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Micromechanisms of fatigue crack growth in a forged Inconel 718 nickel-based superalloy
Materials Science and Engineering A270 (1999) 308 – 322 www.elsevier.com/locate/msea
Micromechanisms of fatigue crack growth in a forged Inconel 718 nickel-based superalloy C. Mercer a, A.B.O. Soboyejo b, W.O. Soboyejo a,* b
a Department of Materials Science and Engineering, The Ohio State Uni6ersity, 2041 College Road, Columbus, OH 43210, USA Departments of Aerospace and Agricultural Engineering, The Ohio State Uni6ersity, 590 Woody Hayes Dri6e, Columbus, OH 43210, USA
Received 8 July 1998; received in revised form 3 May 1999
Abstract The micromechanisms of fatigue crack propagation in a forged, polycrystalline IN 718 nickel-based superalloy are evaluated. Fracture modes under cyclic loading were established by scanning electron microscopy analysis. The results of the fractographic analysis are presented on a fracture mechanism map that shows the dependence of fracture modes on the maximum stress intensity factor, Kmax, and the stress intensity factor range, DK. Plastic deformation associated with fatigue crack growth was studied using transmission electron microscopy. The effects of DK and Kmax on the mechanisms of fatigue crack growth in this alloy are discussed within the context of a two-parameter crack growth law. Possible extensions to the Paris law are also proposed for crack growth in the near-threshold and high DK regimes. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Fatigue crack growth; Nickel-based superalloy; Micromechanisms
1. Introduction The principal application of nickel-based superalloys is for the high-temperature turbine components of modern gas turbine engines. Turbine blades must withstand very high temperatures and also require good creep resistance. Hence, blades are manufactured from cast nickel-based superalloys, where large grain sizes can be engineered to provide the necessary creep properties. In modern engines, blades may be either directionally solidified or may even be single crystals that provide maximum creep resistance. Turbine discs are not subjected to such extreme temperatures as blades but have greater strength requirements imposed on them. As a result, turbine discs are usually manufactured from forged, polycrystalline nickel-base alloys such as Inconel 718. However, in spite of the widespread application of nickel-based superalloys in gas turbine engines, our current understanding of fatigue mechanisms in these materials is still somewhat limited, even after a number of prior investigations [1 – 9]. These investigations have * Corresponding author. Tel.: +1-614-292-0996; fax: + 1-614-2921537.
been largely concerned with mechanisms of fatigue crack initiation, particularly the dislocation configurations that arise during low and high cycle fatigue of nickel alloys. Very limited work appears to have been performed concerning the micromechanisms of cracktip deformation and fracture that occur during fatigue crack propagation. There is, therefore, a need for detailed studies of the micromechanisms of fatigue crack propagation in structural Ni-based superalloys. This paper presents the results of a recent study of the micromechanisms of fatigue crack propagation in IN 718, a typical forged, polycrystalline Ni-based superalloy employed in turbine disc applications. Following a brief description of material processing and microstructure, the experimental techniques are described in detail. Fatigue crack growth rate data at various stress ratios are then presented. Micromechanisms of fracture and crack-tip deformation under cyclic loading are then proposed based on scanning electron microscopy (SEM) studies of fracture surfaces and transmission electron microscopy (TEM) examination of fatigue crack-tip regions. The results of the fractographic analysis are summarized on a fatigue mechanism map. Fatigue crack growth laws are presented for the assessment of the combined effects of the
0921-5093/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 9 ) 0 0 2 1 4 - 2
C. Mercer et al. / Materials Science and Engineering A270 (1999) 308–322 Table 1 Chemical composition of IN 718 forging Element
Weight (%)
Ni C Mn Si Cr Co Fe Mo Nb Ti Al B S P Cu Ta O N Mg
54.03 0.024 0.08 0.08 17.99 0.30 17.55 2.96 5.35 0.940 0.49 0.0027 0.0002 0.008 0.03 0.01 6 ppm 64 ppm 21 ppm
stress intensity factor range, DK, and the stress ratio, R. A detailed discussion of the effects of stress intensity factor range, DK, maximum stress intensity, Kmax, and stress ratio, R, on the fatigue behavior of this material is then presented.
2. Materials The IN 718 forging that was used in this study was supplied by Wyman Gordon (Houston, TX) in the form of a 5.5 mm thick plate. The plate was cut from a triple-melted (vacuum induction melting+ vacuum arc remelting+electroslag remelting), fine-grained billet supplied by Special Metals Corporation (New Hartford, NY). The actual chemical composition of the
forging is given in Table 1. Metallographic analysis was carried out following mechanical polishing and electrolytic etching in oxalic acid solution for approximately 30 s using a 6 V d.c. power supply. A typical optical micrograph of the IN 718 alloy is presented in Fig. 1. The microstructure consists of nearly equiaxed grains of the nickel-rich face-centered cubic solid solution (g phase) with an average grain size of 30 mm. A moderate density of lenticular Ni3Nb precipitates (d phase) was also observed within the g matrix (Fig. 1). The orientations of these d-phase precipitates within the matrix material appeared to be somewhat irregular.
3. Experimental procedures Fatigue crack growth experiments were conducted under constant stress ranges on single edge notched bend (SEN) specimens at stress ratios, R, (R=smin/ smax), of 0.1, 0.3, 0.5 and 0.8. Fatigue crack growth testing was carried out under computer-controlled Mode I loading conditions using a software package that was supplied by Fracture Technology Associates (Pleasant Valley, PA). A cyclic frequency of 10 Hz was used during the tests. Crack growth was monitored continuously during the fatigue testing using a direct current potential drop method. Some of the fatigue tests were carried out until specimen failure occurred. However, most of the tests were stopped prior to specimen failure. The tests were stopped at a stress intensity factor range that corresponded to one of the three distinct regimes of the fatigue crack growth curve, i.e. near-threshold, Paris and high DK regimes [10]. The tests were stopped to allow subsequent TEM examination of the crack-tip regions of the specimens to be carried out in the near-threshold, Paris and high DK regimes. The 3 mm diameter crack-tip TEM foils were taken from the crack-tip region of the specimens and prepared using precision dimpling and ion milling techniques. It is important to note here that the tips of the cracks were located at a distance of approximately one plastic zone from the center of the dimple. The size of the plastic zone, rp, was estimated using the following expression: rp =
Fig. 1. Optical micrograph showing the distribution of Ni3Nb precipitates (d phase) in the general microstructure of forged IN 718 alloy.
309
1 DK p 2sy
2
(1)
where DK is the final stress intensity factor range just prior to stopping the test and sy is the yield stress. Considerable experimental effort was needed to produce the crack-tip foils by the technique already described. For comparison, TEM foils were also taken from undeformed material well away from the fatigue crack.
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Fig. 2. Fatigue crack growth curves (da/dN versus DK) for forged IN 718 alloy, at stress ratios of 0.1, 0.3, 0.5 and 0.8.
These were prepared using the same dimpling and ion milling methods that were used for the preparation of the crack-tip TEM foils. Comparison of the deformed and undeformed material was then carried out in the TEM. Differences between the deformation substructures in the deformed and undeformed material were attributed to the effects of cyclic crack-tip plasticity. Following TEM analysis, the remaining portions of the specimens (not tested to failure) were fractured under monotonic loading. The fracture surfaces of all the specimens were then examined using SEM techniques. Fracture surfaces that corresponded to the near-threshold, Paris and high DK regimes of the fatigue crack growth curve at each stress ratio were examined carefully to determine the effects of the stress intensity factor range on the cyclic fracture mechanisms.
4. Results
4.1. Fatigue crack growth rates The da/dN versus DK fatigue crack growth curves obtained for this alloy at each of the four stress ratios employed are presented in Fig. 2. The plot clearly shows the near-threshold, Paris and high DK regimes of each curve. Stable crack growth was observed at Kmax levels below 50 MPa m. The data are in good agreement with the results obtained from other studies of
similar alloys [1,9]. The Paris exponents, m, for each stress ratio are presented in Table 2. The values of m in Table 2 are typical for a metallic material which generally has a Paris exponent of between 2 and 4 [10]. At Kmax levels above 50 MPa m, the crack growth rates at all four stress ratios were observed to accelerate until catastrophic failure occurred. This region corresponds to the high DK regime of the curves. TEM analysis was carried out on specimens where fatigue testing was halted at DK values of approximately 13, 25 and 35 MPa m for a stress ratio of 0.1. At this stress ratio, these values correspond respectively to the near-threshold regime, the lower part of the Paris regime and the upper part of the Paris regime. Transmission electron microscopy analysis was also performed on a specimen tested at a stress ratio of 0.8 for which fatigue cycling was stopped at a DK of 13.3 MPa m. This value corresponds to the high DK regime of the fatigue curve just prior to catastrophic failure. After failure, scanning electron microscopy Table 2 Variation of Paris exponent, m, with stress ratio, R, for forged IN 718 Stress ratio, R
Paris exponent, m
0.1 0.3 0.5 0.8
3.0 3.4 2.5 1.8
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Fig. 3. Scanning electron micrographs showing fracture surfaces of IN 718 corresponding to (a) the near-threshold regime, (b) the lower Paris regime, (c) the upper Paris regime, and (d) the high DK regime of the fatigue crack growth curve, and (e) the tensile overload region of the specimen, for a stress ratio of 0.1.
analysis of the fracture surfaces of each specimen (from the near-threshold regime until failure) was carried out at all four stress ratios, i.e. R =0.1, 0.3, 0.5 and 0.8.
