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Influence of lamellar orientation on fatigue crack propagation behavior in titanium aluminide TiAl
Materials Science and Engineering A243 (1998) 169 – 175
Influence of lamellar orientation on fatigue crack propagation behavior in titanium aluminide TiAl Hirohisa Shiota a,*, Keiro Tokaji a, Yasuhito Ohta b a
Department of Mechanical and Systems Engineering, Faculty of Engineering, Gifu Uni6ersity, 1 -1 Yanagido, Gifu 501 -11, Japan b Takeiri Factory, Yatomi-cho, Aichi 498, Japan
Abstract Fatigue crack propagation (FCP) behavior of a titanium aluminide (TiAl) with a nearly fully lamellar microstructure has been studied on two different FCP directions relative to the lamellar orientation; i.e. parallel (type A specimen) and perpendicular (type B specimen) to the lamellar orientation, at ambient temperature in laboratory air. It was found that the FCP resistance of the former was considerably lower than that of the latter. Close examinations of crack morphology revealed significant differences between the two FCP directions. In type A specimens, several cracks along lamellae were seen on the surfaces and sections of the specimens, thus uncracked ligaments were formed in the wake of the crack tip. On the contrary, such ligaments were scarcely produced in type B specimens because only the main crack could propagate without remarkable deflections and branching. The FCP rates of type A specimens were decreased gradually with crack extension under constant stress intensity factor range, DK, tests, suggesting the role of crack bridging by uncracked ligaments. Finite element method (FEM) analysis indicated considerably reduced DK experienced at the crack tip, thus the difference in FCP resistance between two FCP directions based on the actual DK at the crack tip after allowing for crack bridging became much larger than that based on the nominal or applied DK. © 1998 Elsevier Science S.A. Keywords: Fatigue crack propagation; Titanium aluminide; Lamellar microstructure; Orientation; Uncracked ligament; Bridging; Finite element method
1. Introduction g-Based titanium aluminides (TiAl) have recently received considerable interest as a structural material. Thus, extensive fundamental studies on the mechanical properties of these materials have been performed, and consequently, it has been indicated that the mechanical properties depended very strongly on microstructure [1]. There are three typical microstructures of TiAl, lamellar microstructure, equiaxed g microstructure and duplex microstructure. Of these microstructures, it has been reported that the lamellar microstructure displayed excellent fracture toughness [1 – 4] and fatigue properties [5,6], thus this microstructure is expected to have potential for practical applications. * Corresponding author. 0921-5093/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S 0 9 2 1 - 5 0 9 3 ( 9 7 ) 0 0 7 9 6 - X
Lamellar orientation is one of the major microstructural variables influencing the mechanical properties of TiAl having a lamellar microstructure. However, very few studies have been reported on the effects of lamellar orientation on mechanical properties [7,8], in particular, fatigue properties which are critical for structural components [6,9–11]. The objectives of the present study are to investigate the effects of lamellar orientation on fatigue crack propagation (FCP) and to better understand the FCP mechanisms. FCP experiments have been carried out using as-cast TiAl with a nearly fully lamellar microstructure, and the FCP characteristics were evaluated for two different FCP directions relative to the lamellar orientation. The effects of the lamellar orientation and the FCP mechanisms are discussed on the basis of detailed examinations on crack propagation paths, crack morphology and fracture surface.
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2. Experimental procedures
2.1. Material and microstructure The material used was as-cast TiAl with 33.9 wt.%Al which was supplied in the form of 100 mm diameter and 210 mm long ingot. The microstructure had a nearly fully lamellar microstructure. Columnar crystals developed toward the center from the circumference of the ingot and lamellae in each colony tended to orient perpendicular to the growth direction of the columnar crystals. The average colony sizes were 534 and 111 mm for the radial and circumferential directions of the ingot, respectively [5]. Compact-tension (CT) specimens with 25 mm width and 5 mm thickness were used for FCP experiments. Two types of the specimens relative to the lamellar orientation were prepared, i.e. the FCP direction is parallel or perpendicular to the lamellar orientation. Fig. 1 shows the schematic illustration of the specimens, where (a) and (b) represent the specimens for which the FCP direction is parallel and perpendicular to the lamellar orientation, respectively, and hereafter both are denoted as type A specimen and type B specimen. The lamellar orientation was slightly different in every colony, but the specimens could be cut from the ingot as shown in Fig. 1 so that the lamellar orientation is almost uniform. Fig. 2(a) illustrates another type of the specimen for which the FCP direction is perpendicular to the lamellar orientation. In this case, a crack grew to the direction parallel to the loading direction, i.e. parallel to the lamellar orientation, as shown in Fig. 2(b). This suggests that the FCP resistance of the direction parallel to the lamellar orientation is extremely low. Therefore, only the type B specimens were employed in the experiments for the FCP direction perpendicular to the lamellar orientation.
