Increase In Strain Rate Sensitivity Research Articles

Nanoindentation creep mechanism of gradient ultrafine lamellar γ+Ni5Zr eutectic using electromagnetic levitation coupled with fall casting

A quaternary Ni50Fe20Cr20Zr10 eutectic alloy was designed based on the Ni–Fe–Cr alloy, and the gradient ultrafine lamellar γ+Ni5Zr eutectic was achieved by means of electromagnetic levitation coupled with fall casting (EML-FC). The temperature field, the process of interface migration, microstructural characteristics and the nanoindentation creep property of the alloy were systematically analyzed. During the rapid solidification, since the conical surface served as the main heat dissipation channel, the solid-liquid interface moved from the conical surface towards the top of the cone axis. The gradual decrease in cooling rate from 105 to 103 K s−1 along this direction led to the formation of the gradient ultrafine lamellar γ + Ni5Zr eutectic with the size from 59 ± 12 to 140 ± 36 nm. The nanoindentation creep behavior and mechanism were analyzed by estimating the strain rate sensitivity and activation volume. As the interlamellar spacing of the eutectic decreased, the nanohardness and creep resistance of the alloy gradually increased owing to an increase in grain boundary density and the enhancement of coupling effect between dislocation and grain boundary. In addition, the creep behavior of alloy was sensitive to the loading rate. Increasing the loading rate led to an increase in strain rate sensitivity from 7.69 × 10−3 to 18.89 × 10−3 and a decrease in activation volume from 29 to 12 b3. This special eutectic structure and its improved nanohardness and creep resistance properties offered a potential opportunity to explore a new generation of alloys for the hot-end components of 972 K ultra-supercritical fossil-fired power plants.

The role of grain size in achieving excellent properties in structural materials

Advanced structural materials are expected to display significantly improved mechanical properties and this may be achieved, at least in part, by refining the grain size to the submicrometer or the nanocrystalline range. This report provides a detailed summary of the role of grain size in the mechanical properties of metals. The effect of grain size on the high temperature behavior and the development of superplasticity is illustrated using deformation mechanism maps and the development of exceptional strength through grain refinement hardening at low temperatures is also discussed. It is shown that the deformation mechanism of grain boundary sliding, as developed theoretically, can be used to effectively predict both the high and low temperature behavior of metals having different grain sizes. This analysis explains the increase in strain rate sensitivity in ultrafine-grained metals with low and moderate melting points and the ability to increase both the strength and ductility of these materials to thereby overcome the strength-ductility paradox. The recent development of hybrid materials is also reviewed and it is demonstrated that, although these hybrids have received only limited attention to date, they provide a potential for making significant advances in the production of new structural materials.

Impact Resistance of Rubberized Alkali-Activated Concrete Incorporating Recycled Aggregate and Recycled Steel Fiber

Alkali-activated concrete (AAC) features excellent mechanical properties and sustainability. The incorporation of crumb rubber (CR), recycled concrete aggregates (RCAs), and recycled steel fibers (RSFs) can further enhance environmental sustainability. This paper mainly investigated the dynamic behaviors of a novel rubberized AAC incorporating RCAs and RSFs (RuAAC) through Split-Hopkinson Pressure Bar (SHPB) tests. The variables included three types of RSF content (1%, 2% and 3%), five types of rubber content (0%, 5%, 20%, 35% and 50%) and five impact pressures (0.5 MPa, 0.6 MPa, 0.7 MPa, 0.8 MPa and 0.9 MPa). Dynamic stress–strain curves, dynamic strength, the dynamic increase factor (DIF), impact toughness and the synergistic effects of RSF and CR were discussed. The results show that increasing RSF and CR contents could improve the impact resistance of RuAAC under impact loading. The RuAAC exhibited significant strain rate sensitivity, and the sensitivity increased with larger contents of RSF and CR. The increase in strain rate sensitivity was more pronounced with higher CR contents, which was reflected in larger dynamic increase factor (DIF) values. Under high impact pressure, the impact toughness was obviously enhanced with higher RSF contents, while the contribution of increased CR content to impact toughness was not apparent, which may be attributed to the fact that this study only calculated the integral under the dynamic stress–strain curve before the peak stress to determine impact toughness, neglecting the potential contribution of CR particles after the peak point. The obvious strain sensitivity exhibited by the RuAAC in the SHPB tests indicated superior impact performance, making it particularly suitable for architectural structures prone to seismic or explosive impacts.

