Strain-hardening Rate Research Articles

Dynamic compressive behavior of a single crystal nickel-base superalloy at ultra-high temperature: mechanism investigation with a modified electric synchronous SHPB technique

A novel experimental technique conducted at a modified automatic split Hopkinson pressure bar (SHPB) for measuring the dynamic compressive behavior at ultra-high temperature up to 1700 °C was developed. A bidirectional electric synchronous assembly system, two high-precision delay controllers and an automatic control mechanism were employed to automate each section in the whole experiment process with high precision and high reliability. The cold contact time (CCT) between specimen and loading bars can be accurately and stably controlled to be shorter than 5 ms and the effect of CCT on temperature distribution can be eliminated. Based on this automatic high-temperature SHPB technique, an experimental investigation into the responses of a new in-service single-crystal Nickel-base superalloy DD10 subjected to impact loading at high temperature was undertaken. The influence of strain rate and temperature on the flow behavior of DD10 was tested and analyzed over a wide range of strain rate (0.001/s-4000/s) and temperature (25°C–1200 °C). The high temperature has an evident effect on the flow stress, strain hardening and strain rate sensibility. An anomalous peak of stress in true stress–temperature curve can be found, and the peak temperature increases with strain rate increasing. Through the microstructural observation, the influence of strain rate and temperature on the compressive deformation and fracture mechanism was discussed. At the high temperature above 1000 °C, the shear deformation mechanism of both γ matrix phase and γ′ precipitate phase is the dominant deformation mechanism at high strain rate, instead of the rafting mechanism of γ′ precipitate phase of under quasi-static loading condition.

Effects of loading rate, temperature, and thickness on the tensile strength of precision adhesive joints

The influences of the micron bondline thickness, temperature, and loading rate on the tensile strength of adhesive joints were studied for the precision adhesive structures, and the fractured surfaces were analyzed by the infrared imaging and SEM methods. The testing results show that the tensile strength increases and then linearly decreases with the increase of bondline thickness; the peak tensile strength is always acquired at the bondline thickness of around 30 μm; the maximum tensile strength increases up to 28.6% as the thickness increases from 10 to 30 μm at the loading rate of 1 mm/min; the strength decreases by more than 33% and finally reaches a closed value at different bondline thicknesses as the temperature rises from −30 to 110 °C. The results indicate that reducing the bondline thickness, less than about 10 μm, could result in a weak bonding interface; the tensile strength increases with the increase of the loading rate, exhibiting the strain-rate hardening effect below the Tg; the plastic-damage characteristic appears and becomes clearer on the fractured surface as the temperature increases. Under the tested conditions, the temperature shows the most significant effect on the tensile strength, then the bondline thickness followed by the loading rate.

A combined experimental and numerical approach that eliminates the non-uniqueness associated with the Johnson-Cook parameters obtained using inverse methods

Johnson-Cook constitutive model is a commonly used material model for machining simulations. The model includes five parameters that capture the initial yield stress, strain-hardening, strain-rate hardening, and thermal softening behavior of the material. These parameters are difficult to determine using experiments since the conditions observed during machining (such as high strain-rates of the order of 10^5/sec - 10^6/sec) are challenging to recreate in the laboratory. To address this problem, several researchers have recently proposed inverse approaches where a combination of experiments and analytical models are used to predict the Johnson-Cook parameters. The errors between the measured cutting forces, chip thicknesses and temperatures and those predicted by analytical models are minimized and the parameters are determined. In this work, it is shown that only two of the five Johnson-Cook parameters can be determined uniquely using inverse approaches. Two different algorithms, namely, Adaptive Memory Programming for Global Optimization (AMPGO) and Particle Swarm Optimization (PSO), are used for this purpose. The extended Oxley’s model is used as the analytical tool for optimization. For determining a parameter’s value, a large range for each parameter is provided as an input to the algorithms. The algorithms converge to several different sets of values for the five Johnson-Cook parameters when all the five parameters are considered as unknown in the optimization algorithm. All of these sets, however, yield the same chip shape and cutting forces in FEM simulations. Further analyses show that only the strain-rate and thermal softening parameters can be determined uniquely and the three parameters present in the strain-hardening term of the Johnson-Cook model cannot be determined uniquely using the inverse method. A combined experimental and numerical approach is proposed to eliminate this determine all parameters uniquely.

