Deformation Behavior of Commercially Pure Titanium Subjected to Blast Assisted Deformation: New Insights on {11-21} Extension Twinning

Abstract

In the present work, the microstructure and texture evolution in commercially pure titanium subjected to blast assisted deformation has been investigated by means of electron backscattered diffraction and transmission electron microscopy. The evolved texture in the deformed material is primarily attributed to the dominant ⟨1010⟩ 64.4° contraction twinning. Other deformation twins were also observed in a low fraction. A uniform dislocation background with other microstructural features observed suggested the formation of a superimposed microstructure in the material. {1121} extension twins (ET2) with a thick uniform pile-up of dislocation along its boundary have formed in the material. Parts of ET2 have detwinned leaving gaps along the twin length, revealing the unstable nature of ET2 twins. The in-depth microstructural analysis reveals the ET2 twin formation mechanism, where the instability developed in the material due to progressive lattice rotation via accumulative slip is relieved by ET2 twin formation by atomic shuffling. The gaps (local detwinning) observed in the present case is attributed to the transient oscillatory response of the material under impulsive loading, which has been previously reported in the literature.

1. Introduction

Titanium and its alloys form an important class of materials owing to their application in aerospace industry [1]. Many aircraft components that are made of titanium and titanium alloys are subjected to critical operating conditions. Such applications demand the understanding of the plastic response of the material under extreme condition. Under normal quasi-static deformation at room temperature, polycrystalline titanium deforms via prismatic and basal slip plus extension twinning. Under dynamic deformation conditions, titanium is expected to undergo different propensities of these deformation modes plus some additional accommodation mechanisms. Many studies have been carried out in the past on the response of titanium and its alloys under high strain rate [2–8] and shock exposure [9–13]. Deformation mechanism involving twinning [7], phase transformation [13–15] and shear banding [3, 4, 8] become important under such conditions. Out of these, twinning is the most common phenomenon that is also prevalent in quasi-static deformation condition. There are various probable twinning systems in titanium, namely, the extension twins ($\{ 10\bar{1}2\} \langle \bar{1}011\rangle $ (ET1) and $\{ 11\bar{2}1\} \langle \bar{1}\bar{1}26\rangle $ (ET2)), and, the contraction twins ($\{ 11\bar{2}2\} \langle 11\bar{2}\bar{3}\rangle $ (CT1), $\{ 10\bar{1}1\} \langle \bar{1}012\rangle $ (CT2) and $\{ 11\bar{2}4\} \langle 22\bar{4}\bar{3}\rangle $ (CT3)) [16–18]. One or more of these twinning systems can operate under different deformation condition.

While the extension twins of the type $\{ 10\bar{1}2\} \langle \bar{1}011\rangle $ are most commonly observed during the deformation of polycrystalline titanium, the $\{ 11\bar{2}1\} \langle \bar{1}\bar{1}26\rangle $ extension twins (ET2) are a special case as it is not a common mode of twinning owing to its unstable nature [19, 20]. In fact, the occurrence of ET2 is reported for specific deformation conditions such as under dynamic deformation [21], deformation at elevated temperature [22], and deformation under high shear strain, as in the case of equal channel angular pressing (ECAP) [23]. As the deformation temperature is increased, the propensity of $\{ 10\bar{1}2\} $ extension twinning decreases and the prismatic and pyramidal slip activity increases [22]. At 815°C, although the overall twinning activity gets reduced and the slip activity remains dominant, the $\{ 11\bar{2}1\} \langle \bar{1}\bar{1}26\rangle $ type twins (ET2) are the only twins observed [22]. In contrast, $\{ 11\bar{2}1\} \langle \bar{1}\bar{1}26\rangle $ and $\{ 10\bar{1}1\} \langle \bar{1}012 \rangle $ twins are the dominant twinning types during room temperature ECAP [23, 24], while $\{ 10\bar{1}1\} \langle \bar{1}012 \rangle $ are the twin types dominated at elevated temperature (350°C) [25]. The twinning shear associated with ET2 is very large (0.63) compared to the other twinning systems [16]. Due to its rare occurrence, ET2 twin system is relatively less investigated when compared to other twinning systems of α-titanium. Jin et al. [21] have investigated the formation mechanism of ET2 in dynamically deformed cp-Ti. It was shown that deformation kink band boundaries evolve into ET2 twin boundaries through accumulative slip. Other recent studies on shock-induced and dynamic deformation of Ti focused on twinning have reported two types of $\{ 10\bar{1}2\} $ sequential twinning [26], abnormal $\{ 11\bar{2}1\} $ twins [27] and $\{ 11\bar{2}1\} $ → $\{ 11\bar{2}2\} $ double twinning [28].

