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A point defect model for fatigue crack initiation in Ni3Al+B single crystals
Acta metall, mater. Vol. 38, No. 6, pp. 1191 1200, 1990 Printed in Great Britain. All rights reserved
0956-7151/90 $3.00 + 0.00 Copyright ~'] 1990 Pergamon Press plc
A POINT DEFECT MODEL FOR FATIGUE CRACK INITIATION IN Ni3A1 + B SINGLE CRYSTALS L. M. H S I U N G and N. S. S T O L O F F Materials Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, U.S.A. (Received 31 M a y 1989)
Abstract--Transmission electron microscopy of boron-doped Ni 3AI single crystals, oriented for single slip and cyclically deformed at room temperature, revealed a high density of dislocation dipoles and point defect clusters. Observations of circular perfect dislocation loops, Frank loops, vacancy tetrahedra and spherical voids provide evidence of vacancy condensation during fatigue cycling at room temperature. It is suggested that lattice misfit develops between persistent slip bands (PSB) and matrix as a result of the generation and coalescence of excess vacancies in PSBs. The misfit strain at PSB/matrix interfaces is considered to increase with increasing cumulative plastic strain. Together with SEM observations of surface topography, it is suggested that fatigue damage in Ni3A1 single crysta!s is initiated by the formation of microvoids (microcracks) at PSB/matrix interfaces. The microvoids (microcracks) break down the coherency of the PSB/matrix interfaces and thereby relieve the accumulated misfit strain at the interfaces. A model of fatigue crack initiation based upon a surface energy criterion is proposed. R6sum~-La microscopie 61ectronique en transmission sur des monocristaux de Ni3A1 dop6s au bore, orient6s pour le glissement simple et d6form6s cycliquement fi la temp6rature ambiante, r6v61e une forte densit6 de dip61es de dislocations et d'amas de d6fauts ponctuels. L'observation de boucles de dislocations circulaires parfaites, de boucles de Frank, de t6tra6dres de lacunes et de cavit6s sph6riques montre l'existence de condensations de lacunes pendant le cyclage fi la temp6rature ambiante. On sugg6re qu'un d6saccord de r+seau se d6veloppe entre les bandes de glissement persistantes (BGP) et la matrice par suite de la germination et de la coalescence de lacunes en exc6s dans les BGP. On consid6re que la contrainte de d6saccord aux interfaces BGP/matrice augmente lorsque la contrainte plastique cumulative croit. GrS,ce /t des observations par MEB de la topographie de surface, on suppose que les d6gS,ts de fatigue dans les monocristaux de Ni3AI sont amorc6s par la formation de microcavitbs (microfissures) aux interfaces BGP/matrice. Les microcavit6s (microfissures) d~truisent la coh6rence des interfaces BGP/matrice et donc relaxent la contrainte de d6saccord accumul6e aux interfaces. Un mod61e d'initiation des fissures de fatique, fond6 sur un crit6re d'6nergie de surface, est propos6. Zusammenfassung--Bor-dotierte Ni3A1-Einkristalle, orientiert f/Jr Einfachgleitung und zyklisch verformt bei Raumtemperatur, zeigen im Durchstrahlungselektronenmikroskop eine hohe Dichte an Versetzungsdipolen und Punktfehleragglomeraten. Die Beobachtung von perfekten Versetzungsringen, Frank-Ringen, Leerstellentetraedern und kugelf6rmigen Hohlr~iumen zeigt, dab Leerstellen wfihrend der Erm/idung bei Raumtemperatur kondensieren. Es liegt nahe, dab sich zwischen persistenten Gleitb/indern und der Matrix eine Gitterfehlpassung also Folge der Bildung und Zusammenlagerung von 1]berschuBleerstellen in den Gleitb~ndern entwickelt. Es wird angenommen, dab die Fehlpassungsverzerrungen an den Grenzfl~ichen zwi~hen Matrix und persistenten Gleitb/indern mit zunehmender kumulativer plastischer Dehnung an~ichst. Nimmt man die Beobachtungen der Oberfl/ichentopografie im Rasterelektronenmikroskop hinzu, dann ergibt sich, dab der Erm/idungsschaden in Ni3A1-Einkristallen mit der Bildung yon Mik rohohlr/iumen (Mikrorissen) an der Grenzfl~iche Matrix/persistentes Gleitband beginnt. Diese zerst6ren die Koh/irenz der Grenzfl/iche und vermindern die kumulierte Fehlpassungsverzerrung. Es wird ein Modell den Beginn der Erm/idungsriBbildung auf der Basis eines Oberfl~ichenenergiekriteriums vorgeschlagen.
INTRODUCTION The monotonic deformation behavior of Ni3AI has been systematically studied since Westbrook [1] first reported that its hardness increased with increasing temperature, see review by Pope and Ezz [2]. In contrast to monotonic properties, fatigue behavior of Ni3Al-base alloys has received relatively little atteno tion. Several recent studies of cyclic hardening and crack initiation and growth under cyclic loading have been reported [3-5]. Cyclic hardening was found to be asymmetric, with the magnitude of the stress asymmetry increasing with increasing strain amplitude. In addition, the nature of the asymmetry between ten-
sion and compression was a function of crystal orientation [4]. An earlier study of fatigue behavior of Ni3AI single crystals by Doherty et al. [6] showed that stage I fatigue cracks were initiated at defects or inclusions, but propagated along slip planes. Stage I cracks along {111} slip planes were noted by Bonda et al. [4]. A recent investigation of fatigue crack initiation in Ni3AI + B single crystals by Hsiung and Stoloff[5] revealed that the initiation of stage I cracks is intimately connected with the formation of persistent slip bands (PSBs) and point defects. In order to understand the mechanisms of fatigue crack initiation in Ni3AI + B single crystals, optical microscopy and electron microscopy (SEM and
1191
1192
HSIUNG and STOLOFF: FATIGUE CRACK INITIATION IN Ni3AI + B CRYSTALS
TEM) were used in this research to investigate the development of fatigue damage in Ni3A1 + B single crystals oriented for single slip. Particular emphasis has been placed upon the development of surface slip band topography, dislocation structures and the role of point defect generation in crack initiation.
EXPERIMENTAL
specimens. Dislocation structures were observed in a JEM-100CXII transmission electron microscope (operated at 100 kV). The weak-beam imaging method was applied to study the dissociation of superdislocations and formation of point defects. Weak-beam images were recorded in the reflection vector g = +__~02 with sg>2.3 × 10-~nm -l corresponding to the g(3g) diffraction condition. Fracture surfaces were examined by SEM.
Single crystals with nominal chemical composition of Ni-24at.%Al-O.25%B were obtained from Pratt
EXPERIMENTAL RESULTS
and Whitney Aircraft Div., United Technology Corp. The crystals were homogenized at 1150°C for 178 h in vacuum. Test specimens were prepared in the form of plates with gage dimensions of 3 x 3 x 9 mm prepared by electro-discharged machining (EDM). All specimens were annealed in vacuum at 1150°C for 50 h and electropolished prior to testing. The orientation of the stress axis is parallel to [~ 13 17], as shown in Fig. 1. This orientation is favorable for the primary octahedral slip system (111) [i01]. Strain-controlled tension-compression cyclic deformation tests, all beginning in tension, were performed on a closed loop machine. Single crystals were held by Wood's metal grips to facilitate alignment. Several tests were interrupted periodically to allow observation of surface slip traces by a Nomarski-type optical microscope or by scanning electron microscopy. The slip planes were determined by two-surface trace analysis. Thin foils for transmission electron microscopy were prepared from gage sections of fatigue 9
~ comp,/f__-//Tens.
7
,
//
~5
///
~
0.1 5~ oo,
o~
3
8[ I
6
oll
Ni3AI+B m Co
~
Cyclic stress-strain response Cyclic strain-hardening curves for specimens cycled at several cyclic strains are shown in Fig. 1. Note the flow stress asymmetry between tension and compression. The magnitude of stress asymmetry became larger as the applied cyclic strain increased.
Surface Topography (I) Optical microscopy Successive surface observations on a specimen cycled at a total-strain amplitude of 0.1% at different cycles were made on the same area of gage section, see Fig. 2(a)-(c). At an early stage of cycling, the observed (111) primary slip bands are densely and somewhat uniformly distributed, Fig. 2(a). As cycling proceeded, some of the bands become coarser in appearance, Fig. 2(b)indicating that strain localization was occurring. Some short and fine slip lines along traces of secondary slip planes also were observed. The density of these slip lines did not increase with increasing number of cycles, and their presence is attributed to local stress concentrations. The coarse primary slip bands eventually developed into PSBlike bands associated with shallow cracks, as shown in Fig. 2(c). To verify that PSBs were formed in fatigued Ni3A1 crystals, a repolishing experiment was carried out with the result shown in Fig. 3(a) and (b). Most of the slip bands observed after the cyclic saturation stage
.
