Stress Dependence Of Dislocation Velocity Research Articles

Modeling of the elastic precursor behavior and dynamic inelasticity of tantalum under ramp wave loading to 17 GPa

In a previous study by Asay et al. [J. Appl. Phys. 106, 073515 (2009)], the inelastic response of annealed and cold-rolled pure polycrystalline tantalum at intermediate strain rates was characterized with ramp wave loading to peak longitudinal stresses of 17 GPa. It was found that the annealed Ta at strain rates of about 106/s exhibited pronounced elastic overshoot, followed by rapid stress relaxation and the amplitude of the elastic precursor depicted essentially no dependence on sample thickness for samples with controlled initial properties, in contrast to the precursor attenuation typically observed in shock wave experiments. The precursor for the cold-rolled sample was more dispersive and did not exhibit the characteristics depicted by the annealed samples. A principal objective of the present study was to gain some insights into this behavior and its implication on the deformation mechanisms for tantalum. Another objective was to gain a fundamental understanding of the dynamic inelasticity of polycrystalline tantalum, its evolution with the processing history, and the resultant thermomechanical behavior. The approach used to achieve these objectives was to first develop a material model that captured the observed material characteristics and then to use numerical simulations of dynamic experiments to gain additional insights into the observed material behavior. The constitutive model developed is based on the concept of dislocation generation and motion. Despite its simplicity, the model works quite well for both sets of data and serves a valuable tool to achieve the research objectives. The tantalum studied here essentially exhibits a strong rate sensitivity and this behavior is modeled through the low dislocation density and the strong stress dependence of the dislocation velocity. For the annealed material, the mobile dislocation density is assumed to be essentially zero in the model. This low dislocation density combined with strong stress dependence of dislocation velocity results in a metastable elastic response and a precursor that shows little attenuation. The increase of mobile dislocations through the cold-rolling process leads to a less rate-sensitive behavior for the cold-rolled tantalum and also the disappearance of the precursor behavior observed for the annealed samples. Both the low dislocation density and the strong rate dependence of the dislocation velocity may be related to the low mobility of the screw dislocations in bcc metals. This low mobility results from its extended, three-dimensional core structure.

Mechanism of Strain Rate Effect Based on Dislocation Theory

Based on dislocation theory, we investigate the mechanism of strain rate effect. Strain rate effect and dislocation motion are bridged by Orowan's relationship, and the stress dependence of dislocation velocity is considered as the dynamics relationship of dislocation motion. The mechanism of strain rate effect is then investigated qualitatively by using these two relationships although the kinematics relationship of dislocation motion is absent due to complicated styles of dislocation motion. The process of strain rate effect is interpreted and some details of strain rate effect are adequately discussed. The present analyses agree with the existing experimental results. Based on the analyses, we propose that strain rate criteria rather than stress criteria should be satisfied when a metal is fully yielded at a given strain rate.

Strain Rate Sensitivities of Face-Centred-Cubic Metals Using Molecular Dynamics Simulation

We use dislocation theory and molecular dynamics (MD) simulations to investigate the effect of atom properties on the macroscopic strain rate sensitivity of fcc metals. A method to analyse such effect is proposed. The stress dependence of dislocation velocity is identified as the key of such study and is obtained via 2-D MD simulations on the motion of an individual dislocation in an fcc metal. Combining the simulation results with Orowan's relationship, it is concluded that strain rate sensitivities of fcc metals are mainly dependent on their atomic mass rather than the interatomic potential. The order of strain rate sensitivities of five fcc metals obtained by analysing is consistent with the experimental results available.

A plasticity model describing yield-point phenomena of steels and its application to FE simulation of temper rolling

To describe the yield-point phenomena of steels, an extended version of the first author’s model (Yoshida, F., 2000. A constitutive model of cyclic plasticity. International Journal of Plasticity 16, 359–380) is proposed on the premise that the material behavior of sharp yield point and the subsequent abrupt yield drop result from a rapid dislocation multiplication and the stress-dependence of dislocation velocity. A specific feature of this model is that it describes well a high upper yield point, the rate-dependent Lüders strain at the yield plateau and the subsequent workhardening, as well as cyclic plasticity characteristics, such as the Bauschinger effect and rate-dependent ratcheting. Using this model, an FE simulation of temper rolling process is conducted in order to clarify its role for the elimination of the yield point of steel sheets. Particularly, the effect of upper yield point on the deformation characteristics in the process is discussed.

Cyclic Plasticity Behavior of Mild Steel with Special Emphasis on Yield-Point Phenomena.

