Low cycle fatigue characteristics of 〈001〉 and randomly aligned superalloy single crystals

Acta metall. Vol. 32, No. 10, pp. 1669-1679, 1984 Printed in Great Britain. All rights reserved

0001-6160/84 $3.00+0.00 Copyright C~) 1984 Pergamon Press Ltd

LOW CYCLE FATIGUE CHARACTERISTICS OF (001) AND RANDOMLY ALIGNED SUPERALLOY SINGLE CRYSTALS D. L. A N T O N United Technologies Research Center, E. Hartford, Connecticut, U.S.A. (Received 23 December 1983; in revised form 10 April 1984)

Abstract--The influence of microstructure on the low cycle fatigue behavior in a model single crystal superalloy has been measured for (001) aligned as well as randomly oriented crystals. Microstructures produced by three heat treatments in (001) aligned as well as randomly oriented crystals. Microstructures produced by three heat treatments in (001) crystals; namely fine 7", coarse 7' and a strain aged V' structure were tested under constant total strain amplitude conditions at temperatures ranging from 650 to 1000°C. Randomly oriented specimens having the coarse V' precipitates were tested at 870°C, SEM evaluation of the fracture surfaces showed fatigue crack initiation related to microporosity below 980°C and oxidation cracking at greater temperatures. No significant effect of the 7' rafting on LCF life was observed. All (001) aligned crystals had cycle lives similar to other directionally solidified superalloys under similar conditions, a possible indication of similar failure mechanisms. Anisotropic fatigue crack growth patterns were identified in (001) crystals with cracks growing fastest in the (011 ) direction and a model was developed to predict this phenomenon. The cycle lives of randomly oriented crystals were observed to increase linearly with decreasing modulus under bulk elastic conditions and yield strain conditions were developed to explain these results. R6sum~-Nous avons mesur6 l'influence de la microstructure sur le comportement en fatigue fi faible nombre de cycles pour un superalliage monocristallin orient6 (001), ainsi que pour des cristaux d'orientation al~atoire. Nous avons soumis ~ des essais dans des conditions d'amplitude de d6formation totale constante entre 650 et 1000°C, les microstructures produites par trois traitements thermiques duns les cristaux (001), fi savoir 7' fin,),' grossier et 7' vieilli. Les 6chantillons orient6s au hasard, pr6sentant des pr6cipit6s 7' grossiers, 6talent test6s fi 870°C. L'6tude des surfaces de rupture par microscopic 61ectronique fi balayage fi montr6 que l'initiation des fissures de fatigue 6tait li6e fi la microporosit6 au-dessous de 980°C et/t une fissuration par oxydation aux temp6ratures plus 61ev6es. Tous les cristaux orient6s (001) avaient des dur6es de vie semblables fi celles des autres superalliages solidifies directionnellement duns des conditions semblables, ce qui pourrait indiquer des m6canismes de rupture semblables. Nous avons remarqu6 des dessius de croissance des fissures de fatigue anisotropes dans les cristaux (001), les fissures croissant plus rapidement duns la direction (011) et nous avons d6velopp6 un mod61e pour pr6voir ce ph~nom~ne. Les dur~es de vie des cristaux orient6s al6atoirement augrnentaient lin6airement lorsqu'on diminuait le module 61astiques et nous proposons des conditions de plasticit6 qui expliquent ces r6sultats. Zusammenfassung--An (001)- und beliebig orientierten Proben einer einkristallinen Modellsuper-

legierung wurde der EinfluB der Mikrostruktur auf das Ermiidungsverhalten bei kleinen Zyklenzahlen untersucht. Die Mikrostruktur wurde in den (001)-orientierten Kristallen mit drei unterschiedlichen Wfirmebehandlungen erzeugt. Feine 7'-grobe 7'- und eine reckgealterte 7'-Struktur wurden unter Bedingungen konstanter Amplitude der gesamten Dehnung bei Temperaturen zwischen 650 und 1000°C verformt. Die beliebig orientierten Proben enthielten grobe 7'-Ausscheidungen und wurden bei 870°C verformt. Die Untersuchung der Bruchflfichen im Rasterelektronenmikroskop zeigte, dab der Beginn des Ermfidungsbruches unterhalb 980°C mit der Mikroporositfit und bei h6heren Temperaturen mit oxidierender RiBbildung zusammenhing. Es konnte kein wesentlicher EinfluB durch 7'-Aufreihung auf die Standzeit gefunden werden. Sfimtliche (001)-orientierte Kristalle wiesen Ermiidungsstandzeiten auf, die denen anderer gerichtet erstarrter Superlegierungen unter sonst gleichen Bedingungen fihnelten. Dies ist ein m6glicher Hinweis auf vergleichbare Bruchmechanismen. Ein anisotropes RiBwachstum wurde in den (001)-orientierten Kristallen gefunden, bei dem Risse am schnellsten in (011 )-Richtungen wachsen. Ein Modell wurde ffir diese Erscheinung entwickelt. Die Standzeiten der beliebig orientierten Kristalle vergr6Berten sich linear mit abnehmendem Modul unter volumenm~iBig elastischen Bedingungen. Zur Erkl/irung dieser Beobachtungen wurden FlieBbedingungen entwickelt.

