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The analysis of fracture toughness and fracture mechanism of Ti60 alloy under different temperatures
Journal of Alloys and Compounds 810 (2019) 151899
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The analysis of fracture toughness and fracture mechanism of Ti60 alloy under different temperatures Runchen Jia a, b, c, Weidong Zeng a, b, c, *, Shengtong He a, b, c, Xiongxiong Gao a, b, c, Jianwei Xu a, b, c a
State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an, 710072, China Defense Technologies Innovation Center of Precision Forging and Ring Rolling, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an, 710072, China c Shaanxi Key Laboratory of High-Performance Precision Forming Technology and Equipment, Northwestern Polytechnical University, Xi'an, 710072, PR China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 June 2019 Received in revised form 13 August 2019 Accepted 15 August 2019 Available online 19 August 2019
Fracture toughness and fracture mechanism of Ti60 alloy with duplex microstructure under different temperature conditions were investigated in the present work. The experimental result shows that the fracture toughness of CT samples increases from the room temperature (40 MPa m1/2) to 400 C (71.45 MPa m1/2) but declines at 600 C (62.55 MPa m1/2). It is observed from fracture surface through SEM that the predominant fracture mechanism has changed from quasi-cleavage fracture at room temperature to ductile fracture at higher temperatures. In addition, the tortuosity of crack propagation path has a limited impact on the fracture toughness. Path selections for crack propagation are obtained through SEM observation which can be summarized as: cut through lamellar a, parallel to lamellar a, bypass the equiaxed ap and cut through the equiaxed ap. Moreover, it is found that the intrinsic contribution is the primary reason leading to the change of the fracture toughness of Ti60 alloy under different temperatures. Meanwhile, it is noteworthy that the area of the crack tip plastic zone increases from RT to 400 C but decreases at 600 C, which is seen as the main impact of temperature on fracture toughness. To be exact, the CT sample with a larger area of the plastic zone could provide a higher K1C value. Furthermore, a prediction model of K1C based on tensile properties is established, which has a good accuracy with experimental results. The model is useful in predicting the fracture toughness of Ti60 alloy at different test temperatures. © 2019 Elsevier B.V. All rights reserved.
Keywords: Ti60 alloys Duplex microstructure Fracture toughness Crack propagation paths Fracture mechanisms
1. Introduction The new generation of high performance aircraft put forward higher requirements for engine service temperature, while fracture toughness is an important design criterion which should be taken into consideration in order to obtain long life safe flight [1e3]. Ti60 titanium alloy, a promising near-a titanium alloy, can serve under high temperature over a long period of time, which makes it an important candidate material for manufacturing the integral impeller of high push-weight ratio engine compressor. After several
* Corresponding author. State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an, 710072, China. E-mail addresses: [email protected] (R. Jia), [email protected] (W. Zeng). https://doi.org/10.1016/j.jallcom.2019.151899 0925-8388/© 2019 Elsevier B.V. All rights reserved.
thermomechanical processing, Ti60 titanium alloy acquires a classical duplex microstructure with equiaxed ap as well as lamellar a. The equiaxed ap with excellent deformation coordination exhibits better ductility and high cycle fatigue properties, while the lamellar a with excellent crack propagation resistance exhibits better creep and fatigue properties. Many investigations about fracture toughness have been done on the impact caused by microstructural morphology [4e6]. However, the effects of temperature on the fracture toughness and fracture mechanism of Ti60 alloy have not been systematically studied. According to G.Lütjering et al., the fracture toughness of the material came from two common contributions: on the one hand, the contribution of the intrinsic fracture toughness usually related to the intrinsic properties of the material; and on the other hand, the contribution of crack tip geometry [7]. Ritchie et al. studied the fracture toughness of advanced material, the result
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demonstrated that the total fracture toughness was affected by two main classes of toughening. The intrinsic toughening mechanism which was an inherent property of the material, and the extrinsic mechanism depended on the crack size and specimen geometry which can be directly reflected in the degree of tortousity of the crack growth path [8]. Therefore, some researchers have studied the relationship between fracture toughness and crack tip tortuosity. I.Cvijovic-Alagic et al. found that the small aspect ratio of a phase contributed to the decrease of the propagation resistance [6]. The enhanced crack propagation resistance was correlated with the larger propensity for crack tip tortousity. Since the crack propagation was hindered by the strong resistance in front, it was forced to change propagation direction and consumed more energy. Thus, more resistance during the crack propagation process makes the material provide higher fracture toughness [9]. The fracture toughness is a critical parameter in damagetolerant design concept, which has an important investigation significance. However, there is no clear conclusion about the effect of the temperature on fracture toughness of Ti60 alloy. In this paper, the impact of temperature on fracture toughness was systematically investigated. The tensile properties and fracture mechanism were also studied through tests. At last, a prediction model of fracture toughness based on tensile properties was established with a good accuracy according to the experimental result.
After heat treatment, the standard tensile samples were machined from the bar samples. Tensile tests were performed at an initial rate of 1 103 s1at room temperature, 200 C, 400 C and 600 C respectively. Gauge dimensions of the tensile specimens are 5 mm in diameter and 35 mm in length, which were shown in Fig. 2. The tensile properties were evaluated at each temperature condition. Finally, optical microscopy (OM) was employed to observe the microstructural morphology of different conditions. Plane-strain fracture toughness tests were carried out on the standard compact tension (CT) samples of four groups under different temperature conditions. Before the tests, each CT sample was inserted a fatigue pre-crack using MTS810 fatigue testing machine. The loading frequency was 12 Hz, and the crack was measured by a 30 reading microscope with a resolution of 0.01 mm. Thus, the pre-crack length could be controlled in less than 2 mm. The dimensions of the CT samples is 63 60 25(mm), and the schematic sample is illustrated in Fig. 2. In addition, the precrack direction is perpendicular to the tensile loading direction of tensile sample, which is also shown in Fig. 2. The fracture surfaces and the crack propagation path were observed by scanning electron microscopy(SEM). 3. Results and discussion 3.1. Tensile properties
2. Experimental procedure The material with duplex microstructure used in the present study was obtained through ingot casting with a bar form. The microstructure analyses of the materials were conducted with Olympus GPM-G3 optical microscopy (OM) and S-4800 scanning electron microscope (SEM). Fig. 1 shows the typical microstructure with equiaxed ap as well as lamellar a of Ti60 alloy. Several pictures of the microstructure were obtained through the SEM observation, the volume fractions and microstructural sizes were measured by utilizing the professional software Image Pro Plus 6.0 (IPP 6.0). To ensure the statistical accuracy, at least 3 pictures of microstructure at different areas were used in the measurement process. The measurement result shows that the volume fraction of equiaxed ap is about 15% with the average size of 20 mm. The average length of lamellar a is 15 mm, and the average width of the lamellar a is 2 mm. In addition, the large lamellar a has the width greater than 5 mm.
Fig. 1. The typical duplex microstructure with equiaxed ap as well as lamellar a of Ti60 alloy.
