High Strain Rate Conditions Research Articles

Experimental methods for determination of mechanical behaviors of materials at high temperatures via the split Hopkinson bars

Full understanding of the thermomechanical behaviors of materials at high strain rates and high temperatures are of great importance from not only scientific meaning but also practical value in engineering structure design and safety assessment. Great efforts have been made for abilities of operation the split Hopkinson bars, the most popular technique for experimental determination of mechanical behaviors of materials over the strain rates from 102 to 104 s−1 over the past 70 years, at high temperatures since 1960s. A review of experiment work is presented in this paper to give an overview of the development of experimental techniques at high temperatures based on Hopkinson bar systems. The principles of the split Hopkinson bar requires the loading bars avoiding temperature gradient or keeping relatively low temperature when performing high temperature testing. Techniques such as performing temperature gradient corrections, rapid heating or using special designed automatically assembled systems were proposed by researchers to enable the operation of the split Hopkinson bars at temperature as high as possible. Moreover, to the application of high speed photographic technique for capturing the dynamic deformation process of the specimen in high temperature Hopkinson bar testing, some key issues of eliminating the strong thermal radiation induced lights oversaturation and de-blurring of images due to insufficient exposure at high temperature and high strain rate condition, as well as fabrication of high contrast speckle pattern for high temperature digital image correlation measurement were also proposed. The technique can now enable the split Hopkinson bar testing to be performed at high temperature up to 1873 K under the loading conditions of compression or tension with the in situ observation and full field measurement of deformation as well. The paper concludes with summaries of the most important achievements and highlighting of the prospects, trends and remaining challenges for future research.

Formability and deformation behavior of DP600 steel sheets during a hybrid quasi-static/dynamic forming process

The purpose of this work was to investigate the formability and deformation behavior of DP600 steel sheets during a hybrid forming process composed of quasi-static forming and dynamic high strain rate electrohydraulic forming (EHF) sequence. The results showed that the ultimate limit major strains under the uniaxial tensile strain path were 40–47%, and those under plane strain and biaxial tensile strain paths were 28–31% and 43–57%, respectively. Compared with quasi-static data, the hybrid data under these three strain paths were improved by 30%, 70%, and 36%, respectively, demonstrating a hyperplasticity characteristic. The quasi-static prestrain had little effect on the ultimate formability, and the hyperplasticity effect of the quasi-statically prestrained specimens mainly depended on the inertial effect and the change in constitutive behavior in the high strain rate EHF loading step. Furthermore, the optimized Johnson-Cook constitutive model of the quasi-statically prestrained sheet during high strain rate condition was obtained by means of dynamic Hopkinson tensile tests, and the numerical simulation results based on this material constitutive were in good agreement with that obtained by experiments, showing an error of less than 5%. Then, the numerical simulation reproduced the propagation and evolution process of the pressure wave from ellipsoid to sphere, and quantified the dynamic deformation behavior of the quasi-statically prestrained specimen during an EHF process. The maximum velocity and strain rate of the prestrained specimen during EHF step were 270 m/s and 3700/s, respectively, and the ultimate height of the deformed specimen was 43 mm.

Simple estimation method for strain rate sensitivity based on the difference between the indentation sizes formed by spherical-shaped impactors

The Johnson-Cook (JC) flow stress model is widely used in finite element analysis (FEA) in various fields to express the deformation behavior of metallic materials under high strain rate conditions. There is a need to facilitate an easier estimate of the JC parameter C, which is a material constant in the JC model associated with strain rate sensitivity. In this study, a simple estimation method for the JC parameter C, based on the difference between the indentation sizes formed by two spherical-shaped impactors, was proposed. The proposed method allows us to estimate the JC parameter C only by measurement of the indentation sizes formed via a high-velocity impact test, a drop impact test, or an indentation test. The fundamental equation was theoretically derived based on the energy conservation during the impact process of the impactor and the expanding cavity model, combined with the JC model and the equation of thermal conduction. To validate the proposed method, FEA was conducted using ten types of target materials under five impact velocity conditions, from 6 × 10−6 to 180 m/s. Based on the indentation depths obtained from FEA, the JC parameter C was estimated and compared with that input into FEA. As a result, it was confirmed that the estimated C is in agreement with that input into FEA within the relative errors of 10% under all impact velocity and target material conditions, except the target material of Ti6Al4V. From the results, it was demonstrated that the proposed method can easily estimate the JC parameter C, that is, the strain rate sensitivity, in the wide range of strain rate from 102 to 105 s−1.

