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.     

Twinning in Be-Cu alloys. Part I

Mechanical twinning has been examined for 99.99% beryllium and for alloys of Be with 0.4 at. % and 2.3 at. % Cu. The yield points have been measured for single twins, and also studies have been made of the behavior of the twin boundaries under pulsating and sign-varying loads. The concentration dependence of the yield points for single twins has been used to estimate the interaction energy for the twinning dislocations with impurity atoms. The Bauschinger effect occurs at the boundaries of the mechanical twins, and the characteristics of this are dependent on the angle of the twin wedge, the impurity concentration, and the number of twinning cycles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 104–108, December, 1972.We are indebted to G. F. Tikhinskiy for providing the alloy crystals used here.     

Dislocation model for an incoherent nonthin twin

A condition for the equilibrium of a nonthin twin is obtained from a dislocation model using the approximation of a continuous distribution of twinning dislocations at twin boundaries. The model of a nonthin twin is shown to be applicable to the elastic and inelastic stages of twinning. The theory of a thin twin is found to be a particular case of the developed dislocation model of a nonthin twin.     

Effect of Al and Cd impurities on the bauschinger effect during the twinning of a zinc crystal

A quantitative study has been made of the Bauschinger effect at various twin boundaries in crystals of pure zinc and of zinc containing Al and Cd impurities. In the pure zinc, the Bauschinger effect is strongest at stretched twin boundaries, while in Zn + Al and Zn + Cd crystals the effect is much weaker at twin boundaries and is approximately the same at different types of boundaries. The stress is a stronger than linear function of the displacement of twin boundaries in the impure crystals for both forward and reverse loading, because of an increase in the friction force acting on the twinning dislocations during motion along the shear plane. An increase in the Al content from 0.1% to 0.3% (by weight), which leads to the appearance of a finely dispersed precipitate, has essentially no affect on the magnitude of the Bauschinger effect.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 59–63, December, 1969.     

Microstructural evolution of AZ31 magnesium alloy subjected to sliding friction treatment

Microstructural evolution and grain refinement mechanism in AZ31 magnesium alloy subjected to sliding friction treatment were investigated by means of transmission electron microscopy. The process of grain refinement was found to involve the following stages: (I) coarse grains were divided into fine twin plates through mechanical twinning; then the twin plates were transformed to lamellae with the accumulation of residual dislocations at the twin boundaries; (II) the lamellae were separated into subgrains with increasing grain boundary misorientation and evolution of high angle boundaries into random boundaries by continuous dynamic recrystallisation (cDRX); (III) the formation of nanograins. The mechanisms for the final stage, the formation of nanograins, can be classified into three types: (i) cDRX; (ii) discontinuous dynamic recrystallisation (dDRX); (iii) a combined mechanism of prior shear-band and subsequent dDRX. Stored strain energy plays an important role in determining deformation mechanisms during plastic deformation.     

Modelling of martensite slip and twinning in NiTiHf shape memory alloys

High-temperature shape memory alloy NiTiHf holds considerable promise for structural applications. An important consideration for these advanced alloys is the determination of the magnitude of the twinning stress. Theoretical stresses for twinning and dislocation slip in NiTiHf martensites are determined. The slip and twinning planes are (0?0?1) and (0?1?1) for monoclinic and orthorhombic crystals, respectively. The determination of the slip and twinning stress is achieved with a proposed Peierls–Nabarro-based formulation informed with atomistic simulations. In the case of the twin, multiple dislocations comprising the twin nucleus are considered. The overall energy expression is minimized to obtain the twinning and slip stresses. The magnitude of the predicted twinning stresses is lower than slip stresses which explains why the NiTiHf alloys can undergo reversibility without plastic deformation. In fact, the predicted critical resolved shear stress levels of 433?MPa for slip and 236?MPa for twinning in the case of 12.5% Hf agree very well with the experimental measurements. The high slip resistance confirms that these materials can be very attractive in load-bearing applications.     

Plasticity and strength of FCC metals with a nanotwinned submicrograined structure

The plasticizing and hardening effects associated with the existence of nanotwins with a density 1/λ (where λ is the average size (thickness) of nanotwin lamellae) in a submicrograined structure of fcc metals have been theoretically discussed in the framework of the dislocation-kinetics approach. The strength of the nanotwinned submicrocrystalline structure, which is increased as compared to the initial submicron structure, is determined, as in the case of nanograin boundaries, by the action of nanotwin boundaries as sources and barriers for moving dislocations that provide the normal Hall-Petch effect for the flow stress σ ∼ γ^−1/2. The inverse Hall-Petch effect σ ∼ γ ^p (where p > 0), as in the case of nanograin boundaries, is associated with the dislocation absorption by the twin boundaries. The related increased strain-rate sensitivity of the flow stresses is responsible for the significant increase in the uniform strain (from 2–3 to 8–9% in the case of nanotwinned copper) during tension of the specimens with nanotwinned submicrograined structures with retaining a high strength of the material.     