Microstructural Evolution and Mechanical Properties of Non-Equiatomic (CoNi)74.66Cr17Fe8C0.34 High-Entropy Alloy.

In this study, we manufactured a non-equiatomic (CoNi)74.66Cr17Fe8C0.34 high-entropy alloy (HEA) consisting of a single-phase face-centered-cubic structure. We applied in situ neutron diffraction coupled with electron backscattered diffraction (EBSD) and transmission electron microscopy (TEM) to investigate its tensile properties, microstructural evolution, lattice strains and texture development, and the stacking fault energy. The non-equiatomic (CoNi)74.66Cr17Fe8C0.34 HEA revealed a good combination of strength and ductility in mechanical properties compared to the equiatomic CoNiCrFe HEA, due to both stable solid solution and precipitation-strengthened effects. The non-equiatomic stoichiometry resulted in not only a lower electronegativity mismatch, indicating a more stable state of solid solution, but also a higher stacking fault energy (SFE, ~50 mJ/m2) due to the higher amount of Ni and the lower amount of Cr. This higher SFE led to a more active motion of dislocations relative to mechanical twinning, resulting in severe lattice distortion near the grain boundaries and dislocation entanglement near the twin boundaries. The abrupt increase in the strain hardening rate (SHR) at the 1~3% strain during tensile deformation might be attributed to the unusual stress triaxiality in the {200} grain family. The current findings provide new perspectives for designing non-equiatomic HEAs.

Explosion/impact response of pure molybdenum at ultra-high strain rate and large strains

In order to study the dynamic mechanical properties of molybdenum under high strain rates, experiments are conducted using Hopkinson dynamic compression testing of a small-sized sample and explosion impact dynamic X-ray study of a flat shaped-charge liner. Experimental data agrees well with theoretical calculations and numerical simulations. Results demonstrate that strain hardening, thermal softening, and strain rate strengthening effects during the impact response process of the molybdenum material vary significantly with different impact conditions in a temperature range of 297–1273 K and a strain rate range of 0.0001–48,000 s−1. Strain rate strengthening and thermal softening effects are particularly apparent in the molybdenum material under impact at medium and high strain rates. At extremely high strain rates and large deformations, the dynamic mechanical response provides evidence of thermal softening and strain hardening effects. Stresses that result in damage to the molybdenum material are primarily attributed to the latter.

Improved tensile properties in heterostructured 1050/7050 Al sheets produced by accumulative roll bonding

Tougher and stronger alloys are desired for structural applications, but the strength-ductility trade-off limits it. In order to overcome this issue, heterogeneous structures can be developed in high-strength materials to restore an acceptable ductility for practical use. In this investigation, dissimilar alloys (1050 and 7050 aluminum alloys) were roll bonded at 450 °C and 500 °C to obtain sheets with a heterogeneous structure in terms of microstructure and composition, and the microstructure and tensile properties were investigated. The final microstructure was a combination of soft and coarse-grained 1050 Al layers together with elongated and ultrafine-grained precipitation strengthened 7050 Al layers. A simultaneous increase in strength and ductility was achieved after six cycles at 500 °C with 343 MPa of ultimate tensile strength and ∼14% of uniform elongation, which was associated with the increase in the strain-hardening rate due to the combination of a coarser and ductile microstructure in the 1050 Al layer and a fine grained and precipitation hardened 7050 Al layer. It was also demonstrated that higher interface density in the heterogeneous structure decreased the dynamic recovery rate and a better combination of strength and ductility was achieved. These findings may determine processing parameters to optimize the roll bonding technology and develop new heterostructured sheets for practical applications.