As shown in Fig. 3, tensile properties of samples at the temperature ranging from room temperature to 600 Cwere investigated including yield strength, ultimate tensile strength, elongation and reduction of area for Ti60 alloy. The result shows that the yield strength and ultimate tensile strength of Ti60 alloy decreases with the increase of the temperature. However, the elongation and reduction of area show a reverse changing tendency with the strength. The experimental results are according to the previous investigation [10]. This phenomenon can be explained by the activated process [11]. Because high temperature will alleviate the dislocation pile-up and more slip systems cloud be activated. Thus, the deformation ability and ductility are improved. 3.2. Fracture toughness and fracture mechanisms The fracture toughness of the four CT samples after tests are shown in Fig. 4. It can be found that the sample at 400 C has the highest fracture toughness up to 71.45 MPa m1. The tendency of fracture toughness increases from RT to 400 C, but declines at 600 C. As shown in Fig. 4, the crack propagation path was divided into three areas. Firstly the expansion zone of the pre-crack, followed by the crack stable expansion zone, and finally the rapid expansion zone of the crack, which have been marked out with yellow curves in Fig. 4. The colors on the samples are related to the colored titanium oxides. It is well known that the main titanium oxides are TiO2, TiO, Ti2O3 and Ti3O5. The colors of TiO2 and TiO were white and golden tinted, respectively. And Ti2O3 and Ti3O5 appear bule and dark violet, respectively. Before fracture toughness, the oxide at the pre-crack expansion zone on the sample surface was TiO2. The CT sample in RT condition had less time to react with oxygen, so there was no obvious distinction can be seen on the sample surface. However, after fracture toughness tests, the CT samples were exposed in higher temperature. On this basis, the volume fraction of TiO was increasing because of the increasing oxidation temperature. Thus, the color on the sample surface changed from light yellow to golden yellow. It is noteworthy that the color of the pre-crack propagation expansion at 600 C is blue. That can be explained by the presence of the oxidation production Ti2O3. In addition, the color on each sample surface is different
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Fig. 2. Schematic specimen and dimensions of the CT and tensile samples.
Fig. 3. Tensile properties and fracture toughness of Ti60 alloy under different temperatures.
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Fig. 4. The CT samples under temperature conditions of (a) room temperature, (b) 200 C, (c) 400 C and (d) 600 C.
because the diverse oxidation production with different oxidation reaction time. On the whole, the oxidation phenomenon in precrack expansion zones were more seriously. Except the fracture surface under room temperature breaks rapidly which has less oxidation reaction time with the air, obvious boundary between stable expansion zone and rapid expansion zone can be observed on the surface of the other three samples. Significant distinction is observed from the stable extension zone and unstable expansion zone of different CT samples. The sample with lager stable expansion zone could provide a relatively higher KIC value. As shown in Fig. 5, compared with the fracture surfaces at the stable expansion zone under higher test temperatures, the fracture morphology of room temperature appears with plenty mini facets, which is a feature of quasi-cleavage. However, with the temperature increasing to 200 C, shallow dimples can be observed on the
fracture surface, which shows the ductile fracture characteristic. At the test temperature of 400 C, dimples on the fracture surface become deeper and larger. When the temperature condition comes to 600 C, the size of dimples becomes larger than that in the other temperatures. Fig. 6 shows the micro fracture surface at stable expansion zone of different samples in higher magnifications. Fig. 6(a) exhibits the fracture in consistent direction with less dimples and tearing ridges, which is a quasi-cleavage feature. This is because the CT sample in room temperature do not have sufficient deformation coordination ability on account of low plasticity, the crack gives priority to propagate along a certain cleavage plane [12]. Thus, the crack propagates more easily with small resistance. In addition, the main crack changes direction as it propagates and the secondary crack is easy to be formed at a boundary, which is marked out with
Fig. 5. Fracture surface under different temperature conditions in 100 magnification. (a) room temperature, (b) 200 C, (c) 400 C and (d) 600 C.
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Fig. 6. Micro fracture surfaces of different temperature conditions samples in different magnifications. (a) room temperature. (b) 200 C. (c) 400 C. (d) 600 C. The magnification of (a) is 1000 . The magnification of (b), (c) and (d) is 500 .
red circles in Fig. 6(a). At a higher temperature of 200 C, as shown in Fig. 6(b), except for the number of the dimples on the fracture surface increases, the phenomenon of fracture in consistent direction within a small area almost disappears. This is because the amount of movable slip systems increases as the temperature increases. In this case, most grains could deform harmoniously, the possibility of crack origination declines and the crack propagation resistance enhances. Hence, just some isolated lamellar a are left on the fracture surface because of relatively difficult-to-deform orientation. As shown in Fig. 6(c), more tearing ridges have appeared on the fracture surface especially in the lamellar a as experimental temperature increases. And tearing ridges could improve the extrinsic resistance of fracture toughness. That means the more tearing ridges appear, and the greater the fracture toughness of the material will be obtained. However, when the temperature condition comes to 600 C, as shown in Fig. 6(d), it is obvious that the dimples become bigger and wider, which is a feature of ductile fracture. Besides, the morphology of lamellar a on the fracture surface has disappeared. That is because in the higher temperature, more slip systems can be actuated and the plasticity is greatly improved. The fracture mechanism under different temperatures is analyzed on the basis of fracture features observed on the fracture surfaces. As mentioned before, fracture toughness is influenced by the tortuosity of the crack propagation path. Thus, the crack propagation path selections through various microstructures are observed using SEM. Fig. 7 shows a more intuitive representation of the relationship between the fracture surface and the microstructure. As shown in Fig. 7(a), the crack propagation path cuts through lamellar a, and it is noteworthy that the direction of the crack propagation is deflected with the different angles of lamellar colonies. The long and thick a platelets promote tortuosity during the main crack propagation process, which can obviously improve the crack growth resistance [13]. Fig. 7(b) shows an almost parallel propagation path with lamellar a boundaries. This phenomenon is attributed to fairly low resistance at the lamellar boundaries, so that crack propagates by interlamellar fracture and changes propagation direction when crossing the colony [6]. Fig. 7(c) shows a
propagation of bypassing the equiaxed ap, which indicates that equiaxed ap boundaries become obstacles to propagation. In this case, the bigger size of equiaxed ap is favourable to improve the crack tip plasticity [14]. The path around the equiaxed ap shows a bulge on the fracture surface. Compared with bypassing the equiaxed ap to expand, crack in Fig. 7(d) shows a completely different way. The crack expands without changing its direction in the propagation process, and leaves an almost linear path on the fracture surface resulting a decrease of fracture toughness [15,16]. From the analysis above, an inference is that path selections during crack propagation in microscale have a great effect on the tortuosity. While, it remains unsufficient to well explain the impact of tortuosity on fracture toughness. Therefore, a more systematic method is in demand to conduct a further investigation. As mentioned above, the fracture toughness is a result of two main contributions: the intrinsic resistance to fracture is related to the properties of the material itself, the extrinsic resistance is reflected by the tortuousity of the crack propagation. In order to determine the percentage of intrinsic fracture contribution and extrinsic fracture contribution at various temperature conditions, a calculation method that takes both intrinsic fracture toughness and extrinsic fracture toughness into account is needed. Through this way, the intrinsic contribution and extrinsic contribution to overall fracture toughness under different temperature conditions can be well examined, which is beneficial for further investigation. According to the theory of linear elastic fracture mechanics, Equation (1) is established [17].
rffiffiffiffiffiffiffiffiffiffiffiffiffi G1C ,E 1 v2
K1C z
(1)
where KIC is the plane strain fracture toughness, GIC is the critical strain energy release rate, E is the elastic modulus, and n is the Poisson's ratio. According to Griffith's theory [18], the critical strain energy release rate of linear elastic materials can be obtained from the following equation:
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Fig. 7. Correspondence between the fracture surface and microstructure as well as the path selections for crack propagation. (a) cut through lameller a; (b) parallel with lameller a; (c) bypass the equiaxed ap; (d) cut through equiaxed ap.
G1C ¼ 2gS
(2)
where Ys represents the surface energy per square meter. Equation (2) means that the crack propagates unsteadily inside the material only when the strain energy release rate of the material exceeds 2Ys. However, metallic deformation includes not only elastic part but also plastic part. Yp is the energy consumed in plastic deformation of crack surfaces. For structural metallic materials, the value of Yp is much higher than the surface energy density Ys. Therefore, in the fracture mechanics of most metallic materials, the modified Griffith-Orowan-Irwin [19] formula is used to approximate its critical strain energy release rate, as shown in Equation (3).
G1C ¼ 2 gs þ gp ¼ 2geff
AV ¼ (3)
Equation (3) is usually applied to plastic metallic materials where Yp is significantly considerable. Ragozin et al. [20]have established the relation between the specific work of uniform deformation AV and the effective surface energy Yeff as:
AV , V ¼ 2geff ,F
(4)
where V is the volume responsible for fracture and F is the area of surface for crack forming. The specific work of uniform deformation AV can be determined from the Equation (5) [21],
V ¼ h,lðεÞ
Fig. 8. Schematic diagram of real length l(ε) and linear length l(0).
