Strain Rate Range Research Articles

Strengthening and ductilization of a refractory high-entropy alloy over a wide strain rate range by multiple heterostructures

To improve the mechanical properties of refractory high-entropy alloy (RHEA), whose strain hardening capacity is relatively weak, over a wide strain rate range, the multi-heterostructure strategy is investigated in this work. Based on the composition and annealing design, the multi-heterostructure consisting of two mutually coherent body-centred cubic solid solution matrices and penetrating complex phases is achieved in TiZrNbTaNi0.05 RHEA (MH-RHEA). Under quasi-static loading, this multi-heterostructure takes both good precipitation strengthening and hetero-deformation-induced hardening effects, diversifies the deformation modes, finally promotes the strain hardening capacity and deformation homogeneity. The tensile yield strength, ultimate tensile strength and elongation of MH-RHEA are 1195 ± 12 MPa, 1235 ± 9 MPa and 22.4 ± 1.0 %, respectively, which are 18 %, 20 % and 50 % higher than those of the base alloy. Under dynamic loading (∼103 s−1), the thermal effect can be neutralized and the deformation localization is avoided. Consequently, a high yield strength of ∼1450 MPa and a large ultimate strain of ∼25 % without fracture at a high strain rate of 2390 s−1 are realized in MH-RHEA. This heterostructure strategy offers a new paradigm to enhance the strength and ductility simultaneously of RHEAs over a wide strain rate range.

Assessing Feed-Forward Backpropagation Artificial Neural Networks for Strain-Rate-Sensitive Mechanical Modeling.

The manufacturing processes and design of metal and alloy products can be performed over a wide range of strain rates and temperatures. To design and optimize these processes using computational mechanics tools, the selection and calibration of the constitutive models is critical. In the case of hazardous and explosive impact loads, it is not always possible to test material properties. For this purpose, this paper assesses the efficiency and the accuracy of different architectures of ANNs for the identification of the Johnson-Cook material model parameters. The implemented computational tool of an ANN-based parameter identification strategy provides adequate results in a range of strain rates required for general manufacturing and product design applications. Four ANN architectures are studied to find the most suitable configuration for a reduced amount of experimental data, particularly for cases where high-impact testing is constrained. The different ANN structures are evaluated based on the model's predictive capability, revealing that the perceptron-based network of 66 inputs and one hidden layer of 30 neurons provides the highest prediction accuracy of the effective flow stress-strain behavior of Ti64 alloy and three virtual materials.

Influence of strain rate on the compressive behavior of heterogeneous Cu/Ta multilayer: A molecular dynamics simulation study

Atomistic simulations are performed to study the compressive response of heterogeneous Cu/Ta multilayer at a wide range of strain rates. The results show that the yield strength and yield strain both increase with the increasing strain rate while the elastic modulus essentially remains invariant. The yield strength increases sharply when the strain rate exceeds the critical value of 109s−1. The yield of the sample at lower strain rate is primarily determined by the dislocation evolution in the hard phase (i.e. Ta layers), while dominated by the atomic amorphization of hard phase at higher strain rate. We show that the heterogeneous nanolayered composite exhibits a good deformation compatibility at lower strain rate but an obvious deformation incompatibility at higher strain rate.

A new way to analyze constitutive analysis and its relation to the microstructure of a Mg-Gd-Y-Zn alloy

It is the first time that we have systematically proved that the activation energy (Q-value) is the main parameter that controls the dynamic recrystallization during hot deformation, and the reliability of the constitutive analysis is entirely dependent on the Q-value. To this end, the hot deformation behavior of a Mg-Gd-Y-Zn alloy was investigated at the temperatures of range 573K-723K under strain rates of range 0.0001–1 s−1. Subsequently, the Q-value ∼ 331.24 kJ mol −1 was achieved. By considering the two different approaches of eliminating the temperatures and then eliminating the strain rates, the lowest Q-values ∼ 259.75 kJ mol −1 and ∼ 295.80 kJ mol −1 were achieved, respectively. Based on the lowest Q-values, the deduced parameters of temperatures range of 623K-723K and strain rates range of 0.0001–0.01 s−1 were evaluated. Interestingly, the numerical simulation exhibited a further lower Q-value ∼ 237.17 kJ mol −1. The difference in the Q-values revealed that the large strain hardenability is due to the high Q-value, while the low strain hardenability is due to the low Q-value. The deduced parameters were also well-matched with the processing maps and the EBSD analysis. Last but not least, the deduced parameters displayed a high accuracy in predicting the flow stresses. Thus, the new approach is of great significance in analyzing the accurate calculation of Q-value, the correctness of constitutive analysis, and evaluating stress-strain behavior.