Dynamic restoration and texture evolution of pure tantalum during warm deformation

Microstructural evolution of pure tantalum during compression at temperatures and strain rates of 600–1100 °C/0.001–1 s−1 has been investigated. The results show that the restoration is mainly achieved by dynamic recovery at 600–800 °C/0.001 s−1 or 1100 °C/0.01–1 s−1, while continuous dynamic recrystallization (CDRX) has been obviously activated at a higher temperature and a lower strain rate of 1100 °C/0.001 s−1. The formation of both subgrains and recrystallized grains has been significantly promoted with temperature rising from 800 to 1100 °C at 0.001 s−1 or strain rate decreasing from 0.01 to 0.001 s−1 at 1100 °C, thus resulting in the obviously increased strain rate sensitivity (m). The deformed microstructures possess a mix of 〈111〉 and 〈100〉 textures. The <111> texture is strengthened when a large fraction of deformed grains develops at minor strains, lower temperatures and higher strain rates. The 〈100〉 texture shows an explosive growth via <100> subgrains bulging into regions with high-density low angle boundaries (LABs) in <111> grains when subgrain fraction has substantially increased after 60% height reduction at 1100 °C/0.001 s−1.

Mechanical behavior of nanorubber reinforced epoxy over a wide strain rate loading

Nanorubber/epoxy composites containing 0, 2, 6 and 10 ​wt% nanorubber are subjected to uniaxial compression over a wide range of strain rate from 8 ​× ​10−4 s−1 to ∼2 ​× ​104 s−1. Unexpectedly, their strain rate sensitivity and strain hardening index increase with increasing nanorubber content. Potential mechanisms are proposed based on numerical simulations using a unit cell model. An increase in the strain rate sensitivity with increasing nanorubber content results from the fact that the nanorubber becomes less incompressible at high strain, generating a higher hydro-static pressure. Adiabatic shear localization starts to occur in the epoxy under a strain rate of 22,000 s−1 when the strain exceeds 0.35. The presence of nanorubber in the epoxy reduces adiabatic shear localization by preventing it from propagating.

Dynamic beam-end tests: Investigation using split Hopkinson bar

The bond between concrete and steel reinforcement is a highly investigated topic under both quasi-static and dynamic loading conditions. Strain rate sensitivity and dynamic increase factor are the key aspects affecting the resulting response of the structure and represent crucial parameters for modelling the impact-related events. Measuring the bond properties under dynamic conditions, however, is a complex task requiring advanced experimental techniques and methodology. In this paper, the bond stress-slip relationships during dynamic pull-out was measured using an innovative technique based on a tensile split Hopkinson bar and a near-to-full-scale beam-end specimen representing an end-part of a reinforced concrete beam.A tensile split Hopkinson bar was used to generate a tensile stress wave with a long duration that pulls a reinforcement bar with a short bond length out of the concrete block. As a very complex wave propagation behavior was observed during the impact, the forward and backward propagating waves have to be separated and subsequently used to properly calculate the bond stress-slip relationship. Two redundant methods utilizing strain gauge signals and digital image correlation for separation of the longitudinal stress waves were employed to solve the problem. The proof-of-concept and applicability of the method which are the main focus of the contribution were demonstrated with a numerical simulation performed in LS-DYNA. An exemplary evaluation of the results of the real tests performed at medium impact velocity with full pull-out of the rebar was performed. The presented method is considered suitable for the evaluation of the dynamic bond stress-slip relationship and produced high-quality results during the initial impact phase and reasonable quality results up to the full pull-out.

