Journal of Science: Advanced Materials and Devices (2018) 478e484 Contents lists available at ScienceDirect Journal of Science: Advanced Materials and Devices journal homepage: www.elsevier.com/locate/jsamd Original Article Fatigue properties of a nanocrystalline titanium based bulk metallic glassy alloy Mitsuhiro Okayasu*, Tomoki Shigeoka Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushimanaka, Kita-ku, Okayama, 700-8530, Japan a r t i c l e i n f o a b s t r a c t Article history: Received 23 August 2018 Received in revised form October 2018 Accepted 14 October 2018 Available online 25 October 2018 To obtain a better understanding of the fatigue properties and crack growth characteristics of a nanocrystalline titanium based bulk metal glasses (Ti-BMG) made by vacuumed casting process, the fatigue failure mechanisms of Ti-BMG have been investigated via S e N and da/dN e DK tests For comparison, the crystalline Ti alloy Ti-Al6V4 was also employed The fatigue strength in the early fatigue stage was high for Ti-BMG due to the high tensile strength However, the fatigue strength decreased significantly in the late fatigue stage The higher slope of S e N relation was detected for Ti-BMG, which crossed that for the Ti-Al6V4 sample around  103 cycles In the higher Region II, the fatigue crack growth rate was of similar level for both Ti-BMG and Ti-Al6V4 due to their similar strain energy In the lower Region II, however, the lower crack growth resistance was obtained for Ti-BMG, as compared to Ti-Al6V4 This was attributed to the high crack driving force for Ti-BMG, caused by the weak roughness-induced crack closure Such crack closing characteristics of Ti-BMG were systematically investigated by various experimental techniques © 2018 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Keywords: Crack closure Metallic glass Titanium Crack growth Fatigue failure mechanism Introduction Since metallic glasses have been developed by the process of rapid cooling in 1960, a large number of scientists has developed the metal glasses for engineering applications, thanks to their high corrosion resistance, good electromagnetic properties and high tensile strength Because the fatigue failure in the engineering components and structures is more than 90% of the total, the fatigue properties are significantly important This is especially true for metallic glasses, as their fatigue strength is not so high despite the high tensile strength Fatigue crack growth behavior in the amorphous structure is considered to be similar to that in polycrystalline steel and aluminum alloys [1] Moreover, the crack growth mechanism is associated with alternating blunting and resharpening of the crack tip The plastic deformation zone ahead of a crack is a source for heat generation, which leads to a change of the fracture mechanism and toughness Crack growth occurs quite readily due to the lack of microstructural barriers, i.e., no grain boundary, resulting in a low fatigue strength * Corresponding author Fax: ỵ81 86 251 8025 E-mail address: mitsuhiro.okayasu@utoronto.ca (M Okayasu) Peer review under responsibility of Vietnam National University, Hanoi The investigation of fracture and fatigue in thin ribbons of a nickel-base metallic glass was carried out by Alpas et al [2] They have found that fatigue crack growth behavior of the high tensile strength and high toughness amorphous alloy is caused by abnormal microstructure and unusual form of plastic deformation Severe deformation in metallic glasses is considered to arise from flow in localized shear bands, in which the veined fracture surface is obtained [3] Compact tension specimens were made from the bulk plates of Zr-Ti-Cu-Ni-Be base alloy to examine the fatigue crack growth behavior, which revealed fracture toughness of KIC ¼ 55 MPa m1/2 [4] Yokoyama et al [5] have examined fatigue properties of various Zr-based systems, and they have concluded €hler curve is different from those of ordinary crystalline that the Wo structural alloys, as the fatigue strength of the Zr-based BMG is very low due to their low slip resistance The low fatigue endurance limit of partially crystallized BMGs with respect to that of fully amorphous alloys was also reported [6] Menzel and Dauskardt [7] have examined the fatigue damage for a Zr-based bulk metallic glass, in which shear bands or mixed-mode cracks, propagating at ~ 49 to the applied stress axis after a few cycles, make the low fatigue strength To understand accurately the crack growth behavior, an examination of the crack growth characteristics in detail is significantly important https://doi.org/10.1016/j.jsamd.2018.10.001 