Discrete Dislocation Plasticity Analysis Research Articles

Slip intermittency and dwell fatigue in titanium alloys: a discrete dislocation plasticity analysis

Slip intermittency and stress oscillations in titanium alloy Ti–7Al–O that were observed using in-situ far-field high energy X-ray diffraction microscopy (ff-HEDM) are investigated using a discrete dislocation plasticity (DDP) model. The mechanistic foundation of slip intermittency and stress oscillations are shown to be dislocation escape from obstacles during stress holds, governed by a thermal activation constitutive law. The stress drop events due to <a>-basal slip are larger in magnitude than those along <a>-prism, which is a consequence of their differing rate sensitivities, previously found from micropillar testing. It is suggested that interstitial oxygen suppresses stress oscillations by inhibiting the thermal activation process. Understanding of these mechanisms is of benefit to the design and safety assessment of jet engine titanium alloys subjected to dwell fatigue.

The effect of strain rate asymmetry on the Bauschinger effect: A discrete dislocation plasticity analysis

A two-dimensional discrete dislocation plasticity model was used to examine the role of strain rate asymmetry on the Bauschinger effect (BE). A simple single crystal single slip plane model was used first to investigate stress–strain response within high strain rate regimes where the rate sensitivity is mainly governed by dislocation nucleation and the free-flight of dislocations. Both the yield strength and the BE of the specimen showed a strong correlation to the forward and reverse deformation rate. Simulations were also carried out on a single crystal with multiple slip systems. The effect of source and obstacle density on the BE and its rate dependence was investigated. We find that the rate dependence of the BE is enhanced by increasing the source density in obstacle-free specimens and is reduced by obstacles when they are present. At low strain rates, where thermally-activated dislocation escape from obstacles becomes the predominant rate-controlling mechanism, the BE of single crystals is only affected by strain rates if the activation energy is low. Grain boundaries in polycrystalline specimens and obstacles with high activation energies act as barriers to dislocation motion, suggesting that the rate dependence under low strain rate regimes is enhanced by decreasing the grain size or reducing the activation energy associated with dislocation escape from obstacles. The effect mechanisms of strain rate asymmetry on the BE can be fundamentally crucial for multiple industrial applications, including lifetime assessments of aero-engine disks, zirconium cladding of nuclear reactor and the spring-back prediction of metal forming.

On the Origin of Plastic Deformation and Surface Evolution in Nano-Fretting: A Discrete Dislocation Plasticity Analysis

Discrete dislocation plasticity (DDP) calculations were carried out to investigate a single-crystal response when subjected to nano-fretting loading conditions in its interaction with a rigid sinusoidal asperity. The effects of the contact size and preceding indentation on the surface stress and profile evolution due to nano-fretting were extensively investigated, with the aim to unravel the deformation mechanisms governing the response of materials subjected to nano-motion. The mechanistic drivers for the material’s permanent deformations and surface modifications were shown to be the dislocations’ collective motion and piling up underneath the contact. The analysis of surface and subsurface stresses and the profile evolution during sliding provides useful insight into damage and failure mechanisms of crystalline materials subject to nano-fretting; this can lead to improved strategies for the optimisation of material properties for better surface resistance under micro- and nano-scale contacts.

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.

On the origin of microstructural discontinuities in sliding contacts: A discrete dislocation plasticity analysis

Two-dimensional discrete dislocation plasticity (DDP) calculations that simulate single crystal films bonded to a rigid substrate under sliding by a rigid sinusoid-shaped asperity are performed with various contact sizes. The contact between the thin film and the asperity is established by a preceding indentation and modelled using a cohesive zone method (CZM), whose behavior is governed by a traction-displacement relation. The emergence of microstructural changes observed in sliding tests has been interpreted as a localized lattice rotation band produced by the activity of dislocations underneath the contact. The depth of the lattice rotation band is predicted to be well commensurate with that observed in the corresponding tests. Furthermore, the dimension and magnitude of the lattice rotation band have been linked to the sliding distance and contact size. This research reveals the underpinning mechanisms for the microstructural changes observed in sliding tests by explicitly modelling the dislocation patterns and highly localized plastic deformation of materials under various indentation and sliding scenarios.