R, of 0.05 in accordance with ASTM-E647 [12]. Crack length was measured by a travelling microscope with 10 mm resolution and crack closure measurements were made by a compliance method using a strain gauge mounted on the back face of the specimen. Crack morphology and fracture surface were examined using
Fig. 1. Schematic illustration of specimens, showing crack propagation direction and lamellar orientation; (a) type A specimen, (b) type B specimen.
Fig. 2. Another type of specimen in which crack propagation direction is perpendicular to lamellar orientation; (a) relation between crack propagation direction and lamellar orientation, (b) fractured specimen.
2.2. Mechanical properties The tensile strength was 255 and 545 MPa for the specimens for which the lamellar orientation is perpendicular (corresponding to type A specimen) and parallel (type B specimen) to the loading direction, respectively. The elongation was significantly larger in the latter (3.2%) than in the former (0.6%).
2.3. Procedures FCP experiments were conducted on a 19.6 kN capacity electro servohydraulic fatigue testing machine operating at a frequency of 10Hz at ambient temperature in laboratory air. After introducing a precrack of 2 mm long, decreasing and increasing stress intensity factor range, DK, tests were performed at a stress ratio,
Fig. 3. Relationship between crack propagation rate and stress intensity factor range.
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Fig. 4. Crack propagation path on the specimen surface in type A specimen.
Fig. 5. Crack profile on the longitudinal section in type A specimen.
an optical microscope and a scanning electron microscope (SEM). As will be described later, several cracks were initiated and grew in type A specimens. In this case, the crack tip furthest from the notch root was regarded as the crack tip of an assumed straight crack.
3. Results
3.1. FCP characteristics The FCP rates, da/dN, are plotted in Fig. 3 as a function of both the nominal and effective stress intensity factor ranges, DK and DKeff ( = Kmax −Kop; Kmax and Kop are the maximum and crack opening stress intensity factors, respectively). As can be seen in the figure, both types of the specimens exhibit a considerable large scatter of da/dN. The slope of the da/dN − DK relationship for type A specimens is steeper than that for type B specimens and the apparent FCP resistance based on the nominal or applied DK is much lower in the former. After allowing for crack closure, i.e., when the data are plotted as a function of DKeff, type A specimens still indicate faster da/dN than type B specimens.
3.2. Crack morphology 3.2.1. FCP direction parallel to the lamellar orientation Crack propagation paths observed on the surface of a type A specimen are shown in Fig. 4. As can be seen in the figure, several cracks are observed. A crack grew from the starter notch, was arrested and subsequently new cracks were initiated at locations away from the crack tip and then grew. Again, these cracks were arrested and newly initiated cracks grew at different
locations. This process is repeated, thus leading to the crack morphology shown in Fig. 4. It was found that a few cracks are connected to each other during the FCP process, but most are not because the crack faces are not coplanar. Based on the observation of the microstructure after the experiment, all cracks were found to have grown along lamellae. Microcracks were not seen at the vicinity of the crack tip of a growing crack [6,13]. The crack profile is shown in Fig. 5, which was observed on the section parallel to the loading direction behind the crack tip. Again several cracks along lamellae can be seen, which are not coplanar, i.e. overlapping cracks on different planes, even inside of the specimen. Similar crack profiles were also observed on different sections behind the crack tip. According to the observation of the crack profiles made on many sections behind the crack tip, the FCP process during which uncracked ligaments are produced with crack extensions is illustrated schematically in Fig. 6. In the figure, the dark coloured area represents the crack plane. In Fig. 6, (I) shows the situation that the colonies with different lamellar orientations, A–C and D–G, are located in front of the crack front, and (II) represents the crack plane after the crack grew into those colonies. As shown in Fig. 6(a), when the crack grows into the colonies A and C in which the lamellar orientations are different from the crack plane, uncracked ligaments can be formed between the colonies A and B because of the crack growth along lamellae in each colony. If the colonies like C are on the specimen surface, then a newly initiated crack away from the crack tip would be seen on the surface. When the crack grows into the colonies E and F as shown in Fig. 6(b), a few cracks along lamellae are generated and thus uncracked ligaments can be produced.
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Fig. 10. SEM micrographs of fracture surface; (a) type A specimen (DK= 8.6 MPa m), (b) type B specimen (DK= 10.0 MPa m).
Fig. 6. Schematic illustrations of propagation process of specimen in which crack propagation direction is parallel to lamellar orientation.
Fig. 7. Heat-tinted fracture surface of type A specimen; (a) macroscopic view and (b) sketch showing heat-tinted region indicated by black color.