The evolution of texture in titanium and its alloys under shock and high strain rate loading conditions is also largely unexplored. To the best of our knowledge, there are only few studies which discusses the texture evolution in pure Ti under extreme strain rate [5, 29, 30]. In the study by Gurao et al. [5], they observed that the texture of high strain rate deformed cp-Ti was characterized by the presence of orientation near $\langle \bar{1}\bar{1}20\rangle $ and $\langle \bar{1}\bar{1}24\rangle $ components, with the latter texture component being stronger. Ren et al. [30] reported transformation of initial split basal texture to a basal texture accompanied by a [0001] TD orientation attributed to $\{ 11\bar{2}2\} $ compression twin. These studies on high-strain rate deformation of Ti were carried out using split-Hopkinson pressure bar [5, 29, 30], where the strain path is primarily monotonic in nature. However, not much information is available in published literature related to texture changes on shock/blast assisted deformation. Moreover, most of the studies on high-strain rate deformation of cp-Ti have employed monotonic loading. In contrast, the material has experienced a transient non-monotonic loading due to the nature of the deformation method employed in the present study. This has resulted in a novel material response and some interesting microstructural features unknown in literature to the best of our knowledge.

In the present study, the microstructural and textural response of cp-Ti subjected to blast assisted loading has been investigated by means of electron back-scattered diffraction (EBSD) and transmission electron microscopy (TEM) based microstructural characterization techniques. In addition, complementing the recent finding of Jin et al. [21], the formation mechanism of $\{ 11\bar{2}1\} $ extension twins (ET2) is revisited to explore the validity of the mechanism proposed. The present study reinforces study by Jin et al. [21] and reports additional finding which clearly displays the unstable nature of ET2 twin and its origin from the “twist” character of instability in the matrix. An in-depth analysis of the microstructure with ET2 twins in focus has been carried out.

2. Methods

2.1 Materials and processing

We wanted a strain-free initial material with equiaxed microstructure for the tests. Commercially pure titanium (cp-Ti) was received in the form of a thick sheet of thickness 3 mm. It was thermo-mechanically processed to annul the effect of prior processing from the as-received condition. The as-received material was, first, cold rolled in a unidirectional (UDR) manner to 90% reduction in thickness. Thereafter, the samples were annealed at 800°C for 5 min to obtain recrystallized microstructure with equiaxed grains. The initial high strain imparted to the material ensured a uniform strain in the material and hence uniform recrystallization on heat treatment. The area average grain size of the initial material was 24 µm. The processed material was cut to discs of 12 mm diameter and the obtained samples were thinned down to 200 µm thickness for further deformation.

2.2 Deformation using shock wave

The discs of cp-Ti were subjected to high strain rate loading on the normal plane of the discs by exposing them to the shock wave in a detonation-driven miniaturized shock tube (MST). In such a loading setup, the material may experience a transient non-monotonic strain before attaining final deformed shape. Schematic of the miniaturized shock tube (MST) setup is shown in Fig. S1(a) (see supplementary). A high-pressure detonation wave is created in the tube by the combustion of the in-situ generated oxyhydrogen mixture. After attaining the required pressure, the gaseous mixture is detonated by triggering a hot wire. A steady detonation wave is produced which travels along the length of the tube. The shock tube was operated in detonation mode. The material was deformed to two strain levels referred as “def1” and “def2”, with the strain of latter being higher than the former. The head-on pressure profile of the detonation (shock) wave measured using PCB 113B22 sensor is shown in Fig. S1(b). The integrated area of the pressure profile gives the impulse per unit area. The peak shock pressure, impulse per unit area and impulse values are tabulated in Table S1 (see supplementary). The pressure profile shows an exponential decay, which is typical of a blast wave pressure profile. Although the material was subjected to blast loading, it is referred as shock loading for uniformity of the text.

2.3 Strain measurement

A sectioned cp-Ti sample is shown in Fig. S2 (see supplementary). The thickness strain at the center of the hat-shaped disc can be obtained from the mid-point deflection [31]. The thickness strain is given as:

  

\begin{equation} \varepsilon_{t} = \ln \frac{\pi r^{2}}{2\pi\rho h} = \ln \frac{r^{2}}{2\rho h} \end{equation} (1)

where,

  

\begin{equation} \rho = \frac{r^{2} + h^{2}}{2h} \end{equation} (2)

and r is the radius of exposed area (4 mm), h is the mid-point deflection, and, ρ, is the radius of curvature.

2.4 Microstructure and microtexture characterization

The initial and the deformed samples were characterized via electron back-scattered diffraction (EBSD) technique. EBSD characterization was done on the transverse plane of the material parallel to the initial rolling direction (RD). The deformed sample was investigated at the mid-point deflection. A detailed information pertaining to microstructural features and microtexture was extracted from the EBSD data.