(5)
where h is the height of the crack tip plastic zone, As shown in Fig. 8, l(ε) is the real length of crack propagation path. Thus, Equation (3) can be changed as:
s 2 εf Ey sy 2sb 3
þ
s2y 2E
(6)
where εf is the fracture ductility, sy is the yield stress, sb is the ultimate tensile strength. The volume caused by fracture can be changed into:
G1C ¼ AV ,V ¼ AV ,lðεÞ ,h
(7)
After substituting Equation (7) into Equation (1), the result is
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E,AV ,h,lð0Þ lðεÞ E,AV ,h,lð0Þ qffiffiffiffiffiffiffiffiffiffiffi ¼ K1C ¼ , , Rpath 2 l 1n 1 n2 ð0Þ
(8)
where l(0) is linear length of the crack propagation path. The ratio of l(ε) to l(0) can be seen as the tortuosity degree of the crack propagation path, which is represented by Rpath. The relationship is well established between the tortuosity of crack propagation path and fracture toughness through this method. Thus, the percentage of the extrinsic contribution of fracture toughness can be easily
R. Jia et al. / Journal of Alloys and Compounds 810 (2019) 151899
obtained if the l(ε)/l(0) is available. In the present work, a method is introduced to calculate l(ε)/l(0). The crack propagation paths of four temperature conditions after image processing are shown in Fig. 9. The professional image processing software Image Pro Plus 6.0 (IPP 6.0) is applied to calculate the crack propagation path tortuosity Rpath of CT samples at four different temperatures, which can extract the crack propagation path of the fracture toughness specimens. In addition, the length of the real path of crack propagation l(ε) and the length of linear path of crack propagation l(0) are measured by the IPP 6.0 software. The tortuosity can be obtained from the calculation of ratio l(ε) to l(0). In order to acquire accurate statistics, it is necessary to conduct the measurement progress with three times, and take the average value of them as the ultimate result, which are shown in Table 1. Given the ratio of l(ε) to l(0), the contribution of extrinsic fracture toughness to the total fracture toughness can be calculated based on Equation (7) mentioned earlier. As shown in Table 1, significantly, the proportion of extrinsic contribution is very small. That indicates the extrinsic contribution has a limited impact on the total fracture toughness. On the contrary, the intrinsic contribution plays a more important role due to a larger proportion in the total fracture toughness. Meanwhile, as shown in Fig. 9, the tortuosity of the propagation path decreases, which is attributed to the decline of strength of lamellar a when the temperature increases. Hence, the influence of path selections are weakened during the propagation, and the crack propagation paths are more flat at higher temperatures. In addition, it can be found from Table 1 and Fig. 9, the crack propagation path at room temperature is the most tortuous in the four temperatures. However, the fracture toughness K1C does not be greatly improved. Although the rougher surface of the CT sample is supposed to achieve higher fracture toughness. That is because the crack consumes more energy during the propagation leading to the increase of crack propagation resistance [22]. Nevertheless, the small proportion reduces the impact of extrinsic contribution to the total fracture toughness. A common rule is that the increasing temperature results in the aggravation of bluntness at the crack tip, which causes the specific gravity of intrinsic contribution increasing with temperature. Overall, the intrinsic contribution is the primary reason leading to such obvious
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Table 1 The tortuosity of the crack propagation path and the percentage of contribution under four temperatures. Temperature conditions
RT
200 C
400 C
600 C
l(ε)/l(0) Extrinsic fracture toughness (MPa m1/2) Percentage of extrinsic contribution(%)
1.25 4.29 10.72
1.20 5.69 8.65
1.18 5.33 7.46
1.16 4.43 7.08
difference between the fracture toughness K1C in different temperature tests. The crack tip plastic zone is a major factor of steady state propagation of crack, which consumes and absorbs the crack tip plastic work and increases the resistance to the propagation of the crack. Therefore, to investigate the intrinsic fracture toughness contribution under the four different temperature conditions, it is necessary to investigate the area of the crack tip plastic zone. A larger plastic zone of the material is better for consuming the plastic deformation work, and the fracture toughness will be improved. B.S.S.Chandra Rao et al. found the fracture behaviour was attributed to the nature of stress field ahead of the crack tip as well as the change in the fracture mechanisms [23]. Various methods have been studied on the size and shape of the plastic zone around a crack tip. P. Zhu et al. suggested a useful method for quantitatively evaluating the shield effect of the plastic zone [24]. Youping Zheng et al. proposed a method to assess the area of the crack tip plastic zone. In Zheng's research, Equation (9) has been made to establish the relationship between KIC and the l which is a parameter of the plastic zone around the crack tip [25]. Fig. 10 shows the schematic diagram of the plastic zone ahead of the crack tip.
K1C
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lpEAV ¼ 4 1 n2 Rpath
(9)
Where l is the long axis of the crack tip plastic zone. The Equation above can be changed as:
l¼
4 1 n2 Rpath 2 K 1C pEAV
Fig. 9. The crack propagation paths of four temperature after image processing. (a) room temperature. (b) 200 C. (c) 400 C. (d) 600 C.
(10)
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assessment of strain distribution around the crack tip is crucial in determination of fracture resistance [6]. Zhongping Zhang et al. [28] have studied on the relationship between the strain-hardening exponent and strength coefficient. According to his research, strain-hardening exponent of several alloys based the method can be calculated conveniently. It provides results that are better than those using the traditional approach through Euqation(11).
!
s*2
Fig. 10. The schematic diagram of the plastic zone ahead of the crack tip.
With using the parameter l, the area of the plastic zone around the crack tip can be estimated, and the results of calculated l under different temperatures are shown in Table 2. As shown in Table 2, there is a significant difference among the areas of the near-tip plastic field in different temperatures. It is notable that the area of plastic zone around crack tip increases as the temperature increases from room temperature to 400 C but decreases at the 600 C. This is consistent with the tendency of KIC which is measured by the experiment. The result indicates that the fracture toughness KIC is mainly affected by the area of the crack tip around the plastic zone. With the increase of temperature, the area of the plastic zone around the crack tip increases remarkably, and it would consume and absorb more crack tip plasticity work, which causes a certain bluntness of the crack tip. Therefore, the crack under high temperature condition is harder to propagate compared with that under low temperature. The resistance greatly increases, which makes the fracture toughness increase significantly. It is reasonable that the fracture toughness is increasing at the temperature range from RT to 400 C. It is notable that the KIC as well as the area of the plastic zone around crack tip both reduce at 600 C. Some investigations have been done to explain the reduction on the basis of the occurrence of dynamic strain aging(DSA) [26]. The interaction of mobile dislocations with interstitial elements can cause the DSA. Such interstitial elements can be O, C and N as well as substituted solutes such as Si. However, the interstitial element is the primary cause of DSA [27]. The presence of DSA causes the reduction of the crack tip plastic area, which makes a negative effect on the absorption of the crack tip plastic work. Therefore, the crack propagation resistance is significantly weakened which contributes to the reduction of fracture toughness at 600 C.
