metals Article
Effect of Basketweave Microstructure on Very High Cycle Fatigue Behavior of TC21 Titanium Alloy Baohua Nie 1 , Zihua Zhao 2, *, Dongchu Chen 1 , Shu Liu 1 , Minsha Lu 1 , Jianglong Zhang 2 and Fangming Liang 1 1
2
*
School of Materials Science and Energy Engineering, Foshan University, Foshan 528000, China;
[email protected] (B.N.);
[email protected] (D.C.);
[email protected] (S.L.);
[email protected] (M.L.);
[email protected] (F.L.) School of Materials Science and Engineering, Beihang University, Beijing 100191, China;
[email protected] Correspondence:
[email protected]; Tel.: +86-010-8231-3264
Received: 1 May 2018; Accepted: 29 May 2018; Published: 30 May 2018
Abstract: This paper discusses the effect of basketweave microstructure on the very high cycle fatigue behavior of TC21 titanium alloy. Ultrasonic fatigue tests at 20 kHz are done on a very high cycle fatigue (VHCF) property of the alloys with 60 µm and 40 µm basketweave size, respectively. Results show that the alloys illustrate step-wise S-N characteristics over the 105 –109 cycle regimes and that fatigue fracture in both of the alloys occur beyond the conventional fatigue limit of 107 cycles. Subsurface crack initiation occurs at low stress amplitude. A fine granular area (FGA) is observed along the α lamella at the subsurface crack initiation site. The mechanism for the subsurface crack initiation is revealed using layer-by-layer-polishing, due to the micro-voids that are introduced at the granular α phase. The colony of α lamella is due to the local stress concentrated between them under the cyclic load. The stress intensity factor range at the FGA front is regarded as the threshold value controlling the internal crack propagation. Furthermore, the effect of the baseketweave size on the very high cycle fatigue limits of the TC21 titanium alloy is evaluated based on the Murakami model, which is consistent with the experimental results. The fatigue life of TC21 titanium alloy is well predicted using the energy-based crack nucleation life model. Keywords: very high cycle fatigue; crack initiation; titanium alloy; basketweave microstructure
1. Introduction High strength titanium alloys are usually used in aeronautical force-bearing components as a result of their high specific strength and excellent corrosion properties [1]. Throughout their ultra-long time service, the components are subjected to cyclic load with high frequency and low amplitude, thus the very high cycle fatigue (VHCF) of titanium alloy has been drawing world wide attention [2,3]. Fatigue failure in high strength titanium alloys occurs beyond the conventional fatigue limit of 107 cycles, and the stress-number of cycles to failure (S-N) curves exhibit a step-wise shape [2] or a decreasing shape [4]. Another important characteristic of these titanium alloys is that the crack initiation site shifts from the surface-induced fracture at low cycle regimes to a subsurface-induced fracture at very high cycle regimes [5], which may be responsible for the variability of the fatigue properties and the step-wise shape of the S-N curve. Thus, it is hazardous to design aeronautical components based on conventional fatigue strength data. Obviously, the microstructure of the titanium alloys significantly affects the fatigue properties and the fatigue crack initiation mechanisms in a very high cycle regime. As for titanium alloys with a bimodal microstructure, α grain size [6–8], grain distribution [9], crystal orientation [10,11], and
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super grain (grain clusters with similar orientation) [12] are important factors of the fatigue crack initiation for titanium alloys. The mechanism of the fine granular area (FGA) was supposed to be the cleavage of primary α grains, followed by the growth and coalescence of the adjacent facets [5,13,14]. The probabilities of faceted crack initiation increase with the value of the stress ratio R (the ratio of the min stress to the max stress), and the rough area, other than the facets characteristics, were observed at the stress ratio of −1 [13]. The formation of a rough area at the ratio of −1 was explained based on the numerous cyclic pressing (NCP) model [14]. However, till now the fracture mechanism and fatigue properties in a very high cycle regime for the titanium alloys basketweave microstructure has not been very well understood. V. Crupi et al. [15] investigated the very high cycle fatigue behavior of Ti6Al4V alloy with both bimodal and lamellar microstructures. The alloy with lamellar microstructure had fatigue strength lower than that with bimodal microstructure, and the crack initiated from the surface without subsurface facets. The investigation by Zuo et al. [5] indicated a very high cycle fatigue crack initiated from α/β interfaces in Ti6Al4V with lamellar microstructure due to the dislocation arrays pile-up at α/β interfaces, where the crack initiation site displayed flat facet characteristics. It is noted that α/β lamellar played an important role in the very high cycle fatigue crack initiation, but the effect of granular α phase, which is a typical microstructure at the grain boundary, has been ignored. TC21 alloy is an α + β titanium alloy usually used in aeronautical force-bearing components due to its fatigue damage tolerance, excellent welding, and formation performance [1]. The VHCF behavior of TC21 titanium alloy with basketweave microstrucutrue was investigated in the present work. A fatigue crack initiation mechanism is revealed using the layer-by-layer-polishing approach to observe the microstructure as well as the defects underneath the crack initiation site. The effect of basketweave on fatigue strength and initiation life is quantitatively estimated based on the fatigue fracture theory. 2. Experimental Procedures 2.1. Materials The material used in this study was TC21 titanium alloy with a nominal chemical composition of Ti-6Al-2Sn-2Zr-3Mo-1Cr-2Nb. The alloy was forged at 940 ◦ C with deformation ratio up to 50%, 80%, air quenching, following as 900 ◦ C for 2 h + air quenching, and then 600 ◦ C for 4 h + air quenching. The thermo-mechanical treatment procedures had basketweave microstrucrture with the mean sizes of 60 and 40 µm, and the granular α phase was observed in both samples (Figure 1a,b). Furthermore, a double lamellar basketweave microstructure, where secondary α lamella was present in β lamella, can be observed in the alloys, as shown in Figure 1c. The alloys with the basekweave size of 60 and 40 µm obtained a high tensile strength of 1070 MPa, 1100 MPa, respectively.
