" " N95- 14484 - NTRS - NASA

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rates when the nominal applied. AK is less than the threshold value,. AKth, determined .... grain, or the crack size may be on the order of a few grain diameters. small. L ... all related to the loss of microstructural and mechanical similitude. When ... sion of slip across a grain boundary ..... clear under what conditions the large ...

N95- 14484

/ ....... "' '" " ANALYSIS

OF SMALL

R. C. McClung,

CRACK

BEHAVIOR

K. S. Chan, Southwest

FOR

AIRFRAME

APPLICATIONS

S. J. Hudak, Jr., and D. L. Davidson Research Institute

San Antonio,

....,..

¢ ,,:,........ :_ ?

Texas

,s...

;i_ :>_....... iii:: ? !:

':":_

ABSTRACT The small fatigue crack problem is critically reviewed from the perspective of airframe applications. Different types of small cracks--microstructural, mechanical, and chemical--are carefully defined and relevant mechanisms identified. Appropriate analysis techniques, including both rigorous scientific and practical engineering treatments, are briefly described. Important materials data issues are addressed, including increased scatter in small crack data and recommended small crack test methods. Key problems requiring further study are highlighted.

INTRODUCTION "Small" fatigue cracks are sometimes the same nominal value of the cyclic crack

observed to grow driving force, AK.

faster Small

than traditional "large" cracks have also been

to grow at non-negligible rates when the nominal applied AK is less than determined from traditional large crack test methods. These phenomena assessment small crack

based on large growth.

crack

analysis

Although the earliest documentation cations [1], small cracks have historically Classic damage tolerance analysis (DTA) flaw regime, and other structural integrity crack growth (FCG) arguments altogether.

methods

can be nonconservative

cracks at observed

the threshold value, AKth, imply that a structural life if the life is dominated

by

of the small crack effect was motivated by aircraft applinot been an important issue for most airframe structures. typically mandates an initial flaw size beyond the small assessments based on safe-life logic neglect explicit fatigue

However, ongoing developments in the airframe industry appear to be increasing the significance of small cracks for fracture control of aircraft structures. It is now recognized that multiple small flaws associated with multiple-site damage (MSD) can degrade residual strength capability in aging aircraft [2, 3]. In response to this observation, the Industry Committee on Widespread Fatigue Damage (WFD) of the Airworthiness Assurance Working Group (AAWG) has recently identified small cracks as a critical issue requiring further focused research [4]. In applications analyses are employed, the equivalent initial flaw size (EIFS) which is back-calculated economic destructive

where durability from some

total life is often well within the small flaw regime [5]. Ongoing improvements evaluation (NDE) capabilities may lead to the re-definition of initial flaw sizes

in nonfor tradi-

tional DTA which are down in the small flaw regime. And in some applications, structural integrity assessments formerly based on safe-life calculations now must be performed with DTA logic. The relevant crack sizes for these applications, however, are often much smaller than those historically associated with the DTA method. The

purpose

of this paper

is to provide

a critical

overview

of the small

crack

problem

in the

context of airframe applications. Different types of small cracks are carefully defined and relevant mechanisms identified. Appropriate analysis techniques, including both rigorous scientific and practical engineering treatments, are briefly described. Important materials data issues are addressed,

463

including increasedscatterin small crack data andrecommendedsmall crack test methods. Key problems requiring further study arehighlighted. Although this paper does provide an expert review of the small

crack

problem,

it is not intended

tant research in the field. Many this paper, and it is not possible

DIFFERENT

"small

to be an exhaustively

researchers or attempted

have contributed to acknowledge

TYPES

All small cracks are not the same. crack" effects in different settings.

OF SMALL

Different Criteria

Before

different

beginning,

types

of small

one note

summary

cracks:

situation. suitable

is needed.

crack" both appear in the literature, and sometimes recent years, however, the two terms have acquired the US research community, the currently accepted

outlined

The

for different small crack

types of behavior

It is critical, therefore, to underanalytical treatments. This review mechanically-small,

terms

"small

crack"

and

and

"short

the two appear to be used interchangeably. In distinct meanings among many researchers. In definition for a "small" crack requires that all

physical dimensions (in particular, both the length and depth of a surface crack) are small in comparison to the relevant length scale. In contrast, a crack is defined as being "short" when only one physical dimension (typically, the length of a through-crack) is small in comparison to the length scale. These definitions are illustrated in Figure 1. However, it should be noted that this distinction has not always employ

been observed in the literature, the terms with nearly reverse

observe which type of "little" tions of short vs. small cracks

and that meanings.

some current authors (esp. in Europe) choose to Whatever the usage, the reader should carefully

crack is present in a given application. are discussed later in the paper. Microstructurally-Small

Some

of the different

implica-

Cracks

A crack is generally considered to be microstructurally-small when all crack dimensions are small in comparison to characteristic microstructural dimensions. The relevant microstructural feature which defines this scaling may change from material to material, but the most common microstructural completely

scale is the grain within a single

size. grain,

The small crack and its crack tip plastic zone may be embedded or the crack size may be on the order of a few grain diameters.

small

)

L

Figure

464

:

i ¸

:

/:

-

1. Schematic

of "small"

and

"short"

cracks,

including

in

CRACKS

microstructurally-small,

on nomenclature

of all impor-

of understanding individually.

mechanisms are responsible which properly characterize

in one situation may be entirely inappropriate in another stand the different types of small cracks before selecting will consider three chemically-small.

complete

to the level all of them

relationship

to microstructure.

!_!_ !!_i _!i_ _i_! :!_i !!ii!i!ii_i!i_! i:!ii _i! iiii ii !i_ !!_!_i ¸!11¸i¸1%! !i!_!i_! !ii_!i!!i! i_%1 i! ii/il !ili!iiiii:_ii!_ii!_i!ii!! !i!!_i?_ !_i!i!i!i!i _!_!ii!ii!ii!i ii!iii !!!iii!! i!!iiiiii i!!ii!!ii!iiiii:i i:iiii!iii_!iiiiii !ii!!iil !iill i!iiii!i i!i!_!_i_i_i_!_i_!!!!i_i_!_i_!_i!_iii_ii!iiiii_i_iii_ii_i!ii_i_ii_!iii_i

alloy

Typical crack growth data for microstructurally-small in Figure 2, along with traditional large crack data

crack growth can occur at nominal AK values rates are often faster than would be predicted Figure 2), and the apparent Paris slope for the data. Crack arrest (momentary or permanent)

cracks are shown for the same material

for a 7075 aluminum [6]. Note that small

below the large crack threshold. Small crack growth by the large crack Paris equation (the dashed line in small crack data can be smaller than for the large crack can occur m these low AK values, and this arrest is

often observed to occur when the crack size, a, is on the order of the grain size, GS (i.e., when the crack tip encounters a grain boundary). However, not all small cracks arrest or even slow down at these microstructural barriers. As the crack continues to grow, the small crack da/dN data often merge with large crack data.

related

Why do microstructurally-small to the loss of microstructural

cracks behave and mechanical

this way? similitude.

Several When

factors are involved, all the crack-tip cyclic plastic

zone size, rp¢, (and sometimes the crack itself) is embedded within the predominant microstructural unit (e.g., a single grain), the crack-tip plastic strain range is determined by the properties of individual grains and not by the continuum aggregate. The growth rate acceleration of small cracks embedded within a single surface grain is primarily due to enhancement of the local plastic strain range resulting from a lower yield stress for optimum slip in the surface grains [7, 8, 9]. This microplastic behavior also causes (and, in turn, is affected by) changes in crack closure behavior [ 10]. As a small crack approaches a grain boundary, the fatigue even arrest, depending on whether or not slip propagates into the sion of slip across a grain boundary in turn depends on the grain ary and cross slip, and the planarity of slip. The transition of the another may require a change in the crack path, which may also resulting properties of grains properties

crack may accelerate, decelerate, or contiguous grain [7]. The transmisorientation, the activities of secondsmall crack from one grain to influence crack closure. The

crack growth behavior is therefore very sensitive to the crystallographic orientation and of individual grains located within the cyclic plastic zone. As the crack grows, the number interrogated by the crack-tip plastic zone increases and the statistically-averaged material become smoother.

However, it is important to note that the fundamental mechanism of crack growth is the same for small and large cracks in the near-threshold regime. In both cases, FCG occurs as an intermittent process involving strain range accumulation and incremental crack extension, followed by a waiting period during which plastic strain range reaccumulates at the crack tip [ 11 ]. Fatigue striations of equivalent spacing have been observed on the fracture tested under equivalent nominal AK ranges, as shown

surfaces in Figure

of both large and small fatigue cracks 2 for 7075 A1 [11]. The essential

difference between large and small cracks is that the number of fatigue cycles less for small cracks, due to differences in the local crack driving force. How

can the behavior

of microstructurally-small

cracks

per identical

be modeled/predicted

striation

is

analytically?

Several different approaches have been developed, ranging from detailed scientific models to simplified engineering treatments. At one extreme, complex micromechanical models attempt to address directly the changes in the local crack driving force. For example, a model derived by Chan and illustrated in Figure 3 incorporates microplastic grains ahead of a Barenblatt-Dugdale crack [7]. The nominal AK is modified by influence tic/macroplastic yield strength, large

ii:ii! ¸!i Zii !iii i iiiii

functions which explicitly scale yielding at the crack

describe tip, and

the effects of microplascrack closure.

465

!

ii/::iiiiiii i.,,i: i ? L

_:_:_-i :_:

10-6

I

i

Striation

i

I

SPacing

®

• LC

o

+

10-7 Average

/°/° +

Inclusion dlus

10-8

+

dOoN m/cy GS= 55 urn IOL9

20= 160 um

I

#

i0-i0

I # #

10-11 1

2

5 AK

,

Figure

2.

FCG

data

for 7075

I 10

I 20

10

20

(MPo_)

I 40

I 80

20

(um)

A1, comparing crack growth and microstructurally-small

I 160

1 320

rates and striation cracks.

spacings

for large

10 .6 Overaged

7075 AI

10 .7

Small Crack Data

_>, 10 .8

i

\ E v

\

Z 10"9 "1o

10 -1o

Small Crack Curve

Large Crack Data

10 -11 0.2

1

10

t_K (MPa,m 1_) Figure

3. Predictions

of a micromechanical

466

_

./i_:i _ _

'



,

'T i:/

_i

,

.



model

for microstructurally-small

cracks.

cracks

Detailed experimental general phenomenological

measurements of near-tip strains and displacements have suggested model for microstructurally-small cracks which has been successfully

a

applied to both engine disc and airframe alloys [ 12, 13]. Small crack growth rates were satisfactorily correlated with large crack data using a parameter/_eq = (E/_kJ) 1/2 = (E Ao _r) 1/2, where the crack tip stress range Ao was calculated from the measured crack-tip strain range and _Sris the cyclic crack-tip opening displacement. The parameter AKeq was found to be simply related to the applied AK according to the expression AKeq --- AKp + UAK, where AKp characterizes the plastic contribution to the crack driving force for small cracks and U is the effective stress range ratio which characterizes crack closure: U -- AKefe/AK. See Figure 4. Note that crack closure alone was not able to correlate the small crack data. Simpler

mechanical

microstructurally-small dealing directly with

treatments

crack complex

have

also been

proposed

to address

FCG

regime. The microstructural

attractive issues.

simplicity of these models Small crack acceleration

behavior

in the

is that they avoid effects are incorpo-

rated through simple modifications to mechanical parameters in the expression for the crack driving force. One such approach is that of E1 Haddad et al. [14], who replaced the actual crack length a by an effective length a + a0 in order to calculate AK. This enhances the predicted crack growth rate when a is very small. A much more sophisticated approach has been developed by Newman [15]. The Newman model is based on computed changes in plasticity-induced crack closure for small cracks growing out of initiation sites simulated as micronotches. Newman has shown reasonably good success in predicting small crack growth rates and total fatigue lives for several different matedais, including airframe alloys. These practical successes are encouraging, but it should be remembered that the simple mechanical treatments do not address the most fundamental causes of the microstructurally-small

crack

effect.

Hence,

the generality

of the models

cannot

be assured.

Two other types of approaches, summarized in Figure 5, may be useful for some engineering applications in which it is not possible or practical to address changes in the driving force explicitly. Stochastic treatments which acknowledge the inherent uncertainties associated with microstructurally-small crack growth could address this uncertainty through appropriate statistical techniques. Formulation and calibration of these techniques would require extensive analysis of statistical-quality small crack data, which is a limitation. Variability of small-crack data is discussed further below. Empirical engineering treatments may be conservative bounding approaches which simply draw some upper bound to the crack growth data in the defined small-crack regime and use that bound as part of a total life computation, or fitting approaches which perform regression on small-crack data to generate a new set of Paris equation constants. be a useful means of avoiding detailed analysis, especially when materials and load histories representative of service conditions. Based

on these

observations

and models,

several

practical

These engineering treatments may small-crack data are available for

suggestions

can be offered

to predict

growth rates for microstructurally-small tion can be extrapolated downward

cracks. In general, it appears that the large-crack Paris equaat least to some microstructural limit. This limit is often esti-

mated as about 5-10 grain diameters equals the grain size [ 16], although microplasticity and closure behavior

[16, 17, 18], or as the point at which the cyclic plastic zone size the actual limit is probably a more complex function of [ 12]. The large-crack threshold should be neglected in this

extrapolation. Some treatment of nominal plasticity and crack closure effects on the crack driving force (discussed at more length in the next section) is often useful to improve agreement with large crack data. However, it must be emphasized that some nonconservatism may remain if the true local microstructural effects have not been addressed. Guidance for addressing these effects can be obtained from various scientific approaches, more general engineering approaches.

although

practical

considerations

may

dictate

the use of

467

:i¸¸¸

•:



_::: :

:::

:

_: :

:_ :__ _::_I:_: _!ii!_:::::_::::•_:/:•i _¸¸i:_•¸¸¸:¸ :'i:!

_!:: !::_%!:_i: !_!!_?!i::•:i!i/ili_:!iii:_i _!_:i:_i!!!_!_!i_!_i_!_i!ii!_:ii_i!_i_:i:_:i!!ii!_!iii_

12 7075 AI

10 8

E

A

small crack

n

large crack

t_

6 v

v

O" O

4

>

(LEFM

Small a/M (rr/M

_

Large

Large/

(single

Small

Large

need

EPFM)

Mechanically

and

Microstructurally (inelastic,

crystal)

Small/

Microstructurally (may

Microstructurally

1)

Mechanically

valid)

Mechanically

< 5-10

Influences

a/rp > 4-20 (ISY and LSY)

and

Microstructurally

1)

Microstructural Small

> 4-20 (SSY)

Mechanically

Large > 5-10

and

Large

Mechanical

a/M

to Mechanical

Small

anisotropic,

stochastic)

Chemically-Small Experiments

on a variety

of ferritic

Cracks

and martensitic

steels

in aqueous

chloride

environments

have shown that under corrosion-fatigue conditions, small cracks can also grow significantly faster than large cracks at comparable AK values [30, 31, 32]. This phenomenon is believed to result from the influence of crack size on the occluded chemistry which develops at the tip of fatigue cracks. The specific mechanism responsible for this "chemical crack size effect" is believed to be the enhanced production of embrittling hydrogen within or more factors which control the evolution

small cracks resulting from a crack size of the crack-tip environment--specifically,

mixing, ionic diffusion, or surface electrochemical different from that responsible for the enhanced mechanically-small fatigue cracks. The

chemical

crack

size

effect

is clearly

dependence of one convective

reactions [33, 34]. This mechanism rate of crack growth in microstructurally-

illustrated

by the data

of Gangloff

in an aqueous NaC1 environment (see Figure 10). Note that corrosion-fatigue from small surface cracks (0.1 to 1 mm deep), as well as short through-thickness

[31]

is distinctly or

for 4130

steel

crack growth rates edge cracks (0.1

- 3

mm), are appreciably faster than corrosion-fatigue crack growth rates from large through-thickness cracks (25 - 40 mm) in standard compact tension specimens. It is also interesting to note that the corrosion-fatigue crack growth rates for small surface cracks decrease with increasing applied stress (at a given AK), and this trend is opposite to the dependence of applied stress on crack growth rates in small fatigue cracks. Moreover, all of the corrosion-fatigue crack growth rates in NaC1 are enhanced compared to those in a moist laboratory air environment, even though the latter were generated with both small and large cracks. Thus, in relation to the fatigue small crack effect, the chemical small crack effect is of potentially greater importance since it can occur over a much larger range of crack sizes

(up to 3 mm).

The chemical crack size effect in high strength nents such as landing gear. Do similar effects occur frames?

472

steels is relevant to aircraft structural compoin high strength aluminum alloys used in air-

_ :_:_:_ _:___ __: __:

.... ::_:_:__::_ _:_::_i_:i:i_ii_i_i i_ ¸__ !_i_'i!i _:!i!: _!_ _!:il¸_i_:i_ _i_: !__i_i_! _i_/_i_!_i _i_ _i:!ii!i_i_i_ ! _?i !i!iliii_i :i_i:%!!iii!ii_:!_ ii_i!!i!ill ii_i!i!i_ii!iii_iiii!!iiiii!!ii!iiii!iii!!ii_i!ii!i!iii!iiil !i_:ii_i_i_i_i_i!iiiiiiii_iiiii_i_!ii_iiii_

10 "1

-

I

i

i i I

i

!

I

I

i

I

I

I

4130 steel ,_

Small Cracks

10'2

-= E S rha°c rt

Z

/

Og

/

10_4

105

Nf

Aerated

,

5

10

,

20

30/0 NaCI

, , , 50

100

AK (MPa.m _) Figure

10.

Corrosion-fatigue

crack

growth data for large in 4130 steel [31].

Although data on the aluminum alloys is sparse at this point, enable an initial assessment of the problem. Data of Piascik

which

lack of a chemical crack size effect chloride environment. Recent data

Several aluminum

minum alloys the aluminum potential

possible

alloys

for the apparent First,

have been generated under small crack data have been

of -700

generally

reasons

can be hypothesized.

mV

been

(versus

under

difference it should

different obtained

the saturated

conducted

potential of -550 mV SCE. load ratios (R), particularly

aerated

calomel

variable

data are available [35] suggest the

in Figure 11. Thus, size effects. Further

in the small

be recognized

crack

in contrast to studies are cur-

behavior

that the data

of steel

on steels

affecting

the crack-tip

and

and

alu-

environment and loading conditions. Specifically, under deaerated conditions and an electrode electrode,

conditions

and,

SCE),

while

in the case

the

steel

of Ref.

small

crack

data

[31 ], an electrode

In addition, most of the aluminum small crack data were obtained in the important low AK regime, while the steel small cracks were

obtained at low load ratios. This difference in load ences in the crack opening displacement. Analytical within cracks indicate that the ratio of crack surface fundamental

preliminary and Gangloff

cracks

in both 2090 and 7075 aluminum alloys exposed to an aqueous from NASA-Langley [36] on 2024-T3 in a similar environment

also support the lack of a chemical crack size effect, as shown steels, aluminum alloys may be immune from chemical crack rently underway to address this question.

have

and chemically-small

at high

ratios may be significant since it causes differmodels for the evolution of the environment area to occluded solution volume is a

environment

[34].

473

2024-T3 In NaCI

:

f=SHz

/15/

,.r0.Cr.o,.. /%z/

lO

o o

lff s

ZI

ZI

"l

ZI

O

2

4

6

O

R = 0.05

ZI

R :

8

0.7-0.8

10

20

AK, MPa4-m Figure

11.

Corrosion-fatigue

Second, the rate controlling aluminum alloys. Crack growth

crack

growth

data for large

and

small

cracks

in 2024-T3

process for environment-enhanced FCG may rates in steels are controlled by electrochemical

A1 [36].

differ in steel and reactions on the

freshly created metal at the crack tip [37]. Studies of aluminum alloys exposed to water vapor suggest that the surface reaction in the aluminum-water system is relatively fast, so that transport of water to the crack tip is the rate controlling process [38]. Unfortunately, specific results on the rate controlling process for aluminum alloys in liquid water are not yet available. Thus, an assessment of whether or not these fundamental differences in rate controlling processes account for the observed differences in chemical crack size effect in these two alloy systems must await further elucidation of the underlying kinetic mechanism(s).

MATERIALS Scatter Even

when

suitable

analysis

techniques

DATA

in Small are able

Crack

ISSUES Data

to predict

the central

tendencies

data, the life prediction task may still be difficult. The remaining problem is the large scatter (sometimes several orders of magnitude) often observed in small crack growth leads to greater uncertainty in life calculations, especially when the small crack regime total life. Analytical gested earlier, may

474

approaches based on simple upper bounds to the small be unacceptably overconservative in some applications.

crack

of small

crack

amount of rate data. This dominates the

regime,

as sug-

i _i
three

is due

major

sources

to stochastic

of this apparent

microstructural

variability

effects:

local

have

been

differences

identified in grain

[ 19].

Some

orientation,

true

micro-

plastic yield strength, and grain boundary effects, which may become especially significant when the crack driving force is small. On the other hand, some apparent variability is actually only an artifact of measurement error. These errors become significant when the crack growth increment becomes small relative to the measurement resolution. Finally, some apparent variability can be attributed to mathematical averaging effects. The normal point-to-point variability is effectively averaged out for most large cracks, when the crack travels a long distance during the measurement interval. Since the small crack travels only a short distance during the measurement interval, this normal variability becomes more evident (as it would be if large cracks were measured at much shorter intervals). The appropriate treatment for small crack scatter depends, at least in part, on the origin of the scatter. Some scatter which is only apparent can be effectively reduced with improvements in the analytical schemes used to process the raw crack growth data, including data filtering and modified incremental polynomial techniques [39]. However, other forms of scatter may require a formal stochastic treatment of the data. Many stochastic FCG models are available in the literature. Unfortunately, many of these models require extensive data of high statistical quality, which is often difficult (expensive) to obtain for small cracks. Other stochastic FCG models designed for practical engineering applications, such as the lognormal random variable (LRV) model, require fewer data and simpler calculations. However, these models are often not able to address the unique scatter associated with small cracks on a consistent basis with the reduced scatter associated with large cracks. New 12 compares data presented

stochastic a modified earlier.

FCG models LRV model

are currently being investigated to address these issues. [19] with the standard LRV approach for the HSLA-80

Figure steel

10 -6

jJ 10 -7 _

HSLA-80 steel 1% and 99% bounds

/ /

"

.,_ ..n-o_.,_

10 -8

_>, 10 -9

z

10 -1(:

"O

10 "11

10 "12

--[]

oom:_

_f _%"

LRVmodel oo

[]

mean j.4 -

10 "13 1

10 AKeff

Figure

12. Stochastic treatments of large based on conventional and modified

(MPa, rn in) and small lognormal

crack data for HSLA-80 random variable models.

steel,

475

.
of small

crack

phenomena

considered, however, many of the required

outside

the

also be significant. Other outor crack arrest as an intrinsic

feature of microstructurally-small crack growth, and the characterization airframe geometries such as fastener holes with residual stresses. for engineering

tures has not yet been fully established. Further study should provide helpful guidance. In those applications

histories

of crack

closure

in practical

analysis

of airframe

struc.

of problems such as MSD in aging aircraft where the growth of small cracks must be

reliable analytical and experimental techniques computations of damage growth with reasonable

are now available confidence.

to perform

CONCLUSIONS .

.

A proper identification of the type priate analytical treatment. Satisfactory tional

.

scientific

work

explanations

is needed

to develop

crack

for small

encountered

crack

satisfactory

behavior

engineering

A practical engineering methodology for mechanically-small the large-crack Pads equation, with appropriate attention ticity modifications to the crack driving force.

is essential

are now

to choosing

available,

an appro-

but some

treatments

for all applications.

cracks to changes

includes in crack

extrapolation closure and

addi-

of plas-

.

Practical engineering methodologies for microstructurally-small cracks are less complete. Available simple mechanics approaches may be useful, but will be inadequate in some applications. Micromechanics and phenomenological approaches provide valuable guidance, but ultimately statistical or simple bounding approaches may be required.

.

It is not entirely clear if aluminum alloys nificant chemically-small crack effect.

.

Small cracks often stochastic variations ical averaging.

.

of small

Guidelines

exhibit significantly greater in the local microstructure,

Alternative

for small

commonly

crack

analytical

in airframe

applications

exhibit

a sig-

scatter in growth rates than large cracks due to measurement error, and decreased mathemat-

techniques

test methods

used

may

are becoming

be required

to address

this variability.

available.

ACKNOWLEDGMENTS The substantial support of research on small cracks and related topics at SwRI over the past fifteen years by AFOSR, AFWAL, NASA, ARO, ONR, and others is gratefully acknowledged. Dr. Tony Torng is thanked for his contributions to the discussion of probabilistic modeling. REFERENCES .

Pearson, S.: Initiation of Fatigue Cracks in Commercial Propagation of Very Short Cracks. Engng Fract. Mech.,

.

Goranson, 43-65.

U. G.:

Elements

of Structural

Integrity

Aluminum Alloys and the Subsequent Vol. 7, 1975, pp. 235-247.

Assurance.

Int. J. Fatigue,

Vol.

16, 1994, pp.

477

3.

Swift, T.: Widespread Structural Airworthiness

4.

Final Report, Industry Committee Working Group, July 1993.

5.

Wanhill, R. J. H.: EGF 1, Mechanical

6.

Lankford, J.: The Growth of Small Struct., Vol. 5, 1982, pp. 233-248.

7.

Chan, K. S., and Lankford, J.: The Role of Microstructural of Small Cracks. Acta Metall., Vol. 36, 1988, pp. 193-206.

Dissimilitude

8.

Morris, W. L., Cox, B. N., and James, M. R.: Acta Metall., Vol. 35, 1987, pp. 1055-1066.

Surface

9.

Davidson, D. L., and Chan, K. S.: The Crystallography of Fatigue Crack Grained Astroloy at 20°C. Acta MetaU., Vol. 37, 1989, pp. 1089-1097.

10.

Suresh, S.: Crack Deflection: Implications Trans. A, Vol. 14A, 1983, pp. 2375-2385.

11.

Lankford, Influence

12.

Hudak, S. J., Jr., Davidson, Small Cracks in Aeroengine

13.

Davidson, D. L.: Small 1988, pp. 2275-2282.

14.

El Haddad, M. H., Smith, K. N., and Topper, T. H.: Fatigue ASMEJ. Engng Mater. Technol., Vol. 101, 1979, pp. 42-46.

15.

Newman, Aluminum

16.

Chan, Large

17.

Lankford, J.: The Influence of Microstructure on the Growth Fract. Engng Mater. Struct., Vol. 8, 1985, pp. 161-175.

18.

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