log s0:2f sb n¼ 2 log 500εf
(11)
where sf is the fracture strength and εf is the fracture ductility, s0.2 is the yield strength and sb is the ultimate tensile strength. The fracture strength of brittle materials can be directly replaced by the ultimate tensile strength, while the fracture strength and ultimate tensile strength of plastic materials cannot be directly equivalent due to the occurrence of necking. An empirical formula can be used to substitute sf,
sf ¼ sb ð1 þ fÞ
(12)
where 4 is the reduction of area. Due to the appearance of necking, the formula can not be able to accurately predict sf. In order to get a more accurate formula for prediction, it is necessary to make a modify of the calculation of Equation (12). Stress in the neck region can be modified by Bridgeman correction formula [29]:
s*f ¼
s
f 2R a 1 þ a ln 1 þ 2R
(13)
where s* is the fracture stress after correction, R is the curvature radius of the neckline contour, and ɑ is the minimum crosssectional area radius of the necking region. Taking the calculation result sf of Equation (12) into the Equation (13), a more reliable stress sf* can be obtained. Hahn and Rosenfield et al. proposed a method to calculate KIC in a convenient way, and mechanical properties were taken into consideration to establish a relationship between the fracture toughness and linear strain distribution in the plastic zone, the Equation is as follow:
1=2 KIC ¼ 2Es0:2 þ ε*f þ l
(14)
3.3. A prediction model of fracture toughness Based on the analysis above, it can be drawn that the intrinsic fracture toughness contribution will greatly affect the total toughness. While the crack tip plastic zone as a primary factor affecting the intrinsic fracture toughness is related to the nature of the material. Thus, tensile properties should be taken into consideration to establish a prediction model of fracture toughness. Moreover, work hardening exponent n has been suggested to be a factor which makes a great effect on fracture toughness [27]. In addition, the
Table 2 Calculated l of the plastic zone around crack tip under different temperature conditions. Temperature conditions
RT
200 C
400 C
600 C
l (mm) KIC (MPa m1/2)
0.276 40
0.886 65.75
1.0831 71.45
0.826 62.55
where εf* is the fracture strain of the crack tip, and l is the length of the crack tip plastic zone mentioned before. Based on the measurement of the length of the plastic zone, they reported that l is proportional to n2 [30]. Hidetoshi Somekawa et al. established a relationship between the plane-strain fracture toughness K1C and the value of strain distribution in the plastic zone based on the Equation (14). They found that the fracture toughness can be well represented by a single line by using the relation of n(s0.2 εf)1/2. On this basis, using the method mentioned before to replace the n in the relation of n(s0.2 εf)1/2, a relationship that considers more influence of the tensile properties was established in the present work [31]. The calculation result is shown in Table 3, and the relationship is described in Fig. 11. From the observation of the result above, higher value of n(s0.2 εf)1/2 obtain higher fracture toughness. It can be concluded that the value of n(s0.2 εf)1/2 is of great significance in determination of fracture toughness.
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Table 3 Calculation results and experimental measured K1C. Temperature conditions
sb(MPa)
sf*(MPa)
n
n(s0.2 εf)1/2(MPa1/2)
K1C (MPa m1/2)
RT 200 C 400 C 600 C
999.3 880 738.3 681.7
1056.6 933.8 785.5 728.5
2.5 102 3.8 102 4.1 102 3.9 102
2.6 101 3.6 101 4.1 101 3.4 101
40 65.75 71.45 62.55
hardening exponent, and closely related to the strain distribution in the crack tip (see Table 4). 4. Conclusion
Fig. 11. The fitting curve of the relationship between fracture toughness and strain distribution in the plastic zone.
Table 4 Experimental measured K1Cexp and predicted K1Cpre. K1C 1/2
K1Cexp(MPa m ) K1Cpre(MPa m1/2) Error(jK1Cexp-K1Cprej)
RT
200 C
400 C
600 C
40 40.8 0.8
65.75 62.8 2.95
71.45 73.8 2.35
62.55 58.4 4.15
In order to analyze the influence of intrinsic fracture toughness in a scientific way, the fitting result can be expressed as a mathematical model as follow:
s2*
!
11 log s0:2f sb pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K1C pre ¼ s0:2 εf þ 16:4 log 500εf
1. With the experimental temperature increased, the predominant fracture mechanism changed from quasi-cleavage fracture to ductile fracture. The fracture surface at room temperature appears as some small facts and smooth fracture characteristic. However, in the case of higher temperatures, the fracture surfaces exhibits bigger dimples and more tearing ridges. 2. Path sections of crack propagation in microscale have diverse influences on the tortuosity. In order to reduce the resistance during the propagation, the crack changes the expand direction whenever necessary. Through the SEM observation, the path selections of propagation can be summarized as: cut through lamellar a, parallel with the lamellar ap, bypass the equiaxed ap and cut through the equiaxed ap. 3. The influence of temperature on fracture toughness K1C of Ti60 alloy was investigated in two aspects. The extrinsic contribution has a limited impact on the total fracture toughness. While the intrinsic contribution is the main factor affecting the fracture toughness as the temperature increases. 4. The contribution of intrinsic fracture toughness is greatly affected by the area of crack tip plastic zone. The calculation results have a consistent tendency with K1C, which indicates that the fracture toughness K1C increases with the growth of the area at the plastic zone tip. In other words, the change in the area of the plastic zone will lead to difference K1C values. 5. A prediction model is well established which based on tensile properties. The prediction result is in a good agreement with the experimental result, and the error of the model is very small. That means the model is useful in predicting the fracture toughness of Ti60 alloy at different test temperatures. Acknowledgement
(15)
To ensure reliable analysis results, verification of the model is necessary. The verification result is shown in Table 4. K1Cexp represents the experimental measured result, and K1Cpre means the predicted result from the model mentioned above. The error between the prediction result and the experimental value is less than 5%. Thus, the results of the prediction model are acceptable and have good accuracy. Based on the analysis above, it can be concluded that the fracture toughness K1C of Ti60 alloy is strongly affected by the intrinsic factors, which is more related to the plastic zone in the crack tip. Meanwhile, a larger area of plastic zone can absorb more crack tip plastic work. Therefore, it can withstand greater stress in the plastic zone. Furthermore, the plastic zone of crack tip plays an important role in the intrinsic factors of the fracture toughness, which is affected by the properties of the material itself. The present result proved that the fracture toughness of Ti60 alloy is sensitive to the yield strength, elongation, strain
The authors would like to acknowledge the financial supports from the Program of National Key Research and Development Plan of China (NO. 2016YFB0301203). In addition, this work was supported by China Postdoctoral Science Foundation (2019M653727) and the Fundamental Research Funds for the Central Universities (3102019TS0404). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
Jalaj Kumar, B. Srivathsa, V. Kumar, Mater. Des. 30 (2009) 1118e1123. I. Balasundar, T. Raghu, Mater. Sci. Eng. A 706 (2017) 104e114. I. Gurappa, J. Mater. Sci. Lett. 22 (2003) 771e774. H.J. Rack, J.I. Qazi, Mater. Sci. Eng. C 26 (2006) 1269e1277. R. Filip, K. Kubiak, W. Ziaja, J. Sieniawski, J. Mater. Process. Technol. 133 (2003) 84e89. G. Lütjering, et al., Mater. Sci. Eng. A 468e470 (2007) 201e209. M.E. Launey, R.O. Ritchie, Adv. Mater. 21 (2009) 2103e2110. I. Cvijovic-Alagic, N. Gubeljak, M. Rakin, Z. Cvijovic, et al., Mater. Des. 53 (2014) 870e880. T. Mitao, S. Isawa, S. Tsuyama, Scripta. Metall. Mater. 26 (1992) 1405e1410. P. Davies, R. Pederson, M. Coleman, Acta Mater. 117 (2016) 51e67. W.J. Jia, W.D. Zeng, Y.G. Zhou, Mater. Sci. Eng. A 528 (2011) 4068e4074.
