Cr-1Fe (Ti-55511) alloy under high strain rate loading conditions, a series of dynamic compression tests on Ti-55511 alloy have been performed at constant strain rates ranging from 350 s−1 to 2900 s−1 by means of split Hopkinson pressure bar technique at room temperature. The different strain and strain rate loading conditions are realized by changing the length and velocity of the striker bar, and high intensive localized shear region is induced in Ti-55511 alloy. The dynamic compression stress-strain response, strain rate hardening effect and strain rate sensitivity, and the fracture behaviour are discussed. The experimental results demonstrate that: The strain rate hardening effect and strain rate sensitivity of Ti-55511 alloy are apparent; Brittle shear bands form at high strain rate loading conditions, and the formation of a shear band does not mean the occurrence of phase transformation; Collapse of the specimens occurs along a plane inclined at an angle of about 45° to the compression axis at room temperature for both quasi-static and dynamic compression loading; The shear-compression zone and tension-shear-compression zone coexist in the fracture surface, and collapse of the specimens is attributed to shear failure mechanism for Ti-55511 alloy under compression loading at room temperature.

Experimental characterization of dynamic behaviour of gelatin-based material using DIC

In this paper, the dynamic response of gelatin-based soft material under impact loading is investigated. The dynamic tests are principally performed by the classical SHPB (Split Hopkinson Pressure Bars) technique. However, due to the very low mechanical impedance of the specimen compared with the Hopkinson bars, the feeble impact forces are measured by highly sensitive piezoelectric polyvinylidene fluoride (PVDF) pressure sensors instead of SHPB measurement system. The PVDF pressure sensors are placed on the interfaces between the specimen and the bars. During the impact test, the non-equilibrium stress state and inhomogeneous strain fields are developed in the specimen; a digital image correlation (DIC) technique is proposed to identify the inhomogeneous displacement fields using high speed photography. A non-parametric approach based on the DIC technique is developed to deduce the transient stress fields in the longitudinal and transverse directions from the displacement fields measured by DIC. The validation of the calculated stress fields is performed by comparing them with the stress measurements from the PVDF pressure sensor at the bottom end of the specimen. Furthermore, stress-strain response is carried out using this approach throughout the specimen. It is clearly shown that the average highest strain rate varies with position in the specimen. This lead to multiple stress-strain relations determined at different strain rates by only one impact test. The significant strain rate sensitivity is observed at the tested rate range from 81/s to 269/s. Under compression loading, the axial stress state is developed as a simple compression only in the central part of the specimen due to the friction at the interfaces between the specimen and the bars. According to the calculated results based on movement of “long waves”, the region of the simple compression stress state in the central part of the specimen is localized. It is observed that the axial stress is much more important than the transverse stress in the central part and this confirms the assumption of uni-axial compression stress state in the specimen.

Dynamic compressive behaviour of weld joints

Materials used in military applications have to withstand multiple threats like ballistics and explosions. Thus, high-strength low alloyed (HSLA) steels are used. The main joining technique for metals is welding. Therefore, analysing the dynamic impact behaviour of high-strength welds is very important to fulfil these demands. Investigation of welds at high strain rates has rarely been conducted in the past. To determine the dynamic impact behaviour of hybrid laser-arc welds, the Split Hopkinson Pressure Bar (SHPB) technique was used. The base material was a quenched and tempered fine-grained armour steel with yield strength of 1100MPa.First, a full hybrid laser-arc weld was investigated by extracting specimens consisting of weld metal and heat affected base material. The influence of two variables, the cooling time between 800°C and 500°C (t8/5) and strength of filler material, on the impact behaviour was studied. The cooling time t8/5 was varied by preheating to influence the microstructure in the HAZ and to analyse the effect on the hardness and dynamic compressive strength.Subsequent analysis to detail the original investigation was carried out by dilatometer heat treatment of specimens to create homogenous subzones of the weld. These specimens have a homogenous microstructure of HAZ and were tested by SHPB to determine the stress-strain characteristics for the different microstructures of HAZ.The results of the weld specimen showed the effect of preheating and filler material strength on the dynamic compressive behaviour. The analysis of the different microstructures of the HAZ indicated that especially the tempered microstructure caused a reduction in dynamic compressive strength.

