Stress-strain Rate Relationship Research Articles

Stress-strain rate relations for high-temperature deformation of two-phase Al-Cu alloys

Al-Cu alloys containing 6, 11, 17, 24 and 33 wt% Cu, annealed for 0.5–100 h, were deformed by the differential strain-rate test technique over a strain-rate range of ≈4×10−6 to 3×10−2s−1 at temperatures ranging from 460–540°C. Superplastic behaviour, with strain-rate sensitivity, m≈0.5, and activation energy, Q=171.5 kJ mol−1, is shown by the Al-24Cu and Al-33Cu alloys at lower strain rates and higher temperatures. All the alloys show m≲0.20 at higher strain rates, but the average activation energy for deformation of the Al-6Cu, Al-11Cu, and Al-17Cu alloys is evaluated to be 480.7 kJ mol−1, in contrast to a lower value of 211 kJ mol−1 for the Al-24Cu and Al-33Cu alloys. Instead of grain size, the mean free path between θ particles is suggested to be a more appropriate microstructural parameter for the constitutive relationship for deformation of the Al-Cu alloys.

High temperature deformation behavior of physical vapor deposited Ti-6Al-4V

A detailed study has been conducted of the high temperature creep and microstructural evolution accompanying the creep deformation of an initially nanocrystalline Ti-6Al-4V alloy. For test temperatures of 600 and 680°C the alloy transformed from an ( α + α′) to a single phase α during creep testing and exhibited exceptionally low creep resistance. During testing between 760 and 900°C, the alloy transformed to a conventional ( α + β) microstructure and exhibited up to ten times the creep rates of conventional grain size (superplastic) Ti-6Al-4V. Creep models based on grain boundary sliding, dislocation and diffusional creep were combined with relationships for phase evolution and grain growth to predict stress—strain rate relationships at each test temperature. The analysis indicates that in the low temperature region dislocation accommodated GBS, in conjunction with diffusional flow, are responsible for creep whilst in the high temperature region diffusion accommodated GBS is the dominant mechanism.

A proposed deformation mechanism for high strain-rate superplasticity

Superplasticity at high deformation rates is desirable in order to make superplastic forming more practical. Recently, superplasticity was achieved at strain rates between 10{sup {minus}2} and 100 s{sup {minus}1} in powder-metallurgy (PM) processed and mechanically alloyed (MA) aluminum alloys. The purpose of this paper is to understand the rate-controlling-deformation mechanisms for ultrafine-grained aluminum materials where high-strain-rate superplasticity is observed. The stress-strain rate relations for IM, PM and MA materials are analyzed in terms of deformation mechanism maps, and in terms of the contribution of subgrain boundaries to the enhancement of grain boundary sliding. Conclusions are as follows: (1) Lattice-diffusion-controlled grain boundary sliding is believed to be the rate-controlling mechanisms for high-strain-rate superplasticity in PM and MA aluminum alloys. (2) Construction of deformation mechanisms maps based on diffusional creep, grain boundary sliding and dislocation creep illustrate the importance of grain size in achieving high-strain- rate-superplasticity. (3) The Ball-Hutchinson model for grain-boundary sliding has been modified to include the influence of subgrain size in enhancing the grain boundary sliding process. (4) The introduction of threshold stress for grain boundary sliding and the important contribution of grain and subgrains permit unification of all superplastic IM, PM and MA aluminum data available.

High temperature plastic flow in TiC-20wt.%Mo 2C-20wt.%Ni cermet

High temperature plastic flow in TiC-20wt.%Mo 2C-20wt.%Ni with a carbide grain size of 1.93 μm is examined at temperatures between 1100 and 1225 °C in compression testing. The flow stress is largely dependent on temperature and strain rate. The log-log plot of stress vs. strain rate is represented by a sigmoidal relationship and is divided into three regions at a constant temperature. The strain rate sensitivity exponent takes the highest value of about 0.6 in the intermediate strain rate region. The stress-strain rate relationship is similar to that in superplastic metals. The rate-controlling mechanism is considered to be the sliding along the carbide-carbide boundaries in the intermediate strain rate region and the dislocation climb in carbide grains in the high strain rate region. The transition from the low to intermediate strain rate region is also discussed.

