Residual life prediction methods for gas turbine components

Materials Scienceand Engineering, A 103 (1988) 49-61

49

Residual Life Prediction Methods for Gas Turbine Components* R. H. VAN STONE

(;I: ,qircn{l?Engines, ('incinnati, Ol145215 (U.S:A.) (ReceivcdOctober 28, 1987:

Abstract

7he use of fracture mechanics in predicting the life of turbine components is reviewed with emphasis on the surface crack and R ratio effects. Several examples of life methods development and verification are reported. The described methodology, which does not directly model crack-closure behavior, accurately predicts the growth of physically short surface cracks and situations where oxMe- and roughness-induced closure are expected to occur. 1. Introduction Over the past few decades the design criteria and techniques used for high technology structures have both changed and increased in complexity. Among the most challenging structures from the design and life prediction perspective are gas turbine engines. Turbine components have complicated geometries containing numerous stress concentrations. This is illustrated in Fig. 1 which shows the geometry of a rim of a high pressure turbine disk. These types of components operate at high stresses with steep stress gradients and often experience thermal-mechanical cycling. Figure 2 shows an example of a thermal-mechanical mission from a military aircraft engine mission [1]. The thermal and stress histories are highly dependent on a variety of factors, including type of engine, mission, location and engine speed. Therefore the analysis of critical locations must be performed according to the stress gradient and thermal-mechanical history at that position. The aircraft engine design engineer has the responsibility for overall design, stress analysis, life analysis, component cost, component per*Papcr presented at the Workshop on the Mechanics and Physics of Crack Growth: Application to Life Prediction, Kcystone, CO, U.S.A.,August 4 7, 1987. 0921-51193/88/$3.50

formance and liaison with the materials, manufacturing and quality engineers. As a result, the design engineer has become increasingly dependent on the technologies being developed by his colleagues with expertise in thermal analysis, finite element modeling, materials behavior and life prediction. In this paper a review is given of one of the technologies currently in use in the design of aircraft engine components: the prediction of crack propagation using linear elastic fracture mechanics (LEFM). The paper has two parts. The first part (Section 2) describes the way that fracture mechanics prediction methods are developed and applied. Several examples of LEFM crack propagation predictions method development and verification will be given. These examples will be restricted to isothermal crack propagation, in the second part of the paper (Section 3) several situations which would be expected to be dominated by crack-closure phenomena will be considered. Experimental results and predictions of crack growth in nickel-base superalloys will be compared with those reported for other materials.

2. Methods development Under the Engine Structural Integrity Program (ENSIP), the lives of critical aircraft engine components are being set by LEFM crack propagation analysis t2-5]. Many of those analyses are performed for physically small surface flaws under the severe loading conditions described previously. As a result, the crack propagation analyses are performed using rather complex computer codes. The basic input into such an analysis includes the location geometry, stress analysis, thermal history and loading spectrum together with the appropriate material properties. The code must be able to deal with a variety of complex conditions, such as the transition © Elsevier Sequoia/Printed in The Netherlands

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between a surface flaw in a thin component to a through-thickness edge crack. The mathematical models embedded in the computer codes are approximations of the real material and crack behavior. The accuracy of the life prediction methodology is highly dependent on the accuracy of these models. The development of these models has several steps: (1) physical understanding and/or experimental test program; (2) methods development; (3) code modification; (4) experimental verification. The first step consists of a combination of literature survey, analytical modeling and experimental evaluation. The methods development stage combines this physical understanding with results of experiments on relatively simple geometries with a simple loading spectrum to

develop a mathematical model. This model is then introduced into the crack propagation prediction computer code. This overall system is then verified by performing experiments of complex geometry test specimens, known as feature tests, which often are cycled using more realistic loading spectra. Both the geometry and the loading cycles are designed to simulate critical locations in aircraft engine components. The growth of cracks in the feature tests must be accurately predicted before this modified code is released for use by design engineers. Before the prediction techniques are described and comparisons with experimental data are given, examples of the methods developed to predict the influence of R ratio on the growth of surface flaws will be described.

