Kolsky Bar Experiments Research Articles

High-throughput quantification of quasistatic, dynamic and spall strength of materials across 10 orders of strain rates

Abstract The response of metals and their microstructures under extreme dynamic conditions can be markedly different from that under quasistatic conditions. Traditionally, high strain rates and shock stresses are achieved using cumbersome and expensive methods such as the Kolsky bar or large spall experiments. These methods are low throughput and do not facilitate high-fidelity microstructure–property linkages. In this work, we combine two powerful small-scale testing methods, custom nanoindentation, and laser-driven microflyer (LDMF) shock, to measure the dynamic and spall strength of metals. The nanoindentation system is configured to test samples from quasistatic to dynamic strain-rate regimes. The LDMF shock system can test samples through impact loading, triggering spall failure. The model material used for testing is magnesium alloys, which are lightweight, possess high-specific strengths, and have historically been challenging to design and strengthen due to their mechanical anisotropy. We adopt two distinct microstructures, solutionized (no precipitates) and peak-aged (with precipitates) to demonstrate interesting upticks in strain-rate sensitivity and evolution of dynamic strength. At high shock-loading rates, we unravel an interesting paradigm where the spall strength vs. strain rate of these materials converges, but the failure mechanisms are markedly different. Peak aging, considered to be a standard method to strengthen metallic alloys, causes catastrophic failure, faring much worse than solutionized alloys. Our high-throughput testing framework not only quantifies strength but also teases out unexplored failure mechanisms at extreme strain rates, providing valuable insights for the rapid design and improvement of materials for extreme environments.

Influence of Sampling Rate on Reproducibility and Accuracy of Miniature Kolsky Bar Experiments

Abstract The purpose of this work is to develop and verify a method for quantitatively analyzing data collected from Kolsky bar experiments and to confirm its validity by comparing it to a finite element (FE) model. This study also aims to demonstrate the need for higher sample rate capture in miniature Kolsky bars, 3.16 mm diameter used in this work, by comparing results from two different data acquisition setups on identically sized experimental setups. We identified that the sample capture rate needed to accurately depict experimental results on small-scale systems is at least 400 kHz, which is far greater than what is typically assumed for lager systems. Finally, a statistical method for evaluating results is presented and expanded upon, which removes the dependence on the knowledge and experience of the experimentalist to interpret the data. Using this analysis technique on the two different systems examined in this study, we find upwards of 3.5 times better loading condition reproducibility and up to a 20 MPa reduction in the standard deviation of the sample stress profile, confirming the need for higher quality frequency capture rates.

Impact of Imperfect Kolsky Bar Experiments Across Different Scales Assessed Using Finite Elements

Abstract Typical Kolsky bars are 10–20 mm in diameter with lengths of each main bar being on the scale of meters. To push 104+ strain rates, smaller systems are needed. As the diameter and mass decrease, the precision of the alignment must increase to maintain the same relative tolerance, and the potential impacts of gravity and friction change. Finite element models are typically generated assuming a perfect experiment with exact alignment and no gravity. Additionally, these simulations tend to take advantage of the radial symmetry of an ideal experiment, which removes any potential for modeling nonsymmetric effects, but has the benefit of reducing computational load. In this work, we discuss results from these fast-running symmetry models to establish a baseline and demonstrate their first-order use case. We then take advantage of high-performance computing techniques to generate half symmetry simulations using Abaqus® to model gravity and misalignment. The imperfection is initially modeled using a static general step followed by a dynamic explicit step to simulate the impact events. This multistep simulation structure can properly investigate the impact of these real-world, nonaxis symmetric effects. These simulations explore the impacts of these experimental realities and are described in detail to allow other researchers to implement a similar finite element (FE) modeling structure to aid in experimentation and diagnostic efforts. It is shown that of the two sizes evaluated, the smaller 3.16-mm system is more sensitive than the larger 12.7 mm system to such imperfections.

