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Advanced thermal gradient mechanical fatigue testing of CMSX-4 with an oxidation protection coating
Available online at www.sciencedirect.com
International Journalof Fatigue
International Journal of Fatigue 30 (2008) 219–225
www.elsevier.com/locate/ijfatigue
Advanced thermal gradient mechanical fatigue testing of CMSX-4 with an oxidation protection coating Bernd Baufeld b
a,b,*
, Marion Bartsch a, Michael Heinzelmann
c
a German Aerospace Center (DLR), Linder Ho¨he, 51147 Ko¨ln, Germany Katholieke Universiteit Leuven, Kasteelpark Arenberg 44, 3001 Leuven, Belgium c University of Applied Sciences Bonn-Rhein-Sieg, 53359 Rheinbach, Germany
Accepted 15 January 2007 Available online 15 March 2007
Abstract Frequently, turbine blades are cooled internally, which generates thermal gradients over the blade wall and, consequently, multi-axial stresses in addition to stresses due to centrifugal forces. In order to study these conditions, a new thermal gradient mechanical fatigue (TGMF) testing equipment with a lamp furnace has been developed. The advantages of this furnace are high power (16 lamps a 1000 W), controlled thermal gradients, high heating and cooling rates, and lamp lives exceeding 8000 thermal cycles. The studied material system was the single-crystalline superalloy CMSX-4 with a NiPtAl oxidation protection coating. Different TGMF tests with a maximal surface temperature of 1050 C, mechanical loads up to 400 MPa, and cycle numbers up to 9000 resulted in microstructural changes and defects, reflecting in each case the particular temperature, thermal gradient, and local stresses. For example, phase evolution of the metal coatings and rafting of the c/c 0 substrate morphology was investigated. Furthermore, cracks at the inner specimen surface and at substrate pores were detected. The observed morphology and defects were related to the applied thermomechanical loads using finite element calculations. 2007 Elsevier Ltd. All rights reserved. Keywords: Defects; Cracks; Stress analysis; Superalloys; Thermomechanical fatigue/cycling
1. Introduction In-service, internally cooled turbine blades experience in addition to centrifugal forces multi-axial mechanical loads due to the temperature difference between the cooled inner and the heated outer blade surfaces. The colder regions shrink, the hotter expand, leading to large in-plane stresses. The resulting stress fields are very complex, which in concur of high temperatures and cyclic loading ensue into very different morphological changes and defect developments at different locations of a blade. Examples for morphological changes and defects are cracks, surface roughening, * Corresponding author. Address: Katholieke Universiteit Leuven, Kasteelpark Arenberg 44, 3001 Leuven, Belgium. Tel.: +32 16 321534; fax: +32 16 321992. E-mail address: [email protected] (B. Baufeld).
0142-1123/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2007.01.034
diffusion, phase transformations, and coarsening of microstructures. Modern turbine blades usually consist of a Ni base superalloy with c matrix and c 0 cubical precipitates. During exposure to high temperatures coarsening of the originally ‘‘sharp’’ c/c 0 microstructure evolves in the thickening of the c phase and the combining of neighbouring c 0 precipitates, which increase both with time and temperature [1]. Neighbouring c 0 cuboids may grow together leading to c 0 platelets, which are oriented randomly perpendicular to all three Æ1 0 0æ directions [2,3]. Besides this isotropic coarsening, the so-called rafting may occur, if the alloy is exposed additionally to sufficiently high mechanical loads (for example [4–10]). Rafting can be discerned between c 0 rods and c 0 plates [8], depending on the stress field. Hence, the resulting rafting structure can be used as indicator of the multi-axial stress field during high temperature exposure.
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Depending on the location in a turbine blade, after service different coarsening and rafting were observed [11–13]. Since rafting may either improve or deteriorate the mechanical properties of a system [1], the development of rafting must be understood for lifetime prediction. In order to study morphological changes and defects, which may occur in-service and limit the performance of turbine blades, CMSX-4 Ni based superalloy with a Pt aluminide oxidation protection coating was subjected in the laboratory to conditions, which simulate the in-service condition as close as possible. The chosen testing methods were the so-called thermal gradient mechanical fatigue (TGMF) testing, which realises cyclic thermal and mechanical loading including a thermal gradient over the specimen wall, thermal gradient fatigue (TGF) testing without an applied mechanical loading but with a thermal gradient, and thermal mechanical fatigue (TMF) testing without a thermal gradient but with mechanical loading. 2. Experimental
observed, which presumably are related with the growth of dendrites during the solidification of the metal. The commercially available platinum-modified aluminide coating was prepared by electroplating platinum and diffusing aluminium into the substrate by chemical vapour deposition. In the as-coated condition this coating has a thickness of 65 lm and consists mainly of two phases roughly described as PtAl2 and b NiAl (Fig. 2). Within the coating a line of residual oxides from the grit blasting and near the substrate W rich precipitates can be found. Frequently, large surface defects in the form of embedded oxides can be observed. The microstructures were investigated by light optical means and with scanning electron microscopy. Standard techniques were applied for the preparation of specimen sections. Length and cross sections with {1 0 0} surfaces of the cubic substrate facilitate the interpretation of the c/c 0 structures of the substrate (Fig. 1). Thus, depending on their orientation, rods and plates may appear either equiaxed or as elongated structures, the latter called henceforth rafts.
2.1. Specimens 2.2. Testing procedure The studied system is composed of a nickel base superalloy CMSX-4 substrate, a NiPtAl oxidation protection coating at the outer surface, and an aluminized inner surface. CMSX-4, a second-generation single-crystalline Ni base superalloy, is characterized by its cubical c/c 0 structure (Ni/Ni3Al). Tubular specimens with an inner diameter of 7 mm and an outer diameter of about 10 mm (before coating) were used for imposing a radial thermal gradient by internal cooling and external heating. The tensile axis of the specimens was nominally in [1 0 0] direction (Fig. 1). Within the single crystal several parallel lines of pores, slightly inclined towards the tensile axis, were
Fig. 1. Schematic drawing of a segment of the tubular specimen, defining the axisymmetric FEM model and the orientation of SEM sections. In addition, rafting variants in dependence of the thermomechanical loading and of the radial position are visualized in form of cubes, platelets and rods.
