Behavior of Branch Cracking and the Microstructural Strengthening Mechanism of Polycrystalline Ni-Base Superalloy, IN100 under Creep Condition* 1

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1 Materials Transactions, Vol. 52, No. 10 (2011) pp to 1884 #2011 The Japan Institute of Metals Behavior of Branch Cracking and the Microstructural Strengthening Mechanism of Polycrystalline Ni-Base Superalloy, IN100 under Creep Condition* 1 Yoshiko Nagumo* 2, A. Toshimitsu Yokobori, Jr., Ryuji Sugiura, Takashi Matsuzaki, Hiroaki Takeuchi* 2 and Yusuke Ito* 2 Graduate School of Engineering, Tohoku University, Sendai , Japan Recently, the development of the high-efficiency technology for gas turbine and jet engine is required to minimize carbon dioxide and nitrogen oxide emission. It is effective way to increase the operational temperature to develop the high-efficiency technology for high temperature instruments. To increase the operating temperature, advanced Ni-base superalloys have been developed as a turbine blade material. Even though a Ni-base superalloy is used for a structural component, creep damages and creep cracks may be caused due to the external tensile load under high temperature conditions. Therefore, a predictive law of creep crack growth life is necessary to maintain operational safety. This study is aimed to clarify the branch cracking behavior due to the microstructural strengthening mechanism of polycrystalline Ni-base superalloy IN100 under the creep condition. The creep crack growth tests were conducted at a temperature of 900 C. The creep crack growth behavior and creep damage formulation were observed by in-situ observational system and FE-SEM/EBSD. Additionally, two-dimensional elastic-plastic creep finite element analyses were conducted for the model which describes the experimental results. The creep crack growth behavior and the creep damage progression were found to be affected by the distribution behaviors of grains and grain boundaries around the notch tip. By comparison of experimental results with mechanical analysis using FEM analyses, mechanisms of the creep crack growth and the creep damage formulation were clarified. [doi: /matertrans.m ] (Received February 28, 2011; Accepted July 21, 2011; Published September 7, 2011) Keywords: branch cracking, creep damage, nickel-base superalloy, finite element analysis, microstructural strengthening 1. Introduction * 1 This Paper was Originally Published in Japanese in J. Japan Inst. Metals 74 (2010) * 2 Graduate Student, Tohoku University To realize the high-efficiency technology for gas turbine and jet engine, advanced Ni-base superalloys, which show an excellent creep resistance due to strengthening microstructure such as cuboidal 0 precipitates, have been developed. 1) When the Ni-base superalloys are used for actual components of structure, creep cracks may be caused by some kinds of external tensile load under high temperature conditions and the notch effects induced by configuration of structural component. In previous work, by some of the present authors, it has been shown that the creep cracks grew in complex manner, which results in the occurrence of branched creep cracks, 2,3) due to the microstructural strengthening mechanism caused by cuboidal 0 precipitates. Additionally, to establish the life assessment procedure, the initiation life of creep crack up to the start of creep crack growth has been noted for creep-brittle material because creep crack length at the region of major portion of total life for creep-brittle material is shorter than that of creep-ductile material and it is rapidly accelerated at the final stage. 4,5) Therefore, it is necessary to clarify the behaviors of creep damage formulation up to the start of creep crack growth related to the microstructural strengthening mechanism in order to detect the creep life of creep-brittle material. In this study, by conducting the creep crack growth tests for Ni-base superalloy using the designed in-situ observational system, 6) the macro and micro-damage formulation was clarified inclusive of the metallographical investigation using FE-SEM/EBSD (Electron Back Scatter Diffraction). Furthermore, on the basis of experimental results, twodimensional elastic-plastic creep finite element analyses were conducted to understand the occurrence mechanism of branched creep crack initiation and growth related to the microstructural strengthening mechanism. 