Impact of hierarchical martensitic structure on deformation twinning in titanium alloys during additive manufacturing

INTRODUCTION

Unlike conventional manufacturing, which relies on subtractive processes (e.g., machining) or forming operations (e.g., casting and forging), additive manufacturing (AM) builds components layer by layer, offering distinct advantages such as high design flexibility, near-net or net-shape production, efficient material utilization, and substantial cost savings^[1,2]. However, AM of metals introduces complex thermal and stress gyrations not typically experienced in conventional metallurgical processes, which affect mechanical properties, fatigue life, and other critical properties^[1-7]. Rapid thermal loading induces thermal stresses that are relieved through plastic deformation, leading to deformed microstructures in as-fabricated components^[3,5].

The α + β type Ti-6Al-4V exhibits an excellent combination of high specific strength, corrosion resistance and thermal stability^[8,9]. Ti-6Al-4V is highly processable via AM methods, including laser powder-bed fusion (L-PBF)^[10-13], laser-directed energy-deposition (L-DED)^[14], electron beam-PBF^[15,16], and wire-arc AM^[17,18]. High cooling rates during L-PBF induce phase transformations from the liquid to the body-centered cubic β phase, then fully to the hexagonal close-packed (HCP) α' phase. Previous studies on L-PBF focused on solid-state phase transformation, revealing the intrinsic annealing effects during the AM process^[10,11,19]. A previous study reports that hierarchical martensite—characterized by its width, length, and aspect ratio—forms under varying peak temperatures and cooling rates during rapid thermal cycles^[20]. Similar hierarchical martensitic structures have also been observed in the top layer of L-PBF Ti alloys and in water-quenched Ti alloys, which do not undergo multiple thermal cycles^[21,22]. These observed hierarchical martensitic structures form as a result of martensite nucleating and growing within prior β grains, where multiple orientation variants and substructures emerge to accommodate transformation strain^[22,23]. Meanwhile, unlike other metals with a face-centered cubic structure, e.g., 316 L stainless steel^[3], pure copper^[24] and Cantor alloy^[25], whose defect structure and associated strengthening mechanisms are well studied, the effects of rapid thermal cycles on the defect structures of as-fabricated Ti parts remain unclear^[26-28]. This knowledge gap hinders further microstructural design in AM components.

Here, we used L-PBF Ti-6Al-4V to investigate defect structures within α' laths. We report that the endpoints of fine martensitic laths can grow within coarse martensitic laths, thereby triggering deformation twinning. The thickness of deformation twins is governed by the contact width of fine martensitic plates. The resulting heterogeneous twin structure impacts the global mechanical properties of the materials.

MATERIALS AND METHODS

RESULTS AND DISCUSSION

Figure 1A presents an EBSD inverse-pole figure (IPF) map of an as-fabricated specimen, presenting acicular α' martensitic phase. The average length and width of these platelets are 8.1 ± 2.0 µm and 0.9 ± 0.4 µm, respectively. The corresponding phase map, Figure 1B, confirms only the α' phase with no β phase detected. Figure 1C presents a grain boundary (GB) map, showing low-angle GBs (LAGBs) with misorientation angles of 2°-10°, high-angle GBs (HAGBs) with misorientation angles > 10°, and 57.42°/{10$$\overline{1}$$1}<1$$\overline{2}$$10> Σ13b boundaries^[29], marked by white, black, and red lines, respectively. The misorientation distribution in Figure 1D follows the Burgers orientation relationship^[30], resulting in five distinct inter-variant misorientations. Peaks at ~10°, ~60°, ~60.83°, ~64°, and ~90° correspond to type 6, type 2, type 3, type 4, and type 5 inter-variant boundaries, respectively^[31,32]. Due to the small 0.83° misorientation difference between type 2 and type 3, an inset IPF in Figure 1D highlights the angular range of 58 to 62. A much higher length fraction is observed for type 4 inter-variant boundaries at ~64°, which makes up 25%. An extra peak at ~57° (pointed by a black arrow) corresponds to {10$$\overline{1}$$1} <1$$\overline{2}$$10> Σ13b boundaries (~10% length fraction). However, thermal stress-induced deformation twins were excluded due to the relatively low spatial resolution of EBSD (~25 nm) and relatively thin thickness (~30 nm) of deformation twins.

