Stress-Induced α″ Martensitic Transformation Mechanism in Deformation Twinning of Metastable β-Type Ti-27Nb-0.5Ge Alloy under Tension

Abstract

In this study, the formation mechanism of the stress-induced α″ martensitic phase in the deformation twinning (DT) band of metastable β-type Ti-27Nb-0.5Ge (at.%) alloy under tension was investigated. A preferential nucleation site for the stress-induced α″ martensitic transformation is inside a DT band with high dislocation density. The α″ martensitic phase developed in the DT band with increasing applied plastic strain. The α″ martensitic phase subsequently grew to intersect other DT bands, forming secondary DT bands themselves in the parent β grains.

1. Introduction

β-Type Ti alloys^1–10) have been widely used as implant biomaterials for artificial hip and knee prostheses because of their excellent biocompatibility, good corrosion resistance, high specific strength, and low elastic modulus. The superior performance of β-type Ti alloys is closely related to deformation twinning (DT)^1–6) or stress-induced martensitic transformation (SIMT)^7–11), where the β (body-centered cubic, BCC) phase transforms to the α″ (orthorhombic) phase during plastic deformation. These deformation modes are efficient in enhancing ductility via twinning-induced plasticity (TWIP)^1–6) or transformation-induced plasticity (TRIP)^7–11), respectively. DT and SIMT in metastable β-type Ti alloys are manifested as double yielding or a strain plateau in the stress-strain curves. The deformation behaviors of alloys are closely related to their phase stability^{2–6,9–11)}. With increasing β-phase stability, deformation of the alloy occurs predominantly by dislocation slip^12,13). On the other hand, deformation behavior of an alloy with low β phase stability leads to dislocation slip accompanied by DT or SIMT. In metastable alloys, either DT or SIMT can occur because the stress associated with dislocation slip increases with decreasing phase stability; thus, both DT and SIMT become favorable deformation modes^{2–6,9–11)}. Recent investigations of metastable β-type Ti alloys¹⁴⁾ showed that TRIP and TWIP offer a unique combination of high strength and high ductility. Such a complex combination of DT and SIMT behaviors has been reported in literature, even though both DT and SIMT play a major role in strain-hardening. Moreover, the mechanism of the unique deformation mode including the behaviors of both DT and SIMT is unclear. In the present study, we focused on the deformation mode of both DT and SIMT in the metastable β-type Ti-Nb-Ge alloys under tension. We also calculated the density of geometrically necessary dislocations (GNDs) based on the Kernel average misorientation (KAM) angle¹⁵⁾.

2. Materials and Methods

Ternary Ti-Nb-Ge alloys with a chemical composition of 27.1 at% Nb, 0.53 at% Ge, and less than 0.01 at% N and O, which exhibit DT behavior during plastic deformation, were chosen for this study. The alloys were prepared using the argon arc-melting method. In the melting process, the alloy buttons were melted eight times for 4 min, and were turned over each time before melting. In order to minimize segregation, all the button-shaped alloys were homogenized at 1273 K for 3.6 ks and then, quenched in ice water to obtain a single β-phase structure. Uniaxial tensile tests were performed using a Shimadzu mechanical tester (AGS-X, Japan) at room temperature with a strain rate of 1.5 × 10⁻³ s⁻¹ using samples with a gauge size of approximately 2 × 2 × 12 mm³. The deformed samples were first polished with 1 μm sized alumina powder, and then polished with colloidal silica. The deformed microstructures were observed using the electron backscatter diffraction (EBSD) method in a scanning electron microscope (SEM, Quanta^TM 250-FEI) operated at 20 kV. The experimental lattice parameters for EBSD measurement are as follows: a = 3.01 Å, b = 4.98 Å, c = 4.65 Å for α″ (orthorhombic) phase¹⁶⁾, a = 3.31 Å for β phase¹⁷⁾, and a = 4.62 Å, c = 2.81 Å for ω phase¹⁸⁾. The EBSD-based crystal orientation map data was analyzed using Orientation-Imaging Microscopy (OIM^TM) equipped with an EBSD measurement system (TexSEM Laboratories Inc., TSL). The normalized vector product of the unit vectors in the measured directions represents the normal of the habit plane expressed in a macroscopic co-ordinate system. The normal of the habit plane was calculated in the co-ordinate system of each grain considered by determining the grain orientation via EBSD. In addition, the GND density was calculated from the EBSD data following the procedure reported by Calcagnotto et al.¹⁵⁾ Transmission electron microscopy (TEM, JEOL-2100F) was performed to characterize the phase of the deformed region.

