Variation Of Strain Rate Sensitivity Research Articles

Rate-Controlling Microplastic Processes during Plastic Flow in FCC Metals: Origin of the Variation of Strain Rate Sensitivity in Aluminum from 78 to 300 K

The thermodynamic response of dislocation intersections with forest dislocations and other deformation products is recorded using the Eyring rate relation wherein the application of shear stress increases the probability of activation at a given strain rate and temperature. The inverse activation volume, 1/ν, can be directly determined by instantaneous strain-rate change and its dependence on flow stress, τ, defines the strain-rate sensitivity, S, through the Haasen plot slope. A linear slope over a large strain interval is observed even for a heterogeneous distribution of obstacles that could be of more than one type of obstacles encountered by the gliding dislocation. It was deduced that ν and τ at each activation site are coordinated by the internal stress resulting in constant activation work (k/S). The stress changes from down-rate changes become larger than that from up-rate changes due to the formation of weaker obstacles, resulting in a composite S, whereas only forest dislocations are detected by the up-change. The additivity of 1/ν was used to separate obstacle species in specially prepared AA1100 and super-pure aluminum from 78 to 300 K. The deduction that repulsive intersection is the rate-controlling process and creates vacancies at each intersection site depending on temperature was validated by observing the pinning and depinning of dislocations via pipe diffusion above 125 K. A new method to separate S for dislocation-dislocation intersections from the intersections with other obstacles and their temperature dependence is presented and validated.

Crystal plasticity analysis of temperature-sensitive dwell fatigue in Ti-6Al-4V titanium alloy for an aero-engine fan disc

This study investigates the temperature-dependent dwell fatigue behavior of Ti-6Al-4V alloy using crystal plasticity finite element method. The dislocation mechanism-based crystal plasticity parameters are calibrated with the data of quasi-static tensile and constant load creep tests at ambient and intermediate temperatures. In particular, the rate-dependent parameters related to slip property are employed to establish the relationship between strain rate sensitivity of a soft α-titanium single crystal and temperature. The variation of strain rate sensitivity with temperature influences the stress redistribution occurring within the hard-soft grain combination, which in turn affects the dwell fatigue sensitivity. Further, the structural analysis for a Ti-6Al-4V fan disc provides the stress fields at takeoff and cruise phases to examine the in-service stress redistribution. The highly localized hoop stress and presence of large macrozones at the bore of the fan disc, rather than the fair rate sensitivity of soft macrozones at working temperatures, are responsible for triggering basal stress enhancement and dwell facet nucleation in hard macrozones.

Influence of pre-straining and heating on strain-rate sensitivity of AA5182-O

The manufacturing process of auto-body parts usually includes forming (i.e., pre-straining) and baking (i.e., heating), which could alter mechanical properties of the substrate materials. The present study clarifies the influence of pre-straining and heating on the strain-rate dependent mechanical performance of aluminum alloy 5182-O (AA5182-O). Quasi-static and intermediate strain-rate tensile tests were conducted with either AA5182-O material as received or processed by different combinations of pre-straining and heating. The quasi-static test results show that the yield strength is enhanced by pre-straining and weakened by heating, while the ultimate strength is less affected. The test results at different strain-rates show a transition of negative to positive strain-rate sensitivity (SRS) at a critical rate below 100 s−1, and it is revealed that pre-straining enhances the negative effect and heating mainly enhances the positive effect. A modified Khan-Liu model that incorporates the non-monotonic SRS is employed to characterize the influence of pre-straining and heating, and electron backscatter diffraction (EBSD) analysis is performed to address the mechanism behind the SRS variation.

The mechanical properties of high strength Al alloy sheet under quasi-static-dynamic loading

To investigate the mechanical properties of high strength Al alloy, the AA2024 was selected and conducted the uniaxial tensile tests at room temperature under different loading modes, namely pure quasi-static (QSD) loading mode, pure dynamic loading mode and quasi-static-dynamic loading mode. The mechanical properties such as yield stress (YS), ultimate tensile stress (UTS), total elongation and strain rate sensitivity were compared. The results shown that the UTS under QSD loading mode is larger than that of quasi-static and pure dynamic loading mode, and dependent on prestrain levels. However, the YS at pure dynamic loading mode is less than that of QSD loading mode at prestrain of 10% but larger than that of prestrain of 6%. In addition, the QSD loading mode would further improve the total elongation of AA2024 compared to the elongation enhancement under pure dynamic loading mode. Finally, the variation of strain rate sensitivity under different loading modes was analyzed to explain the evolution of tensile properties of AA2024.