For EBSD, the samples were subjected to mechanical polishing followed by electropolishing using Struers Lectropol-5 (Struers A/s, Stuttgart, Germany) electro-polisher. Struers trademark A3 electrolyte was used for electropolishing of cp-Ti. EBSD was performed using FEI SIRION scanning electron microscope (SEM; FEI Company, Hillsboro, Oregon) equipped with EBSD detector and a step size within the range of 0.1 µm for various samples. Post-processing of the EBSD data was done using TSL OIM™ analysis software. The qualitative information pertaining to strain distribution was generated from grain orientation spread (GOS) and kernel average misorientation (KAM) plots. Grain boundary character distribution was obtained from the misorientation distribution plots. Microtexture information from the EBSD data was plotted and further texture analysis was carried out using JTEX software [32].

Further, finer microstructural examinations were performed using a FEI Tecnai F30 transmission electron microscope (TEM) operated at 300 kV. The TEM sample of 3 mm disc was mechanically polished to a thickness of ∼80 µm followed by further fine polishing. The cp-Ti samples were electropolished in the perchloric acid and ethanol solution at −30°C in Fishione Twin-Jet Electropolisher^®.

3. Results

The characterization of microstructure and texture of the as-processed cp-Ti material, hereafter referred as the starting material, revealed a microcrystalline equiaxed grains with split basal texture. This material was shock loaded to two different strain levels as mentioned earlier. The strain rate could not be measured during the experiments due to the small scale of the test adopted in the present investigation. However, in previous similar studies on shock/blast assisted deformation of metallic plates, the deformation rate has been measured using DIC and is reported to be of the order of few 1000 s⁻¹ [33, 34]. We expect the deformation rate in the present investigation to be of the same order. We first report the general macroscopic findings in the material after deformation followed by focused and key microstructural features. The results pertaining to the evolution of microstructure and microtexture after shock loading are described in the following sub-sections.

3.1 Impulse and effective strain

Shock waves of different peak impulses were generated by varying oxyhydrogen fill pressure. The peak pressure, impulse per unit area and impulse values corresponding to various oxyhydrogen fill pressures used in the present study are given in Table S1. The impulse used in the present investigation are of relatively lower magnitude compared to a full-scale explosive tests. The oxyhydrogen fill pressure and corresponding strain at the mid-point deflection are presented in Table 1.

Table 1 Oxyhydrogen fill pressures used and the strains obtained in shock-loaded cp-Ti samples.

3.2 Texture evolution on shock loading

Microstructural texture of the material gives a broad perspective of the orientation changes undergone. The (0002) pole figures for the cp-Ti (Ti) sample before and after deformation are shown in Fig. 1. The texture of the starting sample is strong with basal pole split along the transverse direction (TD). The pole figures clearly depict appreciable changes in texture on shock loading. After shock loading, texture weakens and new poles appear at the periphery of the (0002) pole figure close to TD. The poles near the center weaken while those at the periphery strengthens with deformation. There are additional poles near the periphery of pole figure off-center to RD (lower side) and at other positions which are weaker. The shift in the component is around 60°–70°.

Fig. 1

(0002) pole figures of shock loaded cp-Ti with UDR processing: (a) initial, (b) def1 and (c) def2 samples. (online color)

3.3 Microstructural evolution on shock loading

3.3.1 Electron back-scattered diffraction studies

Now firstly we discuss the general spatial microstructural changes in the material. As mentioned earlier, the EBSD scan was done for microstructural characterization in the transverse plane of the sample. The inverse pole figure (IPF) maps obtained from the EBSD data for cp-Ti UDR samples before and after shock loading are shown in Fig. 2. The area average grain size of the initial material was 24 µm. The orientation of the crystal plane parallel to the plane of the sheet (crystal plane normal parallel to the sheet normal direction) is shown in the IPF maps for one-to-one correspondence with pole figure. The morphological features, however, depict the same for the transverse plane. The microstructure of the starting material is recrystallized, as can be observed from the equiaxed morphology and absence of misorientation (color variation) within grains. After shock loading, twins have formed inside the grains. Misorientation development is evident from the contrast variation inside the grains after shock treatment, indicating strain accumulation inside the grains. Twins have formed in majority of grains after deformation. However, it could be noted that there are few grains which did not twin even at a higher strain (def2). Care was taken during the identification of such non-twinned grains. Of the total of 72 gains inspected (considering grain-twin pairs as a single grain), only 11 grains were observed which does not contain twin. These gains were observed to be smaller than 15 µm with an area average grain size of 12.7 µm. Nevertheless, some small grains (d < 15 µm) with twins were also identified. Thus, it can be safely concluded that twinning is prevalent to a lesser extent in the smaller grains (d < 15 µm) when compared to the larger grains (d > 15 µm).