Remaining life assessment of high temperature components using threshold stress concept

The paper first presents global experience, including that of our laboratory, mainly with power plant components to show that it is possible to extend the life of some critical components 2–3 fold over the design life. Different approaches for remaining life assessment are also briefly discussed.It appears that the main creep damage in so far as Cr-Mo and Cr-Mo-V steels are concerned, is an accumulation of creep strain. Hence, this paper suggests a new approach for creep life prediction based on threshold stress concept and stress-strain rate relationship. The approach is based on the analysis of creep and hot tensile data generated on a popular 1 Cr-0·3 Mo-0·25 V steel in the service exposed and the virgin states and also on samples with a wide range of microstructures prepared from the virgin states. A summary of the main finding leading to development of a new approach has been given.

Modelling superplastic deformation of materials with a nonequiaxed microstructure

The superplastic deformation behaviour of a two-dimensional nonequiaxed microstructure is investigated on the basis of the grain-rolling mechanism proposed by Paidar and Takeuchi for an equiaxed microstructure. Analysis shows that not only the deformation geometry but also the dynamics of grain boundary dislocation activity will be altered if grains are elongated rather than equiaxed. Constitutive equations thus derived indicate that the grain aspect ratio can impose a remarkable influence on the superplastic stress-strain rate relationship and such an influence can be quite different if the orientation of the applied stress lies over an angle with respect to the longer axis of the grains. The complexity of modelling the superplastic deformation of engineering materials is also discussed.

Anisotropic, transversely isotropic nonlinear viscosity of rock ice and rheological parameters inferred from homogenization

Abstract The stress-strain rate relations for an anisotropic, incompressible viscous body that is orthotropic, transversely isotropic, are drawn from symmetry considerations. This kind of material forms the largest part of polar ice sheets. The 10 parameters entering the rheological law would be extremely difficult to draw from torsion-compression tests, the only ones that are feasible on ice cores. Nevertheless, homogenization allows to infer them from the statistical distribution of the c- axes and only two parameters that are accessible by readily analyzed pure shear tests. Homogenization is done assuming for any crystal embedded in rock ice a rheology that differs from the one of isolated monocrystals and microscopic stresses at the crystal level equal to the macroscopic stress. Both assumptions are argued, in the light of experimental evidence about a single system of active slip planes, very low dislocation velocities, pile-ups at the grain boundaries, and boundary migrations during strain. These migrations destroy the pile-ups, besides allowing the strains in neighbour crystals to be different.

Influence of flow rule and inertia on the ductile growth of voids

As far as only volume changes are considered, the analysis of void growth during plastic straining of a material can be reduced to the two simple cases of (i) a cylindrical cavity submitted to axial and axisymmetric radial remote loads and (ii) a spherical cavity submitted to remote uniform mean stress. The latter are investigated for materials exhibiting either a power law or a linear stress-strain rate relationship. The influence of strain hardening is also considered in the case of spherical geometry. Finally, inertia effects are investigated. It is shown that both the linear strain rate dependence and inertia effects are likely to decrease void growth rate and thus to improve ductility at high strain rate.

Orientation history and rheology in slates, Kodiak and Afognak Islands, Alaska

Theoretical and experimental studies have shown that slates have a roughly parabolic yield curve in φ - σ and Φ - σ space, where φ is the orientation of cleavage relative to the maximum compressive stress, Φ is the orientation of cleavage relative to the incremental shortening direction and σ is the deviatoric stress. Deformation mechanisms that operate in low-grade rocks such as diffusive mass transfer in a grain boundary fluid, dislocation creep and frictional grain boundary sliding may have stress-strain rate relationships that depend on φ. During a progressive strain history, φ and Φ may vary as a function of the strain path. Thus, the sequence of dominant deformation mechanisms as well as the stress-strain history may depend on the orientation history or variations in Φ as strain accumulates. In the Kodiak Formation, a slate belt in southwest Alaska, the orientation history and deformation mechanisms were evaluated using incremental strain indicators and microstructures. There are four successive textural events: (1) development of a slaty cleavage ( S 2) with antitaxial growth of fibrous quartz and mica in pressure shadows ( Fi 2); (2) static growth of siderite and chlorite porphyroblasts; (3) 10–70° rotation of porphyroblasts relative to S 2 with growth of curved syntaxial siderite fibers; and (4) antitaxial growth of fibrous quartz and micas with local development of a crenulation cleavage ( S 3). Cumulative incremental strain and progressive finite strain histories were determined in 23 samples from syntectonic fibers, and orientation histories were reconstructed from information provided by cumulative incremental strain histories. Textural and strain analyses indicate that: (1) the strain history of nearly all samples can be approximated by two coaxial strain accumulations separated by a rigid rotation; (2) development of crenulation cleavages was dependent on the orientation history and the magnitude of the early strain accumulation (i.e. the degree of mica alignment at the completion of D 2); (3) unstable behavior, or buckling, occurred when suggesting that the angle of internal friction (Ψ) was close to 0° (i.e. basal slip in micas may have been more important than frictional grain boundary sliding); and (4) diffusive mass transfer was accompanied by anisotropic plastic deformation, so the orientation history could be used to reconstruct the σ - ϵ history.