1. INTRODUCTION The initial stages of single crystal superalloy development utilized alloy compositions c o m m o n l y used in equiaxed and directionally solidified castings, A.M. 3.'/lo--c

These alloys, with an abundance of grain boundary strengthening precipitates such as carbides and borides, consistently exhibited fatigue crack initiation at precipitates or at microporosity [1-4]. A number of creep and fatigue studies dealing with these crystals

1669

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ANTON: LOW CYCLE FATIGUE OF SUPERALLOY CRYSTALS

were published in the late 60's and early 70's and still serve as the experimental baseline for single crystal superalloy development [1-7]. The next generation of single crystal superalloys having compositions low in C, B, Zr and Hf reflect the superfluous nature of grain boundary strengtheners. Alloys such as PWA 1480 (alloy 454, [8]) and CMSX-2 [9] are typical of this alloy class. Upon homogenization after casting, these alloys are designated to be microstructurally homogeneous (on a p m scale) except for occasional eutectic 7' islands and inherent casting porosity. In-depth study of the mechanical properties of these alloys has been limited to stress-rupture and creep phenomena [10-11]. The need, therefore, exists to study the fatigue characteristics of such crystals in some detail in order that improvements in solidification techniques and alloy chemistries may lead to increased service lives of this new class of superalloy single crystals. A recent advance made in the strengthening of single crystal superalloys against creep deformation has been to induce the growth of the V' precipitates into "rafts" by use of a strain-aging procedure [10]. Excellent results have been obtained in increasing creep lives of model superalloys as much as 500% in specimens so treated. The present study was carried out in order to determine the effect of temperature, microstructure and crystal orientation on the fatigue lives, fatigue crack initiation sites and crack propagation paths in a model superalloy. The model alloy was chosen because of its excellent castability and the existence of an established creep data base. Such an alloy should serve well in determining fatigue crack initiation, growth and fracture characteristics in homogeneous single crystals. In particular, three microstructures were studied; (1) a standard heat treatment designated as SHT having large semicoherent precipitates (2) the as homogenized microstructure with a fine dispersion of coherent V' precipitates designed as AH and (3) the rafted microstructure where a thermo-mechanical strain aging treatment was given to the specimen in order to induce the growth of 7' rafts. The rafted microstructure was compared to others, in particular with regard to any detriment or benefit in fatigue lives. Furthermore, the effect of crystal orientation, with respect to stress axis, on cycle life was studied. In this fashion the effects of crystallographic direction on modulus, yield strength and crack propagation paths on cycle life were determined.

Bridgman technique. Specimens were subsequently macro-etched to determine single crystal integrity and to remove any surface strained regions which could nucleate new grains upon further heat treatment. Laue back reflection X-ray procedures were used to determine crystal orientations which are given in Fig. 1. Homogenization of microsegregation which occurred during solidification was accomplished by heating in argon at 1320°C for 24h followed by forced air cooling. Microporosity, initially formed due to interdendritic solidification shrinkage, was partially removed in a HIP cycle of 1246°C for 2 h under 103 MPa pressure and furnace cooled. This resulted in an approximate reduction in pore volume fraction and mean pore radius of 50%. Due to the slow furnace cool, a solution treatment of 1320"C for 15 min and forced air cooling resulted in the ashomogenized microstructure, AH. Selected {001) and all randomly oriented specimens also received the standard heat treatment, SHT, and aged as follows: 1080°C/4h/FAC + 870°C/24h/FAC, where F A C stands for forced air cooling. These microstructures have been previously characterized in Ref. [10]. The crystals were machined into specimens having a 25.4 mm gage length and 6.4 mm diameter gage section. A low residual stress grinding technique (resulting in a finish without apparent flaws at 30 x magnification) was used to finish the gage section. Specimens to receive the rafted microstructure (still in the AH condition) were further solutioned at 1320°C (a)

T 8o

6°

4°

2°

<001>

2°

4°

6°

8°

10 °



(b)

2. EXPERIMENTAL

The model alloy used in this study was composed of 9Mo, 13A1, 2Ta and bal. Ni in at.%. Single crystals 5/8" in diameter were grown using a helical grain selector [8] for {001) oriented specimens. The bars were withdrawn through a high gradient furnace in a vacuum of 10 4torr. Randomly oriented crystals were grown in a similar fashion using a modified

B-2 •

• B o4 N <001>

B-5

B-9 •

B-1

8-10 •

B-6 B. 7 < 011>

Fig. 1. Crystallographic orientation of (a) {001) aligned and (b) randomly aligned specimens.

ANTON:

I

LOW CYCLE FATIGUE OF SUPERALLOY CRYSTALS

Table 2. Results of compression tests on (001) oriented crystals d~ a,. % E d~ d~ Test temperature ('C) (MPa) (MPa) (GPa) (GPa) Ede 650 855 699 9.16 42.1 0.46 732 917 841 87.8 26.5 0.30 760 910 841 84.1 24.5 0.29 788 834 739 82.9 30.2 0.36 816 841 795 82.4 18.0 0.22 843 800 706 81.1 29.7 0.37 870 876 756 75.3 33.4 0.44 982 703 468 59.6 39.5 0.66

I

]

