Mobile Dislocation Velocity Research Articles

Modeling hydrogen diffusion in precipitation hardened nickel-based alloy 718 by microstructural modeling

Abstract Environmentally assisted cracking can significantly affect the performance of high strength alloys and limit material selection to minimize the risk of subcritical crack growth in service. UNS N07718 is widely used in marine service applications and under a variety of conditions, such as: alternate immersion, different levels of cathodic protection, and freely corroding galvanic couples, because of its demonstrated corrosion and fracture resistance in these environments. In this work we developed a representative model of the material microstructure including the metal grains, the material texture, and the precipitates along the grain boundaries and within the grains. The microstructural model was subjected to the boundary conditions identified at the notch root of a fracture mechanics sample and the results are used as input for a simulation of hydrogen diffusion from the surface of the notch, assuming the material has been introduced to a hydrogen producing environment. The diffusion of hydrogen was modeled by Fick’s law and included both hydrostatic stress and mobile dislocation velocity as driving forces. The influence of immobile dislocations was also modeled to account for the irreversible trapping. The results show that hydrostatic stress and immobile dislocation trapping can significantly alter the highest concentration of hydrogen and its location within the microstructure towards the fracture process zone. Mobile dislocation velocity has a small influence in determining the hydrogen distribution near the fracture process zone.

Modelling of shock waves in fcc and bcc metals using a combined continuum and dislocation kinetic approach

Recent experimental data has revealed that, over short time scales (on the nanosecond scale), during formation of a shock in metals, amplitude of the ‘elastic’ precursor greatly exceeds the Hugoniot elastic limit (HEL), before decaying to the level of the HEL. Standard continuum scale material models are unable to reproduce this behaviour. To capture this aspect of material behaviour in metals, physical effects related to high rate dislocation mechanics must be taken into consideration (Mayer et al., 2013) and included into the continuum scale material model. The constitutive model developed here is defined at the continuum level, where the evolution of plastic deformation is controlled with a system of equations for three microscale state variables, for each slip system of a single crystal. These three state variables are the density of mobile dislocations, the density of immobile dislocations and the mobile dislocation velocity. The density evolutions of mobile and immobile dislocations are controlled by dislocation kinetic equations, which account for the generation of new dislocations, immobilisation of mobile dislocations and annihilation of dislocations. Dislocation velocity is determined by integration of the equations of motion of the mobile dislocations. The dislocation micromechanics is incorporated into the continuum model using the generalised Orowan equation, which relates plastic strain rate to the density of mobile dislocations and the velocity of mobile dislocations. Evolution of the yield surface is controlled by density of immobile dislocations.The dislocation mechanics model (Krasnikov et al., 2011, Mayer et al., 2013) was combined with the orthotropic continuum scale material model (Vignjevic et al., 2012) with a vector shock equation of state (EOS) (Vignjevic et al., 2008), which was developed for modelling the response of orthotropic metals to high strain rate loading including presence of shockwaves. The continuum model was implemented in the LLNL Dyna3d (Liu, 2004) for linear solid elements.Model validation was performed by comparison of numerical results with experimental data for plate impact tests (uniaxial strain state) for aluminium (fcc), copper (fcc) and tantalum (bcc). The numerical results show that during the first 50ns after impact, the pre-cursor wave has an amplitude similar to the stress level behind the shock front and relaxes to HEL with time (wave propagation). The difference between the experimental and numerical values of the compared variables (longitudinal stress, pulse length, elastic precursor relaxation time) was within 5% for the fcc materials, with the similar accuracy obtained for the bcc material, particularly for loading in the principal material direction.

Dynamic behavior of hydrogen desorption from pure iron and inconel 625 during elastic and plastic deformations

Dynamic behavior of hydrogen desorption from pure iron with a body-centered-cubic lattice and Inconel 625 with a face-centered-cubic lattice was examined during tensile deformation using a quadrupole mass spectrometer in a vacuum chamber integrated with a tensile testing machine. Hydrogen desorption from hydrogen-charged specimens was detected under various strain rates and cyclic stresses. Hydrogen desorption rarely increased under elastic deformation. In contrast, it increased rapidly at the proof stress when plastic deformation began, reached its maximum, and then decreased gradually with increasing applied strain for both pure iron and Inconel 625. This desorption behavior is closely related to hydrogen dragging by moving dislocations. The thermal desorption analysis results showed that the amount of desorbed hydrogen differed at each strain rate. This difference in the amount of desorbed hydrogen transported by dislocations depends on the balance between the hydrogen diffusion rate and mobile dislocation velocity.

