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Growth modes of cracks in creeping type 304 stainless steel
Mechanics of Materials 11 (1991) 1-17 Elsevier
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Growth modes of cracks in creeping Type 304 stainless steel B. Ozmat 1, A.S. Argon and D.M. Parks Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Received 22 May 1989, revised version received 15 March 1990
The modes of initial growth of cracks in creeping Type 304 stainless steel were studied in the 600-775°C range in plane strain and three different test geometries consisting of center cracked panels, double edge notched bars, and compact tension specimens in both annealed material and in some material with 5% initial cold work. In all cases it was found that in samples with pre-fatigue sharpened cracks the initial growth was branched and on planes at 50 o with the median plane of the crack. In other cases of samples with blunt cracks having machined radii of curvature, initial growth was found to remain in the median plane of the crack. In further growth, however, it was noted that while the direction of the branched cracks became later parallel to the median crack plane, the initially planar cracks showed later evidence of branching. This meandering behavior of cracks is a result of the different nature of crack tip strain concentration for initially sharp and initially blunt cracks. While data were limited, a dependence of the average crack speed on a power function of the C * parameter was found for all cases in which crack growth was intergranular.
I. Introduction The growth of cracks in creeping high temperature components has been of considerable interest in the last decade as a possible means of predicting useful service lives of flawed parts. Largely through the stimulus of some fundamental crack tip deformation field solutions many experimental studies have been undertaken in recent years in prominent creep-resistant alloys to measure rates of creep crack growth and to discover the most meaningful means to characterize these rates with generalized driving forces. Both the crack tip field solutions and a small selection of experimental results have been discussed in detail in a recent monograph by Riedel (1987) which can serve also as a broad introduction into this subject. Parallel to this operational approach have been studies to model the growth of creep cracks by damage accumulation in the crack tip field based either on phenomenological descriptions of such damage (Hayhurst, Brown and Morrison, 1984) or on more
1 Now at Texas Instruments Companyin Dallas, Texas, U.S.A. 0167-6636/91/$03.50 © 1991 - Elsevier Science Publishers B.V.
mechanistic considerations of intergranular fracture by nucleation and growth of cavities (Wilkinson and Vitek, 1982; Wilkinson and Biner, 1988; Bassani, 1981; Tvergaard, 1984, 1985, 1986; Riedel, 1985; Hawk and Bassani, 1986). While many of the experimental studies have limited their attention to finding only a suitable correlation between crack growth rate and crack tip driving forces such as K, J, or C*, a few (Manjoine, 1963; Davis and Manjoine, 1953; Leckie and Hayhurst, 1974; Argon et al., 1985) have noted important complications in initiation of crack growth and in non-planar propagation of such cracks over substantial distances, resulting in long transients and posing fundamental questions on both the nature of creep damage and the specific factors that control its ripening. These points have so far been inadequately investigated, particularly in more ductile alloys where questions of whether creep crack growth or quasi-homogeneous damage considerations should govern creep life have largely gone unanswered. Here in the first of several related studies we present the results of an experimental investigation on the modes of creep crack growth in Type
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B. Ozmat et al. / Cracks in 304 stainless steel
304 stainless steel - a prominent ductile solid solution alloy for which the mechanisms of intergranular cavitation had been investigated by Chen and Argon (1981) earlier in considerable detail. While the stress levels in the present investigation are relatively high they have in the large majority of cases produced fracture by intergranular processes.
2. Effects of ductility and initial crack shape on early crack growth Although all creep fractures in polycrystalline metals tend to be intergranular and develop by nucleation and growth of cavities, the early modes of growth of pre-existing cracks can take a number of different paths depending upon the creep ductility of the alloy and the nature of strain concentration around the crack tip. The problem has a close parallel to the growth of cracks in parts undergoing transgranular ductile fracture by nucleation and growth of cavities by plastic flow, as has been discussed by Rice and Johnson (1970). The following are some of the more noteworthy investigations of this phenomenon. Manjoine (1963) conducted creep rupture tests on T head specimens prepared to simulate the loading of turbine rotor groove walls by turbine blades. Conventional tests were performed on C r M o - V rotor steel with differing creep strengths obtained from different heat treatments. Steel A, with a high deformation resistance, showed 2.3% uniaxial elongation at fracture when tested at 538°C with 282 MPa initial stress. Steel B, with a lower deformation resistance, was more ductile, and showed 14% elongation at fracture under the same uniaxial creep fracture conditions. While both specimens failed at comparable times ( -- 1500 h), the T head tests of these two materials showed very different fracture patterns. Crack initiation and early propagation of the ductile steel B involved shear modes of growth which followed along planes of maximum effective stress. In comparison those of steel A propagated along planes of maximum tensile stress. Earlier, Davis and Manjoine (1953) also reported widely differing fracture profiles for creep fracture in tests on 60 °
V-notched specimens of material with differing creep ductilities. For alloys showing low ductility (the refractory alloy 2G), the cracks started near the base of the notch and propagated normal to the axis of the specimen and along the median plane of the notch. However, for the very ductile alloy (12Cr, 3W steel) fracture started at the root of the notch and the crack propagated inward at an angle of about 45 ° to the specimen axis. Gooch (1977) has reported dramatic changes in the creep crack appearance of a 0.5Cr, 0.SMo, 0.25V steel. Cracks in specimens having higher creep resistance and low ductility followed a fracture path that was in the plane of the original spark cut notch with 0.25 mm root radius and 1.5 mm length (aspect ratio of 6). However, the specimens with low creep resistance but larger ductility showed large scale notch root blunting and an initially straight mode of crack growth for about 1 mm, followed by crack extension at an approximately 50 ° angle to the initial crack plane which later formed a leg directed back toward the plane of the original notch. Gooch, King and Briers (1977) also reported similar changes in the fracture appearance of creep cracks in a 2 . 5 C r - l M o weld metal steel upon a matrix softening treatment. Specimens with a Vickers hardness of 187 showed large crack tip opening displacements associated with a 0.5 mm long straight crack advance from the initially spark cut notch of aspect ratio of 26, followed by creep crack growth at a 50 ° angle to the original crack plane. Cracking behavior of the specimens with Vickers hardness values at or above 220 was in the original notch plane. Similar effects of the initial crack starter geometry on the fracture paths of creep cracks were also reported by Hayhurst et al. (1978). In their creep fracture experiments on circumferentially notched circular tension bars of A1 and Cu, two different notch profiles were studied: (a) a circular, so-called Bridgman notch (BN); and (b) a British Standard notch (BSN). Root radius to minimum diameter ratios were 0.67 and 0.055 for the BN and BSN geometries, on the same size bar with maximum to minimum diameter ratios being 1.67 and 1.41 for BN and BSN, respectively. These two specimen geometries were found to have dis-
B. Ozmat et al. / Cracks in 304 stainless steel
tinctly different stationary state stress fields. In the BN the maximum principal tensile stress and effective stress were both in the minimum cross section. While in the BSN the maximum principal stress was in the minimum cross section, the maximum effective stress was at an angle of 50 o to the notch plane. For the BN geometry, fracture processes were confined to the minimum cross section of the notch, whereas in the BSN geometry fracture processes were not similarly confined but were on inclined planes of about 50 o. This was most apparent in the A1 specimens where the fracture criterion depends more strongly on the effective stress, as had been noted first by Johnson and Henderson (1962). In their most recent study, Hayhurst et al. (Hayhurst, Dimmer and Morrison, 1984) reported that in creep tests of Cu and A1 alloy specimens with sharp internally and externally cracked geometries, creep cracks grew on a 40 ° plane and a 55 ° plane with respect to the initial crack, for the cases of Cu and A1, respectively. Thus, in summary we note that in the growth of creep cracks starting from initial grooves, notches, or sharp pre-fatigued cracks there are important transient phases involving non-planar crack growth, particularly in more ductile alloys, consuming substantial fractions of a growth stage that might potentially govern the total life of the part. Before we present the full range of our experimental findings in Type 304 stainless steel, we review briefly in Section 3 below the earlier relevant experimental findings of others on this same material.
3. Earlier creep crack growth experiments on Type 304 stainless steel Type 304 stainless steel which was chosen here for reasons of its simple structure and because of our earlier study of the mechanisms of intergranular fracture in this material (Chen and Argon, 1981), has also been investigated extensively by others in various different experimental geometries. Koterazawa and Iwata (1976) conducted tests in air at 655°C on double-edge-notched plate
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(DENP) and on round-notched bars (RNB) with root radius to notch depth ratios of 0.05 and 0.085 for D E N P and RNB, respectively. Their crack growth rates ranged over four orders of magnitude starting from a low value of 3 x 10-x0 m / s , and appeared to correlate well with K, the Mode I stress intensity factor. Some microscopy observations established the intergranular nature of the crack growth. Koterazawa and Mori (1977) reported on creep crack growth tests in air at 650°C on doubleedge-notched (DENP), center-cracked (CCP) and single-edge-notched (SENP) thin ( t = l . 5 mm) plate specimens. The crack forming defects were simulated with finite root radius notches. The range of experimental crack growth rates were the same as above, and propagation occurred intergranularly, which was supported by microscopy in a D E N P specimen. The authors compared creep crack growth rate results from tests obtained on the different test geometries mentioned above, and showed that C* offers the best means of correlating the experimental measurements, within an order of magnitude of a scatter band. Taira et al. (1979) also conducted creep crack propagation tests at 650°C in air and in a moderate vacuum (1 Torr). A thin (2.3 mm) center cracked plate (CCP) specimen was employed. Two specimens were fatigue pre-cracked. It was observed that the crack growth mode switched to transgranular when the applied nominal stress levels were 176 MPa and higher. The range of intergranular crack growth rates were similar to those of Koterazawa and coworkers (1976, 1977) but were higher in the transgranular mode (3 × 10 -8 to 3 x 10 -6 m / s ) . The crack growth rates correlated best with C * both in air and in vacuum. Yokobori and Sakata's (Yokobori and Sakata, 1979; Yokobori, Sakata and Yokobori, 1979) creep crack growth tests were conducted in the temperature range between 600 and 700°C and in vacuum (10 -5 Tort) on thin (1 mm) specimens of D E N P geometry. The crack growth rates varied over five orders of magnitude from a low of 3 x 10 -11 m / s . The authors noted that growth of cracks begins when the crack tip strains reach a critical value independent of temperature and stress level, obeying a local M o n k m a n - G r a n t criterion, and that
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B. Ozmat et aL / Cracks in 304 stainless steel
subsequent growth rate could be correlated with gl.
Sadananda and Shahinian (1980) measured creep crack growth rates in 304 stainless steel in a 20% cold worked condition at 593°C in vacuum (10 -6 Torr) and in air. Compact tension (CT) specimens with the crack plane lying parallel to the rolling direction, and center-cracked plate (CCP) specimens with side grooves and pre-fatigue sharpened cracks were used. Crack extension
was intergranular in both vacuum and in air, and crack growth rates ranged from 3 × 10 -8 to 3 × 10- 6 m//s" On the basis of an observed K correlation of crack growth rates the authors concluded that cold work enhances crack growth rates and that environmental effects are not pronounced. The growth of cracks, however, was not planar (Sadananda, 1984). In a separate study, Koterazawa and Mori (1980) also reported on creep crack growth rates
Table 1 Details of creep crack growth measurements in other investigations on Type 304 stainless steel Environment
Crack vel. range ( m / s )
Mechanism of crack advance, and mode
Best correlation
655
air
3 x 10 - 1o_ 3×10 -6
Intergranular
K
rounded notch
650
air
(same)
Intergranular
C*
CCP
cut planar crack; prefatigued
650
air and vacuum 1 Tort
(same)
Intergranular, Transgranular at high stress
C*
Yokoboi and Sakata (1980); Yokobori et al. (1980)
DENP
cut cracks
600-700
vacuum 10 -5 Tort
3 x 10 - 11_ 3 × 1 0 -6
Intergranular
K
Sadananda, and Shahinian (1980); Sadananda (1984)
20%cold work CT
cut cracks with side grooves, prefatigued
593
air and vacuum 1 0 - 6 Torr
3 × 10-s_ 3 x 10- 6
Intergranular, branched crack growth
K
Koterazawa and Moil (1980)
DENP CCP
500-700
air
(same)
?
C*
Ohji et al (1980)
CCP RNB CT
cut cracks with rounded root radii
650
air
3x10 -113 x l O -6
?
C*
Saxena (1980)
CCP CT
cut cracks, pre-fatigued
538-705
air
10-9-10 -7
?
C*
Musicco et al. (1982)
CT
cut cracks
550
dry argon
(same)
?
C*
Krompholz et al. (1982)
CT
cut cracks, pre-fatigued
550-750
air
10-11-1(} - 7
heavy oxidation branched crack growth
C*
Authors (References)
Spec. Type a)
Starter crack type
Koterazawa and Iwata (1976)
DENP RNB
60 o round notch
Koterazawa and Mori (1977)
DENP CCP SENP
Taira et al. (1979)
Temperature range
(°c)
a) CCP, center-cracked panels; CT, compact tension; DENP, double-edge-notched panel; RNB, round-notched bar; SENP, single-edge-notched plate.