4.2. Fractography 4.2.1. Stress ratio of 0.1 Typical fatigue fracture surfaces corresponding to the near-threshold regime and lower portion of the Paris regime of this alloy tested at a stress ratio of 0.1 are presented in Fig. 3(a) and (b), respectively. The mode of fracture under cyclic loading at this stress ratio in both regimes appeared to be a transgranular, faceted,
crystallographic fracture mode, as can be seen by the sharp, angular facets in the fracture surfaces (Fig. 3). Very fine fatigue striations were observed on some of the facets, indicating the presence of very localized plasticity during fatigue crack growth in the nearthreshold and lower Paris regimes. It is important to note here that although a faceted, crystallographic fracture mode is often observed in the near-threshold regime of metallic materials [10], it is somewhat unusual for a ductile metal to exhibit this mode of fracture in the Paris or steady-state crack growth regime. Such behavior is generally more typical of more brittle materials. However, Lerch and An-
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tolovich [9] have also observed crystallographic fracture modes occurring up to similar DK levels in the single ´ N4. crystal nickel-based superalloy RENE A possible explanation for this behavior is that, even in the lower Paris regime, stress intensity levels are still significantly below the fracture toughness of IN 718. Hence, the material fractures in a mode that is generally associated with low stress intensity values where the extent of plastic deformation is relatively small. However, as the extent of plasticity increases, a transition in fracture mode to a plasticity-controlled crack-tip blunting mechanism was observed to occur. This is generally associated with the formation of relatively coarse striations, as suggested by Laird and Smith [11]. The transition to a classical striation type of fracture mode corresponding to greater levels of plasticity was observed at stress intensity factor ranges\ 35 MPa m at this stress ratio. These stress intensity factor ranges correspond to the upper Paris regime (Fig. 3(c)). This is generally indicative of a pure fatigue crack growth mechanism that is controlled by duplex slip processes that give rise to crack-tip blunting [11]. It is interesting to note that the transition from the faceted fracture mode to the striation mechanism occurred when the crack-tip opening displacement was approximately equal to the size of the facets on the crystallographic fracture surface (approximately 5 mm). At high DK
levels (\ 45 MPa m), a ductile-dimpled fracture mode was observed in addition to the fatigue striations as the Kmax levels approached the fracture toughness of the IN 718 material (Fig. 3(d)). Hence, the departure of the Paris line in the high DK regime is thought to be due to the additional contributions from ‘static’ or ‘monotonic’ (ductile dimpled) fracture modes (Fig. 3(d)) [12]. The tensile overload region of the fracture surface is compared with the fracture modes in the different fatigue regimes in Fig. 3(e). The classical ductile-dimpled fracture mechanism observed is similar to the monotonic fracture mode observed in the high DK fatigue regime.
4.2.2. Stress ratios of 0.3 and 0.5 The fatigue fracture surfaces observed at stress ratios of 0.3 and 0.5 were very similar to those corresponding to a stress ratio of 0.1, and are presented in Figs. 4 and 5. Crystallographic faceted fracture was observed in the near-threshold and lower Paris regimes, with very fine striations clearly visible on some of the crystallographic facets. The fracture mechanism under cyclic loading was observed to change to more classical crack-tip blunting, indicated by the formation of relatively coarse striations. The transition to the plastic-blunting mechanism was observed to occur at DK levels of 22 and 17 MPa m for stress ratios of 0.3 and 0.5, respectively.
Fig. 4. Scanning electron micrographs showing fracture surfaces of IN 718 corresponding to (a) the near-threshold regime, (b) the lower Paris regime, (c) the upper Paris regime and (d) the high DK regime of the fatigue crack growth curve, for a stress ratio of 0.3.
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Fig. 5. Scanning electron micrographs showing fracture surfaces of IN 718 corresponding to (a) the near-threshold regime, (b) the lower Paris regime, (c) the upper Paris regime and (d) the high DK regime of the fatigue crack growth curve, for a stress ratio of 0.5.
Finally, in the high DK regimes of these two curves, the onset ductile-dimple static fracture modes in combination with striation formation due to cyclic loading, gave rise to the rapid acceleration in crack growth rates observed just prior to catastrophic failure in the final stages of the test.
4.2.3. Stress ratio of 0.8 The fracture surfaces of the specimen fatigue tested at a stress ratio of 0.8 are shown in Fig. 6. A transgranular, crystallographic mode of fracture was observed in the near-threshold regime (Fig. 6(a)), as was observed for the R=0.1 case already described. However, at this R ratio, components of this crystallographic fracture mode were present throughout the Paris regime and well into the high DK regime. Very fine striations were observed on the crystallographic facets in the Paris regime (Fig. 6(b)). Secondary cracking was also apparent on the fracture surfaces within the Paris regime. In the high DK regime, the ductile-dimpled static fracture mode was observed to be active as in the case for R= 0.1. However, as already mentioned, the crystallographic fracture mode was also present in this regime. Therefore, the mode of fracture in the high DK regime at this stress ratio appears to involve a combination of crystallographic fatigue fracture and ductiledimpled static fracture (Fig. 6(c)).
The various fatigue regimes and corresponding fracture mechanisms can now be added to the basic fatigue crack growth curves, and this is shown in Fig. 7. The plots clearly show the DK levels and crack growth rates at which transitions between fatigue regimes and/or fracture modes occur for each stress ratio that was examined.
4.3. Crack-tip deformation mechanisms The TEM micrographs of the undeformed substructure are given in Fig. 8. The micrographs show a deformation-free substructure with a very low dislocation density, typical of an annealed microstructure. The elongated Ni3Nb particles are clearly apparent in the figure. No observable evidence of deformation was detected in these precipitates prior to fatigue loading. The TEM micrographs showing the crack-tip regions for the near-threshold and lower Paris regimes at a stress ratio of 0.1 are presented in Fig. 9. No obvious dislocation or twinning activity was observed in either regime, i.e. very little evidence of plastic deformation was present in the crack-tip regions of these specimens. This is consistent with the SEM fractographic studies discussed, which show a crystallographic fracture mode with no observable plastic deformation.
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The only deformation feature that was observed in the crack-tip regions corresponding to the nearthreshold and lower Paris regimes of this alloy was fracturing or shearing of some of the d-phase (Ni3Nb) precipitates. This phenomenon was observed in both the near-threshold and lower Paris regimes, and is illustrated very clearly in Fig. 9(a). However, no evidence of the cutting of these particles by mobile dislocations was observed. Furthermore, the sheared or fractured portions of the precipitates were not significantly displaced from one another, as is often observed following tensile deformation. This could be due to the partially reversible nature of crack-tip plasticity, causing reversed relative movement of the sheared particle segments, the non-ideal orientation of the shearing plane relative to the plane of the foil, or the fact that the particles had simply fractured due to high local stresses rather than being sheared by the cutting action of glissile dislocations. The nature of the Ni3Nb particle shearing appears to be similar to the shearing of g% (Ni3Al) precipitates reported by Glatzel and Feller-Kniepmeier [4], during fatigue initiation experiments on the alloy CMSX-6. The authors propose that the mechanism of shearing involves a perfect screw dislocation in the g matrix, dissociating at the g/g% interface to produce (i) super partial dislocations in the g% separated by an anti-phase
boundary (APB), or (ii) a super partial dislocation in the g% and a conventional Shockley partial dislocation at the interface, separated by a superlattice intrinsic stacking fault (SISF). They propose that although the energy of the SISF is higher than that of the APB, the second mechanism may be favored because the partial dislocation formed at the interface will reduce misfit stresses. It seems likely, therefore, that the mechanism of fatigue crack propagation in the near-threshold and lower Paris regimes of this material is by transgranular, crystallographic fracture in favored crystallographic directions induced by the separation of atomic bonds directly ahead of the crack-tip. Accommodation of plastic strain ahead of the crack-tip appears to occur via fracturing or shearing of Ni3Nb precipitates, which may occur as a result of high local stresses or some limited amount of dislocation motion (plastic flow). Also, the fact that there was no observable difference in crack-tip deformation characteristics between the nearthreshold and lower Paris regimes suggests that the mechanism of fatigue crack propagation in this material is independent of DK within this range of DK. The TEM micrographs showing the crack-tip region corresponding to the upper part of the Paris regime ( 35 MPa m), at a stress ratio of 0.1 are presented in Fig. 10. The micrographs in Fig. 10(a),(b) show slip
Fig. 6. Scanning electron micrographs showing fracture surfaces of IN 718 corresponding to (a) the near-threshold regime, (b) the Paris regime and (c) the high DK regime of the fatigue crack growth curve, for a stress ratio of 0.8.
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Fig. 7. Fatigue crack growth curves for IN 718 showing positions of fatigue regimes and corresponding fracture modes, for stress ratios of (a) 0.1, (b) 0.3, (c) 0.5 and (d) 0.8.
lines and fine dislocation networks in the g matrix along the face of the crack corresponding to the plasticity that gave rise to the formation of the striations that were observed on the fracture surface in the upper Paris regime. These deformation features were localized, very fine and difficult to find in the TEM image. Extensive deformation or clearly defined dislocation structures were not observed. Fig. 10(c),(d) show some evidence of stacking fault formation in the g matrix and Ni3Nb precipitates, respectively, although no shearing or fracturing of the precipitates was observed at the higher DK level. The presence of stacking faults in both the matrix and precipitates also suggests similarities to the deformation mechanism observed by Glatzel and Feller-Kniepmeier [4].
