Low Cycle Fatigue Behavior of TC21 Titanium Alloy with Bi-Lamellar Basketweave Microstructure

: Low cycle fatigue (LCF) behaviors of TC21 alloy with a bi-lamellar basketweave microstructure were investigated in this paper. The strain fatigue tests were carried out at total strain amplitudes of 1.4% to 2.0%. The cyclic stress response showed the cyclic softening behavior. In addition, the shape of the hysteresis rings exhibited a non-Masing model behavior. The cyclic stress–strain as well as the strain-life equations were obtained. The fatigue life decreased signiﬁcantly with an increasing total strain from 1.4% to 2.0%. The cyclic softening behavior was interpreted by cyclic back stress and friction stress. Low cycle fatigue cracks were predominantly initiated on the surface of the samples. The relationship between the fatigue sub-critical crack and microstructure was also discussed. The cyclic deformation behavior and crack initiation mechanism were revealed on the basis of the deformation microstructure under different strain amplitudes.


Introduction
Titanium alloys are generally used in landing gear and other key load-bearing components in aircrafts [1,2]. As critical load-bearing components, titanium alloy components usually suffer a high cyclic loading during service, which may result in a low cycle fatigue (LCF) fracture. Thus, LCF behavior and properties are essential for the safety and reliability of titanium alloy components.
The microstructure of titanium alloys significantly influences the LCF behavior and properties [3][4][5][6][7][8]. Lei [9] investigated the LCF properties of TA15 titanium alloy with a tri-modal microstructure, Widmanstatten microstructure and bimodal microstructure, and found that the fatigue properties of the tri-modal microstructure were higher than that of the Widmanstatten microstructure and were equivalent to that of the bimodal microstructures. The fatigue crack propagation was more tortuous and had a higher fatigue crack propagation resistance than that of bimodal microstructures. Xu [10] suggested that titanium alloys with lamellar and bimodal microstructures had a different LCF behavior due to their response to the cyclic strain. As for titanium alloys with a tri-modal [11] and bimodal [12,13] microstructure, LCF cracks were initiated from the coarsened slip band in the soft α p phase. However, the shear deformation and spheroidization of β lamellar contributed to the LCF crack initiation for titanium alloys with a Widmanstatten microstructure [14]. Furthermore, the dislocation evolution and the deformation twins were considered as important factors for the cyclic softening of titanium alloys with a lamellar microstructure [15,16].
TC21 titanium alloy was used in aircraft key load-bearing components owing to its high strength and damage tolerance. TC21 titanium alloy was manufactured by a quasi-β forging process to obtain the basketweave microstructure [1]. The LCF behavior of TC21 titanium alloy has attracted much attention. Du [17] reported that the residual compressive stress of both surface shot peening and high velocity oxygen fuel (HVOF) improved the LCF properties of TC21 alloy. Yu [18] found that TC21 alloy with a bimodal microstructure illustrated the characteristic of cyclic softening. The research of Tan [19] suggested that the low cycle fatigue property of a bimodal structure was higher than that of a lamellar structure, and that the low cycle cracks initiated from the slip band in the αp phase for a bimodal microstructure and the α/β phase interface for a lamellar microstructure. However, few investigations on cyclic deformation and fatigue crack nucleation have been reported for titanium alloys with a basketweave microstructure. The LCF behavior of TC21 alloy with a basketweave microstructure is discussed in this paper. Cyclic deformation and the crack initiation mechanism are further investigated to support the application of titanium alloy components.

