Strain Rate Range Research Articles

Characterization and Modelling of Microstructure Evolution and Flow Stress of Single-Phase Austenite and Ferrite Phases in Duplex Stainless Steels

This paper presents an experimental and modeling study to investigate and predict the microstructure evolution for single-phase austenite and ferrite steels with the chemistry of the corresponding phases in a duplex stainless steel SUS329J4L under hot forming conditions. For steels with the compositions corresponding to both austenite and ferrite phases, single-pass hot uniaxial compression tests, stress relaxation tests, and heat treatment tests have been conducted for a temperature range of 1000–1250 °C and strain rates ranging from 0.3 to 30 s−1. The dynamic and static recrystallization mechanisms, as well as the grain growth behavior, were studied, and the material parameters of each mechanism were identified for a semi-empirical microstructure model called StrucSim. Double-compression tests in the same temperature and strain rate range were performed to validate the model, and a good correlation of the flow stress between the experiment and simulation was observed.

Mechanical Properties and Constitutive Model of High-Mass-Fraction Pressed Tungsten Powder/Polytetrafluoroethylene-Based Composites

Heavy metal powders driven by explosions can enhance the near-field lethality of explosive warheads by forming a quasi-pressure field while reducing collateral damage at medium and long ranges. Incorporating polymers into high-content metal powders prevents powder sintering under explosive high pressure, enhancing dispersion uniformity and making them promising for controllable warhead applications. To describe the mechanical behavior of materials under impact loading, this paper investigates the dynamic and static mechanical properties and constitutive modeling of tungsten powder/polytetrafluoroethylene (PTFE) composites. Quasi-static compression tests and split Hopkinson pressure bar (SHPB) dynamic tests were conducted on composites with varying tungsten contents (0 wt%, 70 wt%, 80 wt%, and 90 wt%) and particle sizes (200 μm, 400 μm, and 600 μm), obtaining compressive stress–strain curves over a strain rate range of 0.001 to 3610 s−1. The compressive strength of the composites slightly decreased with increasing tungsten particle size but increased with higher tungsten content. Under quasi-static compression, the compressive strength of the composites with 70 wt% and 80 wt% tungsten was lower than that of pure PTFE. This was due to the bonding strength between the tungsten particles and the resin being weaker than the cohesion within the resin. Additionally, the random distribution of the tungsten particles in the matrix led to shear cracks propagating along the phase interfaces, reducing the compressive strength. The compressive strength of the composites with 90 wt% tungsten exceeded that of pure PTFE, as the packed arrangement of the tungsten particles increased the material strength through particle extrusion and friction during compression. Under dynamic impact, the compressive strength of the composites was higher than that of pure PTFE, primarily due to particle extrusion and friction effects. The composites exhibited significant strain rate sensitivity, with both the compressive strength and critical strain increasing quasi-linearly with the strain rate. Based on the experimental data, a damage-modified Zhu–Wang–Tang (ZWT) viscoelastic model was employed to fit the data, effectively characterizing the uniaxial compressive constitutive behavior of tungsten powder/PTFE composites.

The Microstructures, Mechanical Properties, and Energetic Characteristics of a Novel Dual-Phase Ti40Zr40W10Mo10 High-Entropy Alloy.

High-energy structural materials (ESMs) integrate a high energy density with rapid energy release, offering promising applications in advanced technologies. In this study, a novel dual-phase Ti40Zr40W10Mo10 high-entropy alloy (HEA) was synthesized and evaluated as a potential ESM. The alloy exhibited a body-centered cubic (BCC) matrix with Mo-W-rich BCC precipitates of varying sizes, which increased proportionally with the W content. The compressive mechanical properties were assessed across a range of strain rates, revealing that the W10 HEA sustained a compressive strength of 2300 MPa at a strain rate of 3000 s-1. This exceptional performance is attributed to the uniform distribution of circular Mo-W-rich BCC precipitates. Conversely, in the W13 HEA, the aggregated and large Mo-W-rich precipitates deteriorated its dynamic properties. Furthermore, deflagration behavior was observed during dynamic deformation of W10, highlighting its potential as a high-performance ESM.

