Glide Edge Dislocations Research Articles

Atomistic investigation of the interaction between an edge dislocation and 1/2 interstitial dislocation loops in irradiated tungsten

By impeding dislocation motion, the irradiation-induced dislocation loops cause irradiation hardening and further embrittlement of plasma-facing tungsten in fusion reactors, leading to its performance degradation. But fundamental questions regarding the mechanisms remain to be clarified and predictive model for loop hardening remains to be built. In this paper, interactions between gliding edge dislocations and interstitial dislocation loops (with Burger vector bL = ½<111>) are studied using atomistic simulations. The influences of bL orientations, dislocation-loop intersection positions, loop sizes, and loading conditions (temperature and strain rate) on the interactions are systematically calculated and analyzed. Results show a large variety of interaction mechanisms, depending mainly on the relative orientations of bL to dislocation slip plane, while slightly affected by loading conditions. Although loops with bL parallel to the plane can be easily swept away by gliding dislocations, loops with bL inclined to dislocation slip plane can strongly pin the gliding dislocation by forming a sessile 〈100〉 segment, which would bend the dislocation line into a screw dipole. Thus, high stress is required for the dislocation line to break away from the inclined loops by cross-slip of each individual arm of the screw dipole coupled with glide of the 〈100〉 segment. On the other hand, increasing temperature and/or decreasing strain rate hardly change the above mechanisms, but monotonically reduce the obstruction by these loops. Simplifying the complex motion of the edge dislocation pinned by the inclined loops as a thermally-activated process of a 1/2[111] edge dislocation overcoming barriers, a hardening model for the inclined loops is proposed. This model well describes the dependence of loop strength on loop sizes, temperatures and strain rates. The model is then applied to predict irradiation hardening at experimental strain rates, and it shows reasonable agreement with experimental results.

Influence of High Concentration Vacancy-Type Defects on the Mobility of Edge Dislocation in &lt;i&gt;α&lt;/i&gt;-Iron: An Atomistic Investigation

Many vacancy-type defects (vacancy, vacancy clusters, and hydrogen-vacancy complexes) are generated in metals by plastic deformation in hydrogen environments. In this study, we use extensive molecular dynamics calculations based on a highly accurate interatomic potential to examine how vacancy-type defects affect the mobilities of edge dislocations in α-iron at a temperature range of 300–500 K and a dislocation speed 𝑉d range of 0.1–10 m/s. Under all conditions, the edge dislocation absorbs the vacancies along the slip plane and causes them to migrate with the edge dislocation. Although the necessary shear stress to glide edge dislocation in α-iron containing vacancy increases with dislocation speed, the effect is small compared to the hydrogen effects. The dislocation absorbs the hydrogen-vacancy complex along the slip plane and causes the hydrogen and the jog to migrate with the edge dislocation at low dislocation velocity regimes (𝑉d ≤ 0.1 m/s). Therefore, the hydrogen-vacancy complex exerts a continuous drag effect on the dislocation. At higher dislocation speeds (𝑉𝑑 ≥ 1 m/s), hydrogen does not migrate with the dislocation, resulting in the formation of isolated hydrogen detached from the dislocation and diffused into the material; only vacancy is absorbed. When multiple hydrogen-vacancy complexes are arranged along the slip plane, the dislocation absorbs them if they interact with dislocation at different points rather than at a single point to avoid the formation of a large jog at the colliding segment, and the required shear stress increases as the hydrogen atoms in the dislocation core increase.