B. Ozmat et al. / Cracks in 304 stainless steel
in the 550-700°C temperature range with several annealed DENP specimens and CCP specimens of different sizes with similar geometry. All crack growth was intergranular, and the best correlation of crack growth rates was with the C* parameter. Ohji et al. (1980) performed their crack growth experiments on Japanese SUS 304 SS at 650°C in air on CCP, RNB, and CT specimens. In all of these test specimens, machine-cut notches with finite root radii were employed to initiate the creep cracks. They investigated the specimen geometry, size, relative crack depth, and different load level effects on the creep crack growth rates by means of a single parameter correlation, and concluded that regardless of specimen size and geometry, creep crack growth rates correlate well with a modified C* integral. Their data for d a / d t was nearly linearly dependent on C * Saxena (1980) reported on constant imposed displacement rate creep crack growth tests performed in the 538°C to 705°C range on annealed 304 SS using CCP and CT specimen geometries. All specimens contained fatigue pre-cracks of approximately 2.5 mm. Under imposed displacement rates ranging from 0.025 to 0.3 mm/h, crack growth rates were found to be in the 10 -9 to 10 -7 m / s range. The basic conclusion was that C* provides a good characterization of creep crack growth rates in the CCP and CT geometries. Saxena also compared his results with those of Begley (1980) on creep crack growth in annealed standard CT1 specimens in the same temperature range, and showed that both sets of data fell into the same scatter band, concluding that there is no significant further temperature effect on crack growth in the C* growth regime. Very similar conclusions were reached also by Musicco et al. (1982) on tests on annealed 304 L stainless steel at 550°C in an inert argon environment under constant displacement rate conditions on 15 mm thick CT specimens. Krompholz et al. (1982) performed creep crack growth rate measurements on 18Cr l l N i German austenitic stainless steel (DIN 1.4948, which is very similar to Type 304) in air under constant load conditions, in the 550-750°C range on fatigue pre-cracked CT specimens. The authors observed that in their experirnents in air heavy
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oxidation occurred at the fracture surfaces, as well as considerable blunting at the fatigue to creep crack transition line followed by out of plane branched crack extension. They nevertheless concluded that C* is a better parameter for overall correlation of creep crack growth rates than K or net section stress. The important aspects of these observations are summarized in Table 1. They indicate that most investigators have found that the overall creep crack growth rate could be correlated better with a C* parameter than with K or net section stress. While microscopic observations on the mode and mechanism of crack growth were not always reported, it can be concluded that most growth was intergranular, and showed significant early crack branching particularly in the plane strain CT-type specimen geometries. In the absence of specific reports we conclude that apparent planar growth was found only in the very thin samples which most probably had plane stress deformation characteristics, and those with deep side grooves.
4. Experimental details and results 4.1. Material and specimen preparation
The Type 304 stainless steel was received in the form of hot rolled, annealed, pickled bars or plates. The material was solution treated at 1050°C for 45 min and quenched. After quenching, the specimens were machined to the final dimensions in the solutionized condition. For the preparation of cold worked specimens, a uniform uniaxial plastic tensile elongation was imposed on the material at room temperature by stretching before machining. Notches were introduced by the use of either an electrical discharge machine (EDM) for the center-cracked panel (CCP) specimens, or by a circular saw on a milling machine for double-edge notched (DENP) and compact tension (CT) specimens. Fatigue pre-cracking at room temperature was done on some specimens using a computer controlled MTS machine imposing a final cyclic stress intensity factor of AK = 13 MPa, m 1/2 at an R ratio of 0.1. Prior to the application of the test load, specimens were sensitized at 800°C for
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B. Ozrnat et al. / Cracks in 304 stainless steel
Table 2 Temperature dependence of Young's modulus and yield strength of Type 304 stainless steel Temperature ( o C)
Young's modulus (GPA)
0.2% Yield strength (MPa)
25 600 700 750
197 160 140 138
260 (382 a)) 112 100 90 (132 a)) b)
a) 5% cold worked at room temperature. b) Calculated on the basis of a strain hardening exponent of 0.12.
48 h under high vacuum in the test chamber. The heat treatment process described above yields a well defined family of grain boundary carbides with an average spacing and size of 6 ~tm and 0.4 ~m respectively (Chen and Argon, 1981). Following the heat treatment the average grain size was 60 ~m. The temperature dependence of the 0.2% offset yield strength and elastic modulus of the 304 SS are given in Table 2. Due to its austenitic nature, 304 SS is not heat treatable, and increased strength can only be obtained by cold working. Because of its high strain hardening rate (strain hardening exponent = 0.12), however, substantial elevation of flow stress is achievable with relatively small area reduction. The steady state equivalent creep rate for the Type 304 alloy in an annealed state can be given by the following power-law relationship:
Table 3 Creep rate properties of Type 304 stainless steel determined from data of Blackburn (1972) Temp. (°C)
n
o0 (MPa)
State
600 650 700 750 750
6.72 6.80 6.88 7.19 7.19
129 114 102 91 132 a)
Annealed Annealed Annealed Annealed cold work
a) Calculated on the basis of o0 being the reference deformation resistance of the material in a rapid tension test (Argon and Bhattacharya, 1987).
where
oe is the equivalent tensile stress, o0 a reference tensile deformation resistance and R and T have their usual meaning. According to the most complete data of Blackburn (1972), A = 3.83 × 107 s-1, Q = 67 kcal/mol, and n and o0 are slightly temperature dependent, with a relevant set of values given in Table 3 (these values have been calculated from the best fit functional forms given by Blackburn to fit the power law form given in Eq. (1)).
4.2. Experimental details In all cases crack propagation experiments were carried out in a constant load maintaining modified screw driven testing machine, equipped with a vacuum chamber, maintaining a pressure in the 10 6-10-5 Torr range at test temperature. Test temperatures were achieved by induction heating through specially fashioned water-cooled power coils surrounding the specimens. Through proper design of these coils temperatures in the specimens in the regions of expected crack growth were kept constant within a few degrees of the desired temperature by means of a feed-back control system. In each case this was verified by measuring the temperature distribution with a set of thermocouples in a control experiment. Crack length was measured by the potential drop method intermittently when the radio frequency power was momentarily turned off. Absolute calibration of the potential drop measurements with crack length was accomplished by determining the final crack length in the specimens, by metallographic sectioning after the experiment was over. The full details of the unconventional experimental set up which could accommodate all the different test configurations for which results are described below can be found elsewhere (Ozmat, 1984).
4.3. Experimental results In the course of the experimental study to measure intergranular creep crack growth in 304
B. Ozmat et a L / Cracks in 304 stainless steel
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Table 4A Geometrical details of CCP, DEN and CT specimens Test Spec. Type & Number
Half width, b (mm)
Initial crack length, a (mm)
CCP-1 CCP-2 DEN-1 DEN-2 b) DEN-3 CT-1 CT-2 b)
25.4 25.4 6.5 13.8 25.4 113 97.6
10.4 6.0 3.2 9.0 14.3 61.0 47.0
Initial crack tip radius (mm)
Specimen thickness (mm)
Test temp. ( o C)
Yield strength (MPa)
a)
6.35 6.35 51.0 51.0 12.5 28.0 16.5 c)
600 700 750 750 775 750 750
112 100 90 132 85 90 132
a)
a) a) 0.2 1.15 1.15
a) Fatigue precracked Aa =1 mm at AK =13 M P a - m 1/2. b) With 5% cold work. c) Thickness at bottom of side grooves.
stainless steel three different specimen configurations consisting of center-cracked panels (CCP), d o u b l e - e d g e - n o t c h e d bars ( D E N ) , a n d c o m p a c t t e n s i o n (CT) geometries were used. All specimens were of sufficient thickness to be well i n the p l a n e strain d e f o r m a t i o n regime. Achieving this often required some trial a n d error approach. W i t h i n the experimental range of temperature a n d stress, chosen to retain a stable microstructure, a n d a n i n t e r g r a n u l a r m o d e of crack growth, m a j o r transients were observed in the growth m o d e of cracks in all specimens. This did n o t permit u n a m b i g u o u s m e a s u r e m e n t of crack speed in a satisfactory selfsimilar growth m o d e that would be correlated with a n y generalized crack tip driving force. Therefore,
below we limit our p r e s e n t a t i o n primarily to the description of these initial growth transients in a selection of CCP, D E N , a n d C T specimens, chosen to d e m o n s t r a t e certain special features of the various t r a n s i e n t growths. F o r the record, to aid in discussion, however, calculated C * factors a n d overall average crack speeds are also given, where the latter represents the total final i n c r e m e n t a l crack extension (in the actual growth direction) divided b y the total time of the experiment. The m e t h o d of d e t e r m i n a t i o n of the a p p r o p r i a t e C * values is discussed in A p p e n d i x I. The d i m e n s i o n s a n d test details of the two CCP, the three D E N , a n d the two C T specimens are given i n Tables 4A a n d 4B.
Table 4B Crack extension results in CCP, DEN and CT specimens Test Spec. Type & Number
Nominal Stress a) (MPa)
At, test duration (s)
Crack tip opening (ram)
Aa, creep crack incr. (mm)
Aa / A t
C*
(m/s)
( J / / m 2 S)
CCP-1 b) CCP-2 DEN-1 DEN-2 c) DEN-3 CT-1 CT-2 c)
170 100 90 90 80 104 151
2.16 × 105 2.88 × 105 5.40 x 105 3.96 × 106 5.04 X 105 5.58 X 106 1.37 × 105
1.97 1.07 0.75 0.60 1.70 2.40 1.20
1.43
6.62 × 10- 9 4.86 × 10 - 9 2.96 X 10 - 9 2.93 X 10 - lO 6.75 × 10-9 9.44 X 10- l o 7.16 x 10- s
9.21 X 10- 3
1.40
1.60 1.16 3.40 5.27
9.80
a) Net section tensile stress or nominal total crack tip stress for CT specimens. b) Plane stress. c) With 5% cold work.
1.42 X 10 - 2
2.24 X 10- 3 1.54 × 10- 3 6.47 × 10- 3 1.81 X 10- 3
2.21 × 10- 3
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B. Ozmat et al. / Cracks in 304 stainless steel
In both the CCP-1 and CCP-2 specimens unsymmetrical branched crack growth was observed at the end of 60 and 80 h respectively. As Tables 4A and 4B indicate, the net section stress in CCP-1 was considerably above the short term yield strength of the material at the test temperature. Hence in this case very considerable crack tip plastic deformation occurred, affirmed by the large crack tip opening displacement. Clearly, in this case the crack tip conditions were characteristic of large scale plastic blunting before eventual stress relaxation and possible intergranular crack extension may have occurred. The net section stress in CCP-2 was equal to the short term yield strength of the material, and therefore closer to creep conditions. In both cases, however, microscopy established that the creep crack growth was by intergranular fracture. Moreover, in both of these cases where the starting crack had been sharpened by fatigue pre-cracking, the initial transient creep crack extension was on a slanted plane making an angle of about 55 ° with the median plane of the fatigue pre-crack. Figure 1 shows this unsymmetrical creep crack extension in CCP-2, which is typical for both of these specimens. As is well known (McMeeking and Parks, 1979) the region of dominance of the non-linear singular field of J or C * is very restricted for CCP specimens in which the initial crack length is a substantial fraction of the specimen width. For this rea-
Fig. 1. Branching of the initially sharp crack in the CCP-2 specimen, revealed on an internal polished section.
Fig. 2. Branched crack in polished and lightly etched mid section of DEN-1 specimen.
son experiments were also carried out with DEN specimen configurations. Of these specimens, DEN-1 and DEN-2 were fatigue pre-cracked and tested at 750°C at net section stresses of 90 MPa. While DEN-1 was in annealed form the material for DEN-2 was given a plastic pre-strain of 5% at room temperature, prior to machining the notch, normal to the direction of extension. As reported by Gold et al. (1975) such cold work imparted at room temperature is stable in the test range of 750°C for as long as 8000 h. For the DEN-1 specimen the net section stress of 90 MPa was again equal to the short term yield strength. Because of the higher deformation constraint in the crack tip field of a DEN geometry the crack opening displacement was substantially less than the CCP case, as was the average crack velocity. Figure 2 shows the initial crack extension response in DEN-1 as a well developed case of crack branching and growth over substantial distances on slanted planes making angles of about 45-55 °
B. Ozmat et al. / Cracks in 304 stainless steel
with the plane of the initial fatigue pre-crack. The figure which shows a lightly etched central section through the crack front illustrates dearly the diffuse nature of intergranular cracking that surrounds the crack tip region and results in overall growth of the macro creep crack. In the DEN-2 specimen the net section stress of 90 MPa corresponded only to 68% of the short term yield stress. Therefore, the average crack velocity was an order of magnitude smaller than for DEN-1. Figure 3 shows that the initial crack growth behavior was identical to that in DEN-1 with substantial growth on slanted planes at 55 ° However, the figure also shows that there is here a final tendency of the slanted cracks to turn around and propagate parallel to the plane of the initial fatigue pre-crack. The DEN-3 specimen was provided with a machine cut notch with a finite radius of curvature of 0.2 mm instead of a fatigue pre-crack. The test was carried out at 775°C and at a net section stress of 80 MPa which was 94% of the short term yield stress at the test temperature. The growth of this crack showed an interesting dividing-line behavior. As Fig. 4 shows crack extension started in
Fig. 3. Polished mid section region of DEN-2 specimen showing initial branching of a crack followed by changing of path to become parallel to initial crack plane.