Numerical Analysis on Usability of SHPB to Characterize Dynamic Stress–Strain Relation of Metal Foam

Split Hopkinson pressure bar (SHPB) technique is the most important test method to characterize dynamic stress–strain relations of various materials at different strain rates, and this technique requires uniform deformation of specimen during the experiment. However, some studies in recent years have found obvious deformation localization within metal foam specimens in SHPB tests, which may significantly affect the reliability of the results. Usability of SHPB to characterize dynamic stress–strain relation of metal foam becomes doubtful. In this paper, based on experimental verification, we carried out numerical simulative SHPB tests to study the problem, in which the metal foam specimens were modeled to have 3D meso structures with properties of their matrix material. Numerical simulative SHPB tests of aluminum foam specimens with varying thickness at different strain rates were performed. Deformation distribution in each local region of the specimen was examined and a concept of “effective specimen” was presented. Appropriate specimen thickness and range of testing strain rate were suggested based on quantitative analysis. Finally, we recommended a method how to revise the nominal strain and strain rate measured by traditional SHPB method to acquire the reliable dynamic stress–strain relation.

Mechanical and ballistic analysis of aramid/vinyl ester composites

This study focused on evaluating mechanical and dynamic-mechanical properties of polyaramid/vinyl ester composites, as a function of the fiber content. Furthermore, split Hopkinson pressure bar technique and V50 Ballistic limit tests were performed. Composites were prepared by resin transfer molding (RTM) with different fiber content, samples being identified as AD4, AD5 and AD6 (with 4, 5 and 6 polyaramid layers, respectively). Initially, fiber, void and matrix contents were calculated and statistically analyzed, in different regions of the composites. Mechanical and dynamical mechanical properties of the composites were improved by using higher fiber content. For example, impact strength of AD6 composite was 35% higher than AD4. Moreover, increase in the fiber content promoted an increase in tenacity and stress of the composites, in the same strain rate. Velocity limit in AD6 sample was estimated in ballistics tests and it was concluded that the composite obtained could accomplish the level I requisites of ballistic protection with V50 of 304 m.s−1.

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.

A Method for the Determination of the Viscoelastic Relaxation Modules of PBX by Confined SHPB Measurements

Polymer bonded high explosives (PBX) show viscoelastic material behaviour due to the polymeric binder material. The assessment of safety aspects in the use of PBX requires a profound understanding of the dynamical mechanical behaviour for short loading times. The work presents an experimental set up with split Hopkinson pressure bar techniques (SHPB) that uses a confined material sample for highly dynamical loading conditions. The test method allows the experimental determination of the complete stress-strain-state in the dynamically loaded sample. The SHPB results provide the input data for the developed viscoelastic material description. The material model is based on the Boltzmann superposition principle and requires 2 time dependent relaxation functions for a complete viscoelastic material description. In our case this are the relaxation functions for compression K(t) and shear G(t). A method is presented for the solution of the developed integral equations for these two relaxation functions. The mathematical method is verified with generic viscoelastic models and is finally applied for the characterisation of the PBX KS-32.

Influence of cyclic wetting and drying on physical and dynamic compressive properties of sandstone

The cyclic wetting-drying phenomenon, which is a part of weathering processes, plays a vitally important role in affecting the properties of rock materials. To investigate the effect of wetting and drying cycles on the physical and dynamic compressive properties of rocks, some essential physical properties of sandstone specimens including density, water absorption, porosity, P-wave velocity and slake durability index (SDI) were measured after every 10cycles (for a total of 50cycles). Dynamic compressive tests were conducted using a modified split Hopkinson pressure bar (SHPB) technique for rock specimens. Laboratory tests results showed that, with the increase of wetting and drying cycles, the porosity and water absorption of rock increases while the density, P-wave velocity, SDI, dynamic compressive strength and elastic modulus decrease. In addition, the surface microscopic morphological characteristics of specimens were examined by scanning electron microscope (SEM). It was observed that the micro-cracks grow and expand in rock after cyclic wetting-drying treatments, which is the main cause of the reduction in dynamic compressive strength. Based on experimental results, an empirical equation was established to describe the effect of strain rate and number of wetting and drying cycles on the dynamic compressive strength of rock materials.

