Dislocation Density Field Research Articles

Stored Energy of Plastic and Elastic Origin and Recrystallization

Stored energy is generally considered as a main driving force of recrystallization process. After plastic deformation a high dislocation density and residual stress field remain in a material. Both quantities are at the origin of the stored energy and we call them as the “plastic” and “elastic” parts of this energy. Their orientation distributions can be determined using diffraction and deformation models. Both components of the stored energy are studied in the present work. Their distributions and characteristics are studied for f.c.c. and b.c.c. materials.

115 BCC鉄中における転位場と水素場の相互作用およびその時間発展の解析(OS16.フェーズフィールド法とその応用(2),オーガナイズドセッション)

115 BCC鉄中における転位場と水素場の相互作用およびその時間発展の解析(OS16.フェーズフィールド法とその応用(2),オーガナイズドセッション)

OS0423 BCC鉄中の水素濃度場と転位場のダイナミクス(原子スケールモデリングとナノ・マイクロ実験力学(2))

水素環境下における鉄の塑性変形過程を理解するために,フェーズフィールド法に基づき水素場と欠陥場の非線形相互作用を考慮に入れたメゾスケールでの解析手法を構築する.さらに結晶変形挙動に影響を与え得る転位に着目し,経験的ポテンシャルにより導出した鉄-水素系の化学的・弾性的相互作用に関する基礎データを利用することで,BCC鉄中において転位による水素の存在状態および分布の変化を定量的に評価し,それにともなう転位列の時間発展を解析した.

Stress-free states of continuum dislocation fields: Rotations, grain boundaries, and the Nye dislocation density tensor

We derive general relations between grain boundaries, rotational deformations, and stress-free states for the mesoscale continuum Nye dislocation density tensor. Dislocations generally are associated with long-range stress fields. We provide the general form for dislocation density fields whose stress fields vanish. We explain that a grain boundary (a dislocation wall satisfying Frank's formula) has vanishing stress in the continuum limit. We show that the general stress-free state can be written explicitly as a (perhaps continuous) superposition of flat Frank walls. We show that the stress-free states are also naturally interpreted as configurations generated by a general spatially-dependent rotational deformation. Finally, we propose a least-squares definition for the spatially-dependent rotation field of a general (stressful) dislocation density field.

New nature of the noise of thermally stimulated electron emission from rods under cyclic torsion

A new mechanism of the formation of microfractures producing noise in stimulated electron emission from a metal surface is proposed based on numerical calculations using the weakly dissipative version of the Kolmogorov-Arnold-Moser theory. Phenomenological equations of the evolution of a dislocation density field in a polycrystal supplemented with an analysis of thermodynamic effects allow solutions for flat and rounded cracks. The considered models are confirmed by experimental results.

Substructure, Grain Boundaries, and Microcracks in Long-Operating Metal

Methods of transmission diffraction electron microscopy and x-ray diffraction analysis are used for studying the damaged bent zone of a steam conduit from steel 12Kh1MF that has served for 153,688 h at a pressure of 14 MPa and a temperature of 550°C. The dislocation substructure is studied. The dislocation density and local stress fields created by dislocation charges are determined. Microcracks, pores, and large carbide particles are detected on grain boundaries. The results obtained are used for considering the causes of nucleation of microcracks in the studied part of the steam conduit.

Bending of a single crystal: discrete dislocation and nonlocal crystal plasticity simulations

We have recently proposed a nonlocal continuum crystal plasticity theory that is based on a statistical-mechanics description of the collective behaviour of dislocations. Kinetic equations for the dislocation density fields have been derived from the equation of motion of individual dislocations and have been coupled to a continuum description of single slip. Dislocation nucleation, the material resistance to dislocation glide and dislocation annihilation are included in the formulation. The theory is applied, in this paper, to the problem of bending of a single-crystal strip in plane strain, using parameter values obtained previously from fitting to discrete dislocation results of a different boundary value problem. A numerical solution of the problem is obtained using a finite element method. The bending moment versus rotation angle and the evolution of the dislocation structure are analysed for different orientations and specimen sizes with due consideration of the role of geometrically necessary dislocations. The results are compared to those of discrete dislocation simulations of the same problem. Without any additional fitting of the parameters, the continuum theory is able to describe the dependence on slip plane orientation and on specimen size.

A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations

A two-dimensional nonlocal version of continuum crystal plasticity theory is proposed, which is based on a statistical-mechanics description of the collective behavior of dislocations coupled to standard small-strain crystal continuum kinematics for single slip. It involves a set of transport equations for the total dislocation density field and for the net-Burgers vector density field, which include a slip system back stress associated to the gradient of the net-Burgers vector density. The theory is applied to the problem of shearing of a two-dimensional composite material with elastic reinforcements in a crystalline matrix. The results are compared to those of discrete dislocation simulations of the same problem. The continuum theory is shown to be able to pick up the distinct dependence on the size of the reinforcing particles for one of the morphologies being studied. Also, its predictions are consistent with the discrete dislocation results during unloading, showing a pronounced Bauschinger effect. None of these features are captured by standard local plasticity theories.