Figure 1. Microstructure in the as-fabricated plan-view Ti-6Al-4V specimen. (A) EBSD IPF map and (B) EBSD phase map. (C) Corresponding GB map on top of the image quality map showing three GB types. (D) The corresponding misorientation profile generated from the EBSD data.

To further investigate the microstructure inside a single α' lath, TKD characterization was performed. Figure 2A presents a TKD IPF map of α' martensitic laths from a top layer. Lath A (yellow) measures 1.2 µm in width. Inside lath A, some parallel bent lines (lime green) are observed, matching the orientation of adjacent α' laths and identified as allotriomorphic α'. The average width of these bands is 98 ± 27 nm. This interconnected allotriomorphic α' likely forms via partial transformation back to β during the subsequent thermal cycles. The morphology of these bands differs from deformation twins with twin boundaries (TBs) presented as parallel straight lines, as seen in lath B in Figure 2B. {10$$\overline{1}$$1} contraction twins formed under the stress condition that favours contraction along the c-axis, which is frequently observed within α' martensitic laths in L-PBF Ti alloys^[33]. However, the boundaries between the fine lime green laths in lath A do not belong to any TBs. The corresponding IPF of these laths is given in Figure 2C. According to the rotation angle (~64°) and rotation axis (<$$\overline{10}$$ 5 5 3>), these GBs are type 4 boundaries. The observed phenomenon indicates that fine martensitic plates can form in a layer that experienced limited thermal cycles, and the endpoint can grow into coarse α' laths.

Figure 2. A typical microstructure in a top layer of the as-fabricated Ti-6Al-4V. (A) TKD IPF map showing a hierarchical martensitic structure. (B) GB map showing the distribution of GB types. The colour codes for marking different types of GBs are the same as in Figure 1C . (C) An IPF generated from the blue square region in (A), indicating the boundaries are type 4 inter-variant boundaries.

Figure 3A presents a typical TKD IPF map from a bottom layer (30 mm away from the top surface). The width of lath A is 860 nm. Inside lath A, two groups of bands are observed. One group is orange in colour, sharing the same orientation with the neighbouring coarse α' lath (top-right-hand side). The other group is of lime green colour, presenting a typical twin morphology. Figure 3B identifies the boundaries of orange and lime green bands are type 4 inter-variant boundaries and {10$$\overline{1}$$1} TBs, respectively. Figure 3C and D present the pole figures of <1$$\overline{2}$$10> directions and {10$$\overline{1}$$1} planes, respectively, obtained from the blue rectangle region in Figure 3A. The circled position shows that lime green and green laths share a common <1$$\overline{2}$$10> direction. The lower part of the {10$$\overline{1}$$1} pole figure indicates a group of data points that perfectly overlap and share one group of {10$$\overline{1}$$1} plane. The two pole figures clearly demonstrate that the lime green and green laths form a {10$$\overline{1}$$1} <1$$\overline{2}$$10> twin orientation relationship. Interestingly, all martensite endpoints are linked to a deformation twin. A white arrow points to a typical straight band that is parallel to the detected {10$$\overline{1}$$1} TBs. Due to the relatively thick (~50 nm) TKD specimen, fine features (< 30 nm) in lath A were undetectable. However, as wide parallel straight bands are detected as {10$$\overline{1}$$1} twins, the narrow parallel bands should also be {10$$\overline{1}$$1} TBs. Some of the lime green bands extend beyond lath A. According to the GB map, the straight bands correspond to contraction twins, while the bent bands represent fine martensitic plates, which coincidentally share the same orientation as the contraction twins in lath A.