Unambiguous coupling between acoustic and electromagnetic emissions in plastically deformed crystals

An evident coupling between acoustic (AE) and electromagnetic (EME) emissions has been proved experimentally during plastic deformation of LiF ionic monocrystals under uniaxial compression with simultaneous recording of both AE and EME. The strong correlation between AE and EME demonstrate clearly that the observed EME is caused by dynamical dislocations and charged vacancies in the ionic lattice during work hardening. The theoretical interpretation proposed to explain the observable EME is based on the well-known Stepanov effect that means sweeping-up the charged vacancies of a preferable sign by gliding edge dislocations and formation of charged Cottrell clouds. During work hardening dislocation pile-ups are formed, and a certain nonequilibrium charge density is accumulated at their heads, resulting to the dynamic electric polarization of the deformed crystal. As the external loading increases, a locked dislocation pile-up bursts through the stoppers and quickly loses its bound charge. The relaxation of this charge produces intrinsic polarization currents generating electric pulses strongly correlated with dynamic dislocation process during plastic deformation. To build the theoretical model, it is assumed that the relaxation current can be described as an athermic viscous motion of vacancies under the kinetic friction force ∼Bυ (B is the friction coefficient and υ is the vacancy velocity) in a self-consistent electric field determined by the distribution of the total charge density. The electrical signal generated by an acting slip system has been calculated. By comparing the calculated and experimentally measured electric signal patterns, the friction coefficient for the linear chain of vacancies (the analogue of an edge dislocation extra-plane) in LiF has been estimated to be B≃ 0.9⋅10–5 g cm–1⋅s–1. This value is in accordance with the corresponding coefficient for dislocations in ionic lattices.

Lowering the ductile-to-brittle transition temperature to -36 °C via fine-grained structures in chromium

The inherent ductile-to-brittle transition (DBT) behavior of body-centered cubic (BCC) metals severely limits their applications, and leads to low-temperature brittleness. To enhance the low temperature toughness of BCC metals, we take chromium as an example and design a fine-grained structure with average grain size of 5 μm, which shows a substantial decrease of DBT temperature to -36 °C. Compared with other samples with larger average grain sizes (45–135 μm), the fine-grained chromium still exhibits excellent toughness at -20 °C, and has the highest fracture energy and the yielding load. Our results reveal that numerous grain boundaries act as dislocation sources to emit easy glide edge dislocations at low temperature and also effectively slow down crack propagation, all together toughen ambient brittle chromium.

Time-harmonic analysis of multiple interface cracks in two dissimilar FGM half-planes: In-plane problem

In this study, the dynamic stress intensity factors (DSIFs) at the tip of several cracks located at the interface between two half-planes made of functionally graded materials (FGMs) are calculated using the Distributed Dislocation technique (DDT). In this paper, the in-plane time-harmonic loading is considered and it is assumed that the properties of the FGMs follow the law of exponential function. First, the problem of two dissimilar half-planes that are weakened by an interface Volterra type climb and glide edge dislocation is solved using the Fourier transform, and then, using the DDT, singular integral equations with a singularity of the Cauchy type are extracted. To calculate the DSIFs at the cracks tips, the resulting singular integral equations are numerically discretized and the dislocation densities on the crack surfaces are obtained. Second, the graphs are presented in the numerical results section to show the effects of change in the parameters such as non-homogeneous constant, Poisson ratio, crack length, frequency and interaction between the cracks on DSIFs.

Mixed-mode fracture analysis for two dissimilar half-planes with multiple interface moving cracks

In this paper, the distributed dislocation technique (DDT) is used to calculate the stress intensity factors (SIFs) at the tip of several moving cracks which are located at the interface between two dissimilar non-homogeneous half-planes. In this study, in-plane loading is considered and it is assumed that the properties of the non-homogeneous material change exponentially. First, by employing Fourier and Galilean transforms, the problem of Volterra type climb and glide edge dislocation is solved at the interface of two dissimilar materials, and then the DDT is used to obtain the singular integral equations of Cauchy type. The resulting singular equations are numerically discretized and solved to obtain dislocation density on the crack surfaces to determine the SIFs. Finally, the effects of change in parameters such as gradient non-homogeneous constant, Poisson ratio, crack growth rate and interaction between cracks on SIFs are shown graphically.