//
0.1,
2~ m
....
5
Comp
%
3F--~ 0.08%
"I I_ Ol
0.055%
,
1
. ,,t
i
, ,,i
10 Number
,
, ,,i
10 2
, , ,,i
10 3 of
,
10 4
, ,,i
10 5
cycles
Fig. 1. Cyclic-hardening curves for the [~ 13 17] oriented Ni3AI + B single crystals cycled at several strain amplitudes,
~
~
. . . . . . . . . . .
.....
Fig. 2. Optical micrograph showing successive surface observationsmade on a specimen tested at Aat/: = 0.1%; (a) I cycle, (b) 50 cycles, (c) 1000 cycles.
HSIUNG and STOLOFF:
FATIGUE CRACK INITIATION IN Ni3A1 + B CRYSTALS
100 pm ~
: Fig. 3. Slip band morphology observed on the same area of a specimen tested at Aot~2 = 0.2%; (a) after 50 cycles, (b) after electro-polishing and retesting for one more cycle, was approximately reached (N = 50 cycles), see Fig. 3(a), reappeared after electropolishing and recycling for 1 cycle, see Fig. 3(b). This experiment demonstrated that PSBs can be formed in fatigued Ni3AI cr3stals when the cyclic saturation stage is reached.
(2) Scanning electron microscopy Morphology of persistent slip bands. Figure 4 shows surface slip bands on a specimen cycled at a total A
Fig. 4. SEM micrograph showing distortion (indicated by arrows) and surface damage appearing at PSB/matrix interfaces; A~t.2 = 0.1%, N = 1000 cycles,
1193
..................... Fig. 5. SEM micrograph showing extrusion/intrusion pairs formed on a PSB; AEt/2= 0.15%, N = 1000 cycles. strain amplitude of 0.1% after 1000 cycles. Both distortion and surface damage were observed at interfaces between PSB and its adjacent matrix. The occurrence of distortion indicates that a high strain was accumulated at PSB/matrix interfaces during cycling. The origin of the distortion at the interfaces will be discussed later in this paper. A possible means of relieving the strain is to form intrusions or microcracks at the interfaces to break down the coherency between PSBs and matrices. That is, the PSB/matrix interfaces become sites that are more susceptible to initiation of fatigue cracks. The observation of surface damage at PSB/matrix interfaces provides evidence of the above viewpoint. Figure 5 shows a typical morphology of a PSB developed after 1000 cycles on a specimen cycled at a total-strain amplitude of 0.15%. A morphology of well-developed extrusion/intrusion pairs was observed on a PSB, which is similar to that observed on copper [7]. Observation of microvoids. An example of persistent slip bands accompanied by microvoids is shown in Fig. 6. Microvoids also were found on a fracture surface, as shown in Fig. 7. Some spherical microvoids were formed on the stage I portion of the fracture surface. The observations of microvoids on both PSB and fracture surface indicate that condensation of point
~ "~ ~ " ~ Fig. 6. SEM micrograph showing microvoids formed on a set of PSBs; AEt/2 = 0 . 0 8 % , N = 44,900 cycles.
1194
HSIUNG and STOLOFF: FATIGUE CRACK INITIATION IN Ni3A1+ B CRYSTALS
...... ~ .
. . . . . ~
lla
• Fig. 7. SEM micrograph showing microvoids formed on the stage I portion of a fracture surface; A~,/2=0.08%, N = 44,900 cycles, defects may play an important role in fatigue crack initiation,
(3) Transmission electron microscopy Formation of dislocation dipoles and loops. Figure 8 is a weak-beam dark field image showing a dissociated superdislocation. Several constriction segments can be found at sites A and a, where site A is a constriction of the core of a superdislocation, and site a is a constriction of the core of a superpartial dislocation. Note that although direct observation of dissociated superpartial dislocations is not available
due to their very small separation, the constrictions observed on superpartial dislocations provide indirect evidence for dissociation of a ½[I01] superpartial dislocation into two, ~[TI2] and ~[]11], Shockley partials. After constriction, the core of constricted segments may have redissociated in another slip plane [8], which led to the formation of Kear-Wilsdorf (KW) locks and impeded the motion of the dislocation in the (111) plane. To accommodate the applied strain, the motion of the unconstricted segments led to the formation of jogs as shown at sites A and a in Fig. 8. Dislocation dipoles or loops can be pinched-off as the dislocation moves away, see Fig. 9 (sites F). Note that the observed dislocation loops are lined up and aligned paralleled to the [~20] directions. Formation of point defect clusters. A dislocation dipole can be regarded as a row of point defects (defect cluster) if the opposite dislocations in the dipole are mutually annihilated. Figure 10(a) is a bright field image showing some screw dislocations and dipoles associated with several circular dislocation loops, presumably perfect dislocation loops (at A, B, C). By applying weak-beam dark field imaging on the same area, as shown in Fig. 10(b), a high density of point defect clusters was detected as white dots. The different contrast appearing in areas A, B and C relative to their surroundings shown in Fig. 10(b) indicates that cavities may have formed inside the circular loops due to coalescence of vacancy clusters. Further expansion of these circular loops can lead to either growth into microvoids or collapse and formation of Frank loops.
Lattice misfit between PSB and matrix. Figure 11 shows distortion at the PSB/matrix interfaces observed in a (l~l)-sliced foil prepared from a specimen tested at a total-strain amplitude of 0.08% after
Fig. 8. Weak-beam TEM micrograph showing constrictions and jogs appearing on a dissociated superdislocation; AEt/2= 0.1%, N = l0 cycles, FN (foil normal)~ [l 1l], BD (beam direction) - [111].
Fig. 9. Weak-beam TEM micrograph showing dislocation loops formed in the wake of a screw superdislocation; A~t/2= 0.08%, N = 44,900 cycles, FN ~ [11 l], BD -~ [1 ! l].
HSIUNG and STOLOFF:
FATIGUE CRACK INITIATION IN Ni3A1+ B CRYSTALS
CO~ i
i
,~, ,~ Q ~J o,=pm
1195
tion can be found in Fig. 12(c). These do not arise from radiation damage from the electron beam; the defects appear more frequently with increasing number of fatigue cycles and each foil was prepared by the same technique. The fringes generated in the bright field image, Fig. 12(a), are very similar to the Moir6 fringes observed in crystals containing coherent second phases [9, 10]. These fringes may be caused by lattice misfit between PSB and matrix as a result of atomic displacements around vacancy clusters. While the generation of Moir~ fringes needs to be further studied, the appearance of streaks in the diffraction pattern indicates that vacancy plates or planar-type defects were formed in PSBs during fatigue cycling. The collapse of vacancy plates into planar-type defects at PSBs can lead to lattice misfit between PSB and matrix. A schematic representation of the lattice misfit between PSB and matrix is shown Fig. 13.
DISCUSSION
Fig. 10. TEM micrographs showing formation of circular dislocation loops and point defect clusters: (a) bright-field; (b) weak-beam, AEt.2 = 0.08%, N - 44,900 cycles, FN ~-[111], B D ~- [l 11]. 44,900 cycles. This observation is consistent with what has been shown in SEM observations of surface topography (Fig. 4). Since point defect clusters observed in fatigued Ni3A1 single crystals were mainly generated from dislocation reactions, they were preferentially located in the PSBs. It is suggested that the distortion at the PSB/matrix interfaces is caused by the formation and coalescence of high density vacancy clusters in PSBs during fatigue cycling. The atomic displacements around vacancy clusters in PSBs may lead to lattice misfit between PSB and matrix, Figure 12(a) shows a bright field image observed in a (111)-sliced foil prepared from a specimen tested at a total-strain amplitude of 0.15% after 1000 cycles. Note that streaks, aligned parallel to the [T01], [~11] and [TT2] directions, were generated in the accompanied diffraction pattern. Based on the kinematic theory of electron diffraction [9], an analysis was made as shown in Fig. 12(b). It is suggested that these streaks arose from the formation of vacancy plates or planar-type defects parallel to the beam direction. The vacancy plates or planar-type defects are aligned along the [1~1], [011] and [il0] directions, which is consistent with the orientations of point defect clusters observed at the area from which the diffraction pattern was generated, see Fig. 12(c). Many white dots and platelets aligned parallel to the [~20] direc-
Four typical morphologies of excess-vacancy agglomerates generated by excess vacancies, namely circular dislocation loops, Frank loops, vacancy tetrahedra, and microvoids, were observed in fatigued Ni 3A1 single crystals. Circular dislocation loops were shown in Fig. 10, microvoids were observed on PSBs and fracture surfaces by SEM, see Figs 6 and 7, Frank loops are shown in Fig. 14, and vacancy tetrahedra are shown in Fig. 15. ~
~ ~
I g
~
i ~ t
_tl ~ 9
" o
a
i /~ .~/ \
Y
,, _~'~1~
~ |
f
~
o. 1 F ~ Fig. 11. Bright field TEM micrograph showing distortion (indicated by arrows) appearing at PSB/matrix interfaces; A~,2 = 0.08%, N = 44,900 cycles, FN ~ [1'~1], BD = [1~1].