Figure 3. TKD maps taken from a bottom layer. (A) TKD IPF map showing how hierarchical martensite structure impacts the thickness of deformation twins inside an α' lath. (B) The corresponding GB map on top of the image quality map. The colours used to mark different types of GBs are the same as in Figure 1. Black and white arrows point to linked and non-linked twins, respectively. (C) <1$$\overline{2}$$10> and (D) {10$$\overline{1}$$1} pole figures from the blue rectangle area in (A).

Twins that link to the endpoints of fine martensitic plates laths, i.e., linked twins, are thicker than non-linked twins. A black arrow in Figure 3B points to a linked twin with an average thickness of 73 ± 14 nm. Conversely, the average thickness of non-linked twins is 34 ± 11 nm, half of that of linked twins. The observed thick linked twins appear in the layers 5-30 mm below the top surface. The formation sequence of fine martensitic plates and linked twins is proposed based on the microstructural evolution. Fine martensitic plates can be observed in the top layers, as shown in Figure 2A. However, linked twins appear only in layers subjected to rapid cyclic thermal loadings, indicating that fine martensitic plates formed prior to linked twins.

To avoid underestimation of the density of deformation twins, a TEM-bright-field (BF) image in Figure 4A, taken close to a <1$$\overline{2}$$10>_α zone axis from the same region as shown in Figure 3, shows a high density of parallel lamellae within lath A, which are identified as deformation twins. The number and spatial distribution of these twins, including unindexed non-linked twins, correspond well to the dark-contrast regions in the image quality map in Figure 3B. In addition, several parallel lines with dark contrast are present in the matrix. Figure 4B presents an atomic-resolution STEM-HAADF image taken from the red-boxed region in Figure 4A. The TB is indicated by the black arrow. One of the dark contrast lines is pointed by the white arrow. Figure 4C shows an enlarged STEM-HAADF image taken from the blue-boxed region in Figure 4B. Two stacking sequences, ABAB and ACAC, coexist in this region, indicating the presence of a stacking fault (SF). The formation mechanism of intrinsic I1 SFs has been extensively investigated^[34]. This confirms that the dark-contrast lines are SFs rather than second-order deformation twins. No β phase is detected based on Energy-dispersive X-ray spectroscopy and selected area electron diffraction pattern analysis, indicating the presence of the α' phase only.

Figure 4. (A) A TEM-BF image taken from the same region as Figure 3. (B) A STEM-HAADF image taken from the red-boxed region in (A). The black arrow points to a TB, and the white arrow points to an SF. (C) An enlarged STEM-HAADF image taken from the blue-boxed region in (B).

Numerous studies have investigated factors contributing to twin thickness in polycrystalline metals^[35-39]. Typically, four factors contribute to the twin thickening: grain size, Schmid factor, applied stress, and boundary mobility^[38,39]. A stronger correlation between grain size and twin frequency has been reported compared to twin thickness^[35-37]. The Schmid factor is calculated based on the parent orientation relative to the applied load direction. A higher Schmid factor increases the applied shear stress within a grain, making it easier to exceed the critical resolved shear stress for twinning. In this study, linked and non-linked twins are activated within the same lath, indicating the same grain size and Schmid factor for {10$$\overline{1}$$1} twinning. Meanwhile, the observed linked and non-linked twins are both {10$$\overline{1}$$1} contraction twins formed within the same α lath, indicating an identical crystallographic TB character and, therefore, comparable intrinsic boundary mobility. The distinct morphology difference is thus attributed to the variations in the local applied stress and boundary interactions. A deformation twin represents localized shear within the grain, inducing back stress from the surrounding matrix^[35-37]. It is more likely that the back stress is overcome, leading to the formation of thicker twins when they nucleate at the endpoints of fine martensitic plates. These regions are stress-concentration points, which result in a higher applied stress and, consequently, thicker twins. Such twin linkage facilitates strain partitioning and redistribution among adjacent α laths, effectively reducing local strain concentration and enhancing local plasticity.

