Twins In Titanium Research Articles

Faceting and Twin–Twin Interactions in {1121} and {1122} Twins in Titanium

Twin–twin interactions are an important component of the microstructural evolution of hexagonal close-packed metals undergoing plasticity. These interactions are prevalent because of the predominance of twinning due to limited easy slip modes. Despite their importance, the complexities of the atomic-scale behavior of interacting twins has limited robust characterization. Using interfacial defect theory, we developed a three-dimensional model of twin–twin interactions, double twinning and other complex interfacial reactions that occur between twins acting on different interface planes. Using molecular dynamics, {1122} and {1121} twins in titanium were activated and produced facets, twin–twin interactions and double twins that we characterized with our model. The results showed excellent agreement between the molecular dynamics results and the model. Surprisingly, some highly ordered and mobile boundaries can be produced by these complex reactions, which could provide important insights for higher scale models of plasticity.

Formation of [formula omitted] contraction twins in titanium through reversible martensitic phase transformation

We report the discovery of a non-conventional {112¯2} twinning mechanism in α-titanium through reversible α→ω→α martensitic phase transformations. Specifically, the parent α-phase first transforms into an intermediate ω-phase, which then quickly transforms into a twin α-phase, leading to the formation of {112¯2} contraction twins. In addition, we prove that the reversible α→ω→α phase transformations follow strict orientation relations between the parent α-, intermediate ω-, and twin α-phases. Finally, we demonstrate that our mechanism agrees with classical twinning theory in the shuffle, shear, and conjugate twinning plane. This study reveals the important role of the intermediate ω-phase in the twinning process, adding critical details to the existing mechanism of {112¯2} twinning.

Dislocation dissociation induces secondary twinning in titanium

The twin–twin interaction phenomenon in Ti is studied by incorporating experimental observation and theoretical analysis. Secondary $$ \{ {10\bar{1}2} \} $$ twins are stimulated in primary $$ \{ {11\bar{2}2} \} $$ and $$ \{ {11\bar{2}4} \} $$ via twinning dislocation dissociation. Primary twin variants are found either share the same $$ \langle {10\bar{1}0} \rangle $$ zone axis or with different zone axes. Schmid law, dislocation theory and crystallographic analysis are used to investigate the formation processes and physical mechanisms of the twin–twin interaction phenomenon. Results show that non-Schmid secondary twins are stimulated under the effect of primary twinning interactions. Besides to secondary twinning dislocations, glissile and sessile dislocations generate as a result of primary dislocation dissociation. Glissile dislocation glide on the easy slip prismatic plane, while sessile dislocation accumulates and leads to the increase of local strain.

Shock-induced two types of {10[formula omitted]2} sequential twinning in Titanium

Shock loading causes complicated twinning processes in Ti and Ti alloys. In this work, two types of {101¯2} sequential twinning processes are for the first time reported according to electron backscatter diffraction (EBSD) characterization of titanium sheets that are subjected to shock loading. One is described as {112¯1}⇒P→{101¯2} (TiII⇒P→TjI), i.e., {101¯2} sequential twinning is activated in the parent grain (P) along with {112¯1} twins. The other is described as {112¯2}⇒{112¯4}→{101¯2} (CiI⇒CjII→TkI), i.e., {101¯2} secondary twinning is stimulated inside {112¯4} twin by co-zone {112¯2} twin. A statistical analysis according to EBSD characterization reveals the well-defined crystallographic relations between sequential {101¯2} twin variants and the primary/incoming twins, i.e., TiII⇒P→TiIorTi+1I and CiI⇒Ci+3II → TiI or Ti+1I. We proposed and examined two sequential twinning mechanisms, (i) emissary twinning disconnections at steps along twin boundary for the first case and (ii) shear transformation into the primary twin for the second case, based on dislocation theory and the deformation accommodation ability of the sequential {101¯2} twinning to the shear deformation of the primary/incoming twin. Crystal plasticity modelling is performed to calculate the local stress field associated with the proposed twinning mechanisms. The results demonstrate that the preferred twin variant observed in experiments has the maximum resolved shear stress among the six twin variants. Our work suggests that complicated twinning processes under shock loading obey crystallographic relations according to deformation accommodation ability. The findings from this study can be implemented into meso-/macro-scale crystal plasticity models for predicting mechanical behaviors and texture evolution of polycrystalline aggregates of hexagonal materials.