HOMOGENIZE 1320"/24 HRS/FAC

I

HIP 1246"12 HRS/103 I MPa/FC I AS HOMOGENIZED ],,~-- SOLiTION 1320"/15 MIN/FAC

I

I

] 080 °C/4 HRS/FAC

] 320 *0/15 MfN/WQ

870 *C/24 HRS/FAC

1038*CI15 HRS/207 MPa/FC

+

1671

+

1 ST NO O HE TrREATMENT1 Fig. 2. Summary of heat treatment schedule for cast single crystals. for 15 m i n followed by a water q u e n c h which resulted in the finest 7' distribution possible. Rafting o f the m i c r o s t r u c t u r e was accomplished by loading the specimens at r o o m t e m p e r a t u r e to 207 M P a , heating to 1038°C a n d aging for 15 h at t e m p e r a t u r e followed by cooling a n d final unloading. This resulted in a rafted microstructure previously characterized [10]. A s u m m a r y of the heat t r e a t m e n t procedures a n d the specimen heat t r e a t m e n t schedule are given in Fig. 2 a n d Table 1 respectively. Fully reversed (R = - 1) low cycle fatigue tests were c o n d u c t e d u n d e r c o n s t a n t total strain a m p l i t u d e control at a strain a m p l i t u d e of Ae = 0.01. A triangular w a v e f o r m was used to keep strain rate c o n s t a n t at 0.005 s 1. A n axial extensometer c o n t i n u o u s l y m o n i t o r e d strain a n d a n X - Y recorder was utilized to record load vs displacement data. All testing was c o n d u c t e d in air. M o n o t o n i c c o m p r e s s i o n tests of the s t a n d a r d heat treated material were c o n d u c t e d o n ( 0 0 1 ) aligned specimens in order to determine the effect of tern-

p e r a t u r e o n m o d u l u s a n d yield stress. C o m p r e s s i o n specimens were m a c h i n e d into 5 x 5 x 12 m m right parallelepipeds with their m a j o r axis parallel to the ( 0 0 1 ) __+2 °. Tests were r u n at t e m p e r a t u r e s r a n g i n g from 650 to 1000°C at a strain rate o f 0.005 s -I (equivalent to the fatigue test strain rate). Analyses o f fatigued samples were carried o u t in two fashions. F r a c t o g r a p h y was c o n d u c t e d using a S E M to determine the fatigue failure initiation site a n d also the crack g r o w t h modes. Secondly, the gage sections were cut from the specimens, oriented a n d g r o u n d along a (110) plane parallel to the stress axis. B o t h S E M observations a n d T E M replica analyses were m a d e of these surfaces to determine the m o d e of crack initiation before final failure was obtained. 3. RESULTS 3. I. M o n o t o n i c data

The c o m p r e s s i o n testing was c o n d u c t e d to determine the effect o f t e m p e r a t u r e o n the p r o p o r t i o n a l limit, ap, a n d the 0.2% yield stress, ay, o f these crystals. The d a t a from the compression testing is s u m m a r i z e d in T a b l e 2 a n d Fig. 3. B o t h a v a n d ap display the same functional dependence with temperature. W i t h increasing temperature a gradual rise in stress occurs to a m a x i m u m

Table 1. Heat treatment schedule and results of (001) oriented single crystal fatigue studies Test Cycles to Specimen No. temperature (°C) failure (Nf) Initiation site Standard heat treatment (SHT)

C2 $2 S1 F2 C1 K1 El

32 32 650 650 750 870 982

295 16,846 211,921 172,000 83,942 53,928 4150

Near surface pore Near surface pore Pore Thread Pore Pore Indent

Rafted heat treatment

G1 O1 H1 Jl Q1

650 650 750 870 982

5 6000 76,251 29,805 13,567

Thread Thread Pore Pore Oxidation crack

Homogenized heat treatment

TI D1 M1 W1

650 760 870 982

178,520 205,496 39,161 9245

Bending Pore Pore Oxidation crack

1672

ANTON: LOW CYCLE FATIGUE OF SUPERALLOY CRYSTALS ~ = 0 5 % SEC - 1

1000

8OO

.~600 Lu

E 4oo ~0

O YIELD STRESS • PROPORTIONAL LIMIT

200 1

600

70Q

I S00

I 900

I 10(30

TEMP (*C)

Fig. 3. Proportional limit and average yield stress data from compression tests for standard heat treated (001) aligned specimens. (a)

I

3.2. Fatigue Results for the (001) Orientation The cycle life vs test temperature data for the three microstructures studied are given in Table 1 and Fig. 4. Included on the figure for comparison are results for D.S. Mar M200 under the same conditions. In general, the fatigue lives of the present alloy in all microstructural forms closely approximate that of D.S. Mar M200. The general trends indicate that the rafted material behaves very similarly to other specimens within the range of the data above 650°C. The rafted model alloy may be notch sensitive at 650°C. No accurate cycle lives were determined due

J 16 7 m m

at 750°C. A drop in stress is realized with a minimum at 825°C, followed by an increase to 870°C and decreasing steadily with temperature past 1000°C. This is typical superalloy behavior with yield stress maximum due to the well known strengthening behavior of 7' with temperature. The last two columns of Table 2 give data on the initial work hardening rate, d6/de and modulus normalized work hardening rate, d6/Ede, where rate was measured as the average hardening occurring between the proportional limit and the 0.2% offset yield stress (a v -ap)/0.002. A minimum in the normalized work hardening rate was observed at 800°C. (b)

|

I 667 ~m

Fig. 5. Fracture surface of (001) aligned standard heat

treated specimen illustrating pore initiated fatigue failure.