TKD Kernel Average Misorientation (KAM) maps are generated from the same areas shown in Figures 1 and 2. The overall KAM value is lower in the top layer [Figure 5A] than in the bottom layer [Figure 5B]. The bottom layer underwent more rapid cyclic thermal loadings, leading to significant thermal stress and, therefore, a higher local strain. Moreover, the KAM map indicates that the orientation gradient is not uniform within a martensitic lath in Figure 5B. Three white arrows point to the endpoints of fine martensitic plates. The KAM is higher in these contact regions than the matrix and α lath boundary, indicating a higher local stress state at the endpoint of fine martensitic plates.

Figure 5. TKD KAM maps showing the strain distribution in (A) a top layer and (B) a bottom layer of an as-fabricated Ti-6Al-4V. White arrows point to the endpoint of fine martensitic plates laths.

A statistical analysis examines how twin thickness varies with Schmid factors, shown in Figure 6A. The Schmid factor is calculated along the build direction, where the highest thermal gradient occurs. For non-linked twins, the thickness increases from 18 ± 4 nm at a Schmid factor of 0.08 to 34 ± 11 nm at a Schmid factor of 0.44. With the same Schmid factor, the α lath width plays a significant role in determining the twin thickness. As the α lath width varies from 460 nm to 1.15 µm, relatively high standard deviations are observed. To validate the statistical significance of this trend, p-value is calculated with a value of 0.0408. The value is below 0.05, which indicates the statistical significance of this increasing trend. The average thickness of linked twins also increases with increasing Schmid factors. Linked twins exhibit higher standard deviations within one single α' lath or different α' laths with the same crystal orientation. Notably, the TKD data indicate that the thickness of linked twins never exceeds the contact width at the endpoints of fine martensitic plates, suggesting the possibility that the stress field of fine martensitic plates is localized. Figure 6B plots the ratio of linked and non-linked twin thickness within one α' lath. It increases monotonically as the contact width of fine martensitic plates is increased, indicating the contact width is the dominant factor in twin thickening.

Figure 6. (A) Twin thickness distributions as a function of Schmid factor. (B) Thickness ratio between linked twins and non-linked twins as a function of the contact width of fine martensitic plates. (C-G) The formation sequence of hierarchical martensite and deformation twins. The color code is: coarse martensitic plates (green), fine martensitic plates (purple and yellow), non-linked twins (red), and linked twins (blue).

Figure 6C-G illustrate the microstructural evolution. During the martensitic phase transformation, fine martensitic plates exhibit a higher growth rate than their coarse counterparts due to reduced transformation strain and improved strain accommodation^[22]. Consequently, fine martensitic plates can form and grow into coarse martensitic plates during rapid cooling. After that, thermal stress induces local plastic deformation inside the martensite, triggering the nucleation and growth of both linked twins and non-linked twins.

To explore whether the observed linked twins are a universal feature in Ti alloys fabricated by additive manufacturing, a set of samples produced using L-DED was prepared. Figure 7A presents a typical TKD IPF map from a bottom layer. The average length and width of these platelets are 8.8 ± 3.1 µm and 1.4 ± 0.5 µm, respectively. A black arrow in Figure 7B points to a non-linked twin, while white arrows point to linked twins. Compared with the L-PBF sample shown in Figure 3, both the α' lath thickness and twin thickness are coarser in the L-DED sample. A reduced twin density is observed, which can be attributed to the lower laser energy density during the fabrication process, leading to a smaller thermal gradient and, consequently, lower thermal stress. Linked twins can be also observed in other additively manufactured α-type Ti alloys, which may have been overlooked in previous research^[40,41].

Figure 7. A typical microstructure in a bottom layer of the L-DED Ti-6Al-4V sample. (A) TKD IPF map showing a hierarchical martensitic structure. (B) GB map showing the distribution of GB types. The colour codes for marking different types of GBs are the same as in Figure 1. White and black arrows point to linked twins and non-linked twins, respectively.