Asymptotic crack tip stress, rotation pseudo-stress and dislocation fields for mixed mode I and II cracks in elastic perfectly plastic solids

Nemat-Nasser and Obata (Mech. Mater. 3 (1984) 235) have pointed out that asymptotic stress fields can be constructed around the tip of a general mixed mode I and II crack in elastic perfectly plastic solids with use of elastic sectors whose stress magnitude is below the yield stress. When elastic sectors which are below the yield stress exist the rotation pseudo-stress within an elastic sector is logarithmic singular with distance r from the crack tip. It must also be logarithmic singular within a plastic fan sector that is adjacent to an elastic sector. The areal dislocation density field within a plastic fan adjacent is, therefore, singular as ( r 0/ r)ln( r 0/ r). To justify the existence of below yield stress elastic sectors it is necessary to show that the logarithmic singular stress field produced by the crack plane surface dislocation distribution is canceled by another logarithmic singular stress field produced by the areal dislocation distributions within the fan plastic sectors. This is done so explicitly in this paper.

Why the stress trajectories in the Dean–Hutchinson plastic sector of the growing mode III crack are an unfocused fan

The plastic zone of the growing mode III crack in an elastic perfectly plastic solid consists of two sectors in contact with each other. The sector closer to the crack plane, first studied analytically by Chitaley and McClintock (CM), consists of a fan of straight maximum shear stress trajectories that are focused on the crack tip. The other sector, first analyzed numerically by Dean and Hutchinson (DH), is a ‘radial’ fan of straight lines that are not focused at the crack tip or at another common point. In this paper it is shown with use of the dislocation density field that the need that the stress magnitude in the plastic wake be below the yield stress requires the existence of an unfocused fan in the DH sector. It appears unlikely that this result can be obtained without explicit use of dislocations.

Application of curvilinear coordinates to dislocation density fields around cracks in linear elastic–plastic solids

Dislocation density fields can be found from either gradients of the stress field components (including the rotation pseudo-stress component) or from gradients of the plastic strain components. The latter method is most easily done if the plastic strain components are expressed in an orthogonal curvilinear coordinate system. In this paper are presented appropriate curvilinear coordinate systems for the three types of cracks in plane strain and antiplane strain. The crack is considered to be in a linear elastic–plastic solid with no yield stress. Using these curvilinear coordinates it is possible to complete the earlier dislocation based solution for modes I, II and III cracks in such solids and place on firmer ground the surprising dislocation crack tip anti-shielding result for the mode I crack. Also given in this paper are the equations, in plane strain and antiplane strain, for strain compatibility and stress functions expressed for a general orthogonal curvilinear coordinate system.

Analysis of sublimation growth of bulk SiC crystals in tantalum container

Sublimation growth of SiC bulk crystals in tantalum container is studied both experimentally and theoretically. The model of heterogeneous processes occurred on the side wall of the tantalum container proposed recently in Ramm et al. (Mat. Sci. Eng. B 61–62 (1999) 107) is extended to take into account the process of carbon gettering by the container side wall. We formulate a quasi-steady approach for modeling of the bulk crystal growth. Using this concept we predict evolution of the crystal shape and study processes which govern SiC bulk crystal growth. We apply anisotropic thermal elastic analysis to predict stress distribution in the growing crystal. For the first time a model of dislocation formation is applied for SiC bulk growth to compute dislocation density field in highly stressed areas of the growing crystal.

Dislocation behaviours ahead of crack tip

In this paper, a unified mechanics model for dislocation nucleation, emission and dislocation free zone is proposed based on the Peierls framework. Three regions are identified ahead of the crack tip. The emitted dislocations within the plastic zone in the form of an inverse pile up are treated as discrete elastic edge dislocations. Between that zone and the cohesive zone immediately ahead of the crack tip, there is a dislocation free zone. With the stress field and the dislocation density field in the cohesive zone, respectively, expressed in the first and second Chebyshev polynomial series, and the opening and slip displacements in trigonometric series, a set of nonlinear governing equations are obtained which take into account for the interaction between the emitted dislocations and cohesive zone and the nonlinear interaction between sliding displacement and the opening displacement. After discretization, the governing equations are transformed into a set nonlinear algebraic equations which are solved with Newton-Raphson Method. The results of calculation for pure shearing and combined tension and shear loading after dislocation emission are given in detail. Finally, the process of dislocation nucleation and emission on a pair of symmetric slip planes of angle α with respect to the crack plane under pure mode I load is analysed. The equilibrium positions and the number of emitted dislocation are determined. Several possible competition behaviors of dislocation emission vs cleavage are revealed.

