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.     

Effect of cyclic stresses on the microstructures of hexagonal close packed metals

Slip band extrusions are formed in cadmium, magnesium and titanium, but not in zinc. The extrusions form preferentially in untwinned crystals. Filamentary growths occur at {10¯12} and {11¯21} twin interfaces during cyclic twinning.Possible dislocation interactions at these twin interfaces are described. The dislocation debris produced during cyclic strain in the slip bands and by cyclic twinning is shown to be similar and composed of a high density of dipole loops. It is therefore concluded that the occurrence and distribution of slip band extrusions in metals and the formation of twin boundary filamentary growths can be accounted for by a model based upon the glide of interstitial type dipole loops. Vacancy type loops will then cause crack nucleation in slip bands and deformation twin boundary regions.Twin boundary debris can also cause the observed fragmentation of twins by acting as a barrier to twin boundary movement.The author is grateful to Dr. A. G. Crocker, University of Surrey, for many discussions on the twinning mode in h.c.p. metals and to P. J. E. Forsyth for his interest and encouragement. The paper is published by permission of the Controller, H. M. Stationery Office. Crown copyright is reserved.     

Energy barriers associated with slip–twin interactions

The energetics of slip–coherent twin boundary (CTB) interactions are established under tensile deformation in face centered cubic (fcc) copper with molecular dynamics simulations, exploring the entire stereographic triangle. The CTBs serve as effective barriers in some crystal orientations more than others, consistent with experimental observations. The resulting dislocation structures upon slip–twin reactions are identified in terms of Burgers vector analysis. Visualization of the dislocation transmission, lock formation, dislocation incorporation to twin boundaries, dislocation multiplication at the matrix–twin interface and twin translation, growth, and contraction behaviors cover the most significant reactions that can physically occur providing a deeper understanding of the mechanical behavior of fcc alloys in the presence of twin boundaries. The results make a distinction between deformation and annealing twins interacting with incident dislocations and point to the considerable role both types of twins can play in strengthening of fcc metals.     

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.     

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.     

A disclination model for twinning and de-twinning of nanotwinned copper

The twinning and de-twinning processes within grains of nanotwinned copper (nt-Cu) are schematically demonstrated using the concept of wedge disclination quadrupoles. The stable twin nucleus size and the equilibrium equation of the applied shear stress and twin width during twin growth are obtained. The dependence of the critical resolved shear stress for twinning on the grain size, which conforms to the classic Hall–Petch relationship, is theoretically modelled. Additionally, the disclination quadrupole model for de-twinning is used to interpret the strength softening in nt-Cu. Relative to the classic kinetic and energetic models, this novel approach is more compatible with the experiments.     

Strengthening and softening in gradient nanotwinned FCC metallic multilayers

Plastic-deformation behaviors of gradient nanotwinned (GNT) metallic multilayers are investigated in nanoscale via molecular dynamics simulation. The evolution law of deformation behaviors of GNT metallic multilayers with different stacking fault energies (SFEs) during nanoindentation is revealed. The deformation behavior transforms from the dislocation dynamics to the twinning/detwinning in the GNT Ag, Cu, to Al with SFE increasing. In addition, it is found that the GNT Ag and GNT Cu strengthen in the case of a larger twin gradient based on more significant twin boundary (TB) strengthening and dislocation strengthening, while the GNT Al softens due to more TB migration and dislocation nucleation from TB at a larger twin gradient. The softening mechanism is further analyzed theoretically. These results not only provide an atomic insight into the plastic-deformation behaviors of certain GNT metallic multilayers with different SFEs, but also give a guideline to design the GNT metallic multilayers with required mechanical properties.     

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.     

Establishing the microstructure-strengthening correlation in severely deformed surface of titanium

Surface nanostructuring of engineering materials can be utilised to enhance materials performance for various applications. The aim of this work was to investigate the evolution of microstructure and its correlation with strengthening mechanisms in nanocrystalline commercially pure titanium (cp-Ti) produced by surface mechanical attrition treatment (SMAT). The individual contributions of dislocation slip and twining as the deformation mechanisms during SMAT have been quantified using X-ray line profile analysis and corroborated with transmission electron microscopy and electron backscattered diffraction techniques. It is found that twining is operative only in the early stages of deformation. The absence of twin–twin intersections suggests that twining is not directly responsible for the initial refinement of grain size. Dislocation slip is the major deformation mode, which leads to the refinement of the microstructure by forming low-angle lamellar boundaries. Continuous dynamic recrystallisation is demonstrated to be the mechanism of nanocrystallisation in cp-Ti using detailed microscopic analysis. In contrast to previous studies, which have neglected the contribution of Taylor strengthening, it is observed that a combination of Hall–Petch and Taylor relationships can explain the strength only if separate set of parameters K (Hall–Petch constant) and α (geometrical factor in Taylor relationship) are used for the nanocrystalline surface and severely deformed sub-surface of cp-Ti. Taken together, this work provides new insights into the underlying mechanisms for engineering nanocrystalline materials.     