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Fig. 4. Polished mid section of DEN-3 specimen showing meandering feathery crack emanating from the rounded crack tip region.
a diffuse way roughly in the median plane of the initial rounded notch. In its propagation, however, it showed a repeated tendency to deviate for short stretches from this plane toward either side, resulting in an overall feathery appearance. The repeated attempts of departure of the crack from its plane, in the nature of zones of diffuse intergranular damage is shown better at a larger magnification in Fig. 5. The view at even larger magnification in Fig. 6 shows in much greater detail the surrounding intergranular damage in the form of a high density of grain boundary facet cracks. In the hope of obtaining longer stretches of self-similar crack growth, experiments were also carried out with two compact tension (CT) specimens. The dimensions of these specimens CT-1 and CT-2 are also given in Tables 4A and 4B. The crack tips in both of these specimens were rounded to a radius of 1.15 mm. While the material of CT-1 was in annealed form, that of CT-2 was given a 5 % extension at room temperature parallel to the plane of the crack. Both creep experiments
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B. Ozmat et al. //Cracks in 304 stainless steel
Fig. 5. Polished and lightly etched mid section of DEN-3 specimen showing at intermediate magnification region near the crack tip.
Fig. 6. Higher magnification view of same crack tip region shown in Fig. 5. The light etching delineates clearly the grain boundaries and the many grain boundary facet cracks.
were carried out at 750°C. Figure 7 shows the creep crack in CT-1 as revealed on a longitudinal polished section after the test. The intergranular crack initially propagated for 1 mm roughly along the median plane of the initial machine crack, but then formed two branches making about 50 o with the median plane. One of these branch cracks subsequently changed direction again back toward the median plane, after propagating a length of 1 mm.
The CT-2 specimen was subjected initially to a nominal crack tip stress of 130 MPa which after 220 h produced no crack growth. The crack tip nominal stress was then raised to 151 MPa which resulted in a growth of 9.8 mm in 38 h. Examination of this crack after the test showed, however, that it propagated transgranularly and in a rather brittle appearance as shown in Fig. 8. From these tests we conclude the following: (1) Regardless of specimen geometry, temperature, and cold work, intergranular creep cracks initiating from sharp pre-fatigued cracks follow a
Fig. 7. Polished mid section of crack tip in CT-1 specimer showing an initially straight crack branch in further growth.
B. Ozmat et al. / Cracks in 304 stainless steel
Fig. 8. Polished mid section of crack tip in CT-2 specimen showing the relatively straight transgranular crack.
long initial transient during which growth is along 50 o with the initial median plane. (2) Regardless of specimen geometry and testing conditions, intergranular cracks initiating from notches with notch tip radius to notch depth ratio exceeding 0.01 first followed a straight course and then often also branched. (3) Branched cracking during creep represents an initial transient response of sharp cracks in an intergranular mode of propagation under Mode I conditions. Based on the limited set of observations, however, the long term tendency for the branched cracks is to return to a plane parallel to the median plane - perhaps to branch again later, and so on.
5. Discussion
5.1. The crack path Creep fracture in ductile polycrystalline alloys such as Type 304 stainless steel, is intergranular under typical service conditions. The rate of intergranular cavity growth that governs the early stages of such fracture is usually constrained by creep deformation in the surrounding grain matrix for typical service stresses. Then, fracture is ultimately governed by a local critical strain criterion. At high stresses nearing yield the intergranular cavi-
11
tation process is not completely constrained by creep flow but the cavity nucleation is still governed by a local critical strain criterion. In these aspects intergranular creep fracture has much in common with ductile fracture by the growth and coalescence of cavities, occurring below the diffusive creep regime. It was recognized first by Rice and Johnson (1970) that a fracture criterion based on a local critical strain is difficult to satisfy at the tip of a sharp crack in elastic-plastic fracture where the concentration of equivalent plastic strain does not occur ahead of the crack. Such concentration of strain only becomes possible when significant crack tip blunting transfers it from the slanted planes at 50 ° for the sharp crack (Bassani and McClintock, 1981), into the region ahead of the crack or when the crack starts out with a certain initial radius of curvature. This trend is shown clearly in a finite element study of the creep deformation field around a blunting crack with a high but finite initial sharpness, reported by Argon et al. (1985) (and to be published in more detail elsewhere by Lau, Parks and Argon). In that study a DEN bar, responding only in power-law creep characteristic of Type 304 stainless steel, with an initial a/b = 0.5 and a crack tip radius to uncracked ligament ratio R / c = 3.4 x 10-3, was deformed monotonically until this ratio reached 2.51 × 10 -2. Figure 9, reproduced from that study, shows clearly the moving outward of the cross-over point where the accumulated equivalent creep strain ahead of the crack exceeds that along the inclined plane making an angle of 43 ° with the crack plane. In the initial infinitely sharp creep crack field the equivalent strain rate concentration along the 50 ° plane exceeds that ahead of the crack by more than an order of magnitude (Bassani and McClintock, 1981). Clearly, then, for a crack with an initial sharpness between the pre-fatigued crack and that for which results are given in Fig. 9, the spread of damage will just favor a forward initial growth direction. As our experimental study presented above amply demonstrates, however, the process of long term crack growth is more complex than the presence or absence of an initial favorable condition for forward growth. As Fig. 3 for the DEN-2 specimen with the fatigue sharpened pre-crack
12
B. Ozmat et aL / Cracks in 304 stainless steel
3.2 I I I
I
I
II
2.8--
I
I
1.6" 43*
~__l
II
I
( cR_)I=6.6 4
-
X 10 -3
I
~.~
2, -
t
2.0--
L
(91; ~
1.34 x 10-2
-
3
1.6 --
o.
; " ."..
0
4
8
12 r/c
16
20xlO -3
Fig. 9. Computed distribution of total creep strain around the crack tip undergoing blunting by creep flow for three states of crack opening (from Argon et al. (1985), courtesy of Cambridge University Press).
shows, after an initial response of crack growth along the slanted 50 ° planes, the crack shifts back to a plane parallel to the median plane. The converse effect is shown in Fig. 7 for the CT-1 specimen and in Fig. 5 for the DEN-3 specimens. In both cases an initial finite crack-tip radius of curvature tends to concentrate the initial creep damage process into the region ahead of the crack. However, in both cases the relatively sharp creep crack has a further tendency to spur damage away from the median plane. Since in the latter case the apparent sharp creep crack is surrounded with a deformation and damage field characteristic of the initially blunt crack, the deviation of growth away from the median plane cannot be entirely for the same reason as that for the initially sharp crack in an uncrept sample. Clearly, these two tendencies of branching of the initially sharp crack, and the roughly planar growth in the initially blunted crack, recur during the further extension of creep
cracks in ductile alloys with substantial levels of local strain to fracture (relatively large Monkman-Grant (1956) products of minimum creep rate and time to fracture). This meandering behavior of the crack should result in lower overall growth rates. Two important points need to be noted about these growth transients and the meanderings of creep cracks. First, as should be clear from Figs. 5 and 6, the wave lengths of the meanderings of the cracks have little to do with grain size which is on a scale more than an order of magnitude smaller. In fact the size of a grain boundary facet crack which is the principal element of damage is small enough for adequate smoothing to consider quasi-homogeneous damage models for crack growth, as we discuss in a companion study (Hsia, Argon and Parks, 1991). Second, the level of critical strain for local creep fracture must be an important parameter governing the meandering of the crack. Thus, if continuing crack tip blunting can shift the concentration of total strain away from the inclined zones to the front of the crack before a local intergranular separation condition can be met, fracture will not occur along the zones of initial strain concentration. A critical level of accumulated creep strain is a fracture criterion associated with constrained intergranular cavity growth which is characteristic of Type 304 stainless steel having a large variability of carbide coverage of grain boundaries (Argon et al., 1985; Chen and Argon, 1981). In certain other alloys such as Nimonic 80A (Dyson and McLean, 1977) and Astroloy (Capano et al., 1989), where all grain boundaries have a similar level of carbide coverage, or in the model materials of Ag and Cu with pre-cavitated grain boundaries, studied by some investigators (Capano et al., 1989; Goods and Nix, 1978; Stanzl et al., 1983) cavity growth must be unconstrained. In such materials local fracture is more dependent on the level of maximum principal tensile stress and is less likely to be governed by a critical strain criterion. This should favor planar crack growth since the maximum principal tensile stress is concentrated ahead of the crack for both sharp (Hsia et al., 1991) and blunt cracks, and where deformation induced further blunting does not alter the balance (Ar~on et
13
B. Ozmat et aL / Cracks in 304 stainless steel
al., 1985). In more realistic situations of creep fracture in the presence of oxidizing environments, where such effects hasten local fracture, a similar situation may govern. It is important to note here that some authors who have reported on the growth of creep cracks in relatively ductile alloys such as 1Cr-0.5Mo steel (Riedel and Wagner, 1985), 0.5Cr, 0.SMo, 0.25V steel and 2.25Cr, 1Mo steel (Riedel and Detampel, 1987), have achieved planar growth only through the use of deep side grooves (25% reduction of cross sectional area). Clearly, such practice, even if neutral 'in affecting the nature of creep damage, must accelerate crack growth by not permitting the development of the natural meandering of the creep cracks which we have discussed here. The different initial growth responses of creep cracks are consistent with the ripening of intergranular creep damage in the different deformation fields of sharp and blunt cracks. This has been discussed briefly by us earlier on the basis of a mechanistic damage model (Argon et al., 1985). A somewhat more expanded treatment of this in a non-interactive form was developed by Ozmat (1984) which, however, will not be presented here. A fully interactive damage model explaining the early meandering of creep cracks with different initial conditions, in Type 304 stainless steel and other related alloys is presented in a companion paper (Hsia et al., 1991). 5.2. The crack growth rate
K?(1 - p2)/E (n+l)C* '
i0 -7
'
I
I
0 CT-2 o-t
E
/
.0
As stated earlier, in these experiments it was not possible, with reasonable effort, to obtain substantial ranges of self-similar crack growth in nearly steady state conditions. Nevertheless, the measured growths over the total times under stress were considered as average crack speed and were examined to determine the possible conditions for their growth. Since in nearly all cases net section stresses were quite high, bordering on the short term yield strengths of the alloy, only a possible correlation with C* was sought. This correlation was also the natural choice since in all cases the creep relaxation time t r, tr=
was much less than the total time for crack growth. The appropriate levels of applied C* parameters for the CCP, DEN and CT specimens were calculated according to the procedure prescribed by Riedel (1987), utilizing the published dimensionless h 1 factors calculated for J-controlled fracture (Kumar et al., 1981) for the appropriate specimen geometries. Details of this computation are given in Appendix I. These calculated C* values for the creep properties of 304 stainless steel as determined from the data of Blackburn (1972), and summarized in Table 3 are listed in Table 4B, together with the average crack speeds. In all cases except CT-2 the crack growth was intergranular. In the latter with a pre-strain induced built-in anisotropy of aligned inclusions cracking was transgranular and resulted in a much higher average growth speed. All the calculated average crack velocities are shown plotted against their corresponding C* factors in Fig. 10. Discarding the transgranular crack growth case of the CT-2 specimen, there is a general upward trend apparent in the data and delineated by the best-fit straight line. The slope of this line is 1.06, which is somewhat larger than the expected slope of n / ( n + 1)
(3)
o
/
10-8
<1
DEN-3 o o ~ C C p_ I
/ DEN-I
o
O3
o CCP-2
/
/ 0
CT-I
10-9
7 / /
DEN-2 0
/ ,¢o! l0 - 4
/
,
J 10-3
,
I 10-2
C~ , J / m 2 x s
Fig. 10. Dependence of average crack speed A a / A t on the prevailing C* around the crack tip for the three different specimen geometries investigated.
14
B. Ozmat et al. / Cracks in 304 stainless steel
( = 0.873) of a well established steady state C* controlled crack growth process predicted by theory (Riedel, 1987), and observed to be so in a number of well documented cases (Riedel, 1987; Riedel and Wagner, 1985; Riedel and Detampel, 1987). Considering the very large variations in crack plane the fact that the data is obtained from growth at several different temperatures where the exponents n are different, and the very limited extent of the data, the lack of agreement is not surprising. Clearly, a further contributory factor to the different slope can be the presence of a substantial incubation time in crack growth, particularly in the low C* ranges. Finally, while the stress levels in the experiments reported here have been high, bordering on the yield strength of the alloy, with the exception of the CT-2 specimen, all fractures have been intergranular showing all the characteristics of this fracture mode on the fracture surfaces. Therefore, the phenomena reported here are considered as a limiting form of fracture in fully developed creep fields, supported by the correlation of crack growth obeying a C* criterion. However, from the point of view of external appearances it is also possible to interpret the observations as a limiting form of hot ductile fracture since the C* correlation is basically based on the reinterpretation of a J correlation. Because of the intergranular mode of crack growth we prefer to consider it as a limiting form of creep fracture.