Direct comparison between experiments and dislocation dynamics simulations of high rate deformation of single crystal copper

A long standing challenge in computational materials science is to establish a quantitative connection between the macroscopic properties of plastic deformation with the microscopic mechanisms of dislocations in crystalline materials. Although the discrete dislocation dynamics (DDD) simulation method has been developed for several decades with the goal of addressing this challenge, a one-to-one comparison between the DDD predictions on single crystal stress–strain curves and experimental measurements under identical conditions has not been possible to date. Such a comparison is an essential step towards establishing a dislocation-physics based theory of plasticity and a multiscale framework of the plastic behaviors of crystalline materials. Here we provide direct comparisons between the stress–strain curves of Cu single crystals under high strain rate loading in the [001] and [011] directions obtained from miniaturized desktop Kolsky bar experiments and those from DDD simulations under identical loading conditions. With an appropriate set of parameters, DDD simulations can produce stress–strain curves that are in reasonable agreement with the experimental results. However, the dislocation mobility values needed to achieve this agreement are an order of magnitude lower than expected based on previous measurements and atomistic simulations. We hypothesize that this discrepancy could be caused by drag forces from jogs and point defects produced during the plastic deformation. Cross-slip of screw dislocations is also found to be necessary to capture the experimental stress–strain behavior, especially for the [011] loading direction. This work provides an example of how direct comparisons between DDD simulations and experimental measurements can provide new insight into the fundamental mechanisms of plastic deformation.

A Conical Striker Bar to Obtain Constant True Strain Rate for Kolsky Bar Experiments

Many split Hopkinson pressure bar (SHPB) or Kolsky bar techniques use pulse shaping methods to obtain constant engineering strain rate for the specimen response. However, constitutive models for numerical simulations use the axial rate of deformation which is the true axial strain rate. In this study, we present an equation for the incident bar strain produced by a truncated conical striker bar. These incident bar strains are shaped so that we can obtain constant true strain rate for the specimen.

A Numerical Study of Strain-Rate and Triaxiality Effects in Magnesium Alloys

We report a preliminary computational study of the rate-dependent behavior of a polycrystal magnesium alloy under varying levels of stress triaxiality conditions. Smooth and notched round bar specimens with a strong initial texture are considered to achieve different levels of stress triaxiality. Full three-dimensional crystal plasticity simulations are conducted, which mimic tensile Kolsky bar experiments. The results indicate that the material rate sensitivity couples with the stress state to produce qualitatively different macroscopic responses that are governed by the interacting microscale deformation mechanisms. While the smooth specimens show macroscopic strain localization resulting in stress softening immediately following the initial yield, notched bars exhibit increasingly stable responses with increasing notch acuity. Deformation anisotropy is tempered with increasing stress triaxiality and strain rate. A micromechanical analysis of the deformation activities is presented to explain the macroscale responses. Stress triaxiality distributions in the notch regions provide insights into probable damage mechanisms as a function of the imposed strain rate.

Tensile strength and failure of ultra-high performance concrete (UHPC) composition over a wide range of strain rates

In the fibre reinforced concrete, the geometry, density, distribution and orientation of micro-steel fibres can have a significant effect on mechanical performance. In this study, five different compositions of ultra-high performance concrete (UHPC) with steel fibres were designed and developed for improving the mechanical properties over conventional control concrete. An improvement of around 300% in tensile strength was observed with the addition of micro-steel fibres during quasi-static loading in tension. High strain rate behaviour was also studied using Kolsky bar experiments in tension, which was combined with in-situ imaging to capture failure initiation and progression during loading. From the experimental results, it was found that the binary composition of the UHPC matrix is more rate sensitive than the ternary and quaternary compositions. In addition, the dynamic increase factor (DIF) was found to be lower for specimens with micro-steel fibres in contrast to control with only matrix material. From the fracture and failure analysis of UHPC specimens, it was observed that the micro-steel fibres in the UHPC matrix prevent the splitting failure, and maintain the structural integrity of the specimen beyond peak stress.