Fig. 2

Inverse pole figures (IPF) maps of shock loaded cp-Ti with UDR processing: (a) initial, (b) def1 and (c) def2 samples. (online color)

The grain size distribution (Fig. 3(a)) indicates a change in the grain size after shock loading due to grain fragmentation as a result of twinning. The grain orientation spread (GOS) plot is shown in Fig. 3(b). A shift in GOS to a higher value with strain is clearly observed, however, the GOS is well below 3°. An increase in the number fraction of GOS is noted for lower strains, which is an interesting observation. However, at a larger strain (def2 sample), the GOS value decreases. The KAM distribution (Fig. 3(c)) gets broadened and shifts to the right with strain. The average KAM is, however, less than 2° for all the samples. The misorientation angle distribution is plotted in Fig. 3(d). For reference, MacKenzie misorientation distribution, which represents the misorientation corresponding to random orientation distribution of grains, is also shown. The misorientation distribution in the initial sample is more or less uniform. The important twinning systems observed in titanium with their angle/axis misorientation and twinning shear [16–18] are listed in Table S2 (see supplementary). On shock loading, the misorientation corresponding to the contraction twin $\{ 11\bar{2}2\} \langle 11\bar{2}\bar{3}\rangle $ (CT1) and the extension twin $\{ 10\bar{1}2\} \langle \bar{1}011\rangle $ (ET1) are observed, the former being more prominent. The fraction of ET1 increases slightly with deformation. It is interesting to note that the def2 sample has a lower fraction of CT1 compared to the def1 sample. Misorientation corresponding to ET2 are also observed, however, in small fraction and is displaced from its ideal position [16–18] towards lower misorientation values. The fraction corresponding to misorientation between 2°–5° increases drastically with deformation.

Fig. 3

Grain size distribution plot of shock loaded cp-Ti samples. (online color)

A small region of the def2 sample is examined in greater detail to get a better understanding of the underlying phenomena. The IPF map and the KAM map of the selected region with grain boundary superimposed are shown in Fig. 4(a) and (b) respectively. In all the maps, the high angle random grain boundary (HARB) is represented by black line, low angle grain boundary by orange line, CT1 by red line, ET1 by blue line and ET2 by grey line. The KAM is low and uniform within a grain other than in the regions close to the grain boundaries. Complete twins, broken twins, double twinned regions, and impinging twins are observed in the figure. Twins in general are continuous along the length giving it slender shape. By broken twin we mean twins which are discontinuous and have through width gaps along its length. The CT1 are the most abundant twins present and are complete/continuous. The ET1 are observed as a double twin, usually inside the primary CT1 as indicated by upper arrows (Fig. 4(a)). The grain boundaries surrounding broken twins are HARB. However, segments of these twins have ET2 grain boundary segment. The broken twin segments having ET2 grain boundary segments are also indicated by arrow (lower side). Also, the strain (from KAM map) is high along the boundary indicating heavy dislocation pile up. This suggests that perhaps these were initially ET2 twins whose boundary character has changed. This demands an in-depth investigation. To study the orientation relationship between the parent and twin grains, and to get a better understanding of microstructural evolution, an exploded view of selective grain-twin pairs are shown for clarity (Fig. 5(a)–(e)). Parent grain (P) and observed individual twins (T1-T6) are labelled for identification. Formation of ET1 double twin (T4) inside the primary CT1 twin (T3) is observed (Fig. 5(d)). The double twin (T4) formation has resulted in the change in boundary of original CT1 twin to misorientation angle (∼47°) (P-T4) close to CT2, however, with significant deviation from the ideal relationship (57°). The primary CT1 twin (T3) intersected and penetrated primary twin ET2 (T1) (Fig. 5(c)). The boundary of ET2 (G1 and G2) show similar character on both sides of the intersected region and does not show any influence due to the intersecting grain in the vicinity. ET1 twin (T5) is also observed at the end of ET2 (T1) (Fig. 5(e)). It is not clear how and why ET1 has formed at the end of ET2.

Fig. 4

(a) IPF map and (b) KAM map of selected area of shock loaded Ti def2 sample. The color-coded IPF triangle, the grain boundary type, and the KAM scale bar are shown below the figure. (online color)

Fig. 5

Exploded view of a grain shown in Fig. 4(a) showing various twins breakage, double twinning, and twin-twin interaction. Refer Fig. 4 for decoding boundary type information. (online color)

The primary twin ET2 is of special interest as it shows interesting features, i.e., gap in between twins or broken twin regions. Plenty of such regions are displayed in Fig. 5(a). A finite shear is observed wherever the twins are broken resulting in a macroscopic shear ‘s’ along twin T6 from its tip to toe (M-N). This can be said with affirmation as deformation twins are in general straight and lenticular in shape. The shear is evident and continuous along the length of the ET2 twin T6. However, that is not the case for twin T1. This could be due to the interaction of T1 with other twins such as the T3-T1 intersection. An expanded view of a region in and around the broken twin T1 (Fig. 5(b)) shows that double twin (T2) is present inside T1. The width of twin T1 is considerably small between the broken region and double twin when compared to the thickness of the rest of the twin. A cusp (A) is observed in twin T1 near the broken twin region (Fig. 5(b)), which indicates the initiation of twin breaking process.