6. Conclusions In ductile alloys such as Type 304 stainless steel obeying a local constant critical strain criterion for crack advance, substantial crack plane meandering is observed. Initial growth of pre-fatigued, sharp cracks occurs on planes making 50 o with the median plane of the initial crack. Initial growth of cracks with a finite radius of curvature (exceeding a critical, and presently undetermined amount) is in the median plane of the crack. In further growth, while the initially branched cracks at 50 o planes have been observed to change
their paths later to becoming parallel to the median plane, the converse was found to be the case for planar crack growth emanating from initially blunted cracks, which showed evidence for later branching. While insufficient data were available to determine the crack growth law, a correlation of average crack speed with C* was found, with an exponent considerably larger than the expected value of n / ( n + 1).
Acknowledgement This research had been supported earlier during the period of 1980-1984 by the U.S. Department of Energy under Contract No. DE-AC0277ER04461. We acknowledge also many useful discussions with Professor F.A. McClintock and Professor C:W. Lau (now at Drexel University).
References Argon, A.S. and A.K. Bhattacharya (1987), Primary creep in nickel: experiments and theory, Acta Metall. 35, 1499. Argon, A.S., C.W. Lau, B. Ozmat and D.M. Parks (1985), Creep crack growth in ductile alloys, in: Fundamentals of Deformation and Fracture, B.A. Bilby, K.J. Miller and J.R. Willis, eds. Cambridge Univ. Press, Cambridge, p. 243. Bassani, J.L. (1981), Creep crack extension by grain boundary cavitation, in: Creep and Fracture of Engineering Materials and Structures, B. Wilshire and D.R.J. Owen, eds., Pineridge Press, Swansea, p. 329. Bassani, J.L. and F.A. McClintock (1981), Creep relaxation of stress around a crack tip, Int. J. Solids Struct. 17, 479. Begley, J.A. (1980), unpublished data quoted by A. Saxena (1980). Blackburn, L.D. (1972), lsochonous stress-strain curves for austenitic stainless steels, in: The Generation of Isochonous Stress-Strain Curves, A.O. Schaeter, ed., ASME, New York, p. 15. Capano, M., A.S. Argon and I.-W. Chen (1989), Intergranular cavitation during creep in astroloy, Acta. MetalL 37, 3195. Chen, I.-W. and A.S. Argon (1981), in: Creep cavitation in 304 stainless steel, Acta. Metall. 29, 1321. Davis, E.A. and M.J. Manjoine (1953), Effect of notch geometry on rupture strength at elevated temperatures, in: Strength and Ductility of Metals at Elevated Temperatures', STP-128, ASTM, Philadelphia, p. 67.
Dyson, B.F. and D. McLean (1977), Creep of Nimonic 80A in torsion and tension, Metal Sci. 11, 37.
B. Ozmat et al. / Cracks in 304 stainless steel Gold, M., W.E. Leyda and R.H. Zeisloft (1975), The effect of varying degrees of cold work on the stress-rupture properties of Type 304 stainless steel, J. Eng. Mater. Technol. 97, 305. Gooch, D.J. (1977), The effect of microstructure on creep crack growth in notched bend tests on 0.SCr-0.5Mo-0.25V steel, Mater. Sci. Eng. 27, 57. Gooch, D.J., B.L. King and H.D. Briers (1977), High temperature crack growth in a 2¼Cr-lMo weld metal - effects of tempering, prestrain and grain refinement, Mater. Sci. Eng. 32, 81. Goods, S.H. and W.D. Nix (1978a), The kinetics of cavity growth and creep fracture in silver containing implanted grain boundary cavities, Acta Metall. 26, 739; (1978b), The coalescence of large grain boundary cavities in silver during tension creep, Acta Metall. 26, 753. Hayhurst, D.R., F.A. Leckie and C.J. Morrison (1978), Creep rupture of notched bars, Proc. R. Soc. A360, 243. Hayhurst, D.R., P.R. Brown and C.J. Morrison (1984), The role of continuum damage in creep crack growth, Phil. Trans. R. Soc. A311, 131. Hayhurst, D.R., P.R. Dimmer and C.J. Morrison (1984), Development of continuum damage in the creep rupture of notched bars, Phil. Trans. R. Soc. A311, 103. Hawk, D.E. and J.L. Bassani (1986), Transient crack growth under creep conditions, ,/. Mech. Phys. Solids 34, 191. Hsia, J.K., D.M. Parks and A.S. Argon (1991), Modeling of creep damage evolution around blunt notches and sharp cracks, Mech. Mater. 11, 43. Johnson, A.E. and J. Henderson (1962), Complex-stress creep relaxation and fracture of metallic alloys, Dept. Scientific & Industrial Research, Natl. Eng. Laboratory (Her Majesty's Stationary Office, Edinburgh). Koterazawa, R. and Y. Iwata (1976), Fracture mechanics and fractography of creep and fatigue crack propagation at elevated temperatures, J. Eng. Mater. Technol. 98, 296. Koterazawa, R. and T. Mori (1977), Applicability of fracture mechanics parameters to crack propagation under creep condition, J. Eng. Mater. Technol. 99, 298. Koterazawa, R. and T. Mori (1980), Fracture mechanics and fractography of creep and fatigue crack propagation at elevated temperatures, in: Proceedings Intern. Conf. on Eng. Aspects of Creep, Sheffield, U.K., Soc. Automot. Eng., Warrendale, Vol. 1, p. 219. Krompholz, K., H. Huthmann, E.D. Grosser and J.B. Pierick (1982), Creep crack growth behavior in air and sodium for an unstabilized austenitic stainless steel and assessment of evaluation concepts, Eng. Fracture Mech. 16, 809. Kumar, V., M.D. German and C.F. Shih (1981), An engineering approach for elastic-plastic fracture analysis, EPRI Topical Report NP-1931 (EPRI, Palo Alto). Lau, C.W., D.M. Parks and A.S. Argon, Crack-tip blunting in creeping alloys, to be published. Leckie, F.A. and D.R. Hayhurst (1974), Creep rupture of structures, Proc. R. Soc. A340, 323. Manjoine, M.J. (1963), in, Simulated service testing at elevated temperature, Proceedings of Joint International Conference
15
on Creep, The Institution of Mechanical Engineers, Vol. 1, p. 7. McMeeking, R.M. and D.M. Parks (1979), On criteria for J-dominance of crack-tip fields in large-scale loading, in: Elastic Plastic Fracture, J.D. Landes, J.A. Begley and G.A. Clarke, eds., STP-668, ASTM, Philadelphia, p. 175. Monkman, F.C. and N.J. Grant (1956), An empirical relationship between rupture life and minimum creep rate in creep-rupture tests, Proc. A S T M 56, 593. Musicco, G.G., D.J. Boerman and G. Piatti (1982), Creep crack growth characterization of austenitic stainless steel, in: Advances in Fracture Research, D. Francois, ed., Pergamon Press, Oxford, Vol. 3, p. 1323. Ohji, K., K. Ogura, S. Kubo and S. Katada (1980), The application of modified J-integral to creep crack growth in anstenitic stainless steel and C r - M o - V steel, in: Proc. Int. Conf. on Engineering Aspects of Creep, Sheffield, U.K., Soc. Automot. Eng., Warrendale, Vol. 2, p. 9. Ozmat, B. (1984), Creep crack initiation and growth behavior of AISI 304 stainless steel, ScD Thesis, Dept. Mech. Eng., Massachusetts Institute of Technology. Riedel, H. (1985), A continuum damage approach to creep crack growth, in: Fundamentals of Deformation and Fracture, B.A. Bilby, K.J. Miller, and J.R. Willis, eds., Cambridge Univ. Press, Cambridge, p. 293. Riedel, H. (1987), Fracture at High Temperatures, Springer, Berlin. Riedel, H. and W. Wagner (1985), Creep crack growth in Nimonic 80A and in a 1Cr-1½Mo steel, in: Advances in Fracture Research, S.R. Valluri et al., eds., Pergamon Press, Oxford, Vol. 3, p. 2199. Riedel, H. and V. Detampel (1987), Creep crack growth in ductile, creep-resistant steel, Int. J. Fracture 33, 239. Rice, J.R. and M.A. Johnson (1970), The role of large crack tip geometry changes in plane strain fracture, in: Inelastic Behavior of Solids, M.F. Kanninen et al., eds., McGraw-Hill, New York, p. 641. Sadananda, K. and P. Shahinian (1980), Effect of environment on crack growth behavior in austenitic stainless steels under creep and fatigue conditions, Met. Trans. IlA, 267. Sadananda, K., private communication (1984). Saxena, A. (1980), Evaluation of C* for the characterization of creep-crack-growth behavior in 304 stainless steel, in; Fracture Mechanics, STP-700, ASTM, Philadelphia, p. 131. Stanzl, S.E., A.S. Argon and E.K. Tschegg (1983), Diffusive intergranular cavity growth in creep in tension and torsion, Acta. Metall. 31,833. Taira, S., R. Ohtani and T. Kitamura (1979), Application of J-integral to high temperature crack propagation, Part I Creep crack propagation, J. Eng. Mater. Technol. 101, 154. Tvergaard, V. (1984), On the creep constrained diffusive cavitation of grain boundary facets, J. Mech. Phys. Solids 32, 373. Tvergaard, V. (1985), Effect of grain boundary sliding on creep constrained diffusive cavitation, .L Mech. Phys. Solids 33, 447.
16
B. Ozmat et aL / Cracks in 304 stainless steel
Tvergaard, V. (1986), Analysis of creep crack growth by grain boundary cavitation, Int. J. Fracture 31,183. Wilkinson, D.S. and V. Vitek (1982), The propagation of cracks by cavitation: a general theory, Acta Metall. 30, 1723. Wilkinson, D.S. and S.B. Biner (1988), Creep crack growth simulation under transient stress fields, Metall. Trans. 19A, 829. Yokobori, T. and H. Sakata (1980), Studies on crack growth rate under high temperature creep, fatigue and creep-fatigue interaction - I, Eng. Fract. Mech. 13, 509. Yokobori, T., H. Sakata and A.T. Yokobori Jr. (1980), Studies on crack growth rate under high temperature creep, fatigue and creep-fatigue interaction - II, Eng. Fract. Mech. 13, 523.
type; and h~(a/b, n) the principal numerical result of the evaluation of the deformation field. The values of F(a, b) as well as the tabulated values of hi(a/b, n) are obtainable from Kumar et al. (1981). In the generalization for creep to obtain C* from J, the constitutive relation for non-linear hardening is replaced with its creep constitutive law, i.e. g~ = a g 0 ( o J o 0 ) " = A exp( -
Q/RT)(oe/OO)', (A2)
which gives
Appendix I. Evaluation of C* factors for the CCP, DEN and CT specimens
C*
The generalized reference energy release rate (or energy dissipation rate) factors C* that are considered as driving forces for creep crack growth must be found by numerical techniques for specimen geometries in which the crack takes up a significant portion of the total specimen width. The recommended procedure for this, described by Riedel (1987) utilizes published numerical results obtained by Kumar et al. (1981) for the corresponding rate independent case of the J integral. The evaluation starts with the generic statement of the J integral as
For the specific cases the factors CCP specimens
J = a~oooF(a, b)h,(a/b, n)(oJOo) "+1,
(A1)
where a is the crack length for DEN and CT and the half length for CCP, while b is the specimen width for CT and half width for CCP and DEN geometries (with c = b - a being the uncracked ligament width for CT and half width for CCP and DEN configurations); a%oo and n are the factors characterizing the non-linear strain hardening behavior in the expression ee = OLf.O(Oe/O0) n relating the equivalent strain % to the equivalent stress oe; o. is either the net section tensile stress in the case of the symmetric DEN and CCP specimens, or the nominal bending stress at the crack tip for the CT specimen; F(a, b) a numerical constant, characteristic of the specimen
=Aoo(O,,/Oo) n + l F(a, b)hl(a/b, n) × exp( -
F(a, b)
Q/RT).
(A3)
F(a, b) are:
a ( b b a ) ( ~ - / 2 ) ~+1
(A4)
DEN specimens
b-a F(a, b ) = (0.36b/(b_a) +0.91),+ , .
(A5)
CT specimens
F(a, b)=
b-a {1.455,/[1 + 3(b + a ) / ( b - a)]} "+1' (A6)
where
2a)
---c-+l, c=b-a.
(A7)
(A8)
Using the specific information for material property given in Table 3 and specimen geometries given in Table 4A, together with A = 3.83 × 107 s-1 and Q -= 67 kcal/mol, the following values for h 1 were interpolated from the tables given by
B. Ozmat et al. / Cracks in 304 stainless steel
K u m a r et al. (1981) for the specific specimen types and are CCP-1
h 1 = 2.04
CCP-2
h 1 - 3.32,
DEN-1
h I - 2.28,
DEN-2
h 1 =4.63,
DEN-3
h 1 = 2.754,
CT-1
h 1 - 0.693,
CT-2
h 1 = 0.672.
(plane stress),
17
The above values of h 1 together with the specific evaluation of F ( a , b) lead to the C * values given in the last c o l u m n of Table 4B.