Grain size dependence of modified material constitutive model for OFHC copper

Grain refinement occurs during manufacturing process, and grain size has a significant impact on mechanical properties. It is essential to establish the relationship between grain evolution and plastic behavior. The quasi-static and dynamic compression experiments for three kinds of oxygen-free high-conductivity (OFHC) copper with different grain sizes have been carried out. The true stress–strain curves were corrected to the isothermal curves, in which the temperature dependence of the specific heat capacity was used. It was found that the grain size has a significant influence on the yield stress, strain rate sensitivity, and thermal softening. A new phenomenon-based constitutive model considering the grain size and the coupling between strain hardening and strain rate was developed, and the results of the quasi-static and dynamic compression experiments were used to fit the parameters. The experimental data and the predicted results of the newly developed constitutive model agree well, which proves the constitutive model has a high prediction accuracy. The fitted constitutive model depicted that the strain rate sensitivity increases and thermal softening degree declines as the rise of the grain size of OFHC copper. The developed constitutive model could be used to the numerical simulation for the manufacturing process of OFHC copper considering the grain refinement.

Influence of Strain Rate Sensitivity on Cube Texture Evolution in Aluminium Alloys

The influence of strain rate sensitivity on development of Cube texture and on the morphology of Cube-oriented grains is often neglected in simulations approaches. Therefore, crystal plasticity simulations and experiments were performed up to 73 pct of thickness reduction for cold rolling on Al 6016. It is found, that low values of strain rate sensitivity promote Cube grains fragmentation and avoid formation of transition bands already at 50 to 55 pct thickness reduction. High values of strain-rate sensitivity cause formation of Cube transition bands leaving thin Cube grains in the microstructure and delay their fragmentation. Other texture components are affected by changes in strain rate sensitivity as well. The Copper volume fraction in the final texture diminishes as the strain rate sensitivity decreases, while Brass and S components of the beta fiber show a moderately higher volume fraction when the strain rate sensitivity increases. The final volume fraction of Goss is highest when the strain rate sensitivity is 10−2 but low if the strain rate sensitivity is 10−3 or raises up to 10−1. Recrystallization texture components (P, Q) are not affected by strain rate sensitivity, while the invGoss fraction decreases for high values of strain rate sensitivity. The results found in cold rolling crystal plasticity simulations were compared with experimentally determined Cube distribution and texture components obtained through thickness for Al6016 rolled at 80 m/min and 600 m/min. Further crystal plasticity simulations were performed to predict the influence of strain rate sensitivity during several hot rolling conditions where activity of non-octahedral slip systems was included in the simulations. During hot rolling, high values of strain rate sensitivity contribute to Cube stabilization and promote formation of Copper texture and delay Brass and S.

Plasticity and fracture of AA7075 at elevated strain rates and temperatures

The accurate description of the strain rate and temperature dependent response of Aluminium alloys is a perpetual quest in the hot forming industry. In the present study, uniaxial tension, and notched tension experiments are conducted for an aluminium AA7075-T6 sheet metal at various temperatures and strain rates. The experimental campaign covers strain rates ranging from 0.001/s to 100/s, and temperatures ranging from 20°C to 360°C. We observe low strain rate sensitivity at room temperature, with an increase in strain rate sensitivity as temperature is increased up to 360°C. An YLD2000-3D model is employed to describe the anisotropy of the material. A machine learning based hardening model is employed to capture the complex strain rate and temperature effect on the observed hardening response. Counter-example regularization is utilized to guarantee a convergence in the numeric return-mapping algorithm. Comparing the experimental force-displacement curves with the numerical predictions, the neural network model accurately describes the large deformation response of the material in the post-necking range.

Temperature–dependent dynamic plasticity of micro-scale fused silica

The ability to predict the micro-scale strength and plasticity of fused-silica micro-components is crucial as their miniaturization and applications in harsh environments advance. This study focusses on the micro-mechanical behavior of fused silica micropillars at high temperatures and variable strain rates. 160 micropillars with a diameter of 1.6 µm have been tested at temperatures between −120 °C and 600 °C and strain rates between 10-3 s−1 and 1 s−1, which are to date unexplored conditions. Between −120 °C and 300 °C, the yield strengths (6–8 GPa) and strain rate sensitivities (≤0.03) vary only marginally. However, at 600 °C, a significant decrease in yield strength by more than 50 % (2.5–4.5 GPa) and an increase in strain rate sensitivity by a factor of 3 (0.09) is observed. Post-compression synchrotron-based ptychographic X-ray computed tomography (PXCT) on plastically deformed micropillars revealed a transition in deformation mechanisms: Shear-localization and shear-promoted densification at 25 °C; homogeneous shear-flow and densification limited by radial cracking at 300 °C; and unconstrained shear-flow and limited densification due to weak confinement strength at 600 °C. FEM results support these observations while separating geometric from material-intrinsic effects. These results suggest that the classification of fused silica as a glass that deforms predominantly through densification should be challenged – at least under unconstrained compression, which is the predominant mode of loading in applications.

