Compression Split Hopkinson Pressure Bar Research Articles

Study on the constitutive model of porous titanium alloy

Porous titanium (Ti) alloys usually need high-speed precision machining before they are put into practical applications. Therefore, it is necessary to study the materials’ mechanical properties under conditions of larger strain rate and higher temperature in order to understand the processing mechanism and determine the appropriate processing parameters. In this study, the mechanical properties of porous titanium alloys of two porosities were first investigated by quasi-static compression tests and split Hopkinson pressure bar tests under different conditions. Then, the constitutive models of the flow stress were fitted. From the results of quasi-static compression tests, it was found that the static mechanical properties of porous titanium alloys decreased rapidly with increase in porosity. From the result of the split Hopkinson pressure bar tests, the strain rate sensitivity and temperature sensitivity of porous titanium alloys were determined. The mechanical properties of porous titanium alloys increased with strain rate increase in the range 1000–3000 s−1. The alloys exhibited a temperature-softening effect at 100°C, while they had a temperature-hardening effect at 300°C. The constitutive model could describe the strain-hardening rate of the material appropriately, but the accuracy of the simulated results needed to be improved compared with experimental values.

Thermo⁻Mechanical Behavior and Constitutive Modeling of In Situ TiB2/7050 Al Metal Matrix Composites Over Wide Temperature and Strain Rate Ranges.

The thermo–mechanical behavior of in situ TiB2/7050 Al metal matrix composites is investigated by quasi-static and Split Hopkinson Pressure Bar compression tests over a wide range of temperature (20~30 °C) and strain rate (0.001~5000 s−1). Johnson–Cook and Khan–Liu constitutive models determined from curve fitting and constrained optimization are used to predict the flow stress during deformation. In addition, another Johnson–Cook model calculated from an orthogonal cutting experiment and finite element simulation is also compared in this study. The prediction capability of these models is compared in terms of correlation coefficient and average absolute error. Due to the assumptions in orthogonal cutting theory, the determined Johnson–Cook model from cutting cannot describe the material deformation behavior accurately. The results also show that the Khan–Liu model has better performance in characterizing the material’s thermo–mechanical behavior.

High strain rate response of bio-composites using split Hopkinson pressure bar and digital image correlation technique

ABSTRACTIn this research, high strain rate response and energy absorption characteristics under dynamic compression loading of five different bio-composites were studied using a compression split Hopkinson pressure bar (SHPB) and DIC (digital image correlation) technique. This study is to map suitability of plant-based materials instead of petroleum-based plastic as a constituent raw material in composites. Bio-composites panels were made from Southern yellow pine (SYP), Corn starch (CS), and Methylene diphenyl diisocyanate (MDI) using a Dieffenbacher hot press. The ability of non-contact DIC analysis served as a valuable tool to measure the strains over a large range of deformation in wood-based bio-composites subjected to high strain rate compressive loading. Among all, Material 2 bio-composite with high manufacturing pressure had highest peak strength, shows that material behaviour at high strain rates is strongly dependent on the manufacturing pressure during fabrication. Presence of corn starch marginally increased the energy absorption capacity.

Revealing abnormal {11[formula omitted]1} twins in commercial purity Ti subjected to split Hopkinson pressure bar

The deformation behavior of Ti alloys during conventional deformation, such as rolling and compression, have been extensively investigated, while it is less understood during high strain rate deformation. In the present work, a commercial purity (CP) Ti alloy was subjected to high strain rate (∼600 s−1) compression deformation using a split Hopkinson pressure bar (SHPB) system. By multi-impacts, an accumulative deformation strain of ∼0.15 was achieved. The microstructural evolution has been systematically analyzed by electron backscatter diffraction (EBSD). It is found that the CP-Ti alloy has been deformed predominantly by three different twinning modes, {101¯2} (T1), {112¯1} (T2) and {112¯2} (C1). A large fraction of the {112¯1} (T2) twin boundary (TB) segments are found to be in connection with deformation band (DB) boundary segments with misorientation angles much lower than the theoretical value of the {112¯1} (T2) TB, ∼35°. Based on the analysis of the crystallographic nature of these abnormal {112¯1} (T2) TBs and the calculation of Schmid factor, it is suggested that these abnormal {112¯1} (T2) TBs are evolved from DB boundaries through the accumulative slip of single basal-〈a〉 dislocations, namely a kinking mechanism. This special twinning mode of the {112¯1} (T2) twin has been attributed to the high strain rate deformation during SHPB compression, which is helpful for understanding the deformation and twinning behavior during high strain rate deformation.

