Rate Sensitivity Of Flow Stress Research Articles

A simple dislocation model of deformation resistance of ultrafine-grained materials explaining Hall–Petch strengthening and enhanced strain rate sensitivity

A model is presented where the properties of ultrafine-grained (UFG) materials are explained in terms of the influence of high-angle boundaries on the rates at which dislocations are stored and recovered at the boundaries. The model reproduces the experimental observations that UFG materials reach a steady state where the deformation resistance is independent of strain, that the strain rate sensitivity of flow stress is relatively high and that the steady-state flow stress increases inversely with the square root of grain size. The model results are compared to experimental data for UFG Cu and nanostructured Ni.

High temperature tensile properties and their application to toughness enhancement in ultra-fine grained W-(0-1.5)wt% TiC

Ultra-fine grained (UFG) W-TiC consolidates are very promising for use as divertors in fusion reactors, however, the assurance of room-temperature ductility of UFG W-TiC remains unsettled. The assurance requires a sufficient degree of plastic working for the consolidates and thus overcoming of poor plastic workability in UFG W-TiC by applying superplasticity. Therefore, the magnitudes of elongation to fracture and flow stress which are important measures for plastic working were examined for UFG W-(0–1.5)%TiC (in wt%) at 1673–1973 K where superplasticity occurs without appreciable grain growth. It is shown that the elongation and flow stress are strongly dependent on TiC addition and atmosphere (Ar, H 2) during mechanical alloying (MA). As the TiC addition increases, the elongation significantly increases without appreciable increase in the flow stress level. W-TiC fabricated with MA in H 2 exhibits larger elongation and larger strain rate sensitivity of flow stress than W-TiC with MA in Ar. These results were applied to perform plastic working and the room-temperature bend test results for plastic worked W-1.0%TiC are shown.

Formability of Ultrafine-Grain Mg Alloy AZ31B at Warm Temperatures

Warm formability of ultrafine-grain (UFG) AZ31B Mg alloy in the range of 150 °C to 311 °C is investigated. Refinement of grain size significantly improves the formability primarily through increasing strain rate sensitivity of flow stress and increasing diffuse quasi-stable flow, as compared with the coarse-grain AZ31B alloy. Strain rate sensitivity increases with increasing temperatures, and seems to be connected with dynamic recovery and grain boundary processes. For fine-grain sizes, twinning is inhibited. At 200 °C and strain rates below 2 × 10−4 s−1, the UFG AZ31B alloy demonstrates a high rate of strain hardening up to a true strain of 0.6, in addition to its high strain rate sensitivity, which is responsible for its enhanced formability. Examination of the microstructure shows that there is competition between dynamic grain growth and grain refinement during deformation at modest warm forming temperatures, the former causing hardening and the latter causing softening. Increasing the test strain rate and starting with larger grain size initiates deformation twinning during forming, and assists in the refinement of the coarser grains followed by recrystallization.

Deformability enhancement in ultra-fine grained, Ar-contained W compacts by TiC additions up to 1.1%

Nano-sized Ar bubbles give negative influence on the fracture resistance and occurrence of superplasticity in ultra-fine grained (UFG) W–TiC compacts. In order to enhance deformability in UFG, Ar-contained W–TiC compacts, effects of TiC addition on the high-temperature deformation behavior were examined. W–TiC compacts with TiC additions of 0, 0.25, 0.5, 0.8 and 1.1 wt% were fabricated by mechanical alloying in a purified Ar atmosphere and hot isostatic pressing. Tensile tests were conducted at 1673–1973 K (0.45–0.54 T m, T m: melting point of W) at initial strain rates from 5 × 10 −5 to 5 × 10 −3 s −1. It is found that as TiC addition increases, the elongation to fracture significantly increases, e.g., from 3 to 7% for W–0 and 0.25TiC/Ar to above 160% for W–1.1TiC/Ar when tested at 1873 and 1973 K at 5 × 10 −4 s −1. The flow stress takes a peak at 0.25%TiC and decreases to a nearly constant level at 0.5–1.1%TiC. The ranges of the strain rate sensitivity of flow stress, m, and the activation energy for deformation, Q, with TiC additions are 0.17–0.30 and 310–600 kJ/mol, respectively. The observed effects of the TiC additions on the tensile properties are discussed.