Holistic Approach on the Research of Yielding, Creep and Fatigue Crack Growth Rate of Metals Based on Simplified Model of Dislocation Group Dynamics

The simplified model of numerical analyses of discrete dislocation motion and emission from a stressed source was applied to predict the yield stress, dislocation creep, and fatigue crack growth rate of metals dominated by dislocation motion. The results obtained by these numerical analyses enabled us to link various dynamical effects on the yield stress, dislocation creep, and fatigue crack growth rate with the experimental results of macroscopic phenomena, as well as to link them with theoretical results obtained by the concept of static, continuously distributed infinitesimal dislocations for the equilibrium state under low strain or stress rate conditions. This will be useful to holistic research approaches with concern for time and space scales, that is, in a time scale ranging from results under high strain rate condition to those under static or low strain rate condition, and in a space scale ranging from meso-scale to macro-scale mechanics. The originality of results obtained by these analyses were found by deriving the analytical formulations of number of dislocation emitted from a stressed source and a local dynamic stress intensity factor at the pile-up site of dislocations as a function of applied stress or stress rate and temperature material constants. This enabled us to develop the predictive law of yield stress, creep deformation rate, and fatigue crack growth rate of metals dominated by dislocation motion. Especially, yielding phenomena such as the stress rate and grain size dependence of yield stress and the delayed time of yielding were clarified as a holistic phenomenon composed of sequential processes of dislocation release from a solute atom, dislocation group moving, and stress concentration by pile-up at the grain boundary.

Hot deformation behaviors of WE71 alloy under plain strain compression at elevated temperature

Hot deformation behaviors of WE71 (Mg–7Y-1Nd-0.5Zr) alloy was investigated by plain strain compression tests conducted at temperatures ranging from 350 °C to 500 °C and strain rates varying from 0.01 s-1 to 10 s-1. Results show that the hot deformation of WE71 was accompanied by the precipitation of rich Zr phase with granular shape and block-shaped phase rich in element Y. When deformed at low temperature and high strain rate, the softening behavior of the alloy was synergically determined by shear bands propagation, adiabatic heating, twinning formation and dynamic recrystallization (DRX). For the conditions of high temperature and high strain rate, DRX was the major softening mechanism while the formation and annihilation of extension twinning resulted in a special flow curve characteristic at the strain of around 0.3. According to the microstructural observations, it can be concluded that the irregular flow curves of WE71 alloy during plain strain compression process are mainly ascribed to shear bands propagation, adiabatic heating, twinning formation and DRX.

Carbon Nanotube Peapods Under High-Strain Rate Conditions: A Molecular Dynamics Investigation

ABSTRACTNew forms of carbon-based materials have received great attention, and the developed materials have found many applications in nanotechnology. Interesting novel carbon structures include the carbon peapods, which are comprised of fullerenes encapsulated within carbon nanotubes. Peapod-like nanostructures have been successfully synthesized, and have been used in optical modulation devices, transistors, solar cells, and in other devices. However, the mechanical properties of these structures are not completely elucidated. In this work, we investigated, using fully atomistic molecular dynamics simulations, the deformation of carbon peapods under high-strain rate conditions, which are achieved by shooting the peapods at ultrasonic velocities against a rigid substrate. Our results show that carbon peapods experience large deformation at impact, and undergo multiple fracture pathways, depending primarily on the relative orientation between the peapod and the substrate, and the impact velocity. Observed outcomes include fullerene ejection, carbon nanotube fracture, fullerene, and nanotube coalescence, as well as the formation of amorphous carbon structures.