1196
H S I U N G and STOLOFF:
F A T I G U E C R A C K INITIATION IN Ni3A1 + B CRYSTALS
(b )
Z=(11 1) (~7o)
B.D
......
(~t O)
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/
/
lattice
~ /
x
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~.
Ewald
sphere
%~
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~.
diffraction
Pattern
I ~ (TT2] (211)
Fig. 12. TEM observations on fatigued crystals. (a) Bright field T E M micrograph showing fringes probably arising from the lattice misfit between PSB and matrix; A~t/2=0.15%, N = 1000 cycles, F N -~ [11 l], BD -~ [111]. (b) Diffraction pattern showing streaking arising from the formation of vacancy plates or planar-type defects lying parallel to the beam direction. (c) Weak-beam dark field image of the area shown in (a).
HSIUNG and STOLOFF: FATIGUE CRACK INITIATION IN Ni3AI + B CRYSTALS
1197
am
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'"
"'"
,,
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• .,.,...:
,
+
:
..
:1
:
,,,:..,.
.1.....+.....
Fig. 13. Schematic representation of lattice misfit between PSB and matrix. The observation of excess-vacancy agglomerates in fatigued Ni 3AI crystals provides evidence of vacancy condensation at room temperature. It is suggested that the condensation of excess vacancies at room temperature may be achieved by a pile-up process in association with very short range diffusion. Previous investigations of fatigue damage in ordered alloys have been sparse. The observations of an apparent excess of vacancies formed in Ni3AI crystals under cyclic deformation are in general agreement with mechanisms proposed by Seitz [11], Thompson [12], Antonopoulos et al. [13], Essmann et al. [14], Mughrabi et al. [15] and Polak [16] to explain fatigue crack initiation in f.c.c, metals. Although point defects in fatigued copper have been identified by using weak-beam TEM techniques [13, 17, 18] and the indirect method of electrical resistivity measurement [19-21], direct observations of large point defect agglomerates, e.g. voids and vacancy tetrahedra, in copper fatigued at room temperature were not made. T h e m o d e l s p r o p o s e d b y A n t o n o p o u l o s etal. [13], Essmann et al. [14] and Polak [16] to explain the formation of PSBs and fatigue crack initiation in copper were based on a typical dislocation structure, edge dislocation walls, formed in PSBs. Since no such dislocation structure is observed in fatigued Ni3A1 crystals, the above models can not be applied to explain fatigue crack initiation in Ni3AI single crystals. With this situation in mind, a new model is required for fatigue crack initiation in Ni3A1 single crystals.
Fig. 14. Bright field TEM micrograph showing Frank loops aligned parallel to the traces of the {Ill} planes; A~t/2= 0.08%, N = 44,900 cycles, FN -~ [1'31], BD ~- [101].
Proposed model
Based on SEM observations of fatigue damage formed at PSB/matrix interfaces and TEM verification of lattice misfit between PSB and matrix, a model based upon a surface energy criterion is proposed. Crack nucleation at PSB/matrix interfaces will become energetically favorable if Ue = Ue, a + Um ~ U s (1) where Ue is total elastic strain energy, Us is effective surface energy or work required to create a stable crack with radius of r0 , Uo.ais elastic strain energy du e to applied stress, and Um is misfit strain energy accumulated at a PSB/matrix interface. Us is related to Ys, 7pJ and 7ads [22], which 7s is specific surface energy, 7p~ is energy absorption due to plastic deformation at the crack tip, and 7,ds is surface energy reduction due to adsorption of gaseous species; 7~ds= 0 in vacuum, For a very small crack, 7p~ is negligible. The surface energy is given as [23] 7 =~0 ( a ) 2 (2) E is Young's modulus, a is the lattice constant, and do is the interplanar spacing. Note that for an imperfect crystal with a high concentration of excess vacan-
Fig. 15. Bright field TEM micrograph showing vacancy tetrahedra; AEt/2=0.08%, N=44,900 cycles, FN~[I'~I], BD ~- [ll'l].
1198
HSIUNG and STOLOFF: FATIGUE CRACK INITIATION IN Ni3AI + B CRYSTALS
cies, the work required to create new free surfaces 0'~) should be smaller than the specific surface energy in a perfect crystal, i.e. Ys= 7~ + work done to generate excess vacancies. Thus, Us can be expressed as
(Cv) in slip bands, if the concentration of excess vacancies in the matrix is negligibly small, i.e. Em= klCv
(9)
where k I is a constant; Cv can be further defined as Us = ( ~ - 7ads)'4r0
(3)
where ~,; is given as
Cv = ~ ~ p l ]'yp,.c~m
~,~ = ~
0 < Co < 1.
(4)
During tensile loading 2/tra2COS* 0 n r ° k ~
m2o-2\
+22~)K2
Um =
6m =
2 2 (J/m) for unit width of PSB Em/Znr0
(6)
where £m is the misfit strain. If only translational lattice misfit is considered, Aa i~m " ~ - - , a
and
Aa
=
ap
--
am
(see Fig. 13). The radius of a stable crack (r0) can be obtained by setting Us = Ue,a + U m C - D )'~d~
ro A(Ka~)2 + BE2m A = 2c0s4 0 + m 2 ( l
B-I+
where dC,/d~?pI is the excess-vacancy generation rate in slip bands, 7pl is plastic shear strain, and YpL~mis cumulative plastic shear strain, ( = 2N. A'fp1). Assuming dC,/dTpl is a constant
(5)
where a a = am,x, m is the Schmid factor, # is the shear modulus, 0 is the angle between stress axis and the [111] direction, and K is a stress concentration factor due to surface roughening. The misfit elastic strain energy accumulated at a PSB/matrix interface may be expressed as
+v)
k2)~pl. . . .
C = 8~/~ cog2 a
(11)
Equation (7) can be rewritten as C - D ~Ads r° = A (Kaa)2 + Bk~ ]) 2pl,cum "
(12)
The average radius of vacancy clusters, r c, is considered to be a function of Cv, diffusivity of vacancies (Dr) and temperature (T), i.e.
re =f(Cv, D~, T).
(13)
The quantitative relationship of equation (13) is not available. However, at room temperature, where long range diffusion is negligible, the condensation of vacancy clusters was predominantly achieved by a pile-up process associated with very short range diffusion; thus re can be assumed simply as proportional to the concentration of excess vacancies in slip bands, i.e.
rc=r°c+k3Cv
E2 v
(10)
(14)
o [dCv\ =rc+k3~ypl)']~pl ....
(15)
= r°c+ k4 ~)pl....
(16)
11.2
8E D = --n
(7)
i.e. A, B, C and D are all constants. Note that 0 = 0 for crack nucleation at an external free surface and 0 = 41.2 ° for nucleation in the interior of the [~ 13 17] oriented specimens. Thus, r 0 (external) < r 0 (interior), i.e. crack nucleation at an external surface will be easier than in the interior of the specimen, Similarly, during compressive loading C - D )'~d~ ro=A,(Ktr~)2+BE ~ (8) where tr~=ami ~, A ' = m 2 ( 1 + v ) - - 2 c o # 0 . Since A ' < A, r0 (tension) < ro (compression); thus, r0 (tension) is more critical; Em can be assumed to be proportional to the concentration of excess vacancies
where r 0c is the initial radius of vacancy clusters when C~ is very small. Since the radius of a stable crack (r0) is inversely proportional to ? p2l . . . . . equation (12), and the radius of a vacancy cluster (r¢) is proportional to 7ptxm, equation (16), the variation of r 0 and re with increasing ~,p~.... may be represented by the plot shown in Fig. 16, where r* is the critical radius of a vacancy cluster for nucleation of a stable crack in air, and r* is the critical radius in vacuum. When re > r*, vacancy clusters can grow into stable microvoids (microcracks); when r¢ < r*, large clusters may collapse and form planar faults, Fig. 14. Figure 16 may be used to predict a larger critical radius of vacancy clusters and a greater ),pj,~ in vacuum than in air required to nucleate stable microvoids (microcracks). That is, better fatigue resistance can be achieved in vacuum, which is constant with experimental results [24].