Are rate sensitivity and strength effected by cross-slip in nano-twinned fcc metals

Synthesis of nano-twinned pure Cu by Lu et al. [L. Lu, R. Schwaiger, Z. W. Shan, M. Dao, K. Lu, S. Suresh, Nano-sized twins induce high rate sensitivity of flow stress in pure copper, Acta Mater. 53 (2005) 2169–2179] has produced materials with extremely attractive properties of combined high strength, strain rate sensitivity, and ductility adequate for applications. This note explores the underlying mechanistic reasons for this via a model analysis of dislocation interaction with nano-twinned boundaries. Interestingly, we find that processes like cross-slip, that lead to the absorption and transmission of slip through twin boundaries yet are normally associated with rate insensitive behavior, can lead to high strength and rate sensitivity as observed in experiment.

Deformation kinetics of nanocrystalline nickel

The work hardening and the strain rate sensitivity of flow stress were studied in the temperature range from 298 to 473 K for nanocrystalline (NC) nickel with average grain sizes of about 25 and 80 nm produced by pulsed electrodeposition. The rate of work hardening, the maximum flow stress and the strain rate sensitivity of flow stress increase with decreasing grain size. The data are compared to published data for NC Ni and found to be consistent. The common analysis of strain rate sensitivity in terms of thermal activation is critically discussed. It is proposed that the activation analysis gives information about thermally activated processes at grain boundaries which may be related with recovery of dislocations.

Superplastic deformation in W–0.5 wt.% TiC with approximately 0.1 μm grain size

In order to reveal the occurrence of superplasticity in ultra-fine grained W–TiC, W–0.5 wt.% TiC consolidates were fabricated utilizing mechanical alloying (MA) in purified H 2 (W–0.5TiC–H 2) or Ar (W–0.5TiC–Ar) and hot isostatic pressing. The W–0.5TiC–H 2 and W–0.5TiC–Ar feature equiaxed ultra-fine grains with average diameters of 150 and 70 nm, respectively, and W–0.5TiC–Ar contains a high density of nano-sized Ar bubbles. Tensile tests were conducted at 1673–1973 K (0.45–0.54 T m, T m: melting point of W) at initial strain rates from 5 × 10 −5 to 5 × 10 −3 s −1. It is found that W–0.5TiC–H 2 exhibits a large strain rate sensitivity of flow stress, m, of 0.5–0.6, which is a feature of superplastic materials, whereas W–0.5TiC–Ar exhibits a smaller m value of approximately 0.2. This suggests that the Ar bubbles cause an adverse effect on superplastic deformation. The activation energy for deformation is 300 kJ mol −1 for W–0.5TiC–H 2 and 570 kJ mol −1 for W–0.5TiC–Ar, corresponding to those for grain boundary diffusion and lattice diffusion in W, respectively. Each deformation controlling mechanism is discussed.

On the elevated-temperature deformation behavior of polycrystalline Cu subjected to predeformation by multiple compression

Strain rate sensitivity of flow stress and creep resistance were studied during creep at elevated temperature of 373 K as function of prestrain in multiple uniaxial compression at room temperature for pure Cu99.99 with initial grain size d ≈ 50 μ m. Moderate prestrains ≤ 2 strengthen the material by formation of subgrains with low-angle boundaries, while severe prestrains enhance the strain rate sensitivity and soften the material in the saturation state of deformation. The results are discussed in terms of increase of the fraction of high-angle boundaries in the subgrain structure produced by severe prestraining influencing the balance of generation and annihilation of dislocations.

Current status of ultra-fine grained W–TiC development for use in irradiation environments

Ultra-fine grained (UFG) W–TiC with a high purity matrix of low dislocation density is expected to exhibit improve resistance to irradiation with neutrons and helium ions and the room temperature mechanical properties. Aiming at such UFG W–TiC with the desired microstructure, powders of W with 0.25–0.8 wt% TiC additions were subjected to mechanical alloying (MA) and hot isostatic pressing (HIP), where purified H2 and Ar were used as the MA atmosphere. Microstructural observations and room- and high-temperature mechanical tests were performed for UFG W–TiC before and after neutron irradiation to a fluence of 2×1024 n m−2 at 873 K. It is shown that the MA atmosphere significantly affects grain refinement, room-temperature strength and high-temperature tensile plasticity of UFG W–TiC. W–0.5TiC with H2 in MA (W–0.5TiC–H2) shows a larger strain rate sensitivity of flow stress, m, of 0.5∼0.6 at temperatures from 1673 to 1973 K, which is a feature of superplastic materials. Whereas W–0.5TiC–Ar shows a smaller m value of approximately 0.2. No radiation hardening is recognized in UFG W–0.5TiC–H2 and W–0.5TiC–Ar.