A phenomenological constitutive model of Novel Rheo Gravity Die Cast Al-15Mg2Si-4.5Si-0.01Sr-0.015B composite

The present study discusses the high temperature deformation behaviour as well as phenomenological constitutive model development of the novel Rheo gravity die cast (RGDC) Al-15Mg2Si-4.5Si-0.01 Sr-0.015B composite. Within the scope of the study, uniaxial isothermal compression tests are performed on the RGDC Al-15Mg2Si-4.5Si-0.01 Sr-0.015B composite, covering a range of strain rates from 10−3 to 10 s−1 and deformation temperatures spanning from 250 °C to 450 °C. Analysis using X-ray Diffraction (XRD), Energy dispersive spectroscopy (EDS) and Electron Probe Micro Analyzer (EPMA) revealed the presence of distinct phases within the material, including primary Al, Mg2Si, and elemental Si. The study employed three different constitutive models i.e., the Johnson-Cook (JC), modified Johnson-Cook (mJC), and sine hyperbolic Arrhenius (shA) types, to predict the flow stress of the material as a function of strain, strain rate, and deformation temperature. The results indicated that the sine hyperbolic Arrhenius type model and the modified Johnson Cook model effectively accounted the coupling effect of strain, strain rate, and deformation temperature, which affect the flow stress. Statistical analysis, specifically Pearson coefficient correlation (R), average absolute relative error (AARE) and standard deviations, established a reasonable agreement between the predicted flow stress values and the experimental flow stress data. Furthermore, it is observed that the sine hyperbolic Arrhenius type model exhibited superior accuracy compared to the modified Johnson Cook model, particularly at higher strain levels.

Recrystallization behavior and kinetic analysis of an Al-Cu-Li alloy during hot deformation and subsequent heat treatment

Al-Cu-Li alloys exhibit enhanced performance when possessing a high substructure proportion and a low recrystallization proportion. To achieve this, it necessitates a thorough understanding of recrystallization behavior during its hot working and heat treatment. To this end, isothermal compression tests were conducted on an Al-Cu-Li alloy in the temperature range of 350–500 °C and strain rate range of 0.01–10 s−1. The deformed specimens underwent solution treatment at 530 °C/2 h followed by water quenching, and aging treatment at 155 °C/27 h. The microstructures of the deformed and heat-treated specimens were characterized using electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM). During hot deformation, continuous dynamic recrystallization (CDRX) dominates when the natural logarithm of the Zener-Hollomon parameter (lnZ) >26 and discontinuous dynamic recrystallization (DDRX) predominates when lnZ ≤ 26. A low proportion kinetic model associated with lnZ was constructed to describe the DRX behavior, and the model parameters were optimized using genetic algorithm (GA) to improve accuracy. During heat treatment, substantial static recrystallization (SRX) occurs following deformation at lnZ > 30, while it is limited when lnZ < 27. The comparison of average geometrically necessary dislocations (GNDs) before and after heat treatment reveals that the consumption of dislocations increases with increasing lnZ. Statistical analysis indicates that the density of low/medium angle grain boundaries (L/MAGBs) can be increased and the recrystallization fraction can be decreased within the lnZ range of 24 to 27. Therefore, these specific hot deformation conditions are recommended as the optimal hot working window for the Al-Cu-Li alloy.