A new hardness formula incorporating the effect of source density on indentation response: A discrete dislocation plasticity analysis

Planar discrete dislocation plasticity (DDP) calculations that simulate thin single crystal films bonded to a rigid substrate indented by a rigid wedge are performed for different values of film thickness and dislocation source density. As in prior studies, an indentation size effect (ISE) is observed when indentation depth is sufficiently small relative to the film thickness. The dependence of the ISE on dislocation source density is quantified in this study, and a modified form of the scaling law for the dependence of hardness on indentation depth, first derived by Nix and Gao, is proposed, which is valid over the entire range of indentation depths and correlates the length scale parameter with the average dislocation source spacing. Nano-indentation experimental data from the literature are fitted using this formula, which further verifies the proposed scaling of indentation pressure on dislocation source density.

Discrete dislocation plasticity analysis of the high-temperature cyclic response of composites

Discrete dislocation plasticity (DDP) analysis of the high-temperature cyclic deformation of two-phase composites comprising a plastic matrix and elastic precipitates is presented. Deformation of the matrix is by climb-assisted glide of dislocations while the precipitates deform by a combination of bulk elasticity and stress-driven interfacial diffusion. The DDP calculations predict a cyclically softening response due to the formation of dislocation cell structures within the matrix. The dislocation cell sizes decrease with decreasing size of the unit cell (or equivalently matrix channels) and this results in an increased cyclic softening rate in composites with smaller unit cells. Interfacial diffusion also enhances the formation of dislocation cell structures and thereby promotes cyclic softening. These results are consistent with predictions of the creep behaviour that indicate that the increase in the creep rate (i.e. tertiary creep) is also associated with the formation of dislocation cell structures within the matrix.

Static friction of sinusoidal surfaces: a discrete dislocation plasticity analysis

Discrete dislocation plasticity simulations are carried out to investigate the static frictional response of sinusoidal asperities with (sub)-microscale wavelength. The surfaces are first flattened and then sheared by a perfectly adhesive platen. Both bodies are explicitly modelled, and the external loading is applied on the top surface of the platen. Plastic deformation by dislocation glide is the only dissipation mechanism active. The tangential force obtained at the contact when displacing the platen horizontally first increases with applied displacement, then reaches a constant value. This constant is here taken to be the friction force. In agreement with several experiments and continuum simulation studies, the friction coefficient is found to decrease with the applied normal load. However, at odds with continuum simulations, the friction force is also found to decrease with the normal load. The decrease is caused by an increased availability of dislocations to initiate and sustain plastic flow during shearing. Again in contrast to continuum studies, the friction coefficient is found to vary stochastically across the contact surface, and to reach locally values up to several times the average friction coefficient. Moreover, the friction force and the friction coefficient are found to be size-dependent.

Discrete dislocation plasticity analysis of the effect of interfacial diffusion on the creep response of Ni single-crystal superalloys

Discrete dislocation plasticity (DDP) analysis of the high temperature creep deformation of a single crystal Ni superalloy comprising Ni3Al precipitates (γ′) in a Ni matrix (γ) is presented. The γ′ precipitates remain elastic but can also deform due to the stress-driven inter-diffusion of the Al within the Ni on the γ/γ′ interface while plastic deformation of the γ phase occurs by a combination of dislocation glide and dislocation climb coupled to the diffusion of vacancies. At relatively low applied uniaxial tensile stresses, the creep strain rates are very low in the absence of interfacial diffusion. This is due to the stress-induced pile up of dislocations at γ/γ′ interfaces that serves to inhibit further nucleation and suppresses continued plastic flow in the γ phase. When interfacial diffusion is permitted, the creep rates not only increase but the superalloy also exhibits distinct secondary and tertiary creep regimes. While this change in behaviour is a result of interfacial diffusion, the contribution of the average γ′ strain to the deformation of the superalloy is small. Rather, the diffusional deformation at the interface results in the development of a wavy interface which relaxes the back-stresses of dislocations piled-up at the γ/γ′ interfaces. This permits continued dislocation activity within the γ phase with dislocations arranging themselves into low energy cell-structures in the γ phase via dislocation climb. The formation of these structures results in an increase in the creep strain rate and the onset of the tertiary creep regime. At high applied stresses, the high initial dislocation density within the γ phase results in the continued climb motion of dislocations and an evolving spatial distribution of vacancies within the superalloy. Thus, creep deformation occurs even in the absence of interfacial diffusion although the creep rates are significantly increased when interfacial diffusion is present. The DDP analysis presented here demonstrates the critical role of interfacial diffusion in controlling the creep rates of Ni superalloys and suggests that interface engineering to reduce interfacial diffusion rates will aid in improving the creep performance of these alloys.