In order to study the influence of multi-axial stresses a load-controlled servo-hydraulic testing rig with a newly developed radiation furnace was applied, which is a successor of a prototype [14,15] already employed successfully for the investigation of metal coatings [16] and thermal barrier coatings [17,18]. The gold coated mirror of the furnace consists of 16 segments of ellipses, where in one of the focus lines of each ellipse a 1000 W quartz bulb and at the other, common focus line the specimen is positioned (Fig. 3). With this very effective system fast heating from ambient temperatures up to 1000 C can be achieved within 15 s. Due to an advanced cooling system of the bulbs, their life usually exceed 15,000 heating cycles. A temperature gradient is generated by inner cooling of the specimen with controlled air flow. Mass flow and temperature of the cooling air can be adjusted. For the current
Fig. 2. Cross section of an as-coated specimen showing the two-phased coating consisting of b NiAl (darker contrast) and PtAl2 (brighter contrast), a line of residual oxides and a surface defect.
B. Baufeld et al. / International Journal of Fatigue 30 (2008) 219–225
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number (3000) without failure was achieved for specimen C with a lower mechanical loading (250 MPa). In the case of the TGF testing of specimen D, similar temperature cycle was applied for 9000 cycles, but the mechanical load was held constantly at zero. Specimen E was subjected to 1510 TMF cycles with switched-off internal cooling and a maximum nominal stress of 250 MPa. 3. Results 3.1. Morphology at the surfaces Fig. 3. Schematic drawing of the furnace consisting of 16 mirror segments, where the 16 quartz bulbs at located at one of each focal line and the specimen at their common focal line. The half cylindrical shutters, which block the radiation from the specimen during cooling, are not shown.
investigation an air flow of 100 l/min and an air temperature of about 350 C, entering the tubular specimen from the top were chosen. For a surface temperature of 1050 C under quasi-stationary thermal conditions, a temperature difference of about 70 C over the specimen wall was determined, leading to a radial heat flux of 1.3 MW/ m2. To the authors knowledge besides from the DLR group [14–18] only few reports are available investigating thermal mechanical fatigue with an additionally applied temperature gradient [19]. Fast cooling is obtained with two half cylindrical shutters (not shown in Fig. 3), which are pushed vertically into the furnace interior to block the radiation and which shower the specimen surface with cold compressed air. During cooling, this leads to an inverted radial temperature difference with lower temperatures on the outer surface than inside the specimen. Fig. 4 gives an example for the TGMF cycle with a cycle length of about 2 min and a maximal surface temperature at the axial specimen centre of 1050 C. Specimen A and B were TGMF tested with a nominal mechanical stress of 400 MPa; specimen A for 1000 cycles and specimen B until failure after 1337 cycles (Fig. 5). A higher TGMF cycle
Due to thermal exposure a thermally grown oxide (TGO) developed at the outer coating surface and the originally two-phased outer coating layer (PtAl2 and b NiAl) gradually transformed into a single phased b layer. For specimen A with the shortest time at high temperature (1000 cycles) this transformation is not completed even in the hottest zone, while specimen B (1337 cycles) reflects over 20 mm length a gradual change from the two phased area in the colder zone towards a single phased area in the hottest zone. For specimen C, D, and E, with cycle numbers of 1510 and more, the transformation within the observed region was completed. In addition, with time and temperature, increasingly precipitates with refractory elements from the substrate emerge in the outer coating (Fig. 5b). The inner surface of all specimens is coated with b NiAl and at the interface to the substrate an inter-diffusion zone exists with precipitates of refractory elements from the substrate (Fig. 6a). With increasing time and temperature, such precipitates occur progressively more in the inner coating. Since the temperature of the internal cooling air increases during its path from the top to the bottom of the specimen acquiring and transporting the heat from the specimen, the precipitation zone increases, and the single phase b NiAl zone decreases from top to bottom. Furthermore, a thin and irregular TGO grows at the inner surface. 3.2. Cracks
Fig. 4. Surface temperature and nominal mechanical stress during a TGMF cycle.
For specimen C, D, and E, with respectively no mechanical load applied or with a nominal mechanical stress of 250 MPa no cracks were observed. For specimens A and B with a nominal mechanical stress of 400 MPa, in contrast, various cracks occurred. Usually, they are located at the inner surface (Fig. 6a) and at the pores within the substrate (Fig. 6b). Cracks at the outer surface in the case of specimen B (Fig. 5) are probably related to the final failure of this specimen. They are blunt, occur only in the vicinity of the fracture surface and are not oxidized (Fig. 5b). The cracks on the inner surface and at the inner pores are located in the region with highest temperatures at the axial centre. The surfaces of the cracks at the inner surface are oxidized (Fig. 6a), indicating sufficient time at temperature, which is in contrast to the cracks at the outer
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Fig. 5. Light optical (a) and electron microscopic (b) image of length section of specimen B showing the fracture surface and cracks at internal pores, at the inner surface, and at the outer surface.
surface of specimen B. Usually, they are observed only in the single phased b NiAl layer, but occasionally sharp cracks penetrate into the precipitation zone (Fig. 6a). 3.3. Coarsening and rafting For all specimens increased coarsening of the c/c 0 microstructure was found towards the axial centre of the specimen, i.e. towards the highest temperature, and the following description will focus on this region. Depending on the type of testing and on the radial location, different types of coarsening were observed. One coarsening feature was common to all specimens. It is located in the very vicinity of the interface between substrate and outer coating, has an extension of about 10 lm, and is oriented parallel to the interface (Fig. 7). Rafting with similar features is already reported in literature and called anomalous rafting [1,20–23]. Specimen C, TGMF tested with a maximum nominal stress of 250 MPa, shows a change in the type of rafting over the wall thickness. Near the inner surface, rafting appears in the length section as coarsening in radial direction (Fig. 8a) and in the cross section as isotropic coarsening (Fig. 9). Towards the outer surface this changes, and in the length section isotropic coarsening is observed (Fig. 8b). Towards the interface of the outer coating, the structure remains isotropic until the region of anomalous
rafting is reached (Fig. 7). In the cross section, the coarsening changes from isotropic near the inner surface towards directional coarsening in tangential direction near the outer coating. Since this directionally coarsening is observed at a distance of at least 60 lm from the interface and thus exceeds the width of directionally rafting detected in the length section, it is different to the anomalous rafting. For specimen A, TGMF tested with a maximum nominal stress of 400 MPa, and for specimen E, TMF tested with a maximum nominal stress of 250 MPa, besides the
Fig. 7. Length section of specimen C showing in the vicinity of the coating rafting parallel to the interface (anomalous rafting) and isotropic coarsening towards the substrate.
Fig. 6. Length section of specimen A, showing cracks at the inner surface (a) and at an internal pore (b) (inset: detailed view of crack tip).
