Strain Rate Sensitivity Of Flow Stress Research Articles

Plastic deformation of single crystals of the equiatomic Cr−Mn−Fe−Co−Ni high-entropy alloy in tension and compression from 10 K to 1273 K

The plastic deformation behavior of single crystals of the quinary, equiatomic Cr−Mn−Fe−Co−Ni high-entropy alloy (HEA) with the face-centered cubic structure has been investigated in tension and compression as a function of crystal orientation and temperature from 10 K to 1373 K. The critical resolved shear stress (CRSS) for {111}<110> slip at room temperature is 42−45 MPa. It does not depend much on crystal orientation (i.e., the Schmid law holds true) and the sense (tension vs. compression) of the applied load. The CRSS for {111}<110> slip increases with the decrease in temperature, without showing any significant inertia effects at cryogenic temperatures below 77 K. Extrapolation from the measured yield stresses down to 10 K yields a CRSS value at 0 K of 168 MPa. At cryogenic temperatures, the measured strain-rate sensitivity of flow stress is consistent with a very small activation volume. The concept of stress equivalence holds true both for the temperature dependence of CRSS and the stress dependence of activation volume, indicating that solid-solution hardening is the major strengthening mechanism. Deformation twinning occurs at 77 K but not at room temperature, resulting in higher tensile elongation to failure at 77 K than at room temperature. Deformation twinning at 77 K occurs at a shear stress of 378 MPa on conjugate (1¯1¯1) planes in the form of Lüders deformation after large plastic strain (about 85%) achieved by the stage I (easy glide) and stage II (linear work-hardening) deformation.

Strain-Rate Effect and Constitutive Models for Q550 High-Strength Structural Steel

High-strength structural steel is the tendency in modern construction practice. In this study, quasi-static tension tests and dynamic tests for Q550 with strain rate from 0.00025 to 3831 s−1 were conducted. The results showed that Q550 is dependent on the strain rate, keeping the flow stress increased as the strain rate increases, while Q550 has lower strain-rate sensitivity of flow stress than that of normal mild steel. Based on the experimental data, a proper constant for the key parameter, C, in Johnson–Cook model (J–C) was suggested. Then, a modified J–C model based on a rate-dependent parameter $$C\left( {\dot{\varepsilon }} \right)$$ was recommended to consider the influence of strain-rate effect. New constants of D and p governing the dynamic response of steel in the Cowper–Symonds (C–S) model were also suggested. The C–S model and J–C models with suggested constants provided in the paper were proven to have acceptable prediction accuracy for the dynamic increase factor of Q550. These results may be applied to study the dynamical properties of Q550 and related structural components for future engineering applications.

On the strain rate dependence of the critical strain for plastic instabilities in Al-Mg alloys

The strain/strain rate range of plastic instability in Al-Mg alloys is analyzed within the dynamic strain aging interpretations of the Portevin-Le Chatelier effect. The analysis focuses on several phenomena occurring around the minimum of the critical strain for the onset of serrations vs. applied strain rate curve. The analysis of the strain rate dependence of the flow stress strain rate sensitivity in the neighborhood of this critical point allows explaining the extension of the stability region to larger strains in the inverse behavior range and the shift to larger strain rates of the critical point when the Mg content increases.

High-rate deformation of nanocrystalline iron and copper

Stress–strain curves are recorded during a high-speed impact and slow loading for nanocrystalline and coarse-grained iron and copper. The strain-rate sensitivity is determined as a function of the grain size and the strain. It is shown that the well-known difference between the variations of the strain-rate sensitivity of the yield strength with the grain size in fcc and bcc metals can be extended to other strain dependences: the strain-rate sensitivity of flow stresses in iron decreases with increasing strain, and that in copper increases. This difference also manifests itself in different slopes of the dependence of the strain-rate sensitivity on the grain size when the strain changes.

Experimental investigation and comparative analysis of Ni-18.75 at. % Fe alloy plasticity, in coarse-grained and nano-crystalline states in the 4.2–350 K temperature range

The mechanical properties of a coarse-grained (CG) Ni-18.75 at. % Fe alloy, are studied in the temperature range of 4.2–350 K, under uniaxial compression and a constant strain rate. The average grain size is 35 μm. The temperature dependence of the yield stress is obtained, and the stress-strain curves are analyzed. The temperature dependences of flow stress, strain-rate sensitivity of flow stress, and the activation volume of plastic deformation, are obtained for a plastic strain of ε ≈ 2%. The thermal activation analysis of the experimental data of a coarse-grained alloy showed that plastic deformation at the 35–350 K temperature interval has a thermally-activated character, and is described by a single mechanism. The empirical estimates of the parameters of dislocation interaction with the local barriers, and estimates of the effective and internal stress, are obtained. A comparative analysis of the results is conducted, describing the properties of low-temperature thermally activated plastic deformation of the studied alloy, in both the CG and nanocrystalline (NC) states. It is concluded that in the CG state, within the studied temperature interval, the microscopic barriers controlling the thermally activated plastic flow, are different from the barriers in the NC state. The spectrum of local barriers, which can determine the thermally activated dislocation plasticity in NC and CG states, is discussed.