If the specimen were cut at the x-x section in Fig. 6, then one could observe the crack morphology shown in Fig. 5. As shown in Fig. 6, since the crack grows along lamellae in colonies with slightly different lamellar ori-
entations, several cracks which are not connected to each other can be seen (see Fig. 5). When the lamellar orientation changes in the colonies in front of the crack tip, the cracks sometimes can coalesce and then become a single crack. As such, in type A specimens, cracks can grow by experiencing many branching and coalescences of the crack plane along lamellae. The geometry of colonies and the lamellar orientation are random events, thus the actual FCP process could be much more complicated. A specimen with a fatigue crack was heat-tinted and the fracture surface was observed. The macroscopic appearance of the heat-tinted fracture surface is shown in Fig. 7(a). Dark parts in the figure represent the heat-tinted area. In order to make this clear, the sketch of Fig. 7(a) is illustrated in Fig. 7(b), where the heattinted region is indicated by black color. It can be seen that there are some regions of uncracked ligaments behind the crack tip. When a crack whose crack front is straight and perpendicular to the specimen surface at the crack tip is assumed, the projected area that was not heat-tinted is : 30% of the total area of the assumed crack. The area fraction may not have a quantitative meaning, because of large difference in these situations from specimen to specimen. However,
Fig. 8. Crack propagation path on the specimen surface in type B specimen.
Fig. 9. Crack profile on the longitudinal section in type B specimen.
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the presence of extensive uncracked ligaments behind the crack tip gives an important implication in understanding the FCP mechanisms of type A specimens.
3.2.2. FCP direction perpendicular to the lamellar orientation Crack propagation paths on the surface of a type B specimen is shown in Fig. 8. Only the main crack initiated from the starter notch propagates without remarkable deflections and branching. As can be seen in the figure, no cracks other than the main crack can be seen. By microscopic examination using SEM, very small deflections and branching were seen, but microcracks were not observed around the crack tip. The crack profile on the section perpendicular to the FCP direction is presented in Fig. 9. It can be seen that small deflections are more remarkable compared with those on the specimen surface (Fig. 8). Such deflections take place along colony boundaries and lamellae. Crack profiles were observed on several sections behind the crack tip. Consequently, crack deflections were found to be more remarkable with increasing DK. Very small areas that were not heat-tinted were seen on the fracture surface of type B specimens and almost all of such areas were along lamellae. The area fraction of uncracked ligaments was extremely small compared with type A specimens.
Fig. 12. Crack propagation characteristics before and after constant DK test in type A specimen.
3.2.3. Fractography SEM micrographs of fracture surface for type A and B specimens are shown in Fig. 10. In type A specimens (Fig. 10(a)), predominant fracture mode is flat cleavagelike facets between lamellae, with a small fraction of pattern resulting from FCP across lamellae. This feature is almost the same regardless of DK. In contrast to
Fig. 13. Effect of crack tip shielding due to uncracked ligaments on crack propagation behavior in type A specimen, where the maximum stress intensity factors after allowing for crack bridging were evaluated by FEM analysis using measured crack opening displacements.
the fractography of type A specimens, parallel marks resulting from FCP across lamellae are seen over the entire fracture surface in type B specimens (Fig. 10(b)), and the fracture surface tends to be rougher with increasing DK.
4. Discussion
4.1. Effects of uncracked ligaments in the wake of the crack tip on FCP Fig. 11. Variation of crack propagation rate with crack extension under constant DK test.
Uncracked ligaments were produced in the wake of
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the crack tip with crack extension in type A specimens. Therefore, the actual stress intensity factor at the crack tip is considered to be different from the apparent stress intensity factor computed from the applied load and the crack length measured on the specimen surface. In order to investigate the role of uncracked ligaments in FCP behavior, the variation in da/dN with crack extension was examined under constant DK conditions. The obtained results are represented in Fig. 11. Broken lines shown on this graph indicate the locations where load shedding has been done to achieve a constant DK. It should be noted that in the figure da/dN decreases gradually with crack extension in type A specimens in spite of constant DK conditions. In particular, the crack under the constant DK of 9.3 MPa m arrested at the crack increment of 1.02 mm. As shown in Figs. 4 and 5, several cracks were initiated and grew on different planes, thus uncracked ligaments were formed in the wake of the crack tip. Since such ligaments can support a part of the applied load, the actual stress intensity factor at the crack tip is considered to be decreased compared with the applied stress intensity factor. An increasing DK test was performed using the specimen for which crack arrest has occurred under the constant DK condition of 9.3 MPa m. Fig. 12 shows the comparison between the obtained result (open symbol) and increasing DK test result (solid symbol) before carrying out the constant DK test for the same specimen. Note that the apparent FCP resistance is significantly higher after the constant DK test than before that test. This may be attributed to reduced actual stress intensity factor at the crack tip due to bridging by uncracked ligaments produced during FCP under the constant DK condition. In contrast to type A specimens, da/dN for a type B specimen is nearly constant with crack extension under the constant DK condition as shown in Fig. 11. This is because uncracked ligaments are scarcely produced in type B specimens and thus the crack tip shielding due to bridging does not occur.