The mechanism of fatigue crack growth in this material at DK levels above 30 MPa m, and an R value of 0.1, therefore, appears to be the formation of fatigue striations by localized plasticity immediately adjacent to the crack-face, giving rise to a narrow plastic zone consisting of slip lines, very fine dislocation networks and stacking faults. Transmission electron micrographs showing the crack-tip region corresponding to the high DK regime and a stress ratio of 0.8, are presented in Fig. 11. Slip lines and fine dislocation networks, similar to those observed in the upper part of the Paris regime at a stress ratio of 0.1 (Fig. 10), were also present at the higher stress ratio. However, the density of the deformation was considerably greater in the high DK regime at the higher stress ratio. The micrographs shown in
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Fig. 7. (Continued)
Fig. 11 clearly indicate a higher concentration of slip lines and an increased dislocation density compared with those shown in Fig. 10 for a stress ratio of 0.1. The above results indicate that although the value of DK in the high DK regime at R = 0.8 is lower than that corresponding to the upper Paris regime at R= 0.1, there is greater plasticity associated with fatigue crack growth in the high DK regime, regardless of stress ratio. This suggests that the density of deformation within the plastic zone of a propagating fatigue crack, is dependent on the maximum applied stress intensity, Kmax, and not solely on the stress intensity factor range, DK, which is generally regarded as the primary driving force for fatigue crack growth. Fig. 11(b) shows the slip lines already mentioned, cutting through an Ni3Nb particle. No obvious relative
displacement of segments of the particle, indicating shearing, was observed. However, as stated earlier, this could be due to the partially reversible nature of cracktip plasticity, causing reversed relative movements of the sheared particle segments, or the non-ideal orientation of the shearing plane relative to the plane of the foil. Additionally, the relative displacement of any sheared particle segments is only likely to be of the order of a few Burgers’ vectors ( 0.5–1 nm), and therefore will be difficult to resolve without the use of very high magnifications. Nevertheless, the slip lines can clearly be seen cutting through the Ni3Al precipitate with deformation, in the form of dislocations and/ or stacking faults, being visible within the precipitate. It therefore appears that the cutting of Ni3Al particles, together with plastic deformation within the particles,
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Fig. 8. Transmission electron micrographs showing (a) general undeformed substructure and (b) detail of undeformed Ni3Nb precipitate, in IN 718.
are part of the crack-tip deformation mechanism associated with fatigue crack growth in this alloy.
5. Modeling of fatigue crack growth It is apparent from the presented results that there are up to three different micromechanisms of fatigue crack growth in this alloy. Regimes I – III correspond to the ranges of DK on the fatigue crack growth curve over which these micromechanisms are active. No single fatigue crack growth law is likely to predict all the trends in the fatigue data in the three regimes. However, the linearized form of the Paris law in regime II is often preferred, presumably as a result of its simplicity. The development of mechanistically-based linearized crack growth laws for regimes I and III is, therefore, explored in this section. The relationships between the resulting laws and the Paris law constants are also discussed in some detail. A more complete description is given in Ref. [12]. A schematic illustration showing the material constants and the boundaries of the three regimes of fatigue crack growth is provided in Fig. 12. The constant xo corresponds to the fatigue threshold, while the constant x1 corresponds to the end of regime I where crack growth occurs along specific crystallographic planes (Fig. 3(a)). For DK levels greater than x1, fatigue crack growth occurs by a crack-tip blunting mechanism that gives rise to striations on the fracture surface (Fig. 3(c)). The fatigue crack growth rate in this regime is given by the Paris law, i.e. da/dN = C(DK)m. However, for DK levels greater than x2 (regime III), fatigue crack growth occurs by a combination of fatigue (striations) and monotonic (ductile-dimpled) fracture modes (Fig. 3(d)). The overall growth rate is, therefore, due to the superposition of fatigue and monotonic crack growth modes. Final fracture occurs presumably when Kmax is equal to the fracture toughness, KIc, (this presumption
neglects the possible strain rate effects that may be significant in this regime). In any case, x3 KIc(1−R), where R is the stress ratio, given by R=Kmin/Kmax.
6. Crystallographic fracture regime Fatigue crack growth in the crystallographic fracture regime may be described by a fatigue crack growth law, which is given by: y= log
da x− xo = a1(x−xo)+ b1 dN
(2)
where a1 and b1 are material constants for crack growth in regime I, x=log(DK), xo = log(DKth) and (x− xo)= log(DK/DKth) (Fig. 12). DK is the applied stress intensity factor range and DKth is the fatigue threshold stress intensity factor range. This equation is valid for xo 5 x5x1 and yo 5 y5y1. Eq. (2) can be linearized to obtain: x−xo = a1(x−xo)+ b1 y
(3)
Hence, if a graph of (x− xo)/y is plotted against (x− xo), we should obtain a straight line with a slope of a1 and an intercept with the ordinate of b1. The values of a1 and b1 were found to be 0.05 and 0.19, respectively, for forged IN 718 tested at a stress ratio of 0.1. Hence, at this stress ratio, Eq. (2) provides adequate fit to the data obtained for IN 718 in regime I where the crack growth mode is faceted/crystallographic. However, a transition in the fatigue fracture mode occurs at a DK level where the slope, dy/dx, is equal to m (Fig. 12). The slope, dy/dx, is obtained simply by differentiating Eq. (2). This gives: dy b1 2 = dx [a1(x−xo)+ b1]
(4)
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Hence, dy/dx =m when x =x1. It is also interesting to note that dy/dx = 1/b1 when x =xo. Hence, the limiting value of dy/dx at the fatigue threshold is 1/b1,which is often very difficult to measure experimentally. In any case, the transition point, x1, may be determined simply by solving for x in Eq. (4) if dy/dx is equated to m. Therefore, x1 is given by: x1 = xo +
b1/m −b1 a1
n
8. High DK regime (5)
Substitution of the appropriate material constants into Eq. (5) gives the value of x1 to be 1.21, for a stress ratio of 0.1. This is close to the point where the fracture mode changes from a crystallographic mode to one with fatigue striations across the fracture surface. The constant, x1, therefore corresponds to this transition (Fig. 12).
7. Striation formation regime Fatigue crack growth in the striation formation regime (regime II) is given by the Paris law. This gives: da/dN = C(DK)m
nism. Therefore, it can be seen that the upper part of the Paris regime corresponding to the striation formation regime has a somewhat higher Paris exponent than the average Paris exponent calculated over the entire Paris regime.
(6)
where C and m are material constants, which are typically referred to as the Paris coefficient and Paris exponent, respectively. As usual, the constants C and m may be obtained from a plot of log(da/dN) versus log(DK) as shown in Fig. 12. At a stress ratio of 0.1, the constants C and m for IN 718 were estimated to be 10 − 4.3 and 5.0, respectively, for the regime where crack growth occurred solely by a crack-tip blunting mechanism that gave rise to fatigue striations. It is interesting to note that at R=0.1, the value of m quoted in Table 2 for the entire Paris regime was 3.0, i.e. when the slope was determined for the entire linear regime, including the lower Paris regime where fatigue crack growth occurred by a crystallographic crack growth mecha-
For x\ x2, monotonic fracture modes begin to contribute to the overall crack growth process. The following linearized crack growth law is proposed for this regime [12]: y− y2 = a3(y−y2)+ b3 x− x2
(7)
where a3 and b3 are material constants for the high DK regime (Fig. 12). For values of y and x in regime III, the constants a3 and b3 were found to be 7.5 and 5.0, respectively, for a stress ratio of 0.1. Hence, the linearized expression given in Eq. (7) provides adequate fit of the fatigue crack growth rate data in the high DK regime. It is also interesting to note here that the constants a3 and b3 (Fig. 12) are related to the material constants m and KIc. The relationship between m and b3 may be determined simply by equating dy/dx at the transition point, x2, which corresponds to the DK level at which static fracture modes are first observed. This gives:
)
dy [a (y−y2 + b3)]2 = 3 = b3 = m b3 dx x = x 2
(8)
The onset of catastrophic fracture, x3, may also be predicted by equating the Kmax at the onset of fracture to the fracture toughness, KIc. This gives: x3 = log[KIc(1−R)]
(9)
The material constants in the three regimes of crack growth may, therefore, be related to well known con-
Fig. 9. Transmission electron micrographs showing sheared Ni3Nb precipitates in the crack-tip region of IN 718, correponding to (a) the near-threshold and (b) the lower Paris regimes of the fatigue crack growth curve, at a stress ratio of 0.1.
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Fig. 10. Transmission electron micrographs showing (a) and (b) slip lines and fine dislocation networks in the g matrix, (c) stacking faults in the g matrix and (d) stacking faults in Ni3Nb precipitates, in the crack-tip region of IN 718, correponding to the upper Paris regime of the fatigue crack growth curve, at a stress ratio of 0.1.
stants such as the Paris exponent, m, and the fracture toughness, KIc.
9. Discussion The results of this investigation have clearly indicated that the active mechanisms of fatigue crack growth in this material are dependent upon the range of stress intensity during cyclic loading, DK, and the stress ratio, R. A crystallographic mode of fracture was observed at DK levels corresponding to the near-threshold regime of the fatigue crack growth curve (regime I), at stress ratios of 0.1, 0.3 and 0.5. The presence of very fine fatigue striations on some of these facets is indicative of fracture caused by cyclic loading. A more classical crack-tip blunting mechanism [11] involving the formation of relatively coarse striations, was observed in regime II. Accelerated crack growth, corresponding to the high DK regions of the fatigue crack growth curves, was attributed to a combination of striation formation and the classical ductile-dimpled static fracture mechanism. The latter mechanism is commonly observed in ductile metallic materials following fracture under monotonic loading. Final catastrophic failure occurred
via this ductile-dimpled fracture mode when the maximum stress intensity and the crack tip (Kmax) became equal to the fracture toughness of the material (KIc). The mechanisms of fatigue crack propagation at a stress ratio of 0.8 were, however, somewhat different. As in the cases of the lower stress ratios, crystallographic fracture was observed in the near-threshold regime. However, unlike the lower stress ratios, this fracture mode was observed to be present throughout the Paris regime and well into the high DK regime. Some evidence of striation formation was also observed on the crystallographic facets in the Paris regime, whereas accelerated crack growth in the high DK regime occurred by a combination of crystallographic fatigue fracture and ductile-dimpled static fracture contributions. As before, final catastrophic failure of the material occurred via ductile-dimpled fracture. The fracture mechanisms that occur during fatigue crack growth, therefore, appear not only to be controlled by the stress intensity factor range (DK), but also by the maximum stress intensity (Kmax). It is generally accepted from the Paris equation that DK is the driving force for fatigue crack growth. However, the effects of Kmax must also be assessed, since this parameter clearly affects the micromechanisms of fa-
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Fig. 11. Transmission electron micrographs showing dense slip lines and fine dislocation networks (a) in the g matrix and (b) cutting through a Ni3Nb particle.
