Deformation twinning in nanocrystalline materials

Nanocrystalline (nc) materials can be defined as solids with grain sizes in the range of 1-100 nm. Contrary to coarse-grained metals, which become more difficult to twin with decreasing grain size, nanocrystalline face-centered-cubic (fcc) metals become easier to twin with decreasing grain size, reaching a maximum twinning probability, and then become more difficult to twin when the grain size decreases further, i.e. exhibiting an inverse grain-size effect on twinning. Molecular dynamics simulations and experimental observations have revealed that the mechanisms of deformation twinning in nanocrystalline metals are different from those in their coarse-grained counterparts. Consequently, there are several types of deformation twins that are observed in nanocrystalline materials, but not in coarse-grained metals. It has also been reported that deformation twinning can be utilized to enhance the strength and ductility of nanocrystalline materials. This paper reviews all aspects of deformation twinning in nanocrystalline metals, including deformation twins observed by molecular dynamics simulations and experiments, twinning mechanisms, factors affecting the twinning, analytical models on the nucleation and growth of deformation twins, interactions between twins and dislocations, and the effects of twins on mechanical and other properties. It is the authors’ intention for this review paper to serve not only as a valuable reference for researchers in the field of nanocrystalline metals and alloys, but also as a textbook for the education of graduate students.     

Flaw insensitive fracture in nanocrystalline graphene

We show from a series of molecular dynamics simulations that the tensile fracture behavior of a nanocrystalline graphene (nc-graphene) nanostrip can become insensitive to a pre-existing flaw (e.g., a hole or a notch) below a critical length scale in the sense that there exists no stress concentration near the flaw, the ultimate failure does not necessarily initiate at the flaw, and the normalized strength of the strip is independent of the size of the flaw. This study is a first direct atomistic simulation of flaw insensitive fracture in high-strength nanoscale materials and provides significant insights into the deformation and failure mechanisms of nc-graphene.     

Modeling the dependence of strength on grain sizes in nanocrystalline materials

Abstract

A model was developed to describe the grain size dependence of hardness (or strength) in nanocrystalline materials by combining the Hall–Petch relationship for larger grains with a coherent polycrystal model for nanoscale grains and introducing a log-normal distribution of grain sizes. The transition from the Hall–Petch relationship to the coherent polycrystal mechanism was shown to be a gradual process. The hardness in the nanoscale regime was observed to increase with decreasing grain boundary affected zone (or effective grain boundary thickness, Δ) in the form of Δ^?1/2. The critical grain size increased linearly with increasing Δ. The variation of the calculated hardness value with the grain size was observed to be in agreement with the experimental data reported in the literature.     

Mechanical properties of nanocrystalline materials

The mechanical properties of nanocrystalline materials are reviewed, with emphasis on their constitutive response and on the fundamental physical mechanisms. In a brief introduction, the most important synthesis methods are presented. A number of aspects of mechanical behavior are discussed, including the deviation from the Hall-Petch slope and possible negative slope, the effect of porosity, the difference between tensile and compressive strength, the limited ductility, the tendency for shear localization, the fatigue and creep responses. The strain-rate sensitivity of FCC metals is increased due to the decrease in activation volume in the nanocrystalline regime; for BCC metals this trend is not observed, since the activation volume is already low in the conventional polycrystalline regime. In fatigue, it seems that the S-N curves show improvement due to the increase in strength, whereas the da/dN curve shows increased growth velocity (possibly due to the smoother fracture requiring less energy to propagate). The creep results are conflicting: while some results indicate a decreased creep resistance consistent with the small grain size, other experimental results show that the creep resistance is not negatively affected. Several mechanisms that quantitatively predict the strength of nanocrystalline metals in terms of basic defects (dislocations, stacking faults, etc.) are discussed: break-up of dislocation pile-ups, core-and-mantle, grain-boundary sliding, grain-boundary dislocation emission and annihilation, grain coalescence, and gradient approach. Although this classification is broad, it incorporates the major mechanisms proposed to this date. The increased tendency for twinning, a direct consequence of the increased separation between partial dislocations, is discussed. The fracture of nanocrystalline metals consists of a mixture of ductile dimples and shear regions; the dimple size, while much smaller than that of conventional polycrystalline metals, is several times larger than the grain size. The shear regions are a direct consequence of the increased tendency of the nanocrystalline metals to undergo shear localization.The major computational approaches to the modeling of the mechanical processes in nanocrystalline metals are reviewed with emphasis on molecular dynamics simulations, which are revealing the emission of partial dislocations at grain boundaries and their annihilation after crossing them.     