Prediction of flowability of cohesive powder mixtures at high strain rate conditions by discrete element method

Flow behaviour of powders plays an important role in defining their performance in many industries. In this study, we present our work on prediction of flow characteristics of binary and ternary mixtures under dynamic conditions using Discrete Element Method and simulating the expended mechanical work of a rotating impeller penetrating a packed bed. Three commonly used methods for calculating a mean have been explored to express the mixture Bond number, namely arithmetic, geometric and harmonic mean. This is done by introducing a weighting factor based on the fractional surface area of each component of the mixture. The mixture Bond number is dependent on the interfacial surface energy, particle size and density; and a wide range of Bond number is covered in our study by varying all three. The expended work of impeller shows the clearest trend with the mixture Bond number when it is expressed in terms of the arithmetic mean. Although we only used binary and ternary mixtures (40 different mixtures in total) in this study, the trend should be applicable to multi-component mixtures and therefore useful as a design aide for powder formulation.

Radial and axial inertia stresses in high strain rate deformation of polymer foams

Polymer foams are widely used in applications that require impact energy absorption. Experimental characterization of the impact response of polymer foams is challenging. The primary challenges associated with the characterization of polymer foams in high strain rate conditions are the significant effects of inertia and material compressibility. In this work, we develop analytical solutions for radial and axial inertia stresses that develop during high strain rate deformation of polymer foams. The effects of strain rate increase rate, test piece geometry, density, and Poisson's ratio are discussed in detail. We also provide and discuss results from a case study on the impact response of a closed-cell foam subjected to controlled impact loading, focusing on the importance of inertial effects on the characterization of the dynamic stress-strain response. The analytical approach presented in this work facilitates the determination of the concurrent effects of material compressibility and inertia stresses in the dynamic deformation response of compressible materials.

Effect of trace carbon on the dynamic compressive properties in the as-cast Ti13V11Cr3Al alloy

An as-cast Ti13V11Cr3Al titanium alloy was fabricated via vacuum induction skull melting. The microstructure and mechanical properties of this alloy were characterized via transmission electron microscopy (TEM) combined with energy-dispersive X-ray spectroscopy (EDX) and compression experiments, respectively. The results revealed that trace impurity carbon (0.014 wt%) led to the formation of in-situ needle-like TiC precipitates during solidification. To reveal the underlying mechanism governing this formation, the (Ti13V11Cr3Al)-C pseudo-phase equilibrium diagram was constructed using JMatPro software. The results suggested that the precipitation of TiC will occur if the carbon content is > 0.003 wt%. Under high strain rate conditions, small volume fractions of these precipitates can lead to improvements in the ductility, and retention of the strength (1350 MPa). The as-cast alloy exhibited excellent dynamic plasticity, as evidenced by a critical fracture strain of >35% at a strain rate of 4158/s. In addition, microstructural observation of adiabatic shear bands revealed that debonding of the TiC precipitates from the matrix required considerable energy dissipation. Moreover, a crack propagated along the boundary of the precipitates, thereby leading to significant improvement in the dynamic plasticity from the other respect.

Thermal compression, processing maps and microstructural evolution of as-cast Mg-Gd-Y-Zn-Zr alloy with long period stacking ordered phase