1
Growth modes of cracks in creeping Type 304 stainless steel B. Ozmat 1, A.S. Argon and D.M. Parks Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Received 22 May 1989, revised version received 15 March 1990
The modes of initial growth of cracks in creeping Type 304 stainless steel were studied in the 600-775°C range in plane strain and three different test geometries consisting of center cracked panels, double edge notched bars, and compact tension specimens in both annealed material and in some material with 5% initial cold work. In all cases it was found that in samples with pre-fatigue sharpened cracks the initial growth was branched and on planes at 50 o with the median plane of the crack. In other cases of samples with blunt cracks having machined radii of curvature, initial growth was found to remain in the median plane of the crack. In further growth, however, it was noted that while the direction of the branched cracks became later parallel to the median crack plane, the initially planar cracks showed later evidence of branching. This meandering behavior of cracks is a result of the different nature of crack tip strain concentration for initially sharp and initially blunt cracks. While data were limited, a dependence of the average crack speed on a power function of the C * parameter was found for all cases in which crack growth was intergranular.
I. Introduction The growth of cracks in creeping high temperature components has been of considerable interest in the last decade as a possible means of predicting useful service lives of flawed parts. Largely through the stimulus of some fundamental crack tip deformation field solutions many experimental studies have been undertaken in recent years in prominent creep-resistant alloys to measure rates of creep crack growth and to discover the most meaningful means to characterize these rates with generalized driving forces. Both the crack tip field solutions and a small selection of experimental results have been discussed in detail in a recent monograph by Riedel (1987) which can serve also as a broad introduction into this subject. Parallel to this operational approach have been studies to model the growth of creep cracks by damage accumulation in the crack tip field based either on phenomenological descriptions of such damage (Hayhurst, Brown and Morrison, 1984) or on more
1 Now at Texas Instruments Companyin Dallas, Texas, U.S.A. 0167-6636/91/$03.50 © 1991 - Elsevier Science Publishers B.V.
mechanistic considerations of intergranular fracture by nucleation and growth of cavities (Wilkinson and Vitek, 1982; Wilkinson and Biner, 1988; Bassani, 1981; Tvergaard, 1984, 1985, 1986; Riedel, 1985; Hawk and Bassani, 1986). While many of the experimental studies have limited their attention to finding only a suitable correlation between crack growth rate and crack tip driving forces such as K, J, or C*, a few (Manjoine, 1963; Davis and Manjoine, 1953; Leckie and Hayhurst, 1974; Argon et al., 1985) have noted important complications in initiation of crack growth and in non-planar propagation of such cracks over substantial distances, resulting in long transients and posing fundamental questions on both the nature of creep damage and the specific factors that control its ripening. These points have so far been inadequately investigated, particularly in more ductile alloys where questions of whether creep crack growth or quasi-homogeneous damage considerations should govern creep life have largely gone unanswered. Here in the first of several related studies we present the results of an experimental investigation on the modes of creep crack growth in Type
2
B. Ozmat et al. / Cracks in 304 stainless steel
304 stainless steel - a prominent ductile solid solution alloy for which the mechanisms of intergranular cavitation had been investigated by Chen and Argon (1981) earlier in considerable detail. While the stress levels in the present investigation are relatively high they have in the large majority of cases produced fracture by intergranular processes.
2. Effects of ductility and initial crack shape on early crack growth Although all creep fractures in polycrystalline metals tend to be intergranular and develop by nucleation and growth of cavities, the early modes of growth of pre-existing cracks can take a number of different paths depending upon the creep ductility of the alloy and the nature of strain concentration around the crack tip. The problem has a close parallel to the growth of cracks in parts undergoing transgranular ductile fracture by nucleation and growth of cavities by plastic flow, as has been discussed by Rice and Johnson (1970). The following are some of the more noteworthy investigations of this phenomenon. Manjoine (1963) conducted creep rupture tests on T head specimens prepared to simulate the loading of turbine rotor groove walls by turbine blades. Conventional tests were performed on C r M o - V rotor steel with differing creep strengths obtained from different heat treatments. Steel A, with a high deformation resistance, showed 2.3% uniaxial elongation at fracture when tested at 538°C with 282 MPa initial stress. Steel B, with a lower deformation resistance, was more ductile, and showed 14% elongation at fracture under the same uniaxial creep fracture conditions. While both specimens failed at comparable times ( -- 1500 h), the T head tests of these two materials showed very different fracture patterns. Crack initiation and early propagation of the ductile steel B involved shear modes of growth which followed along planes of maximum effective stress. In comparison those of steel A propagated along planes of maximum tensile stress. Earlier, Davis and Manjoine (1953) also reported widely differing fracture profiles for creep fracture in tests on 60 °
V-notched specimens of material with differing creep ductilities. For alloys showing low ductility (the refractory alloy 2G), the cracks started near the base of the notch and propagated normal to the axis of the specimen and along the median plane of the notch. However, for the very ductile alloy (12Cr, 3W steel) fracture started at the root of the notch and the crack propagated inward at an angle of about 45 ° to the specimen axis. Gooch (1977) has reported dramatic changes in the creep crack appearance of a 0.5Cr, 0.SMo, 0.25V steel. Cracks in specimens having higher creep resistance and low ductility followed a fracture path that was in the plane of the original spark cut notch with 0.25 mm root radius and 1.5 mm length (aspect ratio of 6). However, the specimens with low creep resistance but larger ductility showed large scale notch root blunting and an initially straight mode of crack growth for about 1 mm, followed by crack extension at an approximately 50 ° angle to the initial crack plane which later formed a leg directed back toward the plane of the original notch. Gooch, King and Briers (1977) also reported similar changes in the fracture appearance of creep cracks in a 2 . 5 C r - l M o weld metal steel upon a matrix softening treatment. Specimens with a Vickers hardness of 187 showed large crack tip opening displacements associated with a 0.5 mm long straight crack advance from the initially spark cut notch of aspect ratio of 26, followed by creep crack growth at a 50 ° angle to the original crack plane. Cracking behavior of the specimens with Vickers hardness values at or above 220 was in the original notch plane. Similar effects of the initial crack starter geometry on the fracture paths of creep cracks were also reported by Hayhurst et al. (1978). In their creep fracture experiments on circumferentially notched circular tension bars of A1 and Cu, two different notch profiles were studied: (a) a circular, so-called Bridgman notch (BN); and (b) a British Standard notch (BSN). Root radius to minimum diameter ratios were 0.67 and 0.055 for the BN and BSN geometries, on the same size bar with maximum to minimum diameter ratios being 1.67 and 1.41 for BN and BSN, respectively. These two specimen geometries were found to have dis-
B. Ozmat et al. / Cracks in 304 stainless steel
tinctly different stationary state stress fields. In the BN the maximum principal tensile stress and effective stress were both in the minimum cross section. While in the BSN the maximum principal stress was in the minimum cross section, the maximum effective stress was at an angle of 50 o to the notch plane. For the BN geometry, fracture processes were confined to the minimum cross section of the notch, whereas in the BSN geometry fracture processes were not similarly confined but were on inclined planes of about 50 o. This was most apparent in the A1 specimens where the fracture criterion depends more strongly on the effective stress, as had been noted first by Johnson and Henderson (1962). In their most recent study, Hayhurst et al. (Hayhurst, Dimmer and Morrison, 1984) reported that in creep tests of Cu and A1 alloy specimens with sharp internally and externally cracked geometries, creep cracks grew on a 40 ° plane and a 55 ° plane with respect to the initial crack, for the cases of Cu and A1, respectively. Thus, in summary we note that in the growth of creep cracks starting from initial grooves, notches, or sharp pre-fatigued cracks there are important transient phases involving non-planar crack growth, particularly in more ductile alloys, consuming substantial fractions of a growth stage that might potentially govern the total life of the part. Before we present the full range of our experimental findings in Type 304 stainless steel, we review briefly in Section 3 below the earlier relevant experimental findings of others on this same material.
3. Earlier creep crack growth experiments on Type 304 stainless steel Type 304 stainless steel which was chosen here for reasons of its simple structure and because of our earlier study of the mechanisms of intergranular fracture in this material (Chen and Argon, 1981), has also been investigated extensively by others in various different experimental geometries. Koterazawa and Iwata (1976) conducted tests in air at 655°C on double-edge-notched plate
3
(DENP) and on round-notched bars (RNB) with root radius to notch depth ratios of 0.05 and 0.085 for D E N P and RNB, respectively. Their crack growth rates ranged over four orders of magnitude starting from a low value of 3 x 10-x0 m / s , and appeared to correlate well with K, the Mode I stress intensity factor. Some microscopy observations established the intergranular nature of the crack growth. Koterazawa and Mori (1977) reported on creep crack growth tests in air at 650°C on doubleedge-notched (DENP), center-cracked (CCP) and single-edge-notched (SENP) thin ( t = l . 5 mm) plate specimens. The crack forming defects were simulated with finite root radius notches. The range of experimental crack growth rates were the same as above, and propagation occurred intergranularly, which was supported by microscopy in a D E N P specimen. The authors compared creep crack growth rate results from tests obtained on the different test geometries mentioned above, and showed that C* offers the best means of correlating the experimental measurements, within an order of magnitude of a scatter band. Taira et al. (1979) also conducted creep crack propagation tests at 650°C in air and in a moderate vacuum (1 Torr). A thin (2.3 mm) center cracked plate (CCP) specimen was employed. Two specimens were fatigue pre-cracked. It was observed that the crack growth mode switched to transgranular when the applied nominal stress levels were 176 MPa and higher. The range of intergranular crack growth rates were similar to those of Koterazawa and coworkers (1976, 1977) but were higher in the transgranular mode (3 × 10 -8 to 3 x 10 -6 m / s ) . The crack growth rates correlated best with C * both in air and in vacuum. Yokobori and Sakata's (Yokobori and Sakata, 1979; Yokobori, Sakata and Yokobori, 1979) creep crack growth tests were conducted in the temperature range between 600 and 700°C and in vacuum (10 -5 Tort) on thin (1 mm) specimens of D E N P geometry. The crack growth rates varied over five orders of magnitude from a low of 3 x 10 -11 m / s . The authors noted that growth of cracks begins when the crack tip strains reach a critical value independent of temperature and stress level, obeying a local M o n k m a n - G r a n t criterion, and that
4
B. Ozmat et aL / Cracks in 304 stainless steel
subsequent growth rate could be correlated with gl.
Sadananda and Shahinian (1980) measured creep crack growth rates in 304 stainless steel in a 20% cold worked condition at 593°C in vacuum (10 -6 Torr) and in air. Compact tension (CT) specimens with the crack plane lying parallel to the rolling direction, and center-cracked plate (CCP) specimens with side grooves and pre-fatigue sharpened cracks were used. Crack extension
was intergranular in both vacuum and in air, and crack growth rates ranged from 3 × 10 -8 to 3 × 10- 6 m//s" On the basis of an observed K correlation of crack growth rates the authors concluded that cold work enhances crack growth rates and that environmental effects are not pronounced. The growth of cracks, however, was not planar (Sadananda, 1984). In a separate study, Koterazawa and Mori (1980) also reported on creep crack growth rates
Table 1 Details of creep crack growth measurements in other investigations on Type 304 stainless steel Environment
Crack vel. range ( m / s )
Mechanism of crack advance, and mode
Best correlation
655
air
3 x 10 - 1o_ 3×10 -6
Intergranular
K
rounded notch
650
air
(same)
Intergranular
C*
CCP
cut planar crack; prefatigued
650
air and vacuum 1 Tort
(same)
Intergranular, Transgranular at high stress
C*
Yokoboi and Sakata (1980); Yokobori et al. (1980)
DENP
cut cracks
600-700
vacuum 10 -5 Tort
3 x 10 - 11_ 3 × 1 0 -6
Intergranular
K
Sadananda, and Shahinian (1980); Sadananda (1984)
20%cold work CT
cut cracks with side grooves, prefatigued
593
air and vacuum 1 0 - 6 Torr
3 × 10-s_ 3 x 10- 6
Intergranular, branched crack growth
K
Koterazawa and Moil (1980)
DENP CCP
500-700
air
(same)
?
C*
Ohji et al (1980)
CCP RNB CT
cut cracks with rounded root radii
650
air
3x10 -113 x l O -6
?
C*
Saxena (1980)
CCP CT
cut cracks, pre-fatigued
538-705
air
10-9-10 -7
?
C*
Musicco et al. (1982)
CT
cut cracks
550
dry argon
(same)
?
C*
Krompholz et al. (1982)
CT
cut cracks, pre-fatigued
550-750
air
10-11-1(} - 7
heavy oxidation branched crack growth
C*
Authors (References)
Spec. Type a)
Starter crack type
Koterazawa and Iwata (1976)
DENP RNB
60 o round notch
Koterazawa and Mori (1977)
DENP CCP SENP
Taira et al. (1979)
Temperature range
(°c)
a) CCP, center-cracked panels; CT, compact tension; DENP, double-edge-notched panel; RNB, round-notched bar; SENP, single-edge-notched plate.