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[12] Y.P. Zheng, W.D. Zeng, D. Li, et al., J. Alloy. Comp. 797 (2019) 1402e1414. [13] X.H. Shi, W.D. Zeng, C.L. Shi, H.J. Wang, Z.Q. Jia, Mater. Sci. Eng. A 621 (2015) 143e148. [14] B.S.S. Chandra Rao, M. Srinivas, S.V. Kamat, Mater. Sci. Eng. A 520 (2009) 29e35. [15] P. Zhu, L. Yang, Z. Li, J. Sun, Int. J. Fract. 161 (2010) 131e139. [16] N. Singh, V. Singh, Mater. Sci. Eng. A 485 (2008) 130e139. [17] M. Niinomi, T. Kobayashi, Mater. Sci. Eng. Mater. Sci. Eng. A 213 (1996) 16e24. [18] Y.I. Ragozin, Y.Y. Antonov, Strength Mater. 16 (1984) 179e184. [19] A.A. Griffith, Containing Papers of a Mathematical or Physical Character, 221, 1921, pp. 163e198. [20] N.A. Makhutov, Y.G. Matvienko, S.V. Chernyakov, Mater. Sci. 29 (1993) 109e114. [21] Y.I. Ragozin, Y.Y. Antonov, Strength Mater. 16 (1984) 179e184.
[22] Y.P. Zheng, W.D. Zeng, D. Li, Q.Y. Zhao, et al., J. Alloy. Comp. 709 (2017) 511e518. [23] B.S.S. Chandra Rao, M. Srinivas, S.V. Kamat, Metall. Mater. Trans. A 39 (2008) 1340e1349. [24] W.W. Peng, W.D. Zeng, Y.W. Zhang, C.L. Shi, et al., J. Alloy. Comp. 577 (2013) 633e642. [25] Y.P. Zheng, in: Degree of Doctor of Philosophy, NPU University, 2019. [26] Gunawarman, M. Niinomi, K. Fukunaga, D. Eylon, et al., Sci. Eng. A 308 (2001) 216e224. [27] J.O. Peters, G. Lütjering, Metall. Mater. Trans. A 32 (2001) 2805e2818. [28] Z.P. Zhang, W. Zhao, Q. Sun, C. Li, J. Mater. Eng. Perform. 15 (2006) 19e22. [29] I. Rohr, H. Nahme, K. Thoma, Int. J. Impact Eng. 31 (2005) 401e433. [30] G.T. Hahn, A.R. Rosenfield, ASTM STP, 1968. [31] H. Somekawa, T. Mukai, Scr. Mater. 53 (2005) 1059e1064.
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The analysis of fracture toughness and fracture mechanism of Ti60 alloy under different temperatures Runchen Jia a, b, c, Weidong Zeng a, b, c, *, Shengtong He a, b, c, Xiongxiong Gao a, b, c, Jianwei Xu a, b, c a
State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an, 710072, China Defense Technologies Innovation Center of Precision Forging and Ring Rolling, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an, 710072, China c Shaanxi Key Laboratory of High-Performance Precision Forming Technology and Equipment, Northwestern Polytechnical University, Xi'an, 710072, PR China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 6 June 2019 Received in revised form 13 August 2019 Accepted 15 August 2019 Available online 19 August 2019
Fracture toughness and fracture mechanism of Ti60 alloy with duplex microstructure under different temperature conditions were investigated in the present work. The experimental result shows that the fracture toughness of CT samples increases from the room temperature (40 MPa m1/2) to 400 C (71.45 MPa m1/2) but declines at 600 C (62.55 MPa m1/2). It is observed from fracture surface through SEM that the predominant fracture mechanism has changed from quasi-cleavage fracture at room temperature to ductile fracture at higher temperatures. In addition, the tortuosity of crack propagation path has a limited impact on the fracture toughness. Path selections for crack propagation are obtained through SEM observation which can be summarized as: cut through lamellar a, parallel to lamellar a, bypass the equiaxed ap and cut through the equiaxed ap. Moreover, it is found that the intrinsic contribution is the primary reason leading to the change of the fracture toughness of Ti60 alloy under different temperatures. Meanwhile, it is noteworthy that the area of the crack tip plastic zone increases from RT to 400 C but decreases at 600 C, which is seen as the main impact of temperature on fracture toughness. To be exact, the CT sample with a larger area of the plastic zone could provide a higher K1C value. Furthermore, a prediction model of K1C based on tensile properties is established, which has a good accuracy with experimental results. The model is useful in predicting the fracture toughness of Ti60 alloy at different test temperatures. © 2019 Elsevier B.V. All rights reserved.
Keywords: Ti60 alloys Duplex microstructure Fracture toughness Crack propagation paths Fracture mechanisms
1. Introduction The new generation of high performance aircraft put forward higher requirements for engine service temperature, while fracture toughness is an important design criterion which should be taken into consideration in order to obtain long life safe flight [1e3]. Ti60 titanium alloy, a promising near-a titanium alloy, can serve under high temperature over a long period of time, which makes it an important candidate material for manufacturing the integral impeller of high push-weight ratio engine compressor. After several
* Corresponding author. State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi'an, 710072, China. E-mail addresses: [email protected] (R. Jia), [email protected] (W. Zeng). https://doi.org/10.1016/j.jallcom.2019.151899 0925-8388/© 2019 Elsevier B.V. All rights reserved.
thermomechanical processing, Ti60 titanium alloy acquires a classical duplex microstructure with equiaxed ap as well as lamellar a. The equiaxed ap with excellent deformation coordination exhibits better ductility and high cycle fatigue properties, while the lamellar a with excellent crack propagation resistance exhibits better creep and fatigue properties. Many investigations about fracture toughness have been done on the impact caused by microstructural morphology [4e6]. However, the effects of temperature on the fracture toughness and fracture mechanism of Ti60 alloy have not been systematically studied. According to G.Lütjering et al., the fracture toughness of the material came from two common contributions: on the one hand, the contribution of the intrinsic fracture toughness usually related to the intrinsic properties of the material; and on the other hand, the contribution of crack tip geometry [7]. Ritchie et al. studied the fracture toughness of advanced material, the result
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demonstrated that the total fracture toughness was affected by two main classes of toughening. The intrinsic toughening mechanism which was an inherent property of the material, and the extrinsic mechanism depended on the crack size and specimen geometry which can be directly reflected in the degree of tortousity of the crack growth path [8]. Therefore, some researchers have studied the relationship between fracture toughness and crack tip tortuosity. I.Cvijovic-Alagic et al. found that the small aspect ratio of a phase contributed to the decrease of the propagation resistance [6]. The enhanced crack propagation resistance was correlated with the larger propensity for crack tip tortousity. Since the crack propagation was hindered by the strong resistance in front, it was forced to change propagation direction and consumed more energy. Thus, more resistance during the crack propagation process makes the material provide higher fracture toughness [9]. The fracture toughness is a critical parameter in damagetolerant design concept, which has an important investigation significance. However, there is no clear conclusion about the effect of the temperature on fracture toughness of Ti60 alloy. In this paper, the impact of temperature on fracture toughness was systematically investigated. The tensile properties and fracture mechanism were also studied through tests. At last, a prediction model of fracture toughness based on tensile properties was established with a good accuracy according to the experimental result.
After heat treatment, the standard tensile samples were machined from the bar samples. Tensile tests were performed at an initial rate of 1 103 s1at room temperature, 200 C, 400 C and 600 C respectively. Gauge dimensions of the tensile specimens are 5 mm in diameter and 35 mm in length, which were shown in Fig. 2. The tensile properties were evaluated at each temperature condition. Finally, optical microscopy (OM) was employed to observe the microstructural morphology of different conditions. Plane-strain fracture toughness tests were carried out on the standard compact tension (CT) samples of four groups under different temperature conditions. Before the tests, each CT sample was inserted a fatigue pre-crack using MTS810 fatigue testing machine. The loading frequency was 12 Hz, and the crack was measured by a 30 reading microscope with a resolution of 0.01 mm. Thus, the pre-crack length could be controlled in less than 2 mm. The dimensions of the CT samples is 63 60 25(mm), and the schematic sample is illustrated in Fig. 2. In addition, the precrack direction is perpendicular to the tensile loading direction of tensile sample, which is also shown in Fig. 2. The fracture surfaces and the crack propagation path were observed by scanning electron microscopy(SEM). 3. Results and discussion 3.1. Tensile properties
2. Experimental procedure The material with duplex microstructure used in the present study was obtained through ingot casting with a bar form. The microstructure analyses of the materials were conducted with Olympus GPM-G3 optical microscopy (OM) and S-4800 scanning electron microscope (SEM). Fig. 1 shows the typical microstructure with equiaxed ap as well as lamellar a of Ti60 alloy. Several pictures of the microstructure were obtained through the SEM observation, the volume fractions and microstructural sizes were measured by utilizing the professional software Image Pro Plus 6.0 (IPP 6.0). To ensure the statistical accuracy, at least 3 pictures of microstructure at different areas were used in the measurement process. The measurement result shows that the volume fraction of equiaxed ap is about 15% with the average size of 20 mm. The average length of lamellar a is 15 mm, and the average width of the lamellar a is 2 mm. In addition, the large lamellar a has the width greater than 5 mm.