Molecular dynamics simulation of twinning in devitrite,Na2Ca3Si6O16

Reports of Type II twins are quite rare for most crystal structures. When they do occur, they are usually one of a number of possible twinning modes observed in a particular material. However, for the triclinic phase devitrite, Na₂Ca₃Si₆O₁₆, which nucleates from commercial soda?lime?silica float glass subjected to suitable heat treatments, the only reported twinning mode to date is a Type II twinning mode. In this study, this Type II twinning mode is first examined by molecular dynamics simulation to determine the lowest energy configuration of perfect twin boundaries for the twin mode. This is then compared with the lowest energy configurations of perfect twin boundaries found for six possible Type I twinning modes for devitrite for which the formal deformation twinning shear is less than 0.6. The most favourable twin plane configuration for the Type II twinning crystallography is shown to produce reasonably low twin boundary energies and sensible predictions for the optimum locations of the twin plane, K ₁, and the [1?0?0] rotation axis, η ₁, about which the 180° Type II twinning operation takes place. By comparison, all the Type I twinning modes were found to have very energetically unstable atomic configurations, and for each of these twinning modes, the lowest energy configurations found all led to high effective K ₁ twin boundary energies relative to perfect crystal. These results therefore provide a rationale for the experimental observation of the particular Type II twinning mode seen in devitrite.     

Change in the Bauschinger effect during the relaxation of twinned crystals

Changes taking place in the quantitative characteristics of the Bauschinger effect in wedge-shaped twins are studied in relation to the period for which these are held before untwinning. All the measurements are made in the cleavage plane of single-crystal zinc and Zn-Cu alloys. The Bauschinger displacement of the twin boundaries first increases slightly and then starts diminishing during the delay period. In the course of untwinning, the region of easy untwinning on the (b) relationship diminishes with time in the softened zone; the extent of the softened zone remains constant during the relaxation of the crystals. The suppression of the Bauschinger effect takes place more intensively if the crystal is held under load before untwinning. The change in the quantitative characteristics of the Bauschinger effect may be explained by the diffusion of impurities to the twinning dislocations and dislocation sources and the consequent blocking of these, and also by the relaxation of stresses in the twin boundaries as a result of plastic shears and dislocation reactions between complete and twinning dislocations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 113–117, April, 1971.     

Method for the calculation of the stress fields for a wedge-shaped twin located at the surface of a crystal in the approximation of a continuous distribution of twinning dislocations along twin boundaries

A method is proposed to calculate the stress fields for a wedge-shaped twin located at the crystal surface. A graphic representation of the configuration of the fields of normal and cleavage stresses of a wedge-shaped twin has been obtained. It has been found that the stresses are localized not only at the twin boundaries and at its apex, but also in certain regions distant from the boundaries.     

Alloying effect on grain-size dependent deformation twinning in nanocrystalline Cu–Zn alloys

Grain-size dependency of deformation twinning has been previously reported in nanocrystalline face-centred-cubic metals, which results in an optimum grain-size range for twin formation. Here, we report, for the first time in experiments, the observed optimum grain sizes for deformation twins in nanocrystalline Cu–Zn alloys which slightly increase with increasing Zn content. This result agrees with the reported trend but is much weaker than predicted by stacking-fault-energy based models. Our results indicate that alloying changes the relationship between the stacking-fault and twin-fault energy and therefore affects the optimum grain size for deformation twinning. These observations should be also applicable to other alloy systems.     

Distribution of dislocations and twins in copper and 18Cr-10Ni-Ti steel under shock-wave loading

The distribution of dislocations and twins over the cross section of shock-loaded copper and 18Cr-10Ni-Ti steel specimens is investigated experimentally and numerically. It is found that the volume fraction of twins near the loaded surface and a spall crack is an order of magnitude higher than their fraction at the center of the target. The features of twins arising in different parts of the target are discussed. A model of a twinning mechanism in coarse-grained metals is proposed and used for numerical simulation of the dislocation and twin depth distribution in shock-loaded targets. It is shown that in thin targets (less than 1 mm thick), the distribution of twins can be even more uniform than the distribution of the dislocations density.     

The incorporation of slip dislocations in twins

The conditions for the incorporation of slip dislocations either propagating into a twin or engulfed by a growing twin are studied from the geometrical point of view. The resulting dislocation formed in a twin is independent of the mechanism of the incorporation. Under suitable conditions no stacking faults are formed at the twin boundary. The decomposition of twinning dislocations forming the noncoherent twin boundary is described using complementary partial twinning dislocations. The theory is formulated for both type I and II twins. Compound twins are also briefly treated in the discussion. Using the tensor notation all the formulae are given in the form valid for all crystal structures.The author is greatly indebted to Mr. J. Koík for many helpful comments.     

Nanostructures and deformation mechanisms in a cryogenically ball-milled Al-Mg alloy

An Al-7.6 at.% Mg alloy was ball milled in liquid N₂ for 8 h and its microstructures were investigated using transmission electron microscopy. Electron diffraction confirmed that the resulting powder is a supersaturated Al-Mg solid solution with an fcc structure. Three typical nanostructures with different grain-size ranges and shapes were observed and the deformation mechanisms in these structures were found to be different. High densities of dislocations were found in large crystallites, implying that dislocation slip is the dominant deformation mechanism. The dislocations rearranged to form small-angle subboundaries upon further deformation, resulting in the formation of medium-sized crystallites with diameters of 10-30 nm. In very small crystallites with dimensions less than 10 nm, twinning becomes an important deformation mechanism. The reasons for the different deformation mechanisms were discussed. Some defects, such as twin boundaries, and small- and large-angle grain boundaries were investigated in detail.     