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(b)
(a)
(c) Figure 1. Basketweave microstructures of TC21 titanium alloy: (a) basketweave size of 60 μm (OM); Figure 1. Basketweave microstructures of TC21 titanium alloy: (a) basketweave size of 60 µm (OM); (b) basketweave size of 40 μm (OM) and (c) a double lamellar basketweave microstructure (SEM). (b) basketweave size of 40 µm (OM) and (c) a double lamellar basketweave microstructure (SEM).
2.2. Surface Treatment 2.2. Surface Treatment The specimens underwent electro‐polishing (EP) to remove the machining layers to observe the The specimens underwent electro-polishing (EP) to remove the machining layers to observe the fatigue damage morphology and eliminate its influence on fatigue behavior. Electro‐polishing was fatigue damage morphology and eliminate its influence on fatigue behavior. Electro-polishing was carried out in 59% methanol, 35% n‐butanol, 6% perchloric acid under −20 °C, and 20–25 V voltage. carried out in 59% methanol, 35% n-butanol, 6% perchloric acid under −20 ◦ C, and 20–25 V voltage. 2.3. Ultrasonic Fatigue Test 2.3. Ultrasonic Fatigue Test Fatigue tests were carried out using an ultrasonic fatigue test machine (20 kHz, SHIMADZU, Fatigue tests were carried out using an ultrasonic fatigue test machine (20 kHz, SHIMADZU, Kyoto, Japan) at a constant stress ratio of −1. This method is an accelerated testing method with a Kyoto, Japan) at a constant stress ratio of −1. This method is an accelerated testing method with a frequency far beyond that of the conventional fatigue experiments. The frequency effect is small for frequency far beyond that of the conventional fatigue experiments. The frequency effect is small for ultrasonic fatigue tests under low displacement and small deformation [16]. Very high cycle fatigue ultrasonic fatigue tests under low displacement and small deformation [16]. Very high cycle fatigue behaviors of many metallic materials have been investigated using an ultrasonic fatigue test machine, behaviors of many metallic materials have been investigated using an ultrasonic fatigue test machine, which includes an ultrasonic generator, a piezoelectric converter, an ultrasonic horn, and a computer which includes an ultrasonic generator, a piezoelectric converter, an ultrasonic horn, and a computer control system [17]. An ultrasonic generator transforms 50 or 60 Hz voltage signals into sinusoidal control Ana ultrasonic generator transforms 50 or 60generator Hz voltage signals into sinusoidal signals system with 20 [17]. kHz; piezoelectric converter excited by the transforms the electrical signals with 20 kHz; a piezoelectric converter excited by the generator transforms the electrical signal into a longitudinal mechanical vibration with the same frequency; an ultrasonic signal horn into a longitudinal mechanical vibration with the same frequency; an ultrasonic horn amplifies the amplifies the vibration displacement in order to obtain the required strain amplitude in the middle vibration displacement in order to obtain the required strain amplitude in the middle section of the section of the specimen; a computer control system is necessary to control the load amplitude and specimen; computer control system displacement is necessary to control the load amplitude and acquire the acquire the a test data. The maximum amplitude measured by a dynamic sensor is test data. The maximum displacement amplitude measured by a dynamic sensor is obtained at the obtained at the end of the specimen while the strain excitation in the push‐pull cycles (load ratio R = −1) reaches the maximum in the middle section of the specimen, which produces the required high
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Metals 2018, 8, x FOR PEER REVIEW 4 of 11 end of the specimen while the strain excitation in the push-pull cycles (load ratio R = −1) reaches the maximum in the middle section of the specimen, which produces the required high frequency frequency fatigue stress. In addition, a air compressed cooling gun is necessary to prevent the fatigue stress. In addition, a compressed cooling gunair is necessary to prevent the temperature from temperature from increasing during the tests. increasing during the tests. Considering that that the the amplifier the specimen must atwork at resonance, the specimen Considering amplifier andand the specimen must work resonance, the specimen geometry geometry was designed using the elastic wave theory. Figure 2 shows the geometries of the fatigue was designed using the elastic wave theory. Figure 2 shows the geometries of the fatigue specimens specimens and its dimensions. and its dimensions.