Characterization of twinning in electrodeposited Ni–Mn alloys

Twinning is ubiquitous in electroplated metals. Here, we identify and discuss unique aspects of twinning found in electrodeposited Ni–Mn alloys. Previous reports concluded that the twin boundaries effectively refine the grain size, which enhances mechanical strength. Quantitative measurements from transmission electron microscopy (TEM) images show that the relative boundary length in the as-plated microstructure primarily comprises twin interfaces. Detailed TEM characterization reveals a range of length scales associated with twinning beginning with colonies (～1000?nm) down to the width of individual twins, which is typically <50?nm. We also consider the connection between the crystallographic texture of the electrodeposit and the orientation of the twin planes with respect to the plating direction. The Ni–Mn alloy deposits in this work possess a {110}-fiber texture. While twinning can occur on {111} planes either perpendicular or oblique to the plating direction in {110}-oriented grains, plan-view TEM images show that twins form primarily on those planes parallel to the plating direction. Therefore, grains enclosed by twins and multiply twinned particles are produced. Another important consequence of a high twin density is the formation of large numbers of twin-related junctions. We measure an area density of twin junctions that is comparable to the density of dislocations in a heavily cold-worked metal.     

Atomistic simulation study on twin orientation and spacing distribution effects on nanotwinned Cu films

Affected by twin orientation and spacing distribution, different deformation and failure mechanisms of nanotwinned (NT) Cu films are discovered. For films with the same twin spacing, transition from brittle to ductile and ductile to localized necking with the increase of the slanted angle of twin boundary (TB) from 0° to 90° is examined. Two dominant slip mechanisms: (1) slip intersecting with the TBs; (2) slip parallel to the TBs can uncover the transition mechanisms with consideration of twin orientation. To maintain both relatively high strength and good ductility, the slanted angle can be set close to the ductile to localized necking transition border. Besides, the stress–strain curves obtained in this article show that the mechanical responses on both sides of the turning point 45° are asymmetric. On the other hand, the twin spacing distributions affect the ductility of NT Cu films and have almost no contribution to strengthening. The strength of the NT Cu films mainly depends on the twin density. NT Cu films with different twin spacing have worse ductility than equal twin spacing films due to the local twin spacing asymmetry. The failures can be predicted appearing at TBs adjacent to large twin spacing regions, and the failure propagation direction can also be predicted by knowing the obtuse angle decided by stacking faults and TBs.     

Interactions between slip dislocations and twins in α-uranium I. Geometrical and energetical considerations

The geometrical conditions for the propagation of dislocations through the twins are applied to the main slip and twinning systems in-uranium. The energy of dislocations moving through a twin is calculated using the isotropic elasticity. It is shown that the principal slip system with the Burgers vector [100] can easily propagate only through the {130} compound twins. The possibility of uncommon slip systems in twins crossed by slip bands is thoroughly discussed.     

Nanocrystalline gold with small size: inverse Hall–Petch between mixed regime and super-soft regime

ABSTRACT

Molecular dynamics simulations were used to study the atomic mechanisms of deformation of nanocrystalline gold with 2.65–18?nm in grain size to explore the inverse Hall–Petch effect. Based on the mechanical responses, particularly the flow stress and the elastic-to-plastic transition, one can delineate three regimes: mixed (10–18?nm, dislocation activities and grain boundary sliding), inverse Hall-Petch (5–10?nm, grain boundary sliding), and super-soft (below 5?nm). As the grain size decreases, more grain boundaries present in the nanocrystalline solids, which block dislocation activities and facilitate grain boundary sliding. The transition from dislocation activities to grain boundary sliding leads to strengthening-then-softening due to grain size reduction, shown by the flow stress. It was further found that, samples with large grain exhibit pronounced yield, with the stress overshoot decrease as the grain size decreases. Samples with grain sizes smaller than 5?nm exhibit elastic-perfect plastic deformation without any stress overshoot, leading to the super-soft regime. Our simulations show that, during deformation, smaller grains rotate more and grow in size, while larger grains rotate less and shrink in size.     

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.     