Dynamic Strain Aging in a Newly Developed Ni–Co-Base Superalloy with Low Stacking Fault Energy

Characteristics of dynamic strain aging (DSA) in a Ni–Co-base superalloy were studied by tensile tests at temperatures ranging from 250 °C to 550 °C and strain rates ranging from 3 × 10−5 to 8 × 10−4 s−1. Serrated flow in the tensile stress-strain curves was observed in the temperature range from 300 °C to 500 °C. Normal DSA behavior was found at temperatures ranging from 300 °C to 350 °C, while inverse DSA behavior was observed at temperatures ranging from 400 °C to 500 °C. The yield strength, ultimate tensile strength, elongation, work hardening index, and fracture features were not affected by temperature and strain rates in DSA regime. Negative strain-rate sensitivity of flow stress was observed in DSA regime. The analysis suggests that the ordering of the substitutional solutes around some defects like mobile dislocations and stacking faults due to the thermal activated process may cause the serrations on the tensile curves.

Hydrogen-induced delayed fracture of a Fe–22Mn–0.6C steel pre-strained at different strain rates

Hydrogen-induced delayed fracture under loading was investigated in a Fe–22Mn–0.6C twinning-induced plasticity steel that had been pre-deformed at various strain rates. Hydrogen-induced delayed fracture was suppressed by increasing the strain rate of the pre-deformation. In this study on the strain-rate effect, factors affecting the delayed fracture were found to be the negative strain-rate sensitivity of flow stress, stress drop caused by the relaxation phenomenon, and the increase in material strength due to strain aging.

Analysis of indentation creep

Finite element analysis is used to simulate cone indentation creep in materials across a wide range of hardness, strain rate sensitivity, and work-hardening exponent. Modeling reveals that the commonly held assumption of the hardness strain rate sensitivity (mH) equaling the flow stress strain rate sensitivity (mσ) is violated except in low hardness/modulus materials. Another commonly held assumption is that for self-similar indenters the indent area increases in proportion to the (depth)2 during creep. This assumption is also violated. Both violations are readily explained by noting that the proportionality “constants” relating (i) hardness to flow stress and (ii) area to (depth)2 are, in reality, functions of hardness/modulus ratio, which changes during creep. Experiments on silicon, fused silica, bulk metallic glass, and poly methyl methacrylate verify the breakdown of the area-(depth)2 relation, consistent with the theory. A method is provided for estimating area from depth during creep.

Analysis of the strain-rate sensitivity of flow stresses in nanocrystalline FCC and BCC metals

The dependence of the strain-rate sensitivity coefficient of flow stresses S = dlnσ/dln\(\dot \varepsilon \) on temperature, strain rate, and grain size in nanocrystalline (NC) metals is analyzed quantitatively in terms of the dislocation-kinetics approach taking into account the properties of grain boundaries as sources, sinks, and barriers for moving dislocations. The interaction of moving dislocations with a dislocation forest in nanograin boundaries is shown to be responsible for the fact that the values of this coefficient in NC fcc metals (Cu, Ni) are an order of magnitude greater than those in coarse-grained metals and for the strong dependence of the coefficient S on the above factors. This dependence is largely caused by the annihilation of lattice dislocations in grain boundaries controlled by the activation energy of grain boundary diffusion. The values of the coefficient S in NC bcc metals (α-Fe) are an order of magnitude lower than those in coarse-grained samples, because dislocations move in a Peierls relief in nanograins

Effect of natural ageing on the mechanical properties of molybdenum polycrystals

Natural ageing of 99.95 at.% Mo polycrystals annealed at 700 °C influences its mechanical properties to a considerable extent. It is found that natural ageing for 6 months reduces the ductility by about 70% whereas yield stress and ultimate tensile strength are decreased by about 20 and 18% respectively. The stress-relaxation rate measured at a given initial stress level at which deformation is interrupted to observe stress relaxation at constant strain, is faster in aged specimens compared with that in unaged ones. Similarly, the strain-rate sensitivity of flow stress for a given stress level is also increased on natural ageing. The rate process of stress relaxation and of plastic flow at rather high strains corresponding to the parabolic stage of work hardening appears to be vacancy migration.