Figure 2. Shape and dimensions of the test specimens (unit: mm). Figure 2. Shape and dimensions of the test specimens (unit: mm).
2.4. Observation of Microstructure at the Crack Initiation Site 2.4. Observation of Microstructure at the Crack Initiation Site In order order to to investigate investigate the the fatigue fatigue crack crack initiation initiation mechanism mechanism of TC21 titanium titanium alloy, alloy, the the In of the the TC21 microstructure characteristic at crack initiation site was observed. As for the surface crack initiation, the microstructure characteristic at crack initiation site was observed. As for the surface crack initiation, fracture surface was protected by the resin, then the side of the crack initiation site was etched. The resin the fracture surface was protected by the resin, then the side of the crack initiation site was etched. was resin removed by the acetone and the and microstructure characteristic of the of surface crack crack origin was The was removed by the acetone the microstructure characteristic the surface origin observed by the tilt function of the scanning electron microscope (Hitachi Limited, Tokyo, Japan) for was observed by the tilt function of the scanning electron microscope (Hitachi Limited, Tokyo, Japan) subsurface crack initiation specimens, the fatigue fracture was embedded with the resin, and the exact for subsurface crack initiation specimens, the fatigue fracture was embedded with the resin, and the location of the ofcrack initiation site was by the method. The The microstructure at the exact location the crack initiation site marked was marked by coordinate the coordinate method. microstructure at subsurface crack initiation site was observed using the layer‐by‐layer polishing method. the subsurface crack initiation site was observed using the layer-by-layer polishing method. 3. Results and Discussion 3. Results and Discussion 3.1. S-N Characteristics 3.1. S‐N Characteristics 9 Step-wise characteristics can be observed on the S-N curve over the wide range of the 1055–10 Step‐wise characteristics can be observed on the S‐N curve over the wide range of the 10 –109 cycle regimes for the TC21 titanium alloy with two sizes of basketweave (Figure 3). Fatigue fracture cycle regimes for the TC21 titanium alloy with two sizes of basketweave (Figure 3). Fatigue fracture in both alloys occurs beyond the conventional fatigue limit of 1077 cycles but present very high cycle cycles but present very high cycle in both alloys occurs beyond the conventional fatigue limit of 10 fatigue limits with 530 and 430 MPa, respectively. Step-wise characteristics can be also observed in the fatigue limits with 530 and 430 MPa, respectively. Step‐wise characteristics can be also observed in VHCF of the TC4 titanium alloy with bimodal microstructure [18], however, the research by Zuo [5] the VHCF of the TC4 titanium alloy with bimodal microstructure [18], however, the research by Zuo has shown that the the S-N curve of Ti6Al4V with basketweave decreased continuously and turns [5] has shown that the the S‐N curve of Ti6Al4V with basketweave decreased continuously and turns less sharply at about 5 × 1077 cycles, and there exists no horizontal asymptote and fatigue limit, which cycles, and there exists no horizontal asymptote and fatigue limit, which less sharply at about 5 × 10 could result from the different basketweave sizes. Figure 3 also shows fatigue properties of the alloy could result from the different basketweave sizes. Figure 3 also shows fatigue properties of the alloy with basketweave of 40 µm are higher than thatthat of 60of µm, these these two specimens have a similar with basketweave of 40 μm are higher than 60 although μm, although two specimens have a tensile strength. It is can be attributed to the shorter effective slip length for the specimens with fine similar tensile strength. It is can be attributed to the shorter effective slip length for the specimens basketweave [19]. with fine basketweave [19]. The step-wise characteristics can be the results of the shift of crack initiation mechanism. Based on The step‐wise characteristics can be the results of the shift of crack initiation mechanism. Based SEM observation of all fracture surfaces, for both kinds of alloys, the fatigue cracks initiate from the on SEM observation of all fracture surfaces, for both kinds of alloys, the fatigue cracks initiate from sample’s surface at relatively high stress amplitudes, whereas the crack initiation mode shifts to the the sample’s surface at relatively high stress amplitudes, whereas the crack initiation mode shifts to subsurface with a fine granular area (FGA) initiation model at approximately 600 and 540 MPa over the the subsurface with a fine granular area (FGA) initiation model at approximately 600 and 540 MPa 5 to 10 7 cycle regimes. The crack initiation mechanisms for the surface and wide range of 105 to 107 cycle regimes. The crack initiation mechanisms for the surface and subsurface over the wide range of 10 initiation models are discussed below. subsurface initiation models are discussed below.