to specimen failures in the threads, but too few tests were conducted to conclusively determine notch sensitivity. Due to the change in modulus and yield strength with temperature of this alloy, different amounts of bulk plastic strain were imparted at each temperature for the constant strain amplitude testing. This strain must be differentiated from localized plastic strain that is likely to occur in the vicinity of an inclusion (&er = 1%) or pore. Bulk plastic strain amplitudes, Asp, during the first full cycle were measured at 0.00100, 0.00015 and 0.00010 for specimens E-1 (982"C), K-1 (870°C) and C-1 (760°C), respectively, with specimens F-2 (650°C) and S-2 (32°C) showing no plastic deformation. These small plastic strain amplitudes did not £ lead to measurable cyclic softening, hardening or mean stress shifting. 104 The results of SEM fractography are also given in Table 1 with identification of the failure initiation MMT 143 < 100> SINGLE CRYSTALS O STD H,T. sites. Four categories of initiation sites were obRAFTED Q SOLUTIONED served; namely (1) subsurface pores (2) surface indenD.S. MAR M200 tations (3) oxidation induced surface cracks and (4) I l I I I 10: specimen threads. 600 700 800 900 1000 The predominant form of fatigue crack initiation TEMPERATURE, ~C Fig. 4. Low cycle fatigue lives of single crystal and direc- was at subsurface pores. A typical pore fatigue crack origin is given in Fig. 5. Here specimen S- 1 having the tionally solidified superaUoys.

ANTON: LOW CYCLE FATIGUE OF SUPERALLOY CRYSTALS

~a)

1673

I

_I 10 ~m

10 l,~m

Fig. 6. Porosity induced cracks in (001~ aligned single crystal. SHT microstructure and tested at 650°C is shown. The originating pore is in the center of the squarelike fatigue crack growth (FCG) region. This F C G region is perpendicular to the applied stress axis with the planar square sides parallel to the (110) directions. Final cleavage failure occurred along (111) crystallographic planes as was observed in previous single crystal superalloy studies [2, 4, 5, 12]. It should be pointed out here that initial crack propagation occurred perpendicular to the stress axis and not along the octahedral planes as expected. In order to study pore initiated, fatigue cracks in more detail, failed specimen gage sections were cut parallel to the stress axis on a (110) plane. Observations of this type revealed subsurface pores that had nucleated cracks that had not grown large enough to become critical. A typical pore initiated fatigue crack is given in Fig. 6 for specimen M-1. Here the small cracks are emanating perpendicular to the stress axis. Similar cracks were observed in the other microstructures. Two typical pore originated cracks in the rafted microstructure are shown in Fig. 7, where Fig. 7(a) is an SEM micrograph and Fig. 7(b) is a TEM replica micrograph of specimen J-1. In both cases the crack propagated perpendicularly to the stress axis and parallel to the 7' rafts. One also notices that advancement of the microcrack in Fig. 7(b) disrupts the 7' morphology from the rafted to an irregular coarsened morphology at the advancing crack tip. At room temperature, fatigue origins occurred at near surface pores as illustrated in Fig. 8 for specimen C2 of the SHT microstructure (arrow). Fatigue crack initiation occurred here in an active multiple slip region of the crystal with intersecting slip planes observed on the specimen surface. Subsequent F C G occurred in a thumb nail region emanating from the originating pore. Final failure occurred by a cleavage mode of fracture on { 111} planes. Surface origins occurred in three varieties as given above and will be reported on individually. Surface indentations were intentionally introduced in order to

(b)

!

.] 2.86 ,~m

Fig. 7. Fatigue crack initiated at pore and propagation through matrix in strain aged (001) crystal (a) SEM micrograph and (b) TEM replica. make good extensometer-specimen contact. The need for this type of experimental procedure was discussed previously [13]. As testing proceeded these surface indentations were found to be the initiation site in only specimen E-I, which was probably caused by excessive indentor penetration. Fatigue crack initiations at specimen threads occurred in samples F-2, O-1 and G-1 with the latter two being rafted material. Due to the experimental method used here, the entire specimen was held at temperature during the test and examination of the thread root revealed no grinding flaws. Premature thread failures may then be explained as notch sensitivity at temperature in the rafted condition at 650°C. This may indicate that the rafted microstructure is the more notch sensitive microstructure at lower temperatures than those specimens containing cuboidal precipitates. The final form of surface related failures was oxidation-initiated cracks. While stress-corrosion cracks were observed at the surface of all elevated temperature tests, failure due to these cracks occurred only in 980°C tests. The fracture surface of specimen Q-1 having the rafted microstructure and tested at 980°C is given in Fig. 9 as typical of a corrosion crack initiated fatigue failure. The initiation site is indicated

1674

ANTON:

LOW CYCLE FATIGUE OF SUPERALLOY CRYSTALS

((~}

|

illl

067 mm

I 67/zm

(b)

I

((,])

(b)

I

1

067 mm

i

i

0.2 mm

Fig. 8. Fracture surface of standard heat treated specimen tested at room temperature showing near surface pore initiated fatigue failure.