A physics-based model and simple scaling law to predict the pressure dependence of single crystal spall strength

A homogenized framework for ductile damage accounting for the effect of void growth on the thermomechanical response of single crystals under dynamic loading (CPD-FE) is developed. The current framework extends our prior work (Nguyen et al., 2017) by incorporating the yield function of Han et al. (2013) for porous single crystals to govern the degradation of the macroscopic critical resolved shear stress. Validation of the model against direct numerical simulations shows a significant improvement in accuracy under conditions of macroscopic shear loading. The model parameters are calibrated to Kolsky bar (split-Hopkinson pressure bar) and plate impact experiments, and utilized to predict spall strength of single crystal copper in ⟨100⟩ orientation. Simulation results exhibit favorable agreement with single crystal plate impact tests over a range of strain rates and shock compression pressures. These simulation results are used to further interpret previous experimental observations on the rate and pressure sensitivity of spallation. Lastly, a simple analytical model for spall strength depending on the temperature, strain rate and pressure is proposed, which shows agreement with molecular dynamics (MD) simulations and experimental results. This analytical model of spall strength concisely captures the physical mechanisms governing the effects of pressure, strain rate, and temperature on spall strength.

FE Analysis of Critical Testing Parameters in Kolsky Bar Experiments for Elastomers at High Strain Rate.

The main aim of this research is to present complete methodological guidelines for dynamic characterization of elastomers when subjected to strain rates of 100/s–10,000/s. We consider the following three aspects: (i) the design of high strain rate testing apparatus, (ii) finite element analysis for the optimization of the experimental setup, and (iii) experimental parameters and validation for the response of an elastomeric specimen. To test low impedance soft materials, design of a modified Kolsky bar is discussed. Based on this design, the testing apparatus was constructed, validated, and optimized numerically using finite element methods. Furthermore, investigations on traditional pulse shaping techniques and a new design for pulse shaper are described. The effect of specimen geometry on the homogeneous deformation has been thoroughly accounted for. Using the optimized specimen geometry and pulse shaping technique, nitrile butadiene rubber was tested at different strain rates, and the experimental findings were compared to numerical predictions.

Specimen-Bar Impedance Mismatch Effects on Equilibrium and Rate Constancy for Kolsky Bar Experiments

During a Kolsky bar, also known as a split Hopkinson pressure bar (SHPB), experiment, stress equilibrium and strain rate constancy conditions directly contribute to the measurement quality for rate-sensitive materials. A Kolsky bar specimen is initially at rest, and then gradually accelerated to a desired rate. Stress equilibrium is incrementally achieved by multiple stress pulse reflections inside the specimen to reach the desired mean stress. The critical time to achieve constant strain rate and equilibrium stress depends on the impedance mismatch between the bars and the specimen. This paper examined this critical time based on using linear elastic specimens under uniaxial compression. In the first part, the critical time is experimentally measured for PMMA specimens loaded by aluminum, titanium, and steel bars using linear ramp incident pulses. The results show that increasing impedance mismatch increases the time to reach a constant rate, while the time to satisfy equilibrium remains nearly the same. In the second part, optimal bilinear-shaped incident loadings were evaluated and shown to achieve both conditions faster than linear loadings. The time to satisfy both conditions was mapped via simulation using various bilinear pulses over a wide range of impedance mismatches. The analysis shows bilinear loadings with initial rise time between 1.75 and 2.15 transits in the sample require minimum time to equilibrium. There exists an optimum region of bilinear loadings that can reduce the time to reach constant rate. Within such region, the bilinear slope ratio can be approximated to be a reciprocal function of initial rise time.

Full Field Deformation Measurements in Tensile Kolsky Bar Experiments: Studies and Detailed Analysis of the Early Time History

The very early stages of high rate tensile loading are important when attempting to characterize the response of materials during the transient loading time. To improve understanding of the conditions imposed on the specimen during the transient stage, a series of high rate loading experiments are performed using a Kolsky tensile bar system. Specimen forces and velocities during the high rate loading experiment are obtained by performing a thorough method of characteristics analysis of the system employed in the experiments. The in-situ full-field specimen displacements, velocities and accelerations during the loading process are quantified using modern ultra-high-speed imaging systems to provide detailed measurements of specimen response, with emphasis on the earliest stages of loading. Detailed analysis of the image-based measurements confirms that conditions are nominally consistent with those necessary for use of the one-dimensional wave equation within the relatively thin, dog-bone shaped tensile specimen. Specifically, measurements and use of the one-dimensional wave equation show clearly that the specimen has low inertial stresses in comparison to the applied transmitted force. Though the accelerations of the specimen continue for up to 50 μs, measurements show that the specimen is essentially in force equilibrium beginning a few microseconds after initial loading. These local measurements contrast with predictions based on comparison of the wave-based incident force measurements, which suggest that equilibrium occurs much later, on the order of 40–50 μs .