Materials
The nominal composition of TC21 titanium alloy used in this study is: Ti-6Al-2Zr-2Sn-2Mo-2Nb-1.5Cr (wt%). TC21 alloy was manufactured by a quasi-β forging process [1], and the alloy was heat-treated as follows: 900 • C/2 h + 600 • C/4 h. A lamellar α (α L ) and β transformed matrix (β) microstructure are observed (Figure 1a), and the mean width of α L is 3.4 µm. Furthermore, the fine lamellar α phase, which is also called secondary α s phase, is detected in the β phase with a mean width of 500 nm (Figure 1b). The samples exhibit a high tensile strength of up to 1070 MPa and a high yield ratio ( Figure 2). Crystals 2022, 12, x FOR PEER REVIEW 2 of 11 TC21 titanium alloy was used in aircraft key load-bearing components owing to its high strength and damage tolerance. TC21 titanium alloy was manufactured by a quasi-β forging process to obtain the basketweave microstructure [1]. The LCF behavior of TC21 titanium alloy has attracted much attention. Du [17] reported that the residual compressive stress of both surface shot peening and high velocity oxygen fuel (HVOF) improved the LCF properties of TC21 alloy. Yu [18] found that TC21 alloy with a bimodal microstructure illustrated the characteristic of cyclic softening. The research of Tan [19] suggested that the low cycle fatigue property of a bimodal structure was higher than that of a lamellar structure, and that the low cycle cracks initiated from the slip band in the αp phase for a bimodal microstructure and the α/β phase interface for a lamellar microstructure. However, few investigations on cyclic deformation and fatigue crack nucleation have been reported for titanium alloys with a basketweave microstructure. The LCF behavior of TC21 alloy with a basketweave microstructure is discussed in this paper. Cyclic deformation and the crack initiation mechanism are further investigated to support the application of titanium alloy components.

Materials
The nominal composition of TC21 titanium alloy used in this study is: Ti-6Al-2Zr-2Sn-2Mo-2Nb-1.5Cr (wt%). TC21 alloy was manufactured by a quasi-β forging process [1], and the alloy was heat-treated as follows: 900 °C/2 h + 600 °C/4 h. A lamellar α (αL) and β transformed matrix (β) microstructure are observed (Figure 1a), and the mean width of αL is 3.4 μm. Furthermore, the fine lamellar α phase, which is also called secondary αs phase, is detected in the β phase with a mean width of 500 nm (Figure 1b). The samples exhibit a high tensile strength of up to 1070 MPa and a high yield ratio ( Figure 2).

Low Cycle Fatigue
LCF tests were carried out using a servo-hydraulic testing machine (Instron 8801, Norwood, MA, USA) under the condition of strain-controlled conditions (R ε = −1), sinusoidal waveforms, and a constant strain rate (dε/dt) of 4 × 10 −3 s −1 . A round bar specimen was used for the low cycle fatigue test, as shown in Figure 3. The total strains were loaded at 1.4%, 1.6%, 1.8% and 2.0%. Each fatigue test was carried out until the cyclic stress decreased to 90% of the fatigue stable stress, which was considered as the LCF life.

Low Cycle Fatigue
LCF tests were carried out using a servo-hydraulic testing machine (Instron 8801, Norwood, MA, USA) under the condition of strain-controlled conditions (Rε = −1), sinusoidal waveforms, and a constant strain rate (dε/dt) of 4 × 10 −3 s −1 . A round bar specimen was used for the low cycle fatigue test, as shown in Figure 3. The total strains were loaded at 1.4%, 1.6%, 1.8% and 2.0%. Each fatigue test was carried out until the cyclic stress decreased to 90% of the fatigue stable stress, which was considered as the LCF life. The fracture surfaces and side crack morphology were observed by scanning electron microscopy (Ultim ® Max 65, Oxford, UK). A thin sample was cut close to the fatigue fracture and ground into 50-70 μm, then stamped into a small round sheet with a diameter of 3 mm. Double jet electrolytic thinning was adopted in the electrolyte of 59 pct methanol, 35 pct n-butanol, 6 pct perchloric acid at a voltage of 15 V and a current of 15 mA. The fatigue dislocation structure was observed by Transmission electron microscope (TEM) (JEM-2100, Tokyo, Japan).

Cyclic Stress-Strain Behavior
The cyclic stress curves with respect to different total strain of TC21 titanium alloy are shown in Figure 4. In the range of the total strain from 1.4% to 2%, the cyclic stress decreased rapidly at the initial stage of fatigue, illustrating the typical characteristic of cyclic softening. It is observed that the cyclic stress decreased faster and that the cyclic softening behavior of TC21 titanium alloy was more obvious with the increasing of the total strain from 1.4% to 2%. Similar results have been reported by Xu [15] and Sen [16], The fracture surfaces and side crack morphology were observed by scanning electron microscopy (Ultim ® Max 65, Oxford, UK). A thin sample was cut close to the fatigue fracture and ground into 50-70 µm, then stamped into a small round sheet with a diameter of 3 mm. Double jet electrolytic thinning was adopted in the electrolyte of 59 pct methanol, 35 pct n-butanol, 6 pct perchloric acid at a voltage of 15 V and a current of 15 mA. The fatigue dislocation structure was observed by Transmission electron microscope (TEM) (JEM-2100, Tokyo, Japan).