Compressive mechanical behaviors of Q235B steel over a wide range of temperatures and strain rates

Compressive mechanical behaviors of Q235B steel over a wide range of temperatures and strain rates

A Cellulosic Fibre Foam as a Bicycle Helmet Impact Liner for Brain Injury Mitigation in Oblique Impacts

Bulky cellulosic network structures (BRC) with densities between 60 and 130g/l were investigated as a sustainable alternative to fossil-based foams for impact liners in bicycle helmets. The mechanical properties of BRC foams were characterized across a wide range of strain rates and incorporated into a validated finite element model of a hardshell helmet. Virtual impact tests simulating both consumer information and certification scenarios were conducted to compare BRC-lined helmets against conventional expanded polystyrene (EPS) designs. Results showed that BRC outperformed EPS in oblique impacts, reducing angular accelerations and velocity changes by approximately 33%, particularly for z-axis rotations. The average risk of sustaining AIS2 injuries and concussions was lower for BRC (8% and 34% respectively) compared to EPS (13% and 46%). However, BRC helmets exhibited bottoming out in certain straight impacts, potentially failing certification tests. This limitation was addressed through design modifications. The study demonstrates that cellulosic fibre network structures have the potential to replace fossil-based foams in bicycle helmets while providing adequate protection and improved performance in mitigating rotational forces.

Hot compression behavior and 3D processing maps of Mg-Gd-Y-Zn alloy formed by cold metal transfer wire arc additive manufacturing

Based on hot compression experiments, the hot deformation behavior and workability of the Mg-Gd-Y-Zn alloy fabricated by cold metal transfer wire arc additive manufacturing (WAAM-CMT) were studied. The compression experiments were performed at temperatures ranging from 350 to 500 °C, with strain rates between 0.001 and 1 s−1. The results indicate that the peak stress of the alloy decreases significantly with lower strain rates and higher deformation temperatures. Combined with the analysis of the Arrhenius type equation (Eq.), the average value of the recrystallization activation energy (Q) was 308.4 kJ/mol. Utilizing the Zener-Hollomon parameter, we derived the constitutive Eq. for the deposited Mg-Gd-Y-Zn alloy during hot deformation: [Formula: see text]. Using the dynamic material model, we established a three-dimensional (3D) processing maps for the deposited Mg-Gd-Y-Zn alloy. The main instability domain were temperatures from 350 to 385 °C with strain rates of 0.1 to 1.0 s−1, and temperatures from 435 to 500 °C with strain rates of 0.4 to 1.0 s−1. Considering the power dissipation map, the stable and power-efficient forming domains is in the temperature range from 435 to 500 °C and strain rate range from 0.001 to 0.04 s−1. Due to dynamic recrystallisation (DRX), the grain of the deposited Mg-Gd-Y-Zn alloy is significantly refined after hot deformation. These findings provide valuable guidance for selecting integrated process equipment and optimizing deformation parameters for additive and on-line micro-forged magnesium rare earth alloys.

Enhancing puncture resistance in critical applications: A combined experimental and numerical approach

The qualification of materials for puncture resistance is essential for applications like pressure vessels and transport containers, particularly for the safe transport of radioactive materials. International regulations, set forth by organizations such as the International Atomic Energy Agency (IAEA) and the Atomic Energy Regulatory Commission (AERB), mandate the design of transport packages capable of withstanding various accident scenarios, including puncture, fire, impact, and immersion, to ensure the safety and integrity of radioactive material transport. This paper establishes a correlation between puncture energy ( E) required to penetrate stainless steel and mild steel plates, both with and without lead backing, as a function of plate thickness ( t) and punch diameter ( d). The simulation of strain and damage caused by punch impact is carried out within the elastoplastic region of structural materials, with a focus on the kinetic strengthening of the material. Abaqus finite element software is employed for numerical simulations, with model parameters derived from experimental stress-strain flow curve data using a curve-fitting technique. Dynamic compression experiments were conducted at the Refueling Technology Division (RTD) in the Bhabha Atomic Research Center (BARC) across a range of strain rates from 600 [Formula: see text] to 1750 [Formula: see text] at room temperature, using a Split Hopkinson Pressure bar. Additionally, drop weight tower (DWT) experiments were performed at RTD in the BARC facility to calibrate numerical simulations. These experiments were carried out on both bare and leaded stainless steel (SS304L) and mild steel (SA516Gr70) plates.