Steps and [formula omitted] secondary twinning associated with [formula omitted] twin in titanium

{112¯2} twinning commonly takes place in α-titanium (α-Ti). High-resolution transmission electron microscopies (HRTEM) explored various steps along {112¯2} coherent twin boundary. Topological model of {112¯2} twin revealed twinning disconnections (TDs) that are represented by (bi, ih{112¯2}) corresponding to a step height ih{112¯2} and a shear vector bi. Atomistic simulations were conducted to study the energies and kinetics of TDs. Combining microscopies and atomistic simulations, we concluded that (b3, 3h{112¯2}) is the elementary TD and (b1, h{112¯2}) is the reassembly TD. Steps observed in HRTEM thus can be treated as a reassembly of (b3, 3h{112¯2}) TDs and (b1, h{112¯2}) TDs. In addition, Electron Backscatter Diffraction (EBSD) maps revealed {112¯2}→{112¯1} double twins in α-Ti. Using two-dimensional and three-dimensional atomistic simulations, we demonstrated the nucleation of (b1, h{112¯2}) TD and {112¯2}→{112¯1} double twin through the interaction between basal <a> dislocation and {112¯2} twin. Our results enrich the understanding of {112¯2} twinning including TDs, steps, and {112¯1} secondary twins in hexagonal metals.

Secondary twin variant selection in four types of double twins in titanium

We experimentally characterized four types of double twins in pure titanium and discussed the selection of secondary twin variants based on the apparent Schmid factor (a-SF), the displacement gradient accommodation (DGA), the modified DGA (m-DGA), and the nucleation via dislocation dissociation (NDD). The four types of double twins are classified into two families according to their zone axes: co-family double twins and non-family double twins. Co-family double twins share the zone axis <101¯0>. Non-family double twins have different zone axes with one along <112¯0> and the other along <101¯0>. Experimental observations reveal that the co-family double twins have one secondary twin variant prevailed over others and the non-family double twins have two secondary twin variants preferred than others. The a-SFs associated with secondary twins are always positive once the primary twin is activated, thus predicting no obvious preference for the selection of secondary twin variants. The m-DGA and NDD correctly predict the selection of secondary twin variants, implying that the preferred secondary twin variant would, to the greatest extent, relax plastic deformation associated with the primary twinning and the nucleation of the secondary twin variant is facilitated by the accumulation of available gliding dislocations at the primary twin boundary.

Structure and Stresses in a System of Two Mechanical Twins in Titanium

Structure and Stresses in a System of Two Mechanical Twins in Titanium

Sequential [formula omitted] twinning stimulated by other twins in titanium

We experimentally studied sequential {101¯2} twinning in rolled pure titanium at room temperature and identified a new sequential twinning mechanism, i.e., {101¯2} (TiI) extension twin stimulated by the twin-twin junction of two primary {112¯1} extension twins Ti−1II and TiII, which holds a certain relation Ti−1IITiII→TiI. Schmid factor analysis, as the local stress is taken into account, is able to determine the position of sequential twin variant, but cannot determine the twin variant. Displacement gradient accommodation is used to determine the twin variant. The well-known secondary {101¯2} (TjI) extension twins in primary {112¯2} (CiI) contraction twins (referred to as CiI→TjI double twinning) are also analyzed according to a generalized Schmid factor analysis. Displacement gradient accommodation and twin nucleation based on dislocations dissociation only work well for the most active twin variants, but cannot address other phenomena associated with CiI→TjI double twinning. For rarely activated twin variants, displacement gradient accommodation was not satisfied.