HSIUNG and STOLOFF: FATIGUE CRACK INITIATION IN Ni3A1+ B CRYSTALS ~Vacuum Xk
~Air
\
=: ~
tional to the excess-vacancy generation rate in slip
RoomTemP.
~
1199
bands.
External Surface
Significance of the proposed model
ro
The significance of the proposed model can be summarized as follows: r~ r~ t
I Yc
~,
)'pl,curn
r°
: r.it~,
CC :
of • st~z.
~
e~,~
radius of ~cancy clustexs
r ~ : t::r~tleltl radlu~ o~ ,~..~mmcy clusters ft="
mteumtaon~
=~, : ~ t s ~ , z
,t~z. crack~ air o~ ~=~=y ~t~,t~-, to= , ~ , crack~ ,~,.
a
,~tt.~
..cz~,tion
)'a : c u ~ t l v e
~* •
plastic shear strain r e c ~ z ~
~,,t~t~ , ~ , e=~, i~ air rv: o.=.,,,~.~,,,, ~tut~= ~ ,~_~ ~ nucleate stable cracks in vacuum
to
to
Fig. 16. Schematic of model for fatigue crack nucleation in different test environments.
Number of cyclesfor fatigue crack initiation The misfit strain, Era, can be expressed in the following form by combining equations (9) and (10)
/dCv~ 'm = k l | ~ J ' Y p l . . . . \Uypl/
(17)
and from equation (7) ~m
1. Fatigue cracks form by a nucleation process with a critical crack size. 2. The critical size of a crack nucleus is dependent on test environment, sense of applied stress and misfit strain at PSB/matrix interfaces. 3. Fatigue cracks tend to form at external surfaces of a specimen.
= [(C - D~s)/r°- A (Kaa)2]
4. The model does not require prior surface roughening. However, the presence of surface roughening increases the local stress, resulting in the promotion of crack initiation. 5. The model implies that the morphology of extrusion/intrusion pairs on PSBs is a product of short range vacany migration and mass transfer caused by lattice misfit strain accumulated at the PSB/matrix interfaces. The condensation of vacancies at the interfaces forms intrusions, which break down the coherency between PSB and matrix and relieve the accumulated misfit strain. The counter-flow of atoms may form extrusions at the PSBs. 6. Fatigue resistance can be improved by decreasing the misfit strain at PSB/matrix interfaces, i.e. decreasing the excess-vacancy generation rate in slip bands.
(18) CONCLUSIONS
Combine equation (17), and equation (18), i.e. (19)
Cyclic testing, optical microscopy, SEM and TEM were employed to investigate the development of fatigue damage in Ni3A1 single crystals. The main results obtained in this research are summarized as follows:
(20)
1. Persistent slip bands with a morphology of intrusion/extrusion pairs were observed. 2. Fatigue of Ni3A1 + B single crystals at room temperature can be regarded as a process that continues to generate point defect clusters as long as cyclic plastic strain is applied.
=k~[!C-DT~a~)/~-A(Ka~)21W2(dC~-I
7pl
L
]
o
\d-~pl/
where k5 is a constant. Since 7pl.... = NATp~,
I(.C- DT,a~)/ro-A(Ka~)2]1/2 N = k5 ~
B
~ x
F( l "AypIjl-'. kkUTpl/
The number of cycles for crack initiation in air, N~,~ can be obtained by letting r 0 = r*, i.e. Niair =ks[(C-Dyads)/r*a-A(Ktra)2.] 1/2 • B [ ( i C~'~ l-lx 'A~pl (21) L\ °?pl/ ] Similarly, the number of cycles for crack initiation in vacuum, N i.... can be obtained by letting r0 = r* and 7~d~= 0, i.e. 1/2 ~ ]--I A F ( dCV .Ayp, (22) N~ .... k-~L-C/r~-B L\dypl/ The above derivations reveal that the number of cycles for fatigue crack initiation is inversely propor-
[
=
]
3. Condensation of vacancy clusters at room temperature was detected. 4. Four different morphologies of the condensed vacancy clusters were observed, namely circular dislocation loops, Frank loops, vacancy tetrahedra, and microvoids. 5. It is suggested that lattice misfit between PSB and matrix arises from the generation and coalescence of excess vacancies in PSBs. 6. Fatigue crack initiation can be explained by formation of microvoids (microcracks) at PSB/matrix interfaces. The microvoids break down the coherency of the interfaces and thereby relieve the coherent misfit strain.
1200
HSIUNG and STOLOFF:
FATIGUE CRACK INITIATION IN Ni3A1 + B CRYSTALS
7. A model of fatigue crack initiation in Ni3A1 based u p o n a surface energy criterion is proposed. The model is used to predict the critical size of stable cracks produced by fatigue. Acknowledgements--This research was supported by the National Science Foundation under Grant No. DMR8409593 and the Office of Naval Research under Contract No. N00014-84-K-0276. Many discussions with Dr D . J . Duquette and Dr K. Rajan have been of great benefit and are gratefully acknowledged. The authors are particularly grateful to Dr C. Liaw of Pratt and Whitney Aircraft, Div. of United Technologies Corp. for supplying us with single crystals of Ni3AI + B. REFERENCES 1. J. H. Westbrook, Trans. Am. Inst. Min. Engrs 209, 898 (1957). 2. D. P. Pope and S. S. Ezz, Int. Metall. Rev. 29, 136 (1984). 3. S. S. Ezz and D. P. Pope, Scripta metall. 19, 741 (1985). 4. N. R. Bonda, D. P. Pope and C. Laird, Acta metall. 35, 2371 (1987). 5. L. M. Hsiung and N. S. Stoloff, in Proc. ICSMA 8, Tampere, Finland (edited by P. O. Kettunen et al.), Vol. 1, p. 683. Pergamon Press, Oxford. 6. J. E. Doherty, A. F. Giamei and B. H. Kear, Metall. Trans. A 6A, 2195, (1975).
7. J. Polak, T. Lepisto and P. Kettunen, Mater. Sei. Engng 74, 85 (1985). 8. V. Paidar, D. P. Pope and V. Vitek, Acta metall. 32, 435 (1984). 9. P. B. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley and M. J. Whelan, Electron Microscopy of Thin Crystals. Butterworths, London (1967). 10. J. W. Edington, Practical Electron Microscopy in Materials Science, Philips Tech. Lab., Vol. 3, p. 20. Macmillan, New York. (1975). 11. F. Seitz, Adv. Phys. 1, 43 (1952). 12. N. Thompson and N. J. Wadsworth, Adv. Phys. 7, 72 (1958). 13. J. G. Antonopoulos, L. M. Brown and A. T. Winter, Phil. Mag. 34, 549 (1976). 14. U. Essmann, U. Gosele and H. Mughrabi, Phil. Mag. 44, 405 (1981). 15. H. Mughrabi, R. Wang, K. Differt and U. Essmann, in Fatigue Mechanisms, ASTM STP 811, p. 5 (1983). 16. J. Polak, Mater. Sci. Engng 92, 71 (1986). 17. C. E. Feltner, Phil. Mag. 12, 1229 (1965). 18. K. Rajan, B. Ramaswami and S. M. L. Sastry, Metall. Trans. A 6A, 1959 (1975). 19. J. Polak, Czech. J. Phys. B 19, 315 (1969). 20. J. Polak, Scriptametall. 4, 761 (1970). 21. J. Polak, Mater. Sci. Engng 89, 36 (1987). 22. D. J. Duquette and M. Gell, Metall. Trans. 2, 1325 (1971). 23. J. J. Gilman, in Fracture, p. 193. Wiley, New York (1959). 24. L. M. Hsiung, Ph.D. thesis, Rensselaer Polytechnic Inst., Troy, N.Y. (1989).