Cyclic Stress-Strain Behavior
The cyclic stress curves with respect to different total strain of TC21 titanium alloy are shown in Figure 4. In the range of the total strain from 1.4% to 2%, the cyclic stress decreased rapidly at the initial stage of fatigue, illustrating the typical characteristic of cyclic softening. It is observed that the cyclic stress decreased faster and that the cyclic softening behavior of TC21 titanium alloy was more obvious with the increasing of the total strain from 1.4% to 2%. Similar results have been reported by Xu [15] and Sen [16], for whom titanium alloys with both a bimodal microstructure and lamellar microstructure presented cyclic softening characteristic at a high strain amplitude due to the dislocation annihilation, twins in the α phase [15] and the spheroidization of β lamellar [14]. for whom titanium alloys with both a bimodal microstructure and lamellar microstructure presented cyclic softening characteristic at a high strain amplitude due to the dislocation annihilation, twins in the α phase [15] and the spheroidization of β lamellar [14]. The cyclic stress-strain relationship under LCF is usually described as [20]: The cyclic stress-strain relationship under LCF is usually described as [20]: where ∆ε p is the total plastic strain range, ∆σ is the total stress range, and K and n are the cyclic strength coefficient and cyclic strain hardening index, respectively. ∆ε p and ∆σ can be obtained based on the cyclic hysteresis loop for a half life. According to Equation (1), the data are linearly regressed using double logarithmic coordinates. The obtained K value is 1067.3 MPa and n value is 0.07326; then, we obtain the expression for the cycle stress-strain of TC21 titanium alloy. The fitted cyclic stress-strain curves were compared to the experimental results from uniaxial tension, as shown in Figure 5. It revealed that the cyclic stress was less than the unidirectional tensile stress under the same plastic strain. Thus, the cyclic softening characteristic of TC21 alloy is demonstrated. The cyclic stress-strain relationship under LCF is usually described as [20]: where Δεp is the total plastic strain range, Δσ is the total stress range, and K′ and n′ are the cyclic strength coefficient and cyclic strain hardening index, respectively.
Δεp and Δσ can be obtained based on the cyclic hysteresis loop for a half life. According to Equation (1), the data are linearly regressed using double logarithmic coordinates. The obtained K′ value is 1067.3 MPa and n′ value is 0.07326; then, we obtain the expression for the cycle stress-strain of TC21 titanium alloy. The fitted cyclic stress-strain curves were compared to the experimental results from uniaxial tension, as shown in Figure 5. It revealed that the cyclic stress was less than the unidirectional tensile stress under the same plastic strain. Thus, the cyclic softening characteristic of TC21 alloy is demonstrated.  Figure 6 displays the area of the hysteresis loop as well as the consumed energy increase with the increasing total strain. It can be inferred that the fatigue damage of plastic  Figure 6 displays the area of the hysteresis loop as well as the consumed energy increase with the increasing total strain. It can be inferred that the fatigue damage of plastic deformation increased with the total strain. It is obvious that the hysteresis loops with total strains of 1.4% and 1.6% are relatively small in comparison with those of 1.6% and 2.0%, suggesting that fatigue damage caused by plastic deformation is much less at total strains of 1.4% and 1.6%. deformation increased with the total strain. It is obvious that the hysteresis loops with total strains of 1.4% and 1.6% are relatively small in comparison with those of 1.6% and 2.0%, suggesting that fatigue damage caused by plastic deformation is much less at total strains of 1.4% and 1.6%. Figure 6. The superimposed hysteresis loops of the specimens at different strain levels for TC21 alloy.