2. Creep Crack Growth Tests 2.1 Experimental procedure The material used is polycrystalline Ni-base superalloy IN100 which was developed for jet engine turbine blade. The chemical composition and mechanical properties are shown in Tables 1 and 2, respectively. 7) The specimen used is a Double Edge Notched (DEN) specimen which has V notch in both side of the parallel site of the specimen, as shown in Fig. 1. The creep crack growth tests were performed using in-situ observational testing machine, shown in Fig. 2, with microscope and CCD camera 6) to observe the creep damage formulation and creep crack growth behavior under the Table 1 Chemical composition of IN100 in mass%. C Cr Co Mo Ti Al B r V Ni Bal. Temp. ( C) Table 2 0.2% proof stress (MPa) Mechanical properties of IN100. Tensile stress (MPa) Elongation (%)

2 Branch Cracking Behavior and Microstructural Strengthening of IN Fig. 1 The geometry and size of a DEN specimen. Fig. 3 Characteristic of creep deformation (RNOD). Fig. 2 High temperature creep-fatigue testing machine with in-situ observational system. temperature and load conditions of 900 C and 327 MPa. Furthermore, the microstructural observation was conducted using FE-SEM/EBSD on the interrupted test specimen. 2.2 Experimental results The relative notch opening displacement (RNOD), shown in eq. (1), was proposed as a representative quantity. 8) RNOD ¼ 0 ; ð1þ 0 where is the current value of notch opening displacement at the time of t and 0 is the initial value of notch opening displacement. Creep crack growth tests were conducted with two DEN specimens of IN100 under the condition of 900 C, 327 MPa. The characteristics of RNOD are shown in Fig. 3. The horizontal axis represents the normalized time t=t f, where t is the load application time and t f is the fracture life for each specimen. In Fig. 3, the characteristics of RNOD were found to be different between each specimen, which results in the difference of the life of creep crack growth, h and 84 h respectively, under the same testing condition. The former and the latter are defined as No. 1 and No. 2 specimens, respectively and the reason why the experimental characteristics were different between them are clarified with the in-situ and metallographical investigations. Fig. 4 In-situ observational result of No. 1 specimen (Intergranular). The in-situ observational result of No. 1 specimen at the stage of t=t f ¼ 0:46 is shown in Fig. 4. In Fig. 4, macroscopic creep damage was not observed despite the increase in the RNOD continuously. Therefore, to characterize the micro creep damage, the EBSD analysis was conducted for the interrupted specimen at the point of t=t f ¼ 0:46. The inverse pole figure map and kernel average misorientation (KAM) map obtained from the EBSD analysis are shown in Fig. 5(a) and (b), respectively. Figures 5(a) and (b) show the grain boundary distribution around the notch tip and the distribution of the local crystal misorientation of the analyzed area by colors, respectively. From these results, it is shown that the high KAM value areas distribute along the grain boundaries through the width of the specimen. It is reported that the KAM value corresponds to the creep damage. 9) Therefore, the creep damage of No. 1 specimen was found to distribute along the grain boundaries through the width of the specimen. Additionally, comparison of the creep crack growth path obtained from the microscopic observation, as shown in