type A specimens and the obtained results are represented in Fig. 13. The specimen was the same as that used under the constant DK test. Two Vickers hardness indentations were given at a distance of 70 mm straddling the crack at two locations near the starter notch root and then the distances between the indentations were measured at the applied maximum load. For a CT specimen having the same crack length as measured in the experiment, the stress intensity factor at the crack tip was evaluated by a simplified FEM analysis in which the displacements equal to the measured distances between the indentations were given to the nodes located at the same positions as the indentations. The obtained stress intensity factor is considered to be the actual stress intensity factor at the crack tip at the maximum load. The relationship between da/dN and the obtained Kmax is demonstrated by solid symbols in Fig. 13. As can be seen in the figure, the Kmax values obtained by the FEM analysis are : 33–37% smaller than those computed from the applied load and the crack length measured during the FCP experiments. In the above experiment and FEM analysis, the average bridging stress over the entire region behind the crack tip was considered for the sake of simplification. In general, when the effects of shielding due to bridging are considered, the bridging stress in the wake of the crack tip is evaluated and then the actual stress intensity factor can be obtained by calculating the stress intensity factor due to shielding [14]. In type A specimens, however, sinse uncracked ligaments which act as bridging are produced three-dimensionally over a wide area in the wake of the crack tip, it is very difficult to quantify their length and area. In addition, the geometry of uncracked ligaments is different from specimen to specimen, thus a strict evaluation on the effects of bridging does not appear to have a quantitative meaning. Fig. 13 indicates that the intrinsic FCP resistance for the direction parallel to the lamellar orientation is considerably lower than the apparent one.
4.2. FCP resistance taking into account bridging by uncracked ligaments
5. Conclusions
As shown in Fig. 3, the FCP resistance for the direction parallel to the lamellar orientation was considerably low compared with that for the direction perpendicular to the lamellar orientation. If the effects of bridging by uncracked ligaments are considered, then the difference in FCP resistance between both directions would become much larger. In order to better understand the effects of uncracked ligaments on the FCP behavior of type A specimens, the following experiment and FEM analysis were performed. Additional experiments were conducted using
FCP behavior of a titanium aluminide (TiAl) with a nearly fully lamellar microstructure was investigated on two FCP directions relative to the lamellar orientation. The effects of lamellar orientation on FCP and fracture mechanisms were discussed. The following conclusions can be made. (1) The apparent FCP resistance based on the nominal stress intensity factor range, DK, was higher in the direction perpendicular to the lamellar orientation than in the direction parallel to the lamellar orientation. After allowing for crack closure, this tendency still remained.
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(2) In the direction parallel to the lamellar orientation, uncracked ligaments were produced in the wake of the crack tip, while in the direction perpendicular to the lamellar orientation, they were scarcely produced. (3) Predominant fracture mode for the direction parallel to the lamellar orientation was cleavage-like facets between lamellae, with a small fraction of transgranular cleavage across lamellae. On the other hand, in the direction perpendicular to the lamellar orientation, fracture surface was covered almost entirely with transgranular cleavage across lamellae. (4) The FCP rates in the direction parallel to the lamellar orientation were decreased with crack extension or crack arrest occurred under constant DK conditions. This was attributed to the actual stress intensity at the crack tip reduced by bridging due to uncracked ligaments. (5) Taking into account the effects of bridging due to uncracked ligaments, the difference in FCP resistance between two directions based on the actual stress intensity at the crack tip became much larger than that based on the nominal or applied stress intensity.
Acknowledgements This work was partially supported by the Grant-inAid for Science Research (C) (No. 07 650 763) by the
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Ministry of Education, Science and Culture, Japan. The authors are grateful to Daido Steel for the provision of the material.