A phase field model for high-speed impact based on the updated Lagrangian formulation

High-speed impact problems usually undergo a form of highly localized plastic deformation under high strain rate with intense shock waves. In this paper, we present a coupled phase field model to simulate fracture in these situations. Our model considers the dynamic finite deformation with both strain hardening and strain rate hardening by the Johnson–Cook plasticity model. In particular, the formulation is posed in an updated Lagrangian framework and the constitutive update is realized with a return-mapping algorithm. Considering the tension–compression asymmetry, a new history variable is developed to enforce the irreversibility condition of crack propagation. The effectiveness of the proposed method is validated with a numerical example of 45 steel impact experiment along with two numerical simulations of split Hopkinson bar experiments on concrete and aluminum alloy specimens, where strong shock waves are generated. Besides, the effect of a few parameters is studied, namely, the regularization length parameter, the energy release rate, the initial impact velocity, and parameters of the Johnson–Cook model. These show the correct trend in terms of the time and extent of crack propagation.

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.

Formation of Ultrafine Single-Variant Martensite from Prior Ferrite + Cementite Microstructure and Its Mechanical Properties

Abstract In the present investigation, changes in the single-variant martensite structure of 0.1%C-2%Si-5%Mn steel with a decrease in the prior austenite grain size have been investigated. While prior austenite grain size in the range of 150 to 24 µm led to the formation of martensite with a multi-packet and multi-block structure, a single packet and multi-block martensite structure formed from the prior austenite grain size of about 7 µm. Furthermore, the prior austenite grain size of about 2 µm led to the formation of a single-variant (single-block) martensite structure. This microstructural analysis indicates that the critical prior austenite grain size to form martensite with a single-variant structure is about 2 µm. The tensile strength (TS, 1,490 MPa), uniform elongation (UEL, 7.1 %), and total elongation (TEL, 14.2 %) of the single-variant martensite was found to be higher than that of the multi-packet multi-block martensite (TS = 1,270 MPa, UEL = 6.2 %, and TEL = 13.6 %). The improvement in the mechanical properties of the single-variant martensite was attributed to enhancement in its strain-hardening rate as a result of change in the structure from the multivariant to the single variant.

High strain-rate compression behavior of polymeric rod and plate Kelvin lattice structures

The compressive high strain-rate behavior of polymeric Kelvin lattice structures with rod-based or plate-based unit cells was investigated through experimental techniques and finite element simulations. Polymeric lattice structures with 5x5x5 unit cell geometries were manufactured on the millimeter scale using vat polymerization additive manufacturing and tested at low (0.001/s) and high (1000/s) strain-rates. High strain-rate experiments were performed and validated for a viscoelastic split-Hopkinson (Kolsky) pressure bar system (SHPB) coupled with high-speed imaging and digital image correlation (DIC). Experimental results at both low and high strain-rates show the formation of a localized deformation band which was more prevalent in low relative density specimens and low strain-rate experiments. Strain-rate effects of lattice specimens strongly correlate with effects of the base polymer material; both bulk polymer and lattice specimen demonstrated strain-rate hardening, strain-rate stiffening, and decreased fracture strain under dynamic loading. Results show mechanical failure properties and energy absorption depended strongly on the relative density of the lattice specimen and exhibited distinct scaling between relative density and geometry type (rod, plate) and loading rate. High relative density plate-lattices demonstrated inferior mechanical properties to rod-lattices; however, there exists a critical relative density for a given mechanical property (17%–28%) below which plate-lattices outperform rod-lattices of similar mass. High strain-rate explicit finite element simulations were performed and showed good agreement with the mechanical failure trends and deformation modes observed in the experiments.

