Abstract
In order to detect creep–fatigue damage before the crack initiation stage, an investigation into damage behaviour based on the electron backscattered diffraction (EBSD) method for a polycrystalline nickel base superalloy has been carried out. The average misorientation within grains increases linearly up to the initiation of cracks with the increase in creep strains. Even if stress distributions exist by stress concentration, assessment in all the damage areas allowed the evaluation of creep damage regardless of geometrical influence. Furthermore, the influence of strain rates, introducing fatigue and testing temperatures are hardly observed in the misorientation analysis. Misorientation almost corresponded to inelastic strain regardless of those influences. Quite a small misorientation caused by fatigue led to an equivalent result between creep conditions and creep–fatigue conditions. It is concluded that the misorientation analysis of damaged materials based on the EBSD method allows the quantitative estimation of creep strain and the assessment of remaining creep fracture life.
Keywords
Introduction
IN738LC is a nickel base superalloy that is precipitation strengthened by the γ′ phase in grains; it is used for components requiring high temperature strength, such as the gas turbine blades of high efficiency combined cycle power plants. With extended operating periods at high temperatures, deterioration tendencies such as the coarsening of the γ′ phase or the hardness deterioration of the material are observed. 1 However, a complex inner cooling system of the blades complicates the distribution of temperatures and stresses in the blades, 2 which implies that the relationship between the change of microstructure and creep damage is not clear. The nickel base superalloy has a pronounced brittle property even at high temperatures; therefore, creep degradations such as deformation of components and initiation of microscopic creep voids detected by conventional observation techniques only appear at the end of the available creep fracture life. In order to assess the integrity of a target component, it is important to detect creep damage as inelastic strain. 3
With the current advance in electron backscattered diffraction (EBSD) acquisition systems in conjunction with scanning electron microscopy, 4 it has become possible to make unprecedented submicrometre resolved measurements of the local crystal structure distribution at the millimetre scale. Making full use of these advances, the EBSD method is now widely used in materials characterisation.5,6 Furthermore, many attempts were made to measure the plastic or creep strain of stainless steels,7–17 nickel base alloys7,18–22 and others7,18,23–30 as changes in crystallographic orientation.
Wilkinson and Dingley 23 found that the diffuseness of electron backscatter patterns (EBSPs) increased with plastic strain by cold work using the Al 6061 alloy. A method was presented for quantitative determination of EBSP quality. However, the issue of surface contamination producing similar effects to those of specimen deformation still remained. Sutliff 25 pointed out that previously work had focused on the influence of dislocation density on the intensity profiles of diffraction bands. However, for some materials, such as copper, the strain produces highly organised dislocation structures, and thus, the dislocation density is very inhomogeneous at the submicrometre scale of EBSP. He then found a strong correlation between the known accumulated plastic strain in copper tensile specimens and the quantitative measurements of intragrain misorientation obtained from an analysis of automated EBSP data.
Mino et al.7,19,26 investigated the change in misorientation with creep strain of a gas turbine material. Within each selected grain, they measured the misorientation between an arbitrarily chosen reference point and 10 other points around the reference point. They did show that even though only a few points were used for the evaluation, the relationship between misorientation and plastic strain had a good correlation. Unfortunately, their method cannot be generalised systematically because of their arbitrary manner of choosing the reference point.
Lehockey et al. 18 demonstrated that the integrated misorientation density (IMD) of low angle misorientations correlates with plastic strain in a sufficiently reliable, systematic, and quantifiable manner. The IMD as a parameter used for strain analysis showed less sensitivity to factors that affect the diffracted intensity, such as grain orientation, surface condition and sample preparation. However, Kamaya et al.10,12,15–17 indicated that the acquired correlation curve in IMD cannot be used generally because the IMD parameter greatly depends on the data density of the crystal orientation maps. The misorientation angle typically depends on the distance of measurement points, and it is not always measured accurately, especially when the measured angle is <1°. Instead, Kamaya has suggested a parameter called modified crystal deformation that quantifies the spread of the crystal orientation within individual grains caused by dislocation accumulation during plastic deformation using stainless steels. He has confirmed that the modified crystal deformation has a good correlation with plastic strain introduced by uniform tensile deformation and has a relatively small influence on measurement conditions such as the number of data, the EBSD system, step size in the crystal orientation map, electron beam conditions, grain size or material such as stainless steels and nickel alloys.