References [1] Y.-W. Kim, Mater. Res. Soc. Symp. Proc. 213 (1991) 777–794. [2] K.S. Chan, Y.-W. Kim, Met. Trans. 23A (1992) 1663–1677. [3] R. Gnanamoorthy, Y. Mutoh, N. Masahashi, Y. Mizuhara, J. Soc. Mater. Sci. Jpn. (in Japanese) 43 (1994) 190 – 196. [4] R. Gnanamoorthy, Y. Mutoh, N. Masahashi, Y. Mizuhara, Met. Trans. 26A (1995) 305 – 313. [5] H. Shibata, K. Tokaji, T. Ogawa, H. Shiota, Int. J. Fatigue 18 (1996) 119 – 125. [6] R. Gnanamoorthy, Y. Mutoh, N. Masahashi, Y. Mizuhara, J. Soc. Mater. Sci. Jpn. (in Japanese) 45 (1996) 919 – 926. [7] S. Mitao, T. Isawa, S. Tsuyama, Scr. Metall. Mater. 26 (1992) 1405 – 1410. [8] T. Inui, et al., Acta Metall. Mater. 40 (1992) 3095 –3104. [9] R. Gnanamoorthy, et al., Scr. Metall. Mater. 33 (1995) 907–912. [10] D.L. Davidson, J.B. Campbell, Met. Trans. 24A (1993) 1555– 1574. [11] A. Ueno, H. Kishimoto, Y. Murakami, Fatigue crack propagation characteristics of intermetallic compound TiAI, Proc. 22nd Symp. on Fatigue, Soc. Mater. Sci. Jpn. (in Japanese), 1994, pp. 181 – 184. [12] 1988 Annual Book of ASTM Standards, ASTM, Philadelphia, PA, 1988, p. 636. [13] K.S. Chan, Met. Trans. 22A (1991) 2021 – 2029. [14] J.K. Shang, R.O. Ritchie, Met. Trans. 20A (1989) 897–908.
Influence of lamellar orientation on fatigue crack propagation behavior in titanium aluminide TiAl Hirohisa Shiota a,*, Keiro Tokaji a, Yasuhito Ohta b a
Department of Mechanical and Systems Engineering, Faculty of Engineering, Gifu Uni6ersity, 1 -1 Yanagido, Gifu 501 -11, Japan b Takeiri Factory, Yatomi-cho, Aichi 498, Japan
Abstract Fatigue crack propagation (FCP) behavior of a titanium aluminide (TiAl) with a nearly fully lamellar microstructure has been studied on two different FCP directions relative to the lamellar orientation; i.e. parallel (type A specimen) and perpendicular (type B specimen) to the lamellar orientation, at ambient temperature in laboratory air. It was found that the FCP resistance of the former was considerably lower than that of the latter. Close examinations of crack morphology revealed significant differences between the two FCP directions. In type A specimens, several cracks along lamellae were seen on the surfaces and sections of the specimens, thus uncracked ligaments were formed in the wake of the crack tip. On the contrary, such ligaments were scarcely produced in type B specimens because only the main crack could propagate without remarkable deflections and branching. The FCP rates of type A specimens were decreased gradually with crack extension under constant stress intensity factor range, DK, tests, suggesting the role of crack bridging by uncracked ligaments. Finite element method (FEM) analysis indicated considerably reduced DK experienced at the crack tip, thus the difference in FCP resistance between two FCP directions based on the actual DK at the crack tip after allowing for crack bridging became much larger than that based on the nominal or applied DK. © 1998 Elsevier Science S.A. Keywords: Fatigue crack propagation; Titanium aluminide; Lamellar microstructure; Orientation; Uncracked ligament; Bridging; Finite element method
1. Introduction g-Based titanium aluminides (TiAl) have recently received considerable interest as a structural material. Thus, extensive fundamental studies on the mechanical properties of these materials have been performed, and consequently, it has been indicated that the mechanical properties depended very strongly on microstructure [1]. There are three typical microstructures of TiAl, lamellar microstructure, equiaxed g microstructure and duplex microstructure. Of these microstructures, it has been reported that the lamellar microstructure displayed excellent fracture toughness [1 – 4] and fatigue properties [5,6], thus this microstructure is expected to have potential for practical applications. * Corresponding author. 0921-5093/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S 0 9 2 1 - 5 0 9 3 ( 9 7 ) 0 0 7 9 6 - X
Lamellar orientation is one of the major microstructural variables influencing the mechanical properties of TiAl having a lamellar microstructure. However, very few studies have been reported on the effects of lamellar orientation on mechanical properties [7,8], in particular, fatigue properties which are critical for structural components [6,9–11]. The objectives of the present study are to investigate the effects of lamellar orientation on fatigue crack propagation (FCP) and to better understand the FCP mechanisms. FCP experiments have been carried out using as-cast TiAl with a nearly fully lamellar microstructure, and the FCP characteristics were evaluated for two different FCP directions relative to the lamellar orientation. The effects of the lamellar orientation and the FCP mechanisms are discussed on the basis of detailed examinations on crack propagation paths, crack morphology and fracture surface.