51

2.1, R ratio effects In order to predict crack growth during missions, such as those shown in Fig, 2, it is necessary to have a model which accurately describes the influence of R ratio (R = K m ~ , , / K ....... ) on crack growth behavior. There are two basic approaches for doing this: one is based on closure behavior and the other is semiempirical in nature. Wei and coworkers [6, 7] studied the fatiguecrack-closure behavior in titanium and aluminum alloys and concluded that crack closure is a significant factor in R ratio effects, but it does not explain all the observations, particularly those at highly positive R ratios. They suggested that the influence of R on the stress and strain distribution in the crack tip plastic zone is extremely important in controlling crack growth rates. Because of the large component of high R ratio cycling in aircraft engine missions, the empirically based Walker [8] model is used to predict the crack growth behavior. In this approach, the effective value of K, denoted Kcff , is a function of R, the maximum value of K, denoted K ....... and a material property known as the Walker exponent t?l:

Figure 3(a) shows the variation in crack growth rates with AK as measured in extruded and isothermally forged Rend 95 specimens cycled at 399 °C (750 °F) and 0.33 Hz (20 cycles min i) with different R ratios II 1]. These data were

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52

determined using both surface-flawed [12] and single-edge-notched (SEN) through-crack [13] specimens monitored with direct current potential drop techniques [ 13-15]. The near-threshold data were obtained using the SEN specimen with a load-shedding technique developed for high strength nickel-base superalloys [13, 16]. The surface flaw data describe the crack growth in the depth direction. Figure 3(a) shows that there is good agreement between the surface-flawed and SEN specimens. As R is increased, crack growth is accelerated and there is a lateral shift in the data relative to the AK axis in both the nearthreshold (region I) and the Paris law (region II) regimes• These data were modeled using the dual-Walker-exponent approach and are plotted as a function of K~r: in Fig. 3(b). These data illustrate that this model can be used to collapse a wide range of non-zero R ratio crack growth data to a single population. The curve through these data and the corresponding Walker exponents are used to describe the crack growth properties of this material at this test temperature.

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Predicting the growth of surface cracks is complicated by the variation in K around the periphery of the crack. Room temperature experiments on hot isostatically pressed compacted powder metallurgy Ren6 95 have shown that, even when accounting for the variations in K around the crack, the crack growth rate dc/dN along the surface is slower than the crack growth rate da/dN in the depth direction [11, 15]. These data are shown in Fig. 4(a) for five specimens which were tested at an R ratio of zero but with three values of maximum stress. The K solution obtained by Newman and Raju [17] was used to calculate the values of K at the surface and depth positions. In this case, the da/dN and dc/dN behavior diverge. This results in changing the aspect ratio of the crack as it propagates, as illustrated in Fig. 4(b). The change in crack shape is dependent on stress level even though the crack growth rates are dependent only on AK. These results show that, when performing surface crack fatigue experiments and predictions, it is necessary to consider changes in crack aspect ratio. The behavior illustrated in Fig. 4 can be explained by considering the elastic-plastic finite element analysis of surface flaws under monotonic loading performed by Trantina and coworkers [18, 19]. They showed that, as the

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remote strain increased, there was a significant reduction in the crack tip singularity where the crack intersected the free surface owing to local-

53

ized yielding. Using this model, it was shown that the crack shape locally "tucked in" at the surface, similar to that observed in Ren~ 95 during elevated temperature fatigue crack growth tests [1 l]. Based on these results, a constraint loss model was developed [1 l j which assumed that K at the surface location decreased relative to the elastic K solution in proportion to the plastic zone size:

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The applicability of this model will be demonstrated using the dc/dN data corresponding to the da/dN data previously shown in Fig. 3 [l 1]. Figure 5(a) shows the dc/dN data from the surface flaw experiments as a function of K~u. The values of K~t, (K~ in eqn. (5)) were calculated from the N e w m a n - R a j u K solution and the Walker exponents determined from the da/dN data. The data in Fig. 5(a) show that the dualWalker-exponent R ratio model accurately collapses the dc/dN data to a single population. The values of c~ and fl were determined using regression analysis on the dc/dN data and treating the da/dN curve (Fig. 3(b)) as the da/dN vs. K behavior. Figure 5(b) shows the resulting crack growth curves which can be collapsed onto each other

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54

on the material being evaluated. Yau [21] showed that cracks in Alloy 718 grew slower along the surface than in the depth direction but that the reduction was by a constant factor of K (a = 0 in eqn. (5)). More recently, Carter et al. [22] showed that surface cracks in the aluminum alloy 2124T851 grew faster along the surface than in the depth direction. These results illustrate that the details of surface crack growth are, at best, poorly understood even though physically based models have been developed which accurately predict their behavior.