Static Properties of Kaolinite Samples from Different Structures and the Influence of Strain Rate

This paper conducts triaxial undrained tests on flocculated and dispersed kaolin samples at strain rate range 0.005–1%/min to investigate the effects of structure and strain rate on shear strength. The test results show that the flocculated samples exhibit strain hardening behaviour, while the dispersed samples show strain softening behaviour. The strain rate sensitivity parameter reflects the degree to which shear strength increases with increasing strain rate. The structure affects the strain rate sensitivity parameter, with values of 4.79% and 2.31% for flocculated and dispersed samples, respectively. When the strain rate is 1%/min, due to the low permeability of the dispersed sample, the high strain rate causes a rapid increase in local pore pressure, while the postponed dissipation of excess pore pressure destroys the sample. When studying the influence of clay structure, it is important to use the same strain rate; otherwise, the differences in shear strength may be underestimated.

Experimental and constitutive assessment of tensile flow behavior of AA5083 alloy with microstructural evolution at warm temperatures

The tensile stress-strain response of the AA5083 alloy was investigated over a temperature range of 25 to 300 °C, and strain rate range of 0.001 to 0.1 s−1. A positive sensitivity to temperature along with a small positive correlation with strain rate at elevated temperatures was observed. The developed artificial neural network (ANN) based constitutive model depicted a superior predictability with average absolute relative error of 1.77% as compared to 3.42% and 4.26% for Johnson-Cook (J-C) and Modified Arrhenius (M-A) models, respectively. The detailed microstructural study of strained tensile samples depicted the occurrence of dynamic recovery confirmed by the maximum Kernel Average Misorientation value of 0.84° at 0.01 s−1 strain rate.

The tensile behaviour of paper under high loading rates

This work deals with the strain-rate dependent characterization of paper under uniaxial tension at high strain-rates. Experiments were performed involving a Split Hopkinson bar for high strain-rate testing, comparing the results with conventional quasi-static tests. Tests were conducted in a strain-rate range between 0.0083 and 212 s−1, which is equivalent to testing velocities between 0.0003 and roughly 13.6 m/s. For the first time the change in tensile behaviour of paper is comprehensively characterized and modelled, using the Cowper-Symonds model for strain-rate hardening. The experimental tests showed that the tensile strength as well as the initial stiffness were gradually increasing with increasing strain-rate. The increase in tensile strength between the lowest and the highest strain-rate was 58% on average whereas the mean increase in stiffness between these two strain-rates was almost 115%. Regarding the fracture strain, it was observed that it significantly decreases with increasing strain-rate. While the average fracture strain of the quasi-static tests was at roughly 6% it was close to 3% for the dynamic tests. In case of the Split Hopkinson bar tests, high-speed videos of the samples were made to determine their elongation via target tracking and digital image correlation (DIC). We found that strain localization, which is a highly relevant mechanism for quasi-static tensile failure, is likely related to short term plastic creep of the material as strain localization nearly entirely disappears at high loading rates of paper.

A modified Johnson-Cook constitutive model of Inconel 690 weld overlay taking into account the strain rate softening effect