Thermal deformation of Mg-7.5Gd-2.5Y-1.5Zn-0.5Zr (wt%) as-cast alloy containing LPSO phase was been studied in a temperature range from 623 K to 723 K and a strain rate range from 0.001 to 1 s−1. The microstructural evolution at the various strain rates was also analyzed. The results show that the flow stress decreases significantly with the increase of the deformation temperature. But the peak flow stresses of the alloy increase significantly at high deformation temperature, due to existing both the plentiful lamellar LPSO phase and the fine dynamic DRXed grains. Under the high strain rate conditions, the LPSO phase distorted and formed kink bands. The deformational activation energy (Q) of the alloy is about 234.6 kJ·mol−1. This high Q value mainly owe to profuse lamellar LPSO phase hindering the movement of atoms. With the observation of established processing map of the alloy, some good thermal workabilities are observed in following zones: 723 K, 0.001 < ε < 1 s−1; and the zone with middle temperature and moderate strain rate condition, 673 K, 0.01 < ε < 0.1 s−1. The thermal deformation instability zones are mainly located in the region with high strain rate and lower temperature.

Comparison of Flow Stress of Aluminum Alloy 6061-T6 Obtained From Chip Pulling Orthogonal Cutting and Kolsky Bar Testing

Machining can be used as a test for the flow stress of materials under conditions of high strain (ε > 1) and strain rate (102/s to 106/s). Constitutive models of metallic materials are conventionally obtained by dynamic compression tests such as the Split-Hopkinson (Kolsky) bar test at lower strain (ε < 0.3) and strain rate (103/s to 104/s). To compare the flow stress obtained from both tests under identical conditions, the strain in the primary shear zone (PSZ) in orthogonal cutting tests has been lowered using high rake angle (α = 45°) cutting tools to ε ≈ 0.8, and by adding chip pulling to ε ≈ 0.5. To our knowledge this is the first time that flow stress estimates are obtained from machining at such low strain values. With some modifications, the strain in Kolsky bar testing has been increased up to ε = 0.8, and the stress-strain curve obtained is compared to flow stress estimates from orthogonal cutting tests under the same strain and similar strain rates. The results work, show for the first time, that the flow stress measured from cutting tests agree closely with those obtained from Kolsky bar testing.

Thermomechanical Behavior and Corrosion Resistance of a 316 L Austenitic Stainless Steel

Hot-formed components are constantly exposed to hostile environments with corrosive substances. Microstructural changes caused by thermomechanical processing can be predicted to increase the corrosion resistance of austenitic stainless steels. The objective of this study is to understand the relationship between the dynamic softening mechanisms and corrosion resistance, thus optimizing the hot-forming process. In the current work, the dynamic recrystallization (DRX) behavior of AISI 316 L austenitic stainless steel was studied in the temperature range of 1273 - 1423 K and strain-rate range of 0.1 - 5.0 s-1 using physical simulation. Subsequently, potentiodynamic polarization tests and scanning electron microscopy were performed on the hot-deformed samples to investigate the influence of temperature and strain-rate on the corrosion resistance and mechanical properties. The results indicated that the DRX fractions increased under low-temperature and high strain-rate conditions, resulting in grain refinement. The potentiodynamic polarization tests indicated that the dynamically recovered samples demonstrated high resistance to corrosion compared with the DRX samples. The best route found for the investigated alloy was for the strain to be applied at a temperature of 1423 K and a strain rate of 0.1 s-1.

Effect of novel impact hydroforming technology on the formability of Al alloys

Currently, Aluminium (Al) alloys are increasingly used in the aerospace and automobile industries because of their outstanding properties such as lightweight and corrosion resistance properties. On the other hand, the applications of these materials are limited due to their poor formability especially at room temperature. Although hydroforming technology is one of the technique used to improve the formability of Al alloys, it still cannot fulfil the requirements of designers and manufacturers to form thin-walled complex shaped components. It has been found that high-speed forming is able to improve the formability of lightweight metals at room temperature. Thus, this investigation aims at investigating the effect of the novel technology called impact hydroforming (high-strain-rate forming) on the formability of Al alloys. Impact hydroforming (IHF) technology is proposed by combining the advantages of high-speed forming and hydroforming, and it was used to address the issues of quasi-static hydroforming. A high strain rate uniaxial tensile test was accomplished using Hopkinson tensile bar to investigate the effect of high strain rate on the formability of Al alloys. Thereafter, an IHF bulge experiment setup was developed by making use of a light gas gun which can accelerate the projectile up to 300m/s. The results show that the ductility and the formability of the Al alloy increased under high strain rate conditions, which means that the high-speed forming which is the basics of IHF technology is an appropriate method to improve the formability of Al alloys and form complex shape components.