Brewer et al. 13 published integrated misorientation maps that use a local kernel as the reference point for the map using stainless steels. The reference point is chosen essentially by the kernel average misorientation and using the nearest neighbours. The kernel with the smallest average misorientation becomes the reference point for each grain. The rainbow scale misorientation map contributed to an easily comprehensible damage distribution. This method, however, suffers from the choice of kernel, which is not altogether physically clear.
As mentioned above, most of the studies have mainly looked at the correlation between misorientation and plastic strain at room temperature using smooth specimens. The authors have shown that using a notched specimen31,32 or a smooth specimen, 33 creep damage can be estimated by misorientation analysis for a nickel base superalloy. In the present paper, in order to assess the remaining creep fracture life in the complex conditions of gas turbines, using notched specimens, investigation into the geometrical influence and the influence of test conditions such as strain rates, stress wave forms and temperatures on misorientation development was carried out.
Materials
The material used is IN738LC. The chemical composition of IN738LC is shown in Table 1 and the mechanical properties in Table 2. The specimens used are double edge notched (DEN) specimens and centre notched (CN) specimens
34
in order to compare the geometrical influence on creep damage, as shown in Fig. 1. The elastic stress concentration factor α of the DEN and the CN specimen are 4·84 and 3·0 respectively, though these minimum sectional areas have the same value. The ρ is the notch tip radius. By in situ observation and measurement of notch opening displacement, the relative notch opening displacement (RNOD) was calculated as follows in equation (1) and was dealt with as well as creep strain.
Geometry and size of specimens
Chemical composition of IN738LC (nickel base)/mass-
Mechanical properties of IN738LC
RA/: Reduction of Area/.
Experimental
Creep tests were conducted using the in situ observational creep testing machine, type CATY-T3H/TC2KN manufactured by Yonekura Seisakusyo in Japan, which has the same concept as the machine proposed by Yokobori.35,36 A schematic illustration of the machine and the surrounds of the furnace is shown in Fig. 2. This machine enables us to observe notch opening displacement, which corresponds to creep strain. In addition, crack initiation and crack growth behaviour can be continuously observed while running the tests using a high temperature microscope and a peeping window. A specimen is heated with an infrared condensed lamp, and the temperature was continuously monitored with a spot welded thermocouple in the vicinity of the notch of the specimen surface. 37 The conditions of creep tests were kept at a temperature of 830 or 740°C within ±1°C and gross section stress of 270, 294 and 490 MPa in inert gas condition (99·9999Ar).
Schematic illustrations of in situ observational machine
In the present paper, in order to observe the crystallographic orientation changes by creep strain, creep interruption tests using the DEN and the CN specimens, and creep and/or fatigue EBSD repeat tests using the DEN specimens were performed. In the creep interruption tests, some specific creep specimens were made individually and were individually observed using the EBSD method. On the other hand, in the case of the creep and/or fatigue EBSD repeat tests, a single specimen was alternately subjected to a repeated specific creep strain and EBSD observation; the specimen was removed from the testing machine before each observation. This procedure allows the observation of the tendency of creep and/or fatigue damage progression of identical specimens. Creep–fatigue condition means trapezoidal waves stress at the stress holding time tH of 180 seconds. Fatigue condition means triangle waves stress at the stress holding time tH of 0 s.
Electron backscattered diffraction measurements and analysis
Crystal orientation measurements were made with an EBSD-SEM system, comprising a TSL EBSD system using an orientation imaging microscopy (version 5) interfaced to a JEOL JSM-7001F with a field emission electron gun. The evaluation area was 3·7×1·2 mm on the specimen surface including the top and bottom notch; the edge where processing warps remained was omitted as shown in Fig. 3. The step size of the scanning was 5 μm in axial and transverse directions, which results in 740×240 data points. Misorientations >5° were regarded as grain boundaries, and only grains consisting >30 points were included in the calculation; smaller grains or particles of precipitate were ignored. The EBSD measurement and analysis conditions are shown in Table 3.
Electron backscattered diffraction analysis area on specimen
Electron backscattered diffraction measurement and analysis condition.
As an evaluation parameter which represents the degree of crystal orientation change, the grain reference orientation deviation (GROD) method is used to evaluate the spread of orientation deviation by referring to a certain orientation. 38 Ideally, the undeformed orientation in each grain should be adopted as the reference orientation. However, in practice, the undeformed orientation is usually unknown and is required to be estimated from a deformed sample. Thus, as a reference point, the average orientation in each grain was employed. The schematic illustration of the calculation method is shown in Fig. 4. When deformation is relatively small and the orientation changing directions show isotropy in the space of an inverse pole figure (IPF), it is expected that the average orientations coincide with the undeformed orientation.