0956-7151/90 $3.00 + 0.00 Copyright ~'] 1990 Pergamon Press plc
A POINT DEFECT MODEL FOR FATIGUE CRACK INITIATION IN Ni3A1 + B SINGLE CRYSTALS L. M. H S I U N G and N. S. S T O L O F F Materials Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, U.S.A. (Received 31 M a y 1989)
Abstract--Transmission electron microscopy of boron-doped Ni 3AI single crystals, oriented for single slip and cyclically deformed at room temperature, revealed a high density of dislocation dipoles and point defect clusters. Observations of circular perfect dislocation loops, Frank loops, vacancy tetrahedra and spherical voids provide evidence of vacancy condensation during fatigue cycling at room temperature. It is suggested that lattice misfit develops between persistent slip bands (PSB) and matrix as a result of the generation and coalescence of excess vacancies in PSBs. The misfit strain at PSB/matrix interfaces is considered to increase with increasing cumulative plastic strain. Together with SEM observations of surface topography, it is suggested that fatigue damage in Ni3A1 single crysta!s is initiated by the formation of microvoids (microcracks) at PSB/matrix interfaces. The microvoids (microcracks) break down the coherency of the PSB/matrix interfaces and thereby relieve the accumulated misfit strain at the interfaces. A model of fatigue crack initiation based upon a surface energy criterion is proposed. R6sum~-La microscopie 61ectronique en transmission sur des monocristaux de Ni3A1 dop6s au bore, orient6s pour le glissement simple et d6form6s cycliquement fi la temp6rature ambiante, r6v61e une forte densit6 de dip61es de dislocations et d'amas de d6fauts ponctuels. L'observation de boucles de dislocations circulaires parfaites, de boucles de Frank, de t6tra6dres de lacunes et de cavit6s sph6riques montre l'existence de condensations de lacunes pendant le cyclage fi la temp6rature ambiante. On sugg6re qu'un d6saccord de r+seau se d6veloppe entre les bandes de glissement persistantes (BGP) et la matrice par suite de la germination et de la coalescence de lacunes en exc6s dans les BGP. On consid6re que la contrainte de d6saccord aux interfaces BGP/matrice augmente lorsque la contrainte plastique cumulative croit. GrS,ce /t des observations par MEB de la topographie de surface, on suppose que les d6gS,ts de fatigue dans les monocristaux de Ni3AI sont amorc6s par la formation de microcavitbs (microfissures) aux interfaces BGP/matrice. Les microcavit6s (microfissures) d~truisent la coh6rence des interfaces BGP/matrice et donc relaxent la contrainte de d6saccord accumul6e aux interfaces. Un mod61e d'initiation des fissures de fatique, fond6 sur un crit6re d'6nergie de surface, est propos6. Zusammenfassung--Bor-dotierte Ni3A1-Einkristalle, orientiert f/Jr Einfachgleitung und zyklisch verformt bei Raumtemperatur, zeigen im Durchstrahlungselektronenmikroskop eine hohe Dichte an Versetzungsdipolen und Punktfehleragglomeraten. Die Beobachtung von perfekten Versetzungsringen, Frank-Ringen, Leerstellentetraedern und kugelf6rmigen Hohlr~iumen zeigt, dab Leerstellen wfihrend der Erm/idung bei Raumtemperatur kondensieren. Es liegt nahe, dab sich zwischen persistenten Gleitb/indern und der Matrix eine Gitterfehlpassung also Folge der Bildung und Zusammenlagerung von 1]berschuBleerstellen in den Gleitb~ndern entwickelt. Es wird angenommen, dab die Fehlpassungsverzerrungen an den Grenzfl~ichen zwi~hen Matrix und persistenten Gleitb/indern mit zunehmender kumulativer plastischer Dehnung an~ichst. Nimmt man die Beobachtungen der Oberfl/ichentopografie im Rasterelektronenmikroskop hinzu, dann ergibt sich, dab der Erm/idungsschaden in Ni3A1-Einkristallen mit der Bildung yon Mik rohohlr/iumen (Mikrorissen) an der Grenzfl~iche Matrix/persistentes Gleitband beginnt. Diese zerst6ren die Koh/irenz der Grenzfl/iche und vermindern die kumulierte Fehlpassungsverzerrung. Es wird ein Modell den Beginn der Erm/idungsriBbildung auf der Basis eines Oberfl~ichenenergiekriteriums vorgeschlagen.
INTRODUCTION The monotonic deformation behavior of Ni3AI has been systematically studied since Westbrook [1] first reported that its hardness increased with increasing temperature, see review by Pope and Ezz [2]. In contrast to monotonic properties, fatigue behavior of Ni3Al-base alloys has received relatively little atteno tion. Several recent studies of cyclic hardening and crack initiation and growth under cyclic loading have been reported [3-5]. Cyclic hardening was found to be asymmetric, with the magnitude of the stress asymmetry increasing with increasing strain amplitude. In addition, the nature of the asymmetry between ten-
sion and compression was a function of crystal orientation [4]. An earlier study of fatigue behavior of Ni3AI single crystals by Doherty et al. [6] showed that stage I fatigue cracks were initiated at defects or inclusions, but propagated along slip planes. Stage I cracks along {111} slip planes were noted by Bonda et al. [4]. A recent investigation of fatigue crack initiation in Ni3AI + B single crystals by Hsiung and Stoloff[5] revealed that the initiation of stage I cracks is intimately connected with the formation of persistent slip bands (PSBs) and point defects. In order to understand the mechanisms of fatigue crack initiation in Ni3AI + B single crystals, optical microscopy and electron microscopy (SEM and
1191
1192
HSIUNG and STOLOFF: FATIGUE CRACK INITIATION IN Ni3AI + B CRYSTALS
TEM) were used in this research to investigate the development of fatigue damage in Ni3A1 + B single crystals oriented for single slip. Particular emphasis has been placed upon the development of surface slip band topography, dislocation structures and the role of point defect generation in crack initiation.
EXPERIMENTAL
specimens. Dislocation structures were observed in a JEM-100CXII transmission electron microscope (operated at 100 kV). The weak-beam imaging method was applied to study the dissociation of superdislocations and formation of point defects. Weak-beam images were recorded in the reflection vector g = +__~02 with sg>2.3 × 10-~nm -l corresponding to the g(3g) diffraction condition. Fracture surfaces were examined by SEM.
Single crystals with nominal chemical composition of Ni-24at.%Al-O.25%B were obtained from Pratt
EXPERIMENTAL RESULTS
and Whitney Aircraft Div., United Technology Corp. The crystals were homogenized at 1150°C for 178 h in vacuum. Test specimens were prepared in the form of plates with gage dimensions of 3 x 3 x 9 mm prepared by electro-discharged machining (EDM). All specimens were annealed in vacuum at 1150°C for 50 h and electropolished prior to testing. The orientation of the stress axis is parallel to [~ 13 17], as shown in Fig. 1. This orientation is favorable for the primary octahedral slip system (111) [i01]. Strain-controlled tension-compression cyclic deformation tests, all beginning in tension, were performed on a closed loop machine. Single crystals were held by Wood's metal grips to facilitate alignment. Several tests were interrupted periodically to allow observation of surface slip traces by a Nomarski-type optical microscope or by scanning electron microscopy. The slip planes were determined by two-surface trace analysis. Thin foils for transmission electron microscopy were prepared from gage sections of fatigue 9
~ comp,/f__-//Tens.
7
,
//
~5
///
~
0.1 5~ oo,
o~
3
8[ I
6
oll
Ni3AI+B m Co
~
Cyclic stress-strain response Cyclic strain-hardening curves for specimens cycled at several cyclic strains are shown in Fig. 1. Note the flow stress asymmetry between tension and compression. The magnitude of stress asymmetry became larger as the applied cyclic strain increased.
Surface Topography (I) Optical microscopy Successive surface observations on a specimen cycled at a total-strain amplitude of 0.1% at different cycles were made on the same area of gage section, see Fig. 2(a)-(c). At an early stage of cycling, the observed (111) primary slip bands are densely and somewhat uniformly distributed, Fig. 2(a). As cycling proceeded, some of the bands become coarser in appearance, Fig. 2(b)indicating that strain localization was occurring. Some short and fine slip lines along traces of secondary slip planes also were observed. The density of these slip lines did not increase with increasing number of cycles, and their presence is attributed to local stress concentrations. The coarse primary slip bands eventually developed into PSBlike bands associated with shallow cracks, as shown in Fig. 2(c). To verify that PSBs were formed in fatigued Ni3A1 crystals, a repolishing experiment was carried out with the result shown in Fig. 3(a) and (b). Most of the slip bands observed after the cyclic saturation stage
.