Deformation behavior of ultrafine-grain (UFG) AZ31B Mg alloy at room temperature

To facilitate the wider application of wrought Mg alloys as structural materials, it is desirable to improve the formability and minimize the strength anisotropy inherent in these materials due to low symmetry of their hexagonal close-packed crystal structure. Grain refinement provides a potential approach to achieve these goals in Mg alloys. A study of grain refinement processing is presented in a companion paper [Yang Q, Ghosh AK. Acta Mater, in press]. The present paper deals with the formability of ultrafine-grain (UFG) Mg close to room temperature that has not been explored in the past. The present work examines such effects in UFG Mg prepared from hot-rolled plates by severe plastic deformation. Tension and compression tests in both in-plane and normal-to-plane directions are carried out on coarse- and fine-grain AZ31B Mg alloy at room temperature. It is found that the strain rate sensitivity of flow stress increases considerably due to grain refinement, and it enhances post-uniform elongation in a tension test. At the same time, yield strength is significantly enhanced and becomes more isotropic in the UFG alloy compared to the coarse-grain alloy. A rationale for enhanced strain rate sensitivity is presented, but this topic will be explored in greater detail in future papers.

Unified Constitutive Equations of Viscoplastic Deformation: Development and Capabilities

This paper addresses a viscoplastic constitutive model that allows a consistent way of modeling positive and negative rate sensitivities of flow stress, which is associated with dynamic strain aging occurring in a certain regime of loading rates and temperatures. Based on the concept of continuum mechanics, a phenomenological constitutive model includes the use of a yield surface within the framework of unified viscoplastic constitutive equations. An extension of modeling capability to negative rate sensitivity of flow stress is accomplished through a rate-dependent format of nonlinear kinematic hardening rule that causes the back stress to be rate-dependent. The negative rate sensitivity of the back stress enable to predict the influence of prior strain rate on relaxation behavior, which means that the relaxed stress of the fastest prior strain rate has the smallest magnitude at the end of relaxation period.

Strain rate sensitivity of flow stress under superimposition of ultrasonic oscillatory stress during plastic deformation of RbCl doped with Br − or I −

Strain rate cycling tests were carried out under superimposition of ultrasonic oscillation during plastic deformation of RbCl single crystals doped with Br − or I −. The relation between the strain rate sensitivity λ ( = d τ / d ln ⁡ ε ˙ ) of flow stress and stress decrement Δ τ due to application of oscillation has a stair-like shape and is divided into three regions, two plateaus at low and high Δ τ and the decreasing λ region between them. The stress decrement τ p at the first bending point is considered to be the effective stress due to an impurity and the value of λ p, the difference in λ between the first and second plateau regions is also a part of λ due to an impurity. Values of τ p and λ p were measured from 77 K to room temperature. Assuming the Cottrell–Bilby relation for RbCl crystals doped with Br − or I −. The interaction energies between dislocation and Br − or I − were determined to be 0.50 or 0.58 eV in RbCl, respectively.

Nano-sized twins induce high rate sensitivity of flow stress in pure copper

We have investigated the rate sensitivity of flow stress and the extent of strengthening in polycrystalline copper containing different volume fractions of nano-sized twins, but having the same average grain size. The specimens were produced by pulsed electrodeposition, wherein the concentration of twins was varied systematically by varying the processing parameters. Depth-sensing instrumented indentation experiments performed at loading rates spanning three orders of magnitude on specimens with the higher density of twins (twin lamellae width ∼20 nm) revealed an up to sevenfold increase in rate-sensitivity of hardness compared to an essentially twin-free pure Cu of the same grain size. A reduction in twin density for the same grain size (with twin lamellae width ∼90 nm) also resulted in a noticeable reduction in rate-sensitivity and hardness. The presence of a high density of nano-scale twins is also seen to impart significant hardness, which is comparable to that achieved in nano-grained Cu. Post-indentation analyses of indented Cu with nano-scale twins in the transmission electron microscope reveal deformation-induced displacement of coherent twin boundaries (CTBs), formation of steps and jogs along CTBs, and blockage of dislocations at CTBs. These processes appear to significantly influence the evolution of thermal activation volume for plastic flow which is some three orders of magnitude smaller than that known for microcrystalline Cu. Transmission electron microscopy also reveals CTBs with a high density of dislocation debris and points to the possibility that displaced CTBs may serve as barriers to dislocation motion and that they may also provide sources for dislocation nucleation, especially near stress concentrations, very much like grain boundaries. Possible consequences of these trends for deformation are explored.