Growth of {[formula omitted]} twins in titanium: A combined experimental and modelling investigation of the local state of deformation

In this work we combine experiments and simulations to study the residual deformation state near twins in titanium at different stages of the complete twin growth process, including the twin tip: (i) far from a grain boundary, (ii) approaching a grain boundary, and (iii) intersecting with a grain boundary. High resolution electron backscatter diffraction (HR-EBSD) was used to characterise the local residual stress state and dislocation density distributions. Schmid factors were calculated from both the global deformation state (i.e. remote loading) and local deformation state (i.e. from high angular resolution EBSD). Crystal plasticity finite element modelling was used to simulate the stress field close to twins during loading and unloading. These simulations indicate that while the magnitudes of the localized stress fields close to twin boundaries are reduced upon removing the far field load, the major features of the stress fields in these regions are dominated by accommodation of the twin and thus persist from the peak load state to the unloaded state. We find a good correlation between the active twin variant and the maximum local Schmid factor, while the external loading (i.e. global Schmid factor) plays a less important role. These findings are useful in determining which twins will grow when a sample is deformed, and this has important implications for in service performance as well as texture evolution during mechanical processing.

Twin Interactions in Pure Ti Under High Strain Rate Compression

Twin interactions associated with {11\( \overline{2} \)1} (E2) twins in titanium deformed by high strain rate (~2600 s−1) compression were studied using electron backscatter diffraction technique. Three types of twins, {10\( \overline{1} \)2} (E1), {11\( \overline{2} \)2} (C1), and {11\( \overline{2} \)4} (C3), were observed to interact with the preformed E2 twins in four parent grains. The E1 variants nucleated at twin boundaries of some E2 variants. And the C3 twins were originated from the intersection of C1 and E2. The selection of twin variant was investigated by the Schmid factors (SFs) and the twinning shear displacement gradient tensors (DGTs) calculations. The results show that twin variants that did not follow the Schmid law were more frequently observed under high strain rate deformation than quasi-static deformation. Among these low-SF active variants, 73 pct (8 out of 11) can be interpreted by DGT. Besides, 26 variants that have SF values close to or higher than their active counterparts were absent. Factors that may affect the twin variant selections were discussed.

A novel method for predicting variant selection during primary, secondary and tertiary twinning in titanium

The present paper proposes a novel method based on Schmid׳s law by introducing a calculation of “Normalized Schmid factor” as an indispensable criterion for predicting twin variant selection in commercially pure titanium. Through comparing the calculation with experimental results, this novel method is proved to be a more effective criterion than Schmid׳s law and the accuracy is about 90% during primary, secondary and tertiary twinning variant selection.

Rejoinder to the response by B. Li [1] on our Comment [2] on the paper B. Li, H. El Kadiri and M.F. Horstemeyer ‘Extended zonal dislocations mediating twinning in titanium’

Rejoinder to the response by B. Li [1] on our Comment [2] on the paper B. Li, H. El Kadiri and M.F. Horstemeyer ‘Extended zonal dislocations mediating twinning in titanium’

Comments on “extended zonal dislocations mediating twinning in titanium”

In a recent paper, Li et al. (Philos. Mag. 92 (2012) p.1006) used results of atomistic simulations to advance a growth mechanism of twinning in titanium based on the concept of two elementary twinning dislocations which nucleate and glide in pairs but separately and sequentially on two neighbouring planes. This new Comment was stimulated after A. Serra, D.J. Bacon and R.C. Pond privately raised concerns on this growth model to one of the present authors, H. El Kadiri, who This was a co-author of the original paper (Philos. Mag. 92 (2012) p.1006). We repeated the simulations and obtained nearly the same simulations results as Li et al. However, after re-analysing these results, we have concluded that the extended extrinsic zonal dislocation mechanism claimed to be that for twin growth in titanium is in fact false, confirming the accuracy of the Comment by Serra et al that results of Li and co-authors were misinterpreted.

Reply to the two Comments, by A. Serra, D. J. Bacon and R. C. Pond, and by H. El Kadiri and C. Barrett on B. Li, H. El Kadiri and M.F. Horstemeyer “Extended zonal dislocations mediating twinning in titanium”

Serra, Bacon and Pond argue that, when the direction of the resolved shear stress on the twinning plane is reversed, the K 2 plane for twinning changes from (0 0 0 1) to , and the core structure, configuration and magnitude of the twinning dislocation change from b ±1 to b ±3. I contend that such behaviour has not been observed in any twinning mode in metals. A twinning mode should have a K 2 plane and the corresponding twinning dislocation that is structurally and energetically favourable and independent of the direction of the resolved shear stress. El Kadiri and Barrett echo the Comment by Serra et al. and argue that the one-layer twinning dislocation is an “artifact”, disregarding the fact that all the simulation results converge to one conclusion, i.e. the one-layer twinning dislocation is more favourable than the three-layer zonal dislocation, irrespective of the interatomic potentials used in the simulations. In this Reply, I seek to clarify such misinterpretations regarding twinning dislocation, twinning shear and shuffling in these Comments.