Characterization of the Hot Deformation Behavior and Microstructure Evolution of a New γ-γ′ Strengthened Cobalt-Based Superalloy

Recently, cobalt-based γ-γ′ microstructured superalloys have attracted attention. However, studies on their processing behavior [i.e., processing maps (the variation of strain rate sensitivity (m) with temperature)] are limited. Thus, the high-temperature flow behavior of a γ-γ′ Co-30Ni-10Al-5Mo-2Ta-2Ti-5Cr (at. pct) superalloy was investigated using isothermal compression tests between 1348 and 1498 K at strain rates from 0.001 to 10 s−1. The m contour map was generated using the experimental flow stress values, which were used to locate the optimum hot workability and desired microstructural processing range. A strong dependence of m on the deformation parameters (temperature, strain rate, and strain) was observed. A maximum m value of around 0.3 at 1460 K to 1498 K and strain rates of 0.01 to 0.5 s−1 was found. The deformed samples show a fully recrystallized microstructure at high m. Unstable domains showed the formation of cavities at the grain boundary triple points and cracks along the grain boundaries at high strain rates (1 to 10 s−1), corresponding to m < 0.10. A constitutive model was developed using an Arrhenius hyperbolic sine function, yielding an apparent activation energy of 540 ± 30 kJ mol−1 for hot deformation. This study indicates reasonable formability under certain conditions below the solvus, thus opening possibilities for further thermomechanical treatment.

Layer thickness dependent strain rate sensitivity of Cu/amorphous CuNb multilayer

Strain rate sensitivity of crystalline materials is closely related to dislocation activity. In the absence of dislocations, amorphous alloys are usually considered to be strain rate insensitive. However, the strain rate sensitivity of crystalline/amorphous composites is rarely studied, especially at nanoscale. In this study, we show that the strain rate sensitivity of Cu/amorphous CuNb multilayers is layer thickness dependent. At small layer thickness (below 50 nm), the multilayers demonstrate limited strain rate sensitivity; at relatively large layer thickness (above 100 nm), the strain rate sensitivity of multilayers is close to that of the single layer Cu film. Mechanisms that lead to size dependent variation of strain rate sensitivity in these multilayers are discussed.

Variation of strain rate sensitivity of an aluminum alloy in a wide strain rate range: Mechanism analysis and modeling

The significant variation of strain rate sensitivity (SRS), i.e. the non-linear characteristics of SRS, within wide strain and strain rate ranges in high strain rate forming (HSRF) leads to the complexity of constitutive behaviors of aluminum alloys. Therefore, in order to achieve accurate simulation of HSRF process, a panoramic description of the SRS variation and related mechanisms are required within wide ranges. To address this problem, taking 5A06 aluminum alloy as an example, three distinct SRS zones were determined at 0.001 s−1–5000 s−1 in the present work, including quasi-static negative SRS zone (Zone-I), positive SRS zone at dynamic strain rate (Zone-II) and negative SRS zone at high strain and strain rate (Zone-III). Then, the mechanism for that in Zone-II is attributed to the conversion from dislocation glide to viscous drag through thermal activation analysis. In Zone-III, the dominant mechanisms are the change of dislocation configuration from dislocation cells and dislocation bands to subgrains in adiabatic shear bands in compression and to the increasing volume fraction of voids in tension, respectively, which is proved by SEM and TEM observations. Consequently, the effect of dislocation evolution on the SRS was quantitatively characterized and the nonlinear rate dependent stress responses of the aluminum alloy in a wide strain rate range were captured.

Strain Rate Sensitivity Variation in CuZr-based Bulk Metallic Glass Composites Containing B2-CuZr Phase

Abstract The strain rate sensitivity (SRS) of CuZr-based bulk metallic glass composites (BMGCs) containing a B2-CuZr phase with different volume fractions was investigated by performing uniaxial compression tests in a strain-rate-jump mode. It is found that the SRS exponents of the BMGCs can vary from negative to positive in the strain-rate range from 3.7×10−5 s−1 to 3.7×10−3 s−1 with increasing of the B2-CuZr phase volume fraction. However, the positive SRS exponent of the BMGC with a higher B2-CuZr phase volume fraction up to about 80% is still unexpectedly low. This is attributed to the limited strain-rate-dependence of mechanical behavior of the B2-CuZr phase, which is induced by the martensitic transformation effect of the phase during deformation. It is obvious that the SRS ceiling of the CuZr-based BMGCs is controlled by the B2-CuZr phase.