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2. Experimental procedures
2.1. Material and microstructure The material used was as-cast TiAl with 33.9 wt.%Al which was supplied in the form of 100 mm diameter and 210 mm long ingot. The microstructure had a nearly fully lamellar microstructure. Columnar crystals developed toward the center from the circumference of the ingot and lamellae in each colony tended to orient perpendicular to the growth direction of the columnar crystals. The average colony sizes were 534 and 111 mm for the radial and circumferential directions of the ingot, respectively [5]. Compact-tension (CT) specimens with 25 mm width and 5 mm thickness were used for FCP experiments. Two types of the specimens relative to the lamellar orientation were prepared, i.e. the FCP direction is parallel or perpendicular to the lamellar orientation. Fig. 1 shows the schematic illustration of the specimens, where (a) and (b) represent the specimens for which the FCP direction is parallel and perpendicular to the lamellar orientation, respectively, and hereafter both are denoted as type A specimen and type B specimen. The lamellar orientation was slightly different in every colony, but the specimens could be cut from the ingot as shown in Fig. 1 so that the lamellar orientation is almost uniform. Fig. 2(a) illustrates another type of the specimen for which the FCP direction is perpendicular to the lamellar orientation. In this case, a crack grew to the direction parallel to the loading direction, i.e. parallel to the lamellar orientation, as shown in Fig. 2(b). This suggests that the FCP resistance of the direction parallel to the lamellar orientation is extremely low. Therefore, only the type B specimens were employed in the experiments for the FCP direction perpendicular to the lamellar orientation.
R, of 0.05 in accordance with ASTM-E647 [12]. Crack length was measured by a travelling microscope with 10 mm resolution and crack closure measurements were made by a compliance method using a strain gauge mounted on the back face of the specimen. Crack morphology and fracture surface were examined using
Fig. 1. Schematic illustration of specimens, showing crack propagation direction and lamellar orientation; (a) type A specimen, (b) type B specimen.
Fig. 2. Another type of specimen in which crack propagation direction is perpendicular to lamellar orientation; (a) relation between crack propagation direction and lamellar orientation, (b) fractured specimen.
2.2. Mechanical properties The tensile strength was 255 and 545 MPa for the specimens for which the lamellar orientation is perpendicular (corresponding to type A specimen) and parallel (type B specimen) to the loading direction, respectively. The elongation was significantly larger in the latter (3.2%) than in the former (0.6%).
2.3. Procedures FCP experiments were conducted on a 19.6 kN capacity electro servohydraulic fatigue testing machine operating at a frequency of 10Hz at ambient temperature in laboratory air. After introducing a precrack of 2 mm long, decreasing and increasing stress intensity factor range, DK, tests were performed at a stress ratio,
Fig. 3. Relationship between crack propagation rate and stress intensity factor range.
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Fig. 4. Crack propagation path on the specimen surface in type A specimen.
Fig. 5. Crack profile on the longitudinal section in type A specimen.
an optical microscope and a scanning electron microscope (SEM). As will be described later, several cracks were initiated and grew in type A specimens. In this case, the crack tip furthest from the notch root was regarded as the crack tip of an assumed straight crack.
3. Results
3.1. FCP characteristics The FCP rates, da/dN, are plotted in Fig. 3 as a function of both the nominal and effective stress intensity factor ranges, DK and DKeff ( = Kmax −Kop; Kmax and Kop are the maximum and crack opening stress intensity factors, respectively). As can be seen in the figure, both types of the specimens exhibit a considerable large scatter of da/dN. The slope of the da/dN − DK relationship for type A specimens is steeper than that for type B specimens and the apparent FCP resistance based on the nominal or applied DK is much lower in the former. After allowing for crack closure, i.e., when the data are plotted as a function of DKeff, type A specimens still indicate faster da/dN than type B specimens.
3.2. Crack morphology 3.2.1. FCP direction parallel to the lamellar orientation Crack propagation paths observed on the surface of a type A specimen are shown in Fig. 4. As can be seen in the figure, several cracks are observed. A crack grew from the starter notch, was arrested and subsequently new cracks were initiated at locations away from the crack tip and then grew. Again, these cracks were arrested and newly initiated cracks grew at different
locations. This process is repeated, thus leading to the crack morphology shown in Fig. 4. It was found that a few cracks are connected to each other during the FCP process, but most are not because the crack faces are not coplanar. Based on the observation of the microstructure after the experiment, all cracks were found to have grown along lamellae. Microcracks were not seen at the vicinity of the crack tip of a growing crack [6,13]. The crack profile is shown in Fig. 5, which was observed on the section parallel to the loading direction behind the crack tip. Again several cracks along lamellae can be seen, which are not coplanar, i.e. overlapping cracks on different planes, even inside of the specimen. Similar crack profiles were also observed on different sections behind the crack tip. According to the observation of the crack profiles made on many sections behind the crack tip, the FCP process during which uncracked ligaments are produced with crack extensions is illustrated schematically in Fig. 6. In the figure, the dark coloured area represents the crack plane. In Fig. 6, (I) shows the situation that the colonies with different lamellar orientations, A–C and D–G, are located in front of the crack front, and (II) represents the crack plane after the crack grew into those colonies. As shown in Fig. 6(a), when the crack grows into the colonies A and C in which the lamellar orientations are different from the crack plane, uncracked ligaments can be formed between the colonies A and B because of the crack growth along lamellae in each colony. If the colonies like C are on the specimen surface, then a newly initiated crack away from the crack tip would be seen on the surface. When the crack grows into the colonies E and F as shown in Fig. 6(b), a few cracks along lamellae are generated and thus uncracked ligaments can be produced.