Hydrogen Desorption Behavior of Pure Iron and Inconel 625 during Elastic and Plastic Deformation

The hydrogen desorption behavior of pure iron with a body-centered-cubic (BCC) lattice and Inconel 625 with a face-centered-cubic (FCC) lattice was examined during tensile deformation using a quadrupole mass spectrometer in a vacuum chamber integrated with a tensile testing machine. Hydrogen and water desorption was continuously detected simultaneously under the application of a tensile load and strain to the specimens. Hydrogen desorption promoted by tensile deformation can be found by deducting both fragment hydrogen dissociated from H2O and H2 desorbed under unloading from the total amount of hydrogen desorbed from hydrogen-charged specimens during tensile deformation. Hydrogen desorption from hydrogen-charged specimens was detected under various strain rates of 4.2×10−5/s, 4.2×10−4/s and 4.2×10−3/s. Hydrogen desorption rarely increased under elastic deformation. In contrast, it increased rapidly at the proof stress when plastic deformation began, reached its maximum, and then decreased gradually with increasing applied strain for both pure iron and Inconel 625. This desorption behavior is closely related to hydrogen dragging by moving dislocations. The amount of desorbed hydrogen promoted by tensile deformation was measured by thermal desorption analysis (TDA). The TDA results showed that the amount of desorbed hydrogen differed at each strain rate. The largest amount of desorbed hydrogen promoted by tensile deformation was 16% of the initial hydrogen content in pure iron with a high hydrogen diffusion rate when the specimen was deformed at a strain rate of 4.2×10−4/s. In contrast, that of Inconel 625 with a low hydrogen diffusion rate was 9% of the initial hydrogen content when the alloy was deformed at a strain rate of 4.2×10−6/s. This difference in the amount of desorbed hydrogen transported by dislocations depends on the balance between the hydrogen diffusion rate and mobile dislocation velocity.

Effect of transient change in strain rate on plastic flow behaviour of low carbon steel

Plastic flow behaviour of low carbon steel has been studied at room temperature during tensile deformation by varying the initial strain rate of 3·3 × 10−4s−1 to a final strain rate ranging from 1·33 × 10−3s−1 to 2 × 10−3s−1 at a fixed engineering strain of 12%. Haasen plot revealed that the mobile dislocation density remained almost invariant at the juncture where there was a sudden increase in stress with a change in strain rate and the plastic flow was solely dependent on the velocity of mobile dislocations. In that critical regime, the variation of stress with time was fitted with a Boltzmann type Sigmoid function. The increase in stress was found to increase with final strain rate and the time elapsed in attaining these stress values showed a decreasing trend. Both of these parameters saturated asymptotically at a higher final strain rate.

不均一変形に起因するFe-C合金の延性低下

The correlation between ductility in tensile test and nonuniform deformation has experimentally been investigated under various conditions (testing temperature: 193∼313 K, strain rate: 10−5∼10−1 s−1). Total elongation in specimens with large amounts of solute C is decreased by the dynamic strain aging, under the condition of which necking has a tendency to localize. Consequently the magnitude of local elongation after the maximum load point depends simply upon \barvd⁄(ξvs) only, low values of which are associated with occurrence of the dynamic strain aging, \barvd is average velocity of mobile dislocations, vs is diffusion velocity of C atoms and ξ is a constant depending upon the density and configuration of dislocations. In case of specimens having fine carbides in grains, the ductility deterioration under high strain rates at low temperatures is related to the localization of Lüder’s band.

Mean mobile dislocation velocity in lif crystals under strain

Results of a study of mobile dislocation assembly structure of the LiF crystal under straining are used to determine the dislocation mean velocity, as well as its dependence on the assembly structure and its variation during work hardening. The velocity is found to be several orders of magnitude in excess of the separate dislocation velocity in the undeformed crystal for the same shear stress. An anomalous change in the activation “volume” is discovered as the process changes from microplastic deformation to plastic flow. Elastic interaction of sign-similar mobile dislocations and kinetics of jogs in screw dislocations are treated as sources of the effects observed. [Russian Text Ignored].