Key role of interaction between dislocations and hydrogen-vacancy complexes in hydrogen embrittlement of aluminum: discrete dislocation plasticity analysis

With the development of experimental techniques and characterization methods at the microscopic scale, a high concentration of hydrogen-induced vacancies and their clusters have been detected in a large variety of metals and alloys charged with hydrogen, which is supposed to play an important role in hydrogen-induced fracture process. In hydrogen environment, vacancies and their clusters can trap a certain number of H atoms to form vacancy-H complexes or clusters. To investigate the role of hydrogen-induced vacancies and their clusters in brittle-like failure in hydrogen environment, multi-scale modelling was performed in this work, with a particular attention on the interaction between dislocations and vacancy-H complexes. Firstly, the H-enhanced vacancy formation due to H-induced reduction in vacancy formation energy in Al was modelled by first principles calculations, and a hydrogen-influenced vacancy concentration model was proposed. Then, to capture the interaction between gliding edge dislocations and vacancy-H complexes and clusters, atomistic simulations were performed, and a mesoscale model quantitatively describing the pinning effect of vacancy-H complexes and clusters on the gliding edge dislocations was obtained. Finally, these quantitative models were introduced into a newly developed XFEM-based discrete dislocation plasticity scheme. With this scheme, mode-I crack propagation was simulated, where dislocation emission from crack-tip, dislocation evolution and cohesive crack propagation were considered, with a particular attention to the key role of the hydrogen-influenced dislocation evolution in the brittle-like failure of the H-charged metals. Based on these multi-scale simulations, a pinning effect of H-enhanced vacancies and vacancy-H complexes on edge dislocations was identified, which was proposed to be responsible for the brittle-like failure of Al in hydrogen environment. This pinning effect presents a good agreement with the hydrogen-restricted dislocation mobility observed in in situ fracture experiments.

In-plane transient analysis of two dissimilar nonhomogeneous half-planes containing several interface cracks

In this study, the linear elastic fracture mechanics theory is employed to calculate the dynamic stress intensity factors (DSIFs) of multiple cracks which are located at the interface between two dissimilar nonhomogeneous half-planes subjected to in-plane impacts. The change in the material properties is illustrated by an exponential law. First, the integral transforms and Volterra-type climb and glide edge dislocation at the interface of two dissimilar nonhomogeneous materials are used to obtain the solution. Then, using the distributed displacement technique, singular integral equations with Cauchy singularity are obtained. By solving these equations numerically in the Laplace domain, the dislocation density on the crack faces used to determine the DSIFs is obtained. Finally, numerical results exhibited graphically the effects of the gradient nonhomogeneous constant, crack length, the variation of time and the interaction between of cracks on the DSIFs.

Singularity-free defect mechanics for polar media

We present singularity-free solution for cracks within polar media in which material points possess both position and orientation. The plane strain problem is addressed in this study for which the generalized continua including micropolar, nonlocal micropolar, and gradient micropolar elasticity theories are employed. For the first time, the variationally consistent boundary conditions are derived for gradient micropolar elasticity. Moreover, having reviewed the solution to line defects including glide edge dislocation and wedge disclination from the literature, the fields of a climb edge dislocation within micropolar, nonlocal micropolar and gradient micropolar elasticity are derived. This completes the collection of line defects needed for an inplane strain analysis. Afterward, as the main contribution, using both types of line defects (i.e., dislocation being displacement discontinuity and disclination being rotational discontinuity), the well-established dislocation-based fracture mechanics is systematically generalized to the dislocation- and disclination-based fracture mechanics of polar media for which we have three translations together with three rotations as degrees of freedom. Due to the application of the line defects, incompatible elasticity is employed throughout the paper. Cracks under three possible loadings including stress and couple stress components are analyzed, and the corresponding line defect densities and stress and couple stress fields are reported. The singular fields are obtained once using the micropolar elasticity, while nonlocal micropolar, and gradient micropolar elasticity theories give rise to singularity-free fracture mechanics.

The linear steady state analysis of multiple moving cracks in a piezoelectric half-plane under in-plane electro-elastic loading

In this work, the steady state problem of multiple Yoffe-type cracks propagating in a piezoelectric half-plane within the framework of linear electroelasticity under in-plane electro-elastic loading is studied. At first, the closed-form solution of the moving electric and Volterra type climb and glide edge dislocations are derived using the complex Fourier transforms to achieve the integral equations of a piezoelectric half-plane with several moving cracks. Then, the integral equations with Cauchy-kind singularity are solved numerically to determine the mixed mode stress intensity factors and the electric displacement intensity factors in a piezoelectric medium. Finally, the effects of the loading conditions, crack moving speed, cracks lengths, cracks interactions and geometrical parameters on the field intensity factors are considered.