3 1878 Y. Nagumo et al. (a)900 C, 327MPa, Creep (b)900 C, 327MPa, Creep Fig. 5 SEM/EBSD observational result of No. 1 specimen (Intergranular). Fig. 7 In-situ observational result of No. 2 specimen (Trans and Intergranular). Fig. 6 Creep crack growth path of No. 1 specimen (Intergranular). Fig. 6, the creep crack was found to grow along the creep damage at the grain boundaries, which results in failure. The in-situ observational results of No. 2 specimen at the stage of t=tf ¼ 0:81 is shown in Fig. 7. In Fig. 7, the creep damage initiates in the region of 45 to the extended notch direction. In this creep damage region, creep cracks were found to grow as shown in the microscopic observation result of Fig. 8. The EBSD analytical results are shown in Fig. 9. Figure 9(a) shows that the creep crack grows transgranularly at an angle of 45 to the direction of applied loading. From Fig. 9(b), the crystal orientation of the crack surface is found to be (111) plane, which is one of the plane of slip system of fcc structure h1 10if111g. From these results, it is found that the maximum shear stress plane which inclined at an angle of 45 to the extended notch direction is coincided with the slip plane of the grain as shown in Fig. 10. From these results mentioned above, creep crack for No. 2 specimen was found to grow toward the direction of 45 to the direction of applied Fig. 8 Creep crack growth path of No. 2 specimen (Trans and Intergranular). loading due to the effect of microstructural strengthening, as shown in Fig. 7. This has resulted in the restraint of linear creep crack growth perpendicular to the applied loading. These two different branch cracking behaviors indicate that the creep crack growth and creep damage formulation

4 Branch Cracking Behavior and Microstructural Strengthening of IN Fig. 11 Finite element model with a V notch. Fig. 9 Results of EBSD observation of No. 2 specimen (Trans and Intergranular). Fig. 12 Finite element model with an oblique crack path. Fig. 10 Schematic illustration of maximum shear strain plain of DEN specimen. In the next section, mechanical analyses are conducted using two-dimensional elastic-plastic creep finite element method in order to understand the occurrence mechanism of branched creep crack initiation and the creep damage formulation behavior related to the oblique crack growth. 3. behavior depends on the microstructural distribution around the notch tip. For the polycrystalline Ni-base superalloy which has varieties in the geometry and size of grains, whether the grain boundaries exist near the stress concentration site or not affects the difference of creep crack growth behavior. Additionally, when the grain boundaries do not exist near the stress concentration site, the microstructure around the notch tip can be considered as a single-crystal superalloy for the sheet specimen such as DEN specimen. For the single-crystal superalloy, it is reported that the elastic and plastic anisotropy becomes dominant for the deformation and cracks are easy to grow along the {111} plane below a temperature of 850 C,10) that could be the reason for the crack growth behavior which was found in No. 2 specimen. Two-Dimensional Elastic-Plastic Creep Finite Element Analysis 3.1 Analytical model The FEM models, which imitate the fracture behavior in the experimental results of Figs. 6 and 8, are shown in Figs. 11 and 12, respectively. In the FEM model of Fig. 11, grain boundaries are arranged by the changes in the material properties, as shown in Table 3. Material properties of Table 3 are classified conveniently into the following applications. One is based on the experimental result denoted as Hard:1 in Table 3. The other is postulated that a soft material denoted as Soft:2 in Table 3 is the half value of Hard:1. The width of grain and the location of an initial notch are modeled on the actual grain size and specimen geometry.

5 1880 Y. Nagumo et al. Table 3 Material properties for FEM analysis. Young s Poisson s modulus ratio E v (GPa) Yield stress Y (MPa) Work hardening Norton s law coefficient H p A (GPa) (MPa n h 1 ) Hard: : Soft: : n Provided boundary conditions were properly maintained that vertical nodal displacements are fixed at y ¼ 0 and horizontal nodal displacements are fixed at x ¼ 2:0. Figure 12 is modeled on the quarter part of a DEN specimen shown in Fig. 1. This model enables to grow an oblique creep crack using the nodal force release method with the penalty function which is described in the section Material property is used as the Hard:1 shown in Table 3. 11) Provided boundary conditions were maintained as the same in model of Fig. 11. Both for models, the type of element used is 6-noded triangular isoparametric planar element. The numbers of nodes and elements in Fig. 11 are 424 and 761, respectively. The numbers of nodes and elements in Fig. 12 are 3520 and 1693, respectively. 