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Figure 3. S‐N curve of TC21 titanium alloy with two sizes of basketweave. Figure 3. S‐N curve of TC21 titanium alloy with two sizes of basketweave. Figure 3. S-N curve of TC21 titanium alloy with two sizes of basketweave.
3.2. Fatigue Crack Initiation Analysis
3.2. Fatigue Crack Initiation Analysis The typical surfaces initiation of the TC21 titanium alloy with basketweave of 60 μm and 40 μm 3.2. Fatigue Crack Initiation Analysis are shown in Figure 4. Fatigue crack is initiated from the sample surface under high stress amplitude The typical surfaces initiation of the TC21 titanium alloy with basketweave of 60 μm and 40 μm The typical surfaces initiation of the TC21 titanium alloy with basketweave of 60 µm and and a radial ridge pattern parallel to the crack propagation direction is observed on the fracture are shown in Figure 4. Fatigue crack is initiated from the sample surface under high stress amplitude 40 µm are shown in Figure 4. Fatigue crack is initiated from the sample surface under high stress surface. However, under low stress amplitude direction initiates from the sample subsurface and a radial ridge fatigue pattern crack parallel to the crack propagation is observed on the fracture amplitude and a radial ridge pattern parallel to the crack propagation direction is observed on (Figures 5 and 6). α/β lamellar characteristics are present at the crack initiation site where the fine surface. However, fatigue crack under low stress amplitude initiates from the sample subsurface the fracture surface. However, fatigue crack under low stress amplitude initiates from the sample granular is distributed on α lamella and FGA has the same size as the colony of lamella (Figure 5). (Figures 5 and 6). α/β lamellar characteristics are present at the crack initiation site where the fine subsurface (Figures 5 and 6). α/β lamellar characteristics are present at the crack initiation site where The similar rough area characteristic at the crack initiation site is often observed in bidomal equiaxed granular is distributed on α lamella and FGA has the same size as the colony of lamella (Figure 5). the fine granular is distributed on α lamella and FGA has the same size as the colony of lamella microstructure at R = −1, which was explained based on the numerous cyclic pressing (NCP) model The similar rough area characteristic at the crack initiation site is often observed in bidomal equiaxed (Figure 5). The similar rough area characteristic at the crack initiation site is often observed in bidomal [14]. The probability of rough area at the crack initiation site is decreased with the increase of the microstructure at R = −1, which was explained based on the numerous cyclic pressing (NCP) model equiaxed microstructure at R = −1, which was explained based on the numerous cyclic pressing (NCP) stress ratio of −1 [13]. As for TC21 titanium alloy with basketweave of 40 μm, the fracture surfaces [14]. The probability of rough area at the crack initiation site is decreased with the increase of the model [14]. The probability of rough area at the crack initiation site is decreased with the increase of are similar to that of the alloy with basketweave of 60 μm. Fatigue crack initiates shifts from the stress ratio of −1 [13]. As for TC21 titanium alloy with basketweave of 40 μm, the fracture surfaces the stress ratio of −1 [13]. As for TC21 titanium alloy with basketweave of 40 µm, the fracture surfaces sample surface to the subsurface under a low stress amplitude (Figure 6), however, α/β lamella are similar to that of the alloy with basketweave of 60 μm. Fatigue crack initiates shifts from the are similar to that of the alloy with basketweave of 60 µm. Fatigue crack initiates shifts from the sample characteristics are insignificant at the crack initiation site probably because of the small size of the sample surface to the subsurface under a low stress amplitude (Figure 6), however, α/β lamella surface to the subsurface under a low stress amplitude (Figure 6), however, α/β lamella characteristics α/β lamella. characteristics are insignificant at the crack initiation site probably because of the small size of the are insignificant at the crack initiation site probably because of the small size of the α/β lamella. α/β lamella.
