Dislocation Density In Metals Research Articles

A physics-based crystal plasticity model for the prediction of the dislocation densities in micropillar compression

• Generalized constitutive relations that incorporate the thermally activated and drag mechanisms. • Continuum description of crystal plasticity framework combined with the geometrically necessary dislocation densities and the mobile/immobile statistically stored dislocation densities. • Computation of the geometrically necessary dislocation densities based on the L 1 -norm minimization scheme to provide physical interpretation of the lower bound on overall GND population. • Dislocation mechanisms depending on generation, annihilation, interactions, trapping, and recovery. • Evolution laws of dislocation densities with mechanism-based material parameters. A new nonlocal crystal plasticity model is developed to study the mechanical behavior of face-centered cubic single crystals under heterogeneous inelastic deformation through a crystal plasticity finite element method. The main feature of this work is generalized constitutive relations that incorporate the thermally activated and drag mechanisms to cover different kinetics of viscoplastic flow in metals at a variety of ranges of stresses and strain rates. The constitutive laws are founded upon integrating continuum description of crystal plasticity framework with dislocation densities which is relevant to the geometrically necessary dislocation densities and the statistically stored dislocation densities. The model describes the plastic flow and the yielding of face-centered cubic single-crystal employing evolution laws of dislocation densities with mechanism-based material parameters passed from experiments or small-scale computational models. The geometrically necessary dislocation densities evolve on account of the curl of the plastic deformation gradient where its associated closure failure of the Burgers circuit exists. A minimization scheme termed L 1 -norm is utilized to secure the physical values of the geometrically necessary dislocation densities on slip systems. The evolution equations of statistically stored dislocation densities describe the complex interactions between two distinct dislocation populations, mobile, and immobile statistically stored dislocation dislocations, relying on generation, annihilation, interactions, trapping, and recovery. The experiments of a micropillar compression for the copper single crystal are compared to the computational results obtained using the formulation. The physics-based model clarifies the complex microstructural evolution of dislocation densities in metals and alloys, allowing for more accurate prediction. .

The measurement of the dislocation density using TEM

The line intercept method is well developed for estimating the dislocation density in metals, but its application is limited by the intersection counting, which is deeply depending on the TEM image quality. Manual interscetion counting is quite time and labor consuming. If most of the dislocations has good contrast and homogenous background in an image, it is possible to perform automatic counting by the computer program. In this work a series of imaging conditions were investigated on a slightly deformed IF steel thin foil. Though the invisibility criterion remains applicable for both the conventional transmission electron microscopy (CTEM) and the scanning transmission electron microscopy (STEM), the STEM images revealed more dislocations and had more homogenous background than the CTEM images. The STEM bright field (BF), annular dark field (ADF) and annular bright field (ABF) images at a low index zone axis contained the most dislocations visible and were suitable for automatic intersection counting of dislocations.

Atomic mechanism of cyclic healing effect in dual-phase metastable high entropy alloy

While many experiments and simulations on the high entropy alloy have focused on the deformation mechanisms under monotonic loading, the cyclic deformation behaviors remain largely elusive. In this work, the cyclic deformation behaviors of the dual-phase metastable high entropy alloy Ta0.5HfZrTi were investigated using molecular dynamics simulations with special focus on the interaction between phase boundaries and dislocations. Unlike the monotonic loading, the complex dislocation network formed in the growth of the martensite can be dramatically modified with different cyclic loading patterns. Both cyclic growth and cyclic healing effect were observed in simulations with different loading patterns. As the minimum strain reduces, the isolated dislocations and the unpinned partial dislocation on the stacking fault are found compressed and absorbed by the phase boundaries with the repeated straining. This cyclic healing effect is in distinct contrast to conventional cyclic straining hardening mechanisms with the increased dislocation density in metals and in agreement with the recent experimental observation of absent strain hardening effect in the cyclic response conduced on the metastable HEA recently. The present study provides a platform to probe an atomic-level understanding of the fundamental mechanisms in fatigue of dual-phase metastable HEAs.