Dynamic response of cement-tailings matrix composites under SHPB compression load

Investigating the dynamic response of cemented tailings backfill (CTB) is a challenging task since there is a lack of the sophisticated laboratory device and the costs linked with extraction of ore in the stopes using explosives are relatively high. In this study, the variations in the dynamic peak compressive strength (DPCS), cement-to-tailings ratio (c/t), and curing time (CT) of nine types of cement-tailings matrix composites (CTMC) were investigated under impact loading strain rates ranging from 10 s−1 to 100 s−1 using a split Hopkinson pressure bar (SHPB). Physical and chemical characteristics of tailings from a gold mine were tested. A series of dynamical compressive strength test and microstructural analysis were conducted to determine the relationships between DPCS of CTMC and three factors of average strain rate (ASR), cement-to-tailings ratio (c/t) and curing time. A total of 36 CTMC samples with a diameter × height of 50 mm × 25 mm prepared at different c/t (1:4, 1:6 and 1:8) and CT (28, 56, and 90 d) values were subjected to DPCS test. The results shows that: (1) DPCS results increased with an increase in ASR. Different types of curve fitting were conducted to obtain the correlation between DPCS and ASR. An exponential function was used to explain the relationship between DPCS and ASR. (2) As the ASR increases, the dynamic increase factor (DIF) value increases. The exponential function can be used to characterize the quantitative relation between DIF and lgASR. (3) When the results of the experiment and the ANSYS/LS-DYNA numerical simulation were compared, the stress-strain and the failure characteristics of the CTMC and DPCS with impact velocity are consistent. The results of this study can provide significant reference for the backfill design of underground mining.

Dynamic Properties of Geologic Specimens Subjected to Split-Hopkinson Pressure Bar Compression Testing at the University of Kentucky

Advances in materials science have shown that material behavior varies according to the rate of load application (strain-rate sensitivity). With regards to compressive strength, materials have been observed to exhibit a strengthening, weakening, or negligible response to increasing strain-rates (Zhang and Zhao in Rock Mech Rock Eng 47(4):1411–1478, 2014). Practical experimentation to ascertain these responses has been carried out for over a century, based on the fundamental equipment design pioneered by John Hopkinson in 1872 and modified by Kolsky in 1949. A contemporary Split-Hopkinson Pressure Bar (SHPB) has been constructed at the University of Kentucky (UKY) to research the dynamic properties of various geologic materials for mining and civil engineering applications. Geologic samples are of an inconsistent nature due to inherent discontinuities and large grain size. To ensure test specimens are of adequate size to reflect this inconsistent nature, the SHPB at the UKY has been constructed with component bars of 2 in. (5.08 cm) diameter. Prior publications have discussed various considerations associated with the testing procedure and data processing of this SHPB (dispersion correction, pulse shaping, etc.) (Silva and Lamont 2017). This publication presents the results of materials testing with this SHPB. Three materials were selected: Bedford (Indiana) Limestone, Berea (Ohio) Sandstone, and Aluminum 6061-T6. Two of these are common aggregates found in the mining and construction industries, while the third is an aluminum variant often encountered in industrial applications. Dynamic compression testing of these materials at various strain rates was carried out, and the results are included. Static test results have been included for comparison, and the testing and data analysis procedure are discussed in detail.

Effects of Microstructure on the Dynamic Strain Aging in Ferritic-Pearlitic Steels

Effects of microstructure on the high strain rate high temperature mechanical response and dynamic strain aging of C45 and 27MnCr5 ferritic-pearlitic steels were studied using four different microstructural variants of the standard alloys. The high strain rate high temperature behavior of the steels was studied using a compression Split Hopkinson Pressure Bar device with high temperature testing capabilities. The steels were studied at strain rates up to 4500 s−1 and at temperatures from RT to 680 °C. Strong dynamic strain aging was observed for both steels in the studied temperature range. The results also show that the microstructure has a strong effect on the dynamic strain aging sensitivity of the steel. This is especially true at low plastic strains, where the effect of the microstructure is strongest. The effect of microstructure decreases as plastic strain increases. A coarse-grained microstructure showed the strongest dynamic strain aging sensitivity for both steels.