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Fig. 8. Chemically etched length section of specimen C, showing rafting perpendicular to the tensile direction near the inner surface (a) and isotropic coarsening in the centre of the substrate (b). The symbol ‘‘h’’ in the cartoons indicates the location of the micrograph.
interface and over the axial length of 20 mm, a preferential thickening of the c ligaments perpendicular to the tensile axis took place (Fig. 10). In contrast with conventional rafting, this thickening is not accompanied with the coalescence of neighbouring c 0 precipitates. 4. Finite element modelling
Fig. 9. Ion etched cross section of specimen C near the inner surface. The symbol ‘‘h’’ in the cartoon indicates the location of the micrograph.
anomalous rafting no radial dependence of the rafting was observed. Throughout the whole wall thickness the rafts in the length section appear elongated in radial direction. For the TGF tested specimen D, again with the exception of the anomalous rafting in the vicinity of the outer coating, no directional rafting was observed throughout the whole width of the specimen wall and the structure remained isotropic. However, throughout the whole investigated area, i.e. from inner surface towards the coating
The distribution of axial and hoop stresses over the cross section of a coated specimen during a cycle has been calculated by means of the finite element method (FEM). The axisymmetric, three-dimensional model is based on a sector of a specimen wall (Fig. 1) and comprises the anisotropic single-crystalline substrate and the outer metal coating. As far as available, the material properties were taken in dependence on the temperature (Table 1). The temperatures at the surfaces during the quasi-stationary high temperature sequence of a thermal cycle were taken as boundary conditions, i.e. 1050C at the hot outer surface and 980 C at the inner surface. In Fig. 11, the axial stress distribution over the whole wall for the case of the [0 1 0] radial direction is given for nominal mechanical loads of 0, 250 and 400 MPa. In addition, the hoop and the radial stress are shown. Without an applied mechanical load, axial and hoop stresses decrease from almost +100 MPa at the inner surface towards about 50 MPa at the outer surface. Thus, if no mechanical load is applied axial and hoop stresses are tensile at the inner surface and compressive at the outer Table 1 Coefficient of thermal expansion CTE, thermal conductivity k, density q, heat capacity cp, elastic modulus E, shear modulus, and Poisson ratio m for the single-crystalline substrate and the outer coating for 1100 C
Fig. 10. Length section of TGF specimen D showing the substrate near the axial centre with an inset at higher magnification and a cartoon. The symbol ‘‘h’’ indicates the location of the micrograph.
CTE (106 l/K) k (W/m K) q (g/cm3) cp (J/kg K) E (GPa) G (GPa) m
Substrate
Outer coating
16.2 31.02 8.7 0.960 78.5 93.8 0.39
17.37 29.34 7.47 0.706 40.0 0.35
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of 250 MPa was too small (specimen C), to obtain crack initiation within a reasonable testing time (3000 cycles). 5.2. Coarsening and rafting
Fig. 11. FEM stress distribution in the case of an [0 1 0] radial direction for 980 C at the inner surface (substrate, r = 3.5 mm) and 1050 C at the outer surface (metal coating, r = 5.1 mm). Stresses are given in hoop, axial, and radial direction for a nominal mechanical load of 0 MPa, and in axial direction for a nominal mechanical load of 250 and 400 MPa. For comparison, the respective, temperature dependent yield strength for CMSX-4 [26] and a Pt aluminide [27] is given.
surface. The radial stress is tensile over the whole specimen wall and smaller than 10 MPa. With the application of an additional tensile load in axial direction, the axial stress distribution curve is shifted in positive direction, while hoop and radial stresses are hardly affected. With sufficient high mechanical loads, the specimen may be subjected over the whole wall only to tensile axial stresses (Fig. 11). According to further FEM calculations not shown here, the anisotropy of the substrate has a minor influence on the stresses. For example, with no applied mechanical load, the axial and hoop stresses at the inner surface are only somewhat smaller for the [0 1 0] direction (both 90 MPa, Fig. 11) than for the [0 1 1] direction (hoop stress: 154 MPa, axial stress: 111 MPa). The stress development over the wall is comparable for all directions.
In the following the observed isotropic coarsening and rafting will be related to the stress fields during testing. For simplicity, the discussion will concentrate on locations of the single-crystalline substrate, where the microstructure is oriented in such a way, that the main axes of the former cuboids are parallel to the axial, radial and hoop direction. While for the (0 0 1) length section this is fulfilled everywhere, for the (1 0 0) cross section one is restricted to the locations where one axis of the former cuboids is along the interface or the inner surface. In [8] a rafting prediction chart under multi-axial loading is proposed for the superalloy SRR99. Differently oriented rafting rods or plates develop, depending on the multi-axial stress field. For small stresses an isotropic region is predicted, which will be not shifted by temperature variations, but which will increase or decrease its size. Fig. 12 is an adaptation of this rafting prediction chart, assuming a negligible radial stress. Accordingly, depending on the direction and amount of axial and hoop stresses, isotropic coarsening or rafting rods and plates in axial, radial and hoop directions are expected. It is assumed, that the rafting of CMSX-4 is similar to the one predicted for SRR99, since the material properties are comparable. Especially important for rafting is the misfit parameter, which are for both superalloys negative at room temperature (1.3 · 103 for CMSX-4 [24] and 0.8 · 103 for SRR99 [25]), and both decrease with temperature. At 1000 C, the misfit parameter is for both materials for 103 smaller than at room temperature [24,25]. The axial and hoop stresses for TGMF, TGF, and TMF testing, as calculated by FEM (Fig. 11), are indicated in the rafting chart (Fig. 12) and the resulting predictions are
5. Discussion 5.1. Cracks In the substrate the stresses are considerably smaller than the 0.2% yield stress of CMSX-4 (Fig. 11), but for the coating plasticity is expected. The blunt cracks in the outer coating of specimen B (Fig. 5b) reflect this plasticity. Large tensile axial stresses are predicted for the inner surface (Fig. 11), but for crack initiation in the substrate locations with stress concentration are necessary. This is given for the blunt crack tips in the NiAl layer at the inner surface (Fig. 6a) and at the internal pores (Fig. 6b). With cycle number these cracks may grow leading to the final failure. For the nominal mechanical stress of 400 MPa this was achieved after 1337 cycles. A nominal mechanical stress
Fig. 12. Rafting prediction chart after [8] for SRR99 at 1050C with rradial = 0 MPa, indicating the calculated stresses during TGMF (250 MPa: n, 400 MPa: m), TGF (250 MPa: d), and TMF (¤) testing.