Accounting for the effect of dislocation climb-mediated flow on the anisotropy and texture evolution of Mg alloy, AZ31B

The current study explores the role that dislocation climb has in mediating plasticity a Mg alloy at moderately elevated temperatures. Interrupted tensile tests were performed on samples of Mg alloy, AZ31B, sheet in the O temper condition over a range of strain rates (10-5 to 10-1 s-1) and temperatures (20–350 °C) along the rolling and transverse directions. Experimental measurements of the resulting strain anisotropy and texture evolution were used as constraints during a parametric study employing a new crystal plasticity model (VPSC-CLIMB), which explicitly accounts for the kinematics of dislocation climb. The results reveal that the climb of basal <a> dislocations is not only important for dislocation recovery, but also demonstrate that climb accommodates a significant fraction of the strain in conditions where a power-law creep-type constitutive response prevails. This work does not discredit the notion that non-basal slip of <a> and <c+a> dislocations is important over a wide range of temperatures and strain rates. However, it demonstrates that the activation of dislocation climb as the mechanistic change within the power law regime provides an explanation for a wide range of observations, including the simultaneous reduction in strain anisotropy, slowed texture evolution, and rapid increase in strain rate sensitivity. Finally, it is hypothesized that these conclusions may even apply to cases in which grain boundary sliding and/or dynamic recrystallization are observed.

Rate-depending plastic deformation behaviour in a nickel-base alloy under hydrogen influence

Despite a lot of research activities, the influence of hydrogen on the plastic deformation process is controversially discussed and often underestimated. Therefore, in this work strain rate jump tests were performed, using an electrochemical nanoindentation setup to investigate the deformation processes in a nickel-based alloy 725 under the influence of hydrogen, with the aim of determining thermally activated parameters such as strain rate sensitivity and activation volume. A hydrogen-induced hardness increase of about 8% was detected for all applied strain rates. The measured increase in strain rate sensitivity and the decrease in activation volume could be related to short-range order effects, which can lead to a more localized deformation. Furthermore, the optical evaluation of the remaining imprints showed a clear change in the formation of the plastically deformed zone during hydrogen charging. These insights into the deformation behaviour give further understanding regarding hydrogen-induced localized plasticity.

Effects of Cu Addition on Mechanical Behaviour, Microstructural Evolution and Anti-Corrosion Performance of TiAl-Based Intermetallic Alloy under Different Strain Rates.

TiAl-based intermetallic alloys are prepared with Cu concentrations of 3–5 at.% (atomic ratio). The mechanical properties and microstructural characteristics of the alloys are investigated under static and dynamic loading conditions using a material testing system (MTS) and split-Hopkinson Pressure Bar (SHPB), respectively. The electrochemical properties of the various alloys are then tested in Ringer’s solution. It is shown that the level of Cu addition significantly affects both the flow stress and the ductility of the samples. For Cu contents of 3 and 4 at.%, respectively, the flow stress and strain rate sensitivity increase at higher strain rates. Furthermore, for a constant strain rate, a Cu content of 4 at.% leads to an increased fracture strain. However, for the sample with the highest Cu addition of 5 at.%, the flow stress and fracture strain both decrease. The X-ray diffraction (XRD) patterns and optical microscopy (OM) images reveal that the lower ductility is due to the formation of a greater quantity of γ phase in the binary TiAl alloy system. Among all the specimens, that with a Cu addition of 4 at.% has the best anti-corrosion performance. Overall, the results indicate that the favourable properties of the TiAlCu4 sample stem mainly from the low γ phase content of the microstructure and the high α2 phase content.