Multiscale Analysis and Numerical Modeling of the Portevin-Le Chatelier Effect

The Portevin-Le Chatelier (PLC) effect refers to one type of plastic instability, which often manifests itself as discontinuous yielding and localized deformation in some metallic alloys deformed under certain conditions. A phenomenological model based on a multiscale analysis is developed to investigate the PLC effect. In this model, a new component of stress is introduced, which takes account of the collective interactions between mobile dislocations and solute atoms, to describe the influence of dynamic strain aging (DSA) on the flow stress. The effects of microscopic pinning and unpinning of dislocations on the macroscopic deformation behavior are considered in an integrative and competitive manner. Due to the competition of these two effects during deformation, the alloys may exhibit the negative strain rate sensitivity of flow stress, which is a necessary condition for the occurrence of the PLC effect. A nonuniform spatial distribution of some material parameters was used in the model to reflect the heterogeneous nature of the deformed material, including a linear change of the initial cross-sectional area and a random perturbation of the initial internal stress. Numerical simulations based on this heterogeneous model were carried out for tensile testing of aluminum alloy 2017, by which the serrated yielding and localized deformation behavior were successfully reproduced. The results also indicate the relation between the macroscopic jerky flow and the pinning/unpinning of dislocations at the micro level.

Does nanocrystalline Cu deform by Coble creep near room temperature?

The proposal that nanocrystalline Cu produced by electro deposition (ED) creeps at temperatures slightly above room temperature by diffusive flow via grain boundaries (Coble creep) has been checked by compression tests. It was found that the minimum creep rates obtained in tension are significantly larger than those in compression, probably due to interference of tensile fracture. Scanning electron microscopic investigation showed that the spacing between large-angle grain boundaries is about 10 μm rather than the reported value of 30 nm. Comparison with coarse grained and ultrafine grained Cu produced by equal channel angular pressing showed that the ED-Cu work hardens similarly to coarse grained Cu in contrast to ultrafine grained Cu which reaches its maximum deformation resistance within a small strain interval of 0.04 and has distinctly higher strain rate sensitivity of flow stress. The present results are consistent with the established knowledge that there is no softening by grain boundaries, e.g. due to Coble creep, near room temperature in Cu with grain sizes above 1 μm. The grain boundary effect observed in ultrafine grained Cu is interpreted in terms of modification of dislocation generation and dislocation annihilation by grain boundaries.

Plastic deformation behaviour in Ni 3Ti single crystals with D0 24 structure

The plastic deformation behaviour of Ni 3Ti single crystals with the D0 24 structure was investigated in compression tests. Two slip planes of the type {1 1 ̄ 00} and (0001) were selected depending on crystal orientation. Temperature dependences of the critical resolved shear stress (CRSS), strain rate sensitivity of flow stress, activation volume and dislocation structure were examined. Anomalous strengthening slightly appeared for the {1 1 ̄ 00}<11 2 ̄ 0> prism slip system in a narrow temperature range between 300 and 500 °C. Accompanying the yield stress anomaly (YSA) were small jogs formed on 1/3<11 2 ̄ 0> screw dislocations, acting as pinning points for motion of the dislocations and resulting in a zigzag shape of dislocation lines inclined to the Burgers vector by ±15~20°. In contrast, a remarkable YSA was found for the (0001) basal slip system over a wide temperature range between −196 and 800 °C. At low temperatures at and below 300 °C, 1/3<2 1 ̄ 1 ̄ 0> superlattice dislocations were dissociated into two 1/3<10 1 ̄ 0> super-Shockley partials bounded by an SISF after unloading. Above 300 °C, the dissociation mode of 1/3<2 1 ̄ 1 ̄ 0> superlattice dislocations changed to APB-type splitting accompanied by a large increase in CRSS. The strong YSA was caused by the Kear-Wilsdorf locking of 1/3<2 1 ̄ 1 ̄ 0> screw dislocations from the (0001) slip plane onto the {01 1 ̄ 0} planes.