2.3. Residual life prediction The prediction of crack growth behavior and residual life is, in principle, relatively simple. It consists in determining the values of K, determining the appropriate crack growth rates, incrementing the crack advance and repeating this process until a failure criteria, usually material toughness, is attained. For the case of laboratory test specimens with well-defined K solutions, this is relatively simple; however, for the cases of most interest such as surface flaws growing out of a stress concentration (notch or hole) and cycled under mission conditions, the situation is more difficult. For an arbitrary stress distribution, such as at a stress concentration, the weight function approach originally proposed by Bueckner [23] can be utilized to determine the values of K. For the remainder of this paper, the K values were calculated using the weight function formulation developed by Yau [21] for use with the Newman-Raju [ 17] surface flaw K solution. Let us consider the case of a surface crack growing from a notch which has been loaded to a stress high enough to result in localized yielding. Figure 6 is a schematic diagram showing the elastic stress distribution for this notch at the highest loading point in the mission. All stresses in this figure are normalized relative to the maximum elastic stress at the notch root. The elastic stress distribution is obtained using finite element calculations. When localized yielding occurs at the notch root, the stresses are redistributed as shown in Fig. 6. The elastic-plastic stress distribution is determined using either elastic-plastic finite element or Neuber notch analysis. The line in Fig. 6 labeled elastic-plastic zero load corresponds to the elastic-plastic distribution at zero load. The values of K for a given leg of a mission are calculated for the minimum and maximum

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elastic-plastic stress distributions using the weight function methodology [21]. The value of R is determined from the calculated K values, and Koff is determined using eqn. (1). At surface locations, the value of K~ffis further reduced using the constraint loss model. These values of K~ff are then used to calculate a crack growth rate at the surface and depth positions. The crack size is then incremented, and the entire procedure is repeated until a failure criterion is reached. This approach permits the crack aspect ratio to change as the crack grows. The computer codes used to perform these types of calculation in an automated fashion are fairly complicated. To have good utility to the design engineer, they must be user friendly, compatible with his mission description and materials databases, and cost efficient. Above all else, they must be able to predict accurately the growth of cracks under the complex situations to which they are applied.

55

2.4. Metho& verification The quality of a residual life prediction methodology is not solely the ability to construct accurate crack growth rate curves, but the reliable prediction of both simple laboratory specimens (feature tests) which simulate the geometries (stress concentrations) where this methodology must be applied [5, 11, 21]. Specimens used for fracture mechanics verification contain a small electric-discharge machined notch and are procracked to obtain a sharp crack. Two examples of verification programs will be used to demonstrate the ability of the crack growth methodology previously described to predict residual lives. Figure 7(a) shows three test specimen geometries used

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by Yau [21] to examine the ability of this approach to predict the lives of complex geometries. Specimens of Alloy 718 and Ti-6wt.%AI-4wt.%V were tested over a range of temperatures, missions, stress levels and R ratios. Figure 7(b) shows the variation in the observed and predicted lives with specimen geometry. Most of the lives fall within a factor of 2 of the experimentally observed lives. In a similar study on Rend 94 [11 l, 29 surface-flawed specimens were tested over a range of temperatures, stress levels and R ratios. Figure 8 shows that the methodok)gy, including the constraint-loss model described in Section 2.2, was able to predict the lives of these specimens accurately. The growth of cracks in double-edge-notched Rend 95 specimens were also predicted well even though the fatigue surfaces of some high stress specimens were extremely tortuous [11]. In both of these investigations 111, 21j, the ratio of predicted to observed lives were evaluated statistically using log-normal distributions. The range of the average plus and minus three standard deviations for the life ratio of surfaceflawed test specimens was between 0.5 and 2.0 or within twice the experimentally observed lives. These types of result show that these life prediction methods can accurately predict the residual lives of aircraft engine materials over a wide range of conditions. As a result, aircraft engine designers have a verified crack growth predictive