tigue crack growth and, hence, the overall fatigue behavior of these types of materials. A fracture map showing the active fracture mechanisms that occur under cyclic loading (in the alloy employed in this study) is presented in Fig. 13, as a plot of Kmax versus DK. Diagonal lines that correspond to constant stress ratio conditions radiate from the origin of the map. The points along the diagonal lines, therefore, correspond to the loci of DK and Kmax that are encountered during the fatigue tests. The upper limit of the Kmax axis corresponds to Kmax =KIc, while a stress ratio of zero would correspond to a 45° radial line. It is also important to note that all the fractographic features associated with positive stress ratios between 0 and 1 can be represented within the triangle in the upper half of the quadrant. Similarly, fractographic features corresponding to negative stress ratios between 0 and − 1 could be represented in the triangle in the lower half of the quadrant. The map in the upper half of the quadrant also shows a series of arcs (hyperbolae) that correspond to a transition from one fracture mode to another. These arcs intersect at a common point located on the Kmax axis at a value of 66 MPa m. This point corresponds to the fracture toughness of the material under monotonic loading (i.e. R =1 and DK = 0). The fracture mode will be fully ductile-dimpled fracture under these conditions. It is clearly apparent that the transitions between each fracture mode defined by the arcs in Fig. 13 depend upon both DK and Kmax. Such arcs may, therefore, be used to determine the parametric ranges for the application of fatigue crack growth laws for regimes I, II and III.
fatigue life prediction framework. This may be accomplished by first identifying the appropriate linearized fatigue crack growth laws for the applied DK and Kmax. Furthermore, it is important to note that the transitions in fracture mechanisms may not be identified solely by visual inspection of the da/dN versus DK curves. Hence, the transition points in the fatigue crack growth curves should be related to the underlying fracture mechanisms by careful use of the fracture mechanism maps that show the transitions as functions of DK and Kmax. It is particularly interesting to study the fatigue fracture mechanism map that was obtained in this study (Fig. 13). First, it is apparent that the different mechanisms observed on the fracture surfaces of specimens that were tested at positive stress ratios can be represented within a triangle in the upper half of the Kmax − DK quadrant. This is shown in the plot of Kmax versus DK (Fig. 13). It is also clear that the highest possible value of Kmax in the fracture map corresponds to the locus of points for which Kmax = KIc, the fracture toughness of the material. This defines the upper limit of the fracture triangle. The second set of boundaries
10. Implications The fracture mechanism maps and the fatigue crack growth laws (presented for the low, mid and high DK regimes) can be combined into a mechanistically-based
Fig. 12. Schematic illustration showing the material constants and boundaries of the three regimes of fatigue crack growth.
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Table 3 Summary of fatigue crack growth parameters in the three regimes of crack growth for forged IN 718
Stage I Stage II Stage III
Fig. 13. Fracture map showing the transitions between fatigue fracture modes as a function of DK and Kmax, for forged IN 718.
correspond to the transition between crystallographic and striation-type mechanisms, while the third set of boundaries represent the onset of static/monotonic fracture in addition to the striation fracture mode. The incidence of the static/monotonic fracture mode increases with increasing DK and Kmax in the final stages of fatigue crack growth, and catastrophic failure occurs when Kmax = KIc. It is particularly interesting to note that it may be possible to represent the transition boundaries by equations for hyperbolas or parabolas. However, more detailed mapping is needed to obtain sufficient number of data points to be able to fit appropriate equations for hyperbolas or parabolas. If such equations can be fitted to the transition data, it should be possible to use the transition equations to determine the fatigue mechanisms that are associated with the applied combinations of Kmax and DK. The appropriate linearized fatigue crack growth laws may then be used in the prediction of fatigue crack growth. For example, the dependence of the fatigue crack growth rate, da/dN, on DK and Kmax may be expressed in the form of a two-parameter crack growth law, as proposed by Campbell et al. [13]. This is given by: da/dN =ao(DK)a1(Kmax)a2
(10)
Since the mechanisms of fatigue are different in the near-threshold (regime I), Paris (regime II) and high DK (regime III) regimes, separate constants, ao, a1 and a2 were obtained for the three regimes of crack growth using multiple linear regression techniques [12]. The results are summarized in Table 3 along with the error coefficients, r 2. In addition, the material constants obtained for a single crystal IN 718 alloy are presented in
log ao
a1
a2
r2
r
−10.4 −9.4 −11.6
3.006 3.02 3.49
0.85 0.32 1.31
0.89 0.95 0.93
0.94 0.98 0.97
Table 4 for comparison. The exponents of DK are close to 3 in regimes I and II, and around 3.5 in regime III. However, the exponents of Kmax are greater in the near-threshold and high DK regimes (0.85 and 1.31, respectively) in comparison with the Kmax exponent of 0.32 in the Paris regime. The relatively high exponent of Kmax in the near-threshold regime is associated with a crystallographic crack growth mechanism, while the very high exponent of Kmax in the high DK regime is consistent with a fracture mode that consists of fatigue striations and ductile-dimpled fracture modes. The current paper, therefore, suggests that fatigue mechanism maps (Fig. 13) may be used to determine parametric windows of Kmax and DK for the determination of mechanistically-based fatigue crack growth laws. For example, the transitions between regimes I, II and III were determined from the fatigue maps prior to regression analysis to obtain the empirical constants ao, a1 and a2. The fracture mechanism maps could also be used to identify the parametric ranges for the selection of appropriate crack growth laws during fatigue life calculations. However, it is important to remember that the current maps have been obtained for long cracks in the Forsyth stage II regime [14]. The presented fatigue maps and crack growth laws may therefore be inapplicable to life prediction in the short crack regime.
11. Conclusions 1. The mechanisms of fatigue crack growth in this forged IN 718 alloy have been found to be dependent on both the stress intensity factor range (DK) and the maximum stress intensity (Kmax). Fracture modes under cyclic loading and mechanisms of crack-tip deformation were both found to vary with increasing DK and/or Kmax. Table 4 Summary of fatigue crack growth parameters in the three regimes of crack growth for single-crystal IN 718
Stage I Stage II Stage III
log ao
a1
a2
r2
r
−10.9 −10.0 −16.4
3.88 4.25 3.92
1.60 0.71 6.23
0.76 0.94 0.97
0.87 0.97 0.98
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2. At low values of DK and/or Kmax, corresponding to the near-threshold and lower Paris fatigue regimes, fatigue crack growth progressed via a transgranular, crystallographic fracture mechanism. In experiments conducted at stress ratios of 0.1, 0.3 and 0.5, a transition to a classical crack-blunting fatigue mechanism, involving the formation of relatively coarse striations, occurred in the central region of the Paris regime. Accelerated crack growth towards final failure at these three stress ratios, was attributed to a combination of classical fatigue (striation formation), and Kmax-controlled ductile-dimpled static fracture mode contributions. 3. At a stress ratio of 0.8, the transgranular, crystallographic mode of fracture was active throughout the Paris regime and was also present in the high DK regime. Some evidence of striations was observed in the Paris regime but accelerated crack growth in the high DK regime occurred by a combination of crystallographic fatigue fracture and ductile-dimpled static fracture. The role of Kmax at this stress ratio is of considerable significance. 4. At a stress ratio of 0.1, accommodation of plastic strain directly ahead of the crack-tip during fatigue crack growth in the near-threshold and lower Paris regimes appears to occur by fracture of the Ni3Nb precipitates. In the upper Paris regime, crack-tip deformation during fatigue appears to be associated with the formation of slip bands, fine dislocation networks and stacking faults in the crack-tip region. No fracturing of the Ni3Nb precipitates was observed in the upper Paris regime. 5. Crack-tip deformation in the high DK regime, at a stress ratio of 0.8, was also associated with the formation of slip bands and fine dislocation networks. However, the density of the deformation was found to be greater in this regime than that observed in the Paris regime at a stress ratio of 0.1. 6. New linearized crack growth laws have been formulated for the near-threshold and high DK regimes. Two-parameter extensions to the Paris law have also been proposed for the assessment of the combined effects of Kmax and DK in the near-threshold, Paris and high DK regimes. The regimes of applicability of the fatigue crack growth laws have also been described on a fatigue fracture map within a plot of Kmax versus DK. The map shows the loci of points corresponding to fracture mechanism transitions
.
within a triangle that contains all the possible values of Kmax and DK for positive stress ratios. Constant stress ratio paths are also represented by diagonal lines that radiate from the origin of the Kmax versus DK plot. The presented crack growth laws and fatigue maps are proposed for long cracks in the Forsyth stage II regime.
Acknowledgements The research was supported by The Division of Materials Research of The National, Science Foundation with Dr Bruce MacDonald as Program Monitor. Appreciation is also extended to Dr Padu Ramasundaram of Wyman Gordon, Houston, TX, for providing the material that was used in this study.