B. Ozmat et al. / Cracks in 304 stainless steel
in the 550-700°C temperature range with several annealed DENP specimens and CCP specimens of different sizes with similar geometry. All crack growth was intergranular, and the best correlation of crack growth rates was with the C* parameter. Ohji et al. (1980) performed their crack growth experiments on Japanese SUS 304 SS at 650°C in air on CCP, RNB, and CT specimens. In all of these test specimens, machine-cut notches with finite root radii were employed to initiate the creep cracks. They investigated the specimen geometry, size, relative crack depth, and different load level effects on the creep crack growth rates by means of a single parameter correlation, and concluded that regardless of specimen size and geometry, creep crack growth rates correlate well with a modified C* integral. Their data for d a / d t was nearly linearly dependent on C * Saxena (1980) reported on constant imposed displacement rate creep crack growth tests performed in the 538°C to 705°C range on annealed 304 SS using CCP and CT specimen geometries. All specimens contained fatigue pre-cracks of approximately 2.5 mm. Under imposed displacement rates ranging from 0.025 to 0.3 mm/h, crack growth rates were found to be in the 10 -9 to 10 -7 m / s range. The basic conclusion was that C* provides a good characterization of creep crack growth rates in the CCP and CT geometries. Saxena also compared his results with those of Begley (1980) on creep crack growth in annealed standard CT1 specimens in the same temperature range, and showed that both sets of data fell into the same scatter band, concluding that there is no significant further temperature effect on crack growth in the C* growth regime. Very similar conclusions were reached also by Musicco et al. (1982) on tests on annealed 304 L stainless steel at 550°C in an inert argon environment under constant displacement rate conditions on 15 mm thick CT specimens. Krompholz et al. (1982) performed creep crack growth rate measurements on 18Cr l l N i German austenitic stainless steel (DIN 1.4948, which is very similar to Type 304) in air under constant load conditions, in the 550-750°C range on fatigue pre-cracked CT specimens. The authors observed that in their experirnents in air heavy
5
oxidation occurred at the fracture surfaces, as well as considerable blunting at the fatigue to creep crack transition line followed by out of plane branched crack extension. They nevertheless concluded that C* is a better parameter for overall correlation of creep crack growth rates than K or net section stress. The important aspects of these observations are summarized in Table 1. They indicate that most investigators have found that the overall creep crack growth rate could be correlated better with a C* parameter than with K or net section stress. While microscopic observations on the mode and mechanism of crack growth were not always reported, it can be concluded that most growth was intergranular, and showed significant early crack branching particularly in the plane strain CT-type specimen geometries. In the absence of specific reports we conclude that apparent planar growth was found only in the very thin samples which most probably had plane stress deformation characteristics, and those with deep side grooves.
4. Experimental details and results 4.1. Material and specimen preparation
The Type 304 stainless steel was received in the form of hot rolled, annealed, pickled bars or plates. The material was solution treated at 1050°C for 45 min and quenched. After quenching, the specimens were machined to the final dimensions in the solutionized condition. For the preparation of cold worked specimens, a uniform uniaxial plastic tensile elongation was imposed on the material at room temperature by stretching before machining. Notches were introduced by the use of either an electrical discharge machine (EDM) for the center-cracked panel (CCP) specimens, or by a circular saw on a milling machine for double-edge notched (DENP) and compact tension (CT) specimens. Fatigue pre-cracking at room temperature was done on some specimens using a computer controlled MTS machine imposing a final cyclic stress intensity factor of AK = 13 MPa, m 1/2 at an R ratio of 0.1. Prior to the application of the test load, specimens were sensitized at 800°C for
6
B. Ozrnat et al. / Cracks in 304 stainless steel
Table 2 Temperature dependence of Young's modulus and yield strength of Type 304 stainless steel Temperature ( o C)
Young's modulus (GPA)
0.2% Yield strength (MPa)
25 600 700 750
197 160 140 138
260 (382 a)) 112 100 90 (132 a)) b)
a) 5% cold worked at room temperature. b) Calculated on the basis of a strain hardening exponent of 0.12.
48 h under high vacuum in the test chamber. The heat treatment process described above yields a well defined family of grain boundary carbides with an average spacing and size of 6 ~tm and 0.4 ~m respectively (Chen and Argon, 1981). Following the heat treatment the average grain size was 60 ~m. The temperature dependence of the 0.2% offset yield strength and elastic modulus of the 304 SS are given in Table 2. Due to its austenitic nature, 304 SS is not heat treatable, and increased strength can only be obtained by cold working. Because of its high strain hardening rate (strain hardening exponent = 0.12), however, substantial elevation of flow stress is achievable with relatively small area reduction. The steady state equivalent creep rate for the Type 304 alloy in an annealed state can be given by the following power-law relationship:
Table 3 Creep rate properties of Type 304 stainless steel determined from data of Blackburn (1972) Temp. (°C)
n
o0 (MPa)
State
600 650 700 750 750
6.72 6.80 6.88 7.19 7.19
129 114 102 91 132 a)
Annealed Annealed Annealed Annealed cold work
a) Calculated on the basis of o0 being the reference deformation resistance of the material in a rapid tension test (Argon and Bhattacharya, 1987).
where
oe is the equivalent tensile stress, o0 a reference tensile deformation resistance and R and T have their usual meaning. According to the most complete data of Blackburn (1972), A = 3.83 × 107 s-1, Q = 67 kcal/mol, and n and o0 are slightly temperature dependent, with a relevant set of values given in Table 3 (these values have been calculated from the best fit functional forms given by Blackburn to fit the power law form given in Eq. (1)).
4.2. Experimental details In all cases crack propagation experiments were carried out in a constant load maintaining modified screw driven testing machine, equipped with a vacuum chamber, maintaining a pressure in the 10 6-10-5 Torr range at test temperature. Test temperatures were achieved by induction heating through specially fashioned water-cooled power coils surrounding the specimens. Through proper design of these coils temperatures in the specimens in the regions of expected crack growth were kept constant within a few degrees of the desired temperature by means of a feed-back control system. In each case this was verified by measuring the temperature distribution with a set of thermocouples in a control experiment. Crack length was measured by the potential drop method intermittently when the radio frequency power was momentarily turned off. Absolute calibration of the potential drop measurements with crack length was accomplished by determining the final crack length in the specimens, by metallographic sectioning after the experiment was over. The full details of the unconventional experimental set up which could accommodate all the different test configurations for which results are described below can be found elsewhere (Ozmat, 1984).
4.3. Experimental results In the course of the experimental study to measure intergranular creep crack growth in 304
B. Ozmat et a L / Cracks in 304 stainless steel
7
Table 4A Geometrical details of CCP, DEN and CT specimens Test Spec. Type & Number
Half width, b (mm)
Initial crack length, a (mm)
CCP-1 CCP-2 DEN-1 DEN-2 b) DEN-3 CT-1 CT-2 b)
25.4 25.4 6.5 13.8 25.4 113 97.6
10.4 6.0 3.2 9.0 14.3 61.0 47.0
Initial crack tip radius (mm)
Specimen thickness (mm)
Test temp. ( o C)
Yield strength (MPa)
a)
6.35 6.35 51.0 51.0 12.5 28.0 16.5 c)
600 700 750 750 775 750 750
112 100 90 132 85 90 132
a)
a) a) 0.2 1.15 1.15
a) Fatigue precracked Aa =1 mm at AK =13 M P a - m 1/2. b) With 5% cold work. c) Thickness at bottom of side grooves.
stainless steel three different specimen configurations consisting of center-cracked panels (CCP), d o u b l e - e d g e - n o t c h e d bars ( D E N ) , a n d c o m p a c t t e n s i o n (CT) geometries were used. All specimens were of sufficient thickness to be well i n the p l a n e strain d e f o r m a t i o n regime. Achieving this often required some trial a n d error approach. W i t h i n the experimental range of temperature a n d stress, chosen to retain a stable microstructure, a n d a n i n t e r g r a n u l a r m o d e of crack growth, m a j o r transients were observed in the growth m o d e of cracks in all specimens. This did n o t permit u n a m b i g u o u s m e a s u r e m e n t of crack speed in a satisfactory selfsimilar growth m o d e that would be correlated with a n y generalized crack tip driving force. Therefore,
below we limit our p r e s e n t a t i o n primarily to the description of these initial growth transients in a selection of CCP, D E N , a n d C T specimens, chosen to d e m o n s t r a t e certain special features of the various t r a n s i e n t growths. F o r the record, to aid in discussion, however, calculated C * factors a n d overall average crack speeds are also given, where the latter represents the total final i n c r e m e n t a l crack extension (in the actual growth direction) divided b y the total time of the experiment. The m e t h o d of d e t e r m i n a t i o n of the a p p r o p r i a t e C * values is discussed in A p p e n d i x I. The d i m e n s i o n s a n d test details of the two CCP, the three D E N , a n d the two C T specimens are given i n Tables 4A a n d 4B.
Table 4B Crack extension results in CCP, DEN and CT specimens Test Spec. Type & Number
Nominal Stress a) (MPa)
At, test duration (s)
Crack tip opening (ram)
Aa, creep crack incr. (mm)
Aa / A t
C*
(m/s)
( J / / m 2 S)
CCP-1 b) CCP-2 DEN-1 DEN-2 c) DEN-3 CT-1 CT-2 c)
170 100 90 90 80 104 151
2.16 × 105 2.88 × 105 5.40 x 105 3.96 × 106 5.04 X 105 5.58 X 106 1.37 × 105
1.97 1.07 0.75 0.60 1.70 2.40 1.20
1.43
6.62 × 10- 9 4.86 × 10 - 9 2.96 X 10 - 9 2.93 X 10 - lO 6.75 × 10-9 9.44 X 10- l o 7.16 x 10- s
9.21 X 10- 3
1.40
1.60 1.16 3.40 5.27
9.80
a) Net section tensile stress or nominal total crack tip stress for CT specimens. b) Plane stress. c) With 5% cold work.
1.42 X 10 - 2
2.24 X 10- 3 1.54 × 10- 3 6.47 × 10- 3 1.81 X 10- 3
2.21 × 10- 3
8
B. Ozmat et al. / Cracks in 304 stainless steel
In both the CCP-1 and CCP-2 specimens unsymmetrical branched crack growth was observed at the end of 60 and 80 h respectively. As Tables 4A and 4B indicate, the net section stress in CCP-1 was considerably above the short term yield strength of the material at the test temperature. Hence in this case very considerable crack tip plastic deformation occurred, affirmed by the large crack tip opening displacement. Clearly, in this case the crack tip conditions were characteristic of large scale plastic blunting before eventual stress relaxation and possible intergranular crack extension may have occurred. The net section stress in CCP-2 was equal to the short term yield strength of the material, and therefore closer to creep conditions. In both cases, however, microscopy established that the creep crack growth was by intergranular fracture. Moreover, in both of these cases where the starting crack had been sharpened by fatigue pre-cracking, the initial transient creep crack extension was on a slanted plane making an angle of about 55 ° with the median plane of the fatigue pre-crack. Figure 1 shows this unsymmetrical creep crack extension in CCP-2, which is typical for both of these specimens. As is well known (McMeeking and Parks, 1979) the region of dominance of the non-linear singular field of J or C * is very restricted for CCP specimens in which the initial crack length is a substantial fraction of the specimen width. For this rea-
Fig. 1. Branching of the initially sharp crack in the CCP-2 specimen, revealed on an internal polished section.
Fig. 2. Branched crack in polished and lightly etched mid section of DEN-1 specimen.
son experiments were also carried out with DEN specimen configurations. Of these specimens, DEN-1 and DEN-2 were fatigue pre-cracked and tested at 750°C at net section stresses of 90 MPa. While DEN-1 was in annealed form the material for DEN-2 was given a plastic pre-strain of 5% at room temperature, prior to machining the notch, normal to the direction of extension. As reported by Gold et al. (1975) such cold work imparted at room temperature is stable in the test range of 750°C for as long as 8000 h. For the DEN-1 specimen the net section stress of 90 MPa was again equal to the short term yield strength. Because of the higher deformation constraint in the crack tip field of a DEN geometry the crack opening displacement was substantially less than the CCP case, as was the average crack velocity. Figure 2 shows the initial crack extension response in DEN-1 as a well developed case of crack branching and growth over substantial distances on slanted planes making angles of about 45-55 °
B. Ozmat et al. / Cracks in 304 stainless steel
with the plane of the initial fatigue pre-crack. The figure which shows a lightly etched central section through the crack front illustrates dearly the diffuse nature of intergranular cracking that surrounds the crack tip region and results in overall growth of the macro creep crack. In the DEN-2 specimen the net section stress of 90 MPa corresponded only to 68% of the short term yield stress. Therefore, the average crack velocity was an order of magnitude smaller than for DEN-1. Figure 3 shows that the initial crack growth behavior was identical to that in DEN-1 with substantial growth on slanted planes at 55 ° However, the figure also shows that there is here a final tendency of the slanted cracks to turn around and propagate parallel to the plane of the initial fatigue pre-crack. The DEN-3 specimen was provided with a machine cut notch with a finite radius of curvature of 0.2 mm instead of a fatigue pre-crack. The test was carried out at 775°C and at a net section stress of 80 MPa which was 94% of the short term yield stress at the test temperature. The growth of this crack showed an interesting dividing-line behavior. As Fig. 4 shows crack extension started in
Fig. 3. Polished mid section region of DEN-2 specimen showing initial branching of a crack followed by changing of path to become parallel to initial crack plane.