3.2 Analytical procedure Constitutive laws The constitutive laws used in this analysis are shown as eqs. (2) (5). The characteristic of work-hardening for plastic deformation is approximated by H p ¼ nc 1 ð þ " p Þ n1 ð2þ where n, C 1 and are constant values, respectively. " p is the value of equivalent plastic strain. The Von-Mises criterion was used for yielding condition. On the basis of Norton s law shown in eq. (3), the creep resistant coefficient for creep deformation and the time increment is approximated by eqs. (4) and (5), respectively. _"" p ¼ A n ð3þ H c ¼ d ¼ n 1 " n 1 p ð4þ d" p n Aðt þ C 2 Þ t ¼ " p ð5þ A n H c is creep resistant coefficient and C 2 is the constant value, which is introduced to adjust the value of H p at t ¼ 0, respectively. The parameter t is the time of creep loading. A and n are the material constants expressed by the Norton s law shown in eq. (2). The t i is calculated for each creep node by eq. (4) and the average value of all creep nodes was defined as t. The creep time t is calculated by summation of t, P t Nodal force release method 2) In this analysis, the nodal force release method was used to realize the crack growth. In this method, the penalty function was used to maintain the continuity of deformation between nodes located in the same point along the crack growth path Fig. 13 in 45 to simulate the oblique crack growth. The nodes were preliminarily located of both sides of the oblique crack path, which were constrained mutually as shown in Fig. 13(a). When the crack tip angle becomes larger than some critical angle (2 in this paper), inverse increment loads were applied to these two fixed nodes and these two fixed nodes were released, which result in the growth of oblique creep crack, as shown in Figs. 13(a) and (b). The penalty function is used for retaining the continuity of displacement of nodes which are originally free each other. The potential energy of upper and lower crack surface is expressed as eq. (6). ¼ 1 2 ð^u uþ T p ð^u uþd ð6þ The vectors on the upper and lower surface of crack path are described as ^u and u, respectively. p is the coefficient of penalty function. From the principle of minimum potential energy, the eq. (7) was derived. ¼ ð^u uþ T p ð^u uþd ¼ ^u T p ^ud ^u T p ud ð7þ u T p ^ud þ u T p ud ¼ 0 Thus, the requirement for the continuity of deformation between nodes is described as eq. (8). 2 3 ^u T p ^ud ^u T p ud K p ¼ ð8þ u T p ^ud u T p ud The method of crack extension. By adding the matrix shown in eq. (8) to the total stiffness matrix, the continuity of deformation between nodes is maintained. When the crack opening angle at the crack tip gets larger than the critical value c, the coefficient of penalty function p of the node at the crack tip changes to zero and the reaction force of the crack tip nodes are calculated. The inverse reaction force which is the sign inversion value of the reaction force is applied step-by-step to the releasing nodes The procedure of FEM analysis The flowchart of this analysis is shown in Fig. 14. First, the conditions of all nodes were calculated by the constitutive laws and the judgment of elastic, plastic and creep conditions were conducted. If a node was judged as the plastic condition,

6 Branch Cracking Behavior and Microstructural Strengthening of IN Fig. 14 Flowchart of creep crack growth based on finite element analysis. the coefficient of work hardening H p was calculated. After the plastic deformation increment, H p was replaced by H c in this node and creep analysis was conducted. In FEM analysis for creep deformation, the creep increment time t is also calculated. After that, the requirement of nodal force release was investigated. If the requirement of nodal force release is satisfied, the nodal force release routine is operated and the process of this analysis was iterated. In the conventional algorism of elastic-plastic creep finite element analysis such as Marc and Abaqus, only [D p ] is used to calculate the nodal displacement. The components of creep strain rate were applied as apparent nodal applied loads. The elastic and creep deformation analyses are conducted at a same time for the same node, and the Hoff s analogy is used to calculate the creep deformation, without