Domain instability in an ensemble of dislocations during plastic deformation of crystals

An analysis is made of the nonlinear dynamics of perturbations of the dislocation density and elastic field using a proposed evolution model which takes into account the negative velocity sensitivity of the deforming stresses. As a result of the evolution of domain instability, it is observed that periodic and isolated solutions (solitons) exist for the initial variables.

Description of the kinetics of a model tribopolymerization process

A three‐dimensional system of ordinary differential equations of first order has been proposed to describe the kinetics of a model tribopolymerization process for which a linear coupling of the material surface dislocation density and polyreaction fields is assumed. Another important physical motivation on which the model is based stresses the predominant role of a highly rough surface under friction as a catalyst in the polyreaction process. In consequence, the fractal‐like chemical reaction concept has been applied. It is demonstrated that the system proposed is suitable for describing a variety of tribopolymerization processes and possesses non‐trivial time‐dependent behaviour even in some limiting analytical cases studied. As a specific result, a nonlinear equation generalizing the Vogel–Fulcher temperature‐dependence of the maximum time scale for the polyreaction caused by friction, characteristic of the selective transfer during friction process, has been recovered. Some comparison with an approach made earlier (G.P. Shpenkov, Friction Surface Phenomena (Elsevier, Amsterdam, 1995) pp. 165–172 and Ref. [239] therein) has been presented as well. Certain basic trends of modelling and experiment are in good agreement.

A unified model for dislocation nucleation, dislocation emission and dislocation free zone

In this paper, a unified model for dislocation nucleation, emission and dislocation free zone is proposed based on the Peierls framework. Three regions are identified ahead of the crack tip. The emitted dislocations, located away from the crack tip in the form of an inverse pileup, define the plastic zone. Between that zone and the cohesive zone immediately ahead of the crack tip, there is a dislocation free zone. With the stress field and the dislocation density field in the cohesive zone and plastic zone being, respectively, expressed in the first and second Chebyshev polynomial series, and the opening and slip displacements in trigonometric series, a set of nonlinear algebraic equations can be obtained and solved with the Newton-Raphson Method. The results of calculations for pure shearing and combined tension and shear loading after dislocation emission are given in detail. An approximate treatment of the dynamic effects of the dislocation emission is also developed in this paper, and the calculation results are in good agreement with those of molecular dynamics simulations.

Non-redundant dislocation density field of a circular bar deformed in torsion and the stress gradient hardening effect

The non-redundant dislocation density ϱN is larger than the redundant dislocation density ϱR in part of the plastically deformed region of a circular bar deformed in torsion if it is assumed that stress gradients (and gradients of the rotation pseudo-stress) do not affect the constitutive equation of an elastic-plastic solid. 1. Does anomalous hardening seen in small diameter torsion bars arise because the added non-redundant dislocations increase the work hardening in a manner similar to the hardness produced by redundant dislocations? 2. Or does the increased hardening come about because it is physically impossible for the non-redundant dislocation density to ever be greater than the redundant dislocation density and the solid adjusts to this requirement in the affected regions by either increasing the redundant dislocation or by eliminating both redundant and non-redundant dislocations? In this paper an analysis for the torsion plastic deformation gradient effect is presented based on 2.

Dislocation nucleation and emission from crack tip

The problems of dislocation nucleation and emission from a crack tip are analysed based on Peierls model. The concept adopted here is essentially the same as that proposed by Rice. A slight modification is introduced here to identify the pure linear elastic response of material. A set of new governing equations is developed, which is different from that used by Beltz and Rice. The stress field and the dislocation density field can be expressed as the first and second Chebyshev polynomial series respectively. Then the opening and slip displacements can be expanded as the trigonometric series. The Newton-Raphson Method is used to solve a set of nonlinear algebraic equations. The new governing equations allow us to extend the analyses to the case of dislocation emission. The calculation results for pure shearing, pure tension and combined tension and shear loading are given in detail.

Asymptotic dislocation density fields for cracks in an elastic, perfectly plastic solid

In this paper, details are presented of the asymptotic, non-redundant dislocation density field at a crack tip for pure mode cracks. The problems considered are for cracks in an elastic, perfectly plastic solid in antiplane strain and in perfect plane strain. The proposed asymptotic dislocation density field for the mode I crack is new; the fields for the mode II and mode III cracks are given in greater detail than in earlier papers. Mixed-mode cracks are also examined in the paper. No asymptotic stress or dislocation density fields could be found for them, under the asumption that these fields do not vary in the direction parallel to the crack front.

Dislocation density field-stress field relationships for non-uniform elastic-plastic deformation

Abstract General relationships are given that relate the components of the dislocation density field to (derivatives of) components of the stress field, including the rotation pseudo-stress components.