2468-2179/© 2018 The Authors Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) M Okayasu, T Shigeoka / Journal of Science: Advanced Materials and Devices (2018) 478e484 479 Since Christensen reported the fatigue crack closure as a major problem in the crack propagation study in 1963 [8], this phenomenon has been the significant parameters to understand the fatigue crack growth characteristics The concept of crack closure has been widely applied In this case, Chen et al have proposed valuable crack closure models [9,10] It was considered that, without the crack closure parameter, the fatigue crack growth rates cannot be predicted In particular, the fatigue crack growth behavior in the near-threshold regime is strongly affected by the crack closure effect Although the crack growth behavior of bulk glassy alloy has been examined, there is apparently lack of the study for crack closing characteristics Thus, the aim of this work is to investigate the effect of the extent of crack closure on the crack growth characteristics for a nanocrystalline bulk metallic alloy Experimental 2.1 Material preparation In the present study, the titanium-based nanocrystalline bulk metallic glass was selected (Ti-BMG: Ti41.5Zr2.5Hf5Cu42.5Ni7.5Si1) A tubular Ti-BMG sample (f2.0 (OD)  f1.6 (ID)  200 mm) was made by the high speed vacuumed casting technique, in which copper molds were employed to make the high-speed cooling In the vacuumed casting process, the material was melted in an arc melter under vacuum at approximately 2.5  10À3 Pa, and injected rapidly into a copper mold using a vacuumed casting system designed by Makabe Giken Co., Ltd, where the solidification rate of this vacuumed casting is about 103 K/s The Ti-BMG sample selected has been used for the colliori-type mass flow meter under the vibration In this examination, a commercial crystalline material (titanium alloy Ti-Al6V4) was also employed to compare the mechanical properties the Ti-BMG samples under investigation To study the mechanical properties of Ti-BMG, the test specimens for both samples were originally designed in a dumbbell shape, which machined through electro-discharge machining Fig 1(a) shows the photograph of the specimen and the testing fixture, and Fig 1(b) indicates the specimen configurations for the mechanical testing For the crack growth test, a sharp notch was made to monitor easily the fatigue crack growth rate Fig 2(a) displays the transmission electron microscope (TEM) image of Ti-BMG and X-ray diffraction (XRD) patterns of Ti-BMG and Ti-Al6V4 For Ti-BMG, a nanocrystalline structure and a halo pattern for amorphous structure were obtained in TEM and XRD, respectively On the contrary, crystalline structure of a sharp peak was observed for Ti-Al6V4 To further understand the amorphous structure of Ti-BMG, the electron backscatter diffraction (EBSD) analysis was carried out Fig 2(b) displays the inverse pole figure maps of Ti-BMG and TiAl6V4 As seen, crystal formation is completely collapsed for TiBMG, while the crystal structure was apparently formed for TiAl6V4 Furthermore, after the annealing at 900 C for 15 min, the recrystallization occurred in Ti-BMG with grain size of about 20 mm, which is times higher than that for Ti-Al6V4 2.2 Mechanical properties In the present work, tensile and fatigue tests were carried out using a screw driven type universal testing machine with 50 kN capacity The tensile test was conducted at mm/min until the specimen was fractured completely The stress and strain values were measured by a standard load cell and strain gauge, respectively, which were monitored during the tensile test using a data acquisition system in conjunction with a computer The fatigue strength was examined by two different methods: S - N and da/dN DK tests The relationship between the applied stress amplitude Fig Specimen and testing fixture for the tensile and fatigue tests: (a) photograph and (b) schematic diagram and number of cycles to final failure was investigated in the S - N approach The tensile e tensile cyclic loading was applied at a low cycle frequency Hz up to 105 cycles The da/dN - DK relations were examined after a pre-crack 1.0 mm from the notch tip was created The pre-crack was made under small-scale yielding conditions, where the crack tip was not blunted before the da/dN - DK test The crack length was monitored directly during the cyclic loading using a traveling light type microscope with a resolution of 0.01 mm On the basis of the ASTM standard, DK value was calculated from Eq (1) with the parameters of crack length (a) and applied cyclic stress range (Ds) [11]: pffiffiffiffiffiffiffi