the effect of the creep time. In this FEM analysis, under creep condition, [D c ] is used instead of [D p ], which will be much more realistic than that by conventional methods mentioned above. By this method, a creep increment time t for each node is calculated from the Norton s law using the equivalent stress and the equivalent plastic strain rate in each node, and H c which is used to calculate the creep deformation, is expressed as a function of t as shown in eq. (4). The creep time increment t is the average value of t i for all the nodes, i, under the creep condition calculated by eq. (5). The creep time t is the sum of creep increment time t for all stages. H c for each stage is calculated by eq. (4) using this creep time t. The constant value of C 2 in eq. (4) is the coefficient for maintaining the continuity of H p and H c at the point of before the creep deformation starts. This analysis is conducted under the displacement control. The relationship between the resistance coefficient of creep deformation and the analytical time obtained from the calculated results is shown in Fig. 15. In Fig. 15, the resistance coefficient H c was found to decrease with increase in the creep time. The relationship between stress and strain near the applied stress region for ductile and brittle material is shown in Fig. 16. In Fig. 16, the stress was found to take constant value despite of this analysis is controlled by the displacement. Fig. 15 Relationship between resistance coefficient of creep deformation and time. Fig. 16 Relationship between stress and strain. 3.3 Analytical results Figure 17 shows the creep damage formulation behavior obtained from the FEM analysis using the model of Fig. 11. The results in Figs. 17(i) (iv) indicate the creep damage formation behaviors at the points of 48000, 49500, 50800, and h, respectively. The green, yellow, and red colors in the figure show the elastic, plastic, and creep regions, respectively. The blue region represents the unloading

7 1882 Y. Nagumo et al. Fig. 19 Distribution of equivalent stress on x axis ( ¼ 0 ) around the notch tip. Fig. 17 Creep damage formulation of a notch model in Fig. 11. Fig. 20 Schematic illustration of creep damage concentration at the extended notch direction. Fig. 18 Creep damage formulation of an oblique crack model in Fig. 12. region. From Fig. 17, the creep region initiated from the notch tip in the 45 to the extended notch direction and propagated to the boundaries between the different material properties. From these results, the creep damage propagation around the notch tip was found to be restrained due to the initiation of creep damage at the boundaries. Figure 18 shows the creep damage formulation behavior obtained from the FEM analysis using the model of Fig. 12. The results in Figs. 18(i) (iii) show the creep damage formation behaviors at the points of 66, 96, and 101 h, respectively. From Fig. 18, with increase in the oblique crack length, creep damage was found to propagate and its region distribute toward the direction of crack tip to the extended notch direction. The equivalent stress distributions along the x-axis around the notch tip at each stage are shown in Fig. 19. Figure 19 assures the accumulation of creep damage to the extended notch direction due to the existence of high equivalent stress region. From these results, the fracture mechanism of No. 2 specimen was indicated that, when the creep damage accumulated to the extended notch direction takes the critical value, the micro cracks initiate in front of the notch tip as shown in part A of Fig. 20. And then, these micro cracks linked to the main creep crack, which results in the rapid final failure. 3.4 Comparison of analytical results and experimental results To understand the occurrence of oblique creep crack growth behavior, comparison of the analytical result with experimental result was conducted. For the No. 1 specimen, the creep damage distribution obtained from analytical result of Fig. 17 was qualitatively in good agreement with the creep damage region obtained from experimental result of Fig. 5. It is known that the degree of creep damage accumulation is represented by the plastic strain work Wp