References [1] J. E. King, Fatigue Eng. Mater. Struct. 5 (2) (1982) 177–188. [2] P. A. S. Reed, J. E. King, Scr. Metall. Mater. 26 (12) (1992) 1829 – 1834. [3] J. E. King, Mater. Sci. Technol. 3 (9) (1987) 750 – 764. [4] U. Glatzel, M. Feller-Kniepmeier, Scr. Metall. Mater. 25 (8) (1991) 1845 – 1850. [5] D. J. Morrison, V. Chopra, J. W. Jones, Scr. Metall. Mater. 25 (6) (1991) 1299 – 1304. [6] R. Rahouadj, J. Menigault, M. Clavel, Mater. Sci. Eng. 93 (1987) 181 – 190. [7] S. Chen, G. Gottstein, J. Mater. Sci. 24 (11) (1989) 4094–4099. [8] D. L. Davidson, K. S. Chan, Acta Metall. 37 (4) (1989) 1089– 1097. [9] B. A. Lerch, S. D. Antolovich, Metall. Trans. 21A (8) (1990) 2169 – 2177. [10] S Suresh, Fatigue of Materials, Cambridge University Press, Cambridge, 1991 pp. 202 – 221. [11] C. Laird, G. C. Smith, Philos. Mag. 8 (1962) 847 –857. [12] A.B.O. Soboyejo, C. Mercer, W. O. Soboyejo, Linearized crack growth laws for the characterization of long fatigue cracks, in: J.H. Beynon and R.A. Smith (Eds.), Engineering Against Fatigue, A.A. Balkena, Publishers, Rotterdam, 1998, Chapter 26, pp. 253 – 259. [13] J.P. Campbell, A. L. McKelvey, S. Lillibridge, K. T. Venkateswara Rao and R. O. Ritchie: Fracture and fatigue in g-based TiAl Alloys with fine lamellar microstructures: long and small crack behavior, in: W. O. Soboyejo, T. S. Srivatsan and H. L. Fraser (Eds.), Proceedings of The Symposium on Deformation and Fracture of Ordered Intermetallics III, TMS, Warrendale, PA, 1996, pp. 141 – 157. [14] P.J.E. Forsyth, A two stage process of fatigue crack growth, Proceedings of Cranfield Symosium, Her Majesty’s Stationery Office, London, 1962, pp. 76 – 94.
Micromechanisms of fatigue crack growth in a forged Inconel 718 nickel-based superalloy C. Mercer a, A.B.O. Soboyejo b, W.O. Soboyejo a,* b
a Department of Materials Science and Engineering, The Ohio State Uni6ersity, 2041 College Road, Columbus, OH 43210, USA Departments of Aerospace and Agricultural Engineering, The Ohio State Uni6ersity, 590 Woody Hayes Dri6e, Columbus, OH 43210, USA
Received 8 July 1998; received in revised form 3 May 1999
Abstract The micromechanisms of fatigue crack propagation in a forged, polycrystalline IN 718 nickel-based superalloy are evaluated. Fracture modes under cyclic loading were established by scanning electron microscopy analysis. The results of the fractographic analysis are presented on a fracture mechanism map that shows the dependence of fracture modes on the maximum stress intensity factor, Kmax, and the stress intensity factor range, DK. Plastic deformation associated with fatigue crack growth was studied using transmission electron microscopy. The effects of DK and Kmax on the mechanisms of fatigue crack growth in this alloy are discussed within the context of a two-parameter crack growth law. Possible extensions to the Paris law are also proposed for crack growth in the near-threshold and high DK regimes. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Fatigue crack growth; Nickel-based superalloy; Micromechanisms
1. Introduction The principal application of nickel-based superalloys is for the high-temperature turbine components of modern gas turbine engines. Turbine blades must withstand very high temperatures and also require good creep resistance. Hence, blades are manufactured from cast nickel-based superalloys, where large grain sizes can be engineered to provide the necessary creep properties. In modern engines, blades may be either directionally solidified or may even be single crystals that provide maximum creep resistance. Turbine discs are not subjected to such extreme temperatures as blades but have greater strength requirements imposed on them. As a result, turbine discs are usually manufactured from forged, polycrystalline nickel-base alloys such as Inconel 718. However, in spite of the widespread application of nickel-based superalloys in gas turbine engines, our current understanding of fatigue mechanisms in these materials is still somewhat limited, even after a number of prior investigations [1 – 9]. These investigations have * Corresponding author. Tel.: +1-614-292-0996; fax: + 1-614-2921537.
been largely concerned with mechanisms of fatigue crack initiation, particularly the dislocation configurations that arise during low and high cycle fatigue of nickel alloys. Very limited work appears to have been performed concerning the micromechanisms of cracktip deformation and fracture that occur during fatigue crack propagation. There is, therefore, a need for detailed studies of the micromechanisms of fatigue crack propagation in structural Ni-based superalloys. This paper presents the results of a recent study of the micromechanisms of fatigue crack propagation in IN 718, a typical forged, polycrystalline Ni-based superalloy employed in turbine disc applications. Following a brief description of material processing and microstructure, the experimental techniques are described in detail. Fatigue crack growth rate data at various stress ratios are then presented. Micromechanisms of fracture and crack-tip deformation under cyclic loading are then proposed based on scanning electron microscopy (SEM) studies of fracture surfaces and transmission electron microscopy (TEM) examination of fatigue crack-tip regions. The results of the fractographic analysis are summarized on a fatigue mechanism map. Fatigue crack growth laws are presented for the assessment of the combined effects of the
0921-5093/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 9 ) 0 0 2 1 4 - 2
C. Mercer et al. / Materials Science and Engineering A270 (1999) 308–322 Table 1 Chemical composition of IN 718 forging Element
Weight (%)
Ni C Mn Si Cr Co Fe Mo Nb Ti Al B S P Cu Ta O N Mg
54.03 0.024 0.08 0.08 17.99 0.30 17.55 2.96 5.35 0.940 0.49 0.0027 0.0002 0.008 0.03 0.01 6 ppm 64 ppm 21 ppm
stress intensity factor range, DK, and the stress ratio, R. A detailed discussion of the effects of stress intensity factor range, DK, maximum stress intensity, Kmax, and stress ratio, R, on the fatigue behavior of this material is then presented.
2. Materials The IN 718 forging that was used in this study was supplied by Wyman Gordon (Houston, TX) in the form of a 5.5 mm thick plate. The plate was cut from a triple-melted (vacuum induction melting+ vacuum arc remelting+electroslag remelting), fine-grained billet supplied by Special Metals Corporation (New Hartford, NY). The actual chemical composition of the
forging is given in Table 1. Metallographic analysis was carried out following mechanical polishing and electrolytic etching in oxalic acid solution for approximately 30 s using a 6 V d.c. power supply. A typical optical micrograph of the IN 718 alloy is presented in Fig. 1. The microstructure consists of nearly equiaxed grains of the nickel-rich face-centered cubic solid solution (g phase) with an average grain size of 30 mm. A moderate density of lenticular Ni3Nb precipitates (d phase) was also observed within the g matrix (Fig. 1). The orientations of these d-phase precipitates within the matrix material appeared to be somewhat irregular.
3. Experimental procedures Fatigue crack growth experiments were conducted under constant stress ranges on single edge notched bend (SEN) specimens at stress ratios, R, (R=smin/ smax), of 0.1, 0.3, 0.5 and 0.8. Fatigue crack growth testing was carried out under computer-controlled Mode I loading conditions using a software package that was supplied by Fracture Technology Associates (Pleasant Valley, PA). A cyclic frequency of 10 Hz was used during the tests. Crack growth was monitored continuously during the fatigue testing using a direct current potential drop method. Some of the fatigue tests were carried out until specimen failure occurred. However, most of the tests were stopped prior to specimen failure. The tests were stopped at a stress intensity factor range that corresponded to one of the three distinct regimes of the fatigue crack growth curve, i.e. near-threshold, Paris and high DK regimes [10]. The tests were stopped to allow subsequent TEM examination of the crack-tip regions of the specimens to be carried out in the near-threshold, Paris and high DK regimes. The 3 mm diameter crack-tip TEM foils were taken from the crack-tip region of the specimens and prepared using precision dimpling and ion milling techniques. It is important to note here that the tips of the cracks were located at a distance of approximately one plastic zone from the center of the dimple. The size of the plastic zone, rp, was estimated using the following expression: rp =
Fig. 1. Optical micrograph showing the distribution of Ni3Nb precipitates (d phase) in the general microstructure of forged IN 718 alloy.
309
1 DK p 2sy
2
(1)
where DK is the final stress intensity factor range just prior to stopping the test and sy is the yield stress. Considerable experimental effort was needed to produce the crack-tip foils by the technique already described. For comparison, TEM foils were also taken from undeformed material well away from the fatigue crack.
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Fig. 2. Fatigue crack growth curves (da/dN versus DK) for forged IN 718 alloy, at stress ratios of 0.1, 0.3, 0.5 and 0.8.
These were prepared using the same dimpling and ion milling methods that were used for the preparation of the crack-tip TEM foils. Comparison of the deformed and undeformed material was then carried out in the TEM. Differences between the deformation substructures in the deformed and undeformed material were attributed to the effects of cyclic crack-tip plasticity. Following TEM analysis, the remaining portions of the specimens (not tested to failure) were fractured under monotonic loading. The fracture surfaces of all the specimens were then examined using SEM techniques. Fracture surfaces that corresponded to the near-threshold, Paris and high DK regimes of the fatigue crack growth curve at each stress ratio were examined carefully to determine the effects of the stress intensity factor range on the cyclic fracture mechanisms.
4. Results
4.1. Fatigue crack growth rates The da/dN versus DK fatigue crack growth curves obtained for this alloy at each of the four stress ratios employed are presented in Fig. 2. The plot clearly shows the near-threshold, Paris and high DK regimes of each curve. Stable crack growth was observed at Kmax levels below 50 MPa m. The data are in good agreement with the results obtained from other studies of
similar alloys [1,9]. The Paris exponents, m, for each stress ratio are presented in Table 2. The values of m in Table 2 are typical for a metallic material which generally has a Paris exponent of between 2 and 4 [10]. At Kmax levels above 50 MPa m, the crack growth rates at all four stress ratios were observed to accelerate until catastrophic failure occurred. This region corresponds to the high DK regime of the curves. TEM analysis was carried out on specimens where fatigue testing was halted at DK values of approximately 13, 25 and 35 MPa m for a stress ratio of 0.1. At this stress ratio, these values correspond respectively to the near-threshold regime, the lower part of the Paris regime and the upper part of the Paris regime. Transmission electron microscopy analysis was also performed on a specimen tested at a stress ratio of 0.8 for which fatigue cycling was stopped at a DK of 13.3 MPa m. This value corresponds to the high DK regime of the fatigue curve just prior to catastrophic failure. After failure, scanning electron microscopy Table 2 Variation of Paris exponent, m, with stress ratio, R, for forged IN 718 Stress ratio, R
Paris exponent, m
0.1 0.3 0.5 0.8
3.0 3.4 2.5 1.8
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Fig. 3. Scanning electron micrographs showing fracture surfaces of IN 718 corresponding to (a) the near-threshold regime, (b) the lower Paris regime, (c) the upper Paris regime, and (d) the high DK regime of the fatigue crack growth curve, and (e) the tensile overload region of the specimen, for a stress ratio of 0.1.
analysis of the fracture surfaces of each specimen (from the near-threshold regime until failure) was carried out at all four stress ratios, i.e. R =0.1, 0.3, 0.5 and 0.8.