Further evidence of phase formation through a liquid state stage in electrodeposited metals: Part 3

Results of structural studies of metals electrodeposited exposed to an external force directed perpendicular or at an angle to the crystallization front have been described. It has been found that there is an increase in the dislocation density in metals electrodeposited exposed to a minor external force directed perpendicular to the crystallization front. It has been revealed that the surface layers of electrodeposited metals undergo plastic deformation caused by solid particles that move under the action of a minor external force directed at an angle to the crystallization front. It has been found that the solid particles leave imprints representing the particle shape and morphology at sites of separation from the surface of the metal electrodeposits formed exposed to a minor external force directed at an angle to the crystallization front. The existence of phase formation through a liquid state stage in electrodeposited metals has been proven.

Non-deformation recrystallization of metal with electric current stressing

Recrystallization can be achieved by annealing or electric pulse treatment of plastically deformed metals. The deformation produces a high dislocation density to facilitate nucleation. The present study, however, reports that direct electric current stressing can produce high dislocation density in metals, as revealed by EBSD and high resolution TEM analysis. Recrystallization of brass was thus triggered in situ by the generated Joule heat. The microstructure variations, grain refining, and microhardness of the brass were investigated after non-deformation recrystallization. A 75% improvement in grain size refinement and a 28% enhancement in microhardness in comparison with the annealed as-prepared specimen was achieved with a 4 h, 10 cycle current stressing-quench treatment at a current density of 14000 A/cm2.

The study on the effect of the dislocation density on formation of a closed piecewise-continuous dislocation loop in aluminum

Mathematical model allowing carrying out studies on energy, scale and time characteristics of formation of closed dislocation loop and crystallographic shear zone as a whole, and forming of a dislocation loop for FCC-materials, has been developed. Using the mathematical model study on the effect of the dislocation density on the dynamics of formation of an elementary crystallographic slip bounded by a closed piecewise-continuous dislocation loop in aluminum has been carried out. It has been shown that with decrease in the density of dislocations in metal from 10−12 up to 4·10−11 along different orientations of the expansion of the dislocation loop the maximum value of the dislocation velocity increases by 20-30% and the maximum value of the kinetic energy and the dislocation path increases by almost 2 times. It has been shown that in aluminum the area of elementary crystallographic slip, swept out by the dislocation loop, increases with a decrease in the dislocation density in metal. But, at the same time, regardless of the value of the dislocation density in metal the radius of the dislocation loop in the final configuration along the screw orientation is practically by an order of magnitude less than along the edge orientation.

Localization of plastic flow at high-rate simple shear

This study numerically investigates the influence of the initial perturbations of temperature or dislocation density in metals and of the stress concentrators on the plastic flow localization. The high-rate simple shear of micro-sample is simulated in two-dimensional formulation with use of the continuum mechanics and the dislocation plasticity model. The calculations are performed for the pure aluminum and the aluminum alloy, which differ by the yield stress values and by its temperature dependences. The considered perturbations of temperature or dislocation density lead to restricted localization of the plastic deformation, but they cannot initiate instability of the plastic flow as a self-sustained and increasing process. The more effective reason of the localization is the stress concentration, caused, for example, by boundary conditions. The plastic deformation rate is maximal in the shear stress localization areas and it can be close to zero outside these areas. Analytical estimation of the localization degree is constructed, which is in qualitative agreement with the numerical data; this estimation reveals that the localization degree grows linearly with time at the constant strain rate.

Determination of average dislocation densities in metals by analysis of digitally processed transmission‐electron microscopy images

AbstractThis paper describes an effective and simple procedure to derive information about the dislocation density distribution in metals by applying standard techniques of digital image processing on gray scaled microstructure images obtained from transmission‐electron microscopy. In a representative transmission‐electron microscopy image, two local dislocation density values were investigated by classical methods and were used as input parameter for further processing. A correlation between dislocations and image intensities is assumed such that dark areas in microstructural images are seen as a dense concentration of dislocations. Then, the contrast is increased for each transmission‐electron microscopy photography. In the next step, posterization, a gradation of tone, is applied to these images. From this, a pixel weighted average distribution of gray level correlated dislocation densities is obtained as well as an average value for a given set of images. The implementation of the several processing steps is done in Matlab employing graphical user interfaces.