Annealed steels exhibit a sharp yield point and the subsequent abrupt yield drop followed by the yield plateau (Luders deformation) in their stress-strain curve of uniaxial tension. This paper provides some typical examples of experimental data of cyclic plasticity with special emphasis on the yield-point phenomena for an annealed mild steel, i.e., uniaxial tension at several crosshead speeds;cyclic straining;stress- and strain-controlled ratchetting. In order to describe the stress-strain response characteristics such as the yield-point phenomena, cyclic hardening/softening, the Baus-chinger effect and rate-dependent ratchetting, constitutive modelling of cyclic elasto-viscoplasticity is discussed on the premise that the sharp yield point and the subsequent abrupt yield drop result from the rapid dislocation multiplication and the stress-dependence of dislocation velocity.

A constitutive model of cyclic plasticity

Abstract This paper addresses a constitutive model of cyclic plasticity with special emphasis on the yield-point phenomena. In order to point out the deformation characteristics of a mild steel, four types of experiments were conducted, i.e. uniaxial tension at several crosshead speeds, cyclic straining, and stress- and strain-controlled ratchetting. A viscoplastic constitutive model of cyclic plasticity is proposed on the premise that the phenomena of sharp yield point and the subsequent abrupt yield drop result from rapid dislocation multiplication and the stress-dependence of dislocation velocity. Besides, cyclic plasticity behavior, such as the Bauschinger effect, cyclic hardening/softening characteristics and ratchet-strain accumulation, is described by some kinematic and isotropic hardening rules. The cyclic stress–strain responses predicted by this model agree well with the corresponding experimental results.

Dislocation motion in a crystal having a high Peierls barrier

Abstract Dislocation motion controlled by the kink process is treated as a Brownian motion of a linearly extended object. The stress dependence of dislocation velocity, kink density and some other quantities are calculated. It is shown that when a certain condition is satisfied, the Hirth‐Lothe theory of dislocation velocity is exact.

Movement of dislocations in ice and its plastic deformation

Measurement of the dislocation velocity in single crystals of ice under stress were carried out by several investigators using X-ray topographic techniques. The molecular processes around the moving dislocations in ice have been discussed theoretically by several investigators but they have not been successful in explaining experimental results. On the other hand, the mechanism of plastic deformation of single crystals of ice is gradually being clarified by our knowledge of the stress dependence of dislocation velocity and of the distribution of dislocations in deformed ice crystals, both obtained experimentally.

On the use of the stress relaxation testing method in studies of the mechanical behaviour of geological materials

A summary is presented of the use of stress relaxation testing in studies of the mechanical behaviour of materials with emphasis on the underlying assumptions of the method. It is shown that relaxation testing is a powerful experimental method which could profitably be used in future studies of the mechanical properties of geological materials to augment, but not to replace, the more conventional creep and constant strain rate tests. Stress relaxation data can be analysed to determine important parameters in equations describing (a) laws of flow and fracture, and (b) dislocation dynamics. The variation of the first derivative of any stress relaxation curve with stress can be used to establish the applied stress sensitivity to strain rate and the values of activation parameters such as ‘activation volume’. Such parameters may be used to constrain the inference of the dominant deformation mechanism. This account is illustrated by reference to some recent experiments on polycrystalline, synthetic galena (lead sulphide) and pre-faulted cylinders of Tennessee sandstone deformed over a wide range of environmental conditions. The accurate sensing of the second derivative of a relaxation curve is required to establish parameters relating to dislocation dynamics, e.g. partition between thermal and athermal components of applied stress, and the stress dependence of dislocation velocity. The determination of such parameters is illustrated with new experiments on single crystals of calcite.

Engineering Properties of Fresh-Water Ice

AbstractThe principal engineering problems requiring knowledge concerning the properties of ice are prediction of the maximum force that ice might exert on a structure and determination of the load that can be placed safely on an ice cover. The properties of ice relevant to these problems are discussed. Particular attention is given to the dependence of Young's modulus on the frequency of the stress, strain-rate dependence of the yield and fracture strengths, and the ductile to brittle transition. It is shown that the strain-rate dependence of these properties is consistent with information on the stress dependence of dislocation velocity on the basal plane. The tensile and compressive strengths are also shown to be consistent with current theories of crack initiation and propagation.

Stress dependence of high-temperature creep in Fe−Mo and Fe−Co alloys

The stress dependence of high-temperature creep and the alloying effects on it were investigated both in the ferromagnetic and the paramagnetic temperature regions of alpha iron and Fe−Mo and Fe−Co alloys. The steady-state creep rate,\(\dot \varepsilon _s \), of alpha iron was found to obey a power law relationship,\(\dot \varepsilon _s \propto \sigma ^n \) (n: constant) in the temperature range above 0.5Tm (Tm: the melting temperature). The stress exponent,n, was 4.6 at all the temperatures examined. By addition of molybdenumn decreased to 3, while it remained unchanged by addition of cobalt. It seems that the change inn due to alloying is mainly attributed to the change in activation area for creep,A*, which results in the change in stress dependence of dislocation velocity. The magnetic transformation was found not to influence the stress dependence of\(\dot \varepsilon _s \).

Stress dependence of dislocation velocity in single crystal niobium

The stress dependence of dislocation velocity was measured by etching in niobium single crystals grown by an electron-beam floating-zone technique. The velocity-stress relation was determined with temperature, purity, and low neutron dose levels as variables. The data can be expressed by an equation of the form v ̄ = (τ ∗ τ 0) m∗ in all cases. The exponent m ∗ was found to increase slightly with decreasing temperature, increase strongly with greater impurity content, and to decrease with neutron irradiation up to 8.3 × 10 17 n/cm 2 ( E > 1 MeV). Measurements of the strain-rate sensitivity and the stress relaxation indicated that these techniques were unsatisfactory in determining the exponent m ∗ in the velocity equation. Correlations could be made between the data from etching and mechanical measurements in irradiated samples which suggest that the increase in the upper yield stress upon neutron irradiation is associated with a dynamic resistance to dislocation motion.

Extension of Unoriented Nylon 66 Filaments. III. Superposition of Data

In an effort to understand the molecular mechanism of cold drawing, the tensile creep of unoriented nylon 66 monofilaments as a function of load has been obtained at three different combinations of temperature and moisture content. Qualitatively, an increase in either load, temperature, or moisture content will shift the creep curve to shorter times. These data can be quantitatively correlated by plotting the elongation ε against log t−a+bx+cT+c1σ/(c2+σ). Here t is time, x is % H2O, T is temperature in °K, σ is an average stress in dynes/cm2, and a, b, c, c1, and c2 are constants. The parameters b and c are identical with those previously found to apply to the moisture and temperature dependence of the elastic extension of oriented nylon 66 fibers. The free-volume theory frequently employed for amorphous polymer behavior is shown to be inapplicable since moisture sorption decreases the free volume although it quickens cold drawing. Application of dislocation concepts enables an estimate of the stress dependence of dislocation velocity to be calculated.

Stress dependence of dislocation velocity from stress relaxation experiments

Stress dependence of dislocation velocity from stress relaxation experiments

The effect of work hardening on the stress dependence of dislocation velocity

The effect of work hardening on the stress dependence of dislocation velocity

Slip Systems and Their Critical Shear Stress in 3% Silicon Iron

Single crystals of 3% silicon iron with controlled orientation were deformed in tension between 20°C and -196°C at various strain-rates. The orientation was systematically selected so that the maximum shear stress was in direction on low index planes. The operative slip systems were examined by surface observation and analysis of yield stress. The result showed the existence of {112} system as well as {110} system. The temperature dependence of critical shear stress of the two systems was separately determined and that of {112} system was stronger than that of {110} system. The critical shear stress for slip is different by 5% between two opposite directions on {112} plane. The strain-rate dependence of critical shear stress was also examined and found to be derived from the stress dependence of dislocation velocity.

The stress dependence of dislocation velocity, and its relation to the strain rate sensitivity

The stress dependence of dislocation velocity, and its relation to the strain rate sensitivity

Stress dependence of dislocation velocity inferred from strain rate sensitivity

Stress dependence of dislocation velocity inferred from strain rate sensitivity

A model for yielding with special reference to the yield-point phenomena of iron and related bcc metals

A model for yielding based on dislocation multiplication and velocity characteristics specific to iron and related b.c.c. metals is derived on the premise that dislocations anchored by segregates or precipitates remain locked. The abrupt yield drop is a consequence of rapid multiplication and the stress dependence of dislocation velocity. The model describes continuous and discontinuous yielding, the Lüders' band, the delay-time phenomenon, and offers a unified treatment of these phenomena qualitatively in accord with experiments. Macroscopic strain-rate sensitivity and the Lüders' band front velocity are shown to be related to dislocation-velocity characteristics. The model also accounts for yield-point anomalies associated with strain aging. Although the possibility of unlocking is not excluded, these considerations imply that the importance of unlocking may have been overstated.