Fig. 9. Fracture surface of "rafted" specimen tested at 980°C showing corrosion crack initiation site.

by a n a r r o w in Fig. 9(a) a n d presented in the magnified m i c r o g r a p h of Fig. 9(b). Sectioning the specimen gage along the stress axis revealed t h a t corrosion cracking occurred along the entire gage length of all specimens so observed. This is depicted in Fig. 10 which shows n u m e r o u s corrosion cracks along the gage section of specimen W-1 tested at 982°C.

from crystal to crystal varied greatly in the c o n s t a n t strain tests c o n d u c t e d here. T o aid in u n d e r s t a n d i n g these effects, Table 3 also contains the Schmid factor, m; the m a x i m u m tensile stress at the first reversal, am; the calculated m a x i m u m resolved shear stress, Tm; a n d the m e a s u r e d modulus. The Schmid factor varied only 9 ~ , while the m o d u l u s increased over 1 0 0 ~ from m i n i m u m to m a x i m u m values in this study. F r o m the Schmid factor c o n t o u r s given by L e v e r a n t a n d K e a r [6] for ( I l l ) ( 1 1 0 ) slip, only m o d e r a t e changes in resolved shear stress can be expected for m o s t stress axes except those a p p r o a c h i n g the (111 direction. The m a r k e d effect of m o d u l u s o n cycle life is illustrated in Fig. 11 with linear b e h a v i o r resulting for moduli below 1 2 0 G P a . Specimens h a v i n g a

3.3. Fatigue results f o r random orientations

The stress axes for the r a n d o m l y oriented crystals are given in Fig. l(b) with their resulting cycle lives a n d fatigue crack origins in Table 3. D u e to b o t h m o d u l u s a n d resolved shear stress dependence o n crystal orientation, the degree of plastic d e f o r m a t i o n

Specimen No. B-1 B-2 B-3 B-4 B-5 B-6 B-7 B-9 B-10

Table 3. Results of randomly oriented crystal fatigue studies Cycles to failure a~ zm E Aep Initiation (Nf) (MPa) m (MPa) (GPa) (~o) site 15,199 591 0.48 284 112.0 0.025 Pore 34,676 590 0.45 266 106.3 0.012 Pore 66,731 604 0.47 284 93.7 0.013 Pore 71,344 478 0.46 220 89.4 0.010 Pore 66,401 520 0.48 250 89.4 0.010 Pore 21,553 612 0.49 300 115.7 0.013 Pore 4553 766 0.48 368 119.2 0 . 0 2 7 Surface 1224 782 0.48 375 163.8 0.035 Indentation 1188 763 0.45 343 178.7 0.050 Pore

ANTON: LOW CYCLE FATIGUE OF SUPERALLOY CRYSTALS

(o)

(o)

t

1675

I

I

0.83 mm

i

02 mm

(b)

t

J

0,67 m m

| J 50 #m

(b)

Fig. 10. Cross sectional view o f corrosion cracks in solu-

tioned specimen tested at 980°C sectioned on a (001) plane showing cracks propagating perpendicularly to the stress axis.

Fig. 12. Fracture surfaces of specimens (a) B-6 and (b) B-2 showing deviation of initial fatigue crack growth path from square-like to elliptical. crack growth area deviated from the square-like shape observed previously for (001) oriented crystals, becoming more elliptical. 4. DISCUSSION

greater modulus failed at considerably shorter lives. The departure from this linear relation is clearly due to the onset of general plastic deformation for specimens having moduli above 120 GPa. The fatigue fracture surfaces of specimens B-2 and B-6 are given in Fig. 12. In both cases the fatigue 200

175

150! w 125

10

20

30

40 50 Nf ( × 103)

60

70

80

90

Fig. 11. Low cycle fatigue cycle life versus modulus relationship for randomly oriented crystals tested at 870°C.

4.1. Compression tests The discussion of constant total strain amplitude fatigue tests carried out at various temperatures must consider the modulus and yield behavior changes with temperature. The compression testing results given in Fig. 3 and Table 2 can be explained taking into consideration the microstructural modifications at temperature. The resultant changes in modulus and yield behavior will be later used to explain the fatigue results. Two precipitation systems must be accounted for in this alloy, the 7' and NixMo. The well known 7/7' strengthening and coarsening mechanisms, respectively, are predominantly responsible for the increasing ~rp and cry values from 630 to 750 ° as well as their steadily decreasing values from 750 to 880°C. The reduction in strength and modulus above 750°C is a consequence of the NixMo precipitates going into solution. Furthermore, the temperature dependent critical resolved shear stress can be determined by simply multiplying the proportional limit

1676

ANTON: LOW CYCLE FATIGUE OF SUPERALLOY CRYSTALS

yield stress, %, by the (001) Schmid factor, m<00~>= 0.41 (assuming octahedral slip). The modulus normalized work hardening rate displays a minimum at 816°C corresponding to the dissolution of the NixMo precipitates. Initial work hardening in superalloys is controlled by dislocation-precipitate interactions. Below 800 ° the NixMo precipitates help disrupt easy glide in the 7 matrix by causing dislocations to shear and cross slip around these particles, leading to increased precipitation strengthening. As these precipitates go into solution their absence allows easier slip in the matrix and reduces the initial work hardening. At greater temperatures, planar (111) slip within the ~' precipitates becomes increasingly difficult due to thermally activated cross slip onto cube planes which again increases the initial work hardening rate. This understanding of the initial monotonic plastic behavior is essential in determining mechanisms of fatigue since cyclic damage is dependent on the nature and amount of plastic deformation whether it be in general yielding or at stress concentrators.

