Sub-critical flaw growth

SUB-CRITICAL HERBERT

FLAW

GROWTH?

H.JOHNSON

Department of Materials Science and Engineering, Cornell University, Ithaca, N.Y. and PAUL %Xutment

C. PARIS

of Mechanics, Lehigh University, Bethlehem, Penna

Abdraci-The m@jor evidence bearing upon sub-critical flaw growth in structural materials is reviewed and discussed. Attention is focused upon the growth of preexisting flaws at operating stresses less than the net section yield strength, from both the separate and combined effects of fati& and a&ssive environments. In Section I, the applicability of fracture mechanics concepts to flaw growth is considered. and it is demonstrated that the stress intensity factor may be viewed as the-driving fo&e for both fatigue c&k growth and environmental cracking under static load. This allows a correlation of test results from different specimen geometries, and also a correlation between test results and service failures. Environmental cracking under static load is considered in Section 2. Steels and titanium aHoys in various environments of water, water vapor, hydrogen, and oxygen are discussed. For steels, crack growth in water and saturated water vapor is a thermally activated process. The crack growth activation energy agrees well with the measured value for di&sion of hydrogen. The role of oxygen in inhibiting sub-critical flaw growth in vapor environments is discussed. Fatigue crack growth is considered in Section 3. It is shown that the stress intensity rang is the major factor governing crack growth rates and fatigue fife, with frequency and mean load as secondary variables. Crack gmwth rate laws are considered, and it is construed that the fourth power law holds over the widest range. For an astonishing variety of steels, the fatigue crack growth rate is insensitive to composition. microstructure, and strength level, when the growth rate is plotted as a function of the stress intensity range. The combined effects of fatigue and aggressive environments are considered in Section 4. Some of the environmental behavior patterns in static loading are observed to carry over to fatigue loading. A lack of data for stress intensity ranges less than the threshold is noted. In Section 5, engineering applications are emphasized. Relationships among flaw size, threshold stress intensities in different envi~n~n~, and proof and operating stresses are presented graphically and their interpretation is discussed. For 4340 steel, the role of yield strength level is summarized in a diagram which indicates that environmental cracking is the major problem at yield strengths in excess of 180 ksi. whiie fatigue crack growth is the mJor problem at lower strength levels.

1. INTRODUCTION IN MANY practical fracture problems, the role of sub-critical flaw growth is of major irn~~~ce. This is particularly so when fracture occurs at relatively low stresses and, correspondingly, is not accompanied by general yielding of the net section. This mode of fracture sometimes occurs in structures fabricated from materials of high strength but rather low toughness, or with thick-walled structures of intermediate strength and toughness materials: Cyclic stresses or aggressive environments, or a combination of these two factors, may cause apparently innocuous flaws to grow until they are of a size sufIicient to cause failure. The methodology of fracture mechanics has provided considerable insight into fracture from preexisting flaws, particularly when the fracture is not preceded by net section yielding. It is appropriate, therefore, to apply the concepts of fracture mechanics in analyzing and interpreting sub-critical flaw growth phenomena It is the intent of this paper to explore systematically the application of fracture mechanics to sub-critical flaw growth via both cyclic stresses and aggressive environments, and to describe the behavior patterns which have emerged from past investigatPresented at the National Symposium June 19-21,1967.

on Fracture 3

Mechanics,

Lehigh University,

Bethlehem,

Pa.,

4

H. H. JOHNSON

and P. C. PARIS

tions. However, the paper is not directed to detailed descriptions of possible microstructural or atomistic mechanisms of sub-critical flaw growth. The concept of a critical flaw size for fracture is of central importance, and is taken up first: then the kinetics of sub-critical flaw growth are considered in terms of fracture mechanics concepts. Criticalflaw size A basic tenet of fracture mechanics is that unstable fracture will occur when the stress intensity factor at a crack tip reaches a critical value. Although this critical value will depend upon many factors, including thickness, chemical composition, heat treatment, etc., it is nevertheless possible to determine the critical stress intensity factor by appropriate experimentation. Since an analytic formulation of the stress intensity factor contains parameters representing both the flaw variables, shape and size, and the loading variables, geometry and magnitude, it follows that the critical stress intensity factor represents a critical‘combination of applied stress and flaw size. From the viewpoint of sub-critical flaw growth, however, it is more appropriate to note that the critical flaw size corresponds to a critical combination of applied stress and fracture toughness, as described by the critical stress intensity factor. This concept has been developed in detail by Tiffany and Masters [ 11. A schematic example for surface-flawed specimens in the plane strain fracture mode is given in Fig. 1, which depicts the relation, for a given fracture toughness KIc, between the applied stress u and the critical flaw size, ( a/Q)c,., as calculated from

0;

cr=_

1

Flow Size Fig.

K,, 2

-

1.217r [ C7I *

(1)

, O/o __*

1.Schematic view of concepts of critical Raw size and of minimum flaw growth potential[ I).

The parameter Q may be determined from the flaw shape, material yield strength, and the applied stress. Since it is based on a linear elastic analysis, this relation is valid for applied stresses less than the uniaxial yield strength uw, which is the region of interest to this discussion. This concept may be applied to pressure vessels, where the critical flaw size corresponds to the value of (a/Q)rr at which unstable fracture will occur under an applied

Sub-critical flaw growth

5

stress c generated by the internal pressure. If the critical flaw size is less than the wall thickness, the flaw growth velocity will increase abruptly at the onset of unstable fracture. In steels and aluminum alloys an unstable growth velocity of the order of 5000 ft/ set may develop, and this will lead to a plane strain fracture and frequently shattering of the pressure vessel. A shattering failure is more probable as the relative brittleness of the material increases. In thinner structures or with tougher materials, the critical flaw size may exceed the thickness, and plane stress conditions, corresponding to ‘leak before break,’ will then prevail. Under this condition, the vessel may split rather than shatter. Insurance against either failure mode requires that the seemingly inevitable crack-like flaws be considerably smaller than the critical size for the operating stress level. The life of a pressure vessel may therefore be limited; it depends upon the number of stress cycles or the time under sustained load required to grow an initially sub-critical flaw to a critical size. From ( 1). the maximum initial flaw size (a/Q), in a pressure vessel before it is put into service may be determined by the proof stress level. The relationships among flaw size, proof stress, and operating stress have been considered in some detail by Tiffany and Masters [ 11; a schematic view of the concepts is also presented in Fig. 1. If the operating stress level is designated oO and the proof stress as aa,, where a! is the proof stress factor; then for a given go, the relation between the critical flaw size and maximum initial flaw size may be developed from ( 1) as

As Tiffany and Masters[ 1] have pointed out, the minimum flaw growth potential, i.e. the critical flaw size at failure minus the maximum initial flaw size, at an operating stress go is ( 1 - 1/a”) multiplied by the critical flaw size, or (~2 - 1) multiplied by the maximum initial flaw size. Both the critical and maximum initial flaw sizes will vary throughout a vessel, since the fracture toughness values will almost certainly differ for base metal, weldments, etc. As a multiple of the maximum initial or critical flaw sizes, however, the flaw growth potential is constant for a given proof factor. Sub-critical crack growth description The primary causes of sub-critical flaw growth are cyclic stresses and aggressive environments. It has been customary to characterize these phenomena by a plot of maximum alternating stress versus number of cycles to failure for fatigue, and a plot of applied sustained stress versus time to failure for environmental crack growth. In both instances, the mechanical factor is represented by a gross or net section stress. From the viewpoint of fracture mechanics, however, considerable significance is ascribed to the stress situation in the crack tip vicinity, and this is characterized by the stress intensity factor. It is appropriate, therefore, to inquire into whether or not the mechanical aspects of sub-critical flaw growth phenomena are better characterized by the net section stress or the local stress at the flaw tip, as described by the stress intensity factor. For both fatigue and environmental cracking, definitive experiments show that the stress intensity factor, rather than the net section stress, is the parameter which controls the sub-critical flaw growth rate. In both cases, a comparison was made of test results from center-cracked specimens loaded at the ends and by wedge forces at the center section. For end loaded specimens at constant load, both the stress intensity

6

H. H. JOHNSON

and P. C. PARIS

factor and the net section stress increase as the crack length increases. With wedge force loading, however, an increase in crack length is also accompanied by an increase in net section stress, but the stress intensity factor decreases[2]. Results from the two loading nonfictions, therefore, allow a clear separation of the roles of the net section stress and the stress intensity factor. Comparison of subcritical crack growth rates under cyclic stress show clearly that the stress intensity factor is the controlling parameter in fatigue crack growth. This is shown in Fig. 2 taken from Paris[3], which shows fatigue crack growth rates from both loading configurations for an aluminum alloy.

10-1

Gd

dN

(inkyc)

Fig. 2. Correlation of crack growth rates in 707%T6 ~u~nurn alloyundersinusoi~lo~i~[3].

These results suggest that the fatigue crack growth rate essentially is a unique function of the range of stress intensity factor encountered in cyclic loading and independent of specimen geometry and loading configuration. Other factors, such as the mean value of the stress intensity factor and the loading frequency, are of secondary importance and will be discussed later. This concept in turn suggests that the fatigue crack growth rate should be a constant in a constant stress intensity factor fatigue test, and an experiment demonstrating this has been reported by Swanson[4]. He examined center-notched specimens of clad 7079-T6 aluminum alloy sheet, and varied the maximum load during fatigue crack growth such that either the stress intensity factor or the net section stress remained constant. A constant crack growth rate, independent of crack length, was observed under a constant stress intensity, Fig. 3. For a constant net section stress, the crack growth rate was linear only over the middle range of crack length, and showed a definite decrease at large crack lengths. It may again be concluded that the stress intensity factor is the controlling parameter. Analogous experiments have been reported in the area of environments cracking. Smith, Piper and Downey[5] have used center-cracked specimens to determine the threshold stress intensity for crack initiation with end loading and for crack arrest with wedge-force loading. They used a Ti-8Al-1 MO-IV alloy in an aqueous 3#% NaCl solution. The threshold stress intensity for crack injtiation in end loading was 20-25 ksi

Subcritical flaw growth

Crock Length

(inI

Fig. 3. Constant crack growth rate observed in a constant stress intensity test, clad 7079-T6 aluminum alloy[4].

(in.Y*, and for crack arrest, it was 20-22 ksi (in.)l12, in excellent agreement. The arrest experiment also provides strong support for the concept of a threshold stress intensity in environmental cracking. The relation between crack growth rate and stress intensity factor has been explored for both high strength steels and titanium alloys. Johnson and Willner[6] have reported the results of a constant stress intensity test for a center-cracked H-l 1 steel specimen in a water environment. The results, Fig. 4, show that the crack growth rate was constant over the entire range of crack length. The deviation from linearity occurred only when the total crack length was nearly equal to the specimen width, and the 0.57

I

I

I

H-II; 230 KSI Yirld Q4_

I

I

I

I

Strrngth

Kg 21.5 KSI ‘/?i

.. .*

z

Rrlatlvr

z

Humidily 100% at 80-F.

[ Water

1

0 0.3 c

.

i f 0.2 .u.

.*

.

l

I/ r /

E v O.l-

. / .

,../, 0

, 4

6

12

,

(

I

.

I6 20 Time (min.)

I

24

26

32

Fig. 4. Constant crack growth rate observed in a constant stress intensity environmental crack-

ing test, H-I

1steel in water[6].

8

H. H. JOHNSON

and P. C. PARIS

crack length calibration was no longer valid. In this experiment the entire cross section of the specimen was consumed by environmental crack growth. More recently Van Der Sluys[7] has also shown a constant crack growth rate with a constant stress intensity factor, using a double cantilever beam specimen of 4340 steel in water. From thes&&xperiments, the importance of the stress intensity factor as a controlling parameter is evident. It may therefore be anticipated that, for a given environment-material system, a unique relation will exist between the stress intensity factor and the crack growth rate. There is no reason to expect that the same relation will hold for all systems, and indeed this is substantiated by the available experimental results for steel, titanium, and glass. Johnson and Willner[6] have reported a rather detailed study of crack growth in center-cracked H- 11 steel specimens in the presence of water and water vapor. Typical results for water and fully humidified argon, Fig. 5, show a roughly linear relation between crack growth rate and stress intensity factor. For lower humidities, a linear relation is also observed, but with a smaller slope. .06*

2 E

.07- H-II

Steel,

230

R.H.-100%

5 .06- Water 0 0” I z.osg

.03-

: &

.02-

.m ::

.O, - F

3

0

Y.S.

80’F.

.

.

/’ . 0..

. 5

i/

. /

.04-

a f

KSI

at

.

.

/ ’

1 20 24 Stress Field

I

I

I

26

32

36

Parameter

K (lOOOpsi-in

:

Fig. 5. Crack growth rate vs. stress field intensity, H-l 1 steel in water[61.

A nearly linear relation between crack growth rate and stress intensity factor has also been reported by Steigerwald and Benjamin[8] for 4340 steel in distilled water, using pre-cracked cantilever beam specimens. Their absolute crack growth rates were less than those determined by Johnson and Willner[6], Fig. 5; perhaps this is caused by metallurgical differences, particularly in strength level. Peterson et a/.[93 have also studied pre-cracked cantilever beam specimens of 4340, but in a 3fi NaCl solution. They report crack growth rates comparable to those of Johnson and Willner[6]; a linear relation with stress intensity was also observed for stress intensities from 20 to 40 ksi (in.)lj2, but the growth rate increased more rapidly at higher stress intensities. For high strength steels, the linear relation may be unique to the water environment and rather low stress intensities, since in dry hydrogen, the crack growth rate also increases faster than the stress intensity factor. These and other data indicate that the chlorine ion has little if any influence, and that water and aqueous chloride solutions are roughly equivalent. For Ti-8AI- I MO-I V in aqueous 3#% NaCl solution, a unique relation between crack growth rate and stress inter &y factor has also been reported[5], Fig. 6, but the

Sub-critical flaw growth

Specimen No. I

A

Specimen No. 2:

58 26 L 253 24 .g

Specimen No.3 161Test

l

2nd Test

D

2 = 23-

Crock Growth Rate, A20/ht,

Fig. 6. Crack growth rate vs. stress field iflt~~ity~ solution[5].

(microtnches/sec)

Ti-SAI-1~~lV

in 34% aqueous NaCl

relation note that the crack growth the lower stress are of same for steel[6, 91. feature this system the reported plateau in crack growth at higher stress intensities, and it been suggested that this with an upper limiting of operative stress corrosion For same titanium ahoy, Peterson et al.[9] have also reported rate of same magnitude as Smith et a1.[5]plateau value. The effect upon sub-critical flaw growth has been studied by Irwin[lO] and 1 i-121. Their again a relation between crack growth rate stress intensity with rates of same order magnitude as those for steels[6, 8,9] the titanium 91. definite plateau in growth rate higher forces or intensity factors also indicated, the work Wiederhom [ Some practical i~~lica~i~ns

The evidence just reviewed constitutes a strong case for the stress intensity factor as the controlling mechanical parameter in both environmental and cyclic stress crack extension. This means that different test specimen and flaw geometries and load configurations should yield essentially identical results, and that these results should in turn be directly applicable to practical structures such as pressure vessels. For en~ronmen~ cracking, this concept has been illustrated by Tiffany and Masters[ I] and Brown and Beachem[ 131. Tiffany and Masters f I] compared surface flawed specimens of 4330M steel, both wet and dry, with a hydraulic actuator failure in the presence of moisture. The results, Fig. 7. show both the detrimental effect of moisture and an excellent agreement between test specimen and hydraulic actuator rest&s. Brown and Bea~hem~l3] explored the internal consistency in test results for three different specimen types, the center-cracked and surface-cracked plate, and a precracked cantilever beam. For 4340 steel in a dilute NaCI solution, the same threshold stress intensity (K,,,) was obtained for all three specimen types, Fig. 8. When plotted in terms of net section stress, however, the threshold values were not identical for all

10

H. H. JOHNSON and P. C. PARIS

E f

m

o Surface Flowed Specimens(dry) 0 0.1

1.0

100

Time I Hours;O Fig. 7 Correlation of hydraulic actuator and surface flawed specimen test results, 4330M steel[ 11.

1

loo] l

Center Cracked Specimens

S Surface Cracked Specimens 0 Test IflterFu~ed

0

0

10

I 100

I 1000 Test Duration

(Cmck grew)

Test Interfupted (Crock did not growl

I to.000

100,

Do

(minutes)

Fig. 8. ~o~elation of threshold stress intensity C&J results for three diffen%t specimen con~~ions, 4340 steel in dilute NaCl solution[l3].

three specimens. This again illustrates the importance of the stress intensity factor. The three specimen types did yieId rather systematic differences in failure time, Fig. 8, at a given applied stress intensity. This simply reflects the diierent functional dependences of the stress intensity upon crack length for the three specimens. As would be expected, the shortest failure times were observed for the pre-cracked cantilever beam, which shows the most rapid increase of stress intensity with crack length; the longest failure times were with the center-cracked specimens, in which the increase of stress intensity with crack length is least. For low-cycle fatigue, the correlation between laboratory test results and vessel failures has been explored in detail by Tiffany et a1.f1, 143. Results for a pre-ftawed tank and surface Aawed and sharply notched round bar specimens are shown in Fig. 9.

II

Sub-critical flaw growth

100

^o S

00

6

Q 9 UT0

X

A

Surface Flowed Specimen 0 17’ Diomrter Pmflawed Tank 60 0

I

IO

100

1000

Cycle to Foilurc Fig. 9. Correlation

of fatigue test results for pre-flawed tank, surface flawed and sharply notched round specimens, Ladish D6A-C steel[l4].

It is evident that reasonably identical results are obtained for all three test types. As will be discussed later, the scatter observed is due to secondary variables, including gross section stress, mean stress intensity, and variation of stress intensity with crack length. 2. ENVIRONMENTAL CRACKING UNDER STATIC LOAD The phenomenon of general (pitting) stress corrosion, in contrast to environmental cracking, is of course not new; there are many papers in the literature describing cracking and fracture in stainless steels, aluminum and copper alloys, mild steels, etc., under the combined influence of stress and specific aggressive environments. These alloys are of relatively low strength and are generally insensitive to crack-like flaws, in the sense that fracture (in inert environments) is preceded by through-the-section yielding for both laboratory specimens of normal size and most practical structures. It is not yet clear whether fracture mechanics concepts will be useful in interpreting and analyzing typical stress corrosion tests for this class of alloys, and they will not be considered further. For higher strength materials, such as high strength steels, titanium alloys, and glass, the evidence assembled earlier in this paper demonstrates a clear realm of applicability of fracture mechanics and particularly the concept of the stress intensity factor as a driving force. High strength steels and titanium alloys are frequently nearly immune to environmental cracking when tested in smooth sections[ 15, 161, perhaps because they do not pit readily. When crack-like flaws are present, however, crack extension under discouragingly low stresses may be evident in seemingly mild environments. Much of the current interest in this area stems from problems encountered in hydrostatic proof testing of high strength steel rocket motor casings, and from the more recent discovery[ 161 that many titanium alloys are susceptible to environmental cracking in water when tested in pre-cracked form. Because of this chronology, most of the systematic research papers are devoted to high strength steels in aqueous environments.

12

H. H. JOHNSON

and P. C. PARIS

High strength steels, water, and water vapor As a result of a motor casing failure, Shank and associates[l7] investigated the burst fracture behavior of small scale H-l 1 pressure vessels internally pressurized with water. Burst fractures were observed at unexpectedly low stresses; often a time delay was observed between pressurization and fracture, and the fracture started from the inside surface. It was suggested that the water induced sub-critical crack growth, and that perhaps hydrogen generated by electrolytic action was the actual damaging agent. Irwin, Kies and Bernstein[ 18, 191 analyzed a number of hydrostatic test failures during the rocket motor program, and suggested that environmentally assisted flaw growth was a critical factor. The first systematic study of these phenomena was reported by Steigerwald[20]. For center-cracked H-l 1 and 300M steel specimens in water, sub-critical crack growth and delayed fracture were observed at stresses as low as 10 per cent of the uniaxial yield strength under experimental conditions corresponding to plane strain. To obtain a qualitative understanding of the aggressiveness of different environments, Steigerwald[20] determined failure times for 300M steel with a yield strength of 245 ksi under a net section stress of 75 ksi. The results, Table 1, indicate clearly the aggressive nature of water, the inert nature of air, and the occurrence of sub-critical flaw growth and delayed fracture in a rather substantial number of different environments. As will be discussed later, the inert nature of air is probably due to oxygen. The purity of the different non-aqueous environments was not stated, and this is important. Table 1. Influence of various crack environments on failure time of 300M steel. Steiaerwald 1201 Environment

Failure time

(min) Recording ink Distilled water Amy1 alcohol Butyl alcohol Butyl acetate Acetone Lubricating oil Carbon tetrachloride Benzene Air

0.5 6.5 35.8 28.0 18-O 120-o I so-o No failure in 1280 2241 No failure in 6000

The importance of water content in solution was convincingly demonstrated by Nichols and Rostoker[21], who investigated the fatigue life of a high strength steel in the presence of different polar and metallo-organic liquids. Interestingly, in all systems, a plot of fatigue life against carbon chain length extrapolated to the value for water. Since the solubility of water also increases with carbon chain length, Nichols and Rostoker[2 11 investigated the influence of water content in solution by adding powerful dehydration agents to the solution. Under these conditions, the embrittlement was essentially eliminated, and the authors concluded that water was the sole embrittling agent in all cases. From the viewpoint of fracture mechanics, a significant contribution of Steigerwald [20] was the demonstration that the instability induced by the environment is localized to the crack tip, and the critical stress intensity at the onset of unstable fracture is

13

Sub-critical flaw growth

unaffected by environment, applied stress, and crack length. This is shown in Fig. 10, where the straight line representation indicates a constant, but different, value of K,, for each steel and heat treatment. Identical results have been obtained by others [6,22]. .

60x104 300 m 1025 F Temper W 0) 5, g v) ._ 0 ,a

50 -

40-

1

?! G

30-

E ._ 2t

20 -

:: 0e

IO -

300m

N* b 0

I 0.25

6OOF Tarnpar

H-II Dir stwl I I 1 0.50 O.-r5 1.0 I.25 [Tan Va/w]-’

Fig. IO. Constant stress intensity at unstable fracture, distilled water[20].

The effects of composition and strength level upon failure times and threshold stress intensities are of considerable interest, but not too much systematic information is available. This area is complicated by the possibility of a plane strain to plane stress transition at lower strength levels, unless the specimen thickness is appropriately increased. Such information as is available[9,20,23,24] shows longer failure times and higher threshold intensities at lower strength levels, and also the existence of an incubation period for crack initiation[23]. Because of the incubation period, crack growth rates cannot be estimated even approximately from failure times. The incubation time clearly decreases with flaw sharpness, for Tiner, Gilpin and Toy[25] report incubation times that usually exceed ninety per cent of life for smooth specimens. Peterson et af.[9] have reported the most complete study of the dependence of KI, and &,,, upon strength level. Their data for 4340 steel, Fig. 1 I, shows a substantial drop in Klrcc at yield strength levels in excess of 150 ksi, and a near plateau at strength levels above 200 ksi. The KIIce at these high strength levels is discouragingly low, in agreement with other investigations. Similar results are evident for other steels. However, there does not appear to be any correlation between K,, and Klsec which is independent of chemical composition and microstructure. The same lack of correlation between K,, and K,,,, is evident for titanium alloys [9], Fig. 12. Johnson and Willner[6] have reported a detailed study of the effects of water and water vapor, in argon-water vapor mixtures with oxygen excluded, upon threshold stress intensities and crack growth rates for H-l I steel. The threshold stress intensity increases as the relative humidity decreases, Fig. 13, until for an inert environment of purified argon, the constant load sub-critical crack growth disappears. In the inert environment, it was observed that either crack initiation and unstable fracture were

14

H. H. JOHNSON

and P. C. PARIS

AISI 4340 Tested in Flowing 6so YYDtrr (Key Wsst) Froctun Fmcture

Orientation: WR Toughness Index 0 K 1% (Dry bsok)

I

OL

I

120

loo

I

140 Yield

I

I

L

160 160 200 Strength (KSI)

I

220

240

Fig. 1I. Threshold (K,,,) and unstable fracture (K,,) stress intensities vs. yield strength, 4340 steel in water [9].

Titanium

Alloys

in 3.5%

NoCl Solution

UY “,

loo

y ::

2

Y

5: 0

t 80-

f +

0

A 6AII Sn v 6Al-26Sn p

.

/ 0

.

-0,o “0: .kX Be BP w. $

0

z;;-$.;Sn

.

O

60-

0

.

‘8

40-

.

. . .

20-

:: t

ti

0 0

I

I

20 40 60 Stress Intensity Aequlred

Fig. 12. Lack of correlation

I

I

100 80 for Mechonlcol

I

I20 Fracture

I

I40 K(KSIm

I

between

threshold and unstable fracture stress intensities, titanium alloys in dilute NaCl solution [9].

coincident, or a discontinuous, snapping, ‘popin’ growth was observed only under rising load. It was also evident that the threshold stress intensities were identical in liquid water and in relative humidities in excess of about 60 per cent. This correspondence between liquid water and highly humid environments was also reflected in the measured crack growth rates, Fig. 14. A saturation in crack growth rate with relative humidity is clearly evident at relative humidities in excess of about 60 per cent, and this saturation value is equal to the crack growth rate in liquid water. As will be discussed later, a similar saturation behavior is observed for moisture-enhanced fatigue crack growth in high strength steels.

. _I

15

Sub-critical flaw growth

“”

I

I

I

. Crack initiation o Fracture

0

50

I

0

kv,_

40.*-

Y

Inert

nvlan-

I 30 Y

ment

20

‘SD1

Fig, 13. Threshold (I&)

I al Relative

+

1 1.0 Humidity at 80°F

Same asd Water I IO

(per

loo

Cent)

and unstable fracture (K,,) stress intensities in water and water vapor, H-l 1steel, 230 ksi yield strength[6].

._.,

0

1

.

*o Relatiz

Hum%y

K=36

KSI fi

Q Kg25 KSI fi

1

80 80 at 80DF (per cent)

Fig. 14. Saturation of crack growth rates at relative humidities in excess of about 60 per cent, H-l 1 steel, 230 ksi yield strength[61.

A possible interpretation is that this equivalence results from capillary condensation of water at the crack tip in highly humid environments, after which the crack is effectively propagating in a little pool of bulk liquid. At room temperature, condensation appears to occur at a relative humidity of about 60 per cent, but the temperature dependence of this condensation relative humidity is not known. The condensation interpretation may be used to obtain a rough estimate of the effective radius of curvature of the crack, which must be less than or equal to the curvature at the water vapor-condensed water interface. Capillary condensation

16

H. H. JOHNSON

and P. C. PARIS

because the equilibrium vapor pressure at a vapor-condensed phase interface is dependent upon interface curvature, with higher values for convex surfaces and lower values for concave surfaces. If the crack tip is assumed to be semi-circular, the radius may be computed from the appropriate form]61 of the Kelvin equation relating vapor pressure to the radius of curvature

occurs

lng=-5, 0

where P is the vapor pressure for a radius of curvature p, POthe vapor pressure for a flat surface, p = 03,V the molar volume, and y the surface tension of water. For a pressure ratio of 60 per cent, this equation yields a very small value for p, approximately lo-’ in. There are two sources of error in this approach. First, the thermodynamic assumptions underlying the Kelvin equation become increasingly doubtful for radii less than 1O-s in. Secondly, some experimental data are in substantial disagreement with the Kelvin equation, particularly for small capillaries with radii of the order of microns. The discrepancy is especially severe for water, where radii 30-80 times the values calculated from the Kelvin equation have been reported. On the basis of these considerations, a best estimate of the effective crack tip radius would be about 10e5 in. It must be emphasized that capillary condensation at the crack tip has not been demonstrated directly, but only inferred from the equivalence of crack growth rates and threshold stress intensities in water and highly humid environments. In connection with experiments on moisture-induced crack propagation in glass, Wiederhom[ 121 has presented a detailed discussion of the thermodynamic and dynamic aspects of condensation at moving crack tips, concluding that crack tips are probably dry for glass. The influence of temperature upon threshold stress intensities and crack growth rates is of evident practical and mechanistic interest. Several investigations[6, 7. 261 have established that crack growth rates increase with temperature in water environments, while the behavior pattern with water vapor is more complex[6,26]. A thermally activated mechanism of crack growth is indicated by Fig. 15. The linear Arrhenius relation was observed for both liquid water and water vapor environments saturated at the test temperature. This evidence supports the condensation concept discussed earlier. The apparent activation energy of 9000 Cal/mole is in good agreement with the 8500 Cal/mole obtained in a more ‘recent investigation[7]. The effect of the stress intensity factor upon the activation energy appears to be minor[6,7]. Apparent activation energies are frequently of value in mechanistic considerations. In fact, the values just summarized are remarkably close to both the apparent activation energy for hydrogen-induced crack initiation[27] and the activation energy for hydrogen diffusion [28] in a high strength steel. These values are summarized in Table 2. It seems unlikely that the coincidence of values is accidental, and hydrogen diffusion appears to be an important feature of environmental cracking in water. Nevertheless, from a comparison of crack growth rates and diffusion rates, the hydrogen diffusion process must be extremely localized to the crack tip. It should be noted that both water[29] and water vapor[30] may apparently supply hydrogen to steel via a surface reaction on a clean surface. The temperature dependence of the crack propagation rate in water vapor is somewhat more complex, Fig. IS, and apparently depends essentially on the relative

17

Sub-critical flaw growth

0

\

0

180-F

i

0 Rabtiw Humidity~l00X at last Tmprratun

‘/T

Fig. 15. Temperature

(*K-l

x IO31

dependence of crack growth rate in water and water vapor, H-l

I steel

VI. Table 2. Activation energies foihydro8en diffusion and environmental cracking in high streqpb steels investigator

Experimental description

Activation energy

Beck, Bockris, McBreen and Nanis[28]

Diffusion of ekctrofytic hymn through AM4340 membrane

9220 c&/g-atom

Steigenvald, SchaUer and Troiano[27]

Incubation period for crack initiation in cathodically charged notched rounds

9 I20 c&-atom

johnson and WiIner[6]

Center-cracked plates in water and saturated water vapor(H-11)

9000 caUg*atonj

Van Der Sluys[‘lJ

Pretracked doubk cantikver beam in water 14340)

8500 &/g-atom

humidity at the test temperature. If the environment is saturated at the test temperature, then thermally activated crack growth is observed as described earlier. However, if the environment is unsaturated, and crack growth occurs through contact with water vapor, then the process is not thermally activated, Fig. 15. For a constant absolute humidity, the crack growth rate decreases steadily at elevated tcmperatures[$ 261. This behavior suggests a surface controlled process, where the adsorption potential would decrease with temperature for a constant absolute humidity rather than the volume diffusion process implied by the thermally activated growth rate in water. Over a similar range of tern~~~es, 32-IW’F, the threshold stress intensity for water is remarkably insensitive to temperature and equal to about f 8 ksi (in.)‘@[6].In

EFM-I

18

H. H. JOHNSON

and P. C. PARE

general, the crack growth rate seems more sensitive than the threshold stress intensity to changes in environments and rne~f~~c~ parameters. High strength steel, hydrogen and oxygen

Although hydrogen gas is a more specialized environment, its remarkable influence upon sub-critical flaw growth13 I] is worthy of discussion. As is shown in Fig. 16, sub-critical flaws will initiate at lower stress intensities and propagate at higher rates in 1 atm. of purified hydrogen than in a fully humidified argon environment. It appears that this is yet another facet of the well-known problem of hydrogen embrittlement.

v2 * Purr hydrogen,K- 16,500 p8i’ in l 100% humidified argon,K--22,3OOpsi~~~

OO

I

2

L 4 3 5 Time tminut~)

6

4 7

6

Fig. 16. Sub-critical crack extension in hydrogen (1 attn.1 and humidified argon, H-l 230 ksi yield strength(3 I].

1 steel,

Perhaps it is the most direct form of hydrogen embrittlement, i.e. the initiation and growth of a crack under a known stress intensity and hydrogen pressure. It is generally accepted that hydrogen can enter solid steel only in the atomic (or perhaps ionic) form; further, at room temperature hydrogen gas is essentially completely molecular. However, hydrogen does disassociate upon chemisorption on iron[32], and it may reasonably be assumed that the source of brittleness is the adsorbed hydrogen. Chemisorption of hydrogen upon iron is virtually instantaneous[33] and this is consistent with the lack of an incubation period for crack initiation. The influence of oxygen in vapor environments upon sub-critical crack growth is equally striking, but in the opposite direction, for oxygen prevents initiation from a sub-critical crack, and wilt even stop an afready propagating crack. This effect is displayed in Figs. 17-19, from Hancock and Johnson[3 I], for crack growth in gas mixtures containing varying proportions of argon, water, nitrogen, water vapor, hydrogen, and oxygen. It is evident that as little as O-6 per cent oxygen was sufficient to terminate sub-critical crack growth essentially instantaneously. It is also evident from Fig. 19 that moisture is the dominant component in a moisture-hydrogen environment, which is consistent with the condensation interpretation. An oxygen-stopped crack may be restarted only when oxygen is removed from the gas environment. This suggests that the crack tip surface must adsorb oxygen in preference to hydrogen and water vapor. This is consistent with the well-known affinity of iron for oxygen, as reflected by a very high heat of adsorption and as m~tilayer coverage of iron by oxygen[34]. It has been suggested that this multilayer is essen-

Sub-critical flaw growth

I

I

I

19

1

I

I

I

I:

20- Humldflod Nttrogor Plur Q7Y Own

Humldlfird Nitrogen

0

20

40 Tlmr (Ylnutrr)

80

80

Fig. 17. Influence of oxygen upon subcritical crack growth in humidified nitrogen, 230 ksi yield strength[3 11.

I

,

I

,

I

,

1

H-I 1 steel.

,

.32 -

= 5

.24-

0

4

8

12

I8

Time /Ylnuter 1 Fig. 18. Hydrogen-oxygen

mixtures and subcritical

crack growth, H-l

I steel, 230 ksi yield

strength13II. tially an oxide, and the logical interpretation is that this oxide provides an effective barrier to the passage of hydrogen. Presumably, when the oxygen supply is removed, hydrogen may reduce the oxide, while water and water vapor may either supply hydrogen or perhaps dissolve the oxide. Dissolution seems more probable with water. The hydrogen-reduction hypothesis is consistent with a low energy electrondiffraction investigation [35] of the interaction between nickel and hydrogen and oxygen, which showed both preferential adsorption of oxygen and displacement of the oxygen by hydrogen when the oxygen supply was removed. In separate experiments, it was established that the hydrogen-induced brittleness was not enhanced by prior exposure to hydrogen without stress. Evidently, hydrogen can enter only through a clean, i.e. oxygen-free, surface, and this is provided at the stressed crack tip.

H. H. JOHNSON

20

01 0

Fig. 19. Sub-critical

1

5

I

IO

and P. C. PARIS

I

I

IS 20 Tima(Mhutes)

I

I

25

30

J

crack growth in different water, water vapor. hydrogen, andoxypn ments, H-l I steel,230 ksi yield strength[3 I].

environ-

From an application point of view, the beneficial role of oxygen is indeed fortunate. It seems probable that this confers immunity to sub-critical flaw growth on high strength steel components in many natural vapor environments. For example, crack-propagation curves of H- 1 I steel are virtually identical in air[36] and purified argon[6] environments. Constant load sub-criticalflaw

growth in inert environments

Of’ the various known modes of sub-critical flaw growth, perhaps the most surprising and least understood is sub-critical flaw growth under constant load in a chemically inert environment. The effect has been observed in several laboratories[37-391. An early report[37] showed that sub-critical flaw growth and delayed fracture in AM350 steel was virtually unalfected by water and water vapor, which was in stark contrast to the nearly simultaneous results obtained with H-l 1. Figure 20 shows the insensitivity of the threshold and unstable fracture stress intensities to environmental conditions, which may be compared with Fig. 13 for H- 11. It is evident that sub-critical flaw growth has occurred over a substantial range of stress intensity factor for the purified argon environment, and that this range is quite insensitive to water and water vapor. The crack growth kinetic behavior, Fig. 21, also differs from environmental cracking. Characteristically, the crack growth rate initially decreases, and the crack may halt if the stress intensity factor is low. At higher stress intensities, the crack growth rate passes through a minimum and then increases steadily as unstable fracture approaches. Essentially similar results have been obtained by Li, Talda and Wei[38] for a 0.45 C-Ni-Cr-Mo steel and an 18Ni(250) maraging steel, and by Tiffany[39] for some alluminum alloys. It is to be recalled, however, that sub-critical flaw growth under constant load in the high strength H-l 1 stee1[6] was associated only with aggressive environments and was absent in purified argon. Evidently, the phenomenon is not general, but the metallurgical conditions under which it will appear have scarcely been explored. With respect to

21

Sub-critical flaw growth 200

, # , f

I o Fracture l Inlt!atlon

AM 360

I Fym

Crock Ebx Notch

160 CGD Y

: 0 ; 8-l P 5 E 5

Stable

I

Crack

0

E

Growth

60-

40-

0

EP . ,

1

I

1

I

I

IO

Relative at

Humidity 80%

100

_ X

F

Fig. 20. Threshold and unstable fracture stress intensities for Am350 steelI37).

0.12 ;; at 0.10 Y ‘i 0 g 0.06 : : * 0.06 :: 0’ 0.04

-

Fig. 2 1. Inert environment and constant load sub-critical crack growth with Am350 steel[371.

stress state, however, all cases of inert environment sub-critical flaw growth reported so far have been in the plane stress or mixed plane stress-plane strain region, and in very limited experimentation, it has not been observed in plane strain. Presumably, the mechanism of the sub-critical crack growth mode %volves time dependent deformation processes in the plastic zone at the crack tip, which culminate in slow crack extension. This offers a plausible explanation for the differences between plane stress and plane strain. Flaw blunting may explain some of these effects, since it is well known that true plane strain occurs only when the flaw radius is much less than the plastic zone size. Indeed, Peterson et a/.[91 have reported blunting of sharp cracks in titanium alloys by creep at room temperature, and that this enhances resistance to sub-critical flaw growth in water.

H. H. JOHNSON

22

and P. C. PARIS

Environmental cracking, plane strain and plane stress The influence of stress state at the crack tip upon susceptibility to environmental cracking is of considerable interest. Although no detailed and systematic investigations have been reported, the weight of the evidence is that environmental cracking is largely confined to plane strain conditions, and is of less influence, and perhaps nonexistent, under plane stress conditions. Brown [ 161 in a discussion of the pre-cracked cantilever beam specimen type, has stated that environment-induced cracks will not propagate under stress state conditions where substantial shear lip formation is observed in unstable fracture, i.e. plane stress. He further points out that testing in this region may give a wholly erroneous view of intrinsic resistance to environmental cracking. Piper et a1.[40] have demonstrated, for two titanium alloys, the effect of specimen thickness upon threshold and unstable fracture stress intensities in Fig. 22. It is evident that the threshold stress intensity is much lower, and the range of stress

K,~K~\(38Otnln) In 3.5%

no Cl

Solution

Fig. 22. Threshold (K,,)

and unstable fracture (K,,) stress intensities for two titanium alloys in different thicknesses(401.

intensities for sub-critical flaw growth greater, for the thicker specimens. It appears that the greater restraint and lesser plastic relaxation associated with plane strain conditions are essential features of environment-induced cracking. The circumstances in plane stress are further complicated by the inert environment flaw growth discussed in the previous section, which seems to be emphasized in plane stress. It seems possible that this could be confused with environmental cracking on some occasions. A minimal amount of work has appeared on the effect of aggressive environments upon the plane stress-plane strain transition in high strength steels. Such data as are available, Fig. 23, suggest that the transition is not shifted in thickness, but merely lowered different amounts by water and hydrogen gas [4 1I. 3. FATIGUE CRACK GROWTH Linear elastic stress analysis and crack tip plasticity The evidence shown earlier, Figs. 2 and 3, indicates that the stress intensity factor, K, is the controlling stress parameter for fatigue crack growth. Moreover, the assump tion of a linear-elastic stress analysis to obtain the redistribution of stress due to a

Sub-critical flaw gnnvth

23

I

H-I I Y.S.-210

Kai

I

0

10-3 Rotlo of

Plortlc

Zonr

I

I

10-2

I

10-l Slrr

to

Plot,

TMcknora

ry,,

-

Fig. 23. Threshold and unstable fracture stress intensities vs. ratio of plastic zone size to thickness, H-l 1 steel,230 ksi yield strength[41].

crack is perhaps even more applicable to fatigue loading than monotonic loading. This is because ‘shakedown’ or ‘work hardening* to predominantly elastic action occurs, except for the limited plasticity associated with the crack tip, even when the net or gross section stresses exceed the yield strength of the material. Consequently, the ability to correlate data on crack growth rates, as in Fig. 2, is not ‘stress level limited for elements which are load cycled. Of course, if gross plastic strain cycling is imposed, the linear elastic stress intensity analysis is obviously deficient, even though its empirical use in this situation has met with some success[42,43 1. It is of interest to examine the salient features of crack tip plasticity occurring within the fluctuating elastic field. In contrast to gross plasticity, it is recognized that small scale yielding or other non-linearity near a crack tip does not preclude the applicability of elastic stress intensity analysis. On the other hand, the damage which is accumulated at a crack tip under fatigue loading and which results in progressive growth of the crack must be associated with an irreversible process, more specifically, the plasticity. Because of the extreme stress concentration at a crack tip, plasticity is always present in materials which exhibit ability to flow. Upon reversal of load, plasticity will develop in the opposite sense[3], as illustrated schematically in Fig. 24. In the load drop from point (1) to (2) on the figure, the subsequent compression plastic zone size, wA,developed is estimated by

h,’ wh = 29r(2a,)9’ This estimate of the size, wh, also applies to tension zones formed in loading following unloading. Although the model and simplified analysis are not strictly correct for the larger load excursions in irregular fatigue loadings, they do predict rather well the zone sizes of heavily yielded or damaged material.

24

H. H. JOHNSON and P. C

PARIS

Fig. 24. Successive plastic zones at a crack tip underfatigue toading[3].

This estimate is 4 times smaller than that expected for monotonieahy increasing ioad, since upon reversal in loading sense, the previously plastic material must pass through a change in stress of 2a, to cause yielding in the reversed sense. More irn~~~t* however, is the fact that this estimate of successive zones of yielding depends upon the excursion, hr, in the elastic stress intensity rather than its absolute {or mean) value. Therefore, it is anticipated that the mean load will be of secondary infhrence compared to the range of excursions in creating damage resulting in fatigue crack growth. From the preceding obse~ations of the gross features of crack tip plasticity, it is natural to expect certain patterns to appear in experimental data. These expectations follow from the usual fracture mechanics concepts, with the additional assumptiun that the plasticity is in fact an important measure of the damage and promotes growth of the crack. Since development of crack tip plasticity depends primarily upon AK, it is reasonable to expect the mean Ioad to be of secondary inffuence. This is shown by growth rate data&41 for 2024T3 ~~n~rn alby in Fig. 25, with AK as the loading variable for various related mean load levels y, where

Hudson f45f and Schijve [453report much the same rest&. Frequency is normahy regarded as a secondary variable in fatigue testing, but as it affects the yield point through strain rate effects, it should influence fatigue crack growth rates somewhat. Figure 26 shows the effect of frequency on crack growth rates

Sub-critical flaw growth 50

1

40-

I 0

PO.50

d 0

pt.17 714.50

I

I 0 O**

too.55 9 00 ,:3 4

_ 30b% $ 20x Q IO *m*O* OL I 0

I dl2af

do

.

1200

*

1

i

1

IO

too

IO00

(Ykro-Inches/Cycle)

Fig. 25. Mean load and fatigue crack pwth

I

25

rates in 20%T3 aluminum alloy [#I.

CPM

lom lo loo Cm& Growth Rote A~20)/W~Mkmlnchss~Cyds~

Fig. 26. Frequency and fatigue crack gowth rates in 2024-T3 aluminum alby[44].

in 2024-T3 aluminum alloy where the data tends to order itself with lower frequencies giving higher rates of growth[44]. Similar data on 7075T6 shows no effect for equivalent experimental precision, which is consistent with its known lesser strain rate sensitivity than 2024-T3. Others[46] have made similar observations on ~u~nurn alloys, but little is known of other materials. This lack of data is simply due to all investigators using roughly the same test frequencies for convenience, leaving much to be explored in the highly strain rate sensitive materials. Plane stress vs. plane strain

It is well known that the stress condition at the leading edge of a crack, i.e. plane stress or plane strain, has a large effect on monotonic loading fracture toughness values and on static load environmental crack growth. The role of stress state is often exhibited as thickness effects in tests of plates with through-cracks. Plates which are thick compared to the crack tip plastic zone size develop high constraint at the leading edge of the crack, resulting in typically flat fractures of low apparent toughness, i.e. the plane strain fracture toughness of the material.

H. H. JOHNSON and P. C. PARiS

26 However,

there appears to be a surprising absence of any large effect of stress

condition on fatigue crack growth data. The results of Anderson[47], Hertzberg[rSS], and others show fatigue crack growth rate data with both flat and 45” slant fult shear fracture surfaces on the same diagrams with no apparent difference. However, careful test results by Swanson [4] show a small but distinct drop in growth rate at this fracture mode transition from flat to 45” shear. The lack of a large effect on fracture mode transition in fatigue may perhaps be due to the fact that cyclic plastic straining at the crack tip tends to relax the constraint and almost eliminate its effect. On the other hand, some investigators[49, SO] have ascribed other effects to the fracture mode transition which bear some further attention. And it should be pointed out that since environmental effects appear to be highly sensitive to fracture mode[40], more consider~ion should be given to this point in environments fatigue crack growth. The efecr of high stress intensity, approaching criticaf fracture toughness ( K,)

As pointed out earlier, there seems to be little, if any, effect of gross or net section stress values, even at or above yield, on fatigue crack growth. However, there appears to be some special effect at high K values approaching the K, of the material. In thinner plate tests where final failure tends toward the plane stress mode, i.e. with sizeable shear lips, fatigue crack growth progresses rapidly at K-levels near or above the K,, of the material. At these levels, fatigue crack growth is accompanied by audible ‘pop-in’ and the growth rate data plotted against K shows an acceleration of rate over that normally expected[52,531. This effect is, of course, sensitive to the plate thickness and constraint conditions, and may be accompanied by other effects of approaching instability [54). The e$ect of very low stress intensity values

The phenomena of a ‘threshold level’ below which static load environmental cracking is arrested, and the ‘endurance limit’ in smooth specimen fatigue, lead to the question of whether such threshold levels exist in fatigue crack growth. In data presented in earlier papers[3,44,47], no lower limit was observed for K-levels corresponding to crack growth rates of less than IO-’ in./cycle in several materials. Observations at even lower stress intensity levels were apparently not made since the time required to perform such tests becomes excessive on ordinary fatigue equipment. However, Linder(55] did perform such tests on 7075-T6 ~u~nurn alloy using a high-speed test machine and observed with adequate precision average rates as low as I O-loin.lcycle. His results are shown in Fig. 27. The dashed tine shows the scatter band of data from Fig. 2 to ihustrate the consistency of his results with earlier tests. Linder observed rates averaging less than an atomic spacing per cycle, averaged over many thousands of cycles, which continues to show the consistency of K vs. rate curves to extremely low growth rates. Therefore, from the practical point of view, there appears to be no threshold corresponding to that exhibited by environmental cracking under static load. This is at least very clear for 7075-T6 abuninum alloy where sufficient data on Fig. 27 show that for KiIK,, less than $, fatigue crack growth still exists. Observation of non-propagati~ cracks[56] is sometimes described as a threshold effect, which is contrary to the above conclusions. However, the phenomena of crack growth delays following overloads[57-591, residual stress from other causes, and

27

Subcritical flaw growth

I

I

9

I /

/

Limits

LOL -10 IO

I

I

lO-g

IO+ d(2o) dN

of

l-

Dofa

I

lO-7

I

ICP

(Jq cycle

Fig. 27. Fatigue crack growth rates in 2026T3 aluminum alloy at very low cyclic stress intensitiesI55).

non-homogeneity of material, make the evidence of non-propagating cracks unclear. Since it is common practice in fatigue crack growth tests to initiate cracking at high loads and to run the tests at lower loads, delays in commencement of propagation are expected and observed. Linder[SS] often reported delays of more than 10’ cycles prior to observing crack growth at a reduced load, which then progressed continuously.

Summary of the variables aflecting the rate offatigue crack growth The preceding sections presented the detailed behavioral data patterns observed in fatigue crack growth. The role of the crack tip plasticity was emphasized as a key to understanding these observations. Moreover, all major effects were as might be expected from simple plasticity considerations. Regarding fatigue crack growth as a continuous process, where the local elastic stress intensity, K, surrounding the crack tip plasticity is taken as the controlling loading variable, has met with quite unqualified success over the widest ranges of data available, e.g. in 7075T6 from growth rates of approximately 1O-lo to 1O-* in./cycle. The overriding major variable in causing fatigue crack growth is the range of the stress intensity, AK, (or excursion hk under irregular loadings) for any given material and environment. This is as expected since it is the range which is the predominant cause of alternating plasticity at the crack tip. The mean K level, i.e. y, plays a minor role. Moreover, frequency is a very minor variable for aluminum alloys, whose plastic stress-strain properties exhibit only moderate rate effects. In all observations the stress condition, plane stress vs. plain strain, plays a very minor role as would be expected from reduced constraints accompanying alternating plasticity. Therefore, from a practical viewpoint, one may regard the basic fatigue crack growth rate characteristics of a given material and environment as being established by a plot of AK vs.da/d N over the range of interest. Appropriate shifts in the behavior

28

H. H. JOHNSON

and P. C. PARIS

curve are caused by the minor variables, which in the order of their importance are: 1. mean load, 2. frequency, 3. stress condition. In addition, any other change which affects the stress-strain behavior of the material would correspondingly shift the crack growth rate behavior curve in a moderate way. This view is sufficient to characterize crack growth rate behavior for most applications. For a known crack or flaw in a structure and a known loading pattern, one may determine the AK range, and from the laboratory curve of AK vs. da/d N determine the prospective rate of growth, taking into approximate account the effects of minor variables. Fatigue crack propagation

life

Two means of studying life both for environmental and fatigue crack growth in terms of fracture mechanics variables have been put forth in the preceding discussions. They are 1. experimental determination of crack growth rates followed by numerical integration to estimate life, 2. a direct comparison of applied initial K level in a test or structural component vs. time to failure or life. Since the times to failure in environmental cracking are frequently short above the threshold level, the threshold stress intensity is the important design parameter and there is less interest in contrasting the two approaches in that case. However, the fatigue crack growth life of structures is of high practical interest so that this discussion will emphasize fatigue, even though the analysis applies equally well to environmental cracking. The two approaches may, on first glance, appear to be different, or even contradictory. However, their relationship can be explained with consistency as follows. The crack growth rate behavior without the additional assumptions entailed in choosing a particular growth rate law is expressed by (6) as &=

F(AK,minorvariables).

(6)

The linear elastic crack tip stress intensity, K, is linearly proportional to applied stress, u, and depends upon the configuration and crack size a so that AK may always be represented as AK = Au&u). This equation may be differentiated

(7)

for a constant stress range of loading to give

d(AK) = Aag’(a) and since g(a) in (7) is normally a monotonically inverted as

da

(8)

increasing function of a, it can be

19)

Sub-critical flaw growth

29

Substituting (9) into ( IO) and rearranging results in

(10) where C?(A K/Au) is simply the functional combination of g’(a) whose argument is G(A K/Au). Now, ( 10) came only from (7-9) which in turn depend only on the stress analysis ‘formula’ for the stress intensity factor for a specimen configuration. Therefore, c (A K/AU) represents the effect of specimen geometry. Substituting ( IO) into (6) and integrating gives

d(AW F(AK, minor variables) Au

(11)

which leads to the final form N,= H(K,, K,, Au, minor variables).

(12)

Since F(A K, minor variables) normally depends on AK to nearly the 4th power, this makes the integrand in ( 11) large for small AK and very small for large AK. And since g(a) normally depends on about the qa, the term G (A K/AU) is approximately proportional to Au/AK, which is unimportant compared to the 4th power nature of F (A K, minor variables). Therefore, the integral in ( 11) which becomes H(K,, K,, Au, minor variables) will be very strongly dependent on its lower limit, K,, and only slightly dependent upon K,. It follows as suggested originally by Tiffany[ I], and as shown in Fig. 9, that it is reasonable to neglect K, in H( K,, K,, Au, minor variables). A plot of K, vs. IV, may then be viewed as a representation of the fatigue crack growth properties of a material consistent with ( 12). Moreover, by following back through the analysis leading to ( 12). one can assess the usually modest influence of KC, stress range, specimen configuration, and the minor variables affecting fatigue crack growth rates. Crack propagation laws The possibility that the whole process of fatigue crack growth might be continuummechanical controlled follows from the successful correlation of fatigue crack growth rates in terms of the elastic stress parameter K, and explanation of the role of the various variables from simple crack tip plasticity estimates. If this were so then a dimensional analysis, as suggested by Frost and DugdaIe(601 and more elegantly refined by Liu[61], including only the continuum level stress analysis and stress-strain variables, would be appropriate. The net result of Liu’s analysis is that the crack growth rate should be proportional to the plastic zone size, or n = 2, where $,

= (AK)“.

(13)

Though early data from a limited range of variables seemed to support Liu’s conclusions, more extensive data now seems to support n = 4 as a best integer approximation. Samples of the data are shown on Figs. 28-30, and are also similarly illustrated

30

H. H. JOHNSON

and P. C. PARIS

d(2a) m

(Inchcr/Cyclrl

Fig. 28. Fatigue crack growth rates and a fourth power law for 2024-T3 aluminum alloy [3]. 10;

10;

IO

I 10-a

10-7

10-e

10-5 d(2a) dN

10-4

10-J

I(

(In/Cycle)

Fig. 29. Fatigue crack growth r&es and a fourth power law for 7075~T6 aluminum alloy(31.

elsewhere[3,45,46,52,53,54]. Therefore the simple (dimensional analysis) continuum-mechanical model does not seem appropriate over this wide range of data, but studies of this point are continuing[62]. Many laws of fatigue crack growth have been proposed over the past 15 years. Viewing these laws as empirical fitting of available data, each is legitimate insofar as it represents the data. The questions are always, which data and is the precision of fit sufficient for the purpose for which the law will be used? From preceding discussions, it can be seen that, in general, all the laws should be of the form da/dN = F(AK, minor variables).

16)

The first law which may be modified to suit this form and which fits the data well was that proposed by McEvily and Illg(63]. More recently, Forman[54] proposed a

Sub-critical

I

flawgrowth

31

I

1

10-4

to-5 d(2o) do

(Inches/Cycle)

Fig. 30. Fatigue crack growth rates and a fourth power law for various alloys[3].

law of roughly equivalent precision encompassing better the role of minor variables [45]. These laws are rather complicated in form and therefore do not lend themselves to a better physical understanding of the fatigue cracking process. However, if one must choose laws which can be integrated to compute the crack growth life, then these two are most relevant. On the other hand, it is possible to simply integrate numerically the rate data to compute crack growth lives from given flaw sizes. A law with considerably less precision but perhaps lending better physical insight is the so called 4th power law implied by Figs. 28-30. The law may be written as daldN = V(AK)’

(14)

where V is adjusted to include the effects of minor variables. The data on Figs. 28 and 29 wander about the line representing this law in the same pattern for both 7075-T6 and 2024-T3 aluminum alloys. In this sense, the lack of precision is obvious. But as a simple general rule of thumb, this law fits the widest range of data rather well. The 4th power law offers the advantage of a simple physical interpretation[3]. The volume of the plastic zone at the crack tip for unit length of crack front is proportional to AK’. Therefore, this law implies an almost constant energy dissipation per unit area of crack surface created in fatigue crack growth. This implication seems physically rather reasonable, both in terms of experience with the Griffith type energy analysis of fracture and the key role the crack tip plasticity plays in effecting fatigue crack growth. Moreover, it is rather surprising to note that the 4th power relationship gives a fairly good fit of all data on metal alloys and several other materials, e.g. [64]. The fact that such a simple law can fit data from materials with such widely different microstructures is in itself a curiosity! Perhaps this means that the controlling mechanism of crack growth is similar for all of these materials, which would certainly imply control above the microstructural level. Several authors have proposed microstructural or dislocation mechanisms which lead to a ‘derivation’ of the 4th power relationship[65-68 and others]. However, since

32

H. H. JOHNSON

and P. C. PARIS

the widely different assumptions of each of these derived laws leads to the 4th power relationship, it seems that proposing a mechanism which leads to agreement is not a sufficient test of the mechanism. Moreover, proposing mechanisms which compute the order of magnitude of the constant, V, in ( 14) for various materials[66,67] does not really seem to help either. Anderson[69] pointed out that normalizing the data by taking the ratio of stress-intensity to density, K/p, (or K/E if one prefers) leads to the result that the adjusted V values for all materials are about the same order of magnitude. In conclusion, it is clear that one must explore and test any proposed mechanism more deeply than simply agreement with the 4th power relationship for sinusoidal load-time histories. This point is even better illustrated by the available data on fatigue crack growth rates in steel alloys[3,44,52,53,70]. Figure 31 shows the reference data on such widely different steels as A302B, Ni-MO-V steam turbine rotor steels, 17-7 PH, 3OOM, D6A, H-l I, 250 grade maraging steel, AM 350, and AM 355. The lack of any apparent appreciable difference in fatigue crack growth properties is astounding when the differences in strength, microstructure, etc. are considered. Though this similarity has been known for some years, it is yet to be explained, and anyone who proposes a fatigue crack growth mechanism would do well to review this evidence.

s

I

I

I

50

100

500

* Crack

Growth

Rate

I(

(micm-‘nch~ycle)

Fig. 3 1.Fatigue crack growth rates for different steels [78].

Finally, it is also pertinent to further consider the motivation for proposing laws of fatigue crack growth. As pointed out earlier, plotting data of growth rates da/dN in terms of the stress intensity factor K is sufficient in itself to characterize a materials property for crack growth life computations through direct numerical integration. Also, proposals of .laws based on several mechanisms which lead to agreement with sinusoidal loading data give inconclusive results. So there seems to be rather little motivation other than scientific curiosity for pursuing the matter further, except for one very important problem of broad practical interest. That is the construction of

Subcritical

flaw growth

33

accumulation of damage rules or laws or mechanisms which would permit direct comparisons of fatigue crack growth rates under widely different load-time histories. It would be desirable to measure fatigue crack growth properties in a simple laboratory test under sinusoidal loading and predict growth rates in structures under complex loading of a programmed or random nature. Attempts to apply the simple 4th power-constant work rate interpretation combined with the simple plasticity estimates discussed earlier have led to only modestly reasonable results[3,71,72]. More refinements are required and perhaps the mechanisms of fatigue crack growth must be understood before this is possible.

4. EIWIRONMENT-ACCELERATED

FATIGUE

CRACK GROWTH

In some practical fracture problems, the possibility of sub-critical flaw growth through the combined effects of cyclic stressing and aggressive environments is clearly present. For example, in a program to evaluate the growth of flaws under cyclic load in Ladish D6A-C steel specimens and tanks, Tiffany[ 141 observed that moisture at the flaw reduced the cyclic life span by a factor of ten. Systematic studies of this phenomenon are scarce however, no doubt because of the many experimental variables involved. It is difficult to construct a simple but comprehensive picture of the combined effects of fatigue and environment. At stress intensities above the threshold in a material-environment system, testing experience demonstrates that environmental flaw growth and failure will occur in quite short times. The additional effect of cyclic load might then be best described as ‘fatigue-influenced environmental crack growth’. Even so, if the loading frequency is sufficiently high, the fatigue effects may outpace the environmental reactions, and the flaw growth might well be fatigue dominated. For applied stress intensities less than the threshold, the situation is simpler at least in principle, for then environmental cracking under static load is absent. The situation may then be described as ‘environment-accelerated fatigue crack growth’, since fatigue loading alone would cause cracking. Even here, complications may occur for it is conceivable that fatigue loading alone would produce little crack extension, but that it would also ‘resharpen* the crack in such a way as to perhaps permit relatively large increments of environmental crack extension. Nevertheless, in spite of the complexities cited, it is the authors’ view that in the practical application of sub-critical flaw growth analysis to structures, a simple view will probably be adequate for the vast majority of cases. In point of fact, the scarcity of data requires for the moment that a simple view be adequate. This view is that above the threshold, environmental cracking is so rapid that it is life-limiting; and below the threshold the process may be viewed as ‘environment-accelerated fatigue crack growth’. In both circumstances, more experimental attention must be directed to time-related variables such as load frequency and wave shape. In an early investigation with sharply notched rounds of 4340 at a yield strength of 2 10 ksi, Van Der Sluys[73] showed that failure at 100 cycles or less would occur for an applied stress of 55 per cent of the yield strength in an inert environment, and at 30 per cent of the yield strength in a fully humidified environment. In a recent investigation, Van Der Sluys[74] considered crack propagation in more detail, and showed that the crack growth rate was increased by a factor of 20 in a moist environment. Interestingly, flat fractures were observed in the moist environments, and 45”

and P. C. PARIS

H. H. JOHNSON

34

shear fractures were observed in the dry environment. Thus, the moist environment effects a transition in fracture mode appearance. In cyclic tests where the stress intensity factor was maintained constant by decreasing the load as the crack grew, ~op~tion in a moist environment was observed at constant stress intensities of about 60 ksi (in.)lf2 and higher, far above the probable K Itcc. In direct agreement with the constant K test in static loading[6] described in Section 1, the cracks extended slowly across nearly the entire specimen width until separation occurred. Also in direct agreement, in a dry environment and cyclic load, cracks would not propagate under a constant stress intensity, rather an increasing stress intensity was required, and crack growth occurred only upon the increase in load accompanying an increase in stress intensity factor. Thus, environment-induced cracks perhaps propagate primarily during time at maximum load of the cycle, and pure fatigue cracks propagate primarily during the increasing load. Van Der Sluys[74] developed another interesting point by comparing crack extension per cycle with estimated plastic zone sizes. For crack growth in dry environments, the stress intensity required was sufficiently high that the crack grew in each cycle solely in the plastic zone established during the previous cycle. On the other hand, in the moist environment the cyclic stress intensity was suthciently low that crack extension was into material elastically stressed during prior cycles. However, the applied stress intensities in Van Der Sluy’s work far exceeds the static load threshold (KI,) stress intensities reported[9] for a similar steel and strength level, and no experiments were reported at cyclic stress intensities less than the static threshold stress intensity. Interesting correlations with static load results[6,3 I] were established by Li, Wei and Taldar75.761, who explored a range of metallurgical and environmental parameters. They worked with both a maraging and a 4345 steel, each at two different strength levels, and both dry and humid environments. In both envi~nments, the measured crack growth rates were adequately represented by the 4th power law of ( 14) as is shown by one example in Fig. 32. The environmental effects may be summarized, Table 3, in terms of the measured values of the rate coefficient % of ( 14).

!5AK-15

l

to 30 kri&

4T. C ; -lb -1s -

0

l

0 0

l

0 0

l

0

3 0 2-

0 l

0 *

I0

0 Q

0

0

0 0

0

o

Dehumidified

a

Humid

-

Argon

Arqon, 1009CR.H.

_

0

0

‘*

2

“

I

4

6

L

”

”

’

8

IO

12

i

”

14

f

16x IO4

N, Cycles

Fig. 32. Effect of

moisture upon fatigue crack

growth rate in aO.45C-Ni-Cr-Mo

steel[75].

sub-critical llaw growth Tabk 3. RUC axfficients

35

in humid and dry environments uoder cyclic badI 75,761 CBX ItP

Stal

KI, ksi (in.)‘”

OJX-Ni-Cr-Mo Tempered I hr 400°F 0*45C-Ni-Cr-Mo Tempered I hr 8CUF I8 Ni(300) Maraging steel I8 Ni(250) Manlging steel

Maximum WPM K ksi (in.P

W arllon

wet MS?.“.)

wet

Room

wOEL”.)MO9K.“.)

37

15

I.3

2.0

2.2

2.0

56

I5

I.6

l-7

I.6

I.8

53

I5

I.6

2.0

-

-

110

I5

l-6

1.6

-

-

These data display a number of interesting features. For both steels, environmental increase of the crack growth rate is more evident at the higher strength level, or lower fracture toughness. However, there is no correlation with fracture toughness independent of chemical composition, since both the 18Ni(300) and the 0*4X-Ni-Cr-Mo steel tempered at 800°F have about the same fracture toughness, but a major increase of fatigue crack growth rate with moisture is evident only for the maraging steel. It is also of interest to note that the moisture effect, when it exists, is apparently independent of chemical composition and microstructure. For both steels cycled over identical ranges of stress intensity factor, the moisture enhanced growth rates were identical. It is interesting to speculate that the moisture enhanced growth rate curve (du/dN vs. AK) for a variety of steels might simply lie parallel to the corresponding curve for dry environments. This is clearly a fruitful area for further research. In agreement with results from static loading, an increase in relative humidity seems to lead to a saturation in crack growth rate. This is evident from the dry argon, 40 per cent relative humidity, 100 per cent relative humidity air, and wet argon results for the higher strength 0*4X-Ni-Cr-Mo steel. As before, this may be interpreted in terms of water condensation at the crack tip. However, in contrast to static load results, oxygen does not affect the rate of fatigue crack growth in moist environments. Perhaps the protective oxide layer is continually broken on each loading cycle, and the fresh crack tip is freely accessible to the water vapor. In a natural development from this work, Spitzig, Talda and Wei[77] have studied the effect of dry and wet hydrogen at atmospheric pressure upon fatigue crack growth rates in the 18Ni(250) maraging steel. Their interesting results are summarized in Table 4. It is evident that in complete accord with static load results, hydrogen at atmospheric pressure is a more aggressive environment than moisture; and that in a Tabk 4. Rate coefficient (0 in humid and dry argon and hy&ogcn environment for 18Nit250) mataging stals [ 771 QXIOP Hydrogen

AI@!! Dry I.6

Humid I.6

EY 4.3

-Humid

I -5

36

H. H. JOHNSON

anil P. C. PARIS

moist hydrogen gas, the moisture dominates the hy~ogen. Presum~ly, as in static loading, the condensed pool of water at the crack tip serves as a barrier between the crack tip surface and the hydrogen gas. In the investigations just summarized, there appears to be no results for maximum cyclic stress intensities that are clearly less than the threshold stress intensity in static load. This is regrettable, for the below-threshold region is probably of greatest practical interest. For some titanium alloys, however, it has been clearly demonstrated that moisture can enhance fatigue crack growth by a factor of about four at stress intensities at least as low as one-half of the threshold value[40]. 5. APPLICATIONS OF SUR-CRITICAL FLAW GROWTII ANALYSIS Sub-critical Saws are, of course, but one aspect of the overall concept of a fracture control plan. En~nee~ng experience has demons~ted that most serious structural failures arise from unexpected extension of pre-existing crack-like flaws. To that extent, flaws must be regarded as a seemingly inevitable component of most structures, and their effects are clearly more serious as the operating stress, material strength level, and structural thickness increase. A thorough discussion of the many possible mechanical and metallurgical origins for crack-like flaws has been given by Irwin et a1.[78]. An overall view therefore suggests that improvements in fracture control plans will require coordinated progress in several related technologies, including 1. further attempts to eliminate metallurgical flaws developed in solidification and processing, i~clu~ng inclusions, segregate bands, laminations and porosity; 2. careful control of fab~cation and repair procedures to mitigate such defects as weld and heat affected zone cracks and the development of brittle microst~ctmes; also various forms of mechanical damage during production, such as tool marks and gouges, 3. continued improvement of non-destructive testing techniques, and 4. continued efforts to develop materials with improved resistance to sub-critical flaw propagation. For the moment and at least the near future, however, sub-critical flaws exist and it is useful to consider the behavior patterns discussed in the previous sections in relation to engineering applications. It is appropriate to start with the concept of the critical crack size discussed earlier, Fig. 1. It will be recalled that the critical crack size depended functionally upon the operating stress level and the fracture toughness, as characterized by the critical stress intensity factor. In a structure, the fracture toughness must be expected to vary with location; for metallurgical reasons, it will vary among base plate, weld metal, heat affected zone, etc. and for mechanical reasons with section thickness. It would be desirable to focus attention upon the largest flaw in the region of combined highest operating stress and lowest fracture toughness, and to estimate life from previously measured growth rates. However, at the moment this is usually not possible and more qualitative views must be considered. Proofor overload test

A form of insurance often applied prior to service, particularly with pressure vessels, is a proof test which may consist of either a static or cyclic stress well above the expected stress in application. If the structure withstands the proof test, it is con-

sub-critical flaw growth

37

sidered suitable for use. However, there are several important points to consider in connection with proof testing. From Fig. I and the discussion in Section I, a successful proof test specifies the maximum possible (or initial) flaw size at the beginning of service. Since the operating stress is lower, the critical flaw size for unstable fracture in service is huger than the initial flaw size; and safe operation is assured assuming no sub-critical flaw growth or material degradation as might be caused by irradiation. Proof testing offers subsidiary advantages which may be of importance in some applications. It may relieve long range residual stresses introduced during fabrication, particularly if the proof test is performed at an elevated temperature where the material yield strength will be lower. However, with elevated temperature proof testing, care must be taken to avoid unwanted microstructural and toughness changes of thermal origin, and also permanent changes in dimension. This would be most important, and perhaps a limiting factor, for the higher strength materials. Another benefit of proof testing is the possibility of blunting of preexisting flaws, an effect which should also be enhanced at elevated temperatures. Although this blunting would surely introduce a localized pattern of residual stress upon unloading, it is known that the effect of blunting and the associated residual stress region is to enhance the resistance to subcritical flaw growth by either cyclic stress or aggressive environments. Proof testing at low temperature may also offer advantages. Because the material yield strength increases at low temperatures, it is possible to proof test at a stress well above the operating stress, and perhaps even equal to or higher than the yield strength at the operating temperature. Although residual stress relief and flaw blunting are perhaps less probable at low temperatures, a successful proof test provides substantial assurance. However, proof testing is not the universal panacea, and it may even cause problems that otherwise would not appear. For example, if the proof testing environment is aggressive, then an undesirable amount of crack extension may occur, and not infrequently has, during the proof test. This may even result in an unnecessary failure during proof testing, which is clearly what happened during the hydrotesting of high strength steel motor cases in the late 1950’s. Of course, if failure does not occur during the proof test, the structure will still exhibit enhanced susceptibility to sub-critical flaw growth and fracture in subsequent application. A recent and striking example of this is given in Figs. 33-34 for a titanium ahoy (6Al-4V) proof tested in methanol and operated in static load in Aerozine environments[79]. Methanol was originally used for proof testing in an attempt to avoid the problems often associated with water, but as is shown by Fig. 33, this choice was unexpectedly unfortunate. From the ratio of threshold to unstable fracture stress intensities, both distilled water and Aerozine may be considered as mildly aggressive environments to Ti-6AL4V. Methanol, however, must be characterized as viciously aggressive, with a K,,,/K,, ratio of only O-24. As was pointed out by Tiffany and Masters [79], proof testing at 140 ksi in methanol would cause flaws as small as O+IO2in. to grow during proof. For vessels successful in the proof test, the maximum initial flaw size at the time of the next test or operational cycle is O-023 in. Fig. 33. Consider the effect then of subsequent pressurization at IO5 ksi. At this pressure, flaws as small as 0.003 in. could grow if exposed to methanol and, depending upon the proof time, could grow to almost O-032 in. without failure. If failure did not occur, additional pressure vessel life in other environments could not be guaranteed without an additional proof test or, as noted in Fig. 33, by subsequent

38

H. H. JOHNSON

0.02

and P. C. PARIS

0.04

0.06

Flow Depth .a (Inchrs)

Fig. 33.aEnvironmental cracking behavior diagram for Ti-6Al4V

in 0.053 in. thickness.

:

r

z

100 90 60

Flolr

Depth -Incher

Fig. 34. Environmental cracking behavior diagram for Ti-6AI4V

in 0,024 in. thickness.

control of pressure and temperature to about 85 ksi at 70°F. This combination results in a stress intensity less than the threshold intensity for Aerozine SO for a vessel containing, O-032in. flaw. For vesseis to be exposed only to Aerozine 50 at 105 ksi after the 140 ksi proof test, it is evident that flaw sizes of O-023in. (the size proved by the proof test) are only marginably acceptable at temperatures exceeding 110°F. Figure 34, which was

sub-critical flew #mvth

39

developed for a different flaw depth/wall thickness ratio and therefore a different stress intensity formula, may be interpreted in a similar manner. It is evident that this type of diagram provides a concise summary of the subcritical flaw growth behavior of a material in different environments, and of the corresponding relationships among flaw sizes and operating and proof stresses. A synthesis of environmental cracking under static andfatigue loading

For static load in aggressive environments, the previous discussion has established the threshold stress intensity, KI,cc, as the relevant design parameter. The existence of a threshold stress intensity seems well established, both by the sheer quantity of published data and the elegant crack arrest experiments of Smith et al.[S]. For stress intensities in excess of the threshold, the failure time is generally very short, and loading in this range will almost surely produce failure. The threshold concept for environmental cracking retains some importance in fatigue loading, even though the environment may significantly increase the fatigue crack growth rate at lower stress intensities. Although few data are available, the following picture seems reasonable. At stress intensities above the threshold, dynamic loading may even increase the time to failure, i.e. ‘fatigue-retarded crack growth’, if it proves to be generally true that environmental crack extension occurs only near the maximum cyclic stress intensity. In this case, a strong effect of frequency on the number of cycles to failure may also be observed, with decreasing cycles to failure accompanying a decreased load frequency. The oxygen effect observed in static[3 l] but not dynamic loading may also prove to be a complicating factor. Presumably, as the load frequency is reduced in gas environments containing oxygen, a frequency will be reached at which the oxygen becomes at least partially protective, and then both the life and the number of cycles to failure should increase. At cyclic stress intensites less than the threshold, some of these complicating factors should disappear, for then environment-induced static load crack extension is presumably no longer possible. Under these circumstances, a convenient view of the relation between environmentenhanced flaw growth in static and dynamic loading is as given in Fig. 35 constructed from the data of Piper et af.[40]. Since there is no known threshold effect in environment-enhanced fatigue crack growth, the lower limit of this region is not absolute, but could be determined for a specific application by an estimate of, say, the maximum crack growth rate below which a specified life may be attained. From a practical point of view, the K region below the threshold is probably of greatest interest, and there are virtually no data available. Synthesis of material behavior in fatigue and aggressive environments It is evident that characterization of material behavior in both fatigue and aggressive environments can be accomplished, but rather little discussion has been offered as to how these characterizations are affected by changes in metallurgical variables. Of considerable importance, particularly when weight saving is important, is the role of strength level. Unfortunately, no investigation reported to date has covered a sufficient range of environmental, mechanical, and metallurgical variables to completely characterize the behavior of a given material. It would be desirable to synthesize these aspects into a single diagram which would be useful, at least qualitatively, for predictive purposes. A possible diagrammatic

40

H. H. JOHNSON

and P. C. PARIS

Ti-SAI-i

MO

Duplex Annealed

Environmental Cmckinq

Time to Foilure - hrr Fig. 35. A synthesis of environmental cracking under static and dynamic loading for an 8Al-

1MOtitanium alloy.

representation is given for quenched and tempered 4340 steel in Fig. 36, which is constructed partly from experimental data and partly from engineering estimates. The development of the figure will be described first, and then its inte~ret~ion. Critical flaw sizes calculated from ( 1) are plotted against yield strength level, with the fracture toughness K,, and the threshold stress intensity &,, taken from the data of Peterson et a1.[9], reproduced earlier in this paper as Fig. 1I. The plane strain-plane stress transition was fixed by assuming a plate thickness of O-25in., which put the transition in the yield strength range of 160-190 ksi, and a critical flaw-size range of 0.1-l in. A decrease in plate thickness would, of course, shift the transition to higher yield strengths. In the plane stress regime, K, was assumed to be twice the value of K,, at the yield strength under consideration. For very high yield strengths, above about 180 ksi, an operating stress level equal to the yield point was assumed, since the critical flaw sizes for environmental crack initiation were very small, less than, say 5 X 10T3in. It is generally conceded that residual stresses of yield point magnitude can exist over volumes of this typical linear dimension because of microstructural inhomogeneities, including inclusions, second phase particles, and porosity. Consequently, the yield stress levei is the appropriate design stress. For lower yield strengths, the critical flaw sizes are larger, and residual stresses of microstructural origin are no longer of importance. Here a more conventional safety factor may be used, and the operating stress level has been set at one-half of the yield strength. The fatigue crack growth curve was calculated from ( 1) and the experimental data in Figs. 30-3 1, for an initial fatigue crack growth rate of lo-” in./cycle, an associated stress intensity range AK of 20,000 ksi (in.)1’2and an operating stress level of one-half of the yield strength. This diagram suggests clearly that sub-critical flaw growth of environments origin is the major problem at high yield strengths, in excess of about 180 ksi, and that

41

Sub-critical flaw growth

I

I

I

I

Flaw Growth Bahavior Diagrom for 4340 Steal, 0.25 in lhicknaaa

Flaw Growth I

-

Calculated

- - -

Enqinming Estimate

1

I25

I

I

I

I50 175 200 Yield Strength Level - ksi

1

225

Fig. 36. A synthesis of sub-critical flaw growth by environmental cracking and fatigue for 4340 steel at different strength levels. 0.25 in. thickness.

fatigue is probably less important. Above this yield strength level, the K,,, values are so low that a corresponding fatigue crack growth rate, as determined from the fourth power law or Fig. 3 I, would be negligible, even at stress levels approaching the yield strength. It is not even certain that environment-assisted fatigue crack growth would be a severe problem in this yield strength range, because of the low stress intensities involved. This interpretation is in accord with general engineering experience, which indicates that static load environment cracking becomes much more prevalent at yield strengths above about 180 ksi. At lower strength levels, fatigue and environment-accelerated fatigue become the dominant problems, and static load environmental cracking is much less important and probably absent. This occurs, in part, because of the sharp rise in KIsccat lower yield strengths, with the attendant shift in operating stress from yield stress to one-half of the yield stress, and in part because of the transition to plane stress, in which environmental cracking under static load seems to be largely absent. From this discussion, it is evident that sub-critical flaw growth is only partially understood, and that the behavior of practical structures cannot yet be quantitatively predicted. Behavior patterns have been determined and interpreted for only a limited range of metallurgical, environmental, and loading parameters. This past work has provided considerable physical insight into the nature of sub-critical flaw growth, but clearly much remains to be done before the subject is put on a quantitative basis.

42

H. H. JOHNSON

and P. C. PARIS

authors wish to acknowledge the financial support of the Advanced Research Projects Agency, through the Materials Science Center at Cornell University and the Stress Corrosion Coupling Program at Lehigh University.

Acknowledgentenrs-The

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Publ. No. 381 pp. 249-277 (1965).

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of

Sub-critical flaw growth

43

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In press (1968).

(541 R. G. For-man, V. E. Keamey and R. M. Engle. Numerical analysis of crack propagation in cyclic loaded

structures. A.S.M.E. Paper No. 66-Met-4, (1966). [55] B. M. Linder, Extremely slow crack growth rates in ahuninum alloy 7075-T6. M.S. Thesis, Lehigh University, ( 1965). [56] N. E. Frost, The growth offatigue cracks. 1st Int. Co& on Fracture, Vol. 3, p. I433 ( 1966). [57] C. M. Hudson and H. F. Hardrath, Effects of changing stress amplitude on the rate of fatigue crack propagation in two ahuninum alloys. NAS&Tech. Note. No.-D-960 ( I96 I). [58] S. H. Smith, Random loading fatigue crack growth behavior of some aluminum and titanium alloys. Proc. Symp. on Fatigue ofAircrdt Structures, A.S.T.M. ( I %5). (591 J. Schijve and D. Broek, Crack pmpaganon-the results of a test program based on a gust spectrum with variabk amplitude loading. Aircrqfr Engng 34, No. 405 ( 1962). (601 N. E. Frost and D. S. Dugdak, The propagation of fatigue cracks in sheet specimens. 1. Me& Phys. Soli& 6.92 ( 1958). (611 H. W. Liu. Fatigue crack propagation and applied stress range-an energy approach, Trans. A.S.M.E., Ser. D, 85.1 I6 ( 1963). 1621 F. A. McClintock, Private communication

(1967). [63] A. J. McEvily, Jr. and W. Illg. The rate of crack propagation in two ahuninum alloys. NASA-Tech. No. 4394 ( 1958).

Note

44

H. H. JOHNSON

and P. C. PARIS

(641 H. F. Borduas, L. E. Culner and D. J. Burns, Fracture mechar& analysis of fatiapre crack pact in ~Iy~thyI~~~~. 23rd ANTEC, Society of Plastic Engineers, Detroit ( 1967). [65f J. Weertman, Rate of growth of fatigue cracks calcukated from the theory of in~~~si~ dislocations distributed on a plane. Proc. Ist Int. Conf. on Fracture. Vol. I. D. 153 f 1966). WI A. J. McEvily and R. C. Boettner, On f&igue crack propagat&n in FCC metals. Acfa Metall. ll(1963). [671 J. M. KraRt, On prediction of fatigue crack propagation rate from fracture toughness and plastic flow properties, A.M.5 Trans. 58,69 I ( 1965). [681 J. R. Rice, A note on models of fatigue crack growth. Lehigh Unio. Inst. Res. Rep. ( 1964). W. E. Anderson, Private communication ( 1959). :7”:; A. J. Brothers and S. Yukawa, Fatigue crack propagation in low-alloy heat-treated steels. A.S.M.E. Paper No. 66MET-2 (1966). r711 S. H. Smith, Fatigue crack growth under axial narrow and broad band random loading. Acoustical Fatigue in Aerospace Structures. Syracuse University Press (1965). i721 J. R. Rice, F. P. Beer and P. Paris, On the prediction of some random loading characteristics relevant to fat&e. Acoustical F&g&e in Aerospace Structures. Syracuse University Press t 1965). (731 W. A. Van Der Sluys, Effects of repeated loading and moisture on the fracture toughness of SAE 4340 Steel..!. Baric Engng. Trans. A.S.M.E.

Ser. 0.81.363

(1965).

[741 W. A. Van Der Sluys, The effect of moisture on slow crack growth in thin sheets of SAE 4348 steel under static and repeated loading. J. Baric Engineering, Trans. A.S.M. E. Ser. D, 89 28 ( 1967). P. M. Talda ._and C. [751 -R. P. -Wei,._..~. __-Y. Li, Fatigue crack propagation in some high strength steels. A.S.T.M. Spec. Tech. Publ. No. 4 I5 ( 1967).

[76] C. Y. Li, P. hi. Talda and R. P. Wei, The effect of environments on fatigue-crack propagation in an ultra-high-strength steel. 1nr.J. Fracture Mech. $1.29-36 (1967). [77] W. A. Spitzig, P. hl. Talda and R. P. Wei, Fatigue-crack propagation and fracm8raphic analysis of 18 Ni (250) mar-aging steel tested in argon and hydrogen environments. Engng Fracture Mech. 1, 155-166 (1968). [78] G. R. Irwin, J. hi. Krafft. P. C. Paris and A. A. Wells, Basic aspects of crack growth and fracture. Chap.

7, Rep on Reactor Pressure Vessel Technology. To be issued by Oak Ridge National Laboratory (1968). [79] C. F. Tiffany and J. N. Masters, Investitmtion of the flaw growth characteristics of6A14V titanium used in Apollo spacecraft pressure vessels. Final Rep. NASA, Contr. No. N AS 9-6665 f 1967). (Received 25 July 1967)

R6sumi: - L’bidence majeure portant sur lacroissance de f”lures sous-critique dans des ~~~x structuraux est revue et discutte. L’attention porte sur k driveloppement de f&ures existantes a des tensions de fonctionnement inf&ieures a la risistance limite de la section nette, B lafois du point de vue de t’effet indtpendant et de l’effet combine de miiieux favorisantla fati8ue et I’attaque. Dam la premiere Section, on considere le possibilite d’appliquer les concepts de la mecanique de la rup ture concepts de developpement de ffiure et il est dtmontre que la facteur d’intensitt de la force de tension peut itre envisage en tant que force d’entrabtement B la fois du dCveloppement de rupture par la fatigue et la rupture diie au milieu environnant sous une charge statique. Ceci autorise I’accord des resultats d’essais provenaut de differentes fonnes g6omCtriques d’bprouvettes, et aussi un accord entre ies resuitats d’essais et des d6faillances en tours de service. La rupture sous une charge statique d&ermim?e par le milieu est bud& dam la Section 2. D’aciers et d‘alliages au titanium darts differems miheux: t’eau, la vapeur d’eau, I’hydrogene et I’oxyg&e est discut& Pour les acien, le developpement de la rupture dans l’eau et ia vapeur d’eau satur6e est un pro&e a activation thermique. L%nergie ~~tiv~i~ de la croissance de rupture s’aceorde bien avec la vakur mesuree pour la diffusion de ~hy~~~. La r&e de I’oxygene darts I’ar&t du ~vel~~nt de f&ue souscritique dans un milieu de vapeur d’eau est d&cute. La Section 3 itudie le developpement de rupture du a la fatigue. II est d&nontrt! que la @rune d’intensites de la force de tension est le facteur majeur gouvemant les taux de croissanee de rupture et la d&e de fatigue, la frequence et la charge moyenne &ant des variables secondaires. Les lois du taux de deveioppement de la rupture sont consid&& et il est demontm que la qua&i&me loi de puissance detient lagamme la pius &endue. Pour une surprenante variite d’aciers, le taux de dtveloppement de la rupture par la fatigue est insensible a la composition, a la microstructure et au niveau de resistance, quand le taux de developpement est dCtermin6 en fonction de la gamme d’intensit6 de la tension. L’effet combine de la fatigue et du milieu est traitt darts la Section 4. Quelques modeies de comportement seion le milieu pour des contraintes statiques sont observes pour transferer .ia contrainte de la fatigue. On remarque un manque d’infomations pour les 8ammes d’intensites de tension inferieures au seuil. Dam k Section 5, on souligne les applications m6caniques. Les relations entre f’importance des f&ues, les intensit6s de tension de seuil en dif%rents milieux, et ies tensions de preuve et de travail sont present&s sur un graphique et on discute de leur inte~~t~on. Pour I’acier 4340, le r&e du niveau de la hmite de r&istance est resume en un schema qui indique que la rupture dfte au milieu est un probkme ma&r pour fes t&stances Jimjtes exddant I80 ksi, tandis que le ~~e~p~~nt de la rupture par la fatigue est k probEme majeur pour des niveaux plus faibles de la resistance.

Sub-critical flaw growth

45

B-Die wichtigsten Ergebnisse iiber die RiBerweiterung in Konstruktionsweikstoffen im subkritischen Bereich werden iiberpriift und besprochen. Besondere Beachtung wird dabei dem Anwachsen von bexeits vorhandenen Rissen bei angelegten Spannungen, die unteihalb dei Streck Festigkeitbezogen auf den Restqueischnitt-liegen, unter Beriicksichtigung der jeweiligen wie such gemein samen Auswirkung des Ermtidungs vorgangs bzw. der korrosiven Umgebung geschenkt. Im Abschnitt 1, wird die Anwendungsmiiglichkeit der Methoden der Bruchmechanik aufdie RiSenveiterung behandelt, und es wird gezeigt, dass der Spannungsfaktor als treibende Kraft sowohl fdr den Ermiidungsbruch ah such fdr die umgebungsbedingte Rissbildung unter stactisches Belastung angesehen werden kann. Auf diese Weise wird eine Korrelation der Versuchsergebnisse von Probekdrpem verschiedener Abmessungen, sowie eine Korrelation der Priifergebnisse mit Wartungsproblemen ermiiglicht. Im Abschnitt 2 wird die umgebungsbedingte Rissbildung unter statischer Belastung behandelt. Das Verhalten von Sttilen und Titaniumlegierungen in verschiedenen umgebenden Medien wie Wasser, Wasserdampf, Wasserstoff und Sauentoff wird erortett. Bei Stiihlen ist das Risswachstum in Wasser und gesattigtern Wasserdampf ein thermisch aktivierter Vorgang. Die Aktivierungsenergie Fiir die Ri6erweiterung stimmt gut mit dem bei der Wasserstoffdiffusion gemessenen wert iiberein. Die Rolle des Sauerstoffes bei der Verhinderung des Wachstums von Rissenim subkritischen Bereich in Gasen wird erortert. Abschnitt 3 behandelt die Riflemeiterung beim Ermiidungsvorgang. Es wird gezeigt, daO die Amplitude des Variations bereichs des Spannung Faktors (Ak) hauptsiichlich von Wichtigkeit fdr den Zuwachs der Rit3erweiterung pro Periode (da/dN) und die Ermiidungs festigkeit ist, w&end Frequenz und Durchschnitts last zweitrangige Parameter sind. Gesetzmtigkeiten fur die RiSenveiterung werden betrachtet und es wird gezeigt, dat3 das mit der vierten Potenz in Ak gehende Gesetz im weitesten Bereich Giiltigkeit hat. Fur eine iiberraschende Anzahl von Stilen verschiedener Art ist die RiSzuwachsrate beim Ermiidungs bruch unabhiingig von Anderungen in der Zusammensetzung, dem Mikrogefuge und der Festigkeit. wenn man die Zuwachsrate (da/dN) als eine Funktion der Amplitude des Spannungs Faktors (Ak) auftriigt. fm Abschnitt 4 wird die gleichzeitige Auswirkuna von Ermiiduna und Korrosiver Umgebung behandelt. Es wird festgestellt, dass manche der umgebungs-be&ten Gesetzn&ssigkeiten im Verhahen bei statischer Belastung auf die Ermiidungsbelastung iibertragbarsind. Ein Mangel an MeSwerten fir Ak unterhalb des Schwellwerts wird bemerkt. Im Abschnitt 5. stehen die technischen Anwendungsmoglichkeiten im Vordergrund. Die Beziehungen zwischen RiSgriiBe Schwellwerten der Spannungsiiber iiberhohung Umgebungen in verschiedenen, sowie Priif-und Betriebsspannungen zum Priifen und w&end der Benutzung werden graphisch dargestellt und ihre Auswertung besprochen. Der Einflug der Variation der Streckfestigkeitniveaus fur Stahl 4340 wird in einem Diagramm zusammengefasst, wobei gezeigt wird, dass die umgebungsbedingte Rissbildung das Hauptproblem bei Streckfestigkeiten oberhalb I80 ksi darstellt, w&end bei niedrigeren Festigkeiten das Ermiidungsbruchwachstum das Hauptproblem ist.