Advanced High Strength Steels for Automobile Body Structures

There has been a big demand for increased vehicle safety and weight reduction of auto-bodies. An extensive use of high strength steels is one of the ways to answer the requirement. Since the crashworthiness is improved by applications of higher strength steels to crashworthiness conscious structural components, various types of advanced high strength steels have been developed. The crash energy during frontal collisions is absorbed by the buckling and bending deformations of thin wall tube structures of the crushable zone of auto-bodies. In the case of side collision, on the other hand, a limited length of crushable zone requires the components to minimize the deformation during the collision. The lower the strength during press forming, the better the press formability is expected. However, the higher the strength at a collision event, the better the crashworthiness can be obtained. It can, therefore, be concluded that steels with higher strain rate sensitivities are desired. Combinations of soft ferrite phase and other hard phases were found to improve the strain rate sensitivity of flow stresses. Bake hardening is also one of the ways to improve the strain rate sensitivity of flow stresses.

Effect of fine structure of Pb-In solid solutions on their deformation-induced strengthening at low temperatures

The specific features of low-temperature deformation-induced strengthening of Pb-In single crystals have been studied in a wide range of impurity concentrations. It was shown that a change in the strain-rate sensitivity of flow stress in the concentrated solid solution is connected with the inhomogeneous distribution of impurities. Based on the X-ray diffuse-scattering data, it was found that the short-range order of separation type was formed in these alloys; i.e., the lead atoms were randomly arranged and the indium atoms formed clusters whose characteristic size increased with concentration in a range of 1.0–1.9 nm. In the concentrated alloy, the appearance of coarse impurity clusters as strong obstacles for mobile dislocations in comparison with the impurity atoms and forest dislocations causes not only a sharp increase in the flow stress but also a change in the energy of dislocation-dislocation interaction.

Comments on “The strain-rate sensitivity of flow stress and work-hardening rate in a hot deformed Al-1.0Mg alloy”

Comments on “The strain-rate sensitivity of flow stress and work-hardening rate in a hot deformed Al-1.0Mg alloy”

The strain-rate sensitivity of flow stress and work-hardening rate in a hot deformed Al-1.0Mg alloy

The strain-rate sensitivity of flow stress and work-hardening rate in a hot deformed Al-1.0Mg alloy

Effect of Natural Ageing on the Strain-Rate Sensitivity of Flow Stress in High-Purity Aluminium Polycrystals

Strain-rate-cycling experiments between 4.6 × 10 -3 s -1 and 4.6 × 10 -4 s -1 were performed with 99.996% aluminium polycrystals of mean grain-diameter 0.25, 0.36, and 0.47 mm, which had been annealed at 500°C and aged for six months at room temperature prior to deformation. Similar studies were also carried out with 500 °C annealed but unaged aluminium specimens of the same purity and grain size for comparison. It is observed that yield stress, ultimate tensile stress, fracture stress, and strain-rate sensitivity Δσ of a given flow stress σ in the range 30 to 70 MPa are not influenced by the grain size in both aged and unaged aluminium. However, natural ageing significantly enhances the yield stress as well as the strain-rate sensitivity Δσ of a given flow stress σ by 30% while ultimate tensile stress and fracture stress remain unaffected. Migration of point defects, e.g. vacancies, residual gaseous and metallic impurity atorns etc., to the cores of edge dislocations during ageing seems to be responsible for the increase in yield stress and strain-rate sensitivity of the flow stress. The analysis of the Δσ/σ data in terms of Feltham's single barrier model of plastic flow shows that the intrinsic height of the thermally activable energy barrier (3.4 eV) evaluated for aged aluminium is comparable with that (4.2 eV) for unaged aluminium, and dislocation-dislocation intersection is the rate process of plastic flow.

Loss of Stress Equivalence in the Strain-Rate Sensitivity of Flow Stress in Fine-Grain Polycrystalline Copper

The strain-rate sensitivity of flow stress (3.7 × 10 -3 s -1 ⇄ 3.7 × 10 -4 s -1 ) in fine-grain polycrystalline copper has been studied over the entire stress-strain curve at room temperature. It is observed that the yield stress varies with mean grain diameter (32 to 59 μm) in accord with the Hall-Petch relation, whereas ultimate tensile stress and fracture stress are independent of the grain size. The strain-rate sensitivity Δσ of a given flow stress σ depends on the grain size; it increases as grain size is increased from 32 to 59 μm. For a given grain size, the Cottrell-Stokes ratio Δσ/σ and the product of flow stress σ and associated activation volume V σ remain constant in the entire stress range 50 to 210 MPa studied. Values of both Δσ/σ and V σ σ depend on the grain size. The observations have been accounted for within the framework of Feltham's single barrier model of plastic flow.