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Fig. 10. SEM micrographs of fracture surface; (a) type A specimen (DK= 8.6 MPa m), (b) type B specimen (DK= 10.0 MPa m).
Fig. 6. Schematic illustrations of propagation process of specimen in which crack propagation direction is parallel to lamellar orientation.
Fig. 7. Heat-tinted fracture surface of type A specimen; (a) macroscopic view and (b) sketch showing heat-tinted region indicated by black color.
If the specimen were cut at the x-x section in Fig. 6, then one could observe the crack morphology shown in Fig. 5. As shown in Fig. 6, since the crack grows along lamellae in colonies with slightly different lamellar ori-
entations, several cracks which are not connected to each other can be seen (see Fig. 5). When the lamellar orientation changes in the colonies in front of the crack tip, the cracks sometimes can coalesce and then become a single crack. As such, in type A specimens, cracks can grow by experiencing many branching and coalescences of the crack plane along lamellae. The geometry of colonies and the lamellar orientation are random events, thus the actual FCP process could be much more complicated. A specimen with a fatigue crack was heat-tinted and the fracture surface was observed. The macroscopic appearance of the heat-tinted fracture surface is shown in Fig. 7(a). Dark parts in the figure represent the heat-tinted area. In order to make this clear, the sketch of Fig. 7(a) is illustrated in Fig. 7(b), where the heattinted region is indicated by black color. It can be seen that there are some regions of uncracked ligaments behind the crack tip. When a crack whose crack front is straight and perpendicular to the specimen surface at the crack tip is assumed, the projected area that was not heat-tinted is : 30% of the total area of the assumed crack. The area fraction may not have a quantitative meaning, because of large difference in these situations from specimen to specimen. However,
Fig. 8. Crack propagation path on the specimen surface in type B specimen.
Fig. 9. Crack profile on the longitudinal section in type B specimen.
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the presence of extensive uncracked ligaments behind the crack tip gives an important implication in understanding the FCP mechanisms of type A specimens.
3.2.2. FCP direction perpendicular to the lamellar orientation Crack propagation paths on the surface of a type B specimen is shown in Fig. 8. Only the main crack initiated from the starter notch propagates without remarkable deflections and branching. As can be seen in the figure, no cracks other than the main crack can be seen. By microscopic examination using SEM, very small deflections and branching were seen, but microcracks were not observed around the crack tip. The crack profile on the section perpendicular to the FCP direction is presented in Fig. 9. It can be seen that small deflections are more remarkable compared with those on the specimen surface (Fig. 8). Such deflections take place along colony boundaries and lamellae. Crack profiles were observed on several sections behind the crack tip. Consequently, crack deflections were found to be more remarkable with increasing DK. Very small areas that were not heat-tinted were seen on the fracture surface of type B specimens and almost all of such areas were along lamellae. The area fraction of uncracked ligaments was extremely small compared with type A specimens.
Fig. 12. Crack propagation characteristics before and after constant DK test in type A specimen.
3.2.3. Fractography SEM micrographs of fracture surface for type A and B specimens are shown in Fig. 10. In type A specimens (Fig. 10(a)), predominant fracture mode is flat cleavagelike facets between lamellae, with a small fraction of pattern resulting from FCP across lamellae. This feature is almost the same regardless of DK. In contrast to
Fig. 13. Effect of crack tip shielding due to uncracked ligaments on crack propagation behavior in type A specimen, where the maximum stress intensity factors after allowing for crack bridging were evaluated by FEM analysis using measured crack opening displacements.
the fractography of type A specimens, parallel marks resulting from FCP across lamellae are seen over the entire fracture surface in type B specimens (Fig. 10(b)), and the fracture surface tends to be rougher with increasing DK.
4. Discussion
4.1. Effects of uncracked ligaments in the wake of the crack tip on FCP Fig. 11. Variation of crack propagation rate with crack extension under constant DK test.