Enhanced Constitutive Model for Aeronautic Aluminium Alloy (AA2024-T351) under High Strain Rates and Elevated Temperatures

Success of the numerical simulations depends on the accuracy of the material constitutive relations. Most of the ductile materials exhibit increased strain rate sensitivity at higher strain rates (> 103 s−1) compared to low and medium strain rates. Meanwhile, plastic deformation of any ductile material under high strain rate conditions results in heat generation due to plastic work. Hence, a reliable constitutive model should be able to predict the accurate thermo-mechanical response of the material over a wide range of strain rate loading conditions. In the present work, an enhanced constitutive model for high strain rate and elevated temperature is proposed. For calibration purpose, the stress-strain response of AA2024-T351 is studied under quasi-static and dynamic loading conditions using uniaxial compression and split Hopkinson compressive pressure bar (SHPB) respectively at various temperatures. A threshold strain rate value is identified and used to improve the prediction capabilities of the present model. Later, the proposed model is compared with Johnson-Cook (JC) and Khan-Huang-Liang (KHL) models using the different statistical parameters. This analysis revealed the improved stress-strain prediction capability of the proposed model compared to the others.

Determination of Johnson Cook Parameters in Turning of Micro and Nano Reinforced Aluminum Composites using Trust Region Reflective Algorithm

Accuracy of shear stress estimations plays a vital role in correct prediction of cutting forces in machining. In this study, efforts were directed to obtain better flow stress estimates through determination of novel Johnson Cook (JC) parameters for a number of micro and nano reinforced composite materials. Trust region reflective algorithm (non linear least squares) was used to determine optimum JC constants for each developed material subjected to varying machining parameters under high strain rate conditions. The newer JC constants yielded substantially better shear stress estimates as compared to base alloy JC constants; thus in turn improving cutting force predictability in machining of developed composite materials.

Direct tensile behavior of amorphous metallic fiber-reinforced cementitious composites: Effect of fiber length, fiber volume fraction, and strain rate

In this study, the effects of the fiber length, fiber volume fraction, and strain rate on amorphous metallic fiber-reinforced cementitious composites (AFRCCs) were investigated. The experimental results showed that the amorphous metallic fibers with a 30 mm length had excellent bonding performance with the matrix because of the rough fiber surface, large specific surface area, and high aspect ratio under both static and high strain rate conditions. The fibers, however, were not pulled out from the matrix and were subjected to fracture because the thin-plate shape of the fibers was vulnerable to shear force. On the other hand, the amorphous metallic fibers with a 15 mm length exhibited decreased bonding efficiency with the matrix because of the low aspect ratio and the increased number of mixed fibers, and the fibers were pulled out from the matrix. As the fiber length increased, the tensile strength, strain capacity, and tensile toughness increased because the stress dispersion effect increased alongside the increase in the internal binding force and the crosslinking reaction range inside the matrix. As for the dynamic increase factor (DIF), the amorphous metallic fibers with a 30 mm length exhibited fracture without being pulled out from the matrix. The amorphous metallic fibers with a 15 mm length, however, were pulled out from the matrix, thereby increasing the bonding efficiency of the fiber-matrix interface that is affected by the strain rate. Therefore, it was found that AFRCC-L15 had a higher DIF for the tensile strength, strain capacity, and tensile toughness.

