Dislocation-grain Boundary Interactions Research Articles

A model for physical dislocation transmission through grain boundaries and its implementation in a discrete dislocation dynamics tool

The mechanical behavior of most metals in engineering applications is dominated by the grain size. Physics-based models of the interaction between dislocations and the grain boundary are important to correctly predict the plastic deformation behavior of polycrystalline materials. Dislocation-grain boundary interaction is complex and a challenge to model. We present a model for simulating the physical transmission of dislocations through grain boundaries within Discrete Dislocation Dynamics tools. The properties (glide plane, Burgers vector, initial length) of the transmitted dislocation are chosen based on geometric criteria as well as a maximization of the resolved shear stress of the transmitted dislocation. Additionally, stress and displacement transparency as well as the discontinuity are ensured via a grain boundary dislocation – a butterfly-like geometry in the general case – whose properties are selected to minimize the residual Burgers vector at the interface. This additional ‘grain boundary dislocation’ allows a direct comparison as well as a calibration of the model with experiments on the macroscale particularly for neighboring grains with a high dislocation density contrast. Two basic examples illustrate the model and an application to a 40-grain polycrystal demonstrates the scalability of the approach.

A Lie-algebra-based description of disclination densities and the quantification of partial disclinations in deformed polycrystalline metals

Crystalline defects (e.g., dislocations, disclinations and grain boundaries) play a critical role in determining the mechanical and functional properties of metallic materials. From a physical point of view, dislocations and disclinations are the two fundamental types of topological defects in crystals, which originate from the breaking of translational symmetry and rotational symmetry, respectively. In spite of extensive studies on dislocations in the literature, the effects of disclinations on mechanical properties of metals have not been well recognized, partially due to the lack of an appropriate description for the rotational nature of disclinations. Here we suggest a Lie-algebra-based method to quantify the rotational properties of disclinations, which leads to a convenient way to determine disclination density distribution directly from Electron Backscatter Diffraction data. Through quasi-in-situ Electron Backscatter Diffraction characterizations, three major formation mechanisms of disclinations have been identified in deformed polycrystalline Mg alloys, i.e., dislocation-grain boundary interaction, dislocation redistribution and twin-twin reaction, all of which can be treated as topological reactions among various types of defects under a general framework. Our work not only suggests a new mathematical tool to investigate the interactions and reactions among multiple types of crystalline defects, but also provides a new insight to understand the deformation behaviors of metals and alloys based on dislocation/disclination theory.

Role of Ag segregation on microscale strengthening and slip transmission in an asymmetric Σ5 copper grain boundary

Micropillar compression was used to investigate whether Ag segregation to an asymmetric Σ5[001] grain boundary will lead to measurable strength differences compared to the pure copper bicrystal. Ag segregation was accomplished by deposition and subsequent annealing of an Ag thin-film applied on the surface of the Cu bicrystal. Atom probe tomography analysis indicated Ag segregation at the grain boundary with a peak concentration of 2.3 at.%. While the pristine Σ5 grain boundary shows a yield strength of 288 ± 18 MPa when compressing 1 µm diameter pillars along 〈001〉, micropillars containing an Ag-segregated Σ5 grain boundary demonstrated an increased yield strength of 318 ± 17 MPa. In addition, post-deformation electron microscopy was carried out to examine the active slip systems and slip transmission across Ag-free and Ag-containing bicrystals. The results are compared to reference measurements of the adjacent single crystal grains. The 1 µm pillar diameter promoted deformation governed by dislocation-grain boundary interactions for the bicrystalline pillars. This is the first time that changes in flow stress associated with grain boundary segregation have been quantified locally without interference from other mechanisms such as solid solution strengthening, formation of precipitates or changes in stacking fault energy. The results clearly indicate that purely geometrical models for slip transmission are not sufficient as the local atomic structure and composition influence dislocation transmission through grain boundaries.