Grain refinement and texture evolution during high precision machining of a Ni-based superalloy

Abstract

The grain refinement and texture evolution in the surface gradient microstructure of a Ni-based superalloy induced by high speed machining was studied in this research. The direct evidence of grain refinement induced by dislocation–twin interaction was revealed and the detailed grain refinement process was summarised as deformation twinning, dislocation-twin reaction, localied thinning of nanotwin lamellae and final fracture. The underlying dislocation–twin interaction mechanism was elucidated from the crystallographic perspective. Using electron backscatter diffraction and precession electron diffraction techniques, a multiscale texture analysis covering undeformed coarse grain region, ultrafine grain region and nanograin region was carried out. The texture evolution with decreasing depth to the machined surface was identified as cube in the bulk interior and a mixture of rotated cube {0?0?1}<1?1?0>, cube {1?0?0}<0?0?1>, copper {1?1?2}<1?1?1 > and Goss {1?1?0}<0?0?1> textures in the topmost 1.3-μm-thick nanograin layer. The intrinsic thermomechanical effects of high precision machining are responsible for crystallographic texture transformation.     

Molecular dynamics simulation of the formation of twin boundaries during agglomeration of nanoparticles

The processes controlling early stages of agglomeration of nanoparticles have been investigated by the molecular dynamics method. It has been established that the formation of boundaries with twin misorientation is the main mechanism of structural relaxation during primary agglomeration of nanoparticles. It has been shown that an increase in the temperature leads to an increase in the number of twin boundaries and that their mutual arrangement depends on the misorientation of the nanoparticles. In the case where twin boundaries are noncoplanar, structure relaxation results in the formation of pentagonal twin boundaries. The role of twinning in the formation of interfaces upon compaction of nanoparticles has been discussed.     

Magnetoplastic effect in twinning of bismuth crystals under a concentrated load

Twinning of bismuth crystals under a concentrated load is found to be partly suppressed by a constant magnetic field. The main mechanisms of the influence of a constant homogeneous magnetic field on the twinning of bismuth single crystals subjected to long-term concentrated loading is studied. It is revealed that the length and the number of wedge twins at an indentation decrease in the magnetic field. This suggests a decrease in the mobility of partial twinning dislocations and in the intensity of the nucleation of wedge twin interlayers in a constant magnetic field. Application of the magnetic field increases the width of twins at the mouth. No anisotropy of the magnetoplastic effect is observed upon twinning.     

Statistical analyses of deformation twinning in magnesium

To extract quantitative and meaningful relationships between material microstructure and deformation twinning in magnesium, we conduct a statistical analysis on large data sets generated by electron backscattering diffraction (EBSD). The analyses show that not all grains of similar orientation and grain size form twins, and twinning does not occur exclusively in grains with high twin Schmid factors or in the relatively large grains of the sample. The number of twins per twinned grain increases with grain area, but twin thickness and the fraction of grains with at least one visible twin are independent of grain area. On the other hand, an analysis of twin pairs joined at a boundary indicates that grain boundary misorientation angle strongly influences twin nucleation and growth. These results question the use of deterministic rules for twin nucleation and Hall–Petch laws for size effects on twinning. Instead, they encourage an examination of the defect structures of grain boundaries and their role in twin nucleation and growth.     

Generation and evolution of partial misfit dislocations and stacking faults in thin-film heterostructures

An analysis is made of the specific features in the generation and evolution of partial misfit dislocations at the vertices of V-shaped configurations of stacking fault bands, which terminate in the bulk of the growing film at 90° partial Shockley dislocations. The critical thicknesses h _c of an epitaxial film, at which generation of such defect configurations becomes energetically favorable, are calculated. It is shown that at small misfits, the first to be generated are perfect misfit dislocations and at large misfits, partial ones, which are located at the vertices of V-shaped stacking-fault band configurations emerging onto the film surface. Possible further evolution of stacking-fault band configurations with increasing film thickness are studied.     

Strengthening at nanoscaled coherent twin boundary in f.c.c. metals

This paper analyses slip transfer at the boundary of nanoscaled growth twins in face-centred cubic (f.c.c.) metals for strengthening mechanism. The required stress for slip transfer, i.e. inter-twin flow stress, is obtained in a simple expression in terms of stacking fault energy and/or twin boundary (TB) energy, constriction energy and activation volume. For nanotwinned Al, Cu and Ni, inter-twin flow stress versus twin thickness remarkably shows Hall–Petch relationship. The Hall–Petch slope is rationalized for various reactions of screw and non-screw dislocations at the TB. Additionally, strengthening at the boundary of nanoscaled deformation twins in f.c.c. metals is analysed by evaluating required twinning stress. At small nanograin size, the prediction of deformation twin growth stress shows inverse grain-size effect on twinning, in agreement with recent experimental finding.