Wide Range Of Strain Rates Research Articles

Dynamic Hardening of AISI 304 Steel at a Wide Range of Strain Rates and Its Application to Shot Peening Simulation

The hardening behavior of AISI 304 steel is investigated at various strain rates, from the quasi-static state to ultra-high strain rates, because it is necessary for numerical simulation of high-speed deformation problems. This kind of testing at a wide range of strain rates has not been yet reported in the literature although it is indispensable for accurate numerical analyses where deformation takes place with a wide spectrum of strain rates. AISI 304 steel is a kind of austenitic stainless steel used in various engineering fields, which does not harden by heat treatment, but by cold working such as shot peening. In order to obtain hardening properties at each strain rate, tensile tests were carried out using a universal testing machine of the INSTRON 5583 for the quasi-static state, a high speed material testing machine of a servo-hydraulic type for intermediate strain rates, and a tensile split-Hopkinson bar for high strain rates with a digital image correlation method. The hardening properties at the ultra-high strain-rate region were obtained from Taylor impact test results by calibration with an experimental–numerical hybrid inverse optimization for reliable extrapolation results. Finally, the hardening flow stress curves were obtained at various strain rates from the quasi-static state to ultra-high strain rates by interpolating the data with the extended Lim–Huh model. The result shows that the yield stress of 759 MPa at the quasi-static state increased to 1429 MPa at a strain rate of 106 s−1, which is about 1.9 times of the quasi-static yield stress. As a demonstration example, the dynamic hardening properties obtained were applied to a shot peening simulation that required hardening curves at a wide range of strain rates from the static state to 106 s−1. The simulation result with the dynamic hardening properties is compared to that with the quasi-static properties. The comparison shows a notable difference in the maximum compressive residual stress by 32%, demonstrating that it is important to consider the dynamic hardening properties in such high strain rate simulation as shot peening for accurate simulation results.

High Temperatures Deformation and Formability Evaluation Of α+β Brass Sheet by Experimental and Theoretical Approaches

ABSTRACT The present work proposes a systematic procedure for the evaluation of high temperatures deformation and formability of α + β brass undergoing the stretch forming process. Firstly, flow stress has been predicted by the most popular Johnson-Cook (JC) uniaxial constitutive model at a wide range of temperatures (773 K, 873 K and 973 K) and strain rates (0.001 s−1, 0.01 s−1 and 0.1 s−1). For yielding performance evaluation, FLC integrated with Barlat’89 function has been substituted by the traditional Hill’48 function. The necking curves have been constructed with the uniaxial constitutive model and eminent the Barlat’89 yield criterion. The fracture locus is mathematically derived from the forming limit curves (FLCs). These FLC have been experimentally deceived through a series of standard Nakazima tests. Further, the predicted FLCs by Marciniak–Kuczynski (M–K) model have been compared for different loading conditions. The predicted FLCs with Barlat’89 yield function performed outstanding compared to Hill’48 function. Furthermore, formality studies by means of forming limit diagram, limit dome height and surface strain distribution have been analysed.

Thermo-viscoplastic behavior and constitutive relations for 304 austenitic stainless steel over a wide range of strain rates covering quasi-static, medium, high and very high regimes

Using the recently developed single shear specimen, deformation behavior of 304 austenitic stainless steel is studied systematically over a wide range of strain rates, covering quasi-static (0.001-0.1 s−1), medium (1-10 s−1), high (3000-6000 s−1) and very high (13000-39000 s−1) regimes, and temperatures between 77 and 1073 K were considered. The experimental flow stress curves show that: (1) the flow stress increases slightly at strain rates below 6000 s−1; concerning strain rates above 13000 s−1, however, an obvious flow stress upturn exists; (2) dynamic strain aging (DSA) occurs within the temperature range of 673 to 873 K and strain rates lower than 10 s−1; (3) both temperature sensitivity and strain rate sensitivity of the material are affected by DSA, and bell-shaped sensitivity curves form; (4) with increasing strain rates, peaks of the bell-shaped temperature sensitivity curves move to higher temperature regimes, and the evolution law is equally valid for the influence of temperature on the strain rate sensitivity curves. According to experiments, eight constitutive relations, including three phenomenological, four physical-based, and an artificial neural network, are established, including viscous drag effect at very high strain rates but excluding DSA phenomenon. Prediction capacities of the established constitutive models are checked by testing condition jump tests at randomly chosen strain rates and temperatures. Description capacities of the constitutive models in terms of strain hardening rate, temperature sensitivity and strain rate sensitivity are also analyzed.