Hystersis Loop Analysis
As for the half-life hysteresis loops for the different total strain, the bottoms of the hysteresis loops were moved to the same lowest points to analyze the Masing characteristics, which presented the same proportional limit. The J-integral can be used to deal with  As for the half-life hysteresis loops for the different total strain, the bottoms of the hysteresis loops were moved to the same lowest points to analyze the Masing characteristics, which presented the same proportional limit. The J-integral can be used to deal with the LCF behavior when metal displays Masing characteristics [21]. Figure 7 illustrates that the upper half of the hysteresis loops are non-overlapping under the different total strain; thus, the alloy exhibits a non-Masing behavior. Figure 6. The superimposed hysteresis loops of the specimens at different strain levels for TC21 alloy.
As for the half-life hysteresis loops for the different total strain, the bottoms of the hysteresis loops were moved to the same lowest points to analyze the Masing characteristics, which presented the same proportional limit. The J-integral can be used to deal with the LCF behavior when metal displays Masing characteristics [21]. Figure 7 illustrates that the upper half of the hysteresis loops are non-overlapping under the different total strain; thus, the alloy exhibits a non-Masing behavior.

Strain-Life Relationship
Based on Basquin and Coffin-Manson formulations, the relationship between fatigue and the total strain can be expressed as [22]: where σ f is the fatigue strength coefficient, b is the fatigue strength exponent, ε f is the fatigue ductility coefficient, and c is the fatigue ductility exponent. The strain fatigue parameters, evaluated by linear regression using the least square method, are listed in Table 1.  Figure 8 shows that the Coffin-Manson linear curves are well-fitted; however, Gao [11] reported that the LCF of titanium alloy illustrated a bilinear characteristic due to the different fatigue damages between plastic deformation and elatic deformation. It is indicated that the fatigue damage of TC21 alloy is mainly controlled by elastic strain. Figure 8 also reveals that the transition life from elastic deformation to plastic deformation is only 350 reversals, which is in agreement with that of Ti1023 titanium alloy with 140 cycles [23]. The low transition life can be attributed to the low elastic modulus and high yield ratio of titanium alloy. The fatigue life dominated by plastic deformation was only at 10 2 orders of magnitude; thus, it was inferred that LCF of TC21 alloy was actually controlled by an elastic deformation in a range over 10 3 cycles. cated that the fatigue damage of TC21 alloy is mainly controlled by elastic strain. Figure  8 also reveals that the transition life from elastic deformation to plastic deformation is only 350 reversals, which is in agreement with that of Ti1023 titanium alloy with 140 cycles [23]. The low transition life can be attributed to the low elastic modulus and high yield ratio of titanium alloy. The fatigue life dominated by plastic deformation was only at 10 2 orders of magnitude; thus, it was inferred that LCF of TC21 alloy was actually controlled by an elastic deformation in a range over 10 3 cycles.

TEM Observation of Fatigue Microstructure
As for TC21 titanium alloy with a bi-lamellar basketweave microstructure, the β phase containing the secondary αs phase obtained a high hardness, and the soft αL phase preferentially deformed in the fatigue process. Thus, the fatigue microstructure in the α phase was investigated. Figure 9 shows the deformation microstructure in the αL phase after low cycle fatigue. There are a few free dislocations at the initial state (Figure 9a). At a total strain of 1.4% and 1.6%, the fatigue dislocations in the αL phase exhibit a plane slip (Figure 9b,c) and pile-up at the αL/β interface (Figure 9d). The dislocation density in-

TEM Observation of Fatigue Microstructure
As for TC21 titanium alloy with a bi-lamellar basketweave microstructure, the β phase containing the secondary α s phase obtained a high hardness, and the soft α L phase preferentially deformed in the fatigue process. Thus, the fatigue microstructure in the α phase was investigated. Figure 9 shows the deformation microstructure in the α L phase after low cycle fatigue. There are a few free dislocations at the initial state (Figure 9a). At a total strain of 1.4% and 1.6%, the fatigue dislocations in the α L phase exhibit a plane slip (Figure 9b,c) and pile-up at the α L /β interface (Figure 9d). The dislocation density increases with the total strain (Figure 9e), but the alloy has a relatively low dislocation density in the α phase. It is worth noting that the β phase can be sheared at a high total strain (Figure 9f), and accordingly the alloy exhibited the cyclic softening characteristic. A similar result was also reported for Ti-6242S titanium alloy with a Widmanstatten microstructure [14].