Precise material constitutive models are essential for finite element (FE) cutting simulation and analytical calculations of cutting mechanics. In this work, a split Hopkinson pressure bar (SHPB) equipment was employed to investigate the dynamic mechanical behavior of Inconel 690 weld overlay with a wide range of temperatures (20℃, 200℃, 400℃, 600℃, and 800℃) and strain rates (5000s-1, 7500s-1, 10,000s-1, and 12,500s-1). Based on the material flow characteristics at different loading conditions, a modified Johnson-Cook (JC) constitutive model was established, which takes into account the strain rate softening effect at high strain rates and the softening behavior induced by the competition between work hardening and dynamic recovery at large strains. Compared with the original JC constitutive model, the modified constitutive model can provide a closer correspondence between the predicted flow stresses and experimental data. The modified material constitutive model was introduced into FE simulation for orthogonal cutting of Inconel 690 weld overlay. The results indicate that the average prediction errors for the main cutting force and thrust force are 6.38% and 11.38%, respectively, validating the applicability and reliability of the modified JC constitutive model for cutting simulation applications. This study can provide a mechanical foundation for FE analysis in high-speed cutting of Inconel 690 weld overlay, which is conducive to optimizing cutting parameters, reducing machining costs, and enhancing production efficiency in practical industrial manufacturing.

Effect of the flow behavior and dynamic recrystallization of EH420 marine steel on the morphology evolution of martensite substructures

The hot deformation behavior of EH420 marine steel was investigated by isothermal compression tests in the temperature range of 850~1050°C and the strain rate range of 0.01~10s−1. A high-temperature constitutive model and a hot processing map were developed. The results indicated that the microstructure of EH420 marine steel after hot deformation was mainly bainite and lath martensite. The martensite blocks gradually coarsened with the increase in temperature within the range of 950~1050°C/0.01s-1, and the average width increased from about 0.7 μm to 2.3 μm. At high strain rates, martensite blocks became coarse and disordered due to flow instability. The flow stress curve showed a single peak when the strain rate was low. There were more dynamic recrystallization (DRX) structures, resulting in fine and ordered martensite blocks. Under the deformation conditions of 0.1~10s-1/1000°C, the proportion of high-angle grain boundaries (HAGBs) decreased from 53.5% to 40.7% as the strain rate increased. Meanwhile, the hot deformation mechanism shifted from discontinuous dynamic recrystallization (DDRX) to the combined effect of DDRX and dynamic recovery (DRV) and finally transformed into DRV. The flow stress derived from the constitutive model was consistent with the experimental results. The activation energy of EH420 marine steel was 3.16×105J/mol. The optimal hot processing parameters were 950~1050°C and 0.01~0.1s-1.

New constitutive model and hot processing map for A100 steel based on high-temperature flow behavior

To predict the flow behavior and identify the optimal hot processing window for A100 steel, a constitutive model and a hot processing map were established using true stress-strain data extracted from isothermal compression tests performed at temperatures ranging from 1073 to 1353 K and strain rates varying between 0.01 and 10 s−1. The results indicate a strong linear trend between the logarithmic stress and the reciprocal of temperature, along with a significant quadratic relationship between the logarithmic stress and logarithmic strain rate. With a correlation coefficient of 0.9913, the new constitutive model demonstrates an excellent predictive capability for the flow behavior of A100 steel. A significant dynamic recrystallization occurs when the energy dissipation rate exceeds 25 %, resulting in a uniform equiaxed grain structure after deformation. The unstable regions primarily occur in high strain rate and low-temperature zones, where the microstructures are typically coarse and elongated. This structural characteristic adversely affects the mechanical properties. Avoiding these conditions during hot forming of A100 steel is crucial. The optimal hot forming windows for A100 steel are achieved within a temperature range of 1153–1353K and a strain rate range of 0.01–10 s−1, where complete dynamic recrystallization occurs.

Design of a novel high-speed tensile method for testing the high strain rate tensile behavior of aluminum alloys.

The high-strain rate mechanical behavior of aluminum alloys is crucial for the stability of electromagnetic launch systems. However, current high-strain rate testing methods are not suitable for large-scale screening of materials needed in electromagnetic launch systems due to their low precision and high cost. In this paper, a novel method for high-strain rate tensile testing of aluminum alloys based on magnetic pulse driving was proposed. The method can generate a fast-rising edge and adjustable stress pulses to enable uniaxial tensile deformation, reaching a target strain rate quickly and keeping it constant. Based on the theory of stress wave transmission, a single-point method for measuring stress-strain relationship of the specimen combining digital image correlation (DIC) technology is proposed. Finite element simulations using the explicit finite element software LS-DYNA demonstrate a good agreement between the strains and strain rate with experimental values. Tensile tests were conducted on AA7075 in the strain rate range of 1000-3000s-1, the stress-strain relationship obtained from DIC agrees well with the results of traditional Hopkinson bar experiments.

