Square Root Of Dislocation Density Research Articles

Effect of Ni content and crystallographic orientation on mechanical properties of single-crystal (CoCr)100-x Ni x medium-entropy alloy

Nanoindentation analyses of (CoCr)100-x Ni x medium-entropy alloys with different Ni contents and crystal orientations were carried out by molecular dynamics simulations. Analyses show that the force-displacement curves during elastic deformation are in good accordance with the Hertz contact theory and the elastic modulus is closely related to the Ni contents and crystal orientations. The elastic-plastic transition point appears later in (CoCr)67Ni33 than in other alloys. The plastic deformation was studied by exploring the instantaneous microstructure, which was found to be dominated by homogeneous nucleation of Shockley partial dislocations and the accumulation of stacking faults, and different levels of dislocation density were produced in the alloys with different Ni contents and crystal orientations. By analyzing the evolution of dislocation density and hardness, a linear relationship between the square root of dislocation density and hardness can be revealed, which agrees well with the classical Taylor hardening model, and the empirical constant is found closely related to crystal orientations.

Evaluation of Mechanical Properties of Medium Carbon Steel by Dislocation Microstructure Analysis

Carbon steels realize high strength by quenching, which are used for mechanical elements such as gears and bearings. Martensitic transformation makes harder due to high dislocation density and fine crystal grains. The mechanical performance increase in proportion to their hardness. However, in the case of medium carbon steels, steels quenched and tempered at 290℃ have better mechanical properties than as quenched steels. There are some factors for decrease of mechanical properties such as dislocation density and retained austenite, this study focused on dislocation microstructure. To obtain their dislocation microstructure, line profiles from neutron diffraction were analyzed using convolution multiple whole profile (CMWP) fitting method. It is known that there are as proportional relationships between the square root of dislocation density and yield stress, but the analysis results show no proportional relationship. Therefore, we employed dislocation arrangement parameter to take into account mobile and immobile dislocations. Thus, effective dislocation density was introduced and may be able to explain the relationship with yield stress.

Plastic flow and dislocation strengthening in a dislocation density based formulation of plasticity

Modeling dislocation interaction on a mesoscopic scale is an important task for the description of flow stress and strain hardening in a continuum model. In dislocation based continuum theories, different flow stress formulations are commonly used in the literature. They are usually based on the average dislocation spacing related to the square root of dislocation density, but differ in their degree of homogenization of dislocation interactions, namely whether only total dislocation density is considered in a Taylor term or whether an interaction matrix is used. We analyze the impact of both terms in different crystal orientations as well as homogeneously and inhomogeneously distributed initial dislocation densities. In the dislocation based continuum formulation used here, both terms act as a short-range stress additionally to the ”mean field” long-range stress field of elastic dislocation interaction. We demonstrate that the simplifying assumption of an average over all possible interaction types is a reasonable reduction of complexity in high symmetry systems with homogeneous density distribution. However, we also demonstrate that under specific boundary conditions and for inhomogeneities between slip systems a significantly different density evolution is obtained on slip systems with similar Schmid-factors, when considering different interaction strengths for different types of dislocation interaction. This is in agreement with findings in discrete dislocation dynamics simulations in the literature.

Microstructural Features of Cold-Rolled Carbon Steel Evaluated by X-ray Diffraction Line Profile Analysis and Their Correlation with Mechanical Properties

Line profile analyses of cold-rolled carbon steels were conducted to evaluate microstructural features such as dislocation density, crystallite size, and M values. After the samples were subjected to 40% cold-rolling, dislocation density increased from 7 × 1013 m−2 to 2 × 1015 m−2 and crystallite size decreased from 155 nm to 35 nm. The component ratio of screw and edge dislocations was approximately 1:1, as determined from the evaluation of the q values. The M value that indicated interaction of dislocations substantially decreased during the initial stage of cold-rolling, which means interaction of dislocations becomes strong. Proof stress, hardness, and tensile strength were increased by the cold-rolling process. Furthermore, the ratios between proof stress and hardness were initially 2 and increased to approximately 3. The correlation between the microstructures and the mechanical properties was demonstrated according to the Bailey-Hirsch relationship between flow shear stress and dislocation density. Variations in the proof stress and hardness as a function of the square root of dislocation density indicated that the work-hardening of the material is affected by not only the total amount of dislocations but also other factors, such as crystallite size and arrangement of dislocations.

Influence of stress, temperature, and strain on calcite twins constrained by deformation experiments

Abstract A series of low-strain triaxial compression and high-strain torsion experiments were performed on marble and limestone samples to examine the influence of stress, temperature, and strain on the evolution of twin density, the percentage of grains with 1, 2, or 3 twin sets, and the twin width—all parameters that have been suggested as either paleopiezometers or paleothermometers. Cylindrical and dog-bone-shaped samples were deformed in the semibrittle regime between 20 °C and 350 °C, under confining pressures of 50–400 MPa, and at strain rates of ~ 10− 4–10− 6 s− 1. The samples sustained shear stresses, τ, up to ~ 280 MPa, failing when deformed to shear strains γ > 1. The mean width of calcite twins increased with both temperature and strain, and thus, measurement of twin width provides only a rough estimation of peak temperature, unless additional constraints on deformation are known. In Carrara marble, the twin density, NL (no of twins/mm), increased as the rock hardened with strain and was approximately related to the peak differential stress, σ (MPa), by the relation σ = 19.5 ± 9.8 N L . Dislocation tangles occurred along twin boundaries, resulting in a complicated cell structure, which also evolved with stress. As previously established, the square root of dislocation density, observed after quench, also correlated with peak stress. Apparently, both twin density and dislocation cell structure are important state variables for describing the strength of these rocks.