Although plenty of well-known deformation twins have been identified in the microstructure by comparing them with the misorientation relationship of twin-parent grain pairs reported in literature (Table S2), it is of interest to study the deviation in misorientation relationship in the various identified twin boundaries. The misorientation relationship between various grains marked in Fig. 5 and covering all possible boundaries are tabulated in Table 2 (For full table with remarks see supplementary Table S3). Misorientation angle range is specified as the misorientation is not constant along the boundaries. The twin misorientations have a deviation from the ideal twin relationship, with some boundary having deviation towards lower misorientation angle and others towards higher angle. The misorientation axis is near the ideal twin misorientation relation. However, significant deviation from this could be observed for T5-T1 (double twin-primary twin) misorientation, where T5 has formed at the tail of T1 (ET2). Another interesting feature is that the misorientation angle for P-T1 is different along the two twin boundaries (G1 and G2).

Table 2 Misorientation relationship between various grains marked in Fig. 5 and their classification. Extension twin (TT) and contraction twin (CT).

Thus, multiple identified twin boundaries deviates from their ideal misorientation relation. The lattice misorientation development inside grain and across the boundary may shed some light on the cause of deviation. Hence, the point-to-origin (Fig. 6(a)) and point-to-point (Fig. 6(b)) misorientation line profiles are plotted for various places across twin ET2 (T1 and T5) as depicted in Fig. 5. Three sets of region were identified for probing, namely, twin region adjacent to the broken twin (1-1′, 3-3′, 5-5′ and 7-7′), away from the broken twin (4-4′ and 10-10′) and the broken twin (2-2′, 6-6′, 8-8′ and 9-9′). The point-to-origin misorientation line profile shows the buildup of lattice misorientation close to twin boundary (Fig. 6(a)). However, the buildup is skewed, i.e., more towards one side of twin boundary. This is also evident from the point-to-point misorientation line profile (Fig. 6(b)). The misorientation across the two P-T1 twin boundaries G1 and G2 (Table 2) shows that the misorientation is different at both ends, ranging along G1 from 30°–35° and along G2 from 23°–27°. In contrast, this is not the case for the misorientation profile across broken twin region, which first increases and then decreases. It is interesting to note that the lattice fluctuations are of higher amplitude in and around the broken twin region (Fig. 6(a) and (b)). It is interesting to note the misorientation gap (indicated in Fig. 6(b)) observed in the point-to-point misorientation line profile between the profile across twin (ET2) and that across the broken twin region, even though the two regions are adjacent to each other. There is a jump in the lattice misorientation above a critical value. It appears that this critical value lies between 7°–15°. Nevertheless, the exact value cannot be commented upon, as per the observations in the present investigation. Moreover, this is valid for lattice misorientation about $\langle \bar{1}010\rangle $ as observed, in the present case. It may apply for other misorientation axes also, however, it cannot be said with certainty.

Fig. 6

(a) Point-to-origin and (b) point-to-point misorientation line profile along various regions of ET2 twin as depicted by lines in Fig. 5. (online color)

3.3.2 Transmission electron microscopy studies

A finer level microstructural characterization was carried out using transmission electron microscopy (TEM) for the def2 sample. The montage of the bright field micrographs of the deformed sample is shown in Fig. 7. Regions of uniform dislocations are observed in the TEM micrographs as indicated by the circles in Fig. 7. Dislocation cells are not prevalent in this case. Regions consisting of broken twins are evident, as indicated by white arrows. It is noted that the contrast due to dislocations at the tip of broken twin is lesser, suggesting strain relaxation around the region. There is a heavy pile-up of dislocation at the twin boundary, as can be observed by thick black wall band at the boundary (indicated by black arrow). The thickness of this wall is 300–500 nm and is quite uniform along the boundary. For better clarity, individual TEM micrographs of various regions at higher magnifications are shown in Fig. 8. The region inside a twin is shown in Fig. 8(a) and (b). The twinned region contains dense dislocations and nanotwins (double twins). The region inside the parent grain (Fig. 8(c)) has relatively lesser dislocation density, but the dislocations are uniformly distributed. In Fig. 8(d), slip lines near the twin boundary and uniformly dislocated region can be seen in the parent matrix. This gives an impression of superimposed microstructure containing uniform dislocation and slip lines.

Fig. 7

Montage of TEM micrographs of shock loaded cp-Ti UDR def1 sample. The circled regions highlight regions with uniform and dense dislocation density. The white arrows point the twin break region, while the black arrow shows the thick dense twin walls.

Fig. 8

TEM micrographs of different regions in cp-Ti UDR def1 sample.