Discrete dislocation plasticity analysis of loading rate-dependent static friction.

From a microscopic point of view, the frictional force associated with the relative sliding of rough surfaces originates from deformation of the material in contact, by adhesion in the contact interface or both. We know that plastic deformation at the size scale of micrometres is not only dependent on the size of the contact, but also on the rate of deformation. Moreover, depending on its physical origin, adhesion can also be size and rate dependent, albeit different from plasticity. We present a two-dimensional model that incorporates both discrete dislocation plasticity inside a face-centred cubic crystal and adhesion in the interface to understand the rate dependence of friction caused by micrometre-size asperities. The friction strength is the outcome of the competition between adhesion and discrete dislocation plasticity. As a function of contact size, the friction strength contains two plateaus: at small contact length [Formula: see text], the onset of sliding is fully controlled by adhesion while for large contact length [Formula: see text], the friction strength approaches the size-independent plastic shear yield strength. The transition regime at intermediate contact size is a result of partial de-cohesion and size-dependent dislocation plasticity, and is determined by dislocation properties, interfacial properties as well as by the loading rate.

Discrete dislocation plasticity analysis of contact between deformable bodies of simple geometry

A contact mechanical model is presented where both metal bodies can deform by discrete dislocation plasticity. The model intends to improve on previous dislocation dynamics models of contact, where only a plastically deformable body was considered, flattened by a rigid platen. The effect of the rigid platen was mimicked through boundary conditions acting on the deformable body. While the formulation is general, the simulations presented here are only performed for contact between a plastically deforming body with sinusoidal surface and a flat body that is either elastic or rigid.Results show that the contact conditions, i.e. frictionless and full stick, affect the morphology of the contact as well as the contact pressure distribution. This is because dislocations can glide through the frictionless contact and fragment it, but do not penetrate a sticking contact. Average quantities like mean apparent contact pressure and total plastic slip are, instead, independent of contact conditions and of the details of the contact area.A size dependence is observed in relation to the onset of plastic deformation, where surfaces with smaller wavelength and amplitude require a larger contact pressure to yield than self similar surfaces with larger wavelength. The size dependence is very pronounced when the flat body is rigid, but fades when the compliance of the flat body is large.

Plastic shear response of a single asperity: a discrete dislocation plasticity analysis

We investigate the plastic shear response during static friction of an asperity protruding from a large FCC single crystal. The asperity is in perfectly adhesive contact with a rigid platen and is sheared by tangentially moving the platen. Using discrete dislocation plasticity simulations, we elucidate the plastic shear behaviour of single asperities of various size and shape, in search for the length scale that controls the plastic behaviour. Since plasticity can occur also in the crystal, identification of the length scale that controls a possible size-dependent plastic behaviour is far from being trivial. It is found that scaling down the dimensions of an asperity results in a higher contact shear strength. The contact area is dominant in controlling the plastic shear response, because it determines the size of the zone, in and below the asperity, where dislocation nucleation can occur. For a specific contact area, there is still a dependence on asperity volume and shape, but this is weaker than the dependence on contact area alone.