8 Branch Cracking Behavior and Microstructural Strengthening of IN Fig. 21 The relationship between analytical plastic deformation work W p and analytical RNOD of a notch model. Fig. 23 The relationship between analytical plastic deformation work W p and analytical RNOD of an oblique crack model. Fig. 22 Characteristic of analytical creep deformation of a notch model. Fig. 24 Characteristic of analytical creep deformation of an oblique crack model. in FEM analysis. Figure 21 shows that the plastic strain work W p correlates with the RNOD which is obtained from FEM analysis of model in Fig. 11. In Fig. 21, it was found that the W p increases with increase in the RNOD. Additionally, the characteristic of RNOD obtained from FEM analysis, as shown in Fig. 22, was an excellent correlation with the experimental characteristics of RNOD for No. 1 specimen shown in Fig. 3, which is a linear characteristics. From these results mentioned above, a dispersion of creep damage produces the linear characteristic of RNOD. Figure 23 shows the plastic strain work W p correlates with the RNOD which is obtained from the FEM analysis of model in Fig. 12. In Fig. 23, it was found that with increase in the RNOD, the saturated characteristic of W p was found out. Additionally, the characteristic of RNOD obtained from FEM analysis, as shown in Fig. 24, was an excellent correlation with the experimental characteristics of RNOD for No. 2 specimen as shown in Fig. 3, which is a nonlinear characteristic. From these results mentioned above, an accumulation of creep damage produces the non-linear characteristic of RNOD. 4. Conclusions In this study, the in-situ observational creep crack growth tests using IN100 and FEM analyses were conducted to clarify the effect of microstructural strengthening on crack branching behavior. The following results were obtained. (1) From the in-situ observational test, it is indicated that the creep crack growth behavior of creep brittle material such as IN100 is greatly influenced by the location of grain distribution around the notch tip which has the stress concentration effect, and this is the reason why the creep crack growth showed different behavior. (2) By conducting the two-dimensional elastic-plastic creep finite element analyses and FE-SEM/EBSD analyses, the occurrence mechanism of creep deformation, creep damage formulation and creep crack growth behavior was investigated from the mechanical point of view. It is clarified that the microstructural strengthening mechanism of IN100 was caused by the occurrence of branch cracking due to the microstructural strengthening structure and the grain distribution.

9 1884 Y. Nagumo et al. (3) From the results mentioned above, the combination of microstructural analysis and mechanical analysis was considered to be important for clarifying the mechanism of variation behavior of creep crack growth life which depends on the microstructural distribution around the notch tip for the prediction of creep crack growth life. Acknowledgement The authors are grateful to Dr. A. Fuji in IHI Corporation for supply of the material used. REFERENCES 1) H. Harada and T. Yokokawa: Materia Japan 42 (2003) ) H. Takeuchi, A. T. Yokobori, Jr., S. Hosono, D. Kobayashi and K. Sato: J. Japan Inst. Metals 71 (2007) ) Y. Nagumo, A. T. Yokobori, Jr., R. Sugiura, T. Matsuzaki and Y. Ito: J. Japan. Soc. Strength Fracture Mater. 43 (2009) ) A. T. Yokobori, Jr., T. Uesugi, T. Yokobori, A. Fuji, M. Kitagawa, I. Yamaya, M. Tabuchi and K. Yagi: J. Mater. Sci. 33 (1998) ) A. T. Yokobori, Jr.: Eng. Fracture Mech. 62 (1999) ) A. T. Yokobori, Jr., Y. Kaji and T. Kuriyama: Proc. ICF 10 in the content of special session (special lecture) of CDrom, Honolulu, 2001, Eds by K. Ravi-chandar, B. L. Karihaloo, T. Kishi, R. O. Ritchie, A. T. Yokobori, Jr. and T. Yokobori, (Elsevier-Science, 2001). 7) M. Tabuchi, K. Kubo, K. Yagi, A. T. Yokobori, Jr. and A. Fuji: Eng. Fracture Mech. 62 (1999) ) A. T. Yokobori, Jr., T. Yokobori, T. Kuriyama and T. Kako: Proc. ICF 6, Eds by S. R. Valluri, et al., (Pergamon Press, 1984) p ) Y. S. Sato and H. Kokawa: J. Japan Weld. Soc. 68 (1999) ) P. A. S. Reed, X. D. Wu and I. Sinclair: Metall. Mater. Trans. A 31 (2000) ) Central Research Institute of Electric Power Industry (2000) Research Paper: T99024, in Japanese.