Fig. 1. The typical duplex microstructure with equiaxed ap as well as lamellar a of Ti60 alloy.
As shown in Fig. 3, tensile properties of samples at the temperature ranging from room temperature to 600 Cwere investigated including yield strength, ultimate tensile strength, elongation and reduction of area for Ti60 alloy. The result shows that the yield strength and ultimate tensile strength of Ti60 alloy decreases with the increase of the temperature. However, the elongation and reduction of area show a reverse changing tendency with the strength. The experimental results are according to the previous investigation [10]. This phenomenon can be explained by the activated process [11]. Because high temperature will alleviate the dislocation pile-up and more slip systems cloud be activated. Thus, the deformation ability and ductility are improved. 3.2. Fracture toughness and fracture mechanisms The fracture toughness of the four CT samples after tests are shown in Fig. 4. It can be found that the sample at 400 C has the highest fracture toughness up to 71.45 MPa m1. The tendency of fracture toughness increases from RT to 400 C, but declines at 600 C. As shown in Fig. 4, the crack propagation path was divided into three areas. Firstly the expansion zone of the pre-crack, followed by the crack stable expansion zone, and finally the rapid expansion zone of the crack, which have been marked out with yellow curves in Fig. 4. The colors on the samples are related to the colored titanium oxides. It is well known that the main titanium oxides are TiO2, TiO, Ti2O3 and Ti3O5. The colors of TiO2 and TiO were white and golden tinted, respectively. And Ti2O3 and Ti3O5 appear bule and dark violet, respectively. Before fracture toughness, the oxide at the pre-crack expansion zone on the sample surface was TiO2. The CT sample in RT condition had less time to react with oxygen, so there was no obvious distinction can be seen on the sample surface. However, after fracture toughness tests, the CT samples were exposed in higher temperature. On this basis, the volume fraction of TiO was increasing because of the increasing oxidation temperature. Thus, the color on the sample surface changed from light yellow to golden yellow. It is noteworthy that the color of the pre-crack propagation expansion at 600 C is blue. That can be explained by the presence of the oxidation production Ti2O3. In addition, the color on each sample surface is different
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Fig. 2. Schematic specimen and dimensions of the CT and tensile samples.
Fig. 3. Tensile properties and fracture toughness of Ti60 alloy under different temperatures.
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Fig. 4. The CT samples under temperature conditions of (a) room temperature, (b) 200 C, (c) 400 C and (d) 600 C.
because the diverse oxidation production with different oxidation reaction time. On the whole, the oxidation phenomenon in precrack expansion zones were more seriously. Except the fracture surface under room temperature breaks rapidly which has less oxidation reaction time with the air, obvious boundary between stable expansion zone and rapid expansion zone can be observed on the surface of the other three samples. Significant distinction is observed from the stable extension zone and unstable expansion zone of different CT samples. The sample with lager stable expansion zone could provide a relatively higher KIC value. As shown in Fig. 5, compared with the fracture surfaces at the stable expansion zone under higher test temperatures, the fracture morphology of room temperature appears with plenty mini facets, which is a feature of quasi-cleavage. However, with the temperature increasing to 200 C, shallow dimples can be observed on the
fracture surface, which shows the ductile fracture characteristic. At the test temperature of 400 C, dimples on the fracture surface become deeper and larger. When the temperature condition comes to 600 C, the size of dimples becomes larger than that in the other temperatures. Fig. 6 shows the micro fracture surface at stable expansion zone of different samples in higher magnifications. Fig. 6(a) exhibits the fracture in consistent direction with less dimples and tearing ridges, which is a quasi-cleavage feature. This is because the CT sample in room temperature do not have sufficient deformation coordination ability on account of low plasticity, the crack gives priority to propagate along a certain cleavage plane [12]. Thus, the crack propagates more easily with small resistance. In addition, the main crack changes direction as it propagates and the secondary crack is easy to be formed at a boundary, which is marked out with
Fig. 5. Fracture surface under different temperature conditions in 100 magnification. (a) room temperature, (b) 200 C, (c) 400 C and (d) 600 C.
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Fig. 6. Micro fracture surfaces of different temperature conditions samples in different magnifications. (a) room temperature. (b) 200 C. (c) 400 C. (d) 600 C. The magnification of (a) is 1000 . The magnification of (b), (c) and (d) is 500 .
red circles in Fig. 6(a). At a higher temperature of 200 C, as shown in Fig. 6(b), except for the number of the dimples on the fracture surface increases, the phenomenon of fracture in consistent direction within a small area almost disappears. This is because the amount of movable slip systems increases as the temperature increases. In this case, most grains could deform harmoniously, the possibility of crack origination declines and the crack propagation resistance enhances. Hence, just some isolated lamellar a are left on the fracture surface because of relatively difficult-to-deform orientation. As shown in Fig. 6(c), more tearing ridges have appeared on the fracture surface especially in the lamellar a as experimental temperature increases. And tearing ridges could improve the extrinsic resistance of fracture toughness. That means the more tearing ridges appear, and the greater the fracture toughness of the material will be obtained. However, when the temperature condition comes to 600 C, as shown in Fig. 6(d), it is obvious that the dimples become bigger and wider, which is a feature of ductile fracture. Besides, the morphology of lamellar a on the fracture surface has disappeared. That is because in the higher temperature, more slip systems can be actuated and the plasticity is greatly improved. The fracture mechanism under different temperatures is analyzed on the basis of fracture features observed on the fracture surfaces. As mentioned before, fracture toughness is influenced by the tortuosity of the crack propagation path. Thus, the crack propagation path selections through various microstructures are observed using SEM. Fig. 7 shows a more intuitive representation of the relationship between the fracture surface and the microstructure. As shown in Fig. 7(a), the crack propagation path cuts through lamellar a, and it is noteworthy that the direction of the crack propagation is deflected with the different angles of lamellar colonies. The long and thick a platelets promote tortuosity during the main crack propagation process, which can obviously improve the crack growth resistance [13]. Fig. 7(b) shows an almost parallel propagation path with lamellar a boundaries. This phenomenon is attributed to fairly low resistance at the lamellar boundaries, so that crack propagates by interlamellar fracture and changes propagation direction when crossing the colony [6]. Fig. 7(c) shows a
propagation of bypassing the equiaxed ap, which indicates that equiaxed ap boundaries become obstacles to propagation. In this case, the bigger size of equiaxed ap is favourable to improve the crack tip plasticity [14]. The path around the equiaxed ap shows a bulge on the fracture surface. Compared with bypassing the equiaxed ap to expand, crack in Fig. 7(d) shows a completely different way. The crack expands without changing its direction in the propagation process, and leaves an almost linear path on the fracture surface resulting a decrease of fracture toughness [15,16]. From the analysis above, an inference is that path selections during crack propagation in microscale have a great effect on the tortuosity. While, it remains unsufficient to well explain the impact of tortuosity on fracture toughness. Therefore, a more systematic method is in demand to conduct a further investigation. As mentioned above, the fracture toughness is a result of two main contributions: the intrinsic resistance to fracture is related to the properties of the material itself, the extrinsic resistance is reflected by the tortuousity of the crack propagation. In order to determine the percentage of intrinsic fracture contribution and extrinsic fracture contribution at various temperature conditions, a calculation method that takes both intrinsic fracture toughness and extrinsic fracture toughness into account is needed. Through this way, the intrinsic contribution and extrinsic contribution to overall fracture toughness under different temperature conditions can be well examined, which is beneficial for further investigation. According to the theory of linear elastic fracture mechanics, Equation (1) is established [17].
rffiffiffiffiffiffiffiffiffiffiffiffiffi G1C ,E 1 v2
K1C z
(1)
where KIC is the plane strain fracture toughness, GIC is the critical strain energy release rate, E is the elastic modulus, and n is the Poisson's ratio. According to Griffith's theory [18], the critical strain energy release rate of linear elastic materials can be obtained from the following equation:
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Fig. 7. Correspondence between the fracture surface and microstructure as well as the path selections for crack propagation. (a) cut through lameller a; (b) parallel with lameller a; (c) bypass the equiaxed ap; (d) cut through equiaxed ap.