//
0.1,
2~ m
....
5
Comp
%
3F--~ 0.08%
"I I_ Ol
0.055%
,
1
. ,,t
i
, ,,i
10 Number
,
, ,,i
10 2
, , ,,i
10 3 of
,
10 4
, ,,i
10 5
cycles
Fig. 1. Cyclic-hardening curves for the [~ 13 17] oriented Ni3AI + B single crystals cycled at several strain amplitudes,
~
~
. . . . . . . . . . .
.....
Fig. 2. Optical micrograph showing successive surface observationsmade on a specimen tested at Aat/: = 0.1%; (a) I cycle, (b) 50 cycles, (c) 1000 cycles.
HSIUNG and STOLOFF:
FATIGUE CRACK INITIATION IN Ni3A1 + B CRYSTALS
100 pm ~
: Fig. 3. Slip band morphology observed on the same area of a specimen tested at Aot~2 = 0.2%; (a) after 50 cycles, (b) after electro-polishing and retesting for one more cycle, was approximately reached (N = 50 cycles), see Fig. 3(a), reappeared after electropolishing and recycling for 1 cycle, see Fig. 3(b). This experiment demonstrated that PSBs can be formed in fatigued Ni3AI cr3stals when the cyclic saturation stage is reached.
(2) Scanning electron microscopy Morphology of persistent slip bands. Figure 4 shows surface slip bands on a specimen cycled at a total A
Fig. 4. SEM micrograph showing distortion (indicated by arrows) and surface damage appearing at PSB/matrix interfaces; A~t.2 = 0.1%, N = 1000 cycles,
1193
..................... Fig. 5. SEM micrograph showing extrusion/intrusion pairs formed on a PSB; AEt/2= 0.15%, N = 1000 cycles. strain amplitude of 0.1% after 1000 cycles. Both distortion and surface damage were observed at interfaces between PSB and its adjacent matrix. The occurrence of distortion indicates that a high strain was accumulated at PSB/matrix interfaces during cycling. The origin of the distortion at the interfaces will be discussed later in this paper. A possible means of relieving the strain is to form intrusions or microcracks at the interfaces to break down the coherency between PSBs and matrices. That is, the PSB/matrix interfaces become sites that are more susceptible to initiation of fatigue cracks. The observation of surface damage at PSB/matrix interfaces provides evidence of the above viewpoint. Figure 5 shows a typical morphology of a PSB developed after 1000 cycles on a specimen cycled at a total-strain amplitude of 0.15%. A morphology of well-developed extrusion/intrusion pairs was observed on a PSB, which is similar to that observed on copper [7]. Observation of microvoids. An example of persistent slip bands accompanied by microvoids is shown in Fig. 6. Microvoids also were found on a fracture surface, as shown in Fig. 7. Some spherical microvoids were formed on the stage I portion of the fracture surface. The observations of microvoids on both PSB and fracture surface indicate that condensation of point
~ "~ ~ " ~ Fig. 6. SEM micrograph showing microvoids formed on a set of PSBs; AEt/2 = 0 . 0 8 % , N = 44,900 cycles.
1194
HSIUNG and STOLOFF: FATIGUE CRACK INITIATION IN Ni3A1+ B CRYSTALS
...... ~ .
. . . . . ~
lla
• Fig. 7. SEM micrograph showing microvoids formed on the stage I portion of a fracture surface; A~,/2=0.08%, N = 44,900 cycles, defects may play an important role in fatigue crack initiation,
(3) Transmission electron microscopy Formation of dislocation dipoles and loops. Figure 8 is a weak-beam dark field image showing a dissociated superdislocation. Several constriction segments can be found at sites A and a, where site A is a constriction of the core of a superdislocation, and site a is a constriction of the core of a superpartial dislocation. Note that although direct observation of dissociated superpartial dislocations is not available
due to their very small separation, the constrictions observed on superpartial dislocations provide indirect evidence for dissociation of a ½[I01] superpartial dislocation into two, ~[TI2] and ~[]11], Shockley partials. After constriction, the core of constricted segments may have redissociated in another slip plane [8], which led to the formation of Kear-Wilsdorf (KW) locks and impeded the motion of the dislocation in the (111) plane. To accommodate the applied strain, the motion of the unconstricted segments led to the formation of jogs as shown at sites A and a in Fig. 8. Dislocation dipoles or loops can be pinched-off as the dislocation moves away, see Fig. 9 (sites F). Note that the observed dislocation loops are lined up and aligned paralleled to the [~20] directions. Formation of point defect clusters. A dislocation dipole can be regarded as a row of point defects (defect cluster) if the opposite dislocations in the dipole are mutually annihilated. Figure 10(a) is a bright field image showing some screw dislocations and dipoles associated with several circular dislocation loops, presumably perfect dislocation loops (at A, B, C). By applying weak-beam dark field imaging on the same area, as shown in Fig. 10(b), a high density of point defect clusters was detected as white dots. The different contrast appearing in areas A, B and C relative to their surroundings shown in Fig. 10(b) indicates that cavities may have formed inside the circular loops due to coalescence of vacancy clusters. Further expansion of these circular loops can lead to either growth into microvoids or collapse and formation of Frank loops.
Lattice misfit between PSB and matrix. Figure 11 shows distortion at the PSB/matrix interfaces observed in a (l~l)-sliced foil prepared from a specimen tested at a total-strain amplitude of 0.08% after
Fig. 8. Weak-beam TEM micrograph showing constrictions and jogs appearing on a dissociated superdislocation; AEt/2= 0.1%, N = l0 cycles, FN (foil normal)~ [l 1l], BD (beam direction) - [111].
Fig. 9. Weak-beam TEM micrograph showing dislocation loops formed in the wake of a screw superdislocation; A~t/2= 0.08%, N = 44,900 cycles, FN ~ [11 l], BD -~ [1 ! l].
HSIUNG and STOLOFF:
FATIGUE CRACK INITIATION IN Ni3A1+ B CRYSTALS
CO~ i
i
,~, ,~ Q ~J o,=pm
1195
tion can be found in Fig. 12(c). These do not arise from radiation damage from the electron beam; the defects appear more frequently with increasing number of fatigue cycles and each foil was prepared by the same technique. The fringes generated in the bright field image, Fig. 12(a), are very similar to the Moir6 fringes observed in crystals containing coherent second phases [9, 10]. These fringes may be caused by lattice misfit between PSB and matrix as a result of atomic displacements around vacancy clusters. While the generation of Moir~ fringes needs to be further studied, the appearance of streaks in the diffraction pattern indicates that vacancy plates or planar-type defects were formed in PSBs during fatigue cycling. The collapse of vacancy plates into planar-type defects at PSBs can lead to lattice misfit between PSB and matrix. A schematic representation of the lattice misfit between PSB and matrix is shown Fig. 13.
DISCUSSION
Fig. 10. TEM micrographs showing formation of circular dislocation loops and point defect clusters: (a) bright-field; (b) weak-beam, AEt.2 = 0.08%, N - 44,900 cycles, FN ~-[111], B D ~- [l 11]. 44,900 cycles. This observation is consistent with what has been shown in SEM observations of surface topography (Fig. 4). Since point defect clusters observed in fatigued Ni3A1 single crystals were mainly generated from dislocation reactions, they were preferentially located in the PSBs. It is suggested that the distortion at the PSB/matrix interfaces is caused by the formation and coalescence of high density vacancy clusters in PSBs during fatigue cycling. The atomic displacements around vacancy clusters in PSBs may lead to lattice misfit between PSB and matrix, Figure 12(a) shows a bright field image observed in a (111)-sliced foil prepared from a specimen tested at a total-strain amplitude of 0.15% after 1000 cycles. Note that streaks, aligned parallel to the [T01], [~11] and [TT2] directions, were generated in the accompanied diffraction pattern. Based on the kinematic theory of electron diffraction [9], an analysis was made as shown in Fig. 12(b). It is suggested that these streaks arose from the formation of vacancy plates or planar-type defects parallel to the beam direction. The vacancy plates or planar-type defects are aligned along the [1~1], [011] and [il0] directions, which is consistent with the orientations of point defect clusters observed at the area from which the diffraction pattern was generated, see Fig. 12(c). Many white dots and platelets aligned parallel to the [~20] direc-
Four typical morphologies of excess-vacancy agglomerates generated by excess vacancies, namely circular dislocation loops, Frank loops, vacancy tetrahedra, and microvoids, were observed in fatigued Ni 3A1 single crystals. Circular dislocation loops were shown in Fig. 10, microvoids were observed on PSBs and fracture surfaces by SEM, see Figs 6 and 7, Frank loops are shown in Fig. 14, and vacancy tetrahedra are shown in Fig. 15. ~
~ ~
I g
~
i ~ t
_tl ~ 9
" o
a
i /~ .~/ \
Y
,, _~'~1~
~ |
f
~
o. 1 F ~ Fig. 11. Bright field TEM micrograph showing distortion (indicated by arrows) appearing at PSB/matrix interfaces; A~,2 = 0.08%, N = 44,900 cycles, FN ~ [1'~1], BD = [1~1].