Strength and ductility under dynamic loading in fine- grained IN905XL aluminum alloy

Three IN905XL aluminum alloys with fine grain (1 μm), intermediate grain (3 μm), and coarse grain (5 μm) have been developed by a combination of mechanical alloying (MA) and conventional extrusion in order to investigate their mechanical properties at dynamic strain rates of 1 × 103 and 2 × 103 s−1 and a quasi-static strain rate of 10-3 s−1. Flow stresses are found to increase with decreasing grain size for all the strain rates tested. Negative strain-rate sensitivity of flow stress is observed up to 1 × 103 s−1 in both intermediate- and coarse-grained IN905XL. At the highest strain rate of 2 × 103 s−1 however, all samples showed a positive strain-rate sensitivity of strength. Total elongation at high strain rates is generally larger than that at low strain rates. Total elongation also decreases with grain size for all the strain rates. This decrease in elongation results from an initiation of microcracks at interfaces between the matrix and particles finely dispersed near grain boundary regions, introduced during MA processing; then, this initiation leads elongation of alloys to small limited values.

The Temperature Dependence of the Mechanical Properties of Gamma TiAl

AbstractMechanical properties of a polycrystalline single phased γ Ti47Al51Mn2alloy were studied by compression tests in a wide range of temperature (100 K - 1300 K). We report, in this paper, the temperature dependence of both the flow stress and its strain rate sensitivity. These dependencies show the existence of three temperature domains corresponding to different dislocation motion mechanisms. The temperature dependence of the flow stress strain rate sensitivity is compared with values measured in single crystals1.

Processing map for hot working of powder Metallurgy 2124 Al-20 Vol Pct SiCp Metal Matrix Composite

The constitutive flow behavior of a metal matrix composite (MMC) with 2124 aluminum containing 20 vol pct silicon carbide particulates under hot-working conditions in the temperature range of 300 °C to 550 °C and strain-rate range of 0.001 to 1 s-1 has been studied using hot compression testing. Processing maps depicting the variation of the efficiency of power dissipation given by [2m/(m + 1)] (wherem is the strain-rate sensitivity of flow stress) with temperature and strain rate have been established for the MMC as well as for the matrix material. The maps have been interpreted on the basis of the Dynamic Materials Model (DMM). [3] The MMC exhibited a domain of superplasticity in the temperature range of 450 °C to 550 °C and at strain rates less than 0.1 s-1. At 500 °C and 1 s-1 strain rate, the MMC undergoes dynamic recrystallization (DRX), resulting in a reconstitution of microstructure. In comparison with the map for the matrix material, the DRX domain occurred at a strain rate higher by three orders of magnitude. At temperatures lower than 400 °C, the MMC exhibited dynamic recovery, while at 550 °C and 1 s-1, cracking occurred at the prior particle boundaries (representing surfaces of the initial powder particles). The optimum temperature and strain-rate combination for billet conditioning of the MMC is 500 °C and 1 s-1, while secondary metalworking may be done in the super- plasticity domain. The MMC undergoes microstructural instability at temperatures lower than 400 °C and strain rates higher than 0.1 s-1.

Hot-working characteristics of Zircaloy-2 in the temperature range of 650–950°C

The hot-working characteristics of Zircaloy-2 have been studied in the temperature range of 650 to 950°C and in the strain-rate range of 10−3 to 102 s−1 using power dissipation maps which describe the variation of the efficiency of power dissipation, η = 2m /(m + 1) where m is the strain-rate sensitivity of flow stress. The individual domains exhibited by the map have been interpreted and validated by detailed metallographic investigations. Dynamic recrystallization occurs in the temperature range of 730 to 830°C and in the strain-rate range of 10−2 to 2 s−1. The peak efficiency occurs at 800°C and 0.1 s−1 which may be considered as the optimum hot-working parameters in the α-phase field of Zircaloy-2. Superplastic behaviour, characterized by a high efficiency of power dissipation is observed at temperatures greater than 860°C and at strain rates lower than 10−2 s−1. When deformed at 650°C and 10−3 s−1, the primary restoration mechanism is dynamic recovery, while at rates higher than 2s−1, the material exhibits microstructural instabilities in the form of localized shear bands.