Synergistic influence of La and Zr on microstructure and mechanical performance of an Al-Si-Mg alloy at casting state

The evolution of microstructure and mechanical properties of Al-7Si-0.4Mg alloys doped with La/Zr/La+Zr was investigated by experimental characterization and thermodynamic calculation. The combination of growth restriction effect by La-rich intermetallics and inoculation effect by peritectic Zr-rich cores led to the most dramatic grain refining. Furthermore, eutectic silicon was observed to be refined from avg. 9.8 µm in length within original alloy to avg. 5.8, 8.7, and 6.4 µm under the effect of La/Zr/La+Zr additions, respectively. The length reduction in eutectic silicon was attributed to the shrunk growth space caused by grain refinement and the presence of La-rich phases, as well as the impeded effect of several microns La-rich phases distribute directly on the growth front of Si phase. The strength and ductility were both elevated in the alloys at the casting state alloyed with La, Zr, or La+Zr. Particularly, the simultaneous introduction of La+Zr led to the optimal combination properties with a yield strength of 103 ± 3.4 Mpa, an ultimate tensile strength of 189.2 ± 4.6 Mpa, and fracture elongation of 6.1 ± 0.8%. The enhancement of yield strength was related to the strengthening from grain refining and dispersed precipitates. The improved ultimate tensile strength was ascribed to the higher and more stable strain-hardening rate, resulting from the combined influence of refined microstructures (e.g. grain and eutectic Si), as well as the emergence of La-rich and/or Zr-rich intermetallics. The elevation of fracture elongation was intimately correlated with the refining in eutectic silicon, which relieved the nucleation and development of crack along the interface between silicon and Al matrix.

Biaxial formability and microstructure of an Al-Mg-Si alloy sheet post solution heat treatment

Hot forming-quenching integrated process was developed to fabricate aluminum alloy complex-shaped components by taking advantage of the enhanced formability at the temperature close to solution temperature. But, it is very difficult to evaluate the formability under biaxial tension state and continuous cooling conditions. A measuring method was proposed to evaluate the biaxial formability by combining solution heat treatment and hot gas free bulging test. The effects of temperature and pressurizing rate on the bulging ability and thickness uniformity of an Al-Mg-Si alloy sheet were clarified. The deformation mechanism was revealed by microstructure observation. It is found that excellent formability can be obtained under the high temperature with less heat loss and rapid pressurizing conditions. The limiting strain under rapid pressurizing condition decreases from 1.13 at 500 ℃ to 0.81 at 400 ℃, being at a high strain level. Thickness uniformity can be obviously improved at a higher deformation temperature accompanied by rapid loading due to the remarkable strain-rate hardening effect. Dynamic recovery is the main restoration mechanism, resulting in numerous substructures and unchanged grain size. The obtained biaxial formability closer to actual forming condition can provide fundamental guidance for forming aluminum alloy complex-shaped component by hot forming-quenching integrated process.

Hot Deformation Behavior of PM Ni with Harmonic Microstructure

The hot deformation behavior of a harmonic-structured pure nickel has been studied and compared with the hot deformability of a homogeneously structured nickel. Both materials were produced via the powder metallurgy route through the Spark Plasma Sintering (SPS) of mechanical milled and un-milled powders. Hot deformation was evaluated through compression tests at three different temperatures (400 °C, 800 °C, and 1300 °C), covering a wide range in the homologous temperature spectrum for Ni (from 0.39 to 0.91), and at three different strain rates (0.001, 0.01, and 0.1 s−1). The evaluation of the stress–strain curves showed a higher hot compression resistance for the harmonic-structured nickel, together with higher strain hardening and strain rate sensitivity, thanks to the peculiar microstructural features of this material. Through the metallographic analysis of the specimens after hot compression, different mechanisms were identified as responsible for the deformation behavior in relation to the temperature of testing. While at 400 °C dynamic recrystallization has slightly started, at 800 °C it is widely diffused, and at 1300 °C it is replaced by grain growth and diffusion creep phenomena.

Monitoring Dynamic Recrystallisation in Bioresorbable Alloy Mg-1Zn-0.2Ca by Means of an In Situ Acoustic Emission Technique.