Sensitivity of Dislocation-GB interactions to simulation setups in atomistic models

Dislocation-grain boundary (GB) interactions play an integral role in strengthening of crystalline materials, and are dependent on external loading conditions and atomic arrangements at the grain boundary. While molecular dynamics (MD) simulations can provide critical insights into relationships between these parameters and the exact interaction, the outcomes are sensitive to the computational setup. In this work, we explore the effect of computational setup (system size, GB orientation and boundary conditions) on stress-controlled dislocation-grain boundary (DGB) reactions using MD simulations for a well-studied copper symmetric 〈112〉 tilt boundary. The study demonstrates that the DGB reactions (pinning, absorption, transmission, etc.) are sensitive to the system size and the orientation of the GB to the applied stress. Additionally, the current work shows that there is a critical system size for the dislocation-grain boundary reaction stresses to converge, one which was found to be much larger than the setups in comparable MD studies. This was attributed to the specific stress states and the influence of surfaces, fixed or free, as these computational setups are modified. Finally, a stress-controlled setup with minimal model artifacts is examined, and the effect of coupled Schmid and non-Schmid stress components on the dislocation-GB reactions are discussed.

Nano Mechanical Characterization and Physical Modeling of Plastic Deformation Chapter 1: Dislocation-Grain Boundary Interaction as a Strengthening Factor

Mechanical behaviors of metallic materials in a small scale are characterized and physically modeled based on experimental measurements and computational simulation. Local plasticity in the vicinity of a grain boundary is considered in terms of an interaction between dislocation and grain boundary. It is shown experimentally that nanoindentation technique can detect a resistance to dislocation slip transfer by a grain boundary with a geometrical or a chemical factor. Molecular dynamic simulation revealed that the geometrical effect depends on not only a misorientation but also a combination with a dislocation character. TEM in-situ straining has a great potential to measure directly a critical stress upon slip transfer as well as a dislocation reaction at a grain boundary. Another potential reaction of a dislocation absorption at a grain boundary was discussed based on both the experimental results by TEM in-situ observation and the atomistic simulation in bcc metals.

Experimental investigation of dislocation-grain boundary interaction in coarse-grained high‑manganese steels using quasi in situ electron channelling contrast imaging

Experimental investigation of dislocation-grain boundary interaction in coarse-grained high‑manganese steels using quasi in situ electron channelling contrast imaging

Energetic and atomic structural analyses of the screw dislocation absorption at tilt grain boundaries in BCC-Fe.

The dislocation-grain boundary (GB) interaction plays an important role in GB-related plasticity. Therefore, an atomistic investigation of the interaction provides a deeper understanding of the strength and fracture of polycrystalline metals. In this study, we investigated the absorption of a screw dislocation with a Burgers vector perpendicular to the GB normal and the corresponding symmetric tilt grain boundaries (STGBs) in BCC-Fe based on molecular static simulations focusing on the STGB-dislocation interaction energy and atomistic structural changes at GB. The STGB-screw dislocation interaction depends on the energetical stability of the STGB against the GB shift along the Burgers vector direction. When the interaction exhibited a large attractive interaction energy, the dislocation dissociation and the GB shift along the Burgers vector direction occurred simultaneously. The interaction energy reveals that the interaction depends on the energetical stability of the STGB in terms of the GB shift in addition to the geometrical descriptor of the GB type, such as the Σ value. The same behavior was also obtained in the reaction when the second dislocation was introduced. We also discuss the screw dislocation absorption and rearrangement of the GB atomistic structure in STGB from an energetic viewpoint.