Cyclic Back Stress-Friction Stress Analysis
The cyclic softening and non-Masing behavior can be interpreted by the evolution of back stress and friction stress, which can be calculated from each hysteresis loop according to the reference [11]. As shown in Figure 10a, back stress can be divided into two types for the different total strain. At a low total strain (ε t < 2.0%), the back stress increased slowly at a total strain of 1.8%, while the back stress increased rapidly at total strains of 1.4% and 1.6%. Furthermore, the increase of back stress in the total strain can be attributed to the increase in dislocation density. However, the back stress firstly decreased and then maintained a constant value at a total strain of 2.0%, which can be attributed to the shear of the β phase (Figure 9f).
Friction stress had a decreasing trend with the number of cycles for each total strain. Friction stress can also be divided into two types, as shown in Figure 10b. Friction stress decreased continuously at total strains of 1.8% and 2.0%, while friction stress decreased at two different rates under total strains of 1.4% and 1.6%. The decrease in friction was related to the deformation dislocation. Multiple slip systems of dislocations were activated at a high total strain and promoted the mobility of dislocations [11], which can reduce the frictional internal stress of dislocations.
Cyclic softening behavior can be explained with the evolution of back stress and friction stress. The cyclic softening for each strain amplitude (Figure 4) was attributed to the competition effects between the increase in back stress and the decrease in friction stress. As the decrease in friction stress was larger than the increase in back stress for total strains of 1.4%, 1.6% and 1.8%, respectively, the alloy displayed the cyclic softening characteristic. The cyclic softening at a total strain of 2.0% resulted from the superposition of the decreases in both the back stress and friction stress. The Masing behavior was the result of the cyclic deformation microstructure stability [21]. As for the total strains of 1.4% and 1.6%, a low density of dislocation was observed in the α L phase, while the β phase was sheared at a total strain of 2.0% (Figure 9f). The alloy exhibited a different deformation microstructure at a different total strain. Meanwhile, there was no direct relationship between the cyclic back stress, friction stress and cyclic strain (Figure 10), suggesting the instability of the fatigue microstructure under cyclic deformation. Therefore, TC21 titanium alloy with a basketweave microstructure displayed a non-Masing behavior. creases with the total strain (Figure 9e), but the alloy has a relatively low dislocation density in the α phase. It is worth noting that the β phase can be sheared at a high total strain (Figure 9f), and accordingly the alloy exhibited the cyclic softening characteristic. A similar result was also reported for Ti-6242S titanium alloy with a Widmanstatten microstructure [14].
(e) (f)  back stress and friction stress, which can be calculated from each hysteresis loop according to the reference [11]. As shown in Figure 10a, back stress can be divided into two types for the different total strain. At a low total strain (εt < 2.0%), the back stress increased slowly at a total strain of 1.8%, while the back stress increased rapidly at total strains of 1.4% and 1.6%. Furthermore, the increase of back stress in the total strain can be attributed to the increase in dislocation density. However, the back stress firstly decreased and then maintained a constant value at a total strain of 2.0%, which can be attributed to the shear of the β phase (Figure 9f).
(a) (b) Friction stress had a decreasing trend with the number of cycles for each total strain. Friction stress can also be divided into two types, as shown in Figure 10b. Friction stress decreased continuously at total strains of 1.8% and 2.0%, while friction stress decreased at two different rates under total strains of 1.4% and 1.6%. The decrease in friction was related to the deformation dislocation. Multiple slip systems of dislocations were activated at a high total strain and promoted the mobility of dislocations [11], which can reduce the frictional internal stress of dislocations.
Cyclic softening behavior can be explained with the evolution of back stress and friction stress. The cyclic softening for each strain amplitude (Figure 4) was attributed to the competition effects between the increase in back stress and the decrease in friction stress. As the decrease in friction stress was larger than the increase in back stress for total strains of 1.4%, 1.6% and 1.8%, respectively, the alloy displayed the cyclic softening characteristic. The cyclic softening at a total strain of 2.0% resulted from the superposition of the decreases in both the back stress and friction stress.
The Masing behavior was the result of the cyclic deformation microstructure stability [21]. As for the total strains of 1.4% and 1.6%, a low density of dislocation was observed in the αL phase, while the β phase was sheared at a total strain of 2.0% (Figure 9f). The alloy exhibited a different deformation microstructure at a different total strain. Meanwhile, there was no direct relationship between the cyclic back stress, friction stress and cyclic strain (Figure 10), suggesting the instability of the fatigue microstructure under cyclic deformation. Therefore, TC21 titanium alloy with a basketweave microstructure displayed a non-Masing behavior.