Schematic illustration of misorientation analysis method
Results and discussion
Geometrical influence of stress concentration region
The conditions of the creep tests were kept at a temperature of 830°C and gross section stress of 294 MPa for both cases using DEN specimens and CN specimens. Figure 5 shows the relationship between creep life fraction and the RNOD. The difference of the initial notch opening value between the DEN and the CN specimen made the two curves. The creep interruption tests were conducted in the secondary creep region, and the interrupted specimens were subjected to EBSD observation.
Relationship between creep life fraction and RNOD in the case of using DEN specimens and CN specimens; t/tf: fracture lifetime
Figure 6 shows the GROD maps for each creep fraction on interruption tests. In both cases of using the DEN and the CN specimens, the appearance of misorientation in the vicinity of the notch can be observed from the early stage of creep life, and then the areas of misorientation become larger with the consumption of creep life. In the last stage, the distribution of misorientations was inhomogeneous and tended to be large not only near the notch but also near some grain boundaries. This indicates the characteristics of nickel base superalloys, which show intergranular cracking by intergranular damage in the creep condition.
Grain reference orientation deviation maps of each creep life fraction on creep interruption tests at 830°C×294 MPa
The relationship between creep life fractions and the GROD using the two kinds of specimens is shown in Fig. 7. The misorientation value shows the arithmetic average value throughout the observation areas. The misorientation values at a creep life fraction of 0·0 have a certain value not zero even in the unstrained material, which shows that the orientation measurement has some random measurement errors. As can be seen from Fig. 7, the GROD has a good correlation with creep life fraction, in other words, the GROD curve is very similar to the creep curve shown in Fig. 5. In addition, the geometrical influence between the DEN specimen and the CN specimen was not observed in the scope of this study. One reason is that creep deformation minimised the difference between the two elastic stress concentration factors. Basically, the difference in geometry results in the difference of distribution of stress and creep strain. As has been pointed out in the literature,3,36 however, in the case of assessing macroscopic creep damage (life) based on damage mechanics, the assessment of damage growth behaviour in all the damage areas is important. Therefore, for another reason, the assessment in all the damage areas allowed the evaluation of creep damage regardless of the geometrical influence between the DEN and the CN specimens.
Relationship between creep life fractions and GROD (analysis area average) in the case of using DEN and CN specimens
As mentioned above, crystallographic misorientation analysis based on the EBSD method permits the evaluation of creep life of a brittle material IN738LC without being subjected to the geometrical influence of the stress concentrated areas. Furthermore, the crack initiation has been found at a creep life fraction from ∼0·8 to 0·9, showing that EBSD observation allows the estimation of crack initiation life.
Misorientation development under creep and/or fatigue conditions
In this section, in order to examine the influence of various test conditions on the life estimation, using the DEN specimen, the effects of strain rate, fatigue (stress holding time) and temperatures on misorientation development were systematically investigated.
First, the relationships between fracture life fractions and the RNOD under creep and/or fatigue conditions by the repeat tests are shown in Fig. 8. Deformation when tH = 0 s (pure fatigue) was clearly suppressed. On the other hand, under other conditions, although some discontinuity points with interruption of the tests were found, the RNOD increased linearly up to ∼70 of their fracture lives, followed by an accelerated creep region. In addition, the RNODs under the 740°C creep condition are larger than those seen under other conditions after the fracture life of 0·4.
Relationship between fracture life fractions and RNOD under creep and/or fatigue conditions through repeat tests
To clarify the effect of the strain rate on misorientation development, the creep EBSD repeat tests were conducted under conditions of 830°C×230 MPa and 830°C×294 MPa. As a result, with a decrease in stress from 294 to 230 MPa, creep fracture life lengthened from 110 to 903 h, approximately one order of test time. Grain reference orientation deviation maps of each creep fraction on a creep EBSD repeat test at 830°C×230 MPa are shown in Fig. 9 in addition to an IPF map at last stage. The IPF map in this case is the map where the crystal direction aligned with the sample is normal at each point in the EBSD data, and where the colour shown at each point is correlated to the coloured coded stereographic triangle. The test for low strain rate showed that the change of crystal orientation in the vicinity of notches could be seen in the initial stages of creep fracture life (t/tf = 0·21) ahead of crack initiation (t/tf = 0·74). The misorientation grew in the direction of maximum shear stress over the test times. In addition, misorientation development could be seen at a part of the grain boundaries, and cracks were initiated at the grain boundaries. In the case of a notch edge involving a grain boundary, the grain boundary became the initiation point of cracking. In contrast, in the case of a notch edge not involving a grain boundary, a grain boundary that has the largest misorientation, that is strain, became the initiation point of cracking.