Molecular dynamics study on the effect of electric current on electrically-assisted scratching for crystal copper

Investigation of the effect of electric current on the plastic deformation mechanism of metals during the electrically-assisted machining process is significant in further improving surface properties. In this paper, the molecular dynamics (MD) method is adopted to simulate the electrically-assisted scratching process of crystal copper, obtaining and analyzing the surface morphology, potential energy change, von Mises stress distribution, and crystal defect structure evolution. The MD simulation results show that the electric current effectively expands the dislocation slip range, resulting in a larger plastic deformation zone. Meanwhile, the combined action of the electron wind forces and Joule heating causes more dislocations to proliferate and increases the dislocation density limit, enhancing the plastic deformation ability of the single-crystal copper. Furthermore, the electric current strengthens the dislocation-grain boundary interactions and reduces the hindering effect of the grain boundaries on dislocations, promoting more dislocations to cross the grain boundaries. This work will be helpful for guiding the optimization of surface strengthening techniques to get better surface properties of metals.

Atomic-scale study of dislocation-grain boundary interactions in Cu bicrystal by Berkovich nanoindentation

The plastic behavior of metal materials is mainly dominated by dislocation movement, whereas for polycrystalline metals, dislocation-grain boundary (GB) interactions play a significant role in the mechanical response. In the present work, deformation mechanisms of single crystal and bicrystal Cu workpieces subjected to Berkovich nanoindentation are studied by experiments and molecular dynamics (MD) simulations. The numerical model considers crystallographic orientations of the individual grains determined by electron backscatter diffraction (EBSD) characterization of the designated location on the polycrystalline surface. Experimental results indicate as the distance between the indentation and the GB decreases, the hardness of the tested specimen decreases and Young's modulus increases. Meanwhile, the corresponding simulation results reveal the anisotropic nature of dislocation evolution under the indenter for different crystallographic orientations of the single crystal Cu. Furthermore, GB as a complicated factor to the dislocation motion leads to the unusual deform behavior of materials in the vicinity of the GB, and dislocation-GB interactions introduce different deformation mechanisms. For the GB with a high angle of [1-11] 59.8°, dislocation slip along the GB is believed to play an important role in the decrease of the hardness.

Hydrogen effect on the nanohardness in the vicinity of grain boundary: Experiment and theory

The nanoindentation (NI) technique was employed to investigate the hydrogen effect on nanohardness near grain boundary (GB) of a polycrystalline nickel sample in the present work. An increase of nanohardness due to hydrogen segregation at GB was captured by nanoindentation experiments. With a newly developed GB hardening model, the observed hardening effect upon approaching GB in both H free and H charged polycrystalline Ni was explained. By combining the new GB hardening model with the model depicting dislocation transmission across GB, the hydrogen induced energy barrier enhancement was calculated, which can be used in multi-scale modeling of dislocation–GB interaction. The finding of this work is important for understanding hydrogen embrittlement mechanism of polycrystalline metals.

Multiscale analyses of the interaction between dislocation and Σ9 symmetric tilt grain boundaries in Fe–Si bicrystals by nanoindentation technique

Dislocation–grain boundary (GB) interaction plays a crucial role in the strengthening mechanism of polycrystalline metals. In this study, we evaluated the interaction between dislocation and two types of Σ9 symmetric tilt GBs using combined experimental and computational nanoindentation analyses. The experimental and simulation results are obtained at different spatial scales and are complementary. Experimental nanoindentation, in which the indent position was 1.0 μm offset from the GBs, showed that a considerable plastic zone was formed in the adjacent grain in the case of Σ9{114}, whereas this zone was absent in the case of Σ9{221}. Atomistic analysis provided information on the activated Burgers vector caused by a large resolved shear stress and the change in the GB structure due to dislocation absorption. Moreover, from experimental and computational nanoindentation analyses of the case in which the indent position was exactly on the GB, it was found that the load required for dislocation nucleation from the GB in Σ9{221} was slightly higher than that in the case of Σ9{114}. Dislocation trajectories observed in the on-GB experiments were similar to those in the on-GB simulations, where an activated Burgers vector was detected. The origin of the effects of GBs on dislocation transmission and nucleation was discussed based on the mechanical responses and dislocation behaviors obtained in experiments, activated slip directions in atomistic simulations, and theoretical models for dislocation–GB interaction.