Fatigue Fracture and Crack Analysis
The typical fracture morphologies for TC21 titanium alloy are shown in Figure 11. In the strain range from 1.4% to 2.0%, the fatigue cracks originated from the sample surface.

Fatigue Fracture and Crack Analysis
The typical fracture morphologies for TC21 titanium alloy are shown in Figure 11. In the strain range from 1.4% to 2.0%, the fatigue cracks originated from the sample surface. The fatigue crack was initiated from the linear source on the sample surface at a high strain, where there were many edges with a large height difference (Figure 11a,b). It can be observed in Figure 11d that many radial edges presented on the fracture surface, which was the typical fatigue fracture morphology. Two similar fractures morphologies were observed in Figure 11c. Thus, the fatigue crack was initiated from a multi-point source on the specimen surface at a low strain, where the fatigue crack initiation was determined by micro-plastic damage under macroscopic elastic deformation. The fatigue crack was initiated from the linear source on the sample surface at a high strain, where there were many edges with a large height difference (Figure 11a,b). It can be observed in Figure 11d that many radial edges presented on the fracture surface, which was the typical fatigue fracture morphology. Two similar fractures morphologies were observed in Figure 11c. Thus, the fatigue crack was initiated from a multi-point source on the specimen surface at a low strain, where the fatigue crack initiation was determined by micro-plastic damage under macroscopic elastic deformation. The characteristics of a side crack were observed for LCF at a strain amplitude of 2.0%. Z-shaped steps were presented on the side of the fatigue crack source, and some Zshaped small cracks were also observed near the crack initiation site (Figure 12). The rela-  The characteristics of a side crack were observed for LCF at a strain amplitude of 2.0%. Z-shaped steps were presented on the side of the fatigue crack source, and some Z-shaped small cracks were also observed near the crack initiation site (Figure 12). The relationship between the fatigue sub-crack and microstructure is shown in Figure 13. Slip bands at 45 • to the load direction can be observed on the α L phase and promoted the initiation of fatigue sub-cracks. However, the α L /β interface cannot prevent the β phase from being shear at the total strain of 2.0% (Figure 9f). The connection of these sub-cracks led to the characteristics of Z-shaped steps. Actually, the propagation of sub-cracks was controlled by mechanics rather than the microstructure, and cracks can pass through the three sequential α L phases as a straight line. At a low total strain, slip bands were not obviously observed on the α L phase, and the dislocations were piled up at the α L /β interface (Figure 9d), resulting in the initiation of a crack at the α L /β interface.

Conclusions
1. TC21 titanium alloy displayed cyclic softening and non-Masing behavior that were interpreted on the basis of the cyclic back stress, friction stress and fatigue deformation microstructure. 2. Low cycle fatigue cracks were predominantly initiated from the slip bands on the surface of the samples at a high total strain, and the crack initiation occurred at the αL/β interface at a relatively low total strain.

Conclusions
1. TC21 titanium alloy displayed cyclic softening and non-Masing behavior that were interpreted on the basis of the cyclic back stress, friction stress and fatigue deformation microstructure. 2. Low cycle fatigue cracks were predominantly initiated from the slip bands on the surface of the samples at a high total strain, and the crack initiation occurred at the αL/β interface at a relatively low total strain.

1.
TC21 titanium alloy displayed cyclic softening and non-Masing behavior that were interpreted on the basis of the cyclic back stress, friction stress and fatigue deformation microstructure.

2.
Low cycle fatigue cracks were predominantly initiated from the slip bands on the surface of the samples at a high total strain, and the crack initiation occurred at the α L /β interface at a relatively low total strain. Data Availability Statement: Not applicable.

Conflicts of Interest:
The authors declare no conflict of interest.