The Taylor–Quinney coefficients and strain hardening of commercially pure titanium, iron, copper, and tin in high rate compression

This work presents an investigation on the effects of adiabatic heating and strain rate on the dynamic compressive response of titanium, iron, copper, and tin. The high strain rate tests were carried out with a Split Hopkinson Pressure Bar (SHPB) and the low strain rate tests with a servohydraulic testing machine. The temperature increase of the specimens during deformation was measured with high speed infrared thermography (IRT). The results show that all the investigated materials have positive strain rate sensitivity and temperature increases of up to 65 °C were observed in the high strain rate experiments (500–3100 s−1). Adiabatic heating in all investigated materials increased with strain rate. The temperature increase at the strain rate of 1 s−1 clearly diminished the strain hardening rate of iron and titanium but was seemingly insufficient to impact the mechanical behavior of copper and tin. The Taylor–Quinney coefficients (βint and βdiff) were found to be strain and strain rate dependent. At higher strain rates (1200–3100 s−1), the integral βint was smaller in the beginning of the test (0.2 to 0.7) and increased to approximately 0.8–0.9 at larger plastic strains. The differential βdiff comprised gaussian curves as a function of strain whose maximum values were from 0.9 to 1.2 for the investigated materials. Tin had lower βint and βdiff with higher strain hardening rates, while copper had a higher βint and βdiff with a low strain hardening rate throughout the high strain rate tests. These results indicate that copper had a more stable microstructure during deformation and converted most of the applied plastic work into heat, while tin had a faster evolving microstructure which stored more plastic work in its microstructure during plastic deformation. Furthermore, this suggests that βint and βdiff can be used as parameters to investigate the stability and the microstructural evolution of materials under high strain rate plastic deformation. βdiff is more appropriate to describe the instantaneous thermomechanical behavior of a material and βint is more appropriate for applications which benefit from a single parameter to characterize how efficiently a material converts plastic work into heat up to a given strain level.

Role of strain rate sensitivity of extrafibrillar matrix on fracture in mineralized collagen fibril arrays

Bone is a biological composite possessing complex hierarchical structure, which endows it with extraordinary damage tolerance. Despite the progress on the relationship between fracture behavior and the hierarchical structure of bone, contributions of the submicroscale constituents to fracture resistance of bone remain elusive. In this study, the calculations are carried out for fracture in staggered mineralized collagen fibril (MCF) arrays using the cohesive zone framework. The strain rate hardening of extrafibrillar matrix (EFM), post-yield strain hardening of the EFM, plastic deformation of the MCF caused by mineral/collagen sliding, and debonding of the interface between MCF and EFM are accounted for in the analyses; the individual and combined effects of strain rate sensitivity of the EFM and fracture properties of the EFM-MCF interface are revealed. It is found that for the strong EFM-MCF interface, high degree of strain rate sensitivity of EFM gives rise to low toughness of MCF arrays. Compared with plastic deformations in MCFs and EFM, interfacial debonding provides smaller contribution to toughness of MCF arrays, and plastic dissipation of MCFs is the major source of toughening. For the tough EFM-MCF interface, the toughness of MCF arrays increases with increasing degree of strain rate sensitivity of EFM, and the EFM with high degree of strain rate sensitivity promotes spreading of plastic deformation, leading to amplified damage energy dissipation in interfaces. We have further identified that strain rate sensitivity of the EFM has negligible influence on toughness of MCF arrays in the case of weak EFM-MCF interface, where interfacial debonding serves as the major toughening mechanism. However, the strain rate sensitive EFM can still activate the mechanism of spreading plastic deformation in this case, giving rise to the increase in relative contribution of plastic dissipation in MCFs with increasing strain rate sensitivity of the EFM.