Misorientation and grain boundary orientation dependent grain boundary response in polycrystalline plasticity

This paper studies the evolution of intergranular localization and stress concentration in three dimensional micron sized specimens through the Gurtin grain boundary model (J Mech Phys Solids 56:640–662, 2008) incorporated into a three dimensional higher-order strain gradient crystal plasticity framework (Yalcinkaya et al. in Int J Solids Struct 49:2625–2636, 2012). The study addresses continuum scale dislocation-grain boundary interactions where the effect of crystal orientation mismatch and grain boundary orientation are taken into account through the grain boundary model in polycrystalline metallic specimens. Due to the higher-order nature of the model, a mixed finite element formulation is used to discretize the problem in which both displacements and plastic slips are considered as primary variables. For the treatment of grain boundaries within the solution algorithm, an interface element is formulated and implemented together with the bulk plasticity model. The capabilities of the framework is demonstrated through 3D polycrystalline examples considering grain boundary conditions, grain boundary strength, the orientation distribution and the specimen size. A detailed grain boundary condition and stress concentration analysis is presented. The advantages and the disadvantages of the model is discussed in detail through numerical examples.

High temperature indentation creep mechanisms of metal-ceramic nanolaminates

Creep, as one of the mechanical properties for evaluating the resistance of deformation under a persistent stress, is extremely important in the application of metal/ceramic nanolaminates. In this work, the creep behaviors of Al/SiC nanolaminates with layer thickness of 10 nm and 100 nm were studied by means of nanoindentation in the temperature range from 25 °C to 150 °C. It was found that the stress exponent of nanolaminates for layer thickness of 100 nm increased with an increase in temperature. The stress exponent of Al was obtained by inverse methodology based on the finite element simulations, indicating that the creep mechanism changed from dislocation-grain boundary interaction to Coble creep. In the contrary, nanolaminates with layer thickness of 10 nm exhibited temperature-independent creep behaviors. This was rationalized by the co-deformation of Al and SiC layers beneath the indenter, which was dominated in the whole temperature range. In addition, all of these conclusions were further confirmed by the detailed transmission electron microscopic observation, the activation energy and the activation volume analysis.

Hardening behavior and deformation microstructure beneath indentation in heavy ion irradiated 12Cr-ODS steel at elevated temperature

Hardness behavior and deformation of the microstructure beneath the indentation in 12Cr-ODS steel after exposure to heavy ion irradiation at 573 K were investigated with combined applications of nano-indentation tests, EBSD analysis, and TEM observation. The inhomogeneous nano-indentation hardness behavior was firstly investigated in both non-irradiated and irradiated specimens and compared to those at room temperature (RT) irradiation. Subsequently, TEM observations were performed to understand the deformation behaviors beneath the indentation tested at typical low-indexed orientations. Obvious irradiation hardening was confirmed in both the normal direction (ND) and rolling direction (RD) specimens, and the hardening effect intensified with an increase in irradiation dose. Meanwhile, various anisotropic hardness behaviors were observed such as a lower hardness value and a weaker hardening effect in the RD specimen compared to the ND specimen, and a lower hardness value but a greater hardening effect in [001] orientation relative to [111] orientation. Furthermore, results from 573 K irradiation showed similar anisotropic hardness behaviors with those obtained from RT irradiation, despite the fact that irradiation at 573 K exhibited a weakened irradiation hardening effect in this steel. TEM observation of the deformation microstructure beneath the indentation reveals that (i) the depth of the deformation affected zone varied with orientation, ranging from ~6-9 times that of the indent depth, and (ii) distinct dislocation-grain boundary (GB) interactions beneath the indentations was confirmed to exhibit dependence on the geometric relation between GB and indenter impression direction. Correlation between the anisotropic hardness behavior and microstructural features is discussed based on Schmid factor analysis, comparison of geometric favorability between indenter and possible slip planes, and TEM observation of deformation microstructure. The results conclude that the anisotropic hardness behaviors in the present 12Cr-ODS steel are ascribed to the combined effect of crystal orientation and the non-uniform grain morphology with the existence of the elongated grains having low aspect ratio in the ND plane and nano-layered grains in the RD plane.