Experimental and Numerical Investigations of High-Speed Projectile Impacts on 7075-T651 Aluminum Plates

Simulation of the material failure under high strain rate conditions is one of the most difficult problems in the finite element analyses, and many researchers have tried to understand and reproduce dynamic material fracture. In this study, we investigate a failure criterion that minimizes the mesh dependency at high strain rates and incorporates the criterion into the Johnson-Cook constitutive relationship by developing a user-defined material model. Impact tests were performed using a gas-gun system in order to investigate the response of the 7075-T651 aluminum plate in high-speed collision. On the other hand, numerical simulations are carried out by considering various element sizes and the relationship between element size and failure strain is inversely obtained using numerical results. By accommodating the relationship into the damage model and implementing in the user-defined material model, mesh dependency is significantly reduced, and sufficient accuracy is achieved with alleviated computational cost than the existing damage model. This study suggests an element size-dependent damage criterion that is applicable for impact simulation and it is expected that the criterion is useful to obtain accurate impact responses with a small computational cost.

Corrosion behavior of metastable AISI 321 austenitic stainless steel: Investigating the effect of grain size and prior plastic deformation on its degradation pattern in saline media

The role of grain size and strain rate on the corrosion behavior of plastically-deformed Ti-stabilized austenitic stainless steel (AISI 321) in saline media was investigated. The as-received coarse-grained alloy (CG: ~37 µm) was subjected to thermomechanical processing to develop fine (FG: ~3 µm) and ultrafine (UFG: ~0.24 µm) grained structures. These samples were deformed under high (dynamic) and low (quasi-static) strain-rate conditions to a similar true strain of ~0.86. Microstructural analyses on specimens after deformation prior to corrosion study suggests a shift from the estimated stacking fault energy value of the steel. Electrochemical tests confirm the highest corrosion resistance for UFG specimens due to the formation of the most stable adsorbed passive film. This is followed by FG and CG specimens in that order. For the three grain sizes, the corrosion resistance of specimen deformed under quasi-static loading condition is higher than that subjected to dynamic impact loading while the corrosion resistance of undeformed samples is the least. This work also confirms the non-detrimental effect of TiCs in AISI 321 austenitic stainless steel on its corrosion resistance. However, TiNs were observed to be detrimental by promoting pitting corrosion due to galvanic coupling of TiNs with their surrounding continuous phase. The mechanism of pitting in AISI 321 in chloride solution is proposed.

A Visco-Hyperelastic Constitutive Model for Describing the Mechanical Behavior of the Spinal Cord White Matter Under Various Strain Rate Conditions

The mechanical behavior of the white matter is important for estimating the damage of spinal cord during accidents. In this study, we conduct uniaxial tension testing in vitro of spinal cord white matter under extremely high strain rate conditions (up to 100/s-1). A new visco-hyperelastic constitutive law for modeling the strain rate-dependent behavior of the spinal cord white matter was developed. A set of material constants was obtained using a fitting algorithm to match the uniaxial tension experimental data with various strain rates. These new data in terms of mechanical response at high strain rate provide insight into the spine injury mechanism caused by high-speed impact. Moreover, the proposed constitutive model will allow researchers to perform more realistic finite element modelling and simulation of spinal cord injury damage under various complicated conditions.

Single‐camera special stereo‐digital image correlation applied for accurate virtual fields method identification

AbstractA single‐camera special stereo‐DIC (SS‐DIC) is proposed for accurate virtual fields method (VFM) identification. The single‐camera SS‐DIC allows accurate surface 3D deformation measurements using a single colour camera and a specially designed colour separation device. It not only effectively eliminates the unavoidable out‐of‐plane movement/rotation due to unideal in‐plane loading but also delivers uniformly distributed measurement points that brings great simplicity and convenience for internal virtual work calculation in VFM. In addition, since only a single camera is used for stereovision, the proposed SS‐DIC system requires no complicated synchronisation devices. The effectiveness and practicality of the proposed method are evaluated by heterogeneous deformation experiments of a holed aluminium alloy and 304 stainless steel plate. Combined with a high‐speed colour camera, the proposed method is expected to be a simple and practical method for the calibration of material constitutive model under intermediate and high strain rate conditions using VFM.