Tailoring the Mechanical Properties of Metaluminous Aluminosilicate Glasses by Phosphate Incorporation

The characterisation of aluminosilicate glasses is highly relevant in geosciences and for engineering applications such as reinforcement fibres or touchscreen covers. The incorporation of phosphate as a third network-forming species into these glasses offers unique opportunities for fine-tuning glass properties via changes in glass structure and polymerisation. In this work, we studied melt-quenched aluminosilicate glasses within the system SiO2-Al2O3-Na2O-P2O5 with 50 to 70 mol% SiO2 and up to 7.5 mol% P2O5. All glasses were metaluminous (Al:Na = 1) in order to maximise the degree of polymerisation. Increasing the phosphate content at the expense of NaAlO2 lead to reduced glass polymerisation and density, resulting in a decrease in elastic moduli and hardness and an increase in strain-rate sensitivity. When increasing the silica content by substituting SiO4 for AlO4 tetrahedra, network polymerisation remained mostly unchanged, as confirmed by nearly constant molar volume and hardness. Densification upon indentation was analysed by Raman spectroscopy and finite element analysis. We find that the elastic properties and hardness of metaluminous phospho-aluminosilicate glasses are governed by changes in density and network polymerisation. Other mechanical properties underlie more complex changes in glass structure.

Modelling high temperature deformation of lamellar TiAl crystal using strain-rate enhanced crystal plasticity

Multi-phase lamellar γ-TiAl alloys are highly anisotropic and rate sensitive. At high temperature, the strain rate sensitivity (SRS) increases, which eventually influences the yield behaviour of the alloy. With increasing temperature, the onset of yield changes anomalously showing an increasing or sometimes a decreasing trend. This anomalous behaviour depends on alloy chemistry, lamellar microstructure and anisotropy due to lamellar orientations. To capture the strain rate sensitive deformation behaviour over a wide temperature range and to understand distinct nature of yield anisotropy, a new formulation of the strain rate sensitivity (SRS) expressed by a temperature dependent exponent has been proposed within the framework of the classical power-law based visco-plastic Crystal Plasticity Finite Element Method (CPFEM). In the presented formulation, the evolution of SRS parameter was deduced from laws of thermally activated dislocation motion to obtain temperature-enhanced strain rate sensitivity. Moreover, a dislocation pile-up assisted mechanical threshold stress was incorporated to obtain an “anomalous yield” response. The model was validated for a lamellar PST-TiAl, which is a single crystal consisting of γ-TiAl and α2-Ti3Al lamellar phases. Detailed predictive numerical analysis was performed for an in-depth understanding of temperature enhanced strain-rate sensitivity during local deformation behaviour of TiAl alloy based on slip activities.

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.

Effect of post-deformation annealing on the microstructure and micro-mechanical behavior of Zn–Mg hybrids processed by High-Pressure Torsion

Heterostructured metals have attracted increasing interest because of their unique capability to overcome the strength-ductility tradeoff typically observed in engineering materials. Here, a new strategy for synthesizing heterostructured Zn–Mg hybrids is proposed via high-pressure torsion (HPT) followed by post-deformation annealing (PDA). Experimental results indicate a transition from a relatively homogenous nanograined structure after HPT, to a heterogeneous microstructure, containing a distribution of Mg2Zn11 and MgZn2 intermetallic nanoprecipitates, upon subsequent PDA. This led to a simultaneous increase in hardness and strain rate sensitivity. The observed three-regime strain hardening behavior was suggested to be due to the activation of multiple strengthening mechanisms, including grain refinement, in-situ precipitation, and back-stress strengthening associated with geometrically necessary dislocations. Thus, the mechanical response of Zn–Mg hybrids may be tailored to obtain the desired response for task-specific applications.

Strain-Rate Sensitivity of Nanocrystalline Cu–10Ta to 700,000/s

Several miniature Kolsky bars are used to obtain stress–strain curves for nanocrystalline Cu–10Ta over a range of high strain-rates. The smallest bar (steel) has a 305 μm diameter, and achieved rates up to 700 × 103/s. Different sample sizes are needed to obtain different strain-rates, and it is shown that there is no appreciable sample size effect when different sizes are tested at similar strain-rates, even though the sample sizes vary by over an order of magnitude. No significant increase in strain-rate sensitivity is noted over the strain-rate range studied, i.e., the strength increases linearly with the logarithm of strain-rate from 0.001/s to 700 × 103/s.