3. Results and Discussion

Figure 1 presents the tensile properties and the microstructural morphologies before and after 5% tensile strain of the metastable β-type Ti-27Nb-0.5Ge alloy. The yield strength and tensile strength of the alloy are 110 MPa and 470 MPa, respectively. The nominal stress increases remarkably after the yield point, as indicated by the black arrow in Fig. 1(a), and then, fluctuated with increasing nominal strain. The initial microstructure of the Ti-Nb-Ge alloy consisted of equiaxed polygonal β grains with an average grain size of approximately 300 μm, as shown in Fig. 1(b). After 5% tensile strain, DTs were entirely formed on the β grains, as exhibited in Fig. 1(c).

Fig. 1

(a) Tensile property and optical microscope images (b) before and (c) after 5% tensile strain of the metastable β-type Ti-27Nb-0.5Ge alloy.

Figure 2 shows the EBSD-based images of the Ti-Nb-Ge alloy after 5% plastic strain. The EBSD image quality (IQ) map (Fig. 2(a)) and inverse pole figure (IPF) map (Fig. 2(b)) shows that most of the parent β grains contain one or more lenticular DT bands, as denoted by marks 1, 2, and 3. Overall, in a β grain, one or two variants for the DT were observed to form and grow. However, in this study, the β grains have different variants with a wavy phase in the interior of the DT band, as indicated by the black arrow in the insets of Fig. 2. Their boundary lines can be classified in the IQ map, and their orientations coincide with the orientation of the matrix, as seen in Fig. 2(b). All the wavy phases are mainly formed in single DT bands, as denoted by marks 1 and 2 in Fig. 2, and at the intersections of the DT bands, as denoted by mark 3 in Fig. 2. However, information about this wavy phase has not yet been reported in stable or metastable β-type Ti alloys.

Fig. 2

(a) EBSD-based IQ image and (b) IPF image of deformation microstructure, including lenticular deformation twinning (DT) bands forming within the β grains of the Ti-Nb-Ge alloy at 5% plastic strain. Insets in (a) and (b) are enlarged images of the white square regions marked as 1. In addition, the α″ region on the DT band is indicated by a black arrow in each inset.

Region 3 in Fig. 2 for TEM analysis was prepared using a dual beam-focused ion beam (FIB) equipment with a standard in situ method, as shown in Fig. 3(a). Figure 3(c)–(g) shows that the phase of the wavy region was characterized as α″ martensite by TEM observation. Each selected area diffraction pattern (SADP) was classified as the β, α″, ω₁, or ω₂ phases having a combination given by the orientation relationships (0 0 1)_β//(1 0 0)_α″, (2 $\overline{2}$ 2)_β//(0 0 0 3)_ω1, ($\overline{2}$ 2 2)_β//(0 0 0 3)_ω2, and [1 1 0]_β//[0 0 1]_α″//[1 1 $\overline{2}$ 0]_ω1//[1 1 $\overline{2}$ 0]_ω2 (Fig. 3(g)). In fact, these orientation relationships in the β-Ti alloys have been well established, according to previous studies^11,20–22). Thus, the diffraction spots of the α″ phase such as {1 1 0}_α″, could be interpreted as indicating the presence of α″ martensite, as shown in Fig. 3(d) and (f). In contrast, since the diffraction spots of the α″ phase were too weak in the DT region, as shown in Fig. 3(e), it was considered that the SIMT marginally affected. The ω phase was also observed over the entire β matrix.

Fig. 3

SEM images of (a) region 3 in Fig. 2 and (b) TEM sample via FIB cutting. (b) The bright-field TEM image of the α″ martensite and DT formed on the β matrix. The SADPs of the (d) α″₁, (e) DT, and (f) α″₂ regions marked by the white circles in (c). (g) A schematic image representing the SADPs consisted of the β, α″, ω₁, and ω₂ phases having the specific orientation relationships.