Hot Deformation Behavior and Microstructure Evolution of 2Cr12Ni4Mo3VNbN Steel Used for Last‐Stage Large Blades of Steam Turbine

The hot deformation behavior and microstructure evolution of a recently developed 2Cr12Ni4Mo3VNbN martensitic stainless steel are examined through hot compression tests conducted within the temperature range of 900–1200 °C and the strain rate range of 0.01–10 s−1. The constitutive equation and processing maps corresponding to hot deformation are established. The activation energy for hot deformation of 2Cr12Ni4Mo3VNbN steel is determined to be ≈457491.77 J mol−1. Simultaneously, the microstructure evolution during hot deformation is studied. Based on the processing maps and microstructure evolution analysis, it is concluded that the optimal windows for hot processing are within the temperature range of 1106–1150 °C and the strain rate range of 0.01–2.7 s−1, as well as at 1200 °C within the strain rate range of 1–2.7 s−1, exhibiting a power dissipation efficiency of 0.32. As the temperature increases and the strain rate decreases, the degree of dynamic recrystallization escalates.

Cyclic strain rate dependent behaviour of Alloy 617

This paper investigates the effect of strain rate on the properties of Alloy 617 under low-cycle fatigue (LCF) in room temperature (RT). The LCF life properties and the damage mechanism are studied for this Alloy over a range of strain rate (5E-4 ∼ 1E-2 s−1) under fully-reversed controlled total strain range of 1.2%. It is found that LCF life of Alloy 617 is strongly influenced by the time-dependent mechanism, in terms of slow strain rate test (SSRT). The relationship between total strain, plastic strain, and time to failure with strain rates are established and expressed by means of power law function to describe the fatigue life. Metallography examination is carried out on the fractured specimens with the help of electron microscope and the fractography is discussed to distinguish the effect of SSRT on the physical damage characteristic under LCF loadings.

Effect of non-ideal mixture on flame–spray interaction in counterflow n-heptane/ethanol flames

This work presents a numerical study of bi-component n-heptane/ethanol spray flames in a counterflow to improve the understanding of the effect of non-ideal mixtures on the flame–spray interaction. The simulations of this spray configuration allow for the detailed examination of the real fluid behavior and its influence on gas-phase combustion kinetics for a wide range of relevant parameters, i.e., droplet composition, size, and gas strain rate. The results reveal that due to the large real activity coefficient of n-heptane and the resulting selective evaporation of the heavier component, the burning characteristics of the spray with a high initial ethanol content do not differ if non-ideal mixture is considered. Conversely, the flame structure with a low ethanol content is substantially different, and displacement of the flame towards the spray side of the configuration is found. A multiple reaction zone, displaying both partially-premixed and diffusion flames, exists, which is overestimated spatially if the fluid is assumed ideal. In general, the ideal prediction of real fluid would misinterpret the composition evaporation order, prolonging the droplet lifetime and consequently, enhancing the flame–spray interaction locally, which results in a lower flame temperature. A parameter characterizing the multicomponent droplet penetration is introduced, which highlights the appreciable non-ideal effects that vary with droplet size and composition, and most importantly, further demonstrates the necessity of considering the real fluid properties in design of next-generation engines with blended fuels.

Experimental and kinetic modeling of soot formation in counterflow non-premixed flames of surrogate fuel components: n-dodecane and iso-dodecane

Normal dodecane (n-C12) and iso-dodecane (i-C12) are often used as components for surrogate mixtures of aviation and diesel fuels. Although studies have been performed to understand the combustion and spray behavior of dodecane isomers, the soot formation from the combustion of n- and i-C12 in non-premixed flames is not well studied. In this work, soot volume fraction (SVF) profiles of n- and i-C12 were measured across a wide range of strain rates and mixture conditions in a counterflow burner facility at the University of Connecticut. Neat and binary mixtures of n- and i-C12 were investigated to study the influence of alkane branching on soot formation. A soot model was developed and validated in this study by extending the detailed kinetic model developed at the Lawrence Livermore National Laboratory (LLNL) for the formation of polycyclic aromatic hydrocarbons (PAHs) to simulate soot formation and growth based on the discrete sectional method. Additional gas phase reactions forming pyrene and ring enlargement reactions were added to the existing PAH model. The LLNL kinetic model was validated with SVF data obtained in this work for n-C12 and i-C12 flames along with data available in literature for ethylene, iso-butene, n-heptane, and iso-octane. The soot precursor reactions added in this work were found to play a critical role in simulating the experimentally observed non-linear trend of the peak SVF with increased branched alkanes. Reaction path analysis was conducted to illustrate the fuel structure effects on soot formation pathways in n- and i-C12 mixtures. In view of the satisfactory agreement between modeling results and experimental data, as well as capturing the non-linear variation in peak SVF with the alkane branching for the first time, further investigation within the framework of the soot model is discussed and critical insights are provided into the reaction pathways which require further attention.