-~c

POROSITY INITIATED LIFELIMIT ~1~ CORROSIOCRACK N ~ I F E LIMIT TO=MAXUSEFUL N ~ ' TEMPERATURE

I

TEMPERATURE Fig. 13. Schematic diagram of cycle limit, Ny, as a function of temperature for a general superalloy single crystal. normally apply to Cr bearing superalloys (particularly with a coating) and will not be pursued further. This leaves the study of porosity initiated fatigue failure as the single most important key to increasing LCF lives of these alloys. The maximum stress concentration factor, Kt, for a spherical cavity in an infinite isotropic medium was shown by Timoshenko and Goodier [14] to be independent of cavity diameter and expressed as

4.2. Low cycle fatigue The fatigue data in Fig. 4 illustrates that the 7' microstructure has little effect on the fatigue life at elevated temperatures. This can be easily explained if one analyzes the causes of crack initiation which led to failure. The cyclic failure mode has been shown to be a competitive process between pore initiated failure and oxidation crack initiated failures. At temperatures below 980°C, corrosion cracking at the surface occurs slowly, while cracks initiating at pores grow at a quicker rate and terminate in failure. At 980°C and above, however, surface oxidation crack growth is favored and leads to final failure. The actual temperature at which this transition occurs is of course dependent on alloy chemistry, pore size and distribution. A graphical representation depicting how competitive crack growth yields cyclic failures is given in Fig. 13, where the cycles to failure, N: vs test temperature are plotted and arbitrarily assumed to be log-linear functions of temperature. Of the initiation sites which lead to failure, neither is precipitation dependent. This causes the apparent lack of a microstructural sensitivity. This lack of sensitivity to precipitate morphology also indicates that initial fatigue crack growth is not sensitive to microstructure within the limits of this investigation. In order to further increase the low cycle fatigue life of "chemically homogeneous" single crystals, these two crack initiation sites must be eliminated. In commercially available superalloys, the addition of chromium as an oxidation and sulfidation inhibitor is universal. This alloying modification most probably shifts the corrosion crack initiation limit to temperatures near the useful limit of the alloy. Since the alloy used here is a simple model system, the discussion of corrosion fatigue processes would not

/¢, -

2 7 - 150 1 4 - 10o

-

(1)

at the cavity surface where o is Poisson's ratio. Although this is only an approximation and does not take into account the anisotropic character of the single crystal of interest, it indicates that a HIP cycle will not increase LCF life unless it completely eliminates all porosity since the stress concentration is not a function of the cavity radius. Therefore, a 0.5/~m radius pore has the same stress concentration factor, Kt, as a 10pm radius pore and would therefore be expected to initiate fatigue cracks under the same number of strain cycles. This is, of course, assuming that the cross sectional area of the pore is negligible with respect to the specimen cross section and that the pores are indeed spherical which the micrographs in this study have shown to be only an approximation. In fact a number of the pores resulting in failure had very irregular shapes and appeared to be an agglomeration of a number of pores [see Fig. 5(b)] while the great majority of pores observed in cross section appeared generally spherical in nature (Fig. 6). It is well known that Young's modulus is anisotropic, with the (100) being the low modulus direction in Ni and most cubic alloys, according to the well known relationship [14] 1

=Sll-2(Su

-

S i 2 - 1 ~$44)(1=l 222 + 1213 22 + 12ml~)

(2a)

where E = Young's modulus in any given direction; Su, S~2, $44 = compliance coefficients which are experimentally determined; 1~, 12,/3 = direction cosines of the required stress axis. The compliance coefficients have been determined for this alloy as a function of temperature by Douglas

ANTON: LOW CYCLE FATIGUE OF SUPERALLOY CRYSTALS [16] from room temperature to 700°C by means of ultrasonic measurements. Extrapolations are required above 700°C due to experimental difficulties above this temperature. These compliance coefficients, extrapolated to 800°C, were determined as follows: St1 = 1.22 x 10 -5, S12 = - 5 . 6 6 x 10 - 6 and $44 = 1.03 x 10 -5 MPa 1 and were used for further calculations in this study. This reduces equation (2a) to 1 - (1.22 - 2.54A) x 10 5 MPa-1 E(A)

(2b)

where A is the geometric term relating the squares of direction cosines. Therefore at 800°C, E~00= 8.21 x 104MPa while EH0= 1.71 x 105MPa. The shear modulus, G, can also be expressed as a function of direction similarly. Tests on the randomly oriented specimens clearly showed that under constant strain amplitude cycling, the specimen modulus greatly influenced the fatigue life. The onset of bulk plastic deformation resulted in sharply curtailed fatigue lives indicating that under a given cyclic strain condition the axial yield strain becomes critical. The strain at which general yielding occurs, By, is given by Hook's law as

~(A) 8Y- E(A)

(3)

where the yield stress, ~>.(A)= m~cRss, ~CRSSthe critical resolved shear stress, m the well known Schmid factor relating the specimen slip systems and direction to the applied stress and E(A) the crystallographically dependent modulus. Cycle life has been shown to be dependent on the specimen modulus under bulk elastic conditions as N / = B -- M E(A)