Extended zonal dislocations mediating twinning in titanium

Using molecular dynamics (MD) simulations, the twinning mechanism in titanium (Ti) was studied by analyzing the interfacial structure at the twin boundary (TB). The simulation results reveal interesting twin growth controlled by interfacial dislocations at the TB. The elementary twinning dislocations (bT ) nucleate and glide in pairs but separately and sequentially on two neighboring planes, significantly different from conventional zonal dislocations, which spread over two or more twinning planes with each plane comprising one Burgers vector of an elementary twinning dislocation. The twin growth can be approximately described as These two separate elementary twinning dislocations amount to a net Burgers vector 2bT ≈ 0.16 nm along the twinning vector , with the components in the in-plane direction perpendicular to η 1 canceled out. These results support the classical twinning theory in which a homogeneous shear and local shuffling have to be involved. A mechanism taking into consideration local structure of the twinning plane for such extended zonal dislocations is discussed.

Structure of titanium subjected to dynamic channel-angular pressing in copper shells

It has been established using metallography and electron microscopy that the dynamic channel-angular pressing of titanium in cylindrical copper shells of a sufficient thickness removes the effects of localized deformation in the form of cracks and adiabatic shear bands, which were observed upon deformation without shells. This mode of deformation is effected via the formation of numerous twins; as a result, the initial grains become divided into small regions. Together with twins of ordinary morphology in the form of plates, there are observed wavy bent “noncrystallographic” twins, whose appearance is caused by the rotational deformation modes. Twins in the form of rods have been revealed, which sometimes are grouped into lamellar packets arranged perpendicularly to the longitudinal axis of the sample. The formation of numerous twins in titanium during dynamic channel-angular pressing leads to an increase in the microhardness by 15–35%. Twinning can be used to increase the strength characteristics of titanium, additionally to the creation of nanocrystalline and submicrocrystalline structures.

Misorientations induced by deformation twinning in titanium

The misorientations induced by cold-rolling in commercially pure titanium by twinning and multiple twinning were investigated by electron backscatter diffraction. Three main types of twins occur: compressive twins (64.6° 〈1\overline 100〉) which are predominant, followed by tensile twins of type 1 (84.8° [11\overline 20]) and a few of type 2 (35.1° 〈1\overline 100〉). The main multiple twinning configurations are (i) several variants of a given type of twin inside a given grain and (ii) second-generation tensile twins inside primary compressive twins. All possible misorientations resulting from the combination of two out of the three main twinning systems have been calculated and compared with the experimentally observed twin configurations. This facilitated interpretation of the peak found at 41° 〈5\overline 1\overline 43〉 in the misorientation distribution as the result of double twinning (tensile twins inside primary compressive twins).

Accommodation around {10 [formula omitted]1} twins in titanium

Observation par microscopie electronique en transmission du mecanisme d'accommodation par formation de decrochements de dislocations autour des macles {1011} dans le titane alpha

Incorporation of slip dislocations in twins in titanium

Twinning is an important mode of deformation in hexagonal metals, particularly in titanium, where there are only four independent slip systems. There have been several theoretical treatments of the interaction between slip dislocations and twins in hcp structures, although there has been only limited experimental verification of these interactions. This paper presents the results of a TEM investigation of the decomposition of 1/3&lt;1120&gt; slip dislocations upon penetrating a twin boundary in titanium. The work began as a study of subsurface deformation induced during dry sliding wear of titanium, and later led to in situ tensile straining experiments. Results from both types of experiment are discussed.

Acoustic emission due to deformation twinning in titanium and Ti6Al4V alloy

Acoustic emission due to deformation twinning in titanium and Ti6Al4V alloy