Defect reversibility regulates dynamic tensile strength in silicon carbide at high strain rates

To reveal the relationship between atomic-scale activity and bulk materials properties, we report all-atom molecular dynamics (MD) simulations of the deformation and dynamic failure of mono- and nanocrystalline silicon carbide (SiC) ceramics. We establish a direct link between the reversibility of defects and dynamic tensile strength of a nominally brittle ceramic over a wide range (six orders of magnitude) of strain rates, bridging the simulation regime to current experimental capabilities that enable the observation of lattice dynamics over extremely short timescales. Our results reveal that SiC exhibits a highly reversible deformation twinning mechanism in response to loading along the [001] crystal direction below a critical compression strain. The remarkable reversibility of the active defects allows the crystal to retain its high strength. Beyond a critical strain, the process becomes unstable, and self-activated twin boundary motion is triggered, yielding irreversibly intertwined defects, resulting in a significant reduction in strength.

Effect of rare-earth metals on the hot strength of HSLA steels

Abstract An experimental study was done on the effect of rare-earth metals on a high-strength low-alloy steel. The work was focused in deriving the influence on Ce and La on the hot-working behavior. For this purpose, uniaxial hot-compression tests were carried out in a wide range of temperatures and strain rates. The effect of the rare-earth metals was determined by comparison of the characteristic parameters, describing the constitutive equations of the high-temperature response of the steel with, and without, rare-earth metals. The results showed that rare-earth metals were playing a major significant role on hardening mechanisms rather than on softening by dynamic recovery. On the contrary, rare-earth metals were able to delay the onset of dynamic recrystallization. All the present experimental results suggested that the latter roles are played by solid solution strengthening, through a solute drag effect, and not by precipitated particles.

Hugoniot elastic limit of single-crystal tantalum at normal and elevated temperatures subjected to extreme strain rates

Large-scale nonequilibrium molecular dynamic simulations of impact-induced shock propagation in defect-free single-crystal Ta along the [001] direction is presented, paying particular attention to the formation of elastic-plastic two-wave structures. Plastic deformation and elastic limits of Ta single crystals for various crystal orientations were investigated in a recent paper [R. Ravelo et al., Phys. Rev. B 88, 134101 (2013)]. In the present paper, a comprehensive study on the Hugoniot elastic limit (HEL) and its dependence on associated physical parameters is reported. The observed attenuation of an elastic precursor in a stress-wave profile led to proposing wide-range scaling relations for HEL decay applicable for ultrahigh strain rates. The influence of a lateral dimension on the spatial profile of a stress wave and time profile of free surface velocity (FSV) in the distinct appearance of a spike-valley feature and its consequence on scaling relations is investigated. Further, it is shown that the commonly used method of calculating HEL from a FSV profile is inadequate for submicron-thick samples at high strain rates. The necessary modifications are incorporated that resulted in comparable HEL values by two complimentary approaches of stress and FSV profiles. Simulations carried out for increasing impact strength revealed a power law dependence of HEL with strain rate. A methodology based on extrapolation of stress decay law and strain rate scaling constructed by us is proposed here for prediction of HEL pertaining to larger length samples. Very good agreement between the predicted values and available experimental results makes the modeling robust and applicable for a wide range of strain rates and length scales. Finally, the study is extended for elevated sample temperatures up to melting. Interestingly, yield strength is shown to follow an increasing trend up to a certain temperature, beyond which it decreases. An empirical relation is proposed here for expressing temperature dependence of HEL that explains the observed yield strength anomaly. Results are justified through thermal analysis of shear stress and evolution of dislocation density.