9
Fig. 4. Polished mid section of DEN-3 specimen showing meandering feathery crack emanating from the rounded crack tip region.
a diffuse way roughly in the median plane of the initial rounded notch. In its propagation, however, it showed a repeated tendency to deviate for short stretches from this plane toward either side, resulting in an overall feathery appearance. The repeated attempts of departure of the crack from its plane, in the nature of zones of diffuse intergranular damage is shown better at a larger magnification in Fig. 5. The view at even larger magnification in Fig. 6 shows in much greater detail the surrounding intergranular damage in the form of a high density of grain boundary facet cracks. In the hope of obtaining longer stretches of self-similar crack growth, experiments were also carried out with two compact tension (CT) specimens. The dimensions of these specimens CT-1 and CT-2 are also given in Tables 4A and 4B. The crack tips in both of these specimens were rounded to a radius of 1.15 mm. While the material of CT-1 was in annealed form, that of CT-2 was given a 5 % extension at room temperature parallel to the plane of the crack. Both creep experiments
10
B. Ozmat et al. //Cracks in 304 stainless steel
Fig. 5. Polished and lightly etched mid section of DEN-3 specimen showing at intermediate magnification region near the crack tip.
Fig. 6. Higher magnification view of same crack tip region shown in Fig. 5. The light etching delineates clearly the grain boundaries and the many grain boundary facet cracks.
were carried out at 750°C. Figure 7 shows the creep crack in CT-1 as revealed on a longitudinal polished section after the test. The intergranular crack initially propagated for 1 mm roughly along the median plane of the initial machine crack, but then formed two branches making about 50 o with the median plane. One of these branch cracks subsequently changed direction again back toward the median plane, after propagating a length of 1 mm.
The CT-2 specimen was subjected initially to a nominal crack tip stress of 130 MPa which after 220 h produced no crack growth. The crack tip nominal stress was then raised to 151 MPa which resulted in a growth of 9.8 mm in 38 h. Examination of this crack after the test showed, however, that it propagated transgranularly and in a rather brittle appearance as shown in Fig. 8. From these tests we conclude the following: (1) Regardless of specimen geometry, temperature, and cold work, intergranular creep cracks initiating from sharp pre-fatigued cracks follow a
Fig. 7. Polished mid section of crack tip in CT-1 specimer showing an initially straight crack branch in further growth.
B. Ozmat et al. / Cracks in 304 stainless steel
Fig. 8. Polished mid section of crack tip in CT-2 specimen showing the relatively straight transgranular crack.
long initial transient during which growth is along 50 o with the initial median plane. (2) Regardless of specimen geometry and testing conditions, intergranular cracks initiating from notches with notch tip radius to notch depth ratio exceeding 0.01 first followed a straight course and then often also branched. (3) Branched cracking during creep represents an initial transient response of sharp cracks in an intergranular mode of propagation under Mode I conditions. Based on the limited set of observations, however, the long term tendency for the branched cracks is to return to a plane parallel to the median plane - perhaps to branch again later, and so on.
5. Discussion
5.1. The crack path Creep fracture in ductile polycrystalline alloys such as Type 304 stainless steel, is intergranular under typical service conditions. The rate of intergranular cavity growth that governs the early stages of such fracture is usually constrained by creep deformation in the surrounding grain matrix for typical service stresses. Then, fracture is ultimately governed by a local critical strain criterion. At high stresses nearing yield the intergranular cavi-
11
tation process is not completely constrained by creep flow but the cavity nucleation is still governed by a local critical strain criterion. In these aspects intergranular creep fracture has much in common with ductile fracture by the growth and coalescence of cavities, occurring below the diffusive creep regime. It was recognized first by Rice and Johnson (1970) that a fracture criterion based on a local critical strain is difficult to satisfy at the tip of a sharp crack in elastic-plastic fracture where the concentration of equivalent plastic strain does not occur ahead of the crack. Such concentration of strain only becomes possible when significant crack tip blunting transfers it from the slanted planes at 50 ° for the sharp crack (Bassani and McClintock, 1981), into the region ahead of the crack or when the crack starts out with a certain initial radius of curvature. This trend is shown clearly in a finite element study of the creep deformation field around a blunting crack with a high but finite initial sharpness, reported by Argon et al. (1985) (and to be published in more detail elsewhere by Lau, Parks and Argon). In that study a DEN bar, responding only in power-law creep characteristic of Type 304 stainless steel, with an initial a/b = 0.5 and a crack tip radius to uncracked ligament ratio R / c = 3.4 x 10-3, was deformed monotonically until this ratio reached 2.51 × 10 -2. Figure 9, reproduced from that study, shows clearly the moving outward of the cross-over point where the accumulated equivalent creep strain ahead of the crack exceeds that along the inclined plane making an angle of 43 ° with the crack plane. In the initial infinitely sharp creep crack field the equivalent strain rate concentration along the 50 ° plane exceeds that ahead of the crack by more than an order of magnitude (Bassani and McClintock, 1981). Clearly, then, for a crack with an initial sharpness between the pre-fatigued crack and that for which results are given in Fig. 9, the spread of damage will just favor a forward initial growth direction. As our experimental study presented above amply demonstrates, however, the process of long term crack growth is more complex than the presence or absence of an initial favorable condition for forward growth. As Fig. 3 for the DEN-2 specimen with the fatigue sharpened pre-crack
12
B. Ozmat et aL / Cracks in 304 stainless steel
3.2 I I I
I
I
II
2.8--
I
I
1.6" 43*
~__l
II
I
( cR_)I=6.6 4
-
X 10 -3
I
~.~
2, -
t
2.0--
L
(91; ~
1.34 x 10-2
-
3
1.6 --
o.
; " ."..
0
4
8
12 r/c
16
20xlO -3
Fig. 9. Computed distribution of total creep strain around the crack tip undergoing blunting by creep flow for three states of crack opening (from Argon et al. (1985), courtesy of Cambridge University Press).
shows, after an initial response of crack growth along the slanted 50 ° planes, the crack shifts back to a plane parallel to the median plane. The converse effect is shown in Fig. 7 for the CT-1 specimen and in Fig. 5 for the DEN-3 specimens. In both cases an initial finite crack-tip radius of curvature tends to concentrate the initial creep damage process into the region ahead of the crack. However, in both cases the relatively sharp creep crack has a further tendency to spur damage away from the median plane. Since in the latter case the apparent sharp creep crack is surrounded with a deformation and damage field characteristic of the initially blunt crack, the deviation of growth away from the median plane cannot be entirely for the same reason as that for the initially sharp crack in an uncrept sample. Clearly, these two tendencies of branching of the initially sharp crack, and the roughly planar growth in the initially blunted crack, recur during the further extension of creep
cracks in ductile alloys with substantial levels of local strain to fracture (relatively large Monkman-Grant (1956) products of minimum creep rate and time to fracture). This meandering behavior of the crack should result in lower overall growth rates. Two important points need to be noted about these growth transients and the meanderings of creep cracks. First, as should be clear from Figs. 5 and 6, the wave lengths of the meanderings of the cracks have little to do with grain size which is on a scale more than an order of magnitude smaller. In fact the size of a grain boundary facet crack which is the principal element of damage is small enough for adequate smoothing to consider quasi-homogeneous damage models for crack growth, as we discuss in a companion study (Hsia, Argon and Parks, 1991). Second, the level of critical strain for local creep fracture must be an important parameter governing the meandering of the crack. Thus, if continuing crack tip blunting can shift the concentration of total strain away from the inclined zones to the front of the crack before a local intergranular separation condition can be met, fracture will not occur along the zones of initial strain concentration. A critical level of accumulated creep strain is a fracture criterion associated with constrained intergranular cavity growth which is characteristic of Type 304 stainless steel having a large variability of carbide coverage of grain boundaries (Argon et al., 1985; Chen and Argon, 1981). In certain other alloys such as Nimonic 80A (Dyson and McLean, 1977) and Astroloy (Capano et al., 1989), where all grain boundaries have a similar level of carbide coverage, or in the model materials of Ag and Cu with pre-cavitated grain boundaries, studied by some investigators (Capano et al., 1989; Goods and Nix, 1978; Stanzl et al., 1983) cavity growth must be unconstrained. In such materials local fracture is more dependent on the level of maximum principal tensile stress and is less likely to be governed by a critical strain criterion. This should favor planar crack growth since the maximum principal tensile stress is concentrated ahead of the crack for both sharp (Hsia et al., 1991) and blunt cracks, and where deformation induced further blunting does not alter the balance (Ar~on et
13
B. Ozmat et aL / Cracks in 304 stainless steel
al., 1985). In more realistic situations of creep fracture in the presence of oxidizing environments, where such effects hasten local fracture, a similar situation may govern. It is important to note here that some authors who have reported on the growth of creep cracks in relatively ductile alloys such as 1Cr-0.5Mo steel (Riedel and Wagner, 1985), 0.5Cr, 0.SMo, 0.25V steel and 2.25Cr, 1Mo steel (Riedel and Detampel, 1987), have achieved planar growth only through the use of deep side grooves (25% reduction of cross sectional area). Clearly, such practice, even if neutral 'in affecting the nature of creep damage, must accelerate crack growth by not permitting the development of the natural meandering of the creep cracks which we have discussed here. The different initial growth responses of creep cracks are consistent with the ripening of intergranular creep damage in the different deformation fields of sharp and blunt cracks. This has been discussed briefly by us earlier on the basis of a mechanistic damage model (Argon et al., 1985). A somewhat more expanded treatment of this in a non-interactive form was developed by Ozmat (1984) which, however, will not be presented here. A fully interactive damage model explaining the early meandering of creep cracks with different initial conditions, in Type 304 stainless steel and other related alloys is presented in a companion paper (Hsia et al., 1991). 5.2. The crack growth rate
K?(1 - p2)/E (n+l)C* '
i0 -7
'
I
I
0 CT-2 o-t
E
/
.0
As stated earlier, in these experiments it was not possible, with reasonable effort, to obtain substantial ranges of self-similar crack growth in nearly steady state conditions. Nevertheless, the measured growths over the total times under stress were considered as average crack speed and were examined to determine the possible conditions for their growth. Since in nearly all cases net section stresses were quite high, bordering on the short term yield strengths of the alloy, only a possible correlation with C* was sought. This correlation was also the natural choice since in all cases the creep relaxation time t r, tr=
was much less than the total time for crack growth. The appropriate levels of applied C* parameters for the CCP, DEN and CT specimens were calculated according to the procedure prescribed by Riedel (1987), utilizing the published dimensionless h 1 factors calculated for J-controlled fracture (Kumar et al., 1981) for the appropriate specimen geometries. Details of this computation are given in Appendix I. These calculated C* values for the creep properties of 304 stainless steel as determined from the data of Blackburn (1972), and summarized in Table 3 are listed in Table 4B, together with the average crack speeds. In all cases except CT-2 the crack growth was intergranular. In the latter with a pre-strain induced built-in anisotropy of aligned inclusions cracking was transgranular and resulted in a much higher average growth speed. All the calculated average crack velocities are shown plotted against their corresponding C* factors in Fig. 10. Discarding the transgranular crack growth case of the CT-2 specimen, there is a general upward trend apparent in the data and delineated by the best-fit straight line. The slope of this line is 1.06, which is somewhat larger than the expected slope of n / ( n + 1)
(3)
o
/
10-8
<1
DEN-3 o o ~ C C p_ I
/ DEN-I
o
O3
o CCP-2
/
/ 0
CT-I
10-9
7 / /
DEN-2 0
/ ,¢o! l0 - 4
/
,
J 10-3
,
I 10-2
C~ , J / m 2 x s
Fig. 10. Dependence of average crack speed A a / A t on the prevailing C* around the crack tip for the three different specimen geometries investigated.
14
B. Ozmat et al. / Cracks in 304 stainless steel
( = 0.873) of a well established steady state C* controlled crack growth process predicted by theory (Riedel, 1987), and observed to be so in a number of well documented cases (Riedel, 1987; Riedel and Wagner, 1985; Riedel and Detampel, 1987). Considering the very large variations in crack plane the fact that the data is obtained from growth at several different temperatures where the exponents n are different, and the very limited extent of the data, the lack of agreement is not surprising. Clearly, a further contributory factor to the different slope can be the presence of a substantial incubation time in crack growth, particularly in the low C* ranges. Finally, while the stress levels in the experiments reported here have been high, bordering on the yield strength of the alloy, with the exception of the CT-2 specimen, all fractures have been intergranular showing all the characteristics of this fracture mode on the fracture surfaces. Therefore, the phenomena reported here are considered as a limiting form of fracture in fully developed creep fields, supported by the correlation of crack growth obeying a C* criterion. However, from the point of view of external appearances it is also possible to interpret the observations as a limiting form of hot ductile fracture since the C* correlation is basically based on the reinterpretation of a J correlation. Because of the intergranular mode of crack growth we prefer to consider it as a limiting form of creep fracture.