Thermomechanical processing of titanium, zirconium, magnesium, and zinc in the hcp structure

In the hot working range, these hexagonal close-packed (hcp) metals undergo dislocation deformation with formation of a dynamically recovered substructure at low strains. The stress-strain rate relationship follows the sinh law and the Arrhenius temperature relationship has activation energies similar to creep. Because of adequate slip systems, the low (c/a) axial ratio metals, α-Ti and α-Zr, exhibit well-recovered substructures, with size inversely related to flow stress, up to high strain. Because of the transformation to β at about 0.6T m they do not exhibit dynamic recrystallization. The high c/a ratio metals, Mg and Zn, exhibit mainly basal slip at lower temperatures, but at higher, temperatures exhibit increasing amounts of prismatic slip, which is concentrated near grain boundaries. As the strain rises, subgrain misorientation increases, leading to dynamic recrystallization at the boundaries at which shear zones develop. The hot ductilities are much less than face-centered cubic (fcc) metals because neither dynamic recovery nor recrystallization are as effective in relieving intergranular sliding and fissuring.

除荷過程中のクリープき裂伝ぱ

Crack propagation under sustaining or increasing load conditions in monotonic creep and time-dependent fatigue has been described successfully by the creep J-integral. This paper extends the creep J-integral concept to the crack propagation in decreasing load conditions. Because the J-integral can be originally defined for a linear or nonlinear elastic body even in an unloading condition although it can not for a plastic body, and because the creep J-integral in a creep body is analogous to the J-integral in an elastic one, the creep J-integral can be expected to be valid in the decreasing load (stress relaxation) condition when a unique stress-strain rate relation exists. Crack propagation tests of 0.16% carbon steel were carried out in creep and time-dependent fatigue conditions with the stress relaxation. As the result, the crack propagation rate had a good correlation with the creep J-integral for the stress relaxation period. In time-dependent fatigue, moreover, the crack propagation rate was correlated well with the creep J-integral (or creep J-integral range) independently of the stress waveform. These show the applicability of the creep J-integral concept for crack propagation during the stress relaxation.

On perfectly stress field at a mixed-mode crack tip under plane and anti-plane strain

In [1], under the condition that all the perfectly plastic stress components at a crack tip are functions of ϕ only, making use of equilibrium equations, stress-strain rate relations, compatibility equations and yield condition. Lin derived the general analytical expressions of the perfectly plastic stress field at a mixed-mode crack tip under plane and anti-plane strain. But in [1] there were several restrictions on the proportionality factor γ in the stress-strain rate relations, such as supposing that γ is independent of ϕ and supposing that γ=c or cr−1. In this paper, we abolish these restrictions. The cases in [1], γ=crd (n=0 or-1) are the special cases of this paper.

Rigid-Plastic Finite Element Method for Frictional Materials

The rigid-plastic finite element method for frictional materials is developed. We derive the stress-strain rate relation for rigid plastic materials of the Drucker-Prager type under the assumption of the associated flow rule. We show that it is convenient in the derivation to decompose the stress into two components which are similar to the mean and deviatoric ones in case of materials of the von Mises type. The materials with a relatively high internal friction angle, however, shows somewhat unreasonable velocity field due to the excessive effect of the dilatancy. Therefore, we also develop a numerical technique for the non-associated flow rule to reduce such an effect. We find that the dilatancy angle influences the bearing capacity of the soil structure as well.

The stress—strain-rate relation for transversely isotropic, incompressible fluid

The stress—strain-rate relation for transversely isotropic, incompressible fluid

Red cell deformability and its relevance to blood flow.