B. Baufeld et al. / International Journal of Fatigue 30 (2008) 219–225
sketched schematically in Fig. 1. For TGMF and TGF testing, the hoop stress is compressive at the coating interface and tensile near the inner surface, while for TMF testing the hoop stress is approximately zero over the whole substrate thickness. The axial stresses are, except for the case of TGF testing near the outer coating, compressive for all other investigated cases. According to this rafting chart, for case of TGMF testing with a maximum nominal mechanical stress of 250 MPa, a change from tangential–radial rafting plates near the inner surface to tangential rods near the outer coating are predicted. The plates would appear in cross section as isotropic coarsening (Fig. 7) and in length section as rafts oriented perpendicular to the inner surface (Fig. 6b). The rods would result in isotropic structure in length section (Figs. 6a and 8) and in rafts oriented parallel to the interface of the outer coating. These features were proven for specimen C. For TGMF testing at a higher nominal mechanical stress of 400 MPa and for the TMF testing as well, tangential–radial plates throughout the whole substrate wall are foreseen, and the experimental results (specimen A and E) agree with that. Comparable microstructures of rafting plates perpendicular to the surfaces were found for the leading and the trailing edges of turbine blades after service [11,12,20]. In the case of TGF, for the whole substrate the isotropic coarsening is predicted. Apart from the observed anomalous rafting, this prediction is in accordance with the experimental findings from cross and length sections for specimen D (Fig. 10). The thickening of the c ligament perpendicular to the tensile direction throughout the observed area is not yet explained. Anomalous rafting, which is observed for all investigated specimens in the vicinity of the outer coating interface (Fig. 7), appears as rafts parallel to the interface in cross and length section suggesting tangential–axial rafting plates. Since no large compressive hoop and axial stresses, which are restricted within 10 lm, are expected during the testing (Fig. 11), this variety can not be related with the testing. Anomalous rafting in the vicinity of the coating interface is already reported for turbine blades [12,20] and TMF tested specimens [21]. It was explained with the processing step before the application of the coating, the grid blasting, which introduces deformation into the surface area of the substrate [1,23]. According to these authors, processing related deformation may lead to rafting already during the coating process at high temperatures and further on during service or testing. 6. Conclusion A new TGMF testing set-up has been applied successfully on a system comprising of a CMSX-4 substrate, Pt aluminide outer and an aluminide inner coating for oxidation protection. Similar to the in-service condition, thermal gradients in radial directions were achieved. The resulting multi-axial stresses are reflected in the rafting morphology,
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which can be explained applying finite element modelling. The life limiting process were fatigue cracks, originating either from cracks at the inner coating surface or from internal pores. Acknowledgements The authors are grateful to C. Sick and K. Mull, who have designed and built the mirror furnace, without its outstanding features this investigation would not be possible. Furthermore, they are obliged to P. Agoston for specimen preparation and micrography. The financial support of the ‘‘Deutsche Forschungsgemeinschaft’’ is acknowledged. References [1] Biermann H. Ursachen und Auswirkungen der gerichteten Vergro¨berung (Floßbildung) einkristallinen Nickelbasis-Superlegierungen. Du¨sseldorf: VDI Verlag; 1999. [2] Fahrmann M, Fratzl P, Paris O, Fahrmann E, Johnson WC. Acta Metall Mater 1995;43:1007–22. [3] MacKay RA, Nathal MV. Acta Metall Mater 1990;38:993–1005. [4] Caron P, Khan T. Mater Sci Eng 1983;61:173–84. [5] Saito M, Aoyama T, Hidaka K, Tamaki H, Ohashi T, Nakamura S, et al. Scripta Mater 1996;34:1189–94. [6] Veron M, Brechet Y, Louchet F. Acta Mater 1996;44:3633–41. [7] Lukas P, Cadek J, Sustek V, Kunz L. Mater Sci Eng A 1996;208:149–57. [8] Arrell DJ, Valles JL. Scripta Mater 1996;35:727–32. [9] Mughrabi H, Ott M, Tetzlaff U. Mater Sci Eng A 1997;234– 236:434–7. [10] Reed RC, Matan N, Cox DC, Rist MA, Rae CMF. Acta Mater 1999;47:3367–81. [11] Biermann H, von Grossmann B, Schneider T, Feng H, Mughrabi H. In: Kissinger RD, Deye DJ, Anton DL, Cetel AD, Nathal MV, Pollock TM, Woodford DA, editors. Superalloys, 1996. p. 201–10. [12] von Großmann B. Mikrostrukturelle Bestimmung der lokalen Belastungen in einkristallinen Turbinenschaufeln aus NickelbasisSuperlegierungen. Aachen: Shaker Verlag; 1999. [13] Biermann H, von Grossmann B, Ungar T, Mechsner S, Souvorov A, Drakopoulos M, et al. Acta Mater 2000;48:2221–30. [14] Bartsch M, Marci G, Mull K, Sick C. Adv Eng Mater 1999;1:127–9. [15] Marci G, Mull K, Sick C, Bartsch M. In: Sehitoglu H, Maier HJ, editors. Third symposium on thermo-mechanical fatigue behaviour of materials, West Conshohocken (PA), 1998. p. 296–303. [16] Baufeld B, Bartsch M, Brozˇ P, Schmu¨cker M. Mater Sci Eng A 2004;384:162–71. [17] Baufeld B, Bartsch M, Dalkilic¸ S, Heinzelmann M. Surf Coat Technol 2005;200:282–1286. [18] Bartsch M, Baufeld B, Dalkilic¸ S, Heinzelmann M. Int J Fatigue, in press. [19] Brooks JW, Vermeulen B. TMS Letters 2005;2:21–2. [20] Draper S, Hull D, Dreshfield R. Metall Trans A 1989;20A:683–8. [21] Moretto P, Bressers J. J Mater Sci 1996;31:4817–29. [22] Bressers J, Arrell DJ, Ostolaza KM, Valle´s JL. Mater Sci Eng A 1996;A220:147–54. [23] Biermann H, Tetzlaff U, von Grossmann B, Mughrabi H, Schulze V. Scripta Mater 2000;43:807–12. [24] Glatzel U. Scripta Metall Mater 1994;31:291–6. [25] Mu¨ller L, Link T, Feller-Kniepmeier M. Scripta Metall Mater 1992;26:1297–302. [26] Sengupta A, Putatunda SK, Bartosiewicz L, Hangas J, Nailos PJ, Peputapeck M, et al. J Mater Eng Perform 1994;3:664–72. [27] Pan D, Wright PK, Hemker KJ. Mat Res Soc Symp 2001;654E:M9.3.1–6.