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56 capability which they can use with a high degree of confidence. 3. Closure issues One of the more interesting features of this residual life prediction methodology is that, other than a different Walker exponent for negative R ratios, there is no consideration of crack closure. This is somewhat surprising considering the large amount of published literature generated in recent years on the importance of crack closure. In order to determine whether this is a potential limitation of this predictive method, the phenomena of oxide-induced closure, roughnessinduced closure and short surface cracks in nickel-base superalloys will be considered.

and 538 °C (1000 °F) for R ratios of 0.05 and 0.75 respectively. The cross-over was observed for both R ratios, suggesting that the increased threshold values observed with increasing temperature are not the result of a closure phenomenon. At both temperatures, changes in R Delta

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have reported that oxide-induced closure controls the near-threshold crack growth behavior of Alloy 718 and Ren6 95 respectively. These conclusions were based on agreement between measured oxide thicknesses on fracture surfaces and calculated crack-tip-opening displacement. A variety of structural alloys show the crack growth "cross-over" behavior [26, 27]. Increasing temperature increases both the fatigue crack growth threshold and the region II crack growth rates, resulting in the crossing of the fatigue crack growth curves determined at different temperatures. One rationale for the increasing threshold with increasing temperature is the growth of thicker oxides at the higher temperatures which would result in a larger value K~. This behavior would be similar to that reported for corrosion products in steels by Suresh et al. [28]. Oxideinduced closure would have a smaller influence in high R ratio tests because the crack would be open during more of the cycle. It would then be expected that oxide-induced closure would result in a larger influence on the R ratio in the nearthreshold regime relative to region II. These reports of oxide-induced closure in nickel-base superalloys are in sharp contrast with results from an investigation of DA718 [26], a fine-grained high strength thermomechanically processed version of Alloy 718 [29]. The crack growth behavior of DA718 was investigated as a function of test temperature and R ratio. Figures 9(a) and 9(b) show the results of crack growth rate experiments on DA718 at 149 °C (300 °F)

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57

ratio resulted in a lateral shift of the crack growth data along the A K axis. There is no indication of the larger difference in the near-threshold regime which has been reported for displacement (roughness- or oxide-induced) types of closure mechanism. These data were analyzed using the Walker model and the resultant data are shown in Fig. 10 as a function of Kdf. These results suggest that direct consideration of closure is not necessary to model the crack growth behavior accurately. Figure 10 clearly shows the "'cross-over" behavior. It has been suggested that the cause of the increased threshold with increasing temperature results from localized crack tip blunting by combinations of plasticity and creep [29]. This is further supported by the observation that decreasing test frequency and hold times result in increased crack growth thresholds for Alloy 718 and Rend 95 [1 ]. 3.2. Rottghness-induced closure

Metallurgical conditions which have tortuous crack paths may exhibit roughness-induced closure ~'here the faces of the crack surface inclined to the macroscopic cracking plane make contact at positive loads. This has been reported for a number of alloy systems and loading condi-

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tions [30-36]. Of particular interest to this discussion are the investigations of Gray et al. [35] and Allison [36] on rail steels and titanium alloys respectively. These investigations showed that variations in the microstructure (grain and precipitate sizes) significantly affected the fatigue crack growth rates measured at near-zero R ratios. Coincident with reduced crack growth rates were changes in the deformation modes and fracture surface roughness. It was shown that the microstructural conditions which had different crack growth properties at low R ratios had similar crack growth rates in high R ratio tests. From these data and crack-closure measurements, it was concluded that the differences in crack growth properties were caused by microstructure- and/or defl)rmation-mode-induced changes in crack path tortuousity which resulted in roughhess-induced closure. This type of behavior would significantly influence material selection for aircraft engine or other components which experience a large amount of high R ratio mission cycling. Krueger and coworkers [27, 37] investigated the 427 °C (800 °F) crack growth properties of Alloy 718 as a function of grain size and precipitate size. Nearthreshold and region II crack growth rates were determined in a two by two matrix of grain size (20 and 250 #m) and precipitate size {150 and smaller than 20 nm). Crack growth rates were measured for all four microstructures at R ratios of 0.05 and 0.75. The fracture surfaces of the coarse-grained materials were much rougher than those of the fine-grained microstructures. For all four materials, increasing R ratio resulted in a unifl)rm lateral shift in the crack growth rates [37]. These data were analyzed using the Walker model and are shown in Fig. 11. The Walker exponents for these materials have a relatively narrow range from 0.64 to 0.80. The data for the underaged and overaged materials are shown in Figs. 1 l(a) and 1 l(b) respectively. For each precipitate size, the increasing grain size decreased crack growth rates. This was observed for both the low and the high R ratio data, which is in sharp contrast with the work on steels and titanium alloys [35, 36]. Krueger el al. 1371 concluded from these data, fraetographic observations and detailed deformation mode studies that the fatigue crack growth properties of Alloy 718 at 427 °C are controlled by slip reversibility rather than by roughness-induced closure behavior.