(4)

where B and M are constants having values 2.77 x 105 and 2.33 x 103 respectively in this study. In general under elastic loading conditions it is known that localized plasticity occurs at microstructural inhomogeneities such as inclusions or pores. If the pores are assumed spherical and v isotropic the result is a stress concentration of 3 [14] which should result in substantial plastic deformation. By combining equations (3) and (4), an expression for fatigue life in terms of yield strain, or conversely stress amplitude, may be obtained for bulk elastic loading as follows

N:=B-M

Aa(A)

aT

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4.3. Anisotropic fatigue crack growth The study of anisotropic fatigue crack growth is also of some interest. To begin with, it was quite unexpected that initial crack growth would be of a stage II variety, independent of crystallographic orientation with stage I crack growth completely suppressed. This point is clearly depicted in Fig. 6 which shows initial cracks emanating perpendicular to the stress axis. Of course in the (001) oriented crystals the (100) plane is perpendicular to the stress axis and an argument for initial (100) growth could be mounted, but cracks were also observed to initiate perpendicular to the stress axis in the randomly oriented specimens. This indicated that the initial crack propagation observed here was crystallographically independent and of a stage II variety. In single crystal copper, Cheng and Laird [18] have shown that stage I crack growth is associated with persistent slip band, PSB, formation on a primary slip system with the crack running along this PSB. Stage II crack propagation was found to occur when stresses ahead of the crack tip were high enough to form PSB on a secondary system. For the (001) oriented crystal, an octahedral multiple slip situation is present from the onset of deformation so it may well be expected that no stage I crack growth would occur or that it would be very short. The randomly oriented crystals are, for the most part, in the octahedral single slip region of the stereographic triangle. They may undergo multiple slip, however, if one considers cube slip. Diffusive slip on cube planes can lead to a multiple slip situation and the curtailment of stage I crack growth. This leads one to expect extensive stage I crack growth to occur at lower temperatures where cube slip is inoperative. Such results have in fact been observed [19]. The crack growth front is schematically depicted in Fig. 14 viewing down the (001) direction onto the fracture surface. The fatigue crack origin is located at the center of the square-like region. The square sides are parallel to (110) directions forming corners at the (010) directions from the origin.

(5)

By illustrating the cycle life dependence with modulus, equations (4) and (5) show that for a constant strain amplitude test (i.e. A8 = const.) the cycle life is linearly proportional to the stress amplitude developed and that for constant stress amplitude tests (i.e. A~ = const.), the cycle life is linearly proportional to the inverse of the resulting strain amplitude. The former of these hypotheses has been observed by Khan in CMSX-2 single crystals cycled under similar conditions [17].

[010]

Fig. 14. Fatigue crack initiation site and initial crack growth limit as viewed parallel to the (001) stress axis in an (001) aligned crystal.

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ANTON: LOW CYCLE FATIGUE OF SUPERALLOY CRYSTALS

Paris regime fatigue crack growth rates have been empirically modeled for isotropic media by the following equation [20] if it is assumed that crack growth rate is proportional to the crack opening displacement by da --

dN

AK 2 = B' - -

E%

(6)

where a = c r a c k length; N =cycle number; da/dN = t h e crack growth rate; A K = s t r e s s intensity factor difference; E = material modulus; O'y = yield stress; B' = proportionality constant. The important factor which needs to be evaluated is in what manner crystal anisotropy affects a growing crack. In light of the fact that the elastic-plastic stress state ahead of the crack is not understood, it is a reasonable first assumption that a component of the modulus in the direction of crack growth will influence the crack tip opening displacement since as the crack opens, material will be put into compression ahead of the crack front. By applying crystal anisotropy to equation (6) one can predict a lower crack growth rate in the (110) directions since it has been shown above that E~00= 0.48Ell0. By a Schmid factor analysis for (111) (101) type slip, it is predicted that ~00 = ayH0. (The Schmid factors for the intervening direction varies only slightly in the (001) plane and can be assumed isotropic.) Combining these two factors yields qualitative agreement with the experimental findings that da/dN 1<110>< da/dN I<010> by a factor of approximately 50%. This type of analysis does predict crack growth regions of the geometry observed in Fig. 5. Anisotropic effects may further come into play in the stress intensity factor, AK, given in equation (6). Neuber [21] has shown a thorough stress analysis of blunt internal notches in isotropic media in which the principal tensile and shear stresses were analytically developed. In this study of circular holes of elliptical cross section, notch size estimates of t = 10 # m and blunt notch radii, p = 1.0 nm or a ratio of t/p = 104 are made. Using Neuber's stress equations, a stress concentration, K, = O'max/O'~c , of 127 was calculated. The tests of this study typically generated stresses of 600 MPa which would lead to elastic analysis predictions two orders of magnitude, excess of the general yield stress. Substantial notch root yielding can then be expected and crack blunting should be considered a significant factor in influencing fatigue crack growth rates. It has been reported that cycle rate has a pronounced effect on single crystal creep crack growth in the (001) plane in the [010] direction with blunting of the crack tip occurring at low cycle rates resulting in retarded crack growth rates [22]. This most probably results from tlae diffusional effects of either (011){001} or (112){111} glide ahead of the crack tip resulting in strain rate sensitive crack growth.