High-speed X-ray PCI and XRD During Dynamic Fracture

When a crack or a shear band propagates in a ductile material under impact loading, there is a severe stress concentration and/or strain localization near the tip of the discontinuity. It has been understood that the locally severe and fast deformation can lead to phase transformation and heat generation. The adiabatic conditions cause the local temperature to rise. However, it has been a challenge to experimentally measure the microstructural evolution, such as crystal d-spacing, texture evolution and material phase transitions, associated with the dynamic deformation and fracture process of ductile metallic materials. It is also a challenge for optical high-speed imaging techniques to image the details of the advancing crack tip with sufficient spatial resolution. In the dynamic experiments presented in this article, we used Kolsky bars integrated with a simultaneous X-ray phase contrast imaging (PCI) and diffraction (XRD) technique to study the dynamic deformation and fracture processes during high-rate loading. In such a Kolsky bar experiment, high-speed imaging of the specimen deformation and fracture processes and high-speed X-ray diffraction are recorded simultaneously in real time. The experimental setups and results on the dynamic fracture of an aluminum alloy and a bovine tibia bone are presented and discussed.

Dynamic compressive response of wrapped carbon fibre composite corrugated cores

The experimental study on the compressive response of the carbon fibre composite sandwich structures with corrugated cores is reported. The corrugated core was manufactured from unidirectional carbon fibre pre-impregnated lamina wrapped around destructible triangular prisms. Individual wrapped triangular composite cores of relative density ρ¯≈0.13 are cut from the sandwich beams and tested under both quasi-static compression and dynamic compression at a strain rate up to 8200s−1 using an instrumented direct impact Kolsky bar experiment. Under quasi-static compressive test, as the cores were provided with no lateral confinement, the failure mechanism of the composite core was that of progressive unwrapping of cores due to matrix cracking at the joints of the core webs. Under the dynamic compressive tests, the composite cores demonstrated rate-dependent behaviour. The strain rate dependency was attributed to the suppression of the quasi-static “unwrapping” failure mechanism, and inertial stabilisation of the struts against buckling leading to an upper-bound failure mechanism of crushing of carbon fibre material within the struts.

A New Kolsky Bar Dynamic Spall Technique for Brittle Materials

For many years there have been controversial opinions on the value of dynamic tensile data obtained through the Kolsky bar spall tension technique. This is primarily due to the experimental conditions (i.e., specimen stress state and strain rate) not being well defined for these types of tests, thus making data interpretation and comparisons difficult. In this paper, a new spall theory is presented that ensures constant strain rate deformation while maintaining a uniform tensile stress within a large portion of the specimen. In light of this theoretical framework, pulse shaping was carefully designed to experimentally obtain this solution in Kolsky bar experiments. The incident wave generated under the guideline of the new theory has shown promising results for better refined Kolsky bar spall tension experiments on brittle materials.

Understanding the anomalously long duration time of the transmitted pulse from a soft specimen in a kolsky bar experiment

The reason for the observation of an anomalously long pulse duration time of a signal transmitted from a soft specimen in a Kolsky bar experiment is investigated. A systematic numerical experiment based on explicit finite element analysis has been carried out using elastic specimens with varying elastic moduli. The soft specimen is in a compressive state even after the passage of the pulse because it cannot push the bars, such that a fairly long transmitted pulse is monitored at the gage position of the output bar. The arrival of the second pulse (tensile) from the right-end surface of the output bar releases the first transmitted signal (compressive) coming from the compressed state of the specimen, which puts an end to the fairly long transmitted pulse. Because the observation of a prolonged transmitted pulse is a natural phenomenon, the prolonged transmitted pulse should not annoy researchers in the process of confirming the validity of experiments on soft specimens. Our concern in verifying the validity of experiments can be limited to other aspects such as the process of measurement and the amplification of weak transmitted signals coming from soft specimens.