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the crack changed direction, resulting in a zigzag crack path. One of the major differences in the fracture path was the magnitude of the roughness resulting from the variations in grain size. The influence of crack path tortuosity on the local K was estimated using the model proposed by Suresh [38]. For a zigzag fracture (no flat segments or S=0), that model predicts that K is dependent only on the angle between the fatigue path facets and the macroscopic plane of crack propagation, but not on the size of those facets which in this case corresponds to the grain size. The influence of grain size on the crack growth rates could not be reconciled on the basis of the longer crack lengths for the more tortuous crack path in the coarse-grained materials. The results of this study are in sharp contrast with previous studies on other alloy systems. The ability of the Walker model to predict the influence of R ratio for materials with a large difference in fracture surface roughness suggests that the life prediction methodology previously described would accurately predict the residual lives for cracks in these materials.

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Fig. 11. Crack growth rates of (a) underaged and (b) overaged Alloy 718 determined at 427 °C (800 °F ) for R ratios of 0.05 and 0.75 as a function of K~..

Examination of the crack path showed that for both grain sizes the cracks grew in a transgranular fashion across each grain. At grain boundaries,

3.3. Short surface cracks Recent work [30] on the growth of short cracks has suggested that the rapid growth of short cracks is caused by the absence of a crack wake and the resultant benefits which can be derived from crack closure. Crack growth experiments [11, 39] were performed on physically small surface flaws in extruded and isothermally forged Ren6 95. Precracks were grown from semicircular E D M notches, but the notches were machined away after precracking but prior to the start of the test. These tests had smaller initial flaw sizes than the test specimens used to develop the crack growth properties (Figs. 3 and 5). A total of nine short crack tests were performed over a range of temperatures, maximum stress levels and R ratios [11]. Each specimen was heat tinted [15] several times and residual life calculations were made to predict the life from the crack size corresponding to each heat tint. Figure 12 shows the variation in the predicted-to-observedlife ratio as a function of crack depth. The shortest crack depth was 0.065 mm (0.0025 in). These data show that the growth of short cracks in Ren6 95 can be predicted without consideration of closure. It should be noted that Ren6 95 processed in this fashion has a microstructure with a grain size of approximately 0.005 mm (0.0003 in)

59

and yield strengths in excess of 1000 MPa (150 klbf in--~) for the test temperatures shown in Fig. 12 {40j. As a result, the crack sizes shown in Fig. 12 could be described as long relative to both the microstructure and the crack tip plastic zone size. A further indication of the validity of this life prediction methodology was the ability to predict the inclusion size in DA718 which acted as fatigue crack nucleation sites in conventional fatigue tests from the fatigue crack growth threshold dam shown in Fig. 10 I26]. It is not known at this time whether closure must be considered to obtain accurate residual life predictions for short cracks in materials with larger grain sizes and/or lower strength levels. The near-threshold data reported in this paper have been obtained using a 10 mm (0.4 in) wide SEN specimen geometry with a fatigue starter notch less than 0.25 mm (0.01 in) deep. For these high strength nickel-base superalloys, the crack length at the fatigue crack growth threshold is typically I mm (0.04 in). This crack length is short compared with those in the more frequently used compact specimens. For these crack sizes, the SEN specimen has a lower bending component and a steeper K gradient than the compact specimen has. The differences between the results on the nickel-base superalloys (SEN specimens) and those reported for other materials (compact specimens) may, in part, result from differences between these specimen geometries. Both specimens are subject to problems at