High Strain Rate Deformation of Heat-Treated AA2519 Alloy.

This study examined the effects of heat treatment on the microstructure and dynamic deformation characteristics of AA2519 aluminum alloy in T4, T6, and T8 tempers under high strain rates of 1000-4000 s-1. A Split Hopkinson pressure bar (SHPB) was utilized to characterize the mechanical response, and microstructural analysis was performed to examine the material's microstructure. The findings indicated varied deformation across all three temper conditions. The dynamic behavior of each temper is influenced by its strength properties, which are determined by the aging type and the subsequent transformation of strengthening precipitates, along with the initial microstructure. At a strain rate of 1500 s-1, AA2519-T6 demonstrated a peak dynamic yield strength of 509 MPa and a flow stress of 667 MPa. These values are comparable to those recorded for AA2519-T8 at a strain rate of 3500 s-1. AA2519-T4 exhibited the lowest strength and flow stress characteristics. The T6 temper demonstrated initial stress collapse, dynamic strain aging, and an increased tendency for shear band formation and fracture within the defined strain rate range. The strain rates all showed similar trends in terms of strain hardening rate. The damage evolution of the alloy primarily involved the nucleation, shearing, and cracking of dispersoid particles.

Characterizing and modeling the wide strain rate range behavior of air-filled open-cell polymeric foam

Air-filled open-cell polymeric foams are widely used for absorbing impact energy under various strain rates. Modeling their compression behavior under large deformation across a wide strain rate range remains a challenge, as the air pressure is dominated by viscous effect or inertial effect at different strain rates. In this study, the compression response of air-filled open-cell polyurethane (PU) foam is characterized across a wide strain rate range from 0.0001 s−1 to 5000 s−1. The plateau stress and energy absorption properties of the foam exhibit a power-law dependency on strain rate, showing lower rate sensitivity at quasi-static rates and increased sensitivity at high strain rates. To describe the observed rate sensitivity variation, the effect of airflow resistance is quantitatively modeled and a visco-hyperelastic constitutive model considering air pressure is developed. It shows that at high strain rates, the air pressure can constitute up to 30 % of the energy absorption contribution while it is relatively negligible at quasi-static strain rates, which significantly amplifies the difference in rate sensitivity between quasi-static and high strain rates. Furthermore, a simplified semi-empirical formula is proposed to rapidly estimate the air pressure in open-cell foams at high strain rates. This formula demonstrates the mechanical response transition from open-cell to closed-cell foams with increasing strain rates. This study is meaningful for understanding the dynamic response and the energy absorption capabilities of air or fluid filled open-cell foam.

Stochastic analysis of dynamic fracture of concrete using CT-image based mesoscale models with a rate-dependent phase field method

Concrete structures are commonly exposed to dynamic loads spanning a wide range of strain rates, and the inherent mesoscale heterogeneities complicate stochastic dynamic fracture mechanisms even more. This work develops a numerical framework using mesoscale concrete models based on micro computed tomography (CT) images to investigate such mechanisms with meaningful stochastic analyses. A rate-dependent phase field model is proposed to characterise the dynamic initiation and propagation of cracks by incorporating both micro-viscosity and macroscopic viscoelasticity, which is described by two standard Maxwell elements with different relaxation times to consider a wide range of strain rates. Moreover, the viscoelastic constitutive relation is formulated in the full strain space, which allows for a spectral decomposition of the strain tensor to determine the effective damage driving force, thus effectively addressing the issue of compressive fracture. A numerical implementation scheme is developed by combining user-defined element and material subroutines in ABAQUS/Explicit solver. Extensive Monte Carlo simulations of dynamic tension up to a strain rate of 200 s−1 are performed with statistical analyses. This work reveals the intricate dynamics associated with mesoscale heterogeneities and identifies the critical transition state at 20 s−1. The transition is characterised by changing modes of fracture patterns, stress wave propagation, and load-carrying capacities. A new TDIF–strain rate–standard deviation relation is also proposed and aligns well with the increasing dispersion of experimental data. The relationship between void content and tensile strength reflects the formation characteristics of crack networks, with the void content exhibiting a positive correlation with the TDIF from 20 s−1 to 100 s−1.