Comparison of High-strain Rate Behaviour of OFHC Copper Using Dynamic Indentation and Split Hopkinson Pressure Bar Techniques

The material behaviour can vary with strain rate so it becomes necessary to understand the response of materials under dynamic loading that closely match the service conditions. The high-strain rate behaviour of OFHC copper has been evaluated using split Hopkinson pressure bar (SHPB) technique and dynamic indentation (DI) technique. A comparison of data obtained using these techniques indicated a good match. The effect of strain-rate and microstructure on behaviour of material and strain-rate sensitivity has been discussed.

Experiments to Determine Static and Dynamic Tensile Strength of Deccan Trap Rocks, India

Tensile strength of rocks is an important parameter in the design of underground structures and for various engineering applications. Lack of literature and rapid development of infrastructure in central region of India calls for a need to characterize the mechanical behaviour of rocks in Deccan trap region which is mainly composed of Basalt. In this paper, characterization of tensile behaviour of Basalt rocks from Deccan trap is done at different loading conditions. Indirect test method namely Brazilian test is used to calculate the static indirect tensile strength at a loading rate of 0.2kN/s. Tests are performed on different diameters samples and desirable failure modes are recorded. Tensile strength values recorded at slow loading are obtained to be different for specimen having different diameters. However, strength of rock in engineering problems like blasting, mining, rock bursting and breakage are affected by high loading rates. To consider the dynamic loading effect, a modified split Hopkinson pressure bar technique is used. For dynamic tensile experimentation, Brazilian disc specimen are used which are slightly flattened before testing. The flat ended Brazilian discs (FEBD) are placed diametrically in SHPB setup. Dynamic force equilibrium is successfully achieved for the initial stages of fracture propagation till complete failure of sample. The factor for increase in dynamic tensile strength of Deccan Basalt has been evaluated in this work. Scope of further research has been identified for experimentations on soft rocks to determine their dynamic tensile strength characteristics.

On the Development of Horizontal Impact Test System (HITS): Estimation of Impact Loads and Deceleration

A Horizontal Impact Test System (HITS) will be developed to characterize several energy absorption mechanisms, i.e. axial splitting, tube inversion, deformation/expansion, axial folding, and flattening. There were two alternatives that has been developed for launching mechanism, i.e. spring and Hopkinson pressure bar technique which will be chose further. The HITS mainly consists of a striker bar (impactor), a specimen as in a direct split-Hopkinson pressure bar technique and a die. This paper examines the possibility of using the 70 – 100 mm diameter of the striker bar to be implemented as the impactor for the developed HITS. Afterwards, the size of the striker bar will be a base of determining the launching mechanism. This study was conducted by numerical simulation using LS-DYNA® as the solver. Mild steel was used as a material of specimen. The Cowper-Symonds was used as the constitutive material model for the material of specimen, while the elastic material model was used for the striker bar and the rigid material model was used for the die. Six mechanisms with total of 96 cases of appropriate dimensions were studied. The main purpose of the simulation was to select the range of load cell and accelerometer which would be implemented in the real experimental setup. Based on the result of simulation, the range of load cell was 48 kN to 238 kN, while the range of accelerometer was 358 to 1250 g. Later on, the load vs. displacement can be used for predicting energy absorption for each mechanism.

A novel method in dynamic shear testing of bulk materials using the traditional SHPB technique

This paper aims to propose a novel experimental method to study dynamic shear properties and constitutive behaviors of bulk materials using the traditional split Hopkinson pressure bar (SHPB) technique. In this method, a new kind of double-shear specimen (DSS) and fixture is specially designed for the SHPB system. With this setup configuration, the plastic properties of materials can be obtained conveniently at high strain rates under the state of simple shear. The deformation and failure process of the shear zone can be observed directly by using a high-speed photography. Another advantage of this method is that reloading on the specimen can be prevented for the purpose of post-test observation, with the application of the stress reversal Hopkinson technique (Nemat-Nasser etal., 1991). Using this method, the 603 steel was tested at strain rates from 2500s−1 to 48000s−1. With the aid of finite element analysis (FEA), it's found that the shear stress and shear strain play dominant roles in the stress/strain fields. The distribution of the maximum shear strains in the shear zone showed good consistency with the fracture patterns of the tested samples. Through comparison between the tested and simulated shear stress-shear strain curves, very good agreement is noted for all the tested cases.