Powder-Route Synthesis and Mechanical Testing of Ultrafine Grain Tungsten Alloys

We report a W-rich alloy (W-7Cr-9Fe, at. pct) produced by high-energy ball milling, with alloying additions that both lower the densification temperature and retard grain growth. The alloy’s consolidation behavior and the resultant compacts’ microstructure and mechanical properties are explored. Under one condition, a 98 pct dense compact with a mean grain size of 130 nm was achieved, and exhibited a hardness of 13.5 GPa, a dynamic uniaxial yield strength of 4.14 GPa in Kolsky bar experiments, and signs of structural shear localization during deformation.

Investigation of electroplastic effect at high deformation rates for 304SS and Ti–6Al–4V

Past research has investigated an electroplastic effect for metals, i.e., decreased flow stress and increased elongation, caused by an applied electrical current aiding dislocation motion. There could be a connection between such electrically-assisted forming (EAF) processes and electromagnetic forming (EMF), where induced eddy currents are generated in the workpiece. To investigate this, Kolsky bar experiments with controlled, electrical DC current applied were conducted. Validated temperature values were calculated to assure that variations in resistive heating were determined. The results for current densities up to 180A/mm2 show that at these high deformation rates, an electroplastic effect is not observed.

Stress-driven grain growth in ultrafine grained Mg thin film

Significant grain growth, manifest as a doubling of the average grain size, was triggered during high rate Kolsky bar experiments on ultrafine grained Mg. This grain growth is attributed to the high applied stress and is consistent with recent reports of stress-driven grain boundary migration. The experimental results indicate that stress can trigger grain growth, thereby reducing the importance of thermal activation at very high stresses. This also indicates that stress-assisted grain growth is not restricted to small grained fcc metals.

On the use of non-cylindrical specimens in a split-Hopkinson pressure bar

Despite the practice of using cylindrical specimens in a split-Hopkinson pressure bar (Kolsky bar) experiment, the use of non-cylindrical prismatic specimens is not uncommon. This is convenient when testing extra-soft materials like brain tissues, muscles, or samples that are brittle and cannot be machined to an exact cylindrical shape (like bone-samples). The use of a non-cylindrical sample with a flat surface also renders the specimen amenable to a two-dimensional image correlation algorithm. This research aims to show the feasibility of using non-cylindrical specimens in a Kolsky bar. For this, experiments were conducted with a model material for different model cross-sections at a nearly constant strain rate in the split-Hopkinson pressure bar. The findings suggest the use of a suitable characteristic cross-section dimension of the specimen to determine the critical slenderness ratio while selecting a non-cylindrical prismatic specimen. It has been shown that if the specimen design is governed by the suggested slenderness criterion, then there is no effect of specimen length or cross-sectional shape on the stress–strain curve of the material. Through the use of a computational code, the research also shows the effect of non-uniform axial stress distribution along the cross-section of the specimen, resulting due to specimen geometry. On quantification of the stress non-uniformity along the cross-section of the specimen, the findings indicate that the magnitude of the non-uniformity is both small and temporary.

A Kolsky tension bar technique using a hollow incident tube

Load control of the incident pulse profiles in compression Kolsky bar experiments has been widely used to subject the specimen to optimal testing conditions. Tension Kolsky bars have been used to determine dynamic material behavior since the 1960s with limited capability to shape the loading pulses due to the pulse-generating mechanisms. We developed a modified Kolsky tension bar where a hollow incident tube is used to carry the incident stress waves. The incident tube also acts as a gas gun barrel that houses the striker for impact. The main advantage of this new design is that the striker impacts on an impact cap of the incident tube. Compression pulse shapers can be attached to the impact cap, thus fully utilizing the predictive compression pulse-shaping capability in tension experiments. Using this new testing technique, the dynamic tensile material behavior for Al 6061-T6511 and TRIP 800 (transformation-induced plasticity) steel has been obtained.