Nanomechanics of Hall-Petch relationship in nanocrystalline materials

Classical Hall-Petch relation for large grained polycrystals is usually derived using the model of dislocation pile-up first investigated mathematically by Nabarro and coworkers. In this paper the mechanical properties of nanocrystalline materials are reviewed, with emphasis on the fundamental physical mechanisms involved in determining yield stress. Special attention is paid to the abnormal or ‘inverse’ Hall-Petch relationship, which manifests itself as the softening of nanocrystalline materials of very small (less than 12 nm) mean grain sizes. It is emphasized that modeling the strength of nanocrystalline materials needs consideration of both dislocation interactions and grain-boundary sliding (presumably due to Coble creep) acting simultaneously. Such a model appears to be successful in explaining experimental results provided a realistic grain size distribution is incorporated into the analysis. Masumura et al. [Masumura RA, Hazzledine PM, Pande CS. Acta Mater 1998;46:4527] were the first to show that the Hall-Petch plot for a wide range of materials and mean grain sizes could be divided into three distinct regimes and also the first to provide a detailed mathematical model of Hall-Petch relation of plastic deformation processes for any material including fine-grained nanocrystalline materials. Later developments of this and related models are briefly reviewed.Prof. Frank Nabarro was a physicist by training, a metallurgist by profession and a genius by nature, blessed with a unique ability to treat everyone as his equal. During his later years he was very much interested in the mechanical properties of nanocrystalline materials. This review on that topic is our contribution to the special issue of Progress in Materials Science honoring him.     

Grain growth in porous two-dimensional nanocrystalline materials

Grain growth in two-dimensional polycrystals with mobile pores at the grain boundary triple junctions is considered. The kinetics of grain and pore growth are determined under the assumption that pore sintering and pore mobility are controlled by grain boundary and surface diffusion, respectively. It is shown that a polycrystal can achieve full density in the course of grain growth only when the initial pore size is below a certain critical value which depends on kinetic parameters, interfacial energies, and initial grain size. Larger pores grow without limits with the growing grains, and the corresponding grain growth exponent depends on kinetic parameters and lies between 2 and 4. It is shown that for a polycrystal with subcritical pores the average grain size increases linearly with time during the initial stages of growth, in agreement with recent experimental data on grain growth in thin Cu films and in bulk nanocrystalline Fe.     

Structure and properties of nanocrystalline materials

The present article reviews the current status of research and development on the structure and properties of nanocrystalline materials. Nanocrystalline materials are polycrystalline materials with grain sizes of up to about 100 nm. Because of the extremely small dimensions, a large fraction of the atoms in these materials is located at the grain boundaries, and this confers special attributes. Nanocrystalline materials can be prepared by inert gas-condensation, mechanical alloying, plasma deposition, spray conversion processing, and many other methods. These have been briefly reviewed. A clear picture of the structure of nanocrystalline materials is emerging only now. Whereas the earlier studies reasoned out that the structure of grain boundaries in nanocrystalline materials was quite different from that in coarse-grained materials, recent studies using spectroscopy, high-resolution electron microscopy, and computer simulation techniques showed unambiguously that the structure of the grain boundaries is the same in both nanocrystalline and coarse-grained materials. A critical analysis of this aspect and grain growth is presented. The properties of nanocrystalline materials are very often superior to those of conventional polycrystalline coarse-grained materials. Nanocrystalline materials exhibit increased strength/hardness, enhanced diffusivity, improved ductility/toughness, reduced density, reduced elastic modulus, higher electrical resistivity, increased specific heat, higher thermal expansion coefficient, lower thermal conductivity, and superior soft magnetic properties in comparison to conventional coarse-grained materials. Recent results on these properties, with special emphasis on mechanical properties, have been discussed. New concepts of nanocomposites and nanoglasses are also being investigated with special emphasis on ceramic composites to increase their strength and toughness. Even though no components made of nanocrystalline materials are in use in any application now, there appears to be a great potential for applications in the near future. The extensive investigations in recent years on structure-property correlations in nanocrystalline materials have begun to unravel the complexities of these materials, and paved the way for successful exploitation of the alloy design principles to synthesize better materials than hitherto available.     

Structural nanocrystalline materials: an overview

This paper presents a brief overview of the field of structural nanocrystalline materials. These are materials in either bulk, coating, or thin film form whose function is for structural applications. The major processing methods for production of bulk nanocrystalline materials are reviewed. These methods include inert gas condensation, chemical reaction methods, electrodeposition, mechanical attrition, and severe plastic deformation. The stability of the nanocrystalline microstructure is discussed in terms of strategies for retardation of grain growth. Selected mechanical properties of nanocrystalline materials are described; specifically strength and ductility. Corrosion resistance is briefly addressed. Examples of present or potential applications for structural nanocrystalline materials are given.     