Fabrication and performance evaluation of CICC jacket based on modified N50 austenitic steel for CFETR magnet

The hot deformation behavior of modified N50 austenitic stainless steel in the temperature range 950∼1250 °C and strain rate range of 0.01–50/s was studied by uniaxial compression experiment. The processing map and the constitutive equation for the finite element simulation were established, and the recrystallization mechanism was discussed. The results indicated that the dominant deformation mode DDRX (discontinuous dynamic recrystallization) increased with the rise of deformation temperature while the CDRX (continuous dynamic recrystallization) was on the contrary. There is a decrease in global recrystallization with increasing strain rate, up to a threshold 1/s beyond which the global recrystallization began significantly promotion owing to not only the adiabatic heat and higher stored energy, but also quick Post-DRX mechanism induced by delay quenching. The reasonable hot working interval was determined by a hot working map, then the most suitable hot extrusion parameters (1180°C-100 mm/s) were further obtained with the help of finite element simulation, and ultimately, the industrial hot extrusion trials of N50 pipes with Post-DRX features were further completed. The tensile performance of final jacket pipes was far beyond the current mainstream low-temperature austenitic structural steel and met the requirements of the new generation of superconducting coil jacket materials.

Strong yet ductile eutectic high-entropy FCC/Laves composite fabricated by powder plasma arc additive manufacturing: Mechanical property, microstructure evolution, and constitutive description over a wide range of temperatures and strain rates

To enhance the strength and toughness of metallic materials simultaneously over a wide range of temperatures and strain rates, a eutectic high-entropy FCC/Laves composite with a heterogeneous initial microstructure was fabricated by powder plasma arc additive manufacturing. The mechanical behavior of the composite over a wide range of temperatures and strain rates was tested with the aid of an electronic universal testing machine and an improved Split Hopkinson pressure bar. The high-entropy FCC/Laves composite possesses a unique combination of strength and ductility over the selected temperature and strain rate ranges due to the in situ composite nature with both soft high-entropy FCC phase and hard high-entropy Laves phase. Complicated thermal viscoplastic behavior is presented. To reveal the mechanisms of the complicated thermal viscoplastic behavior, microstructure evolution was characterized. The high-entropy Laves phase, as a kind of multi-component intermetallic, defies convention by displaying plastic deformation at room temperature and different strain rates. Superior damage tolerance of the high-entropy FCC/Laves composite can be achieved over the selected temperature and strain rate ranges with the contribution of deformation twin in FCC phase, as well as dynamic recrystallization over high temperature range. Finally, a constitutive description was developed, which is shown to be able to accurately describe the complicated plastic behavior over a wide range of temperatures and strain rates. These findings suggest promising prospects for advanced material design, opening a new avenue to achieve a fine balance between strength and ductility across different conditions.

Basic Modelling of General Strength and Creep Properties of Alloys

There are excellent methods for modelling physical and elastic properties, for example, those based on ab initio atomistic procedures. For mechanical properties that are controlled by the motion of the dislocations, such methods have not been available in the past. One has been forced to resort to fitting the experimental data with empirical methods by involving a number of adjustable parameters. However, in recent years, methods based on physical principles have been developed for a number of mechanical properties. These methods can predict properties accurately without the use of fitting parameters. A review of such methods will be given, for example, for the modelling of creep deformation in metallic materials. It will be demonstrated that some properties can be described over a wide range of temperatures and strain rates. The advantage of these new methods is that they can be used for prediction, identification of mechanisms and extrapolation of results for new conditions.