Deformation twinning in single-crystal Mg under high strain rate tensile loading: A time-resolved X-ray diffraction study

We investigate deformation twinning in single-crystal Mg with in situ, time-resolved (μs-scale), synchrotron X-ray diffraction under high strain rate split Hopkinson tension bar loading. Extension twinning occurs upon dynamic tension along 〈0001〉, but is absent upon tension along 〈112̄0〉. Such deformation anisotropy is a result of the unipolarity of deformation twinning which depends on directionality and resolved shear stress. The twinning mechanism is common for pure Mg in a wide range of strain rates and different loading conditions (one-dimensional stress and one-dimensional strain).

Investigation of multiplicative decompositions in the form of [formula omitted] and [formula omitted] to extend viscoelasticity laws from small to finite deformations

To model the mechanical response of visco-hyperelastic materials, it is quite common to generalize small deformations responses to finite deformations, which is the main objective of this study. The viscoelastic behavior of hyperelastic materials is modeled in the framework of the multiplicative decomposition of the deformation gradient, which is the generalization of the additive decomposition for small deformations. Based on the second law of thermodynamics, we extend the kinematics, kinetics, and constitutive laws from small to finite deformations based on the well-known three-parameter viscoelastic solid (Zener) model. The constitutive laws are derived in a way that the Clausius-Duhem inequality of thermodynamics is satisfied. We examine both the usual Sidoroff multiplicative decomposition and the reversed one. It is revealed that the reversed multiplicative decomposition can meet the intuitive physical expectations analogous to the small deformation cases, i.e., the stresses in the spring and damper in the Maxwell element are equal, and the dissipated energy in the rheological model equals the work acting on the damper. This is while the Sidoroff multiplicative decomposition does not satisfy these physical expectations, and the results cannot be well interpreted by the second law of thermodynamics as the small deformation cases. To describe the evolution of the irreversible process, we need to introduce a function for the internal dissipation of energy. To this end, we propose a new dissipation function that is inspired by the constitutive behavior of Newtonian fluids. To investigate the model's capability, it is applied to predict the response of elastomers in standard loading conditions over a wide range of strain rates. It is demonstrated that the presented framework can achieve a satisfactory agreement with the mechanical behavior of different visco-hyperelastic materials.

Dynamic deformation behavior of a FeCrNi medium entropy alloy

Deformation behavior of a FeCrNi medium entropy alloy (MEA) prepared by powder metallurgy (P/M) method was investigated over a wide range of strain rates. The FeCrNi MEA exhibits high strain-hardening ability, which can be attributed to the multiple deformation mechanisms, including dislocation slip, deformation induced stacking fault and mechanical twinning. The shear localization behavior of the FeCrNi MEA was also analyzed by dynamically loading hat-shaped specimens, and the distinct adiabatic shear band cannot be observed until the shear strain reaches ~14.5. The microstructures within and outside the shear band exhibit different characteristics: the grains near the shear band are severely elongated and significantly refined by dislocation slip and twinning; inside the shear band, the initial coarse grains completely disappear, and transform into recrystallized ultrafine equiaxed grains by the classical rotational dynamic recrystallization mechanism. Moreover, microvoids preferentially nucleate in the central areas of the shear band where the temperature is very high and the shear stress is highly concentrated. These microvoids will coalesce into microcracks with the increase of strain, which eventually leads to the fracture of the shear band.