G1C ¼ 2gS
(2)
where Ys represents the surface energy per square meter. Equation (2) means that the crack propagates unsteadily inside the material only when the strain energy release rate of the material exceeds 2Ys. However, metallic deformation includes not only elastic part but also plastic part. Yp is the energy consumed in plastic deformation of crack surfaces. For structural metallic materials, the value of Yp is much higher than the surface energy density Ys. Therefore, in the fracture mechanics of most metallic materials, the modified Griffith-Orowan-Irwin [19] formula is used to approximate its critical strain energy release rate, as shown in Equation (3).
G1C ¼ 2 gs þ gp ¼ 2geff
AV ¼ (3)
Equation (3) is usually applied to plastic metallic materials where Yp is significantly considerable. Ragozin et al. [20]have established the relation between the specific work of uniform deformation AV and the effective surface energy Yeff as:
AV , V ¼ 2geff ,F
(4)
where V is the volume responsible for fracture and F is the area of surface for crack forming. The specific work of uniform deformation AV can be determined from the Equation (5) [21],
V ¼ h,lðεÞ
Fig. 8. Schematic diagram of real length l(ε) and linear length l(0).
(5)
where h is the height of the crack tip plastic zone, As shown in Fig. 8, l(ε) is the real length of crack propagation path. Thus, Equation (3) can be changed as:
s 2 εf Ey sy 2sb 3
þ
s2y 2E
(6)
where εf is the fracture ductility, sy is the yield stress, sb is the ultimate tensile strength. The volume caused by fracture can be changed into:
G1C ¼ AV ,V ¼ AV ,lðεÞ ,h
(7)
After substituting Equation (7) into Equation (1), the result is
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E,AV ,h,lð0Þ lðεÞ E,AV ,h,lð0Þ qffiffiffiffiffiffiffiffiffiffiffi ¼ K1C ¼ , , Rpath 2 l 1n 1 n2 ð0Þ
(8)
where l(0) is linear length of the crack propagation path. The ratio of l(ε) to l(0) can be seen as the tortuosity degree of the crack propagation path, which is represented by Rpath. The relationship is well established between the tortuosity of crack propagation path and fracture toughness through this method. Thus, the percentage of the extrinsic contribution of fracture toughness can be easily
R. Jia et al. / Journal of Alloys and Compounds 810 (2019) 151899
obtained if the l(ε)/l(0) is available. In the present work, a method is introduced to calculate l(ε)/l(0). The crack propagation paths of four temperature conditions after image processing are shown in Fig. 9. The professional image processing software Image Pro Plus 6.0 (IPP 6.0) is applied to calculate the crack propagation path tortuosity Rpath of CT samples at four different temperatures, which can extract the crack propagation path of the fracture toughness specimens. In addition, the length of the real path of crack propagation l(ε) and the length of linear path of crack propagation l(0) are measured by the IPP 6.0 software. The tortuosity can be obtained from the calculation of ratio l(ε) to l(0). In order to acquire accurate statistics, it is necessary to conduct the measurement progress with three times, and take the average value of them as the ultimate result, which are shown in Table 1. Given the ratio of l(ε) to l(0), the contribution of extrinsic fracture toughness to the total fracture toughness can be calculated based on Equation (7) mentioned earlier. As shown in Table 1, significantly, the proportion of extrinsic contribution is very small. That indicates the extrinsic contribution has a limited impact on the total fracture toughness. On the contrary, the intrinsic contribution plays a more important role due to a larger proportion in the total fracture toughness. Meanwhile, as shown in Fig. 9, the tortuosity of the propagation path decreases, which is attributed to the decline of strength of lamellar a when the temperature increases. Hence, the influence of path selections are weakened during the propagation, and the crack propagation paths are more flat at higher temperatures. In addition, it can be found from Table 1 and Fig. 9, the crack propagation path at room temperature is the most tortuous in the four temperatures. However, the fracture toughness K1C does not be greatly improved. Although the rougher surface of the CT sample is supposed to achieve higher fracture toughness. That is because the crack consumes more energy during the propagation leading to the increase of crack propagation resistance [22]. Nevertheless, the small proportion reduces the impact of extrinsic contribution to the total fracture toughness. A common rule is that the increasing temperature results in the aggravation of bluntness at the crack tip, which causes the specific gravity of intrinsic contribution increasing with temperature. Overall, the intrinsic contribution is the primary reason leading to such obvious
7
Table 1 The tortuosity of the crack propagation path and the percentage of contribution under four temperatures. Temperature conditions
RT
200 C
400 C
600 C
l(ε)/l(0) Extrinsic fracture toughness (MPa m1/2) Percentage of extrinsic contribution(%)
1.25 4.29 10.72
1.20 5.69 8.65
1.18 5.33 7.46
1.16 4.43 7.08
difference between the fracture toughness K1C in different temperature tests. The crack tip plastic zone is a major factor of steady state propagation of crack, which consumes and absorbs the crack tip plastic work and increases the resistance to the propagation of the crack. Therefore, to investigate the intrinsic fracture toughness contribution under the four different temperature conditions, it is necessary to investigate the area of the crack tip plastic zone. A larger plastic zone of the material is better for consuming the plastic deformation work, and the fracture toughness will be improved. B.S.S.Chandra Rao et al. found the fracture behaviour was attributed to the nature of stress field ahead of the crack tip as well as the change in the fracture mechanisms [23]. Various methods have been studied on the size and shape of the plastic zone around a crack tip. P. Zhu et al. suggested a useful method for quantitatively evaluating the shield effect of the plastic zone [24]. Youping Zheng et al. proposed a method to assess the area of the crack tip plastic zone. In Zheng's research, Equation (9) has been made to establish the relationship between KIC and the l which is a parameter of the plastic zone around the crack tip [25]. Fig. 10 shows the schematic diagram of the plastic zone ahead of the crack tip.
K1C
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lpEAV ¼ 4 1 n2 Rpath
(9)
Where l is the long axis of the crack tip plastic zone. The Equation above can be changed as:
l¼
4 1 n2 Rpath 2 K 1C pEAV
Fig. 9. The crack propagation paths of four temperature after image processing. (a) room temperature. (b) 200 C. (c) 400 C. (d) 600 C.
(10)
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assessment of strain distribution around the crack tip is crucial in determination of fracture resistance [6]. Zhongping Zhang et al. [28] have studied on the relationship between the strain-hardening exponent and strength coefficient. According to his research, strain-hardening exponent of several alloys based the method can be calculated conveniently. It provides results that are better than those using the traditional approach through Euqation(11).
!
s*2
Fig. 10. The schematic diagram of the plastic zone ahead of the crack tip.