Superplastic Forming of Zr-Based Bulk Metallic Glasses

In this paper, the partially crystallized Zr70Cu13.5Ni8.5Al8 bulk metallic glasses (BMGs) were prepared, and their superplastic deformation ability in the supercooled liquid region was studied via compression over a wide range of strain rates from 5 × 10−4 s−1 to 1 × 10−2 s−1. It has been found that the superplastic deformation behavior of the BMGs is strongly dependent on the strain rate and temperature. The flow behavior of the BMGs transformed from Newtonian fluid to non-Newtonian fluid with the increase in the strain rate and the decrease in temperature. Based on the high-temperature compression results, a thermalplastic forming map was constructed, and the optimal superplastic forming parameters were obtained. Then, gears were successfully extruded using part of the optimal thermal processing parameters. Further studies showed that high-temperature extrusion induced the crystallization of the BMGs, which increased the microhardness of the gears.

Rationalization of Ring Fragmentation Data via Simple Kinetic Energy Analysis

The available data on fragmentation of alloy rings at high strain rate has been reviewed and analysed with reference to a classical statistical and energetic model. The data have also been compared to a simple calculation based on the specific kinetic energy of the ring. It is shown that fragmentation data for alloys with over a 20 times difference in strength and 7 times difference in density scatter around a single curve when plotted as a function of specific kinetic energy over a wide range of strain rates. A fit to this curve therefore provides an approximate estimate of the expected fragment number for any ductile metal without requiring any detailed knowledge about the constitutive behaviour or defect population. This fit is better than a prediction based on the classical statistical model, and similar to that for the energetic model, which also requires a knowledge of the fragmentation fracture energy. The observation that specific kinetic energy alone can explain much of the difference observed between alloys suggest that the energy in the system is more important that details of the alloy microstructure or properties in controlling the number of fragments for a material that fails by ductile fracture. The fit does not work for a case where one alloy was heat treated to a condition where brittle failure occurred.

Experimental and phenomenological investigations on the strain rate sensitivity of rigid PVC foams at strain rates of 0.005 s−1 to 600 s−1

Polymeric foams are often subjected to high strain rates in various industrial applications, especially the transportation sector, and experience significant deformations. An in-depth comprehension of the dynamic mechanical characteristics of polymeric foam is essential for devising effective engineering design approaches. Previous studies have extensively utilized Split Hopkinson Pressure Bar (SHPB) apparatuses to test polymeric foams dynamically; however, these studies faced technical limitations in specimen size, preventing compliance with the ASTM D1621 standard test method for rigid cellular plastics. A customized pneumatic apparatus equipped with a massive impacting bullet and sacrificial excess energy absorbing system was employed to complete the mechanical material characterization of Polyvinyl Chloride (PVC) foams, following the ASTM D1621 standard, to address previous technical limitations. PVC foams with six different nominal densities were subjected to strain rates ranging from 0.005 s−1 to 600 s−1. Loading was conducted parallel and perpendicular to the foam rise direction to investigate dynamic anisotropic material characteristics. A comparison of tests conducted at strain rates of 0.005 s−1 and 400 s−1 revealed an average increase of 35.1 % in the plateau stress. The phenomenological Nagy model was combined with a nonlinear Avalle relationship and revised with a new term, supported by findings from the present study, to characterize the complete stress/strain response, for the range of strain rates considered in this research. The calibrated model exhibited an average error of 1.7 % in the predicted plateau stress. The results indicated that testing under a single dynamic strain rate was sufficient to characterize the rate sensitivity of the PVC foam in the dynamic regime. Furthermore, the influence of relative density on the foam rate sensitivity was quantified, revealing a plateau in the strength enhancing effect of density at a nominal relative density of 0.125.

Mesoscale modelling of the dynamic tensile strength enhancement of concrete in spalling tests using interface elements

The dynamic tensile strength of concrete has been experimentally reported to increase significantly with the increase of imposed strain rates. However, the intrinsic mechanisms accounting for the strength increase are not well understood so far. This paper presented numerical simulations based on the spalling technique to further explore mechanisms of the dynamic responses of concrete under impact loadings. Numerical results have been verified and validated against experimental evidence with various strain rates. The validity of utilizing the Novikov acoustic processing approximation for obtaining the spalling strength of concrete is identified and discussed. Results demonstrate that this indirect processing approach could overestimate the spalling strength because real material behavior tends to deviate from its basic assumption. Mechanisms accounting for the spalling strength increase from key aspects including the meso-structure, the strain rate-dependent material behaviour, the micro-crack inertia, and the structural inertial are also identified accordingly. Results demonstrate that the increment of concrete dynamic tensile strength in spalling tests is mainly caused by the strain rate-dependent material behaviour which should be incorporated in the material constitutive description. Besides that, the material heterogeneity also makes a considerable contribution to the increase of dynamic tensile strength in spalling tests and this contribution becomes increasingly prominent with the increase of the imposed strain rates. On the other hand, the structure inertial and the micro-crack inertial have little effect on the increase of spalling strength of concrete and thus may be ignored within the imposed strain rate range in spalling tests.