6. Conclusions In ductile alloys such as Type 304 stainless steel obeying a local constant critical strain criterion for crack advance, substantial crack plane meandering is observed. Initial growth of pre-fatigued, sharp cracks occurs on planes making 50 o with the median plane of the initial crack. Initial growth of cracks with a finite radius of curvature (exceeding a critical, and presently undetermined amount) is in the median plane of the crack. In further growth, while the initially branched cracks at 50 o planes have been observed to change
their paths later to becoming parallel to the median plane, the converse was found to be the case for planar crack growth emanating from initially blunted cracks, which showed evidence for later branching. While insufficient data were available to determine the crack growth law, a correlation of average crack speed with C* was found, with an exponent considerably larger than the expected value of n / ( n + 1).
Acknowledgement This research had been supported earlier during the period of 1980-1984 by the U.S. Department of Energy under Contract No. DE-AC0277ER04461. We acknowledge also many useful discussions with Professor F.A. McClintock and Professor C:W. Lau (now at Drexel University).
References Argon, A.S. and A.K. Bhattacharya (1987), Primary creep in nickel: experiments and theory, Acta Metall. 35, 1499. Argon, A.S., C.W. Lau, B. Ozmat and D.M. Parks (1985), Creep crack growth in ductile alloys, in: Fundamentals of Deformation and Fracture, B.A. Bilby, K.J. Miller and J.R. Willis, eds. Cambridge Univ. Press, Cambridge, p. 243. Bassani, J.L. (1981), Creep crack extension by grain boundary cavitation, in: Creep and Fracture of Engineering Materials and Structures, B. Wilshire and D.R.J. Owen, eds., Pineridge Press, Swansea, p. 329. Bassani, J.L. and F.A. McClintock (1981), Creep relaxation of stress around a crack tip, Int. J. Solids Struct. 17, 479. Begley, J.A. (1980), unpublished data quoted by A. Saxena (1980). Blackburn, L.D. (1972), lsochonous stress-strain curves for austenitic stainless steels, in: The Generation of Isochonous Stress-Strain Curves, A.O. Schaeter, ed., ASME, New York, p. 15. Capano, M., A.S. Argon and I.-W. Chen (1989), Intergranular cavitation during creep in astroloy, Acta. MetalL 37, 3195. Chen, I.-W. and A.S. Argon (1981), in: Creep cavitation in 304 stainless steel, Acta. Metall. 29, 1321. Davis, E.A. and M.J. Manjoine (1953), Effect of notch geometry on rupture strength at elevated temperatures, in: Strength and Ductility of Metals at Elevated Temperatures', STP-128, ASTM, Philadelphia, p. 67.
Dyson, B.F. and D. McLean (1977), Creep of Nimonic 80A in torsion and tension, Metal Sci. 11, 37.
B. Ozmat et al. / Cracks in 304 stainless steel Gold, M., W.E. Leyda and R.H. Zeisloft (1975), The effect of varying degrees of cold work on the stress-rupture properties of Type 304 stainless steel, J. Eng. Mater. Technol. 97, 305. Gooch, D.J. (1977), The effect of microstructure on creep crack growth in notched bend tests on 0.SCr-0.5Mo-0.25V steel, Mater. Sci. Eng. 27, 57. Gooch, D.J., B.L. King and H.D. Briers (1977), High temperature crack growth in a 2¼Cr-lMo weld metal - effects of tempering, prestrain and grain refinement, Mater. Sci. Eng. 32, 81. Goods, S.H. and W.D. Nix (1978a), The kinetics of cavity growth and creep fracture in silver containing implanted grain boundary cavities, Acta Metall. 26, 739; (1978b), The coalescence of large grain boundary cavities in silver during tension creep, Acta Metall. 26, 753. Hayhurst, D.R., F.A. Leckie and C.J. Morrison (1978), Creep rupture of notched bars, Proc. R. Soc. A360, 243. Hayhurst, D.R., P.R. Brown and C.J. Morrison (1984), The role of continuum damage in creep crack growth, Phil. Trans. R. Soc. A311, 131. Hayhurst, D.R., P.R. Dimmer and C.J. Morrison (1984), Development of continuum damage in the creep rupture of notched bars, Phil. Trans. R. Soc. A311, 103. Hawk, D.E. and J.L. Bassani (1986), Transient crack growth under creep conditions, ,/. Mech. Phys. Solids 34, 191. Hsia, J.K., D.M. Parks and A.S. Argon (1991), Modeling of creep damage evolution around blunt notches and sharp cracks, Mech. Mater. 11, 43. Johnson, A.E. and J. Henderson (1962), Complex-stress creep relaxation and fracture of metallic alloys, Dept. Scientific & Industrial Research, Natl. Eng. Laboratory (Her Majesty's Stationary Office, Edinburgh). Koterazawa, R. and Y. Iwata (1976), Fracture mechanics and fractography of creep and fatigue crack propagation at elevated temperatures, J. Eng. Mater. Technol. 98, 296. Koterazawa, R. and T. Mori (1977), Applicability of fracture mechanics parameters to crack propagation under creep condition, J. Eng. Mater. Technol. 99, 298. Koterazawa, R. and T. Mori (1980), Fracture mechanics and fractography of creep and fatigue crack propagation at elevated temperatures, in: Proceedings Intern. Conf. on Eng. Aspects of Creep, Sheffield, U.K., Soc. Automot. Eng., Warrendale, Vol. 1, p. 219. Krompholz, K., H. Huthmann, E.D. Grosser and J.B. Pierick (1982), Creep crack growth behavior in air and sodium for an unstabilized austenitic stainless steel and assessment of evaluation concepts, Eng. Fracture Mech. 16, 809. Kumar, V., M.D. German and C.F. Shih (1981), An engineering approach for elastic-plastic fracture analysis, EPRI Topical Report NP-1931 (EPRI, Palo Alto). Lau, C.W., D.M. Parks and A.S. Argon, Crack-tip blunting in creeping alloys, to be published. Leckie, F.A. and D.R. Hayhurst (1974), Creep rupture of structures, Proc. R. Soc. A340, 323. Manjoine, M.J. (1963), in, Simulated service testing at elevated temperature, Proceedings of Joint International Conference
15
on Creep, The Institution of Mechanical Engineers, Vol. 1, p. 7. McMeeking, R.M. and D.M. Parks (1979), On criteria for J-dominance of crack-tip fields in large-scale loading, in: Elastic Plastic Fracture, J.D. Landes, J.A. Begley and G.A. Clarke, eds., STP-668, ASTM, Philadelphia, p. 175. Monkman, F.C. and N.J. Grant (1956), An empirical relationship between rupture life and minimum creep rate in creep-rupture tests, Proc. A S T M 56, 593. Musicco, G.G., D.J. Boerman and G. Piatti (1982), Creep crack growth characterization of austenitic stainless steel, in: Advances in Fracture Research, D. Francois, ed., Pergamon Press, Oxford, Vol. 3, p. 1323. Ohji, K., K. Ogura, S. Kubo and S. Katada (1980), The application of modified J-integral to creep crack growth in anstenitic stainless steel and C r - M o - V steel, in: Proc. Int. Conf. on Engineering Aspects of Creep, Sheffield, U.K., Soc. Automot. Eng., Warrendale, Vol. 2, p. 9. Ozmat, B. (1984), Creep crack initiation and growth behavior of AISI 304 stainless steel, ScD Thesis, Dept. Mech. Eng., Massachusetts Institute of Technology. Riedel, H. (1985), A continuum damage approach to creep crack growth, in: Fundamentals of Deformation and Fracture, B.A. Bilby, K.J. Miller, and J.R. Willis, eds., Cambridge Univ. Press, Cambridge, p. 293. Riedel, H. (1987), Fracture at High Temperatures, Springer, Berlin. Riedel, H. and W. Wagner (1985), Creep crack growth in Nimonic 80A and in a 1Cr-1½Mo steel, in: Advances in Fracture Research, S.R. Valluri et al., eds., Pergamon Press, Oxford, Vol. 3, p. 2199. Riedel, H. and V. Detampel (1987), Creep crack growth in ductile, creep-resistant steel, Int. J. Fracture 33, 239. Rice, J.R. and M.A. Johnson (1970), The role of large crack tip geometry changes in plane strain fracture, in: Inelastic Behavior of Solids, M.F. Kanninen et al., eds., McGraw-Hill, New York, p. 641. Sadananda, K. and P. Shahinian (1980), Effect of environment on crack growth behavior in austenitic stainless steels under creep and fatigue conditions, Met. Trans. IlA, 267. Sadananda, K., private communication (1984). Saxena, A. (1980), Evaluation of C* for the characterization of creep-crack-growth behavior in 304 stainless steel, in; Fracture Mechanics, STP-700, ASTM, Philadelphia, p. 131. Stanzl, S.E., A.S. Argon and E.K. Tschegg (1983), Diffusive intergranular cavity growth in creep in tension and torsion, Acta. Metall. 31,833. Taira, S., R. Ohtani and T. Kitamura (1979), Application of J-integral to high temperature crack propagation, Part I Creep crack propagation, J. Eng. Mater. Technol. 101, 154. Tvergaard, V. (1984), On the creep constrained diffusive cavitation of grain boundary facets, J. Mech. Phys. Solids 32, 373. Tvergaard, V. (1985), Effect of grain boundary sliding on creep constrained diffusive cavitation, .L Mech. Phys. Solids 33, 447.
16
B. Ozmat et aL / Cracks in 304 stainless steel
Tvergaard, V. (1986), Analysis of creep crack growth by grain boundary cavitation, Int. J. Fracture 31,183. Wilkinson, D.S. and V. Vitek (1982), The propagation of cracks by cavitation: a general theory, Acta Metall. 30, 1723. Wilkinson, D.S. and S.B. Biner (1988), Creep crack growth simulation under transient stress fields, Metall. Trans. 19A, 829. Yokobori, T. and H. Sakata (1980), Studies on crack growth rate under high temperature creep, fatigue and creep-fatigue interaction - I, Eng. Fract. Mech. 13, 509. Yokobori, T., H. Sakata and A.T. Yokobori Jr. (1980), Studies on crack growth rate under high temperature creep, fatigue and creep-fatigue interaction - II, Eng. Fract. Mech. 13, 523.
type; and h~(a/b, n) the principal numerical result of the evaluation of the deformation field. The values of F(a, b) as well as the tabulated values of hi(a/b, n) are obtainable from Kumar et al. (1981). In the generalization for creep to obtain C* from J, the constitutive relation for non-linear hardening is replaced with its creep constitutive law, i.e. g~ = a g 0 ( o J o 0 ) " = A exp( -
Q/RT)(oe/OO)', (A2)
which gives
Appendix I. Evaluation of C* factors for the CCP, DEN and CT specimens
C*
The generalized reference energy release rate (or energy dissipation rate) factors C* that are considered as driving forces for creep crack growth must be found by numerical techniques for specimen geometries in which the crack takes up a significant portion of the total specimen width. The recommended procedure for this, described by Riedel (1987) utilizes published numerical results obtained by Kumar et al. (1981) for the corresponding rate independent case of the J integral. The evaluation starts with the generic statement of the J integral as
For the specific cases the factors CCP specimens
J = a~oooF(a, b)h,(a/b, n)(oJOo) "+1,
(A1)
where a is the crack length for DEN and CT and the half length for CCP, while b is the specimen width for CT and half width for CCP and DEN geometries (with c = b - a being the uncracked ligament width for CT and half width for CCP and DEN configurations); a%oo and n are the factors characterizing the non-linear strain hardening behavior in the expression ee = OLf.O(Oe/O0) n relating the equivalent strain % to the equivalent stress oe; o. is either the net section tensile stress in the case of the symmetric DEN and CCP specimens, or the nominal bending stress at the crack tip for the CT specimen; F(a, b) a numerical constant, characteristic of the specimen
=Aoo(O,,/Oo) n + l F(a, b)hl(a/b, n) × exp( -
F(a, b)
Q/RT).
(A3)
F(a, b) are:
a ( b b a ) ( ~ - / 2 ) ~+1
(A4)
DEN specimens
b-a F(a, b ) = (0.36b/(b_a) +0.91),+ , .
(A5)
CT specimens
F(a, b)=
b-a {1.455,/[1 + 3(b + a ) / ( b - a)]} "+1' (A6)
where
2a)
---c-+l, c=b-a.
(A7)
(A8)
Using the specific information for material property given in Table 3 and specimen geometries given in Table 4A, together with A = 3.83 × 107 s-1 and Q -= 67 kcal/mol, the following values for h 1 were interpolated from the tables given by
B. Ozmat et al. / Cracks in 304 stainless steel
K u m a r et al. (1981) for the specific specimen types and are CCP-1
h 1 = 2.04
CCP-2
h 1 - 3.32,
DEN-1
h I - 2.28,
DEN-2
h 1 =4.63,
DEN-3
h 1 = 2.754,
CT-1
h 1 - 0.693,
CT-2
h 1 = 0.672.
(plane stress),
17
The above values of h 1 together with the specific evaluation of F ( a , b) lead to the C * values given in the last c o l u m n of Table 4B.