Uniaxial tensile tests were performed on the bulk samples, as shown in Figure 8A. The L-PBF Ti-6Al-4V sample demonstrates a relatively higher yield strength of 1,140 ± 5 MPa, and an ultimate tensile strength of 1,220 ± 9 MPa compared with 1,084 ± 34 MPa and 1,161 ± 22 MPa, respectively, for the L-DED samples. Notably, the L-PBF sample also shows a greater tensile ductility and work hardening capacity [Figure 8B], with an elongation to fracture of approximately 10.2% ± 0.8%, compared with a ~7.4% ± 0.2% for the L-DED sample. Many factors contribute to the mechanical strength and ductility of Ti alloys, including α lath thickness, dislocation density, twin density, inter-variant boundary character, and the volume fraction of each phase. In the present study, both samples consist of a fully α′ microstructure with a comparable population of inter-variant boundaries. Coarsening of α′ laths is generally reported to promote tensile ductility by increasing the dislocation mean free path, enhancing strain accommodation capability, albeit at the expense of strength^[42]. However, in contrast to this general trend, the L-PBF sample, despite exhibiting a finer α′ lath thickness (0.9 ± 0.4 µm) than the L-DED sample (1.4 ± 0.5 µm), demonstrates a simultaneous improvement in tensile strength and ductility. The global mechanical properties of materials are strongly influenced by the presence and characteristics of twin structures. A significantly higher twin density can be observed in the L-PBF sample [Figure 3] compared with the L-DED sample [Figure 7]. Similar to conventional GBs, TBs act as effective barriers to dislocation motion, thereby strengthening the material^[43-45]. Additionally, unlike conventional GBs, coherent TBs can enhance dislocation storage capacity, which improves strain hardening and consequently increases ductility^[43]. In HCP materials, as most slip events occur on the basal plane, the formation of twins can effectively accommodate deformation along the direction perpendicular to the basal plane. The reorientation of the local crystal lattice induced by twinning facilitates dislocation motion within twin lamellae, thereby contributing to strain accommodation^[46]. Twin thickness is an important parameter in determining the extent to which TBs influence mechanical properties. A previous study reports an inverse Hall-Petch-type relationship when the twin thickness is refined below 15 nm in pure copper^[43,47]. In α-type Ti alloys, {10$$\overline{1}$$1} contraction twins block the motion of basal <a> and prismatic <a> dislocations, which are the easily activated slip systems. Meanwhile, thicker twins can provide pathways for dislocation glide, facilitate dislocation cross-slip, and promote dislocation-TB interactions^[47]. Although a previous simulation study indicates that TBs could act as potential sites for basal crack initiation due to local stress concentration^[34,48], other experimental studies demonstrate that deformation twinning facilitates dislocation motion in the α matrix with hard orientations, thereby improving impact toughness as well as crack propagation resistance^[49-51]. Post-heat treatment plays a critical role in relieving residual stress and/or promoting the transformation α' phase into the equilibrium α+β phases in AM Ti alloys^[52]. The {10$$\overline{1}$$1} contraction twins are thermally stable at intermediate temperatures below 550 °C, making the observed twins suitable candidates for enhancing the mechanical performance of AM Ti alloys^[53,54].

Figure 8. (A) Engineering tensile stress-strain curves of bulk samples fabricated by L-PBF and L-DED. (B) The corresponding work hardening rates.

CONCLUSIONS

The impact of hierarchical martensite formation on deformation twinning has been revealed in a fully martensitic Ti-6Al-4V fabricated by L-PBF. {10$$\overline{1}$$1} <1$$\overline{2}$$10> deformation twins can be categorized into two types: linked twins and non-linked twins. For non-linked twins, the Schmid factor of the α' laths upon thermal loading along the build direction is the dominant factor influencing their thickness. For linked twins, the contact width of the fine martensitic plates is the primary factor determining the thickness of {10$$\overline{1}$$1} contraction twins. These heterogeneous deformation twins improve the strength, tensile ductility and work-hardening rate of titanium alloys during global mechanical testing. Since hierarchical martensite is inherent to AM Ti alloys, the observed phenomenon is expected to occur in other α-type Ti alloys produced by AM.