The resistance to blood flow is a function of the rheological properties of blood as well as the geometric features of blood vessels. While circulatory investigations generally aim at studying the functions of the heart and blood vessels, there is an increasing realization that blood rheology can also play a significant role in circulatory regulation in health and disease (10, 11). The principal factors determining blood viscosity are hematocrit, plasma viscos­ ity, cell aggregation, and cell deformability (8). This review focuses on the role of the deformability of the red blood cell (RBC) in circulatory regulation under physiological and pathophysiological conditions. 1 Deformability is a relatively general term that describes the ability of a body (RBCs in this case) to change its shape in response to a deforming force. RBC deformation (or strain) can involve a change in cell curvature, a uniaxial deformation, or area expansion (3, 33). The deforming stress (force per unit area) is usually applied from outside the cell, e.g. by fluid shear stress or local membrane aspiration, but it can also originate from within the cell, e.g. RBC swelling in hypotonic medium or fiber formation in deoxygenated sickle cells. The extent, rate, and mode of deformation depend on the magnitude, rate, and direction of the stress. Therefore, the stress-strain (and stress-strain rate) relationships are complex and cannot be described by a single deformability parameter.

On the convected linear stability of a viscoelastic Oldroyd B fluid heated from below

We investigate the linear stability problem of convection by the general Oldroyd B fluid and its Maxwell limit in the presence of rigid or free boundaries and fixed temperature or fixed flux. Comparison with recent results by Rosenblat [9] for the analytically accessible case of free boundary conditions shows a qualitative similarity in the shape of the neutral stability curves. But while Newtonian and Jeffreys (general Oldroyd B) fluids are sharply stabilized by the presence of rigid boundaries, the Maxwell fluid is largely unaffected at even moderately large Prandtl number. The reasons for this are discussed. Also, a discrepancy between the earlier works by Vest and Arpaci [3], and Sokolov and Tanner [4], which treat the case of a Maxwell fluid, is found to be due to algebraic error, and not multivaluedness of the stress-strain rate relation as earlier suggested by Eltayeb [6].

High temperature plastic deformation of two V-Ga alloys with A15 structure

A study of high temperature plastic deformation has been undertaken on alloys of V-18 at. pct Ga and V-23 at. pct Ga. The materials were prepared by arc melting, homogenizing, and transformation annealing, resulting in polycrystalline A15 structure. Through compression testing and load-relaxation testing, plastic deformation has been studied over a strain rate range from 10-6 to 10-2/s and a temperature range from 1000 to 1300 °C. Flow stress decreases with increased temperature and decreased strain rate. Stress-strain rate relations may be fitted with a power law creep expression. The flow stress is influenced by the length of the 1150 °C transformation anneal; longer anneals result in a decrease in flow stresses projected from load relaxation testing. Analysis of compressive yield strength data places the activation energy for A15 V-Ga creep roughly in the 400 kJ/mol range.

Densification behaviour of ceramic powder

A three-dimensional compaction device has been developed to carry out compaction of a ceramic powder. The details of the device, which provides compaction with various stress ratios, are described. A densification criterion for the powder is proposed; this is similar to that for the case for metal powders, but the role of the hydrostatic stress component appears to be different. Stress-strain rate relations are then derived using the concept of plastic potential; experimental results show that the normality of the strain rate vector to the surface which corresponds to the criterion almost holds.

Flow-stress mapping from extrapolated laboratory data

Flow stresses predicted from the generalized hyperbolic sine, flow stress—strain rate relationship and a small programme of hot-torsion and hot-compression tests have been shown to give good agreement with actual extrusion pressures when inserted into established models. The extrapolated data are used to predict an activation energy which enables the data to be presented as a single linear relationship which may find some use in automatic control systems for deformation schedules or provide the foundation of a database for storage, interpolation and extrapolation of flow-stress estimates.

The strain rate sensitivity values in superplastic deformation

Fine-grained superplastic α-β Ti-6Al-4V alloy (where the alloy composition is given in approximate weight per cent) was deformed in the temperature range 750–925°C and at strain rates of 10 −5 −2 × 10 −3 s −1. The results indicate that an increase in the deformation temperature or a decrease in the deformation rate is followed by an increase in the value of the strain-hardening index. In such a situation the stress-strain rate relation can no longer be represented by the conventional power law formulation without evaluating the effect of strain. The common assumption that a large value of the (apparent) strain rate sensitivity parameter is associated with a large amount of superplastic ductility may not be tenable under test conditions where a strain-hardening or strain-softening effect is noticeable.