4. Discussion

Commercially pure titanium (cp-Ti) sheet was shock loaded to form hat shaped specimen in MST. The stress along the thickness (parallel to shock loading direction) is compressive. Thus, there is an in-plane flow of the material. Detailed microstructural investigations were carried out to examine the microstructural changes resulting from shock-induced deformation. Microstructures were examined at the mid-point deflection of the sample, as this represents the highest deformed region. The results obtained in the present investigation (reported in the previous section) are discussed in the following sub-section.

4.1 Texture evolution due to shock loading

Texture gives a macroscopic picture of the bulk crystallographic orientation changes in the material. The pole figures depict a change in texture on shock loading. The texture changes have taken place in such a manner that led to the weakening of initial split basal texture (Fig. 1). The poles have shifted abruptly resulting in a new texture component. Such abrupt change in texture is mainly attributed to twinning. The shift in poles by 60°–70° suggests that $\{ 11\bar{2}2\} \langle 11\bar{2}\bar{3}\rangle $ contraction twin (CT1) (misorientation 64.4° $\langle \bar{1}010\rangle $) is the dominant twinning system. This results in shifting of basal poles away from ND of the (0002) pole figure. The reorientation of grains by twinning takes place in such a manner that the newly twinned orientation acquire favorable slip system (higher Schmid factor). In cp-Ti, CRSS for prismatic and basal slip systems are in the same range [35], rather the CRSS for the prismatic slip is slightly lower than the basal slip [36]. Hence, the grain has a tendency to reorient for favourable slip following twinning with non-basal planes parallel to the sheet plane.

4.2 Microstructural evolution during shock loading

4.2.1 Overall evolution of substructure

Prior to discussion the key microstructural observations are summarized first. Grain fragmentation was observed in the sample primarily due to twinning in the material. Overall, there is a significant change in grain size and grain size distribution shifts towards lower grain size regime. There is an increase in the fraction of LAGB with a peak towards 2° as observed from the misorientation plots. It has been observed that the misorientation inside a grain remains uniform and is limited to 3°. This is a characteristic feature observed in shock deformed material [37]. The presence of small range lattice fluctuation and the continuous change of orientation within a grain [31, 37–39] is limited to 5°. Such homogeneous lattice fluctuations are due to the homogeneous nucleation of dislocations at the shock front [40] resulting in dislocation forest left behind in the material. Twins, particularly nanotwins, can also be generated due to shock passage in material in similar manner. In cp-Ti, both $\{ 11\bar{2}2\} $ contraction twin (CT1) and $\{ 10\bar{1}2\} $ extension twin (ET1) are observed, with CT1 being prominent. Moreover, in cp-Ti, double twinning and twin-twin impingement (interaction) were observed. The $\{ 11\bar{2}1\} $ extension twins (ET2) have also formed, although in a smaller fraction. ET2 is reported to form during high strain rate and shock deformation, hence it is expected.

Let us first discuss the homogeneous dislocation forest observed in deformed cp-Ti. The microstructure of cp-Ti has regions of uniform distribution of dislocation segments as well as dislocations in entangled configuration. The presence of uniform distribution of dislocations is attributed to the shock-induced phenomenon, where a homogeneous forest of dislocations are left behind the shock front as shock wave passes through the material [40]. The dislocations are nucleated at the shock front in order to accommodate the strain between uncompressed and shock compressed crystalline region. In similar fashion, (nano) twin could be generated in region swept by shock front. In addition, features like twins with thick walls are observed (Fig. 7). The thick wall of twins are formed as a result of dislocations piled up at the twin boundary. These thick walls are similar in feature to walls of cell structure in material. However, the wall thickness is uniform along the twin boundary, which usually is not the case with general pile-up of dislocation which account for strain. It could be a special feature of shock passage coupled with macroscopic straining.

In cp-Ti, the uniform dislocations left behind the shock may recover after the passage of the shock wave. The recovery processes appear to be more prominent in the parent grain compared to regions inside the twin. As mentioned in the previous section, a uniform pile-up of dislocation is present along the twin boundary. However, such pile-ups were not observed along the high angle random grain boundaries (HARB). Twin boundaries are stable and have lower energy as compared to HARBs. It is likely that the dislocations generated due to shock passage get easily absorbed in HARBs and hence cease to exist. On the contrary, twin boundaries, due to its low energy, might not absorb shock nucleated dislocations so readily. Slip lines indicating planar slip were observed primarily inside the twinned region with a diffuse background (please refer to Fig. 8(a) and (b)). Such a complex microstructure, which appears to be a superimposition of various microstructural features, is expected to be a result of multiple phenomena occurring due to the passage of shock waves. Therefore, it can be concluded that the macroscopic deformation following shock passage has resulted in a complex microstructure which could result in due to the occurrence of various interdependent microscopic phenomenon, primarily triggered by shock waves.