Climb-Enabled Discrete Dislocation Plasticity Analysis of the Deformation of a Particle Reinforced Composite

The shear deformation of a composite comprising elastic particles in a single crystal elastic–plastic matrix is analyzed using a discrete dislocation plasticity (DDP) framework wherein dislocation motion occurs via climb-assisted glide. The topology of the reinforcement is such that dislocations cannot continuously transverse the matrix by glide-only without encountering the particles that are impenetrable to dislocations. When dislocation motion is via glide-only, the shear stress versus strain response is strongly strain hardening with the hardening rate increasing with decreasing particle size for a fixed volume fraction of particles. This is due to the formation of dislocation pile-ups at the particle/matrix interfaces. The back stresses associated with these pile-ups result in a size effect and a strong Bauschinger effect. By contrast, when dislocation climb is permitted, the dislocation pile-ups break up by forming lower energy dislocation wall structures at the particle/matrix interfaces. This results in a significantly reduced size effect and reduced strain hardening. In fact, with increasing climb mobility an “inverse size” effect is also predicted where the strength decreases with decreasing particle size. Mass transport along the matrix/particle interface by dislocation climb causes this change in the response and also results in a reduction in the lattice rotations and density of geometrically necessary dislocations (GNDs) compared to the case where dislocation motion is by glide-only.

Interaction between neighboring asperities during flattening: A discrete dislocation plasticity analysis

Discrete dislocation plasticity simulations are performed to investigate the role of interaction between neighboring asperities on the contact pressure induced by a rigid platen on a rough surface. The rough surface is modeled as an array of equispaced asperities with a sinusoidal profile. The spacing between asperities is varied and the contact pressure necessary to flatten the surface to a given strain is computed. Plasticity in the asperities and in the crystal below is described by the collective glide of dislocations of edge character.Results show that the mean contact pressure necessary to flatten closely spaced asperities is larger than that required to flatten widely separated asperities. A small dependence on asperity density is already observed for a purely elastic material, but it is enhanced for small asperities, in the presence of dislocation plasticity. Plastic strain gradients, dislocation limited plasticity and interaction between neighboring plastic zones all contribute to what we will call the asperity density effect. Since dislocation limited plasticity plays a dominant role, the asperity density effect will mainly be relevant for surfaces having small asperity roughness.

Discrete dislocation plasticity analysis of dispersion strengthening in oxide dispersion strengthened (ODS) steels

A discrete dislocation plasticity analysis of dispersion strengthening in oxide dispersion strengthened (ODS) steels was described. Parametric dislocation dynamics (PDD) simulation of the interaction between an edge dislocation and randomly distributed spherical dispersoids (Y2O3) in bcc iron was performed for measuring the influence of the dispersoid distribution on the critical resolved shear stress (CRSS). The dispersoid distribution was made using a method mimicking the Ostwald growth mechanism. Then, an edge dislocation was introduced, and was moved under a constant shear stress condition. The CRSS was extracted from the result of dislocation velocity under constant shear stress using the mobility (linear) relationship between the shear stress and the dislocation velocity. The results suggest that the dispersoid distribution gives a significant influence to the CRSS, and the influence of dislocation dipole, which forms just before finishing up the Orowan looping mechanism, is substantial in determining the CRSS, especially for the interaction with small dispersoids. Therefore, the well-known Orowan equation for determining the CRSS cannot give an accurate estimation, because the influence of the dislocation dipole in the process of the Orowan looping mechanism is not accounted for in the equation.

A discrete dislocation plasticity analysis of a single-crystal semi-infinite medium indented by a rigid surface exhibiting multi-scale roughness

Discrete dislocation plasticity was used to analyse plane-strain indentation of a single-crystal elastic–plastic semi-infinite medium by a rigid surface exhibiting multi-scale roughness, characterised by self-affine (fractal) behaviour. Constitutive rules of dislocation emission, glide and annihilation were used to model short-range dislocation interactions. Dislocation multiplication and the development of subsurface shear stresses due to asperity microcontacts forming between a single-crystal medium and a rough surface were examined in terms of surface roughness and topography (fractal) parameters, slip-plane direction and spacing, dislocation source density, and contact load (surface interference). The effect of multi-scale interactions between asperity microcontacts on plasticity is elucidated in light of results showing the evolution of dislocation structures. Numerical solutions yield insight into plastic flow of crystalline materials in normal contact with surfaces exhibiting multi-scale roughness.