Grain reference orientation deviation and IPF maps of each creep fraction on creep EBSD repeat test at 830°C×230 MPa (tf = 903 h)
Then, to consider the effect of fatigue at high temperatures on misorientation development, a high temperature creep–fatigue test (tH = 180 s) and a fatigue test (tH = 0 s) were conducted under the conditions of 830°C×294 MPa. In these tests, similarly to the previous tests, the changes of crystal orientations within their fracture lives were observed by the test observation repeat method. Grain reference orientation deviation maps of both creep–fatigue and fatigue fracture life fraction are shown in Fig. 10. The result of the condition of tH = 180 s (creep–fatigue trapezoidal waveform) shows the remarkable development of misorientation, similar to the creep condition shown in Fig. 9. The intergranular crack was initiated at the tip of the above notch. On the other hand, the transgranular crack initiated and grew perpendicular to the applied stress direction, followed by the intergranular crack growth. The rapid developments of misorientation can be seen along cracks with the progression of creep deformation during hold times. In addition, the result under the condition of tH = 0 s (pure fatigue triangular waveform) showed that the misorientation development ahead of crack initiation was scarcely observed even in the vicinity of the notches. Cracks initiated and grew perpendicular to the applied stress direction to the end of the fracture life. The stress concentration of crack tips at the last stage made large plastic deformation.
Grain reference orientation deviation and IPF maps of each fracture life fraction on repeat tests at 830°C×294 MPa
Figure 11 shows the relationship between fracture life fraction and the GROD under creep and/or fatigue conditions of 830°C×294 MPa and 740°C×490 MPa. Similar relationship between fracture life fraction and the RNOD shown in Fig. 8 was confirmed. It should be noted that the macroscopic measurement data of creep strains and the microscopic measurement data of misorientation are identical. Pure fatigue conditions have a low value of misorientation, and creep or creep–fatigue conditions show a unique creep curve in the relationship between fracture life fraction and the GROD. The results under the two creep conditions of 830°C indicate that the influence of strain rate is completely unobserved. In addition, the effect of introducing fatigue condition to the creep condition is hardly observed in the misorientation analysis. 12
Relationship between creep and/or fatigue life fractions and GROD
Grain reference orientation deviation and IPF half size maps under creep condition of 740°C×490 MPa, t/tf = 0·42
The GROD misorientation directly corresponds to inelastic strain. Quite a small misorientation caused by fatigue led to the equivalent results between creep conditions and creep–fatigue conditions. Moreover, under the creep condition of 740°C×490 MPa, relatively large misorientation development could be seen similar to the RNOD curve shown in Fig. 8. That means the specimen has a significant large grain in the vicinity of the notch, and having no grain boundaries facilitated the developing spread of misorientation around the notch, as shown in Fig. 12.
In summary, straight crack growth from the tip of notches dominates the fracture life in the fatigue condition, whereas with the introduction of stress holding time, the development of misorientation was observed ahead of crack initiation. From the viewpoint of damage accumulation, under creep–fatigue conditions except pure fatigue with obvious crack growth, the progression of misorientation distribution was observed at the stress concentrated region and grain boundaries ahead of a crack initiation. In the case of discussion of the crack growth behaviour on fracture mechanics, it is important to assess these local stress distributions. However, in the case of assessing macroscopic creep damage (life) based on damage mechanics,3,36 the assessment of total misorientations in all the damage areas allows quantitative damage evaluation even for notched samples that have stress and strain distribution.
Conclusions
In order to characterise the damage progression behaviour and to evaluate the creep–fatigue fracture life of IN738LC, the average misorientation within grains as GROD was evaluated using the EBSD by measuring almost all the damage areas in specimens. Particularly, the geometrical influence at stress concentration and the influence of strain rate, fatigue and test temperatures have been investigated. The following results were obtained.
Misorientation development of notched specimens was localised in the stress concentrated region and grain boundaries. However, analysis of almost all the damage area of notched specimens allows the uniform evaluation of macroscopic creep damage before the appearance of obvious defects such as voids or cracks without being subjected to the geometrical influence of the stress concentrated region.
The average misorientation within grains evaluated by the parameter of GROD increases linearly up to the initiation of cracks with the increase in creep strains regardless of the testing temperatures and strain rates or creep–fatigue interaction except pure fatigue conditions, which show obvious crack growth behaviour. It is concluded that the misorientation analysis of damaged materials based on the EBSD method allows the quantitative estimation of creep strain and the assessment of remaining creep–fatigue fracture life.