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elevated temperatures where the oxidation of testing fixtures may prevent the free rotation of the specimen on the loading pins. This problem appears to be more severe for the compact geometry owing to its larger bending component. They would also become more aggravated for near-threshold tests where the loads are low and the crack lengths are long as a result of load- or K-shedding procedures. There is no known direct comparison between the two geometries for nickel-base superalloys; however, comparison of the results reported by McCarver and Ritchie [41] for cast and wrought Rend 95 with those reported here are quite interesting. McCarver and Ritchie [41 I determined the life of short-crack specimens of cast and wrought Rene 95 at R=0.1 as a function of the initial stress intensity factor. From run-out tests, they estimated the threshold value to be approximately 3 MPa m In. The threshold values measured in long-crack experiments at R ratios of 0.1 and 0.8 were 7.7 MPa m ~?- and 3.5 MPa m ~'-~ respectively. From this information, they concluded that there is a major short-crack effect in superalloys which probably results from closure effects. Their data are compared with threshold data of nickel-base superalloys obtained from SEN tests in Fig. 13, The band representing the results of SEN tests on fine-grained nickel-base superalloys was determined from a rather large database. The data points shown within the band are those previously reported in Figs. 5 and 10. The trend of increasing threshold values with increasing temperature described earlier is clearly shown in this figure. It should be noted that the cast and wrought Rend 95 used by McCarver and

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Fig. 13. Fatigue crack growth threshold dam from hmg- and short-crack tests of nickel-base superalloys.

60

Ritchie has a duplex "necklace" grain structure which is substantially different from the microstructures of DA718 and isothermally forged powder metallurgy Ren6 95 used to determine the fine-grain threshold data band. Both the short crack and the R = 0.8, long-crack data fall close to the SEN data scatter band; however, the R=0.1, long-crack data fall outside the band. This is not a direct comparison because of the variations in material, but these data do suggest that threshold values measured at low R ratios in compact specimens may be much higher than those determined for specimens with smaller crack sizes. The impact of specimen geometry on crack closure and near-threshold crack growth rates is a subject which requires more research. The data presented here show agreement between shortcrack, surface flaw crack and SEN crack growth data and the ability of the residual life methodology to predict accurately the residual lives of surface flaws. These results strongly suggest that, for situations where accurate short-crack high stress residual life predictions are required, the values of threshold should be measured in specimen geometries similar to the SEN specimens. 4. Conclusions In this paper, several aspects of the residual life prediction methodology used for aircraft engine components has been reviewed. It has been shown that crack growth rates measured in shortthrough-crack SEN geometries agree well with surface flaw data. In order to predict the growth of surface flaws, differences between the growth in the crack depth direction (da/dN) and those along the surface (dc/dN) must be accurately modeled. The influence of R ratio on both the near-threshold and the region II crack growth rates of nickel-base superalloys can be accurately estimated using the dual-Walker-exponent model. This model does not explicitly consider closure effects; however, results from recent investigations show that crack growth rates and residual lives are predicted well using this model under conditions where oxide- and roughness-induced closure would be expected to occur. The residual lives of physically short cracks were also predicted accurately. Acknowledgments The author would like to express his appreciation to the U.S. Air Force, the U.S. Naval Air

Systems Command and the GE Aircraft Engines which sponsored the research described in this paper. The author is also deeply indebted to K. L. Cooper, M. S. Gilbert, O. C. Gooden, D. D. Krueger, J. H. Laflen, T. L. Richardson, W. V. Ross, M. E. Sauby, T. E. Wallrauch and J. F. Yau for their assistance and helpful suggestions during these investigations. References 1 R. H. Van Stone, Advanced cumulative damage modeling, Rep., 1985 (GE Aircraft Engines, Cincinnati, OH 45215) (U.S. Air Force Contract F33615-84-C-5032). 2 Engine Structural Integrity Program (ENSIP), Mil. Stand. MIL-STD-1783 (USAF), 30 November 1984 (U.S. Air Force). 3 T. T. King, W. D. Cowie and W. H. Reimann, Damage tolerant design concepts for military engines, Proc.