4.2. Fractography 4.2.1. Stress ratio of 0.1 Typical fatigue fracture surfaces corresponding to the near-threshold regime and lower portion of the Paris regime of this alloy tested at a stress ratio of 0.1 are presented in Fig. 3(a) and (b), respectively. The mode of fracture under cyclic loading at this stress ratio in both regimes appeared to be a transgranular, faceted,
crystallographic fracture mode, as can be seen by the sharp, angular facets in the fracture surfaces (Fig. 3). Very fine fatigue striations were observed on some of the facets, indicating the presence of very localized plasticity during fatigue crack growth in the nearthreshold and lower Paris regimes. It is important to note here that although a faceted, crystallographic fracture mode is often observed in the near-threshold regime of metallic materials [10], it is somewhat unusual for a ductile metal to exhibit this mode of fracture in the Paris or steady-state crack growth regime. Such behavior is generally more typical of more brittle materials. However, Lerch and An-
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tolovich [9] have also observed crystallographic fracture modes occurring up to similar DK levels in the single ´ N4. crystal nickel-based superalloy RENE A possible explanation for this behavior is that, even in the lower Paris regime, stress intensity levels are still significantly below the fracture toughness of IN 718. Hence, the material fractures in a mode that is generally associated with low stress intensity values where the extent of plastic deformation is relatively small. However, as the extent of plasticity increases, a transition in fracture mode to a plasticity-controlled crack-tip blunting mechanism was observed to occur. This is generally associated with the formation of relatively coarse striations, as suggested by Laird and Smith [11]. The transition to a classical striation type of fracture mode corresponding to greater levels of plasticity was observed at stress intensity factor ranges\ 35 MPa m at this stress ratio. These stress intensity factor ranges correspond to the upper Paris regime (Fig. 3(c)). This is generally indicative of a pure fatigue crack growth mechanism that is controlled by duplex slip processes that give rise to crack-tip blunting [11]. It is interesting to note that the transition from the faceted fracture mode to the striation mechanism occurred when the crack-tip opening displacement was approximately equal to the size of the facets on the crystallographic fracture surface (approximately 5 mm). At high DK
levels (\ 45 MPa m), a ductile-dimpled fracture mode was observed in addition to the fatigue striations as the Kmax levels approached the fracture toughness of the IN 718 material (Fig. 3(d)). Hence, the departure of the Paris line in the high DK regime is thought to be due to the additional contributions from ‘static’ or ‘monotonic’ (ductile dimpled) fracture modes (Fig. 3(d)) [12]. The tensile overload region of the fracture surface is compared with the fracture modes in the different fatigue regimes in Fig. 3(e). The classical ductile-dimpled fracture mechanism observed is similar to the monotonic fracture mode observed in the high DK fatigue regime.
4.2.2. Stress ratios of 0.3 and 0.5 The fatigue fracture surfaces observed at stress ratios of 0.3 and 0.5 were very similar to those corresponding to a stress ratio of 0.1, and are presented in Figs. 4 and 5. Crystallographic faceted fracture was observed in the near-threshold and lower Paris regimes, with very fine striations clearly visible on some of the crystallographic facets. The fracture mechanism under cyclic loading was observed to change to more classical crack-tip blunting, indicated by the formation of relatively coarse striations. The transition to the plastic-blunting mechanism was observed to occur at DK levels of 22 and 17 MPa m for stress ratios of 0.3 and 0.5, respectively.
Fig. 4. Scanning electron micrographs showing fracture surfaces of IN 718 corresponding to (a) the near-threshold regime, (b) the lower Paris regime, (c) the upper Paris regime and (d) the high DK regime of the fatigue crack growth curve, for a stress ratio of 0.3.
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Fig. 5. Scanning electron micrographs showing fracture surfaces of IN 718 corresponding to (a) the near-threshold regime, (b) the lower Paris regime, (c) the upper Paris regime and (d) the high DK regime of the fatigue crack growth curve, for a stress ratio of 0.5.
Finally, in the high DK regimes of these two curves, the onset ductile-dimple static fracture modes in combination with striation formation due to cyclic loading, gave rise to the rapid acceleration in crack growth rates observed just prior to catastrophic failure in the final stages of the test.
4.2.3. Stress ratio of 0.8 The fracture surfaces of the specimen fatigue tested at a stress ratio of 0.8 are shown in Fig. 6. A transgranular, crystallographic mode of fracture was observed in the near-threshold regime (Fig. 6(a)), as was observed for the R=0.1 case already described. However, at this R ratio, components of this crystallographic fracture mode were present throughout the Paris regime and well into the high DK regime. Very fine striations were observed on the crystallographic facets in the Paris regime (Fig. 6(b)). Secondary cracking was also apparent on the fracture surfaces within the Paris regime. In the high DK regime, the ductile-dimpled static fracture mode was observed to be active as in the case for R= 0.1. However, as already mentioned, the crystallographic fracture mode was also present in this regime. Therefore, the mode of fracture in the high DK regime at this stress ratio appears to involve a combination of crystallographic fatigue fracture and ductiledimpled static fracture (Fig. 6(c)).
The various fatigue regimes and corresponding fracture mechanisms can now be added to the basic fatigue crack growth curves, and this is shown in Fig. 7. The plots clearly show the DK levels and crack growth rates at which transitions between fatigue regimes and/or fracture modes occur for each stress ratio that was examined.
4.3. Crack-tip deformation mechanisms The TEM micrographs of the undeformed substructure are given in Fig. 8. The micrographs show a deformation-free substructure with a very low dislocation density, typical of an annealed microstructure. The elongated Ni3Nb particles are clearly apparent in the figure. No observable evidence of deformation was detected in these precipitates prior to fatigue loading. The TEM micrographs showing the crack-tip regions for the near-threshold and lower Paris regimes at a stress ratio of 0.1 are presented in Fig. 9. No obvious dislocation or twinning activity was observed in either regime, i.e. very little evidence of plastic deformation was present in the crack-tip regions of these specimens. This is consistent with the SEM fractographic studies discussed, which show a crystallographic fracture mode with no observable plastic deformation.
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The only deformation feature that was observed in the crack-tip regions corresponding to the nearthreshold and lower Paris regimes of this alloy was fracturing or shearing of some of the d-phase (Ni3Nb) precipitates. This phenomenon was observed in both the near-threshold and lower Paris regimes, and is illustrated very clearly in Fig. 9(a). However, no evidence of the cutting of these particles by mobile dislocations was observed. Furthermore, the sheared or fractured portions of the precipitates were not significantly displaced from one another, as is often observed following tensile deformation. This could be due to the partially reversible nature of crack-tip plasticity, causing reversed relative movement of the sheared particle segments, the non-ideal orientation of the shearing plane relative to the plane of the foil, or the fact that the particles had simply fractured due to high local stresses rather than being sheared by the cutting action of glissile dislocations. The nature of the Ni3Nb particle shearing appears to be similar to the shearing of g% (Ni3Al) precipitates reported by Glatzel and Feller-Kniepmeier [4], during fatigue initiation experiments on the alloy CMSX-6. The authors propose that the mechanism of shearing involves a perfect screw dislocation in the g matrix, dissociating at the g/g% interface to produce (i) super partial dislocations in the g% separated by an anti-phase
boundary (APB), or (ii) a super partial dislocation in the g% and a conventional Shockley partial dislocation at the interface, separated by a superlattice intrinsic stacking fault (SISF). They propose that although the energy of the SISF is higher than that of the APB, the second mechanism may be favored because the partial dislocation formed at the interface will reduce misfit stresses. It seems likely, therefore, that the mechanism of fatigue crack propagation in the near-threshold and lower Paris regimes of this material is by transgranular, crystallographic fracture in favored crystallographic directions induced by the separation of atomic bonds directly ahead of the crack-tip. Accommodation of plastic strain ahead of the crack-tip appears to occur via fracturing or shearing of Ni3Nb precipitates, which may occur as a result of high local stresses or some limited amount of dislocation motion (plastic flow). Also, the fact that there was no observable difference in crack-tip deformation characteristics between the nearthreshold and lower Paris regimes suggests that the mechanism of fatigue crack propagation in this material is independent of DK within this range of DK. The TEM micrographs showing the crack-tip region corresponding to the upper part of the Paris regime ( 35 MPa m), at a stress ratio of 0.1 are presented in Fig. 10. The micrographs in Fig. 10(a),(b) show slip
Fig. 6. Scanning electron micrographs showing fracture surfaces of IN 718 corresponding to (a) the near-threshold regime, (b) the Paris regime and (c) the high DK regime of the fatigue crack growth curve, for a stress ratio of 0.8.
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Fig. 7. Fatigue crack growth curves for IN 718 showing positions of fatigue regimes and corresponding fracture modes, for stress ratios of (a) 0.1, (b) 0.3, (c) 0.5 and (d) 0.8.
lines and fine dislocation networks in the g matrix along the face of the crack corresponding to the plasticity that gave rise to the formation of the striations that were observed on the fracture surface in the upper Paris regime. These deformation features were localized, very fine and difficult to find in the TEM image. Extensive deformation or clearly defined dislocation structures were not observed. Fig. 10(c),(d) show some evidence of stacking fault formation in the g matrix and Ni3Nb precipitates, respectively, although no shearing or fracturing of the precipitates was observed at the higher DK level. The presence of stacking faults in both the matrix and precipitates also suggests similarities to the deformation mechanism observed by Glatzel and Feller-Kniepmeier [4].