Dislocation-disclination transformations and the reverse Hall-Petch effect in nanocrystalline materials

A relay-race dislocation-disclination model of plastic shear development in nanocrystalline materials is proposed, which is based on the mechanism of switching between translational and rotational deformation modes. The dependence of the external deforming stress on the grain size is calculated. It is shown that the switching from the translational to rotational deformation mode and back explains the reverse Hall-Petch effect in nanocrystalline materials.     

Alloying behaviour in nanocrystalline materials during mechanical alloying

The alloying behaviour in a number of systems such as Cu-Ni, Cu-Zn, Cu-Al, Ni-Al, Nb-Al has been studied to understand the mechanism as well as the kinetics of alloying during mechanical alloying (MA). The results show that nanocrystallization is a prerequisite for alloying in all the systems during MA. The mechanism of alloying appears to be a strong function of the enthalpy of formation of the phase and the energy of ordering in case of intermetallic compounds. Solid solutions (Cu-Ni), intermetallic compounds with low ordering energies (such as Ni₃Al which forms in a disordered state during MA) and compounds with low enthalpy of formation (Cu-Zn, Al₃Nb) form by continuous diffusive mixing. Compounds with high enthalpy of formation and high ordering energies form by a new mechanism christened as discontinuous additive mixing. When the intermetallic gets disordered, its formation mechanism changes from discontinuous additive mixing to continuous diffusive one. A rigorous mathematical model, based on iso-concentration contour migration method, has been developed to predict the kinetics of diffusive intermixing in binary systems during MA. Based on the results of Cu-Ni, Cu-Zn and Cu-Al systems, an effective temperature (T _eff) has been proposed that can simulate the observed alloying kinetics. TheT _eff for the systems studied is found to lie between 0·42–0·52T ₁.     

Phase transformations and phase stability in nanocrystalline materials

The current state of the researches on diffusionless phase transformations, including allotropic, polymorphous and martensitic transformations, and phase stability are reviewed. The behaviors of phase transformation and phase stability in nanocrystalline materials are markedly affected by the non-equilibrium conditions involved in their preparation, as a result, in this review an ideal demonstrating method of critical size for the stability of a high-temperature phase at low-temperatures is suggested, and the intrinsic conditions of the phase stability are clarified. Our recent experiments exhibit that the reversal transformation temperatures of low-temperature phases in nanocrystalline Co bulk metal and Fe–30Ni wt% alloy are significantly raised up over 800 °C when their grain sizes are smaller than about 15 nm, while in the reported experiments of nanocrystalline particles or films the reversal transformation temperature lowers with decreasing grain size or is independent of grain size. Therefore, the author suggests that more experiments and theories for phase stability in reversal transformation should be performed. The study of grain growth kinetics of nanocrystalline materials, as a basic of investigating phase stability, is another attention aspect.     

Fatigue fracture processes in polystyrene

Fatigue crack growth characteristics in polystyrene were studied as a function of stress intensity factor range and cyclic frequency. Precracked single edge notched and compact-tension type specimens made from commercially available polystyrene sheet (mol.wt. =2.7×10⁵) were cycled under constant load at frequencies of 0.1, 1, 10 and 100 Hz, producing growth rates ranging from 4×10^–7 to 4×10^–3 cm/cycle. For a given stress intensity level, fatigue crack growth rates were found to decrease with increasing frequency, the effect being strongest at high stress intensity values. The variable frequency sensitivity of this polymer over the test range studied was explained in terms of a variable creep component. The macroscopic appearance of the fracture surface showed two distinct regions. At low stress intensity values, a highly reflective, mirror-like surface was observed which transformed to a rougher, cloudy surface structure with increasing stress intensity level. Raising the test frequency shifted the transition between these areas to higher values of stress intensity. The microscopic appearance of the mirror region revealed evidence of crack propagation through a single craze while the appearance of the rough region indicated crack growth through many crazes, all nominally normal to the applied stress axis. Electron fractographic examination of the mirror region revealed many parallel bands perpendicular to the direction of crack growth, each formed by a discontinuous crack growth process as a result of many fatigue cycles. The size of these bands was found to be consistent with the dimension of the crack tip plastic zone as computed by the Dugdale model. At high stress intensity levels a new set of parallel markings was found in the cloudy region which corresponded to the incremental crack extension for an individual loading cycle.