(a) (a)
(b) (b)
Figure 4. Fatigue fracture surface of TC21 titanium alloy: (a) basketweave of 60 μm at σ = 550 MPa, N Figure 4. Fatigue fracture surface of TC21 titanium alloy: (a) basketweave of 60 µm at σ = 550 MPa, Figure 4. Fatigue fracture surface of TC21 titanium alloy: (a) basketweave of 60 μm at σ = 550 MPa, N 6 cycles. = 2.37 × 105 cycles; (b) basketweave of 40 μm at σ = 610 MPa, N = 1.15 × 10 6 cycles. N = 2.37 ×5 cycles; (b) basketweave of 40 μm at σ = 610 MPa, N = 1.15 × 10 105 cycles; (b) basketweave of 40 µm at σ = 610 MPa, N = 1.15 × 106 cycles. = 2.37 × 10
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Figure 5. Fatigue fracture surface of TC21 titanium alloy with basketweave of 60 µm at σ = 500 MPa, Figure 5. Fatigue fracture surface of TC21 titanium alloy with basketweave of 60 μm at σ = 500 MPa, Figure 5. Fatigue fracture surface of TC21 titanium alloy with basketweave of 60 μm at σ = 500 MPa, 6 cycles: (a) fatigue crack initiation site; (b) high magnification morphology. N = 6.66 × 1066 cycles: (a) fatigue crack initiation site; (b) high magnification morphology. N = 6.66 × 10 cycles: (a) fatigue crack initiation site; (b) high magnification morphology. N = 6.66 × 10
(a) (a)
(b) (b)
Figure 6. Fatigue fracture surface of TC21 titanium alloy with basketweave of 40 μm at σ = 540 MPa, Figure 6. Fatigue fracture surface of TC21 titanium alloy with basketweave of 40 μm at σ = 540 MPa, Figure 6. Fatigue fracture surface of TC21 titanium alloy with basketweave of 40 µm at σ = 540 MPa, N = 8.51 × 1077cycles: (a) fatigue crack initiation site; (b) high magnification morphology. cycles: (a) fatigue crack initiation site; (b) high magnification morphology. N = 8.51 × 10 N = 8.51 × 107 cycles: (a) fatigue crack initiation site; (b) high magnification morphology.
The microstructure of the surface crack initiation site can be observed by SEM due to the surface The microstructure of the surface crack initiation site can be observed by SEM due to the surface The microstructure of the surface initiation site can be observed by SEM dueinitiates to the surface electro‐polishing treatment shown in crack Figure 7. It It is is obvious obvious that the surface surface crack at α/β α/β electro‐polishing treatment shown in Figure 7. that the crack initiates at electro-polishing treatment shown in Figure 7. It is obvious that the surface crack initiates at α/β interface at a high stress amplitude. The priority deformation of α phase occurs under cyclic load, interface at a high stress amplitude. The priority deformation of α phase occurs under cyclic load, interface at a high stress amplitude.at The deformation of α phase occurs load, and and the the dislocation dislocation concentrates the priority α/β interface interface producing severe local under stress cyclic concentration. and concentrates at the α/β producing severe local stress concentration. the dislocation concentrates at the α/β interface producing severe local stress concentration. Thus, Thus, α/β interface becomes preferential crack initiation sites in a high cycle regime, even in a very Thus, α/β interface becomes preferential crack initiation sites in a high cycle regime, even in a very α/β interface becomes preferential crack initiation sites in a high cycle regime, even in a very high high cycle regime [15]. high cycle regime [15]. cycleFGA is present at the subsurface initiation site for the TC21 alloy, which has no inclusions or regime [15]. FGA is present at the subsurface initiation site for the TC21 alloy, which has no inclusions or FGA is present at the subsurface initiation site for the TC21 alloy, which has no inclusions or porosities. The subsurface initiation of cracks is associated with the microstructural inhomogeneity. porosities. The subsurface initiation of cracks is associated with the microstructural inhomogeneity. porosities. The subsurface of cracks associated with the microstructural The microstructure microstructure at the the initiation subsurface crack isinitiation initiation site is observed observed using the the inhomogeneity. layer‐by‐layer The at subsurface crack site is using layer‐by‐layer The microstructure at the subsurface crack initiation site is observed using the layer-by-layer polishing polishing method. Observation of the subsurface microstructure shows that some micro‐voids are polishing method. Observation of the subsurface microstructure shows that some micro‐voids are method. Observation of the subsurface microstructure shows that some micro-voids are distributed in distributed in α lamella in the vicinity of the coarse granular α phase (Figure 7). It is speculated that distributed in α lamella in the vicinity of the coarse granular α phase (Figure 7). It is speculated that α lamella in the vicinity of the coarse granular α phase (Figure 7). It is speculated that nanocracks