The mechanism of fatigue crack growth in this material at DK levels above 30 MPa m, and an R value of 0.1, therefore, appears to be the formation of fatigue striations by localized plasticity immediately adjacent to the crack-face, giving rise to a narrow plastic zone consisting of slip lines, very fine dislocation networks and stacking faults. Transmission electron micrographs showing the crack-tip region corresponding to the high DK regime and a stress ratio of 0.8, are presented in Fig. 11. Slip lines and fine dislocation networks, similar to those observed in the upper part of the Paris regime at a stress ratio of 0.1 (Fig. 10), were also present at the higher stress ratio. However, the density of the deformation was considerably greater in the high DK regime at the higher stress ratio. The micrographs shown in
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Fig. 7. (Continued)
Fig. 11 clearly indicate a higher concentration of slip lines and an increased dislocation density compared with those shown in Fig. 10 for a stress ratio of 0.1. The above results indicate that although the value of DK in the high DK regime at R = 0.8 is lower than that corresponding to the upper Paris regime at R= 0.1, there is greater plasticity associated with fatigue crack growth in the high DK regime, regardless of stress ratio. This suggests that the density of deformation within the plastic zone of a propagating fatigue crack, is dependent on the maximum applied stress intensity, Kmax, and not solely on the stress intensity factor range, DK, which is generally regarded as the primary driving force for fatigue crack growth. Fig. 11(b) shows the slip lines already mentioned, cutting through an Ni3Nb particle. No obvious relative
displacement of segments of the particle, indicating shearing, was observed. However, as stated earlier, this could be due to the partially reversible nature of cracktip plasticity, causing reversed relative movements of the sheared particle segments, or the non-ideal orientation of the shearing plane relative to the plane of the foil. Additionally, the relative displacement of any sheared particle segments is only likely to be of the order of a few Burgers’ vectors ( 0.5–1 nm), and therefore will be difficult to resolve without the use of very high magnifications. Nevertheless, the slip lines can clearly be seen cutting through the Ni3Al precipitate with deformation, in the form of dislocations and/ or stacking faults, being visible within the precipitate. It therefore appears that the cutting of Ni3Al particles, together with plastic deformation within the particles,
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Fig. 8. Transmission electron micrographs showing (a) general undeformed substructure and (b) detail of undeformed Ni3Nb precipitate, in IN 718.
are part of the crack-tip deformation mechanism associated with fatigue crack growth in this alloy.
5. Modeling of fatigue crack growth It is apparent from the presented results that there are up to three different micromechanisms of fatigue crack growth in this alloy. Regimes I – III correspond to the ranges of DK on the fatigue crack growth curve over which these micromechanisms are active. No single fatigue crack growth law is likely to predict all the trends in the fatigue data in the three regimes. However, the linearized form of the Paris law in regime II is often preferred, presumably as a result of its simplicity. The development of mechanistically-based linearized crack growth laws for regimes I and III is, therefore, explored in this section. The relationships between the resulting laws and the Paris law constants are also discussed in some detail. A more complete description is given in Ref. [12]. A schematic illustration showing the material constants and the boundaries of the three regimes of fatigue crack growth is provided in Fig. 12. The constant xo corresponds to the fatigue threshold, while the constant x1 corresponds to the end of regime I where crack growth occurs along specific crystallographic planes (Fig. 3(a)). For DK levels greater than x1, fatigue crack growth occurs by a crack-tip blunting mechanism that gives rise to striations on the fracture surface (Fig. 3(c)). The fatigue crack growth rate in this regime is given by the Paris law, i.e. da/dN = C(DK)m. However, for DK levels greater than x2 (regime III), fatigue crack growth occurs by a combination of fatigue (striations) and monotonic (ductile-dimpled) fracture modes (Fig. 3(d)). The overall growth rate is, therefore, due to the superposition of fatigue and monotonic crack growth modes. Final fracture occurs presumably when Kmax is equal to the fracture toughness, KIc, (this presumption
neglects the possible strain rate effects that may be significant in this regime). In any case, x3 KIc(1−R), where R is the stress ratio, given by R=Kmin/Kmax.
6. Crystallographic fracture regime Fatigue crack growth in the crystallographic fracture regime may be described by a fatigue crack growth law, which is given by: y= log
da x− xo = a1(x−xo)+ b1 dN
(2)
where a1 and b1 are material constants for crack growth in regime I, x=log(DK), xo = log(DKth) and (x− xo)= log(DK/DKth) (Fig. 12). DK is the applied stress intensity factor range and DKth is the fatigue threshold stress intensity factor range. This equation is valid for xo 5 x5x1 and yo 5 y5y1. Eq. (2) can be linearized to obtain: x−xo = a1(x−xo)+ b1 y
(3)
Hence, if a graph of (x− xo)/y is plotted against (x− xo), we should obtain a straight line with a slope of a1 and an intercept with the ordinate of b1. The values of a1 and b1 were found to be 0.05 and 0.19, respectively, for forged IN 718 tested at a stress ratio of 0.1. Hence, at this stress ratio, Eq. (2) provides adequate fit to the data obtained for IN 718 in regime I where the crack growth mode is faceted/crystallographic. However, a transition in the fatigue fracture mode occurs at a DK level where the slope, dy/dx, is equal to m (Fig. 12). The slope, dy/dx, is obtained simply by differentiating Eq. (2). This gives: dy b1 2 = dx [a1(x−xo)+ b1]
(4)
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Hence, dy/dx =m when x =x1. It is also interesting to note that dy/dx = 1/b1 when x =xo. Hence, the limiting value of dy/dx at the fatigue threshold is 1/b1,which is often very difficult to measure experimentally. In any case, the transition point, x1, may be determined simply by solving for x in Eq. (4) if dy/dx is equated to m. Therefore, x1 is given by: x1 = xo +
b1/m −b1 a1
n
8. High DK regime (5)
Substitution of the appropriate material constants into Eq. (5) gives the value of x1 to be 1.21, for a stress ratio of 0.1. This is close to the point where the fracture mode changes from a crystallographic mode to one with fatigue striations across the fracture surface. The constant, x1, therefore corresponds to this transition (Fig. 12).
7. Striation formation regime Fatigue crack growth in the striation formation regime (regime II) is given by the Paris law. This gives: da/dN = C(DK)m
nism. Therefore, it can be seen that the upper part of the Paris regime corresponding to the striation formation regime has a somewhat higher Paris exponent than the average Paris exponent calculated over the entire Paris regime.
(6)
where C and m are material constants, which are typically referred to as the Paris coefficient and Paris exponent, respectively. As usual, the constants C and m may be obtained from a plot of log(da/dN) versus log(DK) as shown in Fig. 12. At a stress ratio of 0.1, the constants C and m for IN 718 were estimated to be 10 − 4.3 and 5.0, respectively, for the regime where crack growth occurred solely by a crack-tip blunting mechanism that gave rise to fatigue striations. It is interesting to note that at R=0.1, the value of m quoted in Table 2 for the entire Paris regime was 3.0, i.e. when the slope was determined for the entire linear regime, including the lower Paris regime where fatigue crack growth occurred by a crystallographic crack growth mecha-
For x\ x2, monotonic fracture modes begin to contribute to the overall crack growth process. The following linearized crack growth law is proposed for this regime [12]: y− y2 = a3(y−y2)+ b3 x− x2
(7)
where a3 and b3 are material constants for the high DK regime (Fig. 12). For values of y and x in regime III, the constants a3 and b3 were found to be 7.5 and 5.0, respectively, for a stress ratio of 0.1. Hence, the linearized expression given in Eq. (7) provides adequate fit of the fatigue crack growth rate data in the high DK regime. It is also interesting to note here that the constants a3 and b3 (Fig. 12) are related to the material constants m and KIc. The relationship between m and b3 may be determined simply by equating dy/dx at the transition point, x2, which corresponds to the DK level at which static fracture modes are first observed. This gives:
)
dy [a (y−y2 + b3)]2 = 3 = b3 = m b3 dx x = x 2
(8)
The onset of catastrophic fracture, x3, may also be predicted by equating the Kmax at the onset of fracture to the fracture toughness, KIc. This gives: x3 = log[KIc(1−R)]
(9)
The material constants in the three regimes of crack growth may, therefore, be related to well known con-
Fig. 9. Transmission electron micrographs showing sheared Ni3Nb precipitates in the crack-tip region of IN 718, correponding to (a) the near-threshold and (b) the lower Paris regimes of the fatigue crack growth curve, at a stress ratio of 0.1.
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Fig. 10. Transmission electron micrographs showing (a) and (b) slip lines and fine dislocation networks in the g matrix, (c) stacking faults in the g matrix and (d) stacking faults in Ni3Nb precipitates, in the crack-tip region of IN 718, correponding to the upper Paris regime of the fatigue crack growth curve, at a stress ratio of 0.1.
stants such as the Paris exponent, m, and the fracture toughness, KIc.