Variation of strain rate sensitivity with grain size in Cr and other body-centred cubic metals

The strain rate sensitivity (i.e. m-value) of body-centred cubic Cr was measured over a wide grain size range (10−9–10−2 m) using an instrumented nanoindentation technique. The m-value was observed to decrease initially as the grain size was reduced from mm to µm, it reached a minimum, and then increased drastically when the grain size was below 20–30 nm. There was a corresponding variation in activation volume, particularly when the grain size was in the nm range and the grain-boundary-mediated process became dominant. The variation of m-value and activation volume over the entire grain size range could be rationalized by a model based on a double-kink mechanism coupled with the dislocation emission processes from the grain boundaries.

Strain rate sensitivity and related plastic deformation mechanism transition in nanoscale Ag/W multilayers

Nanoscale metallic multilayers are a promising structural material for fabricating the next generation of nanoscale devices. Even though the mechanical properties of the multilayers have been extensively studied, the interpretation for the strain rate sensitivity of the multilayers is still lacking. In present study, the hardness and strain rate sensitivity of Ag/W multilayers with a wide range of modulation period Λ and modulation ratio η deposited by d.c. sputtering deposition were evaluated by nanoindentation testing. X-ray diffraction and transmission electron microscopy were carried out to investigate the texture and microstructure of the multilayers. Experimental results indicated that a mechanism transition occurred as the plastic deformation of the Ag/W multilayers was accommodated by the two constituent layers together at Λ≤50nm, while the plastic deformation localized mainly in Ag layers when Λ>50nm. A modified rule of mixture and plastic deformation localization model was proposed to describe the variation of strain rate sensitivity for the multilayers with smaller and larger Λ, respectively.

Flow behaviour of Nickel Aluminium Bronze under hot deformation

Flow behaviour of a Nickel Aluminium Bronze (NAB) alloy under hot compressive deformation was investigated using a deformation dilatometer. Temperatures of 1023, 1073, 1123 and 1173K and strain rates of 0.1, 1.0 and 10s−1 were used as the forming parameters. The experimental results showed that true stress–strain curves of the alloy exhibited dynamic recovery and dynamic recrystallisation with single-peak stress. Dynamic recovery was dominant at higher temperature and lower strain rate. The peak stress increased as the strain rate and temperature increased. The peak strain also increased with increasing strain rate. However, it was independent of temperature. The flow curves can be represented by the hyperbolic-sine law Arrhenius equation with activation energy of 514.25kJ/mol. Comparisons between predicted flow stresses and experimentally determined results showed that the developed constitutive models were sufficiently accurate to demonstrate flow behaviour at high temperatures of the NAB alloy. This was supported by a correlation coefficient R of 0.981 and an average relative error of 13.42% for the particular test conditions. Dynamic material modelling approach has been used to describe flow stability/instability. For the NAB alloy, the criterion of the strain rate sensitivity, the criterion with regard to the variation of strain rate sensitivity with logε̇ and the criterion of the temperature sensitivity were always satisfied. The critical criterion is the rate of change of the temperature sensitivity with respect to logε̇.

A viscoplastic constitutive model for cyclic hardening in the dynamic strain aging regime

Negative strain rate sensitivity in certain temperature regimes is considered to be a manifestation of dynamic strain aging. Within the framework of unified state variable theory, viscoplastic constitutive equations incorporating the Mises yield criterion are presented to model negative rate sensitivity of the flow stress and its gradual variation with cyclic loading. The modeling capabilities are essentially accomplished by introducing a rate sensitivity parameter into the evolution law of the back stress. The influence of the drag stress and the isotropic stress as well as the rate sensitivity parameter both on the cyclic hardening and the variation of strain rate sensitivity is systemically investigated. Excellent agreement between experimental results reported in the literature and model simulations is obtained, confirming the efficacy of the proposed constitutive model.

Dynamic Recrystallization in Sintered Cobalt during High-Temperature Deformation

The constitutive flow behavior of sintered cobalt in the temperature range 873 to 1473 K (600 to 1200 °C) and at strain rates from 0.001 to 10 s−1 has been studied using constant true strain rate hot compression tests. On the basis of these data, a processing map has been generated that depicts the variation of strain rate sensitivity with temperature and strain rate. The processing map reveals a domain of dynamic recrystallization (DRX) with an optimum condition of processing at 1273 K (1000 °C) and at 10−3 s−1. When deformed within the domain, the stress-strain curves exhibit a single peak followed by flow softening, leading to steady-state behavior. In addition to this, a recently developed approach based on flow curve analysis is used to study the DRX kinetics, which is found to follow an Avrami-type relation.