can nanocracks can propagate by linkage with the micro‐voids in front of the crack tip by cyclic loading nanocracks can propagate by linkage with the micro‐voids in front of the crack tip by cyclic loading propagate by linkage with the micro-voids in front of the crack tip by cyclic loading without much without much plasticity [20]. Taking Figure 6 as an example, the FGA radius is approximately 42 μm without much plasticity [20]. Taking Figure 6 as an example, the FGA radius is approximately 42 μm plasticity [20]. Taking Figure 6 as an example, the FGA radius is approximately 42 µm under 8.51 × 107 7 loading cycles. Considering that most of the fatigue life is spent in the FGA crack under 8.51 × 10 7 loading cycles. Considering that most of the fatigue life is spent in the FGA crack under 8.51 × 10 loading cycles. Considering that most of the fatigue life is spent in the FGA crack propagation [21,22], −13 m/cycle, which propagation [21,22], the average fatigue crack growth rate is approximately 4.9 × 10 −13 m/cycle, which propagation [21,22], the average fatigue crack growth rate is approximately 4.9 × 10
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the average fatigue crack growth rate is approximately 4.9 × 10−13 m/cycle, which is lower than the is lower than the lattice spacing and thereby indicates that the fatigue crack cannot propagate lattice spacing and thereby indicates that the fatigue crack cannot propagate cycle-by-cycle. cycle‐by‐cycle. Figure 7 suggests that the micro-plasticity damage occurs due to the local microstructural Figure 7 suggests that the micro‐plasticity damage occurs due to the local microstructural inhomogeneity. As a result of the severe local stress concentrated at the interface between the granular inhomogeneity. As a result of the severe local stress concentrated at the interface between the α phase and the colony of α/β lamellae under cyclic load, a microcrack is formed in the granular granular α phase and the colony of α/β lamellae under cyclic load, a microcrack is formed in the α phase due to priority deformation, and nanograin layers at the microcrack wake are produced granular α phase due to priority deformation, and nanograin layers at the microcrack wake are by the repeated pressing between the crack surfaces along the α lamella [14]. Micro-voids can be produced by the repeated pressing between the crack surfaces along the α lamella [14]. Micro‐voids introduced at the nanograin boundary, then the coalescence and linkage of the micro-voids results in can be introduced at the nanograin boundary, then the coalescence and linkage of the micro‐voids the separation of the nanograin layer, which displays FGA characteristics. The crack initiation at α results in the separation of the nanograin layer, which displays FGA characteristics. The crack lamella is also reported in very high cycle fatigue of Ti6Al4V, however, the flat facets were displayed initiation at α lamella is also reported in very high cycle fatigue of Ti6Al4V, however, the flat facets on the lamella [5], which may be owing to the absence of the granular α phase in the alloy. The α/β were displayed on the lamella [5], which may be owing to the absence of the granular α phase in the lamellae interface is the weak link for crack initiation, causing a cleavage on the plane with a favorable alloy. The α/β lamellae interface is the weak link for crack initiation, causing a cleavage on the plane orientation because of the restricted operative slip systems. with a favorable orientation because of the restricted operative slip systems.
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Figure 7. Fatigue crack initiation and microstructure characteristics with basketweave of 40 µm: Figure 7. Fatigue crack initiation and microstructure characteristics with basketweave of 40 μm: (a) (a) surface initiation, σ = 610 MPa, N = 1.15 × 106 cycles; (b) subsurface initiation, σ = 540 MPa, 6 cycles; (b) subsurface initiation, σ = 540 MPa, N = 8.51 × surface initiation, σ = 610 MPa, N = 1.15 × 10 7 N= 8.51 × 10 cycles. 107 cycles.
3.3. Effect of Basketweave on Fatigue Fracture Mechanism 3.3. Effect of Basketweave on Fatigue Fracture Mechanism For the subsurface fracture model, the initial stress intensity factor range at the FGA front can be For the subsurface fracture model, the initial stress intensity factor range at the FGA front can calculated using the Murakami model [23]: be calculated using the Murakami model [23]: ∆KFGA = 0.5σa
q √ π areaFGA