DK ¼ Ds p a 1:12 À 0:231 a 4 ỵ 30:39 W a a 2 a 3 ỵ 10:55 21:72 W W W (1) 480 M Okayasu, T Shigeoka / Journal of Science: Advanced Materials and Devices (2018) 478e484 Fig Tensile stressestrain curves for Ti-BMG and Ti-Al6V4 Results and discussion 3.1 Tensile properties Fig presents the representative engineering stress e engineering strain curves for Ti-BMG and Ti-Al6V4 As seen, the stress vs strain curve for Ti-BMG is located at a high level compared to that for Ti-Al6V4: the ultimate tensile stress (sUTS) for Ti-BMG is about 1800 MPa, which is about 60% higher compared to that for TiAl6V4 It is also clear that the linear stressestrain relation with the high elastic constant was observed for the Ti-BMG sample, resulting in no clear plastic deformation In contrast, the plastic deformation (or work hardening behavior) was detected for Ti-Al6V4, e.g., the fracture strain (εf) is about 16% 3.2 Fatigue properties Fig shows the relationship between stress amplitude and cyclic number to failure for Ti-BMG and Ti-Al6V4, i.e., S e N curve As seen, different trend of fatigue properties was detected in both samples, where the fatigue strength for Ti-BMG is higher than that for Ti- Fig (a) TEM image of Ti-BMG and XRD patterns of Ti-BMG and Ti-Al6V4 and (b) IPF maps of the Ti-BMG and Ti-Al6V4 specimens To estimate the crack driving force, the relationship between the applied load and crack opening value (strain) was examined at several stages in Region II of the da/dN vs DK The load e strain curves were measured by a standard load cell and a strain gauge attached on the specimen To understand the failure characteristics, the fracture surface characteristics, including the surface roughness, were investigated using a scanning electron microscope (SEM) and a laser scanning microscope (OLYMPUS, LEXT-OLS4100) Fig Stress amplitude vs number of cycles to failure for Ti-BMG and Ti-Al6V4 M Okayasu, T Shigeoka / Journal of Science: Advanced Materials and Devices (2018) 478e484 481 To understand clearly the fatigue strength of both Ti-BMG and Ti-Al6V4 samples, their S e N curves were quantitatively evaluated by a power law dependence of stress amplitude (sa) and cyclic number to failure (Nf) [14]: sa ¼ sf NÀb f ; MPa Fig Relationship between crack growth rate and stress intensity factor range in Region II (da/dN e DK) for Ti-BMG and Ti-Al6V4 Al6V4 in the early fatigue stage, but the lower fatigue strength for TiBMG in the late fatigue stage Namely, the higher slope of S - N relations is obtained for Ti-BMG, which crosses that for Ti-Al6V4 around  103 cycles as enclosed by the dashed circle in Fig Due to the different slope of S vs N, the endurance limit at 105 cycles for Ti-BMG is more than 10 times lower than that for Ti-Al6V4, namely, 7.6 MPa for Ti-BMG and 117 MPa for Ti-Al6V4 It is reported in the previous study in Ref [12] that there is linear relationship between the ultimate tensile strength (UTS) and fatigue limit for crystalline materials, while UTS for BMGs does not directly affect their fatigue limit Similar result is reported in Ref [13], where no clear relationship between the fatigue limit and the yield strength is detected The reason behind this is not clear at the moment, but it could be affected by the vacancy of atom in BMG [12] (2) where sf is the fatigue strength coefficient and b is the fatigue exponent The values of sf and b for Ti-BMG and Ti-Al6V4 are sf ¼ 33.5 GPa and b ¼ 0.51 (for Ti-BMG) and sf ¼ 1.49 GPa and b ¼ 0.13 (for Ti-Al6V4) In this case, a high fatigue strength is expected for high sf and low b value From this estimation, high sf and high b values, obtained for Ti-BMG, are related to the high and low fatigue strength in the early and the late fatigue stage, respectively To verify the crack growth characteristics in detail, the fatigue crack growth behaviors were investigated Fig shows the relationship between crack growth rate and the stress intensity factor range (da/dN - DK) for both samples In this case, their crack growth rate could be related to that in Region II This is because the low DK value for both sample are about 200 MPa mm1/2, which is much higher than that for the related BMG: 56.9 MPa mm1/2 for Zr-based bulk metallic glass [15] In this case, two distinct regions of fatigue crack growth are identified: the lower and higher Region II L-Region II is the range of crack growth rate above the threshold stress intensity, where the crack propagation speed is slow rate H-Region II is a linear relationship between log da/dN and log DK, i.e., Paris region: da ¼ C DK m ; m=cycle dN (3) where C and m are fatigue crack growth parameters; and C and m