Direct observations of fatigue cracks in single and poly crystals have shown propagation to occur by an alternating slip mechanism on octahedral planes in (011) directions in face centered cubic crystals [23-26]. This is one of two symmetric crack-lattice orientations described by Pelloux [27] for f.c.c, crystals in which decohesion along slip planes was shown to be a mechanism for striation production. The alternating slip mechanism adequately describes the propagation of crack segments in the (011) directions here, but it fails to predict a mechanism for growth in other directions such as (100) where intersecting slip on all four slip planes occurs concurrently. These results lead to the conclusion that the stress state ahead of a sharp crack as given in Ref. [28] needs to be expanded for the elasto-plastic case of a blunted notch to characterize an anisotropic media, such as single crystals, and thus to an understanding of the role of slip deformation processes on crack tip blunting with crystallographic orientation. 5. S U M M A R Y

The y' morphology was shown to have little effect on cycle life to failure at temperatures ranging from 650 to 980°C in (001) oriented crystals. In particular the strain aged (i.e. rafted) 7' led to the same cycle lives as conventionally heat treated superalloys under strain controlled fatigue conditions. At low to intermediate temperatures, fatigue cracks initiated at internal porosity. At 980°C, failures were surface oxidation crack initiated. Competitive crack growth was shown to occur between these two mechanisms. Neither of these initiation mechanisms was related to 7' microstructure resulting in cycle life being independent of 7' morphology. Under elastic loading, randomly grown crystals were shown to have fatigue lives linearly proportional to their calculated Young's modulus through 120GPa after which bulk plastic deformation resulted in cycle lives less than 103. Fatigue crack growth rates were observed to be anisotropic in the (001) plane with maximum crack growth rates occurring in the (010) directions and minimum growth rates in the (011) directions. An analytical model to predict the observed anisotropic fatigue crack growth rates was demonstrated based upon modifying an isotropic model with the crystallographic dependence of the elastic modulus.

Acknowledgements--The author would like to acknowledge the many helpful discussions with Dr D. D. Pearson, with particular regard to crystal growth and preparation, Dr A. F. Giamei and also to Mr L. Favrow for help in conducting the fatigue testing portion of this study. REFERENCES

1. M. Gell and G. R. Leverant, Acta metalL 16, 533 (1968). 2. M. Gell and (3. R. Leverant, Trans. T.M.S.-A.I.M.E, 2 4 2 , 1869 (1968).

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LOW CYCLE FATIGUE OF SUPERALLOY CRYSTALS

3. G. R. Leverant and M. Gell, Trans. T.M.S.-A.LM.E, 245, 1167 (1968). 4. G. R. Leverant and M. Gell, Metall. Trans, 6A, 367 (1975). 5. B. H. Kear and B. J. Piearcy, Trans. T.M.S.-A.LM.E, 239, 1209 (1967). 6. G. R. Leverant and B. H. Kear, Metall. Trans. I, 491 (1970). 7. G. R. Leverant, B. H. Kear and J. M. Oblak, Metall. Trans. 4, 355 (1973). 8. M. Gell, D. N. Duhl and A. F. Giamei, Superalloys 1980(edited by J. Tien, S. Wlodek, H. Morrow, M. Gell and G. Mauers). Am. Soc. Metals, Metals Park, OH (1980). 9. T. Khan and P. caron, Fourth RISO Int. Syrup. on Metallurgy and Mater. Sei., Roskild, Denmark (1983). 10. D. D. Pearson, B. H. Kear and F. D. Lemkey, Creep and Fracture of Engineering Materials (edited by B. Wilshire and D. R. G. Owen), p. 213. Pineridge Press, Swansea, U.K. (1981). 11. R. A. MacKay and R. D. Maier, Metall. Trans. 13A, 1747 (1982). 12. D. L. Anton, Mater. Sci. Engng 57, 97 (1983). 13. D. L. Anton, Seripta metall. 16, 479 (1982). 14. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd ed. McGraw-Hill, New York (1970).

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15, J. F. Nye, Physical Properties of Crystals. Oxford Univ. Press (1969), 16. F. C. Douglas, UTRC Report R79-914549-1 (1979). 17. T. Khan, Personal communication, ONERA, Chatillon Cedex, France (1983). 18. A. S. Cheng and C. Laird, Mater. Sci. Engng 60, 177 (1984). 19. O. Chen, Personal communication, Pratt and Whitney, E. Hartford, CT (1983). 20. A. J. McEvily, The Mierostructure and Design of Alloys, Vol. 2, Proe. 3rd Int. Conf. on the Strength of Metals and Alloys, Cambridge, England, Aug. 20-25 (1973). 21. H. Neuber. Theory of Notch Stresses, 2nd edn. Springer, Berlin (1958). 22. J. S. Croyston and J. W. Martin, in High Temperature Alloys for Gas Turbines (edited by D. Contsouradis), Liege, Oct. (1982). 23. P. Neumann, Aeta metall. 22, 1155 (1974). 24. H. Vehoff and P. Neumann, Aeta metall. 27, 915 (1978). 25. C. Q. Bowles and D. Brock, Int. J. Fract. Mech. 8, 75. (1972). 26. P. Neumann, Z. Metallk. 58, 780 (1967). 27. R. M. N. Pelloux, Trans. Am. Soe. Metals 62, 281 (1969). 28. D. M. Barnett and R. J. Asaro, J. Mech. Phys. Solids 20, 353 (1972).