Mixed mode cracks in annular planes of cylindrical orthotropy subjected to inplane loading

This paper is concerned with the mixed mode crack problem in an orthotropic annular plane. First, the Michell solution is generalized for material of cylindrical anisotropy. Next by using this solution, fundamental solutions of climb and glide edge dislocations are provided for an annular orthotropic plane of cylindrical orthotropy. Then, an analytical solution to stress field of the intact annular plane under normal and shear tractions on its outer boundaries is presented in this article. The distributed dislocation technique is employed to analyze multiple arbitrary oriented interacting cracks in an annular orthotropic plane. The ensuing integral equations are solved numerically to obtain the dislocation density on the surfaces of the cracks. The stress intensity factors are evaluated by using these dislocation densities. The approach of this study is applied to example problems and shown to be accurate for cases where given in the literature. Finally, the effects of crack geometry and location, material anisotropy, and interaction of cracks on the resulting stress intensity factors at the crack tips are studied.

Interactions of multiple cracks in a transversely isotropic piezoelectric plane under mixed mode condition

In this paper, the interactions of multiple cracks in a piezoelectric material under the action of in-plane electromechanical loads are considered. The analytical solution of electric and Volterra climb and glide edge dislocations in an infinite piezoelectric plane are initially obtained by using the Fourier transform. The problem is then formulated by the distributed dislocation technique into a system of singular integral equations where the unknown variables are dislocation density functions on the surfaces of the cracks. These equations are solved numerically for dislocation density functions on the cracks which are used to determine field intensity factors. The results are highly affected by the interaction between multiple cracks and various loading conditions.

Dislocation-based gradient elastic fracture mechanics for in-plane analysis of cracks

The in-plane classical dislocation-based linear elastic fracture mechanics analysis is extended to the case of strain gradient elasticity. Nonsingular stress and smooth-closure crack profiles are derived. As in the classical treatment, the crack is represented by a distribution of climb edge dislocations (for Mode I) or glide edge dislocations (for mode II). These distributions are determined through the solution of corresponding integral equations based on variationally consistent boundary conditions. An incompatible framework is used and the nonsingular full-field plastic distortion tensor components are calculated. Numerical results and related graphs are provided illustrating the nonsingular behaviour of the stress/strain components and the smooth cusp-like closure of the crack faces at the crack tip. The work provides an alternative approach to celebrated “Barenblatt’s treatment” of cracks, without the introduction of a cohesive zone and related to intermolecular forces ahead of the physical crack tip. It also supplements a recent paper by the authors in which the mode III crack, represented by an array of screw dislocations, was solved within the present gradient elasticity framework.

Multiple crack problems in nonhomogeneous orthotropic planes under mixed mode loading conditions

Analytical method based on continuous dislocation technique is developed to examine the mixed mode behavior of a functionally graded orthotropic plane. First, the elastic stress fields in a functionally graded orthotropic infinite plane containing single Volterra types climb and glide edge dislocations are obtained. Using the dislocation solutions, the problem of interacting cracks is reduced to a system of singular integral equations for dislocation density functions on the surfaces of smooth cracks which are solved numerically for the dislocation density. Then, the dislocation density function is applied to calculate the stress intensity factors for several different cases of crack configurations and arrangements.

The mixed-mode analysis of a functionally graded orthotropic half-plane weakened by multiple curved cracks

The problem of functionally graded orthotropic half-plane with climb and glide edge dislocations is solved. Dislocations are used as the building blocks of defects to model cracks of modes I and II. Following a dislocation-based approach, the problem is reduced to a system of singular integral equations for dislocation density functions on the surfaces of smooth cracks. These integral equations enforce the crack-face boundary conditions and are solved numerically for the dislocation density. The numerical results include the stress intensity factors for several different cases of crack configurations and arrangements.