Interaction between Dislocation and Twinning Boundary under Incremental Loading in α-Titanium

The lattice dislocation interacting with grain boundary in the polycrystal exerts an evident influence on the materials' strength and toughness. A comprehensive study regarding the dislocation-twinning boundary(TB)interaction in a-titanium and TB migration is performed by employing molecular dynamic simulation. We analyze the interactions between dislocation and TB, under the conditions of plastic deformation and thermal stress, including the interaction between pure edge(a) dislocation and(1122) TB and the interaction between mixed type(a) dislocations and(1011) TB at 10 K/300 K. The(c + a) pyramidal transmitting slip mode is motivated in the case of edge dislocation-(1122) interaction at 300 K and then transforms into basal-dissociated dislocation after experiencing the complex dissociation and combination. The basal-dissociated pyramidal partial dislocation located in the second grain can be driven to penetrate through the second grain leaving the multiple stacking faults behind. Dissociation of incident basal dislocation on(1011) TB results in a nucleation of a(1011)twin embryo in twin crystals at room temperature. We determine the nature of the generated defects by means of the Burgers circuit analysis.     

Comparison of the deformation behaviour of commercially pure titanium and Ti–5Al–2.5Sn(wt.%) at 296 and 728 K

The tension and tensile-creep deformation behaviours of a fully-α phase commercially pure (CP) Ti and a near-α Ti–5Al–2.5Sn(wt.%) alloy deformed in situ inside a scanning electron microscope were compared. Tensile tests were performed at 296 and 728?K, while tensile-creep tests were performed at 728?K. The yield stress of CP Ti decreased dramatically with increasing temperature. In contrast, temperature had much smaller effect on the yield stress of Ti–5Al–2.5Sn(wt.%). Electron backscattered diffraction was performed both before and after the deformation, and slip trace analysis was used to determine the active slip and twinning systems, as well as the associated global stress state Schmid factors. In tension tests of CP Ti, prismatic slip was the most likely slip system to be activated when the Schmid factor exceeded 0.4. Prismatic slip was observed over the largest Schmid factor range, indicating that the local stress tensor varies significantly from the global stress state of uniaxial tension. The basal slip activity in Ti–5Al–2.5Sn(wt.%) was observed in a larger faction of grains than in CP Ti. Pyramidal ?c?+?a? slip was more prevalent in CP Ti. Although twinning was an active deformation mode in tension tests of the CP Ti, it was rare in Ti–5Al–2.5Sn(wt.%). During creep, dislocation slip was the primary apparent deformation mechanism in CP Ti, while evidence for dislocation slip was much less apparent in Ti–5Al–2.5Sn(wt.%), where grain boundary sliding was dominant. A robust statistical analysis was carried out to assess the significance of the comparative activity of the different slip systems under the variety of experimental conditions examined.     

High resolution transmission electron microscope observation of zero-strain deformation twinning mechanisms in Ag

We have observed a new deformation-twinning mechanism using the high resolution transmission electron microscope in polycrystalline Ag films, zero-strain twinning via nucleation, and the migration of a Σ3{112} incoherent twin boundary (ITB). This twinning mechanism produces a near zero macroscopic strain because the net Burgers vectors either equal zero or are equivalent to a Shockley partial dislocation. This observation provides new insight into the understanding of deformation twinning and confirms a previous hypothesis: detwinning could be accomplished via the nucleation and migration of Σ3{112} ITBs. The zero-strain twinning mechanism may be unique to low staking fault energy metals with implications for their deformation behavior.     

Micromechanistic origin of irradiation-assisted stress corrosion cracking

A multi-scale study of the micromechanics of dislocation–grain boundary interactions in proton and ion-irradiated stainless steels is presented. Interactions of dislocation channels with grain boundaries result in slip transfer, discontinuous slip without or with slip along the grain boundary. The presence of the irradiation damage enhances the importance of the magnitude of the resolved shear stress on the slip system activated by the grain boundary to transfer slip across it. However, the selected slip system is still determined by the minimization of the grain boundary strain energy density condition. These findings have implications for modelling the mechanical properties of irradiated metals as well as in establishing the mechanism for disrupting the grain boundary oxide, which is a necessary prerequisite for irradiation-assisted stress corrosion cracking.     

Flow stress/strain rate/grain size coupling for fcc nanopolycrystals

A Hall–Petch (H–P)-type dependence is demonstrated for reciprocal activation volume measurements for nanocrystalline and conventional grain size, strengthened Ni and Cu materials, consistent with predictions derived from the dislocation pile-up model. The observed H–P dependence indicates that the shear stress for cross-slip must be involved in the full grain size regime for transmission of plastic flow at the grain boundaries of fcc metals.