4.2.2 Evolution of $\{ 11\bar{2}1\} $ extension twins

It is reported in literature that the propensity of $\{ 11\bar{2}1\} $ extension twin (ET2) formation increases on deformation at elevated temperature [22], on dynamic plastic deformation [21] and in ECAP due to high shear strain in each pass [23]. In the present case, ET2 have formed on shock assisted dynamic plastic deformation. It was observed in earlier simulations studies that ET2 twinned crystals do not satisfy the desired mirror symmetry [19] and the twin boundary departs from the twinning plane [20], which implies that ET2 formed under dynamic or high strain rate deformation are relatively high energy defects as compared to other twinning systems. The observations in the present study pertaining to broken ET2 twin and the CT1 (T3) twins penetrating into ET2 (T1) supports the aforementioned fact reflecting relatively unstable nature of ET2 twin as compared to other twinning systems.

Let us now discuss the plausible mechanism of twinning and detwinning/breaking of unstable ET2 twin. ET2 are reported to form via kinking mechanism due to progressive lattice rotation by accumulative slip (mostly single basal ⟨a⟩ slip) [21]. Similar kinking mechanism is observed as could be noticed in the misorientation line profiles along the length of the T1 (ET2) (Fig. 6) and its orientation relationship with parent grain (Table 2) having $\langle \bar{1}010\rangle $ misorientation axis and angle deviating from ideal value. ET2 usually have twin boundary consisting of boundaries with ideal misorientations in segments and connected with boundaries of other misorientations (Fig. 5), when they are formed as a result of kinking due to progressive lattice rotation [21]. This mechanism of ET2 formation is supported under high strain rate and mono-directional shock impact loading, where the excess energy during deformation can result in energetically less favorable twin boundary state [21].

With regard to kinks, there exists a strong relation between kinking, bending and twinning [41–44], especially in HCP metals. Kinking occurs as a result of strain due to bending of the lattice [45]. Any “buckling instability” formed in the matrix due to various reasons which lead to bending of lattice can result in kink formation [46]. Following which the matrix can mechanically twin above a critical stress resulting in stress relief [41]. In the present study, the misorientation gap observed between the misorientation line profiles across ET2 twin (twinned region) (Fig. 6(a)) and across its broken part (detwinned region) (Fig. 6(b)) shows the presence of such instability. When the lattice misorientation reaches a critical value, instability sets in the matrix and the matrix twins. The critical value of point-to-point misorientation for instability should lie between the misorientation gap (7°–15°). This critical value for lattice instability could also be defined in terms of point-to-origin misorientation, which gives a cumulative misorientation of 13°. However, it is not clear at present whether it is the point-to-point misorientation or the point-to-origin misorientation which governs the criteria of instability in the matrix. When the misorientation crosses the critical value, the matrix twins abruptly. Atomic shuffling is the likely twinning mechanism for such a phenomenon. The fact that ET2 twin boundary rarely satisfies mirror symmetry [19] and departs from the twinning plane [20], which is attributed to shuffling as formation mechanism, strongly corroborates this mechanism. Most importantly, the initial stages of progressive lattice rotation involved are not associated with twinning dislocation [21].

A selected area around T1 twin (ET2) and the broken/locally detwinned region are shown in Fig. 9(a). The local lattice orientation and the trace of $\langle \bar{1}010\rangle $ is depicted across the twin and the detwinned region. The corresponding point-to-origin misorientation line profile across the two regions (1-1′ and 2-2′ marked in Fig. 5(b)) is shown separately in Fig. 9(b) for clarity. The misorientation axis $\langle \bar{1}010\rangle $ remains the same across both the regions and is highlighted with red line (Fig. 9(a)). The crystal rotation axis (misorientation axis) lies in the plane of kinking. This implies that the progressive lattice rotation manifests in the form of twist in the lattice. It is different from the mechanism of twin formation by bending and kinking, where the rotation axis is parallel to the plane of kink [45]. In the present case, the instability in the lattice is not associated with bending, but rather twist in the matrix. For this to happen, the character of dislocation resulting in lattice misorientation should be primarily of screw character. The process of lattice twist buildup in the material, with positive and negative lattice rotation, resulting in instability in the matrix (left) and the misorientation across the resulting twin (right) is shown schematically (Fig. 9(c)) summarizing the ET2 twin formation.