Before tensile deformation, the alloy was composed only of β grains with no α″ phase. Thus, the wavy α″ phase could be formed through SIMT under tensile deformation. The wavy α″ martensite nucleated at the interface between the lenticular DT band and the β matrix, and then, expanded to the opposite side of the DT band. Two types of wavy α″ martensite phases formed from both sides of the DT band, as indicated by mark 2 in Fig. 2. It is easy to observe the wavy α″ martensite within the lenticular DT band of the deformed Ti-Nb-Ge alloy. However, the mechanisms of their nucleation and growth are still unclear. The area fraction of the α″ martensite was found to be 0.024 and the thicknesses of the α″ martensite ranged from 2 to 20 μm depending on the plastic stress/strain. The thickness of the α″ martensite in the DT band increased with increasing plastic stress/strain. Furthermore, the α″ martensite phases intersected each other within the DT band, and then, a new DT band formed, as indicated by mark 3 in Fig. 2. Three positions on the microstructure of the plastic-strained Ti-Nb-Ge alloy show the formation of α″ martensite in the DT band. Figure 4 shows the highly-magnified EBSD-IQ maps of three regions, 1, 2, and 3, as indicated in Fig. 2, and the profiles of the misorientation angle and GND density of the blue line on each IQ map. In general, β-Ti alloys within a conventional stabilization factor K_β > 2.4 deform by slip and twinning over the {1 1 2}<1 1 1> system, however, the metastable β-type Ti alloys deform by twinning over the {3 3 2}<1 1 3> system, which is unusual for crystals with a BCC lattice structure^1–6). The Schmid factors of all the possible twin systems for the β matrix and DT bands in region 1 indicated in Fig. 2 are listed in Table 1. The calculation of the Schmid factor is based on the assumption that the habit plane is always {1 1 2}<1 1 1> or {3 3 2}<1 1 3> systems in the alloy. A Schmid factor of (3 3 2)[1 1 $\overline{3}$] (T₃) is the maximum value among all the possible twin systems for the habit plane in the DT band in region 1. In the deformed Ti-Nb-Ge alloy, the lenticular DT bands with habit planes of (3 3 2) or (3 3 $\overline{2}$) were developed preferentially, even though their Schmid factors were lower than those of the (1 1 2) or (1 1 $\overline{2}$) planes. Interestingly, within a lenticular DT band, the developed habit plane for α″ martensite did not remain with that of the metastable β-type Ti alloy. The {1 1 2} plane for α″ martensite in the lenticular DT bands formed, even though their Schmid factors were lower than those of the (3 3 2) or (3 3 $\overline{2}$) planes. The habit plane between the DT and α″ martensite was determined to be (1 1 $\overline{3}$) [1 1 1] (T₂) (Table 1). The misorientation angles of the two types of habit planes, i.e., {3 3 2}<1 1 3> and {1 1 2}<1 1 1>, are 50.5° and 58°, respectively¹⁹⁾. As the plastic strain increased, the area of α″ martensite in the lenticular DT band expanded to the opposite side of the DT band, as shown in Fig. 4(b). The GND density also increased with the expansion of α″ martensite. In addition, the misorientation angle on the interface between the β matrix and α″ martensite decreased significantly up to 10°, and their interface relationship decreased with increasing plastic strain. On the other hand, the {1 1 2} plane for α″ martensite in the lenticular DT band remained, even though the plastic strain increased. The GND density in α″ martensite also increased upon approaching DT band. Furthermore, it was difficult to observe the {3 3 2} plane, as indicated by the red dotted line in α″ martensite. The {1 1 2} plane for α″ martensite in the DT band, as indicated by the yellow dotted line, was observed clearly, as shown in Fig. 4(b). Zimmerman and Humbert⁷⁾ reported that the characteristics of the habit planes of α″ martensite, induced by stress within the β-type Ti alloys, are dispersed around the (3 1 2) plane. However, the formation of wavy α″ martensite in β-type Ti alloys has not yet been reported. Surprisingly, the (1 1 2) habit plane for wavy α″ martensite is formed in metastable β-type Ti-Nb-Ge alloys.