1196
H S I U N G and STOLOFF:
F A T I G U E C R A C K INITIATION IN Ni3A1 + B CRYSTALS
(b )
Z=(11 1) (~7o)
B.D
......
(~t O)
O00
,
/
/
lattice
~ /
x
lI
~.
Ewald
sphere
%~
(1 o T]
~.
diffraction
Pattern
I ~ (TT2] (211)
Fig. 12. TEM observations on fatigued crystals. (a) Bright field T E M micrograph showing fringes probably arising from the lattice misfit between PSB and matrix; A~t/2=0.15%, N = 1000 cycles, F N -~ [11 l], BD -~ [111]. (b) Diffraction pattern showing streaking arising from the formation of vacancy plates or planar-type defects lying parallel to the beam direction. (c) Weak-beam dark field image of the area shown in (a).
HSIUNG and STOLOFF: FATIGUE CRACK INITIATION IN Ni3AI + B CRYSTALS
1197
am
" • ...
"!ii
" " "
'"
"'"
,,
*00'06i6
~_--.~ _~ ~ o i
~_~,_~_i
_~,-/-P~-¢-
_i_
• ......
• .,.,...:
,
+
:
..
:1
:
,,,:..,.
.1.....+.....
Fig. 13. Schematic representation of lattice misfit between PSB and matrix. The observation of excess-vacancy agglomerates in fatigued Ni 3AI crystals provides evidence of vacancy condensation at room temperature. It is suggested that the condensation of excess vacancies at room temperature may be achieved by a pile-up process in association with very short range diffusion. Previous investigations of fatigue damage in ordered alloys have been sparse. The observations of an apparent excess of vacancies formed in Ni3AI crystals under cyclic deformation are in general agreement with mechanisms proposed by Seitz [11], Thompson [12], Antonopoulos et al. [13], Essmann et al. [14], Mughrabi et al. [15] and Polak [16] to explain fatigue crack initiation in f.c.c, metals. Although point defects in fatigued copper have been identified by using weak-beam TEM techniques [13, 17, 18] and the indirect method of electrical resistivity measurement [19-21], direct observations of large point defect agglomerates, e.g. voids and vacancy tetrahedra, in copper fatigued at room temperature were not made. T h e m o d e l s p r o p o s e d b y A n t o n o p o u l o s etal. [13], Essmann et al. [14] and Polak [16] to explain the formation of PSBs and fatigue crack initiation in copper were based on a typical dislocation structure, edge dislocation walls, formed in PSBs. Since no such dislocation structure is observed in fatigued Ni3A1 crystals, the above models can not be applied to explain fatigue crack initiation in Ni3AI single crystals. With this situation in mind, a new model is required for fatigue crack initiation in Ni3A1 single crystals.
Fig. 14. Bright field TEM micrograph showing Frank loops aligned parallel to the traces of the {Ill} planes; A~t/2= 0.08%, N = 44,900 cycles, FN -~ [1'31], BD ~- [101].
Proposed model
Based on SEM observations of fatigue damage formed at PSB/matrix interfaces and TEM verification of lattice misfit between PSB and matrix, a model based upon a surface energy criterion is proposed. Crack nucleation at PSB/matrix interfaces will become energetically favorable if Ue = Ue, a + Um ~ U s (1) where Ue is total elastic strain energy, Us is effective surface energy or work required to create a stable crack with radius of r0 , Uo.ais elastic strain energy du e to applied stress, and Um is misfit strain energy accumulated at a PSB/matrix interface. Us is related to Ys, 7pJ and 7ads [22], which 7s is specific surface energy, 7p~ is energy absorption due to plastic deformation at the crack tip, and 7,ds is surface energy reduction due to adsorption of gaseous species; 7~ds= 0 in vacuum, For a very small crack, 7p~ is negligible. The surface energy is given as [23] 7 =~0 ( a ) 2 (2) E is Young's modulus, a is the lattice constant, and do is the interplanar spacing. Note that for an imperfect crystal with a high concentration of excess vacan-
Fig. 15. Bright field TEM micrograph showing vacancy tetrahedra; AEt/2=0.08%, N=44,900 cycles, FN~[I'~I], BD ~- [ll'l].
1198
HSIUNG and STOLOFF: FATIGUE CRACK INITIATION IN Ni3AI + B CRYSTALS
cies, the work required to create new free surfaces 0'~) should be smaller than the specific surface energy in a perfect crystal, i.e. Ys= 7~ + work done to generate excess vacancies. Thus, Us can be expressed as
(Cv) in slip bands, if the concentration of excess vacancies in the matrix is negligibly small, i.e. Em= klCv
(9)
where k I is a constant; Cv can be further defined as Us = ( ~ - 7ads)'4r0
(3)
where ~,; is given as
Cv = ~ ~ p l ]'yp,.c~m
~,~ = ~
0 < Co < 1.
(4)
During tensile loading 2/tra2COS* 0 n r ° k ~
m2o-2\
+22~)K2
Um =
6m =
2 2 (J/m) for unit width of PSB Em/Znr0
(6)
where £m is the misfit strain. If only translational lattice misfit is considered, Aa i~m " ~ - - , a
and
Aa
=
ap
--
am
(see Fig. 13). The radius of a stable crack (r0) can be obtained by setting Us = Ue,a + U m C - D )'~d~
ro A(Ka~)2 + BE2m A = 2c0s4 0 + m 2 ( l
B-I+
where dC,/d~?pI is the excess-vacancy generation rate in slip bands, 7pl is plastic shear strain, and YpL~mis cumulative plastic shear strain, ( = 2N. A'fp1). Assuming dC,/dTpl is a constant
(5)
where a a = am,x, m is the Schmid factor, # is the shear modulus, 0 is the angle between stress axis and the [111] direction, and K is a stress concentration factor due to surface roughening. The misfit elastic strain energy accumulated at a PSB/matrix interface may be expressed as
+v)
k2)~pl. . . .
C = 8~/~ cog2 a
(11)
Equation (7) can be rewritten as C - D ~Ads r° = A (Kaa)2 + Bk~ ]) 2pl,cum "
(12)
The average radius of vacancy clusters, r c, is considered to be a function of Cv, diffusivity of vacancies (Dr) and temperature (T), i.e.
re =f(Cv, D~, T).
(13)
The quantitative relationship of equation (13) is not available. However, at room temperature, where long range diffusion is negligible, the condensation of vacancy clusters was predominantly achieved by a pile-up process associated with very short range diffusion; thus re can be assumed simply as proportional to the concentration of excess vacancies in slip bands, i.e.
rc=r°c+k3Cv
E2 v
(10)
(14)
o [dCv\ =rc+k3~ypl)']~pl ....
(15)
= r°c+ k4 ~)pl....
(16)
11.2
8E D = --n
(7)
i.e. A, B, C and D are all constants. Note that 0 = 0 for crack nucleation at an external free surface and 0 = 41.2 ° for nucleation in the interior of the [~ 13 17] oriented specimens. Thus, r 0 (external) < r 0 (interior), i.e. crack nucleation at an external surface will be easier than in the interior of the specimen, Similarly, during compressive loading C - D )'~d~ ro=A,(Ktr~)2+BE ~ (8) where tr~=ami ~, A ' = m 2 ( 1 + v ) - - 2 c o # 0 . Since A ' < A, r0 (tension) < ro (compression); thus, r0 (tension) is more critical; Em can be assumed to be proportional to the concentration of excess vacancies
where r 0c is the initial radius of vacancy clusters when C~ is very small. Since the radius of a stable crack (r0) is inversely proportional to ? p2l . . . . . equation (12), and the radius of a vacancy cluster (r¢) is proportional to 7ptxm, equation (16), the variation of r 0 and re with increasing ~,p~.... may be represented by the plot shown in Fig. 16, where r* is the critical radius of a vacancy cluster for nucleation of a stable crack in air, and r* is the critical radius in vacuum. When re > r*, vacancy clusters can grow into stable microvoids (microcracks); when r¢ < r*, large clusters may collapse and form planar faults, Fig. 14. Figure 16 may be used to predict a larger critical radius of vacancy clusters and a greater ),pj,~ in vacuum than in air required to nucleate stable microvoids (microcracks). That is, better fatigue resistance can be achieved in vacuum, which is constant with experimental results [24].