Evaluation of Changes in Dislocation Density in TI-CP2 in the Process of Quasi-Static Loading Using Electrical Resistance Measurements

The paper focuses on the development of new methodology to evaluate increase of dislocation density in metals using electrical resistance measurements. Titanium specimens have been quasi-statically loaded with Instron testing machine till fracture and electrical resistance of the specimens have been monitored during the tests. Dislocation density was recovered from electrical resistance measurements and from SEM images before and after loading. Thus obtained results are shown to be in good agreement. The methodology developed in the present paper may be used for accurate monitoring of dislocation density in-situ.

アルミニウムの低温塑性疲労挙動に及ぼすひずみ振幅変化の影響

In order to study the behavior of lattice defects during low-cycle fatigue tests with strain-amplitude change, electrical resistivity was measured on wire (0.55mm in dia.) of polycrystalline aluminium (99.999%) which had been torsionally fatigued at 77K. Two different total surface-strain amplitudes, 1.8 and 4.4%, were used.The dislocation density in metal during cyclic straining after changing the strain amplitude was given byρ1/2=ρs1/2[1-[1-ρi1/2β/α]e]-(β/2)γρs=(α/β)2where α is a constant, β is a constant depending on strain-amplitude, γ is the cumulative plastic strain, and ρi is the dislocation density prior to the strain-amplitude change. In this study, the constant β was estimated from the peak torque versus cumulative plastic strain curve for fatigued metal.The concentration of point defects in metal during cyclic straining at 77K was represented as follows:C=Cs[1-1-P/K2-β/2[K2e-(β/2)γ-β/2-K2P/1-Pe-K2γ]]+Cie-K2γCs=K1α2/K2β, P=ρi1/2β/αwhere K1 and K2 are constants, Cs is the concentration of saturated point defects, and Ci is the concentration of point defects prior to the strain-amplitude change.The experimental data was analysed on the assumption that the increment in resistivity in fatigued metal is related to the number of dislocations and point defects asΔR/ΔRs=mρ/ρs+mC/Cs, m+n=1where ΔRs is the saturation value in resistivity, ΔR is the increment in resistivity, and m and n are constants.

Formation of dislocations in metals during the diffusion of low-solubility surface-active substances

The formation of dislocations during diffusion in solids was analyzed. Calculations relating to the diffusion of surface-active substances (SAS) in metals, at temperatures for which the Rebinder effect is manifested, were carried out. It was shown that this effect is most intensely manifested when the depth of diffusion is on the order of tens of interatomic spacings. It was established that, when SAS diffuse to such a depth, the dislocation density in metals reaches 1012–1013 cm/cm3 which leads to embrittlement and crack nucleation even at low stress levels. A diffusional model of grain boundaries, taking into account the formation of dislocations during diffusion, was analyzed. It was noted that thermal stresses contribute to the formation of dislocations when high-melting metals are tinned with low-melting metals.

The estimation of dislocation densities in metals from X-ray data

Recent work has shown that substructures are formed within the grains of a cold-worked polycrystalline metal. In this paper, methods are described by which the density of the excess dislocations of one sign in the boundaries between the particles can be found from data obtained from X-ray diffraction photographs. The methods may be extended to give estimates of the excess and total dislocation densities within the particles and the densities in annealed metals. The results for both cold-worked and annealed metals show that the present estimates are less than the usually accepted values. The discrepancy in the case of the cold-worked metals could be due to a different distribution of dislocations in the boundaries which may not be detected by the existing X-ray methods; however a strict comparison cannot be made until more reliable data are available from other physical measurements. It is shown that the usually accepted figure for the dislocation density in annealed metals has no theoretical or experimental support and that the dislocation density in some metal crystals may be very much less.