Fig. 4

Highly-magnified EBSD-IQ maps of regions (a) 1, (b) 2, and (c) 3 in Fig. 2, and (d, e, f) the misorientation angle and GND density corresponding to each blue line x–y on the IQ map.

Table 1 Schmid factors, m, of all the possible twin systems for the matrix and the twin in position on Fig. 2.

Position	Matrix/Twin	code	Twin system						m
			h	k	l	u	v	w
A	Matrix ($\overline{7}$  19 $\overline{2}$ )[$\overline{3}\ \overline{1}$   1]	T1	1	1	2	1	1	$\overline{1}$	0.214
		T2	1	1	$\overline{2}$	1	1	1	0.386
		T3	3	3	2	1	1	$\overline{3}$	0.410
		T4	3	3	$\overline{2}$	1	1	3	0.082
	Twin ($\overline{18}$  23 $\overline{33} $ )[19 12 $\overline{2}$ ]	T1	1	1	2	1	1	$\overline{1}$	0.413
		T2	1	1	$\overline{2}$	1	1	1	0.470
		T3	3	3	2	1	1	$\overline{3}$	0.416
		T4	3	3	$\overline{2}$	1	1	3	0.306
C	Matrix ($\overline{2}$  25 3)[$\overline{7}$  1 $\overline{13}$ ]	T1	1	1	2	1	1	$\overline{1}$	0.241
		T2	1	1	$\overline{2}$	1	1	1	0.409
		T3	3	3	2	1	1	$\overline{3}$	0.426
		T4	3	3	$\overline{2}$	1	1	3	0.106
	Twin 1 ($\overline{15}\ \overline{11}$   14) [3 1 4]	T1	1	1	2	1	1	$\overline{1}$	0
		T2	1	1	$\overline{2}$	1	1	1	0.290
		T3	3	3	2	1	1	$\overline{3}$	0.396
		T4	3	3	$\overline{2}$	1	1	3	0.158

Figure 4(c) shows the occurrence of a secondary DT band at the encounter point at which two α″ martensite regions in the DT band cross each other. The Schmid factors of all the possible twin systems for the matrix and primary DT band in position 3 indicated in Fig. 2 are listed in Table 1. The habit plane between the primary DT band and β matrix was determined to be (3 3 2)[1 1 $\overline{3}$] (T₃), which has a high Schmid factor. In addition, the secondary DT band occurs with a habit plane of (3 3 $\overline{2}$)[1 1 3] (T₄), even though the habit plane for the secondary DT band has a low Schmid factor²³⁾. Furthermore, the GND density in the secondary DT band decreased after the formation of the DT band. The GND density at the encounter point was the highest, and it decreased significantly within the secondary DT band. The decrease in the GND density after the formation of the secondary DT band is an indication that α″ martensite contributed to the formation of another DT band, because the GND density in α″ martensite was high and increased with increasing plastic strain before the formation of the secondary DT band.

4. Summary

Stress-induced α″ martensite, which developed in the lenticular DT bands of the β phase, transformed into a secondary DT band in a deformed Ti-Nb-Ge alloy with a metastable β phase. The habit planes for the lenticular DT band in the parent β grain were identified as the (3 3 2) plane, which is a typical habit plane for metastable β-type Ti alloys. However, the plane for α″ martensite in the lenticular DT band was determined to be (1 1 2), which is a typical habit plane for the stable β-type Ti alloys. A wavy α″ martensite in the lenticular DT bands formed at the interface between the lenticular DT band and β matrix, which expanded up to 20 μm with increasing plastic strain. The GND density, which is based on the EBSD-KAM misorientation angle, was reduced in the secondary DT band. Thus, wavy α″ martensite acts as a nucleation site for the secondary DT band in the metastable β-type Ti-Nb-Ge alloys.

Acknowledgements

The authors are grateful for financial support provided by the Korea Institute for Industrial Technology (KITECH) through the research and development grant for “Development of 3D printing process for hyper functional materials (EO160012)”.

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