Analysis of Grain Growth during Superplastic Deformation

The microstructural mechanism of grain growth during superplastic deformation is studied in this paper. A new model that considers grain growth is proposed and applied to conventional superplastic materials (Zn-Al alloy, LY12CZ alloy, and 7475 Al alloy). The relationships between the strain, strain rate, test temperature, initial grain size and grain growth in superplastic materials are discussed. The theoretical predictions for superplastic deformation that are presented show good agreement with the experimental data. The effect of the variation of strain rate sensitivity (m value) on the strain limit of superplastic deformation is investigated, and the theoretically calculated values are compared with the experimental results.

The effect of strain rate sensitivity evolution on deformation stability during superplastic forming

The most important characteristic of superplastic materials is the high sensitivity of flow stress to deformation rate. In general, a constant strain rate sensitivity index value is usually used for calibrating models describing superplastic deformation. However, experimental results indicate that the strain rate sensitivity index depends on strain rate, strain and does not remain constant during deformation. In this work, the effects of strain rate sensitivity variation on the stability of deformation during superplastic forming are examined using finite element simulations in conjunction with a microstructure-based constitutive model. The model is experimentally calibrated and validated for the AZ31 magnesium alloy. The results clearly show the importance of accounting for the variation of strain rate sensitivity in modeling and simulating superplastic forming.

Characterization of superplastic behaviour in the (α+β) phase field of Zr–2.5wt.%Nb alloy

Abstract The effect of grain size on superplastic deformation in Zr–2.5 wt.%Nb was studied by constructing processing maps (which depict the variation of strain rate sensitivity with temperature and strain rate) in the temperature range of 650–830 °C and strain rate range of 5 × 10 −6 to 2 × 10 −3 s −1 . The occurrence of superplastic domain with respect to temperature and strain rate was identified for three grain sizes (4, 10 and 16 μm). The 4 μm grain size material exhibited a domain centered around 800 °C and 10 −4 s −1 , exhibiting a ductility of 700%. With increasing grain size the domain shifts to higher temperatures and lower strain rates. A detailed characterization of deformed microstructure revealed equiaxed grain structure (curved boundaries) with considerable grain growth within the superplastic domain. Creep equation was used to evaluate the parameters of superplastic deformation, which resulted in activation energy of 125 kJ/mol and a grain size exponent of 1.6. The accommodation mechanism for superplastic deformation was deduced to be either non-conservative jog motion or grain boundary migration, with the rate controlling step for both being the grain boundary diffusion of Zr and Nb in β phase.

Influence of various divalent impurities on dislocation density in KCl:Mg2+, Ca2+, Sr2+ or Ba2+ single crystals

Single crystals of nominally pure KCl and KCl doped with Mg2+, Ca2+, Sr2+ or Ba2+ were deformed by compression at 77–254 K; during the tests strain-rate cycling was conducted in association with ultrasonic oscillation. The data were analyzed in terms of strain-rate sensitivity ((Δτ′/Δlneέ)) versus stress decrement (Δτ). The curve for KCl doped with the divalent impurities has two bending points and two plateau regions. It is proposed that the variation of strain-rate sensitivity at the second plateau place on the curve with shear strain (Δ(Δτ′/Δlneέ)/Δe) is due to a change in forest dislocation density with shear strain. The forest dislocation density for the specimens seemed to increase by the divalent additions in the compression test on account of the jogs on the screw dislocations. It depended on the concentration of impurities and also on the size of impurity in the specimens at a given temperature. Unfortunately, it was not possible to determine whether a change in the size of impurity influences mobile dislocation density, ρ, from the values of Δρ/Δτ′ for KCl doped with Ca2+, Sr2+ or Ba2+.

Strain rate sensitivity effects with forming characteristics of superplastic Ti6Al4V

Tensile superplastic deformation of Ti6Al4V sheet material has been studied in the temperature range 875–950°C and at strain rates 5 × 10 −4 s −1, 1 × 10 −3 s −1, and 5 × 10 −3 s −1. The strain rate sensitivity variation with strain, total elongations, and the thickness and width profiles of the deformed specimens were measured for the above experimental conditions. The results have been analyzed and verified for their practical significance in superplastic forming.

Influence of variation of strain rate sensitivity on limit strain of superplasticity

Superplasticity is associated with large tensile elongation and high strain rate sensitivity. This paper analyzes theoretically the influence of variation of high strain rate sensitivity on necking and limit strain. Topics considered include metals, plasticity, strain rate, tensile properties, elongation, and sensitivity analysis.