Cantor-derived medium-entropy alloys: bridging the gap between traditional metallic and high-entropy alloys

The year 2004 marked the beginning of a new era in the design of metallic materials, as the concept of multiple principal component alloys, commonly known as High-Entropy Alloys (HEAs), was proposed by Cantor and Yeh. The unexpected single-phase microstructure, instead of the expected brittle intermetallic compounds, was attributed to the large entropy of mixing and immediately caught the attention of the scientific community. Today, HEAs are considered important advanced materials and a broad range of alloys using nominally the same design principle have been investigated. Despite that, the CrMnFeCoNi (Cantor) alloy stands out as the most successful HEA due to its outstanding mechanical properties and microstructure. In this scenario, variants of the Cantor alloy, named medium-entropy alloys (MEAs), are gaining significant interest as they display a better industrial potential than both HEAs and traditional alloys. These variants of the Cantor alloy with only three or four main elements result in 15 possible combinations. The microstructure of these alloys is discussed in terms of advanced characterization as well as thermodynamic parameters and computational simulation. Their phase stability is addressed over a wide range of temperatures and strain rates. The mechanical properties, especially the fracture toughness, of the CrFeCoNi and CrCoNi alloys have been reported to be even superior to those of the Cantor alloy and most modern engineering alloys. This is associated with the formation of a continuous sequence of strengthening mechanisms, including hierarchical twin networks, which serve to prolong the strain hardening. The present article reviews and critically assesses, for the first time, recent advances in these Cantor-derived MEAs.

Nonlinear visco-hyperelastic tensile constitutive model of spray polyurea within wide strain-rate range

Spray polyurea (SPUA) is widely used as a protective coating material for structures subjected to the intensive impulsive loadings, attributed to its prominent large tensile deformation capacity and strain-rate hardening effect. This paper aims to study the tensile properties of SPUA within a wide strain-rate range both experimentally and theoretically. Firstly, by reasonably designing the geometry and dimension of specimens, a series of quasi-static and dynamic uniaxial tensile tests were carried out, and the nonlinear stress-strain curves corresponding to the strain-rates ranging from 10−3 s−1 to 103 s−1 were obtained. It showed that the mechanical properties of SPUA are sensitive to the strain-rate, i.e., the elastic modulus and tensile stress increase with the rising of the strain-rate, while the fracture strain is linearly negatively correlated with the logarithm of strain-rate. Then, a nonlinear visco-hyperelastic (NVHE) constitutive model composed of a 3rd-order polynomial hyperelastic model and seven Prony series terms describing the viscoelastic properties were established, and the corresponding twenty-three model parameters were calibrated through a multi-objective optimization based on genetic algorithm. Furthermore, based on the finite element program ABAQUS/Explicit, the validations of the proposed NVHE model and the parameters determination approach are verified by the present tensile test and existing drop hammer impact test. This work could provide a helpful reference for the retrofitting design of the protective structures.

A novel crystal plasticity model incorporating transformation induced plasticity for a wide range of strain rates and temperatures

Transformation induced plasticity (TRIP) is an effect common to several classes of advanced high strength steels (AHSS) with promising automotive applications. This effect is characterized by the transformation of retained austenite (RA) to martensite, resulting in increased hardening, increased fracture resistance, and improved formability. Accurate thermo-mechanical modeling over a range of strain-rates and temperatures is critical to fully utilize the improved performance of AHSS exhibiting the TRIP effect. In this work, a novel thermodynamically consistent rate-dependent crystal plasticity formulation is developed, which incorporates strain-rate and temperature dependent strain-induced martensitic transformation. Thermodynamic arguments are used to derive plastic slip and transformation driving forces accounting for various physical mechanisms (e.g. applied stress, temperature, crystal orientation, stored dislocation energy), as well as a constitutive law governing temperature evolution. RA and transformed martensite mechanical thermo-elasto-viscoplastic behavior is explicitly modeled, and a modified Taylor homogenization law is proposed to determine strain partitioning while accounting for transformation. The model is then calibrated and validated for a QP3Mn alloy over a large range of temperatures (-10°C–70°C) and strain-rates (5 × 10-4s−1–200s−1). The evolution of the Taylor–Quinney coefficient and the orientation dependence of transformation are found to match well with trends in literature. The fully calibrated model is compared to a model recalibrated without strain-rate dependent transformation, demonstrating that capturing strain-rate dependent transformation may be necessary even for materials where no direct experimental strain-rate dependence. Plane strain and equibiaxial tension simulations are conducted using the calibrated model, showing that increasing triaxiality results in increased transformation. An extension to the calibrated model is proposed for materials which do not match the predicted trend.