(1) (1) where σa is the stress amplitude and areaFGA is the area of FGA at the crack origin. In ultrasonic fatigue where σa is the area FGA is area part of FGA at cycle the crack In ultrasonic with a mean loadstress equalamplitude to zero (Rand = −1), only thethe tensile of the has aorigin. predominant effect fatigue with a mean load equal to zero (R = −1), only the tensile part of the cycle has a predominant on the fatigue crack propagation [24]. Thus, ∆KFGA is calculated by substituting σa into Equation (1) effect on instead of the ∆σ. fatigue crack propagation [24]. Thus, ΔKFGA is calculated by substituting σa into Equation (1) instead of Δσ. the stress intensity factor range at FGA and fatigue life is shown in The relationship between The relationship between the stress intensity factor range at FGA and fatigue life is shown in Figure 8. The alloy with basketweave of 60 µm and 40 µm have the same of ∆KFGA value, which has value, which has a aFigure 8. The alloy with basketweave of 60 μm and 40 μm have the same of ΔK scattering zone ranging from 3.8 MPa·m1/2 to 4.5 MPa·m1/2 (Figure 8), andFGA can be considered as 1/2 to 4.5 MPa∙m1/2 (Figure 8), and can be considered as the scattering zone ranging from 3.8 MPa∙m the threshold for the crack growth ∆Kth [24]. Zhao et al. [25] supposed that the growth of FGA was threshold by for the the crack microstructure, growth ΔKth [24]. et al. crack [25] cannot supposed that the when growth FGA zone was restricted related andZhao the FGA propagate the of plastic restricted by the related microstructure, and the FGA crack cannot propagate when the plastic zone size ahead of the FGA crack tip is equal to the characteristic dimension of the materials. Thus, the value of ΔKFGA can be evaluated as [26]:
K FGA 0.5 a area FGA
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Metals 2018, 8, x FOR PEER REVIEW 8 of 11 size ahead of the FGA crack tip is equal to the characteristic dimension of the materials. Thus, the value of ∆KFGA can be evaluated as [26]:
K FGA 4.342 √ b
(2) (2) ∆KFGA = 4.342µ b Equation (2) implies that ΔKFGA is a function of the shear modulus μ and the Burgers vector b of Equation (2) implies that ∆KFGA is a function of the shear modulus µ and1/2the Burgers vector b of materials. According to Equation (2), the value of ΔK FGA is about 3.54 MPa∙m for TC21 alloy, which 1/2 for TC21 alloy, which materials. According to Equation (2), the value of ∆K is about 3.54 MPa · m 1/2 FGA is consistent with various experimental results of 3.4–4.0 MPa∙m [26,27], but slightly lower than 1/2 [26,27], but slightly lower than this is consistent with various this experiment data. experimental results of 3.4–4.0 MPa·m experiment As for data. subsurface crack initiation, FGA is found along the basketweave (Figures 5 and 6), As for subsurface crack initiation, FGA is found along the basketweave (Figures 5 and 6), indicating the significant effect of basketweave on the hindering of FGA. Chapetti [28] assumed that indicating themicrostructure significant effect ofthe basketweave the hindering of FGA. Chapetti [28] assumed the strongest was barrier for on fatigue crack propagation at the critical nominal that the strongest microstructure was the barrier for fatigue crack propagation at the critical nominal stress range needed for a continued crack growth (microstructural threshold). Fatigue crack is stress range needed for a continued crack growth (microstructural threshold). Fatigue crack is assumed assumed to be hindered at the first basketweave under very high cycle fatigue limit stress; the FGA to be hindered at the first basketweave under very high cycle fatigue limit stress; the FGA area can be area can be treated as a circular area with a radius equal to basketweave. From Equation (1), a very treated as a circular area with a radius equal to basketweave. From Equation (1), a very high cycle high cycle fatigue limit of titanium alloy with basketweave microstructure can be expressed as fatigue limit of titanium alloy with basketweave microstructure can be expressed as
2ΔK FGA 2ΔK th σ a = 2∆KFGA = 2∆Kth p √area σa = p √ area = π area α/β π area FGA FGA
(3) (3)
α/β
1/2. The very high The typical ΔK for the alloy with basketweave of 60 and 40 μm are 4 MPa∙m The typical ∆Kth for ththe alloy with basketweave of 60 and 40 µm are 4 MPa·m1/2 . The very high cycle cycle fatigue limit for the alloy with basketweave of 60 and 40 μm are 438 and 536 MPa based on fatigue limit for the alloy with basketweave of 60 and 40 µm are 438 and 536 MPa based on Equation (3), Equation (3), which with are the consistent with results. the experimental results. Therefore, basketweave which are consistent experimental Therefore, basketweave size remarkably affectssize the remarkably affects the properties very high fatigue properties of isthe TC21 titanium alloy and of is very high cycle fatigue of cycle the TC21 titanium alloy and responsible for the variability responsible for the variability of fatigue properties. fatigue properties.
Figure 8. Relationship between the stress intensity factor range at FGA and fatigue life. Figure 8. Relationship between the stress intensity factor range at FGA and fatigue life.