HSIUNG and STOLOFF: FATIGUE CRACK INITIATION IN Ni3A1+ B CRYSTALS ~Vacuum Xk
~Air
\
=: ~
tional to the excess-vacancy generation rate in slip
RoomTemP.
~
1199
bands.
External Surface
Significance of the proposed model
ro
The significance of the proposed model can be summarized as follows: r~ r~ t
I Yc
~,
)'pl,curn
r°
: r.it~,
CC :
of • st~z.
~
e~,~
radius of ~cancy clustexs
r ~ : t::r~tleltl radlu~ o~ ,~..~mmcy clusters ft="
mteumtaon~
=~, : ~ t s ~ , z
,t~z. crack~ air o~ ~=~=y ~t~,t~-, to= , ~ , crack~ ,~,.
a
,~tt.~
..cz~,tion
)'a : c u ~ t l v e
~* •
plastic shear strain r e c ~ z ~
~,,t~t~ , ~ , e=~, i~ air rv: o.=.,,,~.~,,,, ~tut~= ~ ,~_~ ~ nucleate stable cracks in vacuum
to
to
Fig. 16. Schematic of model for fatigue crack nucleation in different test environments.
Number of cyclesfor fatigue crack initiation The misfit strain, Era, can be expressed in the following form by combining equations (9) and (10)
/dCv~ 'm = k l | ~ J ' Y p l . . . . \Uypl/
(17)
and from equation (7) ~m
1. Fatigue cracks form by a nucleation process with a critical crack size. 2. The critical size of a crack nucleus is dependent on test environment, sense of applied stress and misfit strain at PSB/matrix interfaces. 3. Fatigue cracks tend to form at external surfaces of a specimen.
= [(C - D~s)/r°- A (Kaa)2]
4. The model does not require prior surface roughening. However, the presence of surface roughening increases the local stress, resulting in the promotion of crack initiation. 5. The model implies that the morphology of extrusion/intrusion pairs on PSBs is a product of short range vacany migration and mass transfer caused by lattice misfit strain accumulated at the PSB/matrix interfaces. The condensation of vacancies at the interfaces forms intrusions, which break down the coherency between PSB and matrix and relieve the accumulated misfit strain. The counter-flow of atoms may form extrusions at the PSBs. 6. Fatigue resistance can be improved by decreasing the misfit strain at PSB/matrix interfaces, i.e. decreasing the excess-vacancy generation rate in slip bands.
(18) CONCLUSIONS
Combine equation (17), and equation (18), i.e. (19)
Cyclic testing, optical microscopy, SEM and TEM were employed to investigate the development of fatigue damage in Ni3A1 single crystals. The main results obtained in this research are summarized as follows:
(20)
1. Persistent slip bands with a morphology of intrusion/extrusion pairs were observed. 2. Fatigue of Ni3A1 + B single crystals at room temperature can be regarded as a process that continues to generate point defect clusters as long as cyclic plastic strain is applied.
=k~[!C-DT~a~)/~-A(Ka~)21W2(dC~-I
7pl
L
]
o
\d-~pl/
where k5 is a constant. Since 7pl.... = NATp~,
I(.C- DT,a~)/ro-A(Ka~)2]1/2 N = k5 ~
B
~ x
F( l "AypIjl-'. kkUTpl/
The number of cycles for crack initiation in air, N~,~ can be obtained by letting r 0 = r*, i.e. Niair =ks[(C-Dyads)/r*a-A(Ktra)2.] 1/2 • B [ ( i C~'~ l-lx 'A~pl (21) L\ °?pl/ ] Similarly, the number of cycles for crack initiation in vacuum, N i.... can be obtained by letting r0 = r* and 7~d~= 0, i.e. 1/2 ~ ]--I A F ( dCV .Ayp, (22) N~ .... k-~L-C/r~-B L\dypl/ The above derivations reveal that the number of cycles for fatigue crack initiation is inversely propor-
[
=
]
3. Condensation of vacancy clusters at room temperature was detected. 4. Four different morphologies of the condensed vacancy clusters were observed, namely circular dislocation loops, Frank loops, vacancy tetrahedra, and microvoids. 5. It is suggested that lattice misfit between PSB and matrix arises from the generation and coalescence of excess vacancies in PSBs. 6. Fatigue crack initiation can be explained by formation of microvoids (microcracks) at PSB/matrix interfaces. The microvoids break down the coherency of the interfaces and thereby relieve the coherent misfit strain.
1200
HSIUNG and STOLOFF:
FATIGUE CRACK INITIATION IN Ni3A1 + B CRYSTALS
7. A model of fatigue crack initiation in Ni3A1 based u p o n a surface energy criterion is proposed. The model is used to predict the critical size of stable cracks produced by fatigue. Acknowledgements--This research was supported by the National Science Foundation under Grant No. DMR8409593 and the Office of Naval Research under Contract No. N00014-84-K-0276. Many discussions with Dr D . J . Duquette and Dr K. Rajan have been of great benefit and are gratefully acknowledged. The authors are particularly grateful to Dr C. Liaw of Pratt and Whitney Aircraft, Div. of United Technologies Corp. for supplying us with single crystals of Ni3AI + B. REFERENCES 1. J. H. Westbrook, Trans. Am. Inst. Min. Engrs 209, 898 (1957). 2. D. P. Pope and S. S. Ezz, Int. Metall. Rev. 29, 136 (1984). 3. S. S. Ezz and D. P. Pope, Scripta metall. 19, 741 (1985). 4. N. R. Bonda, D. P. Pope and C. Laird, Acta metall. 35, 2371 (1987). 5. L. M. Hsiung and N. S. Stoloff, in Proc. ICSMA 8, Tampere, Finland (edited by P. O. Kettunen et al.), Vol. 1, p. 683. Pergamon Press, Oxford. 6. J. E. Doherty, A. F. Giamei and B. H. Kear, Metall. Trans. A 6A, 2195, (1975).
7. J. Polak, T. Lepisto and P. Kettunen, Mater. Sei. Engng 74, 85 (1985). 8. V. Paidar, D. P. Pope and V. Vitek, Acta metall. 32, 435 (1984). 9. P. B. Hirsch, A. Howie, R. B. Nicholson, D. W. Pashley and M. J. Whelan, Electron Microscopy of Thin Crystals. Butterworths, London (1967). 10. J. W. Edington, Practical Electron Microscopy in Materials Science, Philips Tech. Lab., Vol. 3, p. 20. Macmillan, New York. (1975). 11. F. Seitz, Adv. Phys. 1, 43 (1952). 12. N. Thompson and N. J. Wadsworth, Adv. Phys. 7, 72 (1958). 13. J. G. Antonopoulos, L. M. Brown and A. T. Winter, Phil. Mag. 34, 549 (1976). 14. U. Essmann, U. Gosele and H. Mughrabi, Phil. Mag. 44, 405 (1981). 15. H. Mughrabi, R. Wang, K. Differt and U. Essmann, in Fatigue Mechanisms, ASTM STP 811, p. 5 (1983). 16. J. Polak, Mater. Sci. Engng 92, 71 (1986). 17. C. E. Feltner, Phil. Mag. 12, 1229 (1965). 18. K. Rajan, B. Ramaswami and S. M. L. Sastry, Metall. Trans. A 6A, 1959 (1975). 19. J. Polak, Czech. J. Phys. B 19, 315 (1969). 20. J. Polak, Scriptametall. 4, 761 (1970). 21. J. Polak, Mater. Sci. Engng 89, 36 (1987). 22. D. J. Duquette and M. Gell, Metall. Trans. 2, 1325 (1971). 23. J. J. Gilman, in Fracture, p. 193. Wiley, New York (1959). 24. L. M. Hsiung, Ph.D. thesis, Rensselaer Polytechnic Inst., Troy, N.Y. (1989).