Dislocation-grain boundary interaction in metallic materials: Competition between dislocation transmission and dislocation source activation

Dislocation transmission across grain boundary (GB) and activation of dislocation source in adjacent grains are considered common features of dislocation-GB interactions in regulating mechanical properties and behaviors of metallic materials and structures. However, it is currently unclear which of dislocation transmission and dislocation source activation plays the dominant role in regulating dislocation-GB interaction. To study the competition between dislocation transmission and dislocation source activation, a theoretical framework is established based on a dislocation pile-up model. It is found that both dislocation transmission and dislocation source activation exhibit strong dependence on the GB misorientation angle. The critical transmission stress derived based on an energy method also depends on the grain size in a scaling form similar to the Hall-Petch relation. The outgoing slip systems during dislocation transmission are successfully predicted and agree with experimental observations. Regarding the dislocation source activation, the critical activation stress is investigated by examining the local stress fields generated by single and multiple slip dislocation pile-ups. It is found that compared with single slip dislocation pile-up, the result of multiple slip dislocation pile-ups displays lower critical activation stresses and exhibits feature of sensitivity to loading direction, interpreting the reported results of dislocation source activation in polycrystals. Further comparison between dislocation transmission and dislocation source activation for ⟨100⟩ tilt GBs indicates that the dislocation transmission prevails at low angle GB, while dislocation source activation is prone to occur at high angle GB. Our theoretical studies quantify the dislocation-GB interaction induced by dislocation pile-ups, shed light on the competition between dislocation transmission and dislocation source activation, and might provide essential guidance for high-performance metallic material design.

Theoretical framework for predicting solute concentrations and solute-induced stresses in finite volumes with arbitrary elastic fields

A theoretical model for computing the interstitial solute concentration and the interstitial solute-induced stress field in a three-dimensional finite medium with any arbitrary elastic fields was developed. This model can be directly incorporated into two-dimensional or three-dimensional discrete dislocation dynamics simulations, continuum dislocation dynamics simulations, or crystal plasticity simulations. Using this model, it is shown that a nano-hydride can form in the tensile region below a dissociated edge dislocation at hydrogen concentration as low as χ0=5×10−5, and its formation induces a localized hydrogen elastic shielding effect that leads to a lower stacking fault width for the edge dislocation. Additionally, the model also predicts the segregation of hydrogen at Σ109(13 7 0)/33.4∘ symmetric tilt grain boundary dislocations. This segregation strongly alters the magnitude of the shear stresses at the grain boundary, which can subsequently alter dislocation-grain boundary interactions and dislocation slip transmissions across the grain boundary. Moreover, the model also predicts that the hydrogen concentration at a mode-I central crack tip increases with increasing external loading, higher intrinsic hydrogen concentration, and/or larger crack lengths. Finally, linearized approximate closed-form solutions for the solute concentration and the interstitial solute-induced stress field were also developed. These approximate solutions can effectively reduce the computation cost to assess the concentration and stress field in the presence of solutes. These approximate solutions are also shown to be a good approximation when the positions of interest are several nanometers away (i.e. long-ranged elastic interactions) from stress singularities (e.g. dislocation core and crack tip), for low solute concentrations, and/or at high temperatures.

Effects of electron beam manufacturing induced defects on fracture in Inconel 718

The effects of electron beam manufactured (EBM) process-induced defects on local microstructural failure initiation and propagation in IN 718 have been investigated. Predictions for transgranular fracture, based on local cleavage plane stresses, and for intergranular fracture, based on dislocation-grain boundary (GB) interactions and evolving dislocation pileups, were combined with a crystalline dislocation-density plasticity approach to understand the influence of AM process-induced defects, such as porosity, NbC precipitates, and regions of dry powder. High local stresses along the peripheries of pores caused crack nucleation, and mismatches in deformation behavior between NbC precipitates and the surrounding matrix led to local stress gradients that induced crack nucleation and decohesion at precipitate/matrix interfaces. Regions of unmelted powder had significant stress accumulations that initiated failure at low nominal strains. Failure due to high localized stresses near regions of unmelted powder was dominant over precipitate/matrix decohesion and crack nucleation near pore peripheries. Based on the predictions, the mechanical behavior of AM alloys is governed by local dislocation-density evolution near process-induced defects, which preferentially nucleate material failure. Furthermore, interactions between these different defect types can significantly accelerate failure initiation and propagation.

Synthesis and mechanical testing of grain boundaries at the micro and sub-micro scale

Abstract The important role of grain boundaries for the mechanical properties of polycrystalline materials has been recognized for many decades. Up to now, the underlying deformation mechanisms at the nano- and micro scale are not understood quantitatively. An overview of the synthesis and subsequent mechanical testing of specific grain boundaries at the micro and sub-micro scale is discussed in the present contribution, including various methods for producing one or multiple specific, crystallographically well-defined grain boundaries. Furthermore, established micromachining methods for isolating and measuring local dislocation-grain boundary interactions are portrayed. Examples of the techniques described are shown with to the aid of copper grain boundaries.

Anneal hardening and elevated temperature strain rate sensitivity of nanostructured metals: Their relation to intergranular dislocation accommodation

Nanocrystalline materials exhibit various properties or phenomena not common in the conventional grain size regime, including enhanced strain rate sensitivity for FCC metals or strength increase during recovery annealing. These peculiarities are associated with the enhanced confinement of plasticity. Accordingly, the interaction of dislocations with the numerous grain boundaries, the boundary state as well as its local chemistry are of importance for a complete understanding. Due to the various influencing factors, determination of the dominant and rate controlling processes remains challenging. Here, we present a study on selected nanostructured FCC materials where dislocation-grain boundary interactions have been studied earlier for their coarse grained counterparts. High temperature nanoindentation revealed for all materials a pronounced increase of strain rate sensitivity when exceeding a certain temperature, peaking prior to the occurrence of significant grain growth. Static annealing of samples close to these peak temperatures leads, for sufficiently small grain sizes, to a maximum hardness increase. Interestingly, despite the nanocrystalline grain size, these temperatures perfectly agree with those obtained earlier for annihilation of lattice dislocations at grain boundaries in coarse-grained samples. This suggests that at elevated temperatures the dominant mechanism controlling the enhanced rate sensitivities in nanocrystalline metals is the thermally activated annihilation of lattice dislocations at grain boundaries. Measurements of activation energies being close to reported values for grain boundary diffusion further support this concept.

Cold rolled tungsten (W) plates and foils: Evolution of the tensile properties and their indication towards deformation mechanisms

This paper is the second part of our series on ultrafine-grained (UFG) tungsten produced by cold rolling. The aim of this paper is to determine tensile properties, with a focus on uniform elongation and flow stress, and to identify the mechanism of plastic deformation in cold rolled tungsten plates and foils. For this purpose, five plates have been rolled out of a single sintered compact with increasing degrees of deformation, which enables the analysis of mechanical properties with changing microstructure without influence from the chemical composition.Uniaxial tensile tests have been performed in the range of room temperature to 800°C. The tensile curves show a clear trend of increased strength for finer microstructures and simultaneously evolving room temperature ductility in the low temperature regime for cold rolled plates. The thinnest foil (100μm) behaves uniquely by forming a plateau in the stress-strain curve, which hints at a change in the deformation mechanism.Analyzing the temperature and grain size dependence of the flow stress reveals that the bulk plasticity is still controlled by screw dislocations and further suggests a change in the dislocation-grain boundary interactions from blocking at low homologous temperatures to absorbing at elevated temperatures.A fracture analysis of cold rolled tungsten foils confirms a plastic deformation prior to fracture and reveals a steady transition from brittle towards lamellar fracture for the highly deformed tungsten foils.