Research on Compression Failure Characteristics and Damage Constitutive Model of Steel Fiber-Reinforced Concrete with 2% Copper-Coated Fibers Under Impact Load.

This study systematically investigates the mechanical properties of plain concrete (PC) and 2% steel fiber reinforced concrete (SFRC) under both static and dynamic loading conditions, utilizing advanced mechanical testing equipment and dynamic impact testing methods. The strain rate range studied spans from 10-4 s-1 to 483.12 s-1. Under static loading conditions, the maximum bearing capacity and energy absorption capacity of 2% SFRC are 2.16 times and 3.83 times greater than those of PC, respectively, indicating a significant enhancement in toughness and resistance to failure. Under dynamic loading conditions, the energy absorption capacity of SFRC increases to 6.36 times that of PC. The impact failure behavior of SFRC was analyzed using the split-Hopkinson pressure bar-digital image correlation (SHPB-DIC) method, revealing that the failure was primarily driven by splitting tension. The failure process was subsequently categorized into four distinct stages. At high strain rates, the dynamic enhancement factor, peak stress, and peak strain of SFRC exhibit a linear increase with strain rate, whereas the energy absorption capacity increases in a nonlinear manner. This study presents a simplified viscoelastic constitutive model with four parameters and develops a damage-based viscoelastic constitutive model with seven parameters, demonstrating its broad applicability. The findings offer both theoretical insights and experimental evidence to support the use of SFRC under high strain rate conditions.

Enhancing the superplastic deformation capabilities of the Ti-6Al-4V alloy using superimposed oscillations

This study investigates the effect of imposing low frequency, low amplitude oscillations during uniaxial tensile tests on the mechanical behaviour of the Ti-6Al-4V alloy under a typical superplastic temperature of 900 °C. Different material models were used to simulate these tests with the finite element software ABAQUS. A creep strain power model fit through an iterative FEA process yielded a high correlation to the force/displacement and thinning results from uniaxial tensile tests. The developed material models with and without oscillation materials were also used to simulate a free-bulge forming process within the strain rate range of 0.0003 to 0.01 s−1 under constant strain rate testing. Within the domain of the parts formed in this study, the improvement in the forming time ranged from a 120 % reduction at elevated strain rates and reduced part complexity to 520 % in the most complex part geometry.

Effects of strain rate, temperature and microstructure on mechanical properties of (CoCrNi)94Al3Ti3 medium-entropy alloy: Experiments and constitutive modeling

Mechanical properties and microstructure evolution of as-cast, solution-treated and aged (CoCrNi)94Al3Ti3 medium-entropy alloys (MEAs) are investigated under uniaxial compression at strain rates from 10−3 to 3700 s−1 within temperatures from 123 to 573 K. Compared to the single-phase solution-treated MEA, spherical nanosized particles result in an increase in the yield stress approximately by 55 % (to 586 MPa) and 73 % (to 655 MPa) for the as-cast and aged (CoCrNi)94Al3Ti3, respectively. At ambient temperature, the as-cast and aged alloys demonstrate significantly higher dynamic strain rate sensitivity. At a fixed strain rate, the yield strengths and flow stresses increase with decreasing temperature for all three alloys. The as-cast and aged alloys exhibit significantly higher yield strength primarily due to precipitation strengthening of the coherent ordered L12 precipitates. Dislocation slip dominates the plastic deformation and leads to the weak but apparent 〈110〉 texture along the loading direction, and no deformation twins are observed in all alloys. Besides, Khan-Liu constitutive models are developed and can well describe the plastic flow of three alloys over a wide range of strain rates and temperatures.