The tensile behaviour of the biocompatible alloy Mg-1Zn-0.2Ca (in wt.%) in the fine-grained state, obtained by severe plastic deformation via multiaxial isothermal forging, has been investigated in a wide range of temperatures (20 ÷ 300) °C and strain rates (5 × 10−4 ÷ 2 × 10−2) s−1 with the measurements of acoustic emission (AE). The dependences of mechanical properties, including the yield stress, ultimate strength, ductility, and the strain-hardening rate, on the test temperature and strain rate, were obtained and discussed. It is shown for the first time that an acoustic emission method is an effective tool for in situ monitoring of the dynamic recrystallisation (DRX) process. The specific behaviour of the acoustic emission spectral density reflected by its median frequency as a function of strain at various temperatures can serve as an indicator of the DRX process’s completeness.

Strain hardening behavior of friction welded beta titanium alloy Titan 1023 used for aeronautical applications

The experimental true stress – true strain data has been evaluated for the solution treated and aged beta titanium alloy Titan 1023 in comparison with the solid state welded samples. 14 mm diameter rods extracted out of Titan 1023 rolled bars were welded employing rotary friction welding with optimized parameters. Strain hardening parameters for samples in solution treated, aged condition and welded samples were determined using Holloman equation with the data obtained by carrying out tensile testing at ambient temperatures employing a strain rate of 3x10−4S−1. Strain hardening rate in terms of Crussard-Jaoul (C-J) plots of the alloy in all pre and post treated conditions were elucidated. Work hardening capacity of the alloy in STA and welded conditions were determined and presented. The effect of resultant microstructures on the strain hardening behavior is discussed in the current study.

Effect of Tempering Treatment on Microstructural Evolution and Mechanical Behavior of Heavy-Wall Heat Induction Seamless Bend Pipe.

In this paper, the microstructure and mechanical properties of heavy-wall seamless bend pipe after quenching at different tempering temperatures, including 550 °C, 600 °C, 650 °C, and 700 °C, were studied. Microstructure and dislocations observations were characterized by means of an optical microscope, a scanning electron microscope, a transmission electron microscope, and X-ray diffraction. As the tempering temperature increases, the dislocation density in the test steel gradually decreases, and the precipitation behavior of (Nb, V)(C, N) increases. The sample tempered at 650 °C exhibits a granular bainite structure with a dislocation cell structure and a large number of smaller precipitates. The yield platforms of tempered samples at 650 °C and 700 °C are attributed to the pinning effect of the Cottrell atmosphere on dislocations. The sample tempered at 650 °C not only presents the highest strength, but also the highest uniform elongation, which is attributed to the higher strain-hardening rate and instantaneous work-hardening index. This is closely related to the multiplication of dislocations, the interaction between dislocations and dislocations, and the interaction between dislocations and precipitates during plastic deformation of the 650 °C-tempered samples with low dislocation density, which delays the occurrence of necking.

Inelastic behavior of tungsten carbide at high pressures

Tungsten carbide (WC) is commonly used in plate impact experiments for generating high pressures due to its combination of high impedance and high strength. In pressure-shear plate impact (PSPI) experiments, WC is used as anvil plates, which sandwich a thin sample of the material of interest. At pressures up to its HEL (∼5 GPa), an elastic response may be assumed for the anvil plate, enabling a straightforward analysis to extract the shear strength of the material. At higher pressures, exceeding the HEL, the inelastic behavior of WC must be taken into account to extract the shearing resistance of the material of interest. We report the results of pressure-shear plate impact experiments conducted in the pressure range of 9–37 GPa. Two modeling approaches are considered to account for the inelastic behavior of WC: (1) an elasto-plastic response, accounting for strain and strain-rate hardening, and (2) a brittle-like response, which incorporates pressure hardening and damage. The material models were calibrated using numerical simulations to reconstruct the measured free surface velocity components in the normal and transverse directions. Both models effectively simulate the measured velocity profiles. Above 20 GPa, the brittle model appears to better capture the experimental trends. The calibrated models for WC enable the reconstruction of the experimental data from the current work, as well as from results reported by others, for a broad range of pressures.