International Journalof Fatigue
International Journal of Fatigue 30 (2008) 219–225
www.elsevier.com/locate/ijfatigue
Advanced thermal gradient mechanical fatigue testing of CMSX-4 with an oxidation protection coating Bernd Baufeld b
a,b,*
, Marion Bartsch a, Michael Heinzelmann
c
a German Aerospace Center (DLR), Linder Ho¨he, 51147 Ko¨ln, Germany Katholieke Universiteit Leuven, Kasteelpark Arenberg 44, 3001 Leuven, Belgium c University of Applied Sciences Bonn-Rhein-Sieg, 53359 Rheinbach, Germany
Accepted 15 January 2007 Available online 15 March 2007
Abstract Frequently, turbine blades are cooled internally, which generates thermal gradients over the blade wall and, consequently, multi-axial stresses in addition to stresses due to centrifugal forces. In order to study these conditions, a new thermal gradient mechanical fatigue (TGMF) testing equipment with a lamp furnace has been developed. The advantages of this furnace are high power (16 lamps a 1000 W), controlled thermal gradients, high heating and cooling rates, and lamp lives exceeding 8000 thermal cycles. The studied material system was the single-crystalline superalloy CMSX-4 with a NiPtAl oxidation protection coating. Different TGMF tests with a maximal surface temperature of 1050 C, mechanical loads up to 400 MPa, and cycle numbers up to 9000 resulted in microstructural changes and defects, reflecting in each case the particular temperature, thermal gradient, and local stresses. For example, phase evolution of the metal coatings and rafting of the c/c 0 substrate morphology was investigated. Furthermore, cracks at the inner specimen surface and at substrate pores were detected. The observed morphology and defects were related to the applied thermomechanical loads using finite element calculations. 2007 Elsevier Ltd. All rights reserved. Keywords: Defects; Cracks; Stress analysis; Superalloys; Thermomechanical fatigue/cycling
1. Introduction In-service, internally cooled turbine blades experience in addition to centrifugal forces multi-axial mechanical loads due to the temperature difference between the cooled inner and the heated outer blade surfaces. The colder regions shrink, the hotter expand, leading to large in-plane stresses. The resulting stress fields are very complex, which in concur of high temperatures and cyclic loading ensue into very different morphological changes and defect developments at different locations of a blade. Examples for morphological changes and defects are cracks, surface roughening, * Corresponding author. Address: Katholieke Universiteit Leuven, Kasteelpark Arenberg 44, 3001 Leuven, Belgium. Tel.: +32 16 321534; fax: +32 16 321992. E-mail address: [email protected] (B. Baufeld).
0142-1123/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2007.01.034
diffusion, phase transformations, and coarsening of microstructures. Modern turbine blades usually consist of a Ni base superalloy with c matrix and c 0 cubical precipitates. During exposure to high temperatures coarsening of the originally ‘‘sharp’’ c/c 0 microstructure evolves in the thickening of the c phase and the combining of neighbouring c 0 precipitates, which increase both with time and temperature [1]. Neighbouring c 0 cuboids may grow together leading to c 0 platelets, which are oriented randomly perpendicular to all three Æ1 0 0æ directions [2,3]. Besides this isotropic coarsening, the so-called rafting may occur, if the alloy is exposed additionally to sufficiently high mechanical loads (for example [4–10]). Rafting can be discerned between c 0 rods and c 0 plates [8], depending on the stress field. Hence, the resulting rafting structure can be used as indicator of the multi-axial stress field during high temperature exposure.
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B. Baufeld et al. / International Journal of Fatigue 30 (2008) 219–225
Depending on the location in a turbine blade, after service different coarsening and rafting were observed [11–13]. Since rafting may either improve or deteriorate the mechanical properties of a system [1], the development of rafting must be understood for lifetime prediction. In order to study morphological changes and defects, which may occur in-service and limit the performance of turbine blades, CMSX-4 Ni based superalloy with a Pt aluminide oxidation protection coating was subjected in the laboratory to conditions, which simulate the in-service condition as close as possible. The chosen testing methods were the so-called thermal gradient mechanical fatigue (TGMF) testing, which realises cyclic thermal and mechanical loading including a thermal gradient over the specimen wall, thermal gradient fatigue (TGF) testing without an applied mechanical loading but with a thermal gradient, and thermal mechanical fatigue (TMF) testing without a thermal gradient but with mechanical loading. 2. Experimental
observed, which presumably are related with the growth of dendrites during the solidification of the metal. The commercially available platinum-modified aluminide coating was prepared by electroplating platinum and diffusing aluminium into the substrate by chemical vapour deposition. In the as-coated condition this coating has a thickness of 65 lm and consists mainly of two phases roughly described as PtAl2 and b NiAl (Fig. 2). Within the coating a line of residual oxides from the grit blasting and near the substrate W rich precipitates can be found. Frequently, large surface defects in the form of embedded oxides can be observed. The microstructures were investigated by light optical means and with scanning electron microscopy. Standard techniques were applied for the preparation of specimen sections. Length and cross sections with {1 0 0} surfaces of the cubic substrate facilitate the interpretation of the c/c 0 structures of the substrate (Fig. 1). Thus, depending on their orientation, rods and plates may appear either equiaxed or as elongated structures, the latter called henceforth rafts.
2.1. Specimens 2.2. Testing procedure The studied system is composed of a nickel base superalloy CMSX-4 substrate, a NiPtAl oxidation protection coating at the outer surface, and an aluminized inner surface. CMSX-4, a second-generation single-crystalline Ni base superalloy, is characterized by its cubical c/c 0 structure (Ni/Ni3Al). Tubular specimens with an inner diameter of 7 mm and an outer diameter of about 10 mm (before coating) were used for imposing a radial thermal gradient by internal cooling and external heating. The tensile axis of the specimens was nominally in [1 0 0] direction (Fig. 1). Within the single crystal several parallel lines of pores, slightly inclined towards the tensile axis, were
Fig. 1. Schematic drawing of a segment of the tubular specimen, defining the axisymmetric FEM model and the orientation of SEM sections. In addition, rafting variants in dependence of the thermomechanical loading and of the radial position are visualized in form of cubes, platelets and rods.