Inelastic deformation micromechanism and modified fragmentation model for silicon carbide under dynamic compression

The underlying micromechanism remains to be clarified for the bulk inelastic behaviour of specific ceramics under impact loads. In this study, the silicon carbide materials were subjected to the split-Hopkinson pressure bar compression in which the strain rate was not constant but increased to the dynamic level at high stresses. The inelastic deformation occurs in the high strain rate stage in compression, followed by the final transgranular fracture. The post-test fragments were examined in both the SEM and high resolution TEM. It was found that macroscopic inelastic behaviour is dominated by the dislocation motion and the localised amorphisation that arise at high strain rates. The damage and thus the degraded modulus in the dynamic inelastic deformation were incorporated to modify a dynamic fragmentation model to evaluate the fragment size as a function of strain rates. The modified model more accurately predicts the size of fragments produced at high strain rates.

Dynamic response of ceramic shell for titanium investment casting under high strain-rate SHPB compression load

The mechanical performances of ceramic mold are crucial for the quality of casts in investment casting. However, most of the previous researches were focused on the quasi-static performance which is not sufficient for the accurate failure analysis of shell mold under complex stress state. In this investigation, dynamic mechanical behaviors of Al2O3-SiO2 ceramic shell for investment casting have been studied using split Hopkinson pressure bar (SHPB) at high strain rates. Sand pack samples and pure slurry samples were considered for the testing in order to further understand the mechanism of fracture. Weibull approach was then applied to describe the strength distribution of ceramic shells. The dynamic increase factor (DIF) of compressive strength increased from 1.23 (863 s−1) to 2.03 (1959 s−1) indicating the high dependency of mechanical property to strain-rate. The cross-section and fracture surface were analyzed through scanning electron microscopy (SEM). The microstructural investigations showed that the crack propagation in the ceramic shell is mainly through the weak interface between sand particles and slurry region under quasi-static load. At high strain-rate, the crack propagation path is different which extends through the well sintered slurry region and even runs through the sand particles. The mechanism of crack propagation path is analyzed based on Griffith criterion. In addition, the feature of stress-strain curves indicates the layered structure which plays an important role in the process of fracture.

High Strain Rate and High Temperature Behavior of Ti–6Al–4V Alloy Under Compressive Loading

The titanium alloy (grade 5) is a two-phase material, which finds significant applications in aerospace, medical, marine fields, owing to its superior characteristics like high strength-to-weight ratio, excellent corrosion resistance, and good formability. Hence, the dynamic characteristics of the Ti-6Al-4V alloy are an important area to study. A compressive split Hopkinson pressure bar (SHPB) was used to evaluate the dynamic properties of Ti-6Al-4V alloy under various strain rates between 997 and 1898s−1, and at temperatures between −10 °C and 320 °C. It was evident that the material strength is sensitive to both strain rate and temperature; however, the latter is more predominant than the former. The microstructure of the deformed samples was examined using electron back-scattered diffraction (EBSD). The microscopic observations show that the dynamic impact characteristics of the alloy are higher at higher strain rates than at quasi-static strain rates. The SHPB tests show that the force on the transmitter bar is lower than the force on the incident bar. This indicates that the dynamic equilibrium cannot be achieved during high rate of damage evolution. Various constants in Johnson–Cook (JC) model were evaluated to validate the results. An uncertainty analysis for the experimental results has also been presented.

Development of a constitutive model for DPX2 explosive

There is a significant challenge in simulating the behaviour of PBXs under high strain rate impact loading. A Porter-Gould physically based constitutive model has been developed for the DPX2 explosive. A series of quasi-static compression and tensile tests over a range of temperatures were performed together with DMA tests to calibrate the model. In particular tests were performed for different L/D ratios to understand the complex localisation and damage behaviour of the material. High rate tests on the compression Split Hopkinson Pressure Bar (SHPB) for a range of temperatures were then used for validation of the model under idealised stress states. Some model development is still required, particularly at lower temperatures near the glass transition temperature. In addition a series of classical Taylor Tests were used to validate the model under impact loading conditions at room temperature. The DYNA3D simulations gave very good results compared to the experiments for these impact conditions.