Dynamic mechanical properties and constitutive model establishment of QSTE420 steel

The uniaxial tensile tests of QSTE420 steel under different strain rates were carried out using an electronic universal material testing machine, a high-speed tensile testing machine and a split Hopkinson tension bar (SHTB) device, the engineering stress-strain curves of steel within the range of 0.001– 1000 s−1 were obtained and the mechanical properties of steel at different strain rates were analyzed. The results show that in the static strain rate range of 10−3– 10−2 s−1, the yield strength and tensile strength of QSTE420 steel exhibit minimal variation, fluctuating between 430– 434 MPa and 507– 515 MPa, respectively; while the uniform elongation and elongation at break remain approximately at 12% and 35%, respectively. In the high strain rate range of 10−1– 103 s−1, both yield strength and tensile strength exhibit a consistent increase in direct correlation with the tensile rate. Specifically, the yield strength increases from 444 to 607 MPa and the tensile strength increases from 523 to 640 MPa as the strain rate escalates from 10−1 to 103 s−1. Moreover, the elongation at break demonstrates a general increasing trend and reaches its peak value of 45.65% at 100 s−1. The morphology of fracture surfaces under different strain rates are observed by Scanning Electron Microscopy (SEM). The fracture appearance analysis reveals numerous dimples in the fracture, indicating a ductile fracture. Furthermore, the comparison demonstrates that steel exhibits enhanced plasticity at a strain rate of 100 s−1. Based on the experimental results, the Johnson-Cook constitutive model was established and modified. The modified Johnson-Cook model exhibits a higher determination coefficient (R2) compared to the original version, signifying an improved fitting accuracy.

Identification of thermo-viscoplastic behavior for AA6061 under in-plane biaxial loadings

This work aims to investigate the thermo-visco-plastic behavior of an aluminum alloy (AA6061) sheet metal submitted to in-plane biaxial loadings under warm conditions. Biaxial tensile tests are performed in a temperature range from room temperature to 160 °C, and in a strain rate range from quasi-static to the so-called “intermediate” strain rate (up to few s−1). The specimen shape used in this study has been previously defined and validated by the authors to identify the viscoplastic hardening models of metallic alloys at large strains. A specific device leading to a uniform temperature in the sample is associated with a dynamic biaxial traction bench to carry out the temperature and strain rate dependent characterizations. From these experiments, both the experimental forces measured on each axis of the in-plane biaxial specimen and the principal strains at the center of the specimen are obtained. These experimental data are then used in an inverse analysis loop, based on a finite element model of the biaxial test, to calibrate the parameters of a thermo-viscoplastic strain hardening model by minimizing the difference between the experimental and numerical principal strains at the center point of the specimen. Finally, it is shown that the identified hardening model well predicts the flow stress of AA6061 under different temperatures and strain rates for a strain level of up to 40%.

Compressive double yielding in high-density polyethylene over a wide range of strain rates

We investigated the effects of the strain rate on compressive yielding in high-density polyethylene at the strain rates from 10−5–103 s−1. High strain rates promoted distortion in the crystalline lattice, leading to the martensitic transformation from the orthorhombic to monoclinic phase. We explained the strain-rate dependence of the stress by two Eyring processes assigned to the crystalline and amorphous deformation in the low- and high-strain-rate regions, respectively. The crossover strain rate drastically decreased with increasing molecular weight, which we ascribed to an increased fraction of stress transmitters. We attributed the strain-rate dependence during compression to tie molecules and/or tie links (i.e. the amorphous chains that connect lamellar crystals to each other).