Failure Behavior of Laser Metal Deposited Additive Manufacturing Ti-6Al-4V: Effects of Stress State and Initial Defects.

To investigate the mechanical property and failure behavior of laser metal deposited additive manufacturing Ti-6Al-4V (LMD Ti64) in a wide range of stress states and strain rates, different types of specimens were tested at strain rates of 0.001-5000/s. Numerical simulations were conducted to collect the local fracture strain at the critical position where the failure happened for all specimens. By comparing with Ti64 alloy manufactured by different techniques, the failure behavior of LMD Ti64 alloy shows a stronger sensitivity to Lode angle parameter and strain rate. The role of initial defects in failure was discussed. It is found that high laser power and overlap ratio can improve the failure behavior by reducing the number of initial defects. The initial defects on the fracture surface at much higher strain rates were observed, indicating that the initial crack rather than initial void acts as the crack growth point leading to the final fracture at higher strain rates. The scanning electron microscope observation of the fracture surface shows that the failure mechanism of LMD Ti64 alloy varies from different stress states and strain rates. The failure mechanism is characterized by the shear fracture at the negative stress triaxiality, whereas the void growth fracture plays a dominant role in the failure mechanism of LMD Ti64 alloy at a high stress triaxiality on the quasi-static loading condition.

A constitutive model for poly-methyl-methacrylate over a wide range of strain rates and temperatures

This study proposes a three-dimensional elasto-viscoplastic constitutive model to depict the rate- and temperature-dependent behaviour of poly-methyl-methacrylate (PMMA) under a variety of strain rates and temperature ranges at finite deformations. Yield stress is described via incorporating an appropriate Young's modulus into the Argon's model. The effects of temperature and strain rate are incorporated into the Young's modulus. Subsequently, a new empirical equation has been suggested to describe the softening behaviour over a wide range of strain rates and temperatures. Further, the temperature dependence of the fraction of plastic work rate converted to heat (β factor) has been studied. In addition, the expressions of hardening parameters (Cr and N) under a changing temperature in the full network model that represents the strain-hardening characteristics of polymers have been proposed. Moreover, a method to calibrate the values of newly introduced parameters has been introduced as well. The experimental results demonstrate that the new softening model can predict softening behaviour at various strain rates (from 0.0003 s−1 to 4300 s−1) and temperatures (from 298 K to the glass transition temperature θg).

Identification and formulation of stress-strain relationship for pure nickel and Inconel 718 in a wide strain rate range （10<sup>−3</sup>/ss~10<sup>4</sup>/ss）

Cold spraying is a surface coating technique in which a powder material is impacted on a base material at high speed without melting to form a dense coating layer. However, the stress-strain relationship in the strain rate range of 5 × 103 to 2 × 104/ss , which is required for Cold spraying, has not yet been sufficiently obtained. In this study, stress-strain relationships of pure nickel and Inconel 718 as target materials in a wide range of strain rates from quasi-static strain rate (10−3/ss) to ultra-high strain rate up to 104/ss were investigated by means of a Split Hopkinson bar method and a high-speed material testing machine (TS2000 Saginomiya co. Ltd.). From the experimental results, the stress-strain relationships of pure nickel and Inconel 718 in the wide strain rate range were clarified and a strain rate sensitive constitutive model was formulated by referring the Tanimura-Mimura (2009) model.