Dynamic Deformation Behaviour and Dislocation Substructure of AZ80 Magnesium Alloy over a Wide Range of Temperatures

The high strain rate deformation behaviour and dislocation substructure of AZ80 magnesium alloy are investigated at strain rates of 8x102 s-1, 1.5x103 s-1 and 2.2x103 s-1 and temperatures of-100 ºC, 25 ºC and 300 ºC using a compressive split-Hopkinson pressure bar system. The flow stress, work hardening coefficient, strain rate sensitivity and temperature sensitivity all increase with increasing strain rate or decreasing temperature. Moreover, the dynamic deformation behaviour is well described by the Zerilli-Armstrong hcp constitutive equation. Transmission electron microscopy observations show that the dislocation density increases with a higher strain rate or a lower temperature. Finally, the flow stress varies linearly with the square root of the dislocation density in accordance with the Bailey-Hirsch model.

Damage detection versus heat dissipation in E-glass/Epoxy laminated composites under dynamic compression at high strain rate

In this investigation, a new experimental technique in which the deformation, damage mode, and the temperature are measured simultaneously during a high strain rate on laminated composites materials. The composites consist of unidirectional E-glass fibers reinforced epoxy polymer composites used in industrial applications. The experimental setup consists of a compression Split Hopkinson Pressure Bar (SHPB), a high-speed infrared camera and a high-speed Fastcam rapid camera. Specimens, with cubic like a shape, are impacted at different strain rates ranging from 200 to 2000 s−1. During impact test, the specimen surface is controlled and monitored with the infrared camera which provides thermal images in time sequence and with high-speed camera which acquires the damage progressive in specimens. Experimental results show that the damage throughout specimens differs and the temperature change depending on the damage mode and their maximum exceed 219 °C.

Temperature-dependent variation in dynamic deformation behaviour and dislocation substructure in AZ80 magnesium

ABSTRACTThe dynamic deformation behaviour and dislocation substructure of AZ80 magnesium alloy are investigated at strain rates of 8 × 102, 1.5 × 103 and 2.2 × 103 s−1 and temperatures of −100, 25 and 300°C using a compressive split-Hopkinson pressure bar system. The flow stress, work hardening coefficient, strain rate sensitivity and temperature sensitivity all increase with increasing strain rate or decreasing temperature. Moreover, the dynamic deformation behaviour is well described by the Zerilli–Armstrong hexagonal close packed (hcp) constitutive equation. Catastrophic failure occurs at all three temperatures under strain rates of 1.5 × 103 and 2.2 × 103 s−1. Transmission electron microscopy observations show that the dislocation density increases with a higher strain rate or a lower temperature. Finally, the flow stress varies linearly with the square root of the dislocation density in accordance with the Bailey–Hirsch model.This paper is part of a thematic issue on Light Alloys.

Curved nanotwinned structure in Ni induced by dynamic compression

Nanotwinned metals exhibit many interesting deformation behavior when compared to nanocrystalline materials with similar characteristic length scale. In this study, the deformation behavior of a nanotwinned Ni produced with a Ni-carbonyl chemical vapor deposition process was investigated via split Hopkinson pressure bar compression testing for strain rates ranging from 200 to 4100 s−1. This report will focus on the observation and analysis of an interesting microstructure formed as a result of the dynamic deformation; the collective curvature of the twin boundaries that makes up the nanotwinned structure. Furthermore, the curved twin boundaries tend to remain parallel to each other despite the introduction of curve. It is proposed that the formation of such a microstructure via dynamic deformation is likely a result of dislocation interactions with the twin boundaries forming steps made up of incoherent twin boundaries. A curvature can be formed with a large number of these steps formed on any single twin boundaries. The activation of this unique mechanism is dependent on the high strain rates, whereas the extent of operation is dependent on the extent of plastic deformation.