With using the parameter l, the area of the plastic zone around the crack tip can be estimated, and the results of calculated l under different temperatures are shown in Table 2. As shown in Table 2, there is a significant difference among the areas of the near-tip plastic field in different temperatures. It is notable that the area of plastic zone around crack tip increases as the temperature increases from room temperature to 400 C but decreases at the 600 C. This is consistent with the tendency of KIC which is measured by the experiment. The result indicates that the fracture toughness KIC is mainly affected by the area of the crack tip around the plastic zone. With the increase of temperature, the area of the plastic zone around the crack tip increases remarkably, and it would consume and absorb more crack tip plasticity work, which causes a certain bluntness of the crack tip. Therefore, the crack under high temperature condition is harder to propagate compared with that under low temperature. The resistance greatly increases, which makes the fracture toughness increase significantly. It is reasonable that the fracture toughness is increasing at the temperature range from RT to 400 C. It is notable that the KIC as well as the area of the plastic zone around crack tip both reduce at 600 C. Some investigations have been done to explain the reduction on the basis of the occurrence of dynamic strain aging(DSA) [26]. The interaction of mobile dislocations with interstitial elements can cause the DSA. Such interstitial elements can be O, C and N as well as substituted solutes such as Si. However, the interstitial element is the primary cause of DSA [27]. The presence of DSA causes the reduction of the crack tip plastic area, which makes a negative effect on the absorption of the crack tip plastic work. Therefore, the crack propagation resistance is significantly weakened which contributes to the reduction of fracture toughness at 600 C.
log s0:2f sb n¼ 2 log 500εf
(11)
where sf is the fracture strength and εf is the fracture ductility, s0.2 is the yield strength and sb is the ultimate tensile strength. The fracture strength of brittle materials can be directly replaced by the ultimate tensile strength, while the fracture strength and ultimate tensile strength of plastic materials cannot be directly equivalent due to the occurrence of necking. An empirical formula can be used to substitute sf,
sf ¼ sb ð1 þ fÞ
(12)
where 4 is the reduction of area. Due to the appearance of necking, the formula can not be able to accurately predict sf. In order to get a more accurate formula for prediction, it is necessary to make a modify of the calculation of Equation (12). Stress in the neck region can be modified by Bridgeman correction formula [29]:
s*f ¼
s
f 2R a 1 þ a ln 1 þ 2R
(13)
where s* is the fracture stress after correction, R is the curvature radius of the neckline contour, and ɑ is the minimum crosssectional area radius of the necking region. Taking the calculation result sf of Equation (12) into the Equation (13), a more reliable stress sf* can be obtained. Hahn and Rosenfield et al. proposed a method to calculate KIC in a convenient way, and mechanical properties were taken into consideration to establish a relationship between the fracture toughness and linear strain distribution in the plastic zone, the Equation is as follow:
1=2 KIC ¼ 2Es0:2 þ ε*f þ l
(14)
3.3. A prediction model of fracture toughness Based on the analysis above, it can be drawn that the intrinsic fracture toughness contribution will greatly affect the total toughness. While the crack tip plastic zone as a primary factor affecting the intrinsic fracture toughness is related to the nature of the material. Thus, tensile properties should be taken into consideration to establish a prediction model of fracture toughness. Moreover, work hardening exponent n has been suggested to be a factor which makes a great effect on fracture toughness [27]. In addition, the
Table 2 Calculated l of the plastic zone around crack tip under different temperature conditions. Temperature conditions
RT
200 C
400 C
600 C
l (mm) KIC (MPa m1/2)
0.276 40
0.886 65.75
1.0831 71.45
0.826 62.55
where εf* is the fracture strain of the crack tip, and l is the length of the crack tip plastic zone mentioned before. Based on the measurement of the length of the plastic zone, they reported that l is proportional to n2 [30]. Hidetoshi Somekawa et al. established a relationship between the plane-strain fracture toughness K1C and the value of strain distribution in the plastic zone based on the Equation (14). They found that the fracture toughness can be well represented by a single line by using the relation of n(s0.2 εf)1/2. On this basis, using the method mentioned before to replace the n in the relation of n(s0.2 εf)1/2, a relationship that considers more influence of the tensile properties was established in the present work [31]. The calculation result is shown in Table 3, and the relationship is described in Fig. 11. From the observation of the result above, higher value of n(s0.2 εf)1/2 obtain higher fracture toughness. It can be concluded that the value of n(s0.2 εf)1/2 is of great significance in determination of fracture toughness.
R. Jia et al. / Journal of Alloys and Compounds 810 (2019) 151899
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Table 3 Calculation results and experimental measured K1C. Temperature conditions
sb(MPa)
sf*(MPa)
n
n(s0.2 εf)1/2(MPa1/2)
K1C (MPa m1/2)
RT 200 C 400 C 600 C
999.3 880 738.3 681.7
1056.6 933.8 785.5 728.5
2.5 102 3.8 102 4.1 102 3.9 102
2.6 101 3.6 101 4.1 101 3.4 101
40 65.75 71.45 62.55
hardening exponent, and closely related to the strain distribution in the crack tip (see Table 4). 4. Conclusion
Fig. 11. The fitting curve of the relationship between fracture toughness and strain distribution in the plastic zone.
Table 4 Experimental measured K1Cexp and predicted K1Cpre. K1C 1/2
K1Cexp(MPa m ) K1Cpre(MPa m1/2) Error(jK1Cexp-K1Cprej)
RT
200 C
400 C
600 C
40 40.8 0.8
65.75 62.8 2.95
71.45 73.8 2.35
62.55 58.4 4.15
In order to analyze the influence of intrinsic fracture toughness in a scientific way, the fitting result can be expressed as a mathematical model as follow:
s2*
!
11 log s0:2f sb pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K1C pre ¼ s0:2 εf þ 16:4 log 500εf
1. With the experimental temperature increased, the predominant fracture mechanism changed from quasi-cleavage fracture to ductile fracture. The fracture surface at room temperature appears as some small facts and smooth fracture characteristic. However, in the case of higher temperatures, the fracture surfaces exhibits bigger dimples and more tearing ridges. 2. Path sections of crack propagation in microscale have diverse influences on the tortuosity. In order to reduce the resistance during the propagation, the crack changes the expand direction whenever necessary. Through the SEM observation, the path selections of propagation can be summarized as: cut through lamellar a, parallel with the lamellar ap, bypass the equiaxed ap and cut through the equiaxed ap. 3. The influence of temperature on fracture toughness K1C of Ti60 alloy was investigated in two aspects. The extrinsic contribution has a limited impact on the total fracture toughness. While the intrinsic contribution is the main factor affecting the fracture toughness as the temperature increases. 4. The contribution of intrinsic fracture toughness is greatly affected by the area of crack tip plastic zone. The calculation results have a consistent tendency with K1C, which indicates that the fracture toughness K1C increases with the growth of the area at the plastic zone tip. In other words, the change in the area of the plastic zone will lead to difference K1C values. 5. A prediction model is well established which based on tensile properties. The prediction result is in a good agreement with the experimental result, and the error of the model is very small. That means the model is useful in predicting the fracture toughness of Ti60 alloy at different test temperatures. Acknowledgement
(15)
To ensure reliable analysis results, verification of the model is necessary. The verification result is shown in Table 4. K1Cexp represents the experimental measured result, and K1Cpre means the predicted result from the model mentioned above. The error between the prediction result and the experimental value is less than 5%. Thus, the results of the prediction model are acceptable and have good accuracy. Based on the analysis above, it can be concluded that the fracture toughness K1C of Ti60 alloy is strongly affected by the intrinsic factors, which is more related to the plastic zone in the crack tip. Meanwhile, a larger area of plastic zone can absorb more crack tip plastic work. Therefore, it can withstand greater stress in the plastic zone. Furthermore, the plastic zone of crack tip plays an important role in the intrinsic factors of the fracture toughness, which is affected by the properties of the material itself. The present result proved that the fracture toughness of Ti60 alloy is sensitive to the yield strength, elongation, strain
The authors would like to acknowledge the financial supports from the Program of National Key Research and Development Plan of China (NO. 2016YFB0301203). In addition, this work was supported by China Postdoctoral Science Foundation (2019M653727) and the Fundamental Research Funds for the Central Universities (3102019TS0404). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
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