In order to study the influence of multi-axial stresses a load-controlled servo-hydraulic testing rig with a newly developed radiation furnace was applied, which is a successor of a prototype [14,15] already employed successfully for the investigation of metal coatings [16] and thermal barrier coatings [17,18]. The gold coated mirror of the furnace consists of 16 segments of ellipses, where in one of the focus lines of each ellipse a 1000 W quartz bulb and at the other, common focus line the specimen is positioned (Fig. 3). With this very effective system fast heating from ambient temperatures up to 1000 C can be achieved within 15 s. Due to an advanced cooling system of the bulbs, their life usually exceed 15,000 heating cycles. A temperature gradient is generated by inner cooling of the specimen with controlled air flow. Mass flow and temperature of the cooling air can be adjusted. For the current
Fig. 2. Cross section of an as-coated specimen showing the two-phased coating consisting of b NiAl (darker contrast) and PtAl2 (brighter contrast), a line of residual oxides and a surface defect.
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number (3000) without failure was achieved for specimen C with a lower mechanical loading (250 MPa). In the case of the TGF testing of specimen D, similar temperature cycle was applied for 9000 cycles, but the mechanical load was held constantly at zero. Specimen E was subjected to 1510 TMF cycles with switched-off internal cooling and a maximum nominal stress of 250 MPa. 3. Results 3.1. Morphology at the surfaces Fig. 3. Schematic drawing of the furnace consisting of 16 mirror segments, where the 16 quartz bulbs at located at one of each focal line and the specimen at their common focal line. The half cylindrical shutters, which block the radiation from the specimen during cooling, are not shown.
investigation an air flow of 100 l/min and an air temperature of about 350 C, entering the tubular specimen from the top were chosen. For a surface temperature of 1050 C under quasi-stationary thermal conditions, a temperature difference of about 70 C over the specimen wall was determined, leading to a radial heat flux of 1.3 MW/ m2. To the authors knowledge besides from the DLR group [14–18] only few reports are available investigating thermal mechanical fatigue with an additionally applied temperature gradient [19]. Fast cooling is obtained with two half cylindrical shutters (not shown in Fig. 3), which are pushed vertically into the furnace interior to block the radiation and which shower the specimen surface with cold compressed air. During cooling, this leads to an inverted radial temperature difference with lower temperatures on the outer surface than inside the specimen. Fig. 4 gives an example for the TGMF cycle with a cycle length of about 2 min and a maximal surface temperature at the axial specimen centre of 1050 C. Specimen A and B were TGMF tested with a nominal mechanical stress of 400 MPa; specimen A for 1000 cycles and specimen B until failure after 1337 cycles (Fig. 5). A higher TGMF cycle
Due to thermal exposure a thermally grown oxide (TGO) developed at the outer coating surface and the originally two-phased outer coating layer (PtAl2 and b NiAl) gradually transformed into a single phased b layer. For specimen A with the shortest time at high temperature (1000 cycles) this transformation is not completed even in the hottest zone, while specimen B (1337 cycles) reflects over 20 mm length a gradual change from the two phased area in the colder zone towards a single phased area in the hottest zone. For specimen C, D, and E, with cycle numbers of 1510 and more, the transformation within the observed region was completed. In addition, with time and temperature, increasingly precipitates with refractory elements from the substrate emerge in the outer coating (Fig. 5b). The inner surface of all specimens is coated with b NiAl and at the interface to the substrate an inter-diffusion zone exists with precipitates of refractory elements from the substrate (Fig. 6a). With increasing time and temperature, such precipitates occur progressively more in the inner coating. Since the temperature of the internal cooling air increases during its path from the top to the bottom of the specimen acquiring and transporting the heat from the specimen, the precipitation zone increases, and the single phase b NiAl zone decreases from top to bottom. Furthermore, a thin and irregular TGO grows at the inner surface. 3.2. Cracks
Fig. 4. Surface temperature and nominal mechanical stress during a TGMF cycle.
For specimen C, D, and E, with respectively no mechanical load applied or with a nominal mechanical stress of 250 MPa no cracks were observed. For specimens A and B with a nominal mechanical stress of 400 MPa, in contrast, various cracks occurred. Usually, they are located at the inner surface (Fig. 6a) and at the pores within the substrate (Fig. 6b). Cracks at the outer surface in the case of specimen B (Fig. 5) are probably related to the final failure of this specimen. They are blunt, occur only in the vicinity of the fracture surface and are not oxidized (Fig. 5b). The cracks on the inner surface and at the inner pores are located in the region with highest temperatures at the axial centre. The surfaces of the cracks at the inner surface are oxidized (Fig. 6a), indicating sufficient time at temperature, which is in contrast to the cracks at the outer
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Fig. 5. Light optical (a) and electron microscopic (b) image of length section of specimen B showing the fracture surface and cracks at internal pores, at the inner surface, and at the outer surface.
surface of specimen B. Usually, they are observed only in the single phased b NiAl layer, but occasionally sharp cracks penetrate into the precipitation zone (Fig. 6a). 3.3. Coarsening and rafting For all specimens increased coarsening of the c/c 0 microstructure was found towards the axial centre of the specimen, i.e. towards the highest temperature, and the following description will focus on this region. Depending on the type of testing and on the radial location, different types of coarsening were observed. One coarsening feature was common to all specimens. It is located in the very vicinity of the interface between substrate and outer coating, has an extension of about 10 lm, and is oriented parallel to the interface (Fig. 7). Rafting with similar features is already reported in literature and called anomalous rafting [1,20–23]. Specimen C, TGMF tested with a maximum nominal stress of 250 MPa, shows a change in the type of rafting over the wall thickness. Near the inner surface, rafting appears in the length section as coarsening in radial direction (Fig. 8a) and in the cross section as isotropic coarsening (Fig. 9). Towards the outer surface this changes, and in the length section isotropic coarsening is observed (Fig. 8b). Towards the interface of the outer coating, the structure remains isotropic until the region of anomalous
rafting is reached (Fig. 7). In the cross section, the coarsening changes from isotropic near the inner surface towards directional coarsening in tangential direction near the outer coating. Since this directionally coarsening is observed at a distance of at least 60 lm from the interface and thus exceeds the width of directionally rafting detected in the length section, it is different to the anomalous rafting. For specimen A, TGMF tested with a maximum nominal stress of 400 MPa, and for specimen E, TMF tested with a maximum nominal stress of 250 MPa, besides the
Fig. 7. Length section of specimen C showing in the vicinity of the coating rafting parallel to the interface (anomalous rafting) and isotropic coarsening towards the substrate.
Fig. 6. Length section of specimen A, showing cracks at the inner surface (a) and at an internal pore (b) (inset: detailed view of crack tip).