Dynamic shear characteristics of titanium alloy Ti-6Al-4V at large strain rates by the split Hopkinson pressure bar test

The focus of this paper is the dynamic shear characteristics of titanium alloy Ti-6Al-4V at large strain rates. Dynamic load testing of titanium alloy Ti-6Al-4V are performed by the split Hopkinson pressure bar (SHPB) at different strain rates, which involve the SHPB compression test and the SHPB shear test. The material behaviour during the tests are measured and recorded. The strain rates for the compression and shear tests range from 5.0 ×102s−1 to 9.0 ×103s−1 and 1.0 ×104s−1 to 3.0 ×105s−1, respectively. The effect of competing mechanisms—strain rate hardening and thermal softening—on the adiabatic shear band is analysed. A size effect on shear band width is also found. According to the results, a modified Johnson–Cook (J–C) constitutive model is applied to tests at an ultrahigh strain rate. Furthermore, a finite element method (FEM) simulation is conducted to validate different aspects of the methodology. The SHPB shear test is confirmed as a process of pure shear. A comparison of the shear stress-strain curves from the mechanical tests and simulation show good agreement based on the modified J-C constitutive model.

High Strain Rate Compressive Behaviour of Selective Laser Melted Ti-6Al-4V

Ti-6Al-4V alloy is one of the most important engineering alloys, combining attractive properties with inherent workability. The aim of this study is to investigate the effect of strain rate on the compressive mechanical properties of Ti6Al4V alloy manufactured by a selective laser melting process. The mechanical tests were performed by means of a compression split Hopkinson pressure bar apparatus under high strain rate ranging from 1400 s-1 to 4500 s-1. The true stress-strain curves obtained from static and dynamic compressive tests show strain rate sensitivity from quasi-static (peak strength 1300MPa) to high strain rate (peak 1500 MPa). Within the high strain rate range tested, the strain rate sensitivity is not remarkable. The fractographic analysis shows a relatively smooth and smeared fractured surface along with a dimple like structure. The observation of elongated dimples confirms the operation of a dynamic shear failure mechanism for the additively manufactured Ti-6Al-4V parts.

Mechanical behaviour of glass fibre reinforced composite at varying strain rates

Here we report the results of compressive split Hopkinson pressure bar experiments (SHPB) conducted on unidirectional glass fibre reinforced polymer (GFRP) in the strain rate regime 5 × 102–1.3 × 103 s−1. The maximum compressive strength of GFRP was found to increase by as much as 55% with increase in strain rate. However, the corresponding relative strain to failure response was measured to increase only marginally with increase in strain rates. Based on the experimental results and photomicrographs obtained from FE-SEM based post mortem examinations, the failure phenomena are suggested to be associated with increase in absorption of energy from low to high strain rates. Attempts have been made to explain these observations in terms of changes in deformation mechanisms primarily as a function of strain rates.

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.

High Strain Rate Response of A356/Al2O3 Aluminum Alloy MMCs Using Ls-Dyna

Aluminum alloy Metal Matrix Composites (MMCs) have evoked a keen interest in recent times for potential applications in aerospace, defense, marine and automotive industries owing to their superior strength to weight ratio and high temperature resistance despite the higher manufacturing costs. The ability to withstand dynamic loading is an important design criteria for many structures in above applications. The Split Hopkinson Pressure Bar (SHPB) also referred to as Kolsky bar is a commonly used setup for high strain rate test in strain rate range from 102 to 104 s-1. The high strain rate data is required for safety and structural integrity assessment of structures subjected to dynamic loading. As high strain rate data is not easily available in open literature need was felt for setting up such high strain rate testing. Four distinctly different A356/Al2O3 Aluminum alloy MMCs reinforced with 0, 4, 8 and 12% fiber volume fraction of aluminum oxide (Al2O3) particles were prepared using stir casting process. These four different MMCs were numerically characterised with SHPB test setup using Ls-Dyna software. The compressive stress-strain behavior was obtained at different strain rates ranging from 100 to 1200 s-1. The high strain rate results of compressive SHPB for all specimens were obtained in the form of stress-strain graphs, which strongly indicates that the high strain rate affects on the dynamic mechanical behaviour of MMC materials. These results are helpful to select the MMCs for structural applications where materials go under dynamic loading.