3D numerical investigation of the detonation wave propagation influence on the triangular plate deformation using finite rate chemistry model of LS-DYNA CESE method

In this article, an immersed boundary method which couples a Lagrangian structure solver with an Eulerian fluid solver with a chemistry model capable of detonation computation for H2O2 is developed to achieve the fluid-structure interaction, the deformation, and the damage of a thin plate subjected to a gaseous detonation loading. The Johnson-Cook material model was used for the plate which incorporates strain hardening, temperature softening, and strain rate effects. The detonation wave is modeled using LS-DYNA finite rate chemistry model incorporated in conservative element solution element solver. Other objectives of this numerical simulation such as estimation of deflection and stress state failure mechanism of material at high strain rate were derived based on a strain-rate dependent failure criterion. The simulated deformation pattern and the effect of pre-detonation pressure are compared with experimental results and a good agreement was acquired. Further additional simulations revealed that the pre-detonation pressure, ignition point location, and longitudinal capacity of the cylinder have great influences on the deformation and sensed pressure of the plate.

A directional framework of similarity laws for geometrically distorted structures subjected to impact loads

• The directional framework of similarity laws for structural impact is proposed, especially for geometric distortion . • Spatial directions and structural geometric characteristics are explicitly expressed in dimensionless numbers . • Correction methods of the velocity, the density and the geometry are used to address various distortion problems at scaling. • Various dimensionless response equations can be clearly, concisely and perfectly expressed. • Refined scaling analyses under the proposed framework are given numerically. A directional framework of similarity laws, termed oriented-density-length-velocity (ODLV) system, is suggested for the geometrically distorted structures subjected to impact loads. The distinct feature of the framework is that the newly proposed oriented dimensions, dimensionless numbers and scaling factors for all basic physical quantities are explicitly expressed by three characteristic lengths of spatial directions, which overcomes the inherent defects only with one scalar length in the traditional dimensional analysis. Meanwhile, similarity laws of the directional stresses, strains and displacements are expressed by different power law relationships of the ratios of undistorted characteristic lengths to distorted characteristic lengths. Therefore, the ability of similarity theory to express structural geometric characteristics are effectively developed. Based on the newly proposed framework, the non-scalabilities of geometric and material distortion (including strain hardening and strain rate effects) and the gravity effects could be compensated by correction methods of velocity, density and geometry. The analytical models of beams subjected to impact mass and impulsive velocity are verified. The results show that the proposed framework has excellent performance for expressing various dimensionless response equations and geometrically distorted scaling. A numerical model of circular plate subjected to dynamic pressure pulse is further carried out to verify the geometrically distorted scaling of the directional components of displacement, strain and stress. The refined analysis results show that, structural dimensionless responses in different directions can behave good consistency between the scaled model and the prototype in both the spatial and the temporal fields, with the correction of the directional physical quantities using different powers of the ratios of characteristic lengths.

Significant lattice-distortion effect on compressive deformation in Mo-added CoCrFeNi-based high-entropy alloys

Large lattice distortion is an essential feature of high-entropy alloys (HEAs). Herein, the deformation behaviors of three types of as-cast CoCrFeNi-based HEAs, which contained 0, 7.9, and 17.1 wt% Mo, were comparatively studied through compressive tests and microstructural observations. The intrinsic lattice distortion increased mainly as a function of the Mo content. By virtue of both the local strain incompatibility inside the coarse columnar grains of the as-cast microstructures and low dislocation mobility in HEAs, domain rotations were induced at low strains. Meanwhile, simple shear occurred between domains and produced a new boundary network in the microstructure. The large lattice distortion of the high-Mo HEA (17.1 wt%) gave rise to intense planar slip bands, on which a large number of dislocations slipped and impinged on strain-induced boundaries. As a result of the high back-stress hardening, the high-Mo HEA exhibited enhanced strain-hardening. At high strains, the stress concentration events increased as the lattice distortion of the HEAs increased; this promoted twin growth in the high-Mo HEA. The high-Mo HEA was highlighted with a high strain-hardening rate over a wide strain range. In this study, high-strength as-cast HEAs were developed based on the utilization of the lattice-distortion effect.