3.4. Effect of Basketweave on Fatigue Life 3.4. Effect of Basketweave on Fatigue Life Considering that most of the total VHCF fatigue life is consumed by the crack initiation stage, Considering that most of the total VHCF fatigue life is consumed by the crack initiation stage, fatigue life of TC21 alloy can be estimated using an energy‐based crack nucleation life model, which fatigue life of TC21 alloy can be estimated using an energy-based crack nucleation life model, which can be calculated as [17]: can be calculated as [17]: 3 2 M33 c 4πµ 4 hh2 M c NN i = 2 i 3 2 2 3 2 2 2 µ2 2 ] 0.005d 1− ((1 υ))2 + ξMM2 0.005d(∆σ (−2Mk 2Mk)[)[π ∆σ ]
(4) (4)
where ∆σ is the stress amplitude for the stress ratio of −1. μ, ν are the shear modulus and Poisson’s ratio of material, d is the microstructure characteristics size, and it is the size of basketweave in this paper, c is the size of crack, which is herein considered as the size of FGA, M is the Taylor factor and
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where ∆σ is the stress amplitude for the stress ratio of −1. µ, ν are the shear modulus and Poisson’s ratio of material, d is the microstructure characteristics size, and it is the size of basketweave in9 of 11 this Metals 2018, 8, x FOR PEER REVIEW paper, c is the size of crack, which is herein considered as the size of FGA, M is the Taylor factor and is 9 cycles, is equal 2, 2Mk the fatigue limit defined as the strength fatigue at strength at 10 the life of parameters 109 cycles, equal to 2,to 2Mk is theis fatigue limit defined as the fatigue the life of hparameters h and ξ can be determined by the fitting of the S‐N curves, and then the nucleation life and ξ can be determined by the fitting of the S-N curves, and then the nucleation life curves for curves for different microstructure can be established. different microstructure can be established. Based on the fatigue data of TC21 alloy with basketweave microstructure, parameters h and ξ Based on the fatigue data of TC21 alloy with basketweave microstructure, parameters h and ξ are fitted as 0.9 and 0.0001, 0.0001, and the prediction prediction of of the the subsurface subsurface crack nucleation life life is shown in are fitted as 0.9 and and the crack nucleation is shown in Figure 9. It is suggested that the energy‐based crack nucleation life model can be well used to predict Figure 9. It is suggested that the energy-based crack nucleation life model can be well used to predict the subsurface crack nucleation life, and the large basketweave size significantly reduces the fatigue the subsurface crack nucleation life, and the large basketweave size significantly reduces the fatigue life. Thus, fatigue properties can be improved by the refinement of basketweave. life. Thus, fatigue properties can be improved by the refinement of basketweave.
Figure 9.9. Comparison fatigue life life with with different different basketweave basketweave size size versus versus the the Figure Comparison of of the the predicted predicted fatigue experimental data. experimental data.
4. Conclusions 4. Conclusions The conclusions are summarized as follows: The conclusions are summarized as follows: (1) Step-wise S-N characteristics are are observed on a TC21 alloy withalloy two sizes oftwo basketweave (1) Step‐wise S‐N characteristics observed on a titanium TC21 titanium with sizes of 5–109 cycle regimes. The fatigue property of the alloy with basketweave of over 105 –109 cycle regimes. The fatigue property of the alloy with basketweave of 40 µm is higher basketweave over 10 40 μm is higher than that of 60 μm. than that of 60 µm. (2) Fatigue crack initiates from the surface α/β phase interface at a relatively high stress amplitude, (2) Fatigue crack initiates from the surface α/β phase interface at a relatively high stress amplitude, whereas the fatigue crack appears the sample subsurface at a relatively low stress whereas the fatigue crack sitesite appears at theat sample subsurface at a relatively low stress amplitude; amplitude; α/β lamellar characteristic present at the crack initiation site of the alloy where α/β lamellar characteristic is present atis the crack initiation site of the alloy where FGA is found FGA is found alongside basketweave. alongside basketweave. (3) Very high cycle cycle fatigue fatigue limits limits of of TC21 TC21 titanium titanium alloy alloy with with basketweave basketweave microstructure microstructure are are (3) Very high evaluated based on the Murakami model, which are consistent with the experimental results. evaluated based on the Murakami model, which are consistent with the experimental results. The fatigue fatigue life life of TC21 titanium well predicted tan energy‐based crack The of TC21 titanium alloy alloy is wellis predicted using tanusing energy-based crack nucleation nucleation life model. life model. Author and D.C. conceived and designed the experiments; J.Z., M.L., F.L.M.L., and S.L. performed Author Contributions: Contributions: Z.Z. Z.Z. and D.C. conceived and designed the experiments; J.Z., F.L. and S.L. the experiments; B.N. analyzed the experiments, and wrote the paper. performed the experiments; B.N. analyzed the experiments, and wrote the paper. Funding: This work was supported by the National Natural Science Foundation of China (Grant No. 51571009). Funding: This work was supported by the National Natural Science Foundation of China (Grant No. 51571009). Special funds for the scientific and technological development of Guangdong (2017A010103029). Foshan programs Special for the scientific technological Guangdong (2017A010103029). Foshan of sciencefunds and technology research and (2017AB003941), thedevelopment “5511” projectof driven innovation program of Yichun City, the talent research start-up program of Foshan University (gg040940). programs of science and technology research (2017AB003941), the “5511” project driven innovation program of Yichun City, the talent research start‐up program of Foshan University (gg040940).
Conflicts of Interest: The authors declare no conflict of interest.
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Conflicts of Interest: The authors declare no conflict of interest.
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