МОДЕЛИРОВАНИЕ РАСПРЕДЕЛЕНИЯ ОСТАТОЧНОЙ ПОРИСТОСТИ МЕТАЛЛИЧЕСКОГО ИЗДЕЛИЯ ПРИ АДДИТИВНОМ ПРОИЗВОДСТВЕ С ПОСЛОЙНОЙ ПРОКОВКОЙ

Porosity, which occurs in products made of aluminum-magnesium alloys synthesized by wire-arc surfacing, significantly worsens the characteristics of fatigue strength. The developed technology of hybrid additive manufacturing with layer-by-layer forging of each deposited layer of material is able to minimize the porosity of the product. To select the rational parameters of the technological process, the evolution of the porosity distribution over the cross-section of a linear element after its single forging with a pneumatic hammer is investigated. A numerical model of the process is constructed in the LS-DYNA® package, where the Gurson–Tvergaard–Needleman relations are taken as constitutive equations of plastic deformation of the material and porosity evolution. To determine the parameters of the Johnson–Cook hardening law, tests of the AMg6 alloy were performed in a wide range of strain rates. The impact of the pneumatic hammer in the numerical model was calibrated using an accelerometric and strain-gauged steel target, as well as by distortions of the cross-section of a forged bar made of AMg6 alloy. Calculations according to the model are compared with experimental data, for which two linear segments were made by additive manufacturing with and without layer-by-layer forging, from the cross-sections of which the slots processed for pore visualization were prepared. With this method of pressure treatment, the decrease in porosity in the boundary layer of the workpiece mainly depends on the accumulated plastic deformations and does weakly sensitive the appearance of a stressed state. The model allows you to predict the size of the area under the hammer head depending on the processing mode, within which the porosity is eliminated by forging. The use of such modes will ensure the manufacturing of products without residual porosity in the processes of additive manufacturing by surfacing with layer-by-layer forging.

Tensile Deformation Behaviors of Pure Ti with Different Grain Sizes Under Wide-Range of Strain Rate

Tensile Deformation Behaviors of Pure Ti with Different Grain Sizes Under Wide-Range of Strain Rate

Hot Deformation Behavior and Strain Rate Sensitivity of α+β Brass Sheet by Uniaxial Material Constitutive Equations

The present work proposes a systematic procedure for evaluation of high temperatures deformation and formability of α+β Brass undergoing the uniaxial tensile test conditions. Firstly, uniaxial tensile tests were conducted on Universal Testing Machine (UTM) with loading capacity of 100 KN at temperature of 773K, 873K and 973K with a quasi-static strain rates of 0.001s-1, 0.01 s-1 and 0.1s-1. Hot tensile flow stress behaviors have been affected significantly by test temperatures and strain rates for Brass. Drop-in yield and ultimate tensile strength have been observed at approximately 58 % and 68 % with a rise in test temperature from 773 K to 973 K. Around 30% improvement has been observed in % elongation with rise in test temperature. Further, flow stress has been predicted by most popular Johnson Cook (JC) uniaxial constitutive model at wide range of temperatures (773K, 873K and 973K) and strain rates (0.001s-1,0.01 s-1 and 0.1s-1). Further, yield loci have been plotted at various temperatures using Hill 1948 and Barlat 1989 yield function. Barlat 1989 has followed experimental results correctly in all test temperatures.

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.

Strength Characterization of Soils' Properties at High Strain Rates Using the Hopkinson Technique-A Review of Experimental Testing.

The paper presents a review of crucial experiments and the latest publications, presenting the previous and current trends in experimental research in 2018–2021 in the area of soil dynamic interaction based on the Hopkinson bar technique. A review of investigated experimental test stands was made, in particular, cohesive and non-cohesive soil specimens prepared with different dimensions and densities. From this study, it can be concluded that the dynamic response of the soil depends on many factors, e.g., density, cohesion, moisture and grain structure of the soil specimen. There is still a noticeable interest in SHPB experiments performed in both 1D and 3D versions under modified conditions (frozen/heated soil specimen, different degree of water saturation content of the soil sample) in a wide range of strain rates 102–104 s−1, which is a large field for further research. The need to learn about the characteristics of various types of soil (both cohesive and non-cohesive) for the selection of structural design solutions for the protection elements of critical infrastructure was emphasized.