values for Ti-BMG are  10À11 and 1.4, which are relatively closed to those for Zr41.25Ti13.75, Ni10Cu12.5Be22.5 bulk metallic glass (C ¼ 2.4  10À10 and m ¼ 1.7) [7] As seen in Fig 5, different crack growth characteristics are observed The resistance to crack growth in L-Region II appears to be substantially lower for Ti-BMG, Fig Laser scanning microscope images of the fracture surfaces after the fatigue tests (more than 104 cycles) for (a) Ti-BMG and (b) Ti-Al6V4 482 M Okayasu, T Shigeoka / Journal of Science: Advanced Materials and Devices (2018) 478e484 Fig The models of the ideal crack and crack closure: (a) ideal crack opening and closing and (b) roughness-induced crack closure compared to that for Ti-Al6V4, although the crack growth rate for both samples is similarly observed in H-Region II Such crack growth rate in L-Region II might be associated with their endurance limits due to the low crack propagation rate, as shown in Fig 4, namely the higher crack growth rate in L-Region II is related to the lower endurance limits for Ti-BMG On the other hand, similar crack growth rate in H-Region II is attributed to the similar mechanical properties However, it could be questionable, since the mechanical properties of both samples were quite different, e.g., tensile and fatigue strength It is general consideration that the strain energy is attributed to their Fig Stress intensity factor (K) vs strain showing the stress intensity factor at crack closing (Kcl), the maximum (Kmax) and the minimum stress intensity factors (Kmin) for (a) Ti-BMG and (b) Ti-Al6V4 M Okayasu, T Shigeoka / Journal of Science: Advanced Materials and Devices (2018) 478e484 483 was measured in the specimen behind the ligament to estimate the crack opening displacement value From Fig 8, the K vs strain exhibits a concave shape with different slope, in which the high slope of K vs strain is detected at the low DK level, which signifying an acceleration in the reduction of the measured strain value at the minimum stress intensity factor (Kmin) It is also seen that a concave unloading portion is apparently reflected at the low K level (Kcl), which is the stress intensity factor at crack closing action (fracture surface contact) [17] As in Fig 8, the Kcl value depends on the DK level, where the lower the DK, the higher the Kcl With increasing the DK value, the slope of K vs strain decreases which would be affected by severe deformation around the crack tip There are several crack closure models to quantify the actual crack driving force The incorporation of crack closing effects in terms of the effective stress intensity factor range involves the maximum and the minimum stress intensity factor Based upon this, the effective stress intensity factor range (DKeff) can be estimated by DKeff ¼ Kmax e Kcl Based on the DKeff values, the variation Fig Variation of the ratio of DKeff and DK (U) as a function of DK for Ti-BMG and Ti-Al6V4 crack growth rate, as the strain ahead of crack tip can absorb the crack driving force From the stressestrain curves in Fig 3, the strain energy for Ti-BMG and Ti-Al6V4 can be estimated as 135 MPa (for TiBMG) and 124 MPa (for Ti-Al6V4) Because of similar strain energy of both Ti-BMG and Ti-Al6V4, the high crack growth rate for Ti-BMG in L-Region II is inconsistent, whereas the similar crack growth rate of both samples in H-Region II is applicable To understand the different fatigue properties, fracture surface observation was carried out using the laser scanning microscope after the fatigue crack growth tests Fig displays the fracture surfaces of Ti-BMG and Ti-Al6V4 It should be noted that both samples were fracture after cyclic loading of more than 104 cycles It is clear that the crack growth characteristics are obviously different A relatively smooth crack growth surface could be seen for Ti-BMG, while a coarse fracture surface was obtained for Ti-Al6V4 The mean surface roughness was Ra ¼ 968 nm for Ti-Al6V4, which is about twice rougher than that for Ti-BMG Such a difference in the roughness of the fracture surface could make a change of the crack growth resistance, because of different severity of crack closure, i.e., roughness-induced crack closure Such crack closing characteristic can be interpreted as follows It is considered that roughnessinduced crack closure occurs severely in the low crack growth rate (L-Region II), and the mechanism of the roughness-induced crack closure can be interpreted using Fig [16] To understand the crack closing mechanism easily, ideal crack opening and closing are indicated in Fig 7(a) Due to flat crack surfaces without plastic deformation, roughness- and