Uncracked ligaments were produced in the wake of
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the crack tip with crack extension in type A specimens. Therefore, the actual stress intensity factor at the crack tip is considered to be different from the apparent stress intensity factor computed from the applied load and the crack length measured on the specimen surface. In order to investigate the role of uncracked ligaments in FCP behavior, the variation in da/dN with crack extension was examined under constant DK conditions. The obtained results are represented in Fig. 11. Broken lines shown on this graph indicate the locations where load shedding has been done to achieve a constant DK. It should be noted that in the figure da/dN decreases gradually with crack extension in type A specimens in spite of constant DK conditions. In particular, the crack under the constant DK of 9.3 MPa m arrested at the crack increment of 1.02 mm. As shown in Figs. 4 and 5, several cracks were initiated and grew on different planes, thus uncracked ligaments were formed in the wake of the crack tip. Since such ligaments can support a part of the applied load, the actual stress intensity factor at the crack tip is considered to be decreased compared with the applied stress intensity factor. An increasing DK test was performed using the specimen for which crack arrest has occurred under the constant DK condition of 9.3 MPa m. Fig. 12 shows the comparison between the obtained result (open symbol) and increasing DK test result (solid symbol) before carrying out the constant DK test for the same specimen. Note that the apparent FCP resistance is significantly higher after the constant DK test than before that test. This may be attributed to reduced actual stress intensity factor at the crack tip due to bridging by uncracked ligaments produced during FCP under the constant DK condition. In contrast to type A specimens, da/dN for a type B specimen is nearly constant with crack extension under the constant DK condition as shown in Fig. 11. This is because uncracked ligaments are scarcely produced in type B specimens and thus the crack tip shielding due to bridging does not occur.
type A specimens and the obtained results are represented in Fig. 13. The specimen was the same as that used under the constant DK test. Two Vickers hardness indentations were given at a distance of 70 mm straddling the crack at two locations near the starter notch root and then the distances between the indentations were measured at the applied maximum load. For a CT specimen having the same crack length as measured in the experiment, the stress intensity factor at the crack tip was evaluated by a simplified FEM analysis in which the displacements equal to the measured distances between the indentations were given to the nodes located at the same positions as the indentations. The obtained stress intensity factor is considered to be the actual stress intensity factor at the crack tip at the maximum load. The relationship between da/dN and the obtained Kmax is demonstrated by solid symbols in Fig. 13. As can be seen in the figure, the Kmax values obtained by the FEM analysis are : 33–37% smaller than those computed from the applied load and the crack length measured during the FCP experiments. In the above experiment and FEM analysis, the average bridging stress over the entire region behind the crack tip was considered for the sake of simplification. In general, when the effects of shielding due to bridging are considered, the bridging stress in the wake of the crack tip is evaluated and then the actual stress intensity factor can be obtained by calculating the stress intensity factor due to shielding [14]. In type A specimens, however, sinse uncracked ligaments which act as bridging are produced three-dimensionally over a wide area in the wake of the crack tip, it is very difficult to quantify their length and area. In addition, the geometry of uncracked ligaments is different from specimen to specimen, thus a strict evaluation on the effects of bridging does not appear to have a quantitative meaning. Fig. 13 indicates that the intrinsic FCP resistance for the direction parallel to the lamellar orientation is considerably lower than the apparent one.
4.2. FCP resistance taking into account bridging by uncracked ligaments
5. Conclusions
As shown in Fig. 3, the FCP resistance for the direction parallel to the lamellar orientation was considerably low compared with that for the direction perpendicular to the lamellar orientation. If the effects of bridging by uncracked ligaments are considered, then the difference in FCP resistance between both directions would become much larger. In order to better understand the effects of uncracked ligaments on the FCP behavior of type A specimens, the following experiment and FEM analysis were performed. Additional experiments were conducted using
FCP behavior of a titanium aluminide (TiAl) with a nearly fully lamellar microstructure was investigated on two FCP directions relative to the lamellar orientation. The effects of lamellar orientation on FCP and fracture mechanisms were discussed. The following conclusions can be made. (1) The apparent FCP resistance based on the nominal stress intensity factor range, DK, was higher in the direction perpendicular to the lamellar orientation than in the direction parallel to the lamellar orientation. After allowing for crack closure, this tendency still remained.
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(2) In the direction parallel to the lamellar orientation, uncracked ligaments were produced in the wake of the crack tip, while in the direction perpendicular to the lamellar orientation, they were scarcely produced. (3) Predominant fracture mode for the direction parallel to the lamellar orientation was cleavage-like facets between lamellae, with a small fraction of transgranular cleavage across lamellae. On the other hand, in the direction perpendicular to the lamellar orientation, fracture surface was covered almost entirely with transgranular cleavage across lamellae. (4) The FCP rates in the direction parallel to the lamellar orientation were decreased with crack extension or crack arrest occurred under constant DK conditions. This was attributed to the actual stress intensity at the crack tip reduced by bridging due to uncracked ligaments. (5) Taking into account the effects of bridging due to uncracked ligaments, the difference in FCP resistance between two directions based on the actual stress intensity at the crack tip became much larger than that based on the nominal or applied stress intensity.
Acknowledgements This work was partially supported by the Grant-inAid for Science Research (C) (No. 07 650 763) by the
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Ministry of Education, Science and Culture, Japan. The authors are grateful to Daido Steel for the provision of the material.
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