9. Discussion The results of this investigation have clearly indicated that the active mechanisms of fatigue crack growth in this material are dependent upon the range of stress intensity during cyclic loading, DK, and the stress ratio, R. A crystallographic mode of fracture was observed at DK levels corresponding to the near-threshold regime of the fatigue crack growth curve (regime I), at stress ratios of 0.1, 0.3 and 0.5. The presence of very fine fatigue striations on some of these facets is indicative of fracture caused by cyclic loading. A more classical crack-tip blunting mechanism [11] involving the formation of relatively coarse striations, was observed in regime II. Accelerated crack growth, corresponding to the high DK regions of the fatigue crack growth curves, was attributed to a combination of striation formation and the classical ductile-dimpled static fracture mechanism. The latter mechanism is commonly observed in ductile metallic materials following fracture under monotonic loading. Final catastrophic failure occurred
via this ductile-dimpled fracture mode when the maximum stress intensity and the crack tip (Kmax) became equal to the fracture toughness of the material (KIc). The mechanisms of fatigue crack propagation at a stress ratio of 0.8 were, however, somewhat different. As in the cases of the lower stress ratios, crystallographic fracture was observed in the near-threshold regime. However, unlike the lower stress ratios, this fracture mode was observed to be present throughout the Paris regime and well into the high DK regime. Some evidence of striation formation was also observed on the crystallographic facets in the Paris regime, whereas accelerated crack growth in the high DK regime occurred by a combination of crystallographic fatigue fracture and ductile-dimpled static fracture contributions. As before, final catastrophic failure of the material occurred via ductile-dimpled fracture. The fracture mechanisms that occur during fatigue crack growth, therefore, appear not only to be controlled by the stress intensity factor range (DK), but also by the maximum stress intensity (Kmax). It is generally accepted from the Paris equation that DK is the driving force for fatigue crack growth. However, the effects of Kmax must also be assessed, since this parameter clearly affects the micromechanisms of fa-
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Fig. 11. Transmission electron micrographs showing dense slip lines and fine dislocation networks (a) in the g matrix and (b) cutting through a Ni3Nb particle.
tigue crack growth and, hence, the overall fatigue behavior of these types of materials. A fracture map showing the active fracture mechanisms that occur under cyclic loading (in the alloy employed in this study) is presented in Fig. 13, as a plot of Kmax versus DK. Diagonal lines that correspond to constant stress ratio conditions radiate from the origin of the map. The points along the diagonal lines, therefore, correspond to the loci of DK and Kmax that are encountered during the fatigue tests. The upper limit of the Kmax axis corresponds to Kmax =KIc, while a stress ratio of zero would correspond to a 45° radial line. It is also important to note that all the fractographic features associated with positive stress ratios between 0 and 1 can be represented within the triangle in the upper half of the quadrant. Similarly, fractographic features corresponding to negative stress ratios between 0 and − 1 could be represented in the triangle in the lower half of the quadrant. The map in the upper half of the quadrant also shows a series of arcs (hyperbolae) that correspond to a transition from one fracture mode to another. These arcs intersect at a common point located on the Kmax axis at a value of 66 MPa m. This point corresponds to the fracture toughness of the material under monotonic loading (i.e. R =1 and DK = 0). The fracture mode will be fully ductile-dimpled fracture under these conditions. It is clearly apparent that the transitions between each fracture mode defined by the arcs in Fig. 13 depend upon both DK and Kmax. Such arcs may, therefore, be used to determine the parametric ranges for the application of fatigue crack growth laws for regimes I, II and III.
fatigue life prediction framework. This may be accomplished by first identifying the appropriate linearized fatigue crack growth laws for the applied DK and Kmax. Furthermore, it is important to note that the transitions in fracture mechanisms may not be identified solely by visual inspection of the da/dN versus DK curves. Hence, the transition points in the fatigue crack growth curves should be related to the underlying fracture mechanisms by careful use of the fracture mechanism maps that show the transitions as functions of DK and Kmax. It is particularly interesting to study the fatigue fracture mechanism map that was obtained in this study (Fig. 13). First, it is apparent that the different mechanisms observed on the fracture surfaces of specimens that were tested at positive stress ratios can be represented within a triangle in the upper half of the Kmax − DK quadrant. This is shown in the plot of Kmax versus DK (Fig. 13). It is also clear that the highest possible value of Kmax in the fracture map corresponds to the locus of points for which Kmax = KIc, the fracture toughness of the material. This defines the upper limit of the fracture triangle. The second set of boundaries
10. Implications The fracture mechanism maps and the fatigue crack growth laws (presented for the low, mid and high DK regimes) can be combined into a mechanistically-based
Fig. 12. Schematic illustration showing the material constants and boundaries of the three regimes of fatigue crack growth.
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Table 3 Summary of fatigue crack growth parameters in the three regimes of crack growth for forged IN 718
Stage I Stage II Stage III
Fig. 13. Fracture map showing the transitions between fatigue fracture modes as a function of DK and Kmax, for forged IN 718.
correspond to the transition between crystallographic and striation-type mechanisms, while the third set of boundaries represent the onset of static/monotonic fracture in addition to the striation fracture mode. The incidence of the static/monotonic fracture mode increases with increasing DK and Kmax in the final stages of fatigue crack growth, and catastrophic failure occurs when Kmax = KIc. It is particularly interesting to note that it may be possible to represent the transition boundaries by equations for hyperbolas or parabolas. However, more detailed mapping is needed to obtain sufficient number of data points to be able to fit appropriate equations for hyperbolas or parabolas. If such equations can be fitted to the transition data, it should be possible to use the transition equations to determine the fatigue mechanisms that are associated with the applied combinations of Kmax and DK. The appropriate linearized fatigue crack growth laws may then be used in the prediction of fatigue crack growth. For example, the dependence of the fatigue crack growth rate, da/dN, on DK and Kmax may be expressed in the form of a two-parameter crack growth law, as proposed by Campbell et al. [13]. This is given by: da/dN =ao(DK)a1(Kmax)a2
(10)
Since the mechanisms of fatigue are different in the near-threshold (regime I), Paris (regime II) and high DK (regime III) regimes, separate constants, ao, a1 and a2 were obtained for the three regimes of crack growth using multiple linear regression techniques [12]. The results are summarized in Table 3 along with the error coefficients, r 2. In addition, the material constants obtained for a single crystal IN 718 alloy are presented in
log ao
a1
a2
r2
r
−10.4 −9.4 −11.6
3.006 3.02 3.49
0.85 0.32 1.31
0.89 0.95 0.93
0.94 0.98 0.97
Table 4 for comparison. The exponents of DK are close to 3 in regimes I and II, and around 3.5 in regime III. However, the exponents of Kmax are greater in the near-threshold and high DK regimes (0.85 and 1.31, respectively) in comparison with the Kmax exponent of 0.32 in the Paris regime. The relatively high exponent of Kmax in the near-threshold regime is associated with a crystallographic crack growth mechanism, while the very high exponent of Kmax in the high DK regime is consistent with a fracture mode that consists of fatigue striations and ductile-dimpled fracture modes. The current paper, therefore, suggests that fatigue mechanism maps (Fig. 13) may be used to determine parametric windows of Kmax and DK for the determination of mechanistically-based fatigue crack growth laws. For example, the transitions between regimes I, II and III were determined from the fatigue maps prior to regression analysis to obtain the empirical constants ao, a1 and a2. The fracture mechanism maps could also be used to identify the parametric ranges for the selection of appropriate crack growth laws during fatigue life calculations. However, it is important to remember that the current maps have been obtained for long cracks in the Forsyth stage II regime [14]. The presented fatigue maps and crack growth laws may therefore be inapplicable to life prediction in the short crack regime.
11. Conclusions 1. The mechanisms of fatigue crack growth in this forged IN 718 alloy have been found to be dependent on both the stress intensity factor range (DK) and the maximum stress intensity (Kmax). Fracture modes under cyclic loading and mechanisms of crack-tip deformation were both found to vary with increasing DK and/or Kmax. Table 4 Summary of fatigue crack growth parameters in the three regimes of crack growth for single-crystal IN 718
Stage I Stage II Stage III
log ao
a1
a2
r2
r
−10.9 −10.0 −16.4
3.88 4.25 3.92
1.60 0.71 6.23
0.76 0.94 0.97
0.87 0.97 0.98
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2. At low values of DK and/or Kmax, corresponding to the near-threshold and lower Paris fatigue regimes, fatigue crack growth progressed via a transgranular, crystallographic fracture mechanism. In experiments conducted at stress ratios of 0.1, 0.3 and 0.5, a transition to a classical crack-blunting fatigue mechanism, involving the formation of relatively coarse striations, occurred in the central region of the Paris regime. Accelerated crack growth towards final failure at these three stress ratios, was attributed to a combination of classical fatigue (striation formation), and Kmax-controlled ductile-dimpled static fracture mode contributions. 3. At a stress ratio of 0.8, the transgranular, crystallographic mode of fracture was active throughout the Paris regime and was also present in the high DK regime. Some evidence of striations was observed in the Paris regime but accelerated crack growth in the high DK regime occurred by a combination of crystallographic fatigue fracture and ductile-dimpled static fracture. The role of Kmax at this stress ratio is of considerable significance. 4. At a stress ratio of 0.1, accommodation of plastic strain directly ahead of the crack-tip during fatigue crack growth in the near-threshold and lower Paris regimes appears to occur by fracture of the Ni3Nb precipitates. In the upper Paris regime, crack-tip deformation during fatigue appears to be associated with the formation of slip bands, fine dislocation networks and stacking faults in the crack-tip region. No fracturing of the Ni3Nb precipitates was observed in the upper Paris regime. 5. Crack-tip deformation in the high DK regime, at a stress ratio of 0.8, was also associated with the formation of slip bands and fine dislocation networks. However, the density of the deformation was found to be greater in this regime than that observed in the Paris regime at a stress ratio of 0.1. 6. New linearized crack growth laws have been formulated for the near-threshold and high DK regimes. Two-parameter extensions to the Paris law have also been proposed for the assessment of the combined effects of Kmax and DK in the near-threshold, Paris and high DK regimes. The regimes of applicability of the fatigue crack growth laws have also been described on a fatigue fracture map within a plot of Kmax versus DK. The map shows the loci of points corresponding to fracture mechanism transitions
.
within a triangle that contains all the possible values of Kmax and DK for positive stress ratios. Constant stress ratio paths are also represented by diagonal lines that radiate from the origin of the Kmax versus DK plot. The presented crack growth laws and fatigue maps are proposed for long cracks in the Forsyth stage II regime.
Acknowledgements The research was supported by The Division of Materials Research of The National, Science Foundation with Dr Bruce MacDonald as Program Monitor. Appreciation is also extended to Dr Padu Ramasundaram of Wyman Gordon, Houston, TX, for providing the material that was used in this study.
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