Misfit disclination dipoles in nanocrystalline films and coatings

A theoretical model is proposed for describing the special physical micromechanism of misfit stress relaxation in nanocrystalline (NC) films and coatings. According to this model, under certain conditions, grain boundary sliding occurs in NC films and coatings, which is accompanied by the formation of an ensemble of disclination dipoles (rotational defects). These dipoles produce elastic stress fields, which partially compensate misfit stresses in NC films and coatings. Using the proposed model, it is shown that the nucleation of disclination dipoles in a film (coating) can significantly decrease the total energy of the film/substrate composite for the AlN/6H-SiC and GaN/6H-SiC systems over a wide range of structural parameter values.     

Effect of cooperative nanograin boundary sliding and migration on dislocation emission from a blunt nanocrack tip in nanocrystalline materials

Theoretical model is suggested that describes the effects of the cooperative nanograin boundary sliding and stress-driven nanograin boundary migration (CNGBSM) process on the lattice dislocation emission from an elliptically blunt nanocrack tip in deformed nanocrystalline materials. Within the model, CNGBSM deformation near the tip of growing nanocrack carries plastic flow, produces two dipoles of disclination defects and creates high local stresses in nanocrystalline materials. By using the complex variable method, the complex form expression of dislocation force is derived, and critical stress intensity factors for the first lattice dislocation emission are obtained under mode I and mode II loading conditions, respectively. The combined effects of the geometric features and strengths of CNGBSM deformation, nanocrack blunting and length on critical SIFs for dislocation emission depend upon nanograin size and material parameters in a typical situation where nanocrack blunting and growth processes are controlled by dislocation emission from nanocrack tips. It is theoretically shown that the cooperative CNGBSM deformation and nanocrack blunting have great influence on dislocation emission from blunt nanocrack tip.     

Generation of disclination dipoles and nanoscopic cracks in deformed nanoceramic materials

The processes of generation of disclination dipoles and nanoscopic cracks (nanocracks) in deformed nanoceramic materials are investigated theoretically. It is demonstrated that disclination dipoles are formed at grain boundaries in the course of grain-boundary sliding. The geometric features of the generation of disclination dipoles are analyzed. The conditions under which the nucleation of nanocracks in the vicinity of the disclination dipoles is energetically favorable are calculated for the nanoceramic materials α-Al₂O₃ (corundum) and 3C-SiC (the cubic phase of silicon carbide). The equilibrium lengths of these nanocracks are also calculated. It is shown that the equilibrium lengths of nanocracks can be comparable to the grain size. As a consequence, these nanocracks can coalesce, thus eventually resulting in the brittle fracture of nanoceramic materials.     

Grain size refinement due to relaxation of disclination junction configurations in the course of plastic deformation of polycrystals

A model is proposed for the formation of the substructure in polycrystals during plastic deformation. According to this model, fragmentation of a grain occurs through the formation of a system of diagonal low-angle boundaries, which originate at the edges of a rectangular grain. Misorientation boundaries form through relaxation of a nonsymmetric junction quadrupole disclination configuration accumulated at the grain corners under severe deformation when the disclination strength reaches a certain critical value. The energetics of this process is analyzed. A general case is considered where the disclinations at the junctions of the chosen grain differ in strength. The energetic approach used makes it possible to determine the misorientation angle ω_x of the resulting boundaries corresponding to the maximum energy gain and to find the dependence of this angle on the degree of asymmetry of the quadrupole configuration of junction disclinations. According to the proposed model, the splitting of a grain with a short edge greater than 0.5 μm is energetically favorable and decreases the latent energy of the grain for any ratio between the junction disclination strengths if the grain length-to-width ratio is less than 30. It is shown that the minimum possible grain size in the proposed model does not exceed 0.1 μm.     

Continuous description of a grain boundary in forsterite from atomic scale simulations: the role of disclinations

We present continuous modelling at inter-atomic scale of a high-angle symmetric tilt boundary in forsterite. The model is grounded in periodic arrays of dislocation and disclination dipoles built on information gathered from discrete atomistic configurations generated by molecular dynamics simulations. The displacement, distortion (strain and rotation), curvature, dislocation and disclination density fields are determined in the boundary area using finite difference and interpolation techniques between atomic sites. The distortion fields of the O, Si and Mg sub-lattices are detailed to compare their roles in the accommodation of lattice incompatibility along the boundary. It is shown that the strain and curvature fields associated with the dislocation and disclination fields in the ‘skeleton’ O and Si sub-lattices accommodate the tilt incompatibility, whereas the elastic strain and rotation fields of the Mg sub-lattice are essentially compatible and induce stresses balancing the incompatibility stresses in the overall equilibrium.     

To the Question of Forming Geometrically Necessary Disclinations in Triple Junctions of Grain Boundaries in Metals

The Bollman and King models are tested by means of molecular dynamics simulation for the formation of geometrically necessary disclinations in triple junctions of grain boundaries in metals. It is shown that the stresses arising in a triple junction due to the non-multiple lengths of low-angle tilt boundaries to the distance between grain boundary dislocations is not compensated for mainly by the formation of an additional disclination in the junction (the King model) but by the bending of one or several grain boundaries, accompanied by the displacement of grain boundary dislocations. A triple junction of the Bollman U-type (containing a geometrically necessary disclination) is not formed at the conjugation of tilt boundaries with common misorientation along the junction or at the conjugation of mixed-type boundaries.     

Effects of boundary inclination and boundary type on shear-driven grain boundary migration

A series of molecular dynamics simulations was performed on a bicrystal to which a fixed shear rate was applied parallel to the boundary plane. Under some conditions, grain boundary motion is coupled to the relative tangential motion of the two grains. In order to investigate the generality of this type of coupled shear/boundary motion, simulations were performed for both special (low Σ) and general (non-Σ) [010] tilt boundaries over a wide range of grain boundary inclinations. The data point to the existence of two critical stresses: one for coupled shear/boundary motion and the other for grain boundary sliding. For the non-Σ boundaries, the critical stress for coupled shear/boundary motion is typically smaller than that for sliding; coupled shear/boundary motion occurs for all inclinations. For Σ5 boundaries, for which the critical stress is smaller and depends on boundary inclination, coupled shear/boundary motion occurs for some, but not all inclinations.     

Crack-stimulated generation of deformation twins in nanocrystalline metals and ceramics

A theoretical model is proposed that describes the generation of deformation twins near brittle cracks of mixed I and II modes in nanocrystalline metals and ceramics. In the framework of the model, a deformation twin nucleates through stress-driven emission of twinning dislocations from a grain boundary distant from the crack tip. The emission is driven by both the external stress concentrated by the pre-existent crack and the stress field of a neighbouring extrinsic grain boundary dislocation. The ranges of the key parameters, the external shear stress, τ, and the crack length, L, are calculated within which the deformation-twin formation near pre-existent cracks is energetically favourable in a typical nanocrystalline metal (Al) and ceramic (3C-SiC). The results of the proposed model account for experimental data on observation of deformation twins in nanocrystalline materials reported in the literature. The deformation-twin formation is treated as a toughening mechanism effectively operating in nanocrystalline metals and ceramics.     

Effect of grain boundary sliding on the toughness of ultrafine grain structure steel: A molecular dynamics simulation study

Molecular dynamics simulations are carried out to investigate the mechanisms of low-temperature impact toughness of the ultrafine grain structure steel. The simulation results suggest that the sliding of the {001}/{110} type and {110}/{111} type grain boundary can improve the impact toughness. Then, the mechanism of grain boundary sliding is studied and it is found that the motion of dislocations along the grain boundary is the underlying cause of the grain boundary sliding. Finally, the sliding of the grain boundary is analyzed from the standpoint of the energy. We conclude that the measures which can increase the quantity of the {001}/{110} type and {110}/{111} type grain boundary and elongate the free gliding distance of dislocations along these grain boundaries will improve the low-temperature impact toughness of the ultrafine grain structure steel.     

Nanocrack nucleation in polycrystalline silicon during grain-boundary sliding

A theoretical model is proposed to describe nanocrack nucleation in polycrystalline silicon. In terms of this model, nanocrack nucleation is stimulated by grain-boundary sliding, which creates sources of local stresses in triple junctions of grain boundaries. The relaxation of these local stresses is the main driving force of nanocrack nucleation near triple junctions in polycrystalline silicon, in which grain-boundary sliding contributes substantially to plastic deformation under cyclic loading at room temperature. The model is used to calculate the critical external stress required for nanocrack nucleation in polycrystalline silicon.     

Dislocation-disclination models of grain boundary migration in ultrathin nanocrystalline films

The dislocation-disclination models describing the athermal migration of grain boundaries in stretched ultrathin nanocrystalline films have been proposed. The cases where the grain boundary emerges on a free surface of the film or is located in its central region have been considered. The changes in the total energy of the system due to the migration of the grain boundary have been calculated, the critical stresses of the onset of migration and the transition from a stable migration to an unstable migration have been determined, and the equilibrium positions of the grain boundary have been found. The dependences of the calculated parameters on the length, the misorientation angle, the position, and the orientation of the grain boundary in the film, as well as on the film thickness, have been investigated. It has been shown that the critical stresses responsible for the onset of migration of the grain boundary and its transition to an unstable regime decrease with a decrease in the thickness of the film. The critical stresses determining the transition from the stable migration to the unstable migration decrease with an increase in the grain size. The closer is the grain boundary to the surface of the film, the more pronounced is the tendency of the grain boundary toward migration.     

Dislocation mechanism of hollow fiber sliding during ceramic nanocomposite fracture

A dislocation model is proposed for describing the sliding of hollow fibers (and, in particular, carbon nanotubes) as a mechanism of elastic energy relaxation near cracks in ceramic nanocomposites. In this model, the sliding of a hollow cylindrical fiber occurs through the formation of a prismatic circular dislocation loop gliding along the boundary between the fiber and the matrix. The energy characteristics of this process are calculated, and the critical stress required for the barrierless nucleation and glide of such a loop is determined. It is shown that the critical stress increases with the ratio between the shear moduli of the matrix and the fiber and (over a wide range of changes in this ratio) with the fiber wall thickness.     

Mode II brittle fracture assessment using an energy based criterion

In this paper the minimum strain energy density criterion is modified to predict the values of mode II fracture toughness reported in the literature for several brittle and quasi-brittle materials. The experimental results are all related to mode II fracture tests performed on the semicircular bend specimen. The modified mode II fracture criterion takes into account the effect of T-stress (in addition to the singular terms of stresses/strains) when calculating the strain energy density factor at a very small critical distance from the crack tip. It is shown that the proposed criterion provides significantly better predictions for mode II fracture toughness compared with the classical minimum strain energy density criterion.     

Stimulation and Suppression of Grain Boundary Sliding by Intragranular Slip in Zinc Bicrystals

The influence of intragranular slip on grain boundary sliding is studied in originally compatible zinc bicrystals with symmetric tilt boundary. The experiment is designed to separate different effects of intragranular slip on the boundary sliding and establish their mechanisms. Grain boundary sliding with and without development of intragranular slip is observed. The rate of sliding accompanied by slip is more than five times of that without slip. A good correlation between the boundary sliding and intragranular slip prior to slide hardening is established. Slide hardening followed by the negative sliding near one end of the boundary and strain hardening in the boundary vicinity, are observed at the last stages of deformation. For the case of formation of slip induced glissile grain boundary dislocations of opposite signs the possibility of their contribution to total grain boundary sliding, is analyzed. The effect of the increase in the rate of sliding is explained in terms of the accommodation of sliding by slip and appearance of additional glissile grain boundary dislocations of one sign due to strain incompatibility. Contribution of these different dislocation mechanisms to the increase in the sliding rate is determined for the stage of deformation preceding slide hardening. It is supposed that the effect of slide hardening and negative sliding as well as boundary curving is created by non-smooth boundary and small degree of incompatibility caused by straining.     

Plasticity limit of metals during hot plastic deformation

A model of plasticity limit has been derived in the condition of hot plastic deformation, where dynamic recrystallization takes place, through the ratio between the rate of grain boundary sliding and the overall deformation rate. If fracture occurs preferentially at the grain boundaries we can replace the grain boundary deformation through the energy needed to cause fracture and express the temperature influence on the deformation stress. The plasticity limit is then the function of Zener-Hollomon parameter and deformation stress, where the exponent of deformation stress has a value of –4·3.     

A unified theory for brittle and ductile shear mode fracture

A unified theory captures both brittle and ductile fracture. The fracture toughness is proportional to the applied stress squared and the length of the crack. For purely brittle solids, this criterion is equivalent to Griffith's theory. In other cases, it provides a theoretical basis for the Irwin-Orowan formula. For purely ductile solids, the theory makes direct contact with the Bilby-Cottrell-Swinden model. The toughness is highest in ductile materials because the shielding dislocations in the plastic zone provide additional resistance to crack growth. This resistance is the force opposing dislocation motion, and the Peach-Koehler force overcomes it. A dislocation-free zone separates the plastic zone from and the tip of the crack. The dislocation-free zone is finite because molecular forces responsible for the cohesion of the surfaces near the crack tip are not negligible. At the point of crack growth, the length of the dislocation-free zone is constant and the shielding dislocations advance in concert. As in Griffith's theory, the crack is in unstable equilibrium. The theory shows that a dimensionless variable controls the elastoplastic behaviour. A relationship for the size of the dislocation-free zone is derived in terms of the macroscopic and microscopic parameters that govern the fracture.     

Effect of dislocation distribution in twin boundaries on the nucleation of microcracks at the twin tip

The effect of dislocation distribution in the boundaries of an arrested twin on the nucleation of microcracks at its tip is investigated. The twin is simulated by a double step pileup (cluster) of twinning dislocations located in adjacent slip planes. The equilibrium equations for dislocations are solved numerically. Clusters with different total numbers of dislocations and with different ratios of the numbers of dislocations at the upper and lower twin boundaries are considered. The formation of microcracks as a result of coalescence of head dislocations according to the force and thermally activated mechanisms is analyzed. The equilibrium configurations of a single twin boundary and of the twin are calculated. It is found that the condition for microcrack formation at the twin tip considerably depends on the ratio of the numbers of dislocations in twin boundaries. In the limit, this condition coincides with the condition of crack formation at the tip of a single twin boundary with the same total number of dislocations. It is shown that thermally activated formation of a microrack corresponds to lower values of the critical stress.     

Grain boundary sliding and lattice dislocation emission in nanocrystalline materials under plastic deformation

A theoretical model is proposed to describe the physical mechanisms of hardening and softening of nanocrystalline materials during superplastic deformation. According to this model, triple interface junctions are obstacles to glide motion of grain boundary dislocations, which are carriers of grain boundary glide deformation. Transformations of an ensemble of grain boundary dislocations that occur at triple interface junctions bring about the formation of partial dislocations and the local migration of triple junctions. The energy characteristics of these transformations are considered. Pileups of partial dislocations at triple junctions cause hardening and initiate intragrain lattice sliding. When the Burgers vectors of partial dislocations reach a critical value, lattice dislocations are emitted and glide into adjacent grains, thereby smoothing the hardening effect. The local migration of triple interface junctions (caused by grain boundary sliding) and the emission of lattice dislocations bring about softening of a nanocrystalline material. The flow stress is found as a function of the total plastic strain, and the result agrees well with experimental data.     

Atomistic simulation of plasticity and fracture of nanocrystalline copper under high-rate tension

A molecular dynamics simulation of the plastic deformation and the onset of fracture of nanocrystalline metals is performed using the example of copper. Successive stages of the response of the microstructure of a metal to deformation are considered, namely, grain boundary sliding, the nucleation and gliding of dislocations, and the formation and growth of microdamage nuclei. The influence of the grain size of a nanocrystal on its plasticity and strength is studied.     

The use of Electronic Speckle Pattern Interferometry (ESPI) in the crack propagation analysis of epoxy resins

The ESPI (electronic speckle pattern interferometry) technique at high magnification levels is demonstrated to be of considerable value in interpreting the fracture behaviour of epoxy resins. The fracture toughness of powder coating system at different thicknesses has been measured using a TDCB (tapered double cantilever beam) technique and the deformation zone at the tip of the moving crack monitored. Initial indications are that a mechanistic changeover occurs at a critical bond (coating) thickness and that this is synonymous with the occurence of a fracture toughness maximum, which in turn is associated with a deformation zone of specific diameter.