Fig. 9

(a) IPF map of a section of T1 twin with local crystal orientation and $\langle \bar{1}010\rangle $ trace along 1-1′ and 2-2′ (marked in Fig. 5(a)). Trace in red line is the twist (rotation) axis. (b) Point-to-origin misorientation along 1-1′ and 2-2′. (c) Schematic showing $\{ 11\bar{2}1\} $ twin (ET2) formation as a result of lattice twist. (online color)

4.2.3 Local detwinning of $\{ 11\bar{2}1\} $ twins

Let us address the aspects of ET2 detwinning. Parts of ET2 twin were broken or locally detwinned along the twin length resulting in through gaps, which indicates its unstable nature. The formation of such feature in ET2 can be understood from the transient non-monotonic deformation response of the blast loaded sheet. The plates subjected to blast/shock loading shows a different deformation response ranging from mid-point oscillations [47, 48] to counter-intuitive behavior (CIB) [49–52]. The counter-intuitive response is when the final deflection is contrary to the direction of impulsive loading. The deformation response of the material depends on the material parameter (including shape and thickness) and on various parameter associated with impulsive load [49]. CIB [50] and the final configuration of the plates [52] were found to depend on the timing and magnitude of the peak negative pressure relative to the dynamic response of the structure, and, the ratio between positive and negative impulses. Similarly, in the present study, it can be expected that during the impulsive blast loading, the material has experienced transient oscillatory behavior about the mid-point deflection before attaining the final deformed configuration. During the transient nature of deformation, ET2 ($\{ 11\bar{2}1\} $ extension twins) must have formed in the initial stage. However, on attaining final configuration, which is less than the initial transient mid-point deflection, the unstable ET2 have detwinning intermittently along its length under the local shear experienced inside parent grain in the final configuration. As the ET2 forms via progressive lattice rotation followed by kinking, on detwinning, the twins reverts back to the parent grain orientation. This is supported by the fact that dislocation-based kink bands (specifically incipient kink bands) are fully reversible in nature [46]. Additionally, the reversible nature of defects which are formed due to shock passage was experimentally reported by Bisht et al. [53] in cp-Ti. In the absence of any remnant macroscopic strain in the material, shock induced defect can revert back to parent (original) condition. This corroborates well with detwinning of ET2, an unstable twin, observed in the present study. The detwinning process, like the ET2 twinning process, is likely via atomic shuffling, a plausible mechanism also accounted for reverting defects in shock exposed material [53].

5. Conclusion

Commercially pure titanium was subjected to blast loading. Evolution of microstructure and crystallographic texture were investigated in the deformed samples by means of EBSD and TEM. The following conclusions can be drawn based on the analyses of microstructural features and microtexture formed in the material.

• (1)    Significant textural changes occur in the material subjected to shock loading. The evolution of texture is primarily attributed to the active deformation twinning systems, i.e., $\langle \bar{1}010\rangle $ 64.4° contraction twins (dominant) and $\langle 11\bar{2}0 \rangle $ 85° extension twins, which in-line with observations from other previous studies.
• (2)    There is an increase in the fraction of misorientation below 5° during deformation which implies an increase in strain and dislocation content in the material, as generally observed in a deformed material. However, a higher density of dislocations is observed in the materials which is homogeneously spread in the matrix. This is typical of a material exposed to shock wave. Moreover, the inside of the twinned region contains relatively higher density of dislocation as compared to the region in the parent grain.
• (3)    The evolution of observed complex microstructure is attributed to the passage of shock wave through the material followed by macroscopic straining of the sample.
• (4)    Unstable $\{ 11\bar{2}1\} $ extension twins were observed with strain relaxation near the region of twin breakage. In addition, a thick but uniform pile-up of dislocations of few 100 nm was observed along the twin boundary which was not observed along the high angle random grain boundaries (HARBs).
• (5)    $\{ 11\bar{2}1\} $ twins were observed to form via kinking mechanism due to progressive lattice rotation by accumulative slip. The twin forms once a critical value of misorientation is reached, above which lattice instability sets in and the lattice twins via atomic shuffling. The twinning act as strain relief mechanism.
• (6)    The progressive lattice rotation observed for ET2 formation is of twist character, unlike lattice bending observed earlier. The twist characteristic of lattice misorientation requires dislocations of screw character in dislocation accumulation region.
• (7)    The ET2 twins detwinning behavior with width-wise through gaps (broken) at places in its length. This displays a reversible nature of ET2. The detwinning observed in ET2 is accounted for by a series of phenomena. First factor is the deformation response of plates/disc subjected to shock/blast impulsive loading, where the specimen can undergo transient oscillatory behavior, i.e., results in mid-point oscillation and/or counter-intuitive behavior in material before attaining final deformed shape. Thus, some amount of strain reversal is anticipated in the material. Secondly, ET2 is reported to forms via kinking mechanism, and, such twins are reported to show reversible detwinning behavior. This is also in harmony with earlier reports of reversible nature of shock induced defects in cp-Ti [53].

Acknowledgments

Funding from the Department of Science and Technology (India) through grant DST/RC UK/14 AM/2012 for the project “Modeling of Advanced Materials for Simulation of Transformative Manufacturing Processes (MAST)” is gratefully acknowledged. Kumamoto University cooperated in the publication.

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