NA TO A GARD Structures and Materials Panels Specialists' Meeting on Damage Tolerance Concepts for Critical Engine Components, San Antonio, TX, April 1985, to be punished. 4 J. M. Larsen and T. Nicholas, Eng. Fract. Mech., 22 (1985) 77-91. 5 T. Nicholas, J. H. Laflen and R. H. Van Stone, A damage tolerant design approach to turbine engine life prediction, in V. Weiss (ed.), Proc. Conf. on Life Prediction for High-temperature Gas Turbine Materials, in EPRI Rep. AP-4477, April 1986 (Electric Power Research Institute, Palo Alto, CA). 6 T.T. Shih and R. P. Wei, Eng. Fract. Mech., 6 (1974) 19. 7 K.D. Uganst, T. T. Shih and R. P. Wei, Crack closure and fatigue crack growth in 2219-T 851 aluminum alloy, Rep. AFOSR-TR-76-1247, August 1976 (Lehigh University, Institute of Fracture and Solid Mechanics, Bethlehem, PA 18015) (U.S. Air Force Office of Scientific Research Contract). 8 K. Walker, Effects of Environment and Complex Load

History on Fatigue Life, ASTM Spec. Tech. Publ., 462 (1970) 1. 9 R. H. Van Stone, The influence of temperature and stress ratio on the crack growth behavior of Ren6 95, GE Rep. 82-640, 1982 (GE Aircraft Engines, Cincinnati, OH

45215). 10 A. M. Sullivan and T. W. Crooker, Analysis of fatiguecrack growth in high strength steel, Part J, stress level and stress ratio effects at constant amplitude, ASME Paper 75-WA/PVP-22 {American Society for Mechanical Engineers). 11 R. H. Van Stone, M. S. Gilbert, O. C. Gooden and J. H. Laflen, ASTM Spec. Tech. Publ., 969 (1988) 637. 12 A. Coles, W. Johnson and H. G. Popp, J. Eng. Mater. Technol., 98 (1976) 305. 13 M. E Henry, GE Corporate Research and Development, Schenectady, NY, unpublished research, 1983. 14 R. P. Gangloff, Fatigue Eng. Mater. Struct., 4 (1982) 15-31. 15 R. H. Van Stone and T, L. Richardson, in W. Cullen, R. Landgraf, L. Kaisand and J. Underwood (eds.), Auto-

(~1

mated Test Methods ]or f'racture and Fatigue Crack Growth, ASTM Spec. Tech. Publ., 877 (1985) 148-166. 16 D.D. Krueger, M.S. Thesis, University of Cincinnati, Cincinnati, OH, 1984. 17 J. C. Newman and I. S. Raju, Stress intensity factor equations for cracks in a three-dimensional finite body, NAS4 Tech, Memo. 78805, 1981 (Langley Research Center, National Aeronautics and Space Administration, Hampton, VA ). 18 G. Trantina, H. G. deLorenzi and W. W. Wilkening, Eng. Fra~'t. Alec'h., 17 ( 1983 ) 925- 938. 19 G. I'rantina and H. G. deLorenzi, Elastic-plastic fracture mechanics analysis of small cracks, Critical t¥oblems in Svstetns l)esign, Proc. Army A),mp. on Solid Mechanics, September 1982, in Rep. AMMRC, MS 82-4, 1982 (U.S. Army Materials and Mechanics Research Center). 21) J. R. Rice, ASTM Spee. Teeh. Publ., 41511967) 247 309. 21 J.F. Yau, in J. H. Underwood, R. Chair, C. W. Smith, D. P. Wilhelm, W. A. Andrews and J. C. Newman (eds.), Proc. 17th Natl. A)'mp. on Fracture Mechanics, in A S T M Spec. 7Fch. l'ubl., 905(1986) 601-624. 22 1). W. Carter, W. R. Canda and J. A. Blind, Surface fla,A. crack growth in plates of finite thickness, Rep. A F W A L TR-86-4034, January 1987 (Department of Engineering Mechanics. U.S. Air F'orce Academy, Colorado Springs, CO 808401 ,',Air Force Wright Aeronautical Laboratories contract. 23 H. F. Bucckner, Z. Angew. Math. Mech., 51 (19711 97 109. 24 J. L. Yuen, P. Roy and W. D. Nix, Metall. Tram. A, 15 (19851) 1769 1775. 25 k. P. Zawada and T. Nicholas, The effect of loading history on closure behavior in Rent} 95, submitted to ASTM. 26 R. H. Van Stone and D. D. Krueger, Investigation of direct aged Inconel 718 fatigue behavior, Final Rep. December 1984 (GE, Cincinnati, OH 45215)(NAVAIR Contract N0t)019-82-C-0373 I. 27 R. H. Van Stone and I). D. Krueger, ASTM Spec. Tech. l'ubl., 909 (1988) 883-91t6. 28 S. Suresh, O. F. Zamiski and R. O. Ritchie, Memll. Trans. A, 12!i 1981) 1435-1443. 29 J. F. Barker, D. D. Krueger and D. R. Chang, Thermomechanical processing of Inconel 718 and its effect on