plasticity-induced crack closures not occur significantly In this case, the crack surfaces are opened and those are closed completely after removed the applied load In contrast, because of the rough fracture surfaces in Fig 7(b), the crack surfaces make a contact each other before removing the loading This occurrence makes reduction of the crack driving force leading to the low crack growth rate, i.e., roughness-induced crack closure for Ti-6Al4V in L-Region II 3.3 Crack closure characteristics Due to the difference in the crack growth rate in L-Region II for TiBMG and Ti-Al6V4, the extent of crack closure has been investigated Fig displays the relationship between K and strain for both Ti-BMG and Ti-Al6V4 samples obtained in Region II Note that the strain value Fig 10 Relationship between log da/dN and log DK (log DKeff) in L-Region II for (a) Ti-BMG and (b) Ti-Al6V4 484 M Okayasu, T Shigeoka / Journal of Science: Advanced Materials and Devices (2018) 478e484 of U (DKeff/DK) as a function of DK for both samples is shown in Fig From this, it is appeared that the value of U is altered depending on DK, where the U value for the Ti-BMG is overall higher than that for Ti-Al6V4 This occurrence is reflected by the weak crack closure for Ti-BMG, resulting in the high crack growth rate at the low DK region In this case, severe crack closure occurred for Ti-Al6V4 due to the rough fracture roughness Because of ductile properties for Ti-Al6V4, crack blunting and constraining of the shear bands may have also enhanced fatigue crack growth resistance, i.e., plasticity-induced crack closure Based on the DKeff values obtained, the relationship between log da/dN and log DK (log DKeff) in the L-Region II for both Ti-BMG and Ti-Al6V4 was indicated in Fig 10 As seen, the da/dN vs DKeff for TiAl6V4 is shifted to the left-hand side due to the severe crack closure In contrast, the da/dN vs DKeff for Ti-BMG did not shift significantly compared to the Ti-Al6V4 one It is convinced from this result that the crack growth rate is not delayed for Ti-BMG, because of weak crack closure arising from the smooth fracture surface Note that, in this case, no clear microstructural barrier of Ti-BMG is also significant factor It is therefore the BMG samples not have high fatigue properties Conclusion An examination has been made of the fatigue and crack growth properties for Ti-BMG and Ti-Al6V4 crystalline structures, the fatigue failure characteristics of Ti-BMG have been clarified The fatigue strength for Ti-BMG was high in the early fatigue stage due to the high tensile strength However, the fatigue strength decreased in the late fatigue stage The higher slope of S e N relations was obtained for Ti-BMG, which crossed those for the Ti-Al6V4 sample around  103 cycles Fracture surface for Ti-BMG after the fatigue test was dominated by the smooth surface Rough fracture surface was obtained for the Ti-Al6V4, which was about twice higher than that for Ti-BMG The fatigue crack growth rate in H-Region II of the fatigue stage for Ti-BMG was similarly observed for the Ti-Al6V4 sample, which was attributed to the similar strain energy level In contrast, the different crack growth rate was obtained in L-Region II: the higher crack growth resistance was found for Ti-Al6V4, as compared to Ti-BMG This was attributed to the reduction in the crack driving force arising from the different severity of crack closure, e.g., roughness-induced crack closure Because of the smooth fracture surface for Ti-BMG, the crack growth rate enhanced Acknowledgments The authors would like to express their appreciation to Professor Mitsuru Watanabe for his helpful comments and suggestions on the manuscript References [1] C.J Gilbert, V Schroeder, R.O Ritchie, Mechanisms for fracture and fatiguecrack propagation in a bulk metallic glass, Metall Mater Trans A 30A (1999) 1739e1753 [2] A.T Alpas, L Edwards, C.N Reid, Fracture and fatigue crack propagation in a nickel-base metallic glass, Metall Trans A 20 (1989) 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DKeff values, the variation Fig Variation of the ratio of DKeff and DK (U) as a function of DK for Ti-BMG and Ti-Al6V4 crack growth rate, as the strain ahead of crack tip can absorb the crack driving... [2] A. T Alpas, L Edwards, C.N Reid, Fracture and fatigue crack propagation in a nickel-base metallic glass, Metall Trans A 20 (1989) 1395e1409 [3] K.M Flore, R.H Dauskardt, Local heating associated... G.Y Wang, P.K Liaw, Y Yokoyama, M Freels, R .A Buchanan, A Inoue, C.R Brooks, Effects of partial crystallization on compression and fatigue behavior of Zr -based bulk metallic glasses, J Mater