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Fig. 8. Chemically etched length section of specimen C, showing rafting perpendicular to the tensile direction near the inner surface (a) and isotropic coarsening in the centre of the substrate (b). The symbol ‘‘h’’ in the cartoons indicates the location of the micrograph.
interface and over the axial length of 20 mm, a preferential thickening of the c ligaments perpendicular to the tensile axis took place (Fig. 10). In contrast with conventional rafting, this thickening is not accompanied with the coalescence of neighbouring c 0 precipitates. 4. Finite element modelling
Fig. 9. Ion etched cross section of specimen C near the inner surface. The symbol ‘‘h’’ in the cartoon indicates the location of the micrograph.
anomalous rafting no radial dependence of the rafting was observed. Throughout the whole wall thickness the rafts in the length section appear elongated in radial direction. For the TGF tested specimen D, again with the exception of the anomalous rafting in the vicinity of the outer coating, no directional rafting was observed throughout the whole width of the specimen wall and the structure remained isotropic. However, throughout the whole investigated area, i.e. from inner surface towards the coating
The distribution of axial and hoop stresses over the cross section of a coated specimen during a cycle has been calculated by means of the finite element method (FEM). The axisymmetric, three-dimensional model is based on a sector of a specimen wall (Fig. 1) and comprises the anisotropic single-crystalline substrate and the outer metal coating. As far as available, the material properties were taken in dependence on the temperature (Table 1). The temperatures at the surfaces during the quasi-stationary high temperature sequence of a thermal cycle were taken as boundary conditions, i.e. 1050C at the hot outer surface and 980 C at the inner surface. In Fig. 11, the axial stress distribution over the whole wall for the case of the [0 1 0] radial direction is given for nominal mechanical loads of 0, 250 and 400 MPa. In addition, the hoop and the radial stress are shown. Without an applied mechanical load, axial and hoop stresses decrease from almost +100 MPa at the inner surface towards about 50 MPa at the outer surface. Thus, if no mechanical load is applied axial and hoop stresses are tensile at the inner surface and compressive at the outer Table 1 Coefficient of thermal expansion CTE, thermal conductivity k, density q, heat capacity cp, elastic modulus E, shear modulus, and Poisson ratio m for the single-crystalline substrate and the outer coating for 1100 C
Fig. 10. Length section of TGF specimen D showing the substrate near the axial centre with an inset at higher magnification and a cartoon. The symbol ‘‘h’’ indicates the location of the micrograph.
CTE (106 l/K) k (W/m K) q (g/cm3) cp (J/kg K) E (GPa) G (GPa) m
Substrate
Outer coating
16.2 31.02 8.7 0.960 78.5 93.8 0.39
17.37 29.34 7.47 0.706 40.0 0.35
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of 250 MPa was too small (specimen C), to obtain crack initiation within a reasonable testing time (3000 cycles). 5.2. Coarsening and rafting
Fig. 11. FEM stress distribution in the case of an [0 1 0] radial direction for 980 C at the inner surface (substrate, r = 3.5 mm) and 1050 C at the outer surface (metal coating, r = 5.1 mm). Stresses are given in hoop, axial, and radial direction for a nominal mechanical load of 0 MPa, and in axial direction for a nominal mechanical load of 250 and 400 MPa. For comparison, the respective, temperature dependent yield strength for CMSX-4 [26] and a Pt aluminide [27] is given.
surface. The radial stress is tensile over the whole specimen wall and smaller than 10 MPa. With the application of an additional tensile load in axial direction, the axial stress distribution curve is shifted in positive direction, while hoop and radial stresses are hardly affected. With sufficient high mechanical loads, the specimen may be subjected over the whole wall only to tensile axial stresses (Fig. 11). According to further FEM calculations not shown here, the anisotropy of the substrate has a minor influence on the stresses. For example, with no applied mechanical load, the axial and hoop stresses at the inner surface are only somewhat smaller for the [0 1 0] direction (both 90 MPa, Fig. 11) than for the [0 1 1] direction (hoop stress: 154 MPa, axial stress: 111 MPa). The stress development over the wall is comparable for all directions.
In the following the observed isotropic coarsening and rafting will be related to the stress fields during testing. For simplicity, the discussion will concentrate on locations of the single-crystalline substrate, where the microstructure is oriented in such a way, that the main axes of the former cuboids are parallel to the axial, radial and hoop direction. While for the (0 0 1) length section this is fulfilled everywhere, for the (1 0 0) cross section one is restricted to the locations where one axis of the former cuboids is along the interface or the inner surface. In [8] a rafting prediction chart under multi-axial loading is proposed for the superalloy SRR99. Differently oriented rafting rods or plates develop, depending on the multi-axial stress field. For small stresses an isotropic region is predicted, which will be not shifted by temperature variations, but which will increase or decrease its size. Fig. 12 is an adaptation of this rafting prediction chart, assuming a negligible radial stress. Accordingly, depending on the direction and amount of axial and hoop stresses, isotropic coarsening or rafting rods and plates in axial, radial and hoop directions are expected. It is assumed, that the rafting of CMSX-4 is similar to the one predicted for SRR99, since the material properties are comparable. Especially important for rafting is the misfit parameter, which are for both superalloys negative at room temperature (1.3 · 103 for CMSX-4 [24] and 0.8 · 103 for SRR99 [25]), and both decrease with temperature. At 1000 C, the misfit parameter is for both materials for 103 smaller than at room temperature [24,25]. The axial and hoop stresses for TGMF, TGF, and TMF testing, as calculated by FEM (Fig. 11), are indicated in the rafting chart (Fig. 12) and the resulting predictions are
5. Discussion 5.1. Cracks In the substrate the stresses are considerably smaller than the 0.2% yield stress of CMSX-4 (Fig. 11), but for the coating plasticity is expected. The blunt cracks in the outer coating of specimen B (Fig. 5b) reflect this plasticity. Large tensile axial stresses are predicted for the inner surface (Fig. 11), but for crack initiation in the substrate locations with stress concentration are necessary. This is given for the blunt crack tips in the NiAl layer at the inner surface (Fig. 6a) and at the internal pores (Fig. 6b). With cycle number these cracks may grow leading to the final failure. For the nominal mechanical stress of 400 MPa this was achieved after 1337 cycles. A nominal mechanical stress
Fig. 12. Rafting prediction chart after [8] for SRR99 at 1050C with rradial = 0 MPa, indicating the calculated stresses during TGMF (250 MPa: n, 400 MPa: m), TGF (250 MPa: d), and TMF (¤) testing.