properties, Proc. Syrup. on Advattced ltigh-7~'mperature Alloys: Processing and Properties, American Society for Metals, Metals Park, OH, 1986, pp. 125-137. 30 S. Suresh and R. O. Ritchie, Near-threshold fatigue crack propagation: a perspective on the role of crack closure, in D. L. Davidson and S. Suresh (eds. I, Fat(~ue ('rack (;rowth Threshold Concepts, Metallurgical Society of AIME, Warrendale, PA, 1984, pp. 227-261. 31 S. Suresh, Scr. MetalL, 16 (1982) 995-999. 32 S. Suresh, Eng. f+aet. Mech., 18 ',1983! 577 5t)3. 33 S. Suresh and A. K. Vasudevam Application of fatigue threshold concepts to variable amplitude crack propagation. in D. L. Davidson and S. Suresh ~eds.), f.ittigue ('nick Growth ThreshoM ('ottcel)lL Metallurgical Society of AIME, Warrendale, PA, 1984, pp. 361-378. 34 R. A. Venables, M. A. Hicks and J. E. King, Influence of stress ratio on fatigue thresholds and structure sensitive crack growth in Ni-base superalloys, in D. L. I)avidson and S. Suresh (eds.), Fatigue ('rack Growth "lhreshold ('onc~721s, Metallurgical Society of AIME, Warren&de, PA, 1984, pp. 341-357. 35 G.T. Gray III, A. W. Thompson, J. C. Williams and 1). H. Stone, in J. B~icklund, A. Biota and C. J. Bcevcrs (eds.L Proc. l~'t Int. ConjZ on k~ttigue Iltresho/ds': l')tndamenlal and Engineering Applications. Stockhohn, ,hme 1 3, 198l, Engineering Materials Advisory Services, Warier, 1982, pp. 345 36t). 36 J. E. Allison, Investigation of the influcnce of slip character on the fatigue crack growth properties of titanium alloys, Ph.D.. Thesis, Carnegie Mellon University, Pittsburgh, PA, 1983. 37 D. D. Krueger. S. D. Antolovich and R. H. Van Slonc, Metall. Trans. A, 18 ( 1987 ) 1431 - 1449. 38 S. Suresh, MetalL l)~ans. A, 16(1985) 249-26{). 39 W. V. Ross and M. E. Sanby, GE Aircraft Engines, Cincinatti, OH 45215. unpublished research. 1985. 411 1). R. Chang, D. D. Krueger and R. A. Sprague, in IM. Gell, C. S. Katovich, R. H. Bricknell, W. B. Kent and J. F. Radavich ,,eds.), Sttperalloys 1984, Proc. 5t17 l,t. 8ytnp. on Superallo U, Seven 51)rings, 15t, October 7-1I, 1984, Metallurgical Society of AIME, Warrendale, PA, 1984, pp. 245 273. 41 J. F. McCarver and R. O. Ritchie, Mater. Sci. l;'ttL,., 55 (1982) 63-67.