A Discrete Dislocation Plasticity Analysis of a Single-Crystal Half-Space Indented by a Rigid Cylinder

Elastic-plastic indentation of a single-crystal half-space by a rigid cylinder was analyzed by discrete dislocation plasticity. Short-range dislocation interactions were modeled by a set of constitutive rules of dislocation emission, glide, pinning (by obstacles), and annihilation. The occurrence of the first dislocation dipole, multiplication of dislocations, and evolution of subsurface stress field were examined in terms of contact load, dislocation source density, slip-plane distance and orientation angle, and indenter radius. In the presence of defects (dislocation sources), the critical load for dislocation initiation is less than that of a defect-free medium and depends on dislocation source density, slip-plane distance, and indenter radius. The critical indenter radius resulting in deformation under the theoretical material strength is determined from numerical results, and the role of dislocation obstacles is interpreted in terms of their spatial density. Simulations provide insight into yielding and plastic deformation of indented single-crystal materials, and establish a basis for developing coarse-grained plasticity models of localized contact deformation in polycrystalline solids.

Cylindrical nano-indentation on metal film/elastic substrate system with discrete dislocation plasticity analysis: A simple model for nano-indentation size effect

The cylindrical nano-indentation on metal film/elastic substrate is computationally studied using two-dimensional discrete dislocation plasticity combined with the commercial software ANSYS®, with a focus on the storage volume for geometrically necessary dislocations (GNDs) inside the films and the nano-indentation size effect (NISE). Our calculations show that almost all GNDs are stored in a rectangular area determined by the film thickness and the actual contact width. The variations of indentation contact width with indentation depth for various film thicknesses and indenter radii are fitted by an exponential relation, and then the GND density underneath the indenter is estimated. Based on the Taylor dislocation model and Tabor formula, a simple model for the dependence of the nano-indentation hardness of the film/substrate system on the indentation depth, the indenter radius and the film thickness is established, showing a good agreement with the present numerical results.

A dislocation-dynamics-based derivation of the Frank–Read source characteristics for discrete dislocation plasticity

In this paper, the main characteristics of Frank–Read (F–R) sources used in a mechanism-based discrete dislocation plasticity (M-DDP) analysis are estimated by employing a recently developed non-singular continuum elastic theory of dislocations. The critical nucleation stress, τnuc, is determined more accurately because the dislocation core effects are considered precisely by atomistically-informing the dislocation dynamics simulations. The nucleation time is calculated and compared with the previous predictions. The dependence of the drag coefficient of dislocations on dislocation line orientation, which affects the nucleation time and also the shape of the emitted dislocation loop, is considered. In M-DDP simulations, τnuc used for sources is calculated based on the assumption of an infinite domain. In reality, however, the critical nucleation stress is affected by other F–R sources. It is proposed in this paper that the critical nucleation stress should be modified by considering the effects of other dislocation sources. To this end, τnuc should be determined for an F–R source in a finite cell with periodic boundary conditions.

Discrete dislocation plasticity analysis of single crystalline thin beam under combined cyclic tension and bending

The cyclic plastic response of a single crystalline thin beam subject to combined cyclic tension and bending is analyzed using two-dimensional discrete dislocation plasticity. In this contribution, special attention is paid to the difference in the inherent mechanism of the size effect for different cyclic loads. Results show that the cyclic plastic response has a strong size effect for both cyclic pure tension–compression and pure bending. However, the inherent mechanisms are different. The dislocation starvation mechanism dominates the cyclic tension–compression while the geometrically necessary dislocation dominates the cyclic pure bending. When the combined cyclic tension and bending are applied to the thin beam, the cyclic moment–rotation response shows strong size effect while the stress–strain response shows weak or even no size effect. In addition, it is also found that the cyclic loading paths have considerable influences on the shape of the cyclic stress–strain loops.