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sketched schematically in Fig. 1. For TGMF and TGF testing, the hoop stress is compressive at the coating interface and tensile near the inner surface, while for TMF testing the hoop stress is approximately zero over the whole substrate thickness. The axial stresses are, except for the case of TGF testing near the outer coating, compressive for all other investigated cases. According to this rafting chart, for case of TGMF testing with a maximum nominal mechanical stress of 250 MPa, a change from tangential–radial rafting plates near the inner surface to tangential rods near the outer coating are predicted. The plates would appear in cross section as isotropic coarsening (Fig. 7) and in length section as rafts oriented perpendicular to the inner surface (Fig. 6b). The rods would result in isotropic structure in length section (Figs. 6a and 8) and in rafts oriented parallel to the interface of the outer coating. These features were proven for specimen C. For TGMF testing at a higher nominal mechanical stress of 400 MPa and for the TMF testing as well, tangential–radial plates throughout the whole substrate wall are foreseen, and the experimental results (specimen A and E) agree with that. Comparable microstructures of rafting plates perpendicular to the surfaces were found for the leading and the trailing edges of turbine blades after service [11,12,20]. In the case of TGF, for the whole substrate the isotropic coarsening is predicted. Apart from the observed anomalous rafting, this prediction is in accordance with the experimental findings from cross and length sections for specimen D (Fig. 10). The thickening of the c ligament perpendicular to the tensile direction throughout the observed area is not yet explained. Anomalous rafting, which is observed for all investigated specimens in the vicinity of the outer coating interface (Fig. 7), appears as rafts parallel to the interface in cross and length section suggesting tangential–axial rafting plates. Since no large compressive hoop and axial stresses, which are restricted within 10 lm, are expected during the testing (Fig. 11), this variety can not be related with the testing. Anomalous rafting in the vicinity of the coating interface is already reported for turbine blades [12,20] and TMF tested specimens [21]. It was explained with the processing step before the application of the coating, the grid blasting, which introduces deformation into the surface area of the substrate [1,23]. According to these authors, processing related deformation may lead to rafting already during the coating process at high temperatures and further on during service or testing. 6. Conclusion A new TGMF testing set-up has been applied successfully on a system comprising of a CMSX-4 substrate, Pt aluminide outer and an aluminide inner coating for oxidation protection. Similar to the in-service condition, thermal gradients in radial directions were achieved. The resulting multi-axial stresses are reflected in the rafting morphology,
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which can be explained applying finite element modelling. The life limiting process were fatigue cracks, originating either from cracks at the inner coating surface or from internal pores. Acknowledgements The authors are grateful to C. Sick and K. Mull, who have designed and built the mirror furnace, without its outstanding features this investigation would not be possible. Furthermore, they are obliged to P. Agoston for specimen preparation and micrography. The financial support of the ‘‘Deutsche Forschungsgemeinschaft’’ is acknowledged. References [1] Biermann H. Ursachen und Auswirkungen der gerichteten Vergro¨berung (Floßbildung) einkristallinen Nickelbasis-Superlegierungen. Du¨sseldorf: VDI Verlag; 1999. [2] Fahrmann M, Fratzl P, Paris O, Fahrmann E, Johnson WC. Acta Metall Mater 1995;43:1007–22. [3] MacKay RA, Nathal MV. Acta Metall Mater 1990;38:993–1005. [4] Caron P, Khan T. Mater Sci Eng 1983;61:173–84. [5] Saito M, Aoyama T, Hidaka K, Tamaki H, Ohashi T, Nakamura S, et al. Scripta Mater 1996;34:1189–94. [6] Veron M, Brechet Y, Louchet F. Acta Mater 1996;44:3633–41. [7] Lukas P, Cadek J, Sustek V, Kunz L. Mater Sci Eng A 1996;208:149–57. [8] Arrell DJ, Valles JL. Scripta Mater 1996;35:727–32. [9] Mughrabi H, Ott M, Tetzlaff U. Mater Sci Eng A 1997;234– 236:434–7. [10] Reed RC, Matan N, Cox DC, Rist MA, Rae CMF. Acta Mater 1999;47:3367–81. [11] Biermann H, von Grossmann B, Schneider T, Feng H, Mughrabi H. In: Kissinger RD, Deye DJ, Anton DL, Cetel AD, Nathal MV, Pollock TM, Woodford DA, editors. Superalloys, 1996. p. 201–10. [12] von Großmann B. Mikrostrukturelle Bestimmung der lokalen Belastungen in einkristallinen Turbinenschaufeln aus NickelbasisSuperlegierungen. Aachen: Shaker Verlag; 1999. [13] Biermann H, von Grossmann B, Ungar T, Mechsner S, Souvorov A, Drakopoulos M, et al. Acta Mater 2000;48:2221–30. [14] Bartsch M, Marci G, Mull K, Sick C. Adv Eng Mater 1999;1:127–9. [15] Marci G, Mull K, Sick C, Bartsch M. In: Sehitoglu H, Maier HJ, editors. Third symposium on thermo-mechanical fatigue behaviour of materials, West Conshohocken (PA), 1998. p. 296–303. [16] Baufeld B, Bartsch M, Brozˇ P, Schmu¨cker M. Mater Sci Eng A 2004;384:162–71. [17] Baufeld B, Bartsch M, Dalkilic¸ S, Heinzelmann M. Surf Coat Technol 2005;200:282–1286. [18] Bartsch M, Baufeld B, Dalkilic¸ S, Heinzelmann M. Int J Fatigue, in press. [19] Brooks JW, Vermeulen B. TMS Letters 2005;2:21–2. [20] Draper S, Hull D, Dreshfield R. Metall Trans A 1989;20A:683–8. [21] Moretto P, Bressers J. J Mater Sci 1996;31:4817–29. [22] Bressers J, Arrell DJ, Ostolaza KM, Valle´s JL. Mater Sci Eng A 1996;A220:147–54. [23] Biermann H, Tetzlaff U, von Grossmann B, Mughrabi H, Schulze V. Scripta Mater 2000;43:807–12. [24] Glatzel U. Scripta Metall Mater 1994;31:291–6. [25] Mu¨ller L, Link T, Feller-Kniepmeier M. Scripta Metall Mater 1992;26:1297–302. [26] Sengupta A, Putatunda SK, Bartosiewicz L, Hangas J, Nailos PJ, Peputapeck M, et al. J Mater Eng Perform 1994;3:664–72. [27] Pan D, Wright PK, Hemker KJ. Mat Res Soc Symp 2001;654E:M9.3.1–6.