Mechanism of the HIP bonding of Zircaloy-4 in the α-phase field

The HIP bonding of as-received annealed Zircaloy-4 sheet of relatively large grain size has been investigated at elevated temperatures (770–810 °C) in the α-phase field. Studies of plastic flow behaviour showed that the material had a constant strain rate sensitivity of flow stress, m∼0.2, ( n∼5) over a wide range of strain rates. The activation energy over this temperature range was consistent with power law creep as the rate controlling process for deformation. Bonding studies at 800 °C showed that interface void closure occurred by constrained plastic collapse and diffusion. The progressive increase of plastic constraint during void closure led to a dominance of diffusion. When the constraint of inter-void ligaments was introduced into an earlier model, this gave an improved agreement between prediction and experiment for diffusion bonding (DB) of the α-phase.

On the mechanism of dislocation creep of calcite at high temperature: Inferences from experimentally measured pressure sensitivity and strain rate sensitivity of flow stress

Previous laboratory experiments on coarse grained calcite materials at intermediate conditions of stress and temperature have shown low strain rate sensitivity of flow stress, expressed by standard power law stress exponents n ≥ 7. This conflicts with conventional models for creep controlled by dislocation climb (n = 3–4.5), a recovery mechanism widely used to explain steady‐state dislocation creep. This paper addresses the question whether dislocation cross slip rather than climb is the mechanism controlling creep of calcite at intermediate conditions. New uniaxial compression tests were performed on calcite single crystals and Carrara marble at T = 800–1000°C, = 10−4–2 × 10−7 s−1, and P = 100–600 MPa. Emphasis was on the pressure (P) and strain rate () sensitivity of flow stress, because these form potential ways for discriminating between climb and cross slip models. Both single crystals and Carrara marble demonstrated a small increase in flow stress with increasing pressure (∼1.6% per 100 MPa) at constant strain rate and temperature. The low strain rate sensitivity of flow stress was confirmed, though n gradually changes with stress or temperature rather than taking a constant value. Evaluation of the experimental data against microphysical models indicated that cross slip controlled by dissociation of dislocations offers the best explanation for the observed mechanical behavior. If the associated creep equation is used to estimate flow stresses under natural conditions, the resulting values at T &lt; 500°C are substantially less than those following from previous flow laws. The influence of pressure on the behavior of marble, however, can be safely ignored for most practical purposes.

Effects of Temperature, Strain Rate and Ferrite Grain Size on Tensile Flow Stress for Ferrite-Pearlite Steels.

Tensile tests below room temperature were conducted to investigate effects of temperature, strain rate and ferrite grain size on tensile flow stress for ferrite-pearlite (FP) steels with ferrite grain sizes between 3.6 and 46.2 μm. The temperature and strain rate sensitivity of flow stress for the FP steels is almost independent of ferrite grain size. The flow stress for the FP steels is expressed by Hall-Petch equation; σ=σ0+KD-1/2, where D refers to ferrite grain size and σ0 and κ constants. The slope κ of the equation is almost identical being independent of strain, temperature and strain rate. By summarizing the experimental results, it is possible to describe the flow stress of the FP steels by the following equation, σ=σt+182+5.8D-1/2+900ε where σt and ε mean thermal component of stress and true strain, respectively; σt is influenced by ε, temperature and strain rate.

Superplastic behaviour of ultrafine-grained Ti–6A1–4V alloys

Superplastic behavior of the ultrafine-grained (UFG) Ti–6A1–4V alloy produced by high pressure torsion (HPT) has been studied. High elongations (more than 500%) have been observed in this alloy during tensile tests at relatively low temperatures and high strain rates. At the same time, the superplastic behavior of this alloy has several specific features such as the relatively low values of strain rate sensitivity of flow stress and significant strain hardening. Moreover, it was shown that the alloy, processed by HPT, demonstrates an outstanding room temperature strength about 1500 MPa after superplastic deformation.