Distributed dislocation technique for cracks based on non-singular dislocations in nonlocal elasticity of Helmholtz type

In the present paper, the distributed dislocation technique is extended for crack problems within Eringen’s theory of nonlocal elasticity of Helmholtz type. Employing distributed dislocation technique, non-singular stresses of cracks of modes I, II and III are obtained using the non-singular stresses of climb edge, glide edge and screw dislocations and dislocation density functions which are solutions of the non-singular integral equations of distributed dislocation technique. The cracks are modeled by a continuous distribution of straight dislocations. The nonlocal elasticity solutions of crack problems do not contain a stress singularity. We found that the non-singular crack stresses are zero at the crack tip or near the crack tip.

Multiple interacting cracks in an orthotropic layer

The stress fields in an orthotropic layer containing climb and glide edge dislocations are obtained by means of the complex Fourier transform. Stress analysis in the intact layer under in-plane point loads is also carried out. These solutions are employed to derive integral equations for the layers weakened by several interacting cracks subject to in-plane deformation. The integral equations are of Cauchy singular type. These equations are solved numerically for the density of dislocations on a crack surface. The dislocation densities are utilized to derive stress intensity factor for cracks. Several examples are solved and the interaction between the two cracks is investigated.

Effects of temperature on the interactions of helium–vacancy clusters with gliding edge dislocations in α-Fe

The interaction of helium–vacancy (He–V) clusters with a gliding a/2<111>{110} edge dislocation in α-Fe is investigated by molecular dynamics methods under a constant strain rate at temperatures of 100–600K. A number of small HenVm (n/m=0–4) clusters initially placed at different positions relative to the slip plane are comparatively studied. The results show that the interaction of He–V clusters with gliding edge dislocations depends on the helium-to-vacancy (He/V) ratio, the position of the clusters relative to the slip plane, the cluster size, and also temperature. The obstacle strength of the He–V clusters relevant to the dislocation motion generally increases with increasing He/V ratio at the same temperature, but decreases slightly with increasing temperature for the same He–V cluster. One of the interesting results is that He–V clusters do not move along with the dislocation, even at 600K.

Effects of temperature on the interactions of helium–vacancy clusters with gliding edge dislocations in α-Fe

The interaction of He–vacancy (He–V) clusters with a gliding a/2〈111〉{110} edge dislocation in α-Fe is investigated by molecular dynamics methods under constant strain rate at different temperatures. A number of small HenVm (n/m=0–4) clusters initially placed at the same position on the slip plane are comparatively studied. The results show that the interaction of the He–V clusters with gliding edge dislocations depends on not only the helium-to-vacancy (He/V) ratio and the cluster size, but also temperature. The obstacle strength of the He–V clusters to the dislocation generally increases with increasing He/V ratio at the same temperature, but decreases with increasing temperature for the same He–V cluster. Furthermore, the small He–V clusters with the same He/V ratio have a small effect on the dislocation mobility at low temperatures. The results are discussed in terms of the pressure and atomic configurations of He atoms in the He–V clusters. One of the interesting results is that the He–V clusters remain almost at their original positions without their original configurations, and do not move along with dislocation, even at 600K.

Mixed mode axisymmetric annular cracks in a finite layer: Off angle crack initiation

The solutions of axisymmetric Volterra type climb and glide edge dislocations are obtained in a layer by means of the Hankel transforms. Utilizing the same procedure, Green’s function solution is obtained for a layer under self-equilibration normal ring traction. The distributed dislocation technique is used to construct integral equations for a system of co-axial annular cracks where the layer is under axisymmetric normal loads. These equations are solved numerically to obtain dislocation density on the cracks surfaces. The results are employed to determine stress intensity factors for annular and penny-shaped cracks and the interaction between two co-axial penny-shaped cracks is studied. Moreover, the stress intensity factors of the interacting cracks are determined such that they can be further used in conjunction with strain energy density (SED) failure criterion to obtain the possible direction of crack initiation that may not be apparent under mixed mode conditions.