Ferrite Transformation Kinetics of Severely Hot-Deformed Austenite

The ferrite transformation kinetics of severely hot-deformed austenite has been studiedby considering ferrite nucleation from dislocation cell blocks inside austenite grains. The size ofdislocation cell blocks and ferrite grain size just after phase transformation are acknowledged to beinversely proportional to the square root of dislocation density. It is found that the ferrite nucleationrate in this area can reach the saturated state at a high temperature just under Ae3, and the ferritetransformation finishes within a very short time. The kinetics of ferrite volume fraction and theferrite grain growth after phase transformation for plain carbon (0.1%C, 0.2%Si, 1.0%Mn) steelhave been studied using a THERMECMASTER hot-compression testing machine. These modelscan be applied to the hot and warm forming processes of plain carbon steel to predict the ferritetransformation from severely deformed austenite.

Quantitative evaluation of dislocation density using minor-loop scaling relations

Relationships between minor hysteresis loops and dislocation density have been investigated at various temperatures from 10 to 600 K in polycrystalline nickel with tensile deformation. It was revealed that coefficients obtained from scaling relations between parameters of minor-loops are in linear proportion to stress at all measuring temperatures below its Curie temperature. Considering that dislocation density is generally in proportion to the square root of true stress, it is concluded that the coefficients are related with the square root of dislocation density. This method using minor hysteresis loops is useful for quantitative evaluation of dislocation density because of its very low measurement field.

Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics

The problem of the collective behavior of straight parallel edge dislocations is investigated. Starting from the equation of motion of individual dislocations a continuum description is derived. It is shown that the influence of the short range dislocation-dislocation interactions on the dislocation dynamics can be well described by a local back stress which scales like the square root of dislocation density plus a non-local diffusion-like term. The value of the corresponding diffusion coefficient is determined numerically, and implications for size effects in plasticity are discussed.

Modeling grain size and dislocation density effects on harmonics of the magnetic induction

Microstructural attributes of steels affect hysteretic magnetic properties because the microstructure affects domain wall movement and pinning. Two important features are grain size and dislocation density. The consensus experimentally is that the coercivity tends to be linearly related to the inverse of the average grain diameter and to the square root of the dislocation density. In this article, these experimental tendencies are utilized in formulating the dependence of the hysteresis parameters of the Jiles–Atherton model as a function of grain size and dislocation density. The results are then used in computing the first and third harmonics of the magnetic induction as a function of grain size and dislocation density. This is done via an adaptation of a hysteresis model formulated by Jiles for higher excitation frequencies. The results indicate that the harmonic amplitudes decrease monotonically with inverse grain size and the square root of dislocation density. Since increasing inverse grain size and dislocation density are correlated with increasing tensile strength, the results are consistent with experimental results for the decrease of the harmonic amplitudes with increasing tensile strength in automotive steels. Also, the harmonic amplitudes decrease with increasing excitation frequency, consistent with experiment.

Grain-size strengthening in terms of dislocation density measured by resistivity

The effect of grain size on flow stress has been investigated in terms of dislocation density. The measurement of dislocation density was made for nickel having a high stacking fault energy, by means of electrical resistivity with which the dislocation density can be measured up to larger strains compared with transmission electron microscopy. It was found that the dislocation density for a given strain in specimens deformed in tension at 77 and 295 K increases in a linear manner with the reciprocal of grain size. It was also ascertained that the flow stress is proportional to the square root of dislocation density, irrespective of grain size, deformation temperature and the amount of plastic strain (ϵ). From the above two relationships, an equation between flow stress and grain size was obtained in a general form, which gives the Hall-Petch relation as the limited case at yield point or at small strains.

The stress-strain behaviour of single crystals and polycrystals of face-centered cubic metals—a new dislocation treatment

A model intended to describe the stress-strain behavior of monocrystals and polycrystals of f.c.c. metals is presented. The treatment based on average rather than specific dislocation processes, is used to deduce an equation relating the total dislocation density and strain. The expression so derived is then combined with the well-established relationship between stress and the square root of dislocation density to obtain the stress-strain curve. It is shown that the theory describes the deformation hardening of copper single crystals and polycrystals with fair accuracy. The parameters introduced in the model (and their variation with temperature) are given a simple physical interpretation.

変形したCu-Al単結晶における転位密度について

Dislocation densities in deformed Cu-2.5 at%Al, Cu-5.0 at%Al, Cu-10 at%Al and Cu-15 at%Al were measured by counting etch pits on the {111} plane. The relation between the dislocation density and some of the physical properties were studied.The results obtained were as follows:(1) The dislocation density increased proportionally with strain in stage I. In stage II the same relation was obtained, though the increasing rate of dislocation density was larger.(2) The dislocation density on the (111) plane was higher than that on the (11\bar1). Dislocation densities on these two planes became similar with increasing strain. In Cu-2.5 at%Al dislocation density on the two planes were of the same order at the beginning of the stage II, but in Cu-15 at%Al there was a larger difference in dislocation density even at the largest stress measured.(3) In stage I the dislocation density was proportional to stress. In stage II the square root of dislocation density was proportional to stress. This relation holds not only for the primary dislocation density but also for the secondary dislocation density.(4) In the equation τ=αGbN1⁄2, α∼0.65 was obtained for all the Al concentrations examined.(5) The rate of strain hardening in stage I was found to be proportional to the increasing rate of dislocation density for all the specimens.