Determination of the velocity of mobile dislocations by nuclear spin relaxation measurements

AbstractWolf's general theory of rotating‐frame nuclear spin‐lattice relaxation is applied to the effect caused by dislocations moving at an average velocity v. Equations are presented for the dependence of the NMR relaxation rate R on the mean waiting time τ of a dislocation before an obstacle, valid in both the weak‐and the strong‐collision regions. In the latter the Slichter‐Ailion‐Rowland‐Fradin theory applies. Nuclear spin relaxation tests on 23NaCl and 23NaF single crystals deformed at constant strain rates ϵ confirm the theory. The experimental data for the predicted maximum in R (reached only for NaCl at ϵm = 20 s―1) yield directly τm = 2.8 × 10―5 s, the mobile fraction of dislocations Qm/Qt = 0.26. The value of ϵm, together with the mean distance between obstacles of ≈ 2 × 10―4 cm, derived from the slope of the curve in the strong‐collision region, leads to vm = 7.1 cm s―1, corresponding to a mobile dislocation density ϱm = 1.4 × 108 cm−2.

An ideally viscoplastic analysis of the yield point phenomenon

A very crude approximation to the dependence of the velocity of mobile dislocations on applied stress is to assume that for stresses below a certain level the velocity is zero and for stresses at this level the velocity can take any required value. This first order approximation leads to a predicted material response which is that of the perfectly plastic model. In the present paper a second order approximation is examined. In particular the implications of the inclusion of an upper limit to the dislocation velocity are explored with reference to the phenomenon of the upper yield point and subsequent yield drop. An analytical expression for the upper yield stress is developed which is an upper bound to the actual upper yield stress in a material.

Comments on “density and velocity of mobile dislocations”

Comments on “density and velocity of mobile dislocations”

Reply to comments on density and velocity of mobile dislocations

Reply to comments on density and velocity of mobile dislocations

Density and velocity of mobile dislocations

Density and velocity of mobile dislocations

The initiation of yielding in silicon-iron

An experimental program was conducted in which the etch pit technique was used for the direct observation of dislocation configurations at various stages of yielding. Poly-crystalline tensile specimens of 3 per cent silicon-iron were loaded in tension at constant strain rate and by load pulses. A new model of the delay-time for yielding at constant applied stress is presented. Three assumptions used are (a) no dislocation motion occurs below a critical resolved shear stress, (b) the yielding rate is dependent upon the velocity of mobile dislocations, and (c) the end of the delay period occurs when yielding of the grains has spread continuously through the thickness of the specimen. This model is consistent with the experimental observations and explains the true static upper yield point and the shape of the strain vs. time curve at constant applied stress. The model also yields reasonable values for the stress concentration factor on grains in the critical cross-section that are least favorably oriented for slip.

The influence of grain size on the nature of portevin-lechatelier yielding

Abstract When the grain size dependence of dislocation density is applied to Cottrell's theory of the Portevin–Lechatelier effect, the result indicates that the critical strain ∊0, necessary to initiate serrated flow, should depend on the grain size μ, at constant strain rate, according to the relationship ∊0 = (constant)μ p , where p=n/(m + β). The parameters n and (m + β) are evaluated by dislocation density measurements and strain rate experiments respectively to give ∊0 ∝ μ½. Direct experimental determination of ∊0 as a function of grain size is in agreement with that predicted theoretically, indicating that the effect arises from the influence of grain size on the average velocity of mobile dislocations. The period and amplitude of the serrations decrease with increasing grain size. This effect is consistent with the idea that each serration corresponds to a yield point followed by a local Luders strain. The period and amplitude of the serrations decrease with increasing grain size. This effect is co...

In support of a model of creep based on dislocation dynamics

Abstract Dislocation measurements obtained after creep of Fe-3·0% Si by Barrett et al. (1966) have been analysed. It is shown that mean mobile dislocation velocity is linearly related to mobile dislocation density in support of a previous model of creep (Webster 1966). Furthermore, the creep curves calculated using these results correlate well with experimental creep curves.

A widely applicable dislocation model of creep

Abstract A physical model, based on the average behaviour of large numbers of dislocations, is proposed to explain a wide variety of creep curves. The model, which is consistent with others in the literature, predicts that the rate of change of mobile dislocation density obeys zero, first and second-order kinetics. Whereas other models consider the mean velocity of mobile dislocations to be independent of dislocation density, here the velocity is allowed to decrease with increasing density to allow for work-hardening. Arguments are developed to show the form of this dependence. The resultant creep equation is able to predict most of the shapes of creep curves observed in practice, including an incubation period. Comparison of the expression with experimental data for a variety of materials (both single and polycrystalline) and conditions shows very good quantitative agreement indicating the validity of the assumptions made. Further confirmation of the model is provided by the fact that the analysis predicts a linear relation between dislocation density and strain for small strains, an observation frequently made in practice.