Astm stp 1122 1992

However, in the last decade, research on the small-crack effect in numerous materials has indicated that crack propagation from a microstructural defect 5 to 20 ixm in size consumes a la

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STP 1122

Advances in

Fatigue Lifetime

Predictive Techniques

M R Mitchell and R W Landgraf, editors

ASTM Publication Code Number (PCN):

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Library of Congress Cataloging-in-Publication Data

Advances in fatigue lifetime predictive techniques/M R Mitchell

and R W Landgraf, editors

p c m - - ( S T P ; 1122)

Includes bibliographical references and index

ISBN 0-8031-1423-0

1 M a t e r i a l s - - F a t i g u e 2 Fracture mechanics 3 Service life

(Engineering) I Mitchell, M R (Michael R.), 1941-

II Landgraf, R W III Series: A S T M special technical

or in part, in any printed, mechanical, electronic, film, or other distribution and storage media, without the written consent of the publisher

is 0-8031-1423-0 92 $2.50 + 50

Peer Review Policy

Each paper published in this volume was evaluated by three peer reviewers The authors addressed all of the reviewers' comments to the satisfaction of both the technical editor(s) and the A S T M Committee on Publications

The quality of the papers in this publication reflects not only the obvious efforts of the authors and the technical editor(s), but also the work of these peer reviewers The A S T M Committee on Publications acknowledges with appreciation their dedication and contribution

to time and effort on behalf of ASTM

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Foreword

The A S T M Symposium on Advances in Fatigue Lifetime Predictive Techniques was held

on 24 April 1990 in San Francisco, California A S T M Committee E-9 on Fatigue sponsored

the event

The symposium chairmen and editors of this volume were M R Mitchell, Rockwell

International, Scienc~ Center, Thousand Oaks, California, and R W Landgraf, Virginia

Polytechnic Institute and State University, Blacksburg, Virginia

Downloaded/printed by

University of Washington (University of Washington) pursuant to License Agreement No further reproductions authorized

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Contents

Overview

G E N E R A L A P P R O A C H E S Fatigue Mechanics: An Assessment of a Unified Approach to Life P r e d i c t i o n - -

J C N E W M A N , JR.~ E P P H I L L I P S , M, H S W A I N , A N D R A E V E R E T T , JR

A Fracture Mechanics Based Model for Cumulative Damage Assessment As Part of

Fatigue Life Prediction M V O R M W A L D , P, H E U L E R , A N D T S E E G E R 28

E L E V A T E D T E M P E R A T U R E P H E N O M E N A Thermo-Mechanical Fatigue Life Prediction Methods H SEHITOGLU

Evaluation of the Effect of Creep and Mean Stress on Fatigue Life Using a Damage

Mechanics A p p r o a c h - - N M ABUELFOUTOUH

Cumulative Creep-Fatigue Damage Evolution in an Austenitic Stainless S t e e l - -

M A M c G A W

Application of a Thermal Fatigue Life Prediction Model to High-Temperature

Aerospace Alloys B1900 + H f and Haynes 188 G R HALFORD,

R S U N D E R

Contribution of Individual Load Cycles to Crack Growth under Aircraft Spectrum

Loading R SUNDER

Fatigue Crack Growth from Narrow-Band Gaussian Spectrum Loading in 6063

Aluminum Alloy P s VEERS A N D J A V A N D E N A V Y L E

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Modeling High Crack Growth Rates under Variable Amplitude Loading

D J D O U G H E R T Y , A U DE K O N 1 N G , A N D B M H I L L B E R R Y

A Probabilistic Fracture Mechanics Approach for Structural Reliability Assessment

of Space Flight Systems s S U T H A R S H A N A , M C R E A G E R , D E B B E L E R , A N D

S m a l l Crack Growth in Multiaxial Fatigue s c REDDY AND A FATEMI

Failure Modes in a Type 316 Stainless Steel under Biaxial Strain Cycling

Fatigue Life Prediction and Experimental Verification for an Automotive

Suspension Component Using Dynamic Simulation and Finite Element

Analysis w K BAEK AND R I STEPHENS

Plasticity and Fatigue Damage Modeling of Severely Loaded Tubing s M TIPTON

A N D D A N E W B U R N

Electric-Potential-Drop Studies of Fatigue Crack Development in Tensile-Shear Spot

W e l d s - - M H SWELLAM, P KURATH, AND F V LAWRENCE

Life Prediction of Circumferentially Grooved Components under Low-Cycle

Fatigue K HATANAKA, X FUJIMITSU, S SH1RA1SHI, AND J OMORI

Reliability Centered Maintenance for Metallic Airframes Based on a Stochastic

Crack Growth Approach s O M A N N I N G , J N Y A N G , F L P R E T Z E R , A N D

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Fatigue Lifetime Monitoring in Power Piants P c RICCARDELLA,

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STP1122-EB/Jan 1992

Overview

The ability to predict accurately the service performance of engineering structures sub- jected to fatigue loading, always a formidable challenge, has become a goal of increasing importance throughout the design community Few industries have escaped the intense competitive pressures to develop safer, more durable products, in less time, and at reduced cost The situation is further complicated by the increasing sophistication of engineering structures and the use of higher performance, but often less forgiving, materials Fatigue is

of particular concern because it is, arguably, the most prevalent failure mode in practice and one of the more difficult to deal with

Fortunately, materials and mechanics researchers remain active in this important field, and the last decade has seen significant improvements in our understanding of fatigue phenomena and in our ability to deal with it in engineering practice Some impressive new tools and techniques are becoming available to assist designers in more reliably assessing the fatigue performance of a variety of components and structures Such a capability provides the opportunity to develop more optimized designs by anticipating potential problem areas and by allowing consideration of a broader range of alternatives Nearly all major industries aerospace, power generation, ground transportation are in the process of integrating such new methods into their respective design procedures

The intent of the ASTM Symposium on Advances in Fatigue Lifetime Predictive Tech- niques, the first on this topic, was to bring together a cross-section of fatigue researchers and practitioners to review, in detail, recent progress in the development of methods to predict fatigue performance of materials and structures and to assess the extent to which these new methods are finding their way into practice A major challenge associated with the development of these advanced technologies is to insure that they are transferred to the engineering community in a timely manner

Coverage is purposely broad and includes a range of materials, mechanics, and structures viewpoints and approaches to the fatigue analysis problem Contemporary strain-based fatigue and fatigue crack propagation methodologies are represented, and problems in the areas of high temperature behavior, spectrum loading, and multiaxial fatigue are addressed Significantly, a number of papers are concerned with applications of modern methods in engineering practice, thus providing an important perspective on the overall utility of modern techniques to real-world problem solving

The first two papers provide valuable overviews of current efforts to develop general analysis approaches, incorporating both crack initiation and propagation considerations, to fatigue life prediction These methods incorporate our latest understanding of short crack behavior and the influence of crack closure phenomena in explaining a variety of mean stress, threshold, and load interaction effects Such developments represent an interesting and productive blend of cyclic deformation and fracture mechanics concepts to handle the difficult problem of cracks growing in plastic strain fields

Next, six papers cover a range of elevated temperature phenomena and serve to effectively review progress and problems associated with thermomechanical fatigue, creep-fatigue, thermal fatigue, and cycle- and time-dependent crack growth While considerable progress

is evident, there remain a number of unresolved issues in this area before truly general design approaches are available

Copyright 9 1992 by ASTM International www.aslm.org

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2 ADVANCES IN FATIGUE LIFETIME PREDICTIVE TECHNIQUES

The many problems associated with predicting lifetimes under spectrum loading conditions

are addressed in the following five papers Here much attention is focused on crack closure

behavior to explain overload and varying R-ratio effects that are characteristic of service

spectrum The application of probabilistic fracture mechanics to structural reliability as-

sessment is also covered

In the area of multiaxial fatigue, a series of four papers give evidence there has been

significant progress in observing and understanding initiation and propagation processes

under in-phase and out-of-phase loading This is providing the basis for more rational and

useful design approaches by focusing attention on critical shear planes at local regions in a

structure to which damage accumulation models are applied Recent efforts dealing with

biaxial fatigue at elevated temperature and welds under non-proportional loading are also

included in the coverage

Finally, a series of ten application papers provide evidence that considerable progress is

being made in transferring new techniques into practice, often with encouraging results

Coverage includes automotive, airframe, and power generation structures with detailed

treatments of pressurized tubes, spot welds, lap joints, and various notched geometries

Thermographic stress analysis techniques are also covered along with residual stress effects

on stress intensities

In total, the 27 papers contained in this volume provide a valuable review and update of

progress and opportunities in this continually evolving field One is left with a sense of

optimism that many of the challenging problems relating to material and structural fatigue

performance are solvable, and that substantial progress is being made in developing and

implementing the requisite technologies Of particular significance is the profound influence

that modern experimental and analytical tools have had in contributing to this progress

The capability to study and evaluate materials and components in the laboratory under

simulated service conditions has been a boon to the experimentalists Likewise, rapid ad-

vances in computational power are providing the vehicle for making the often sophisticated

analytical approaches a reality

We would be remiss if we were to fail to mention the two papers that shared the A S T M

Committee E-9 Award for Best Symposium Paper: ~ Crack Growth from Narrow-

Band Gaussian Spectrum Loading in 6063 Aluminum Alloