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• Stress–strain curves of Al-4Cu/graphene and Cu-2Ag/graphene composites are theoretically calculated. • Graphene in GBs provides higher strengthening than graphene in grain interiors. • The fraction of GB area occupied by graphene crucially affects strain hardening. A model is suggested that describes plastic deformation of metal alloys reinforced with graphene. Within the model, the flow stress, yield and ultimate strength and the critical uniform elongation are calculated as functions of the structural parameters of the composites. It is demonstrated that a high strength of the composites requires that a significant part of grain boundary area should be occupied by graphene platelets, whereas grain size and platelet length exert small effects on the strength of the composites. It is shown that the addition of graphene can lead to a significant increase in strength at expense of a moderate decrease in ductility. Thus, the optimum graphene content should be high enough to provide a high proportion of grain boundary area occupied by graphene but still sufficiently small to avoid graphene agglomeration. [ABSTRACT FROM AUTHOR]

Models of ceramic-graphene nanocomposites are used to study how the manufacturing process-dependent arrangement of reduced graphene oxide (rGO) inclusions governs nano-crack network development. The work builds upon recent studies of such composites where a novel combinatorial approach was used to investigate the effect of rGO arrangements on electrical conductivity and porosity. This approach considers explicitly the discrete structure of the composite and represents it as a collection of entities of different dimensions - grains, grain boundaries, triple junctions, and quadruple points. Here, the combinatorial approach is developed further by considering the effects of rGO agglomerations, stress concentrators and adhesion energies on intergranular cracking. The results show that the fracture networks can be effectively controlled by the local ordering of rGO inclusions to allow for a concurrent increase in the strength and conductivity of the ceramic composites. It is shown that the ratio of local stress concentrators related to rGO inclusions and cracks is the most significant factor affecting the nano-crack network topology. The local spatial arrangement of rGO inclusions becomes an effective tool for controlling nano-crack network topology only when this ratio approaches one. It is anticipated that these results will inform future design of toughness-enhanced composites. • Effect of rGO spatial distribution on composite cracking revealed by discrete methodology. • Fracture network controlled by the ratio of local stress concentrators due to inclusions and cracks. • Diversity of network topologies achieved by increasing the number of rGO agglomerations. • The effect of the initial rGO fraction on the fracture network topology is not monotonous. [ABSTRACT FROM AUTHOR]

A model is proposed for multiple cracking of graphene platelets in deformed laminated metal-graphene composites. Within the model, the first crack formed in a graphene platelet in the stress field of an applied load and a dislocation pileup emits dislocations that are accumulated near neighboring graphene platelets and lead to their cracking. Next, the process of dislocation emission from the existing cracks, their accumulation near neighboring graphene platelets and the cracking of these platelets repeats, eventually leading to multiple cracking of graphene platelets. We calculated the critical stress for the onset of cracking as a function of the structural parameters of the composites. The effect of amorphous layers around graphene platelets on fracture of metal-graphene composites is also briefly discussed. [ABSTRACT FROM AUTHOR]

A theoretical model is suggested which describes grain boundary (GB) sliding and its accommodation through dislocation slip in ultrafine-grained and nanocrystalline metals. The initial stage of the accommodating dislocation slip represents emission of lattice dislocations from triple junctions into grain interiors. The lattice dislocations emitted from a triple junction slip across a grain and are absorbed by an opposite GB where they are dissociated into GB dislocations that climb along the GB. In the situation where these GB sliding and accommodating processes are dominant, stress-strain dependences are calculated in ultrafine-grained copper. With the calculated dependences, we found that pronounced strain hardening occurs which is related to the accommodation processes and associated formation of disclinations at triple junctions of GBs. It is theoretically revealed that the special (new) strain hardening mechanism under discussion can play a significant role in enhancing ductility of ultrafine-grained and nanocrystalline metals at comparatively low temperatures. [ABSTRACT FROM AUTHOR]

A model is suggested that describes the combined effects of crack bridging and ceramic/graphene interface strength on the fracture toughness of fully dense ceramic/graphene composites. Within the model, we consider the situation where ceramic/graphene interfaces are weaker than the matrix grain boundaries and are therefore more prone to cracking. Using the fracture mechanics combined with the percolation theory, we calculate the effects of graphene content and interface strength on the fracture toughness of composites. The dependences of the fracture toughness on the graphene content and the sizes of the graphene platelets are calculated in the exemplary case of alumina/graphene composites. The calculations reveal the transition from toughening, associated with crack bridging, to fracture toughness reduction due to crack percolation over ceramic/graphene interfaces. They demonstrate that ceramic/graphene composites with high toughness should have large graphene platelets and/or small grain size. • We study interface and intergranular fracture in ceramic/graphene composites. • Crack percolation over graphene interfaces reduces fracture toughness. • Crack bridging by graphene leads to toughening. • The optimum graphene content is balanced by crack bridging and crack percolation. • Long graphene platelets and small grain size provide maximum fracture toughness. [ABSTRACT FROM AUTHOR]

The free surface effects on grain boundary (GB) deformation mechanisms mediated by GB sliding and migration processes in nanocrystalline materials are theoretically described. Particular attention is devoted to the specific features of the GB sliding and the cooperative GB sliding and migration processes occurring near free surfaces in nanocrystalline materials. The critical stresses, energies and geometric parameters which characterize the GB deformation mechanisms in question are calculated. The role of the free surface effects in the interpretation of experimental data on the GB sliding and migration processes in nanocrystalline materials is discussed. [ABSTRACT FROM AUTHOR]

[Display omitted] • The onset of plastic deformation in metal-graphene nanocomposites is modeled. • Plastic deformation occurs via dislocation transmission across grain boundaries. • Expanding dislocation loops bypass graphene platelets at grain boundaries. • This increases the yield strength of metal-graphene composites. A model is suggested that describes the onset of plastic deformation in metal-graphene nanocomposites. Within the model, the plastic deformation of a deformed metal-graphene nanocomposite is realized through the generation of perfect or partial dislocation loops. These loops nucleate at grain boundaries (GBs) of the metallic matrix and expand across grains. The expanded dislocation loops promote the nucleation and expansion of secondary dislocation loops in adjacent grains, thereby realizing dislocation transmission across GBs. Within the model, we have calculated the critical stresses, τ c 1 and τ c 2 , for the generation of a secondary perfect or partial dislocation loop and for the bypass of the graphene inclusion by the secondary loop. The critical stress τ c 2 increases with an increase in the graphene concentration and with a decrease in the thickness of the inclusion. This implies that the addition of graphene can raise the critical stress for the expansion of the secondary dislocation loops and thus increase the yield strength of metals. [ABSTRACT FROM AUTHOR]

Emission of lattice dislocations from grain boundaries (GBs) specified by deformation-distorted structures with periodic fluctuations of misorientation in deformed ultrafine-grained (UFG) materials is theoretically described. It is theoretically revealed that (i) the dislocation emission from deformation-distorted GBs is significantly enhanced as compared to that from structurally equilibrated GBs; and (ii) the enhancement effect depends on the parameters specifying the deformation-distorted GBs. The influence of deformation-distorted GBs as dislocation sources on the tensile ductility of UFG materials is discussed. [ABSTRACT FROM AUTHOR]

Abstract: A theoretical model is suggested which describes generation and growth of nanoscale cracks (nanocracks) near tips of blunt cracks in nanocrystalline solids. Within the model, stress concentration near pre-existent/growing blunt cracks induces grain boundary sliding which leads to formation of dislocations at triple junctions of grain boundaries. The superposition of the external stress concentrated near tips of blunt cracks and stresses created by these dislocations is capable of initiating generation and growth of nanocracks. The characteristics of the nanocrack generation and growth in nanocrystalline Al and α-Fe are calculated, and the effects of these processes on toughness/ductility of nanocrystalline solids are discussed. [Copyright &y& Elsevier]

Abstract: A new mechanism of fracture toughness enhancement in nanocrystalline metals and ceramics is suggested. The mechanism represents the cooperative grain boundary (GB) sliding and stress-driven GB migration process near the tips of growing cracks. It is shown that this mechanism can increase the critical stress intensity factor for crack growth in nanocrystalline materials by a factor of three or more and thus considerably enhances the fracture toughness of such materials. [Copyright &y& Elsevier]

Abstract: A special micromechanism for the formation of elongated nanoscale voids at grain boundaries (GBs) in deformed nanocrystalline materials is suggested and theoretically described. Within our description, the formation of nanoscale voids represents a slow (diffusion-controlled) process driven by release of the elastic energy of GB disclination configurations formed due to GB sliding. It is demonstrated that the nucleation of elongated nanoscale voids at GB disclination dipoles occurs as an energetically favorable process in deformed nanocrystalline Ni and Al2O3 (sapphire) in wide ranges of their parameters. [Copyright &y& Elsevier]

Abstract: Aspects of the ductile vs. brittle response of nanocrystalline and ultrafine-grained (UFG) materials are theoretically examined. The focus of this study is on the combined effects of grain boundaries (GBs) and blunting of cracks on the fracture toughness of nanocrystalline and UFG materials in a typical situation where crack blunting and growth processes are controlled by dislocation emission from crack tips. Within our description, lattice dislocations emitted from cracks are stopped at GBs, resulting in blunting of cracks. Both crack blunting and the stress fields of the arrested dislocations hamper further dislocation emission from cracks in nanocrystalline and UFG materials. As a result, crack blunting is suppressed, while crack growth is enhanced. The combined effects of GBs and blunting of cracks on the dislocation emission, further crack blunting and growth processes depend on grain size and material parameters. The dependence of the maximum number of dislocations, emitted by a crack, and the critical stress intensity factor on grain size (ranging from 10 to 300nm) in Al and α-Fe is calculated. It is demonstrated that a decrease in grain size from 300 to 10nm in Al and α-Fe decreases their critical stress intensity factors by a factor of 2–3 and thereby dramatically reduces the toughness/ductility of these materials. [ABSTRACT FROM AUTHOR]

Abstract: Dislocation behavior in porous solids with different 2D arrangements of closed cylindrical voids is discussed. It is suggested that in many cases important for practice, the approximation of two closest voids may be quite effective. The stress field and strain energy of a screw dislocation in an elastically isotropic solid containing two cylindrical voids are rigorously derived by the technique of infinite ensembles of image dislocations and analyzed in detail. The image force exerted by the voids on such a dislocation is also calculated and studied. As a limiting case of the solution obtained, we derive the stress field of a screw dislocation in a half-space containing a cylindrical void. [Copyright &y& Elsevier]

Abstract: A theoretical model is suggested which describes the combined effects of grain boundary (GB) sliding and diffusion on strain hardening and ductility of nanocrystalline materials (NCMs). Within the model, GB sliding creates disclination dipoles near triple junctions, inducing high elastic stresses and resulting in pronounced strain hardening. At the same time, GB diffusion partly relieves disclination stresses, thereby decreasing strain hardening. It is theoretically shown that good ductility of NCMs can be reached due to optimization of GB sliding and diffusion processes providing optimum strain hardening. The latter suppresses plastic strain instability and thus enhances tensile ductility. At the same time, with the optimum strain hardening, the applied stresses reach their critical level at which NCMs fracture only if overall plastic strain is sufficiently large. [Copyright &y& Elsevier]

The effect of grain size on the blunting of cracks in nanocrystalline materials is described theoretically. Within our description, lattice dislocations emitted from cracks are stopped at grain boundaries. The stress fields of these dislocations suppress further dislocation emission from cracks in nanomaterials, and the suppression depends on grain size. The dependence of the number of dislocations emitted by a crack on grain size in nanocrystalline Ni is calculated, and characterizes the grain size effect on crack blunting. [Copyright &y& Elsevier]

Abstract: Theoretical models are suggested that describe the effects of stress-driven migration of grain boundaries (GBs) on both the formation of nanoscale cracks (nanocracks) and the growth of comparatively large cracks in deformed nanocrystalline ceramics and metals. The GB migration under consideration is driven by the applied stress, carries plastic flow and produces quadrupoles of disclination defects in nanocrystalline materials. The disclinations create high local stresses capable of initiating the formation of nanocracks. In this paper, the conditions at which the formation of nanocracks is energetically favorable are theoretically described. The external stress values needed to initiate nanocrack formation near the disclinations in nanocrystalline metals (Al and Ni) with the finest grains and nanoceramics are estimated. In addition, we estimated the effect of the stress-driven migration of GBs on the growth of pre-existing, comparatively large cracks in nanocrystalline Ni with the finest grains. [Copyright &y& Elsevier]

A model is suggested which describes a special mechanism for rotational deformation (plastic deformation accompanied by crystal lattice rotation) in nanocrystalline metals and ceramics. Within the model, the special rotational deformation occurs in a nanograin through formation of immobile disclinations whose strengths gradually increase during the formation process as a result of grain boundary sliding and diffusion. The conditions are calculated at which the special rotational deformation is energetically favorable in nanocrystalline Ni, α-Al2O3 (corundum) and TiN-based ceramics. [Copyright &y& Elsevier]

Abstract: A theoretical model is suggested which describes the suppressing effect of grain boundary diffusion on the nanocrack generation in nanocrystalline materials under high strain rate superplastic deformation. In the framework of the model, grain boundary sliding intensively occurs in deformed nanocrystalline materials and causes the storage of grain boundary dislocations at triple junctions of grain boundaries. Relaxation of the stresses of these dislocations occurs via either the nanocrack generation or enhanced diffusional mass transfer in vicinities of triple junctions, depending on the material, structure and deformation parameters. If the former relaxation mechanism is dominant, nanocracks are intensively generated and converge giving rise to the brittle behavior of a nanocrystalline specimen. If the second relaxation mechanism is dominant, diffusion suppresses the nanocrack generation and thereby promotes superplastic deformation in a nanocrystalline material. [Copyright &y& Elsevier]

A theoretical model is suggested which describes the generation and evolution of nanoscale cracks (nanocracks) at triple junctions of grain boundaries in deformed nanocrystalline materials. In the framework of the model, nanocracks in nanocrystalline materials are nucleated at triple junctions due to accumulation of the dislocation charge, that accompanies grain boundary sliding through triple junctions. The model accounts for experimental observation [Acta Mater. 51 (2003) 387] of triple junction nanocracks in deformed nanocrystalline Ni. With results of the model, the effects of grain boundary diffusion on suppression of nanocrack generation in nanocrystalline materials exhibiting enhanced ductility and superplasticity are discussed. [Copyright &y& Elsevier]

A model is suggested that describes the observed dependences of the strength of laminated metal/graphene composites on the lateral size of graphene platelets. Within the model, these dependences are associated with the accumulation of dislocations at metal/graphene interfaces and dislocation pinning by the edges of graphene platelets. It is shown that the strength of laminated metal/graphene composites depends not only on graphene platelet dimensions and the orientation of the applied load but also on the specific energies of metal/graphene interfaces and lamella boundaries. This can enable one to control the strength of laminated metal/graphene composites by tuning their interface properties. • We model the plastic deformation of laminated metal/graphene composites. • The model considers dislocation accumulation and dynamic recovery at lamella boundaries and metal/graphene interfaces. • The observed dependences of the flow stress on the platelet length and loading direction are explained. • It is shown that the strength of the composites can be controlled by their interface energies. [ABSTRACT FROM AUTHOR]

• We study grain boundary (GB) sliding near crack tips in ceramic/graphene composites. • GB sliding near crack tips can induce cracking in neighboring GBs. • GB sliding can reduce fracture toughness of ceramic/graphene composites. • The effect is significant for small grain sizes and not too small graphene platelets. A model is suggested describing the effect of grain boundary (GB) sliding on the fracture toughness of ceramic/graphene composites. Within the model, GB sliding near the tip of a large mode I crack initiates the formation of a new nano- or microcrack at an adjacent GB. The new crack merges with the pre-existent one, thus providing crack propagation. For the situation where the suggested crack growth mechanism restricts the fracture toughness of ceramic/graphene composites, we calculated the dependence of the fracture toughness on grain size and lateral dimensions of graphene platelets. The calculations demonstrated that GB-sliding-assisted crack growth reduces fracture toughness, and the effect is strongest for the case where grain size is small and the lateral graphene platelet dimensions are close to the sizes of GBs. The results of the calculations agree with the experimental data on the fracture toughness of alumina/graphene composites. [ABSTRACT FROM AUTHOR]

A model is proposed explaining enhanced strength of ultrafine-grained alloys that contain grain boundary (GB) solute segregations. In the framework of the proposed model these segregations are treated as homogeneous ellipsoidal inclusions and act as the sources of elastic stresses affecting the emission of lattice dislocations from GBs. These segregations pin the ends of lattice dislocation segments at the initial stage of dislocation propagation along GBs, and the unpinning requires a load increase, leading to the enhanced yield strength. We calculate the contribution of GB segregations to the yield strength for the ultrafine-grained 1570 Al alloy. We demonstrate that the maximum yield strength of this alloy is achieved in the case of clustered, nearly spherical Mg segregations with a high Mg concentration and a diameter to thickness ratio of 1.0–1.4, depending on the Mg concentration inside segregations. We also briefly discuss the possible role of GB dislocations in the formation of such concentrated solute segregations as well as the influence of GB segregations on the strengthening of alloys containing nanoscale twins. The results of the calculations agree well with experimental data. • Enhanced strength of alloys containing grain boundary segregations is modeled. • Segregations are the sources of elastic stresses increasing the yield strength. • Small segregations with a high solute concentration provide maximum strengthening. [ABSTRACT FROM AUTHOR]

Abstract: Theoretical models are suggested which describe the effects of intergrain sliding on crack growth in nanocrystalline metals and ceramics. Within the models, stress concentration near cracks initiates intergrain sliding which is non-accommodated at low temperatures and effectively accommodated at intermediate temperatures. The first model is focused on the non-accommodated intergrain sliding which leads to generation of dislocations at triple junctions of grain boundaries. These dislocations cause partial stress relaxation in the vicinities of crack tips and thereby hamper crack growth. It is shown that the non-accommodated intergrain sliding increases fracture toughness by 10–30% in nanocrystalline Al, Ni and 3C–SiC. The second model deals with the case of intermediate temperatures. Within this model, intergrain sliding is effectively accommodated by diffusion-controlled climb of grain boundary dislocations. The accommodated intergrain sliding in nanocrystalline materials results in crack blunting which, in its turn, leads to an increase (by a factor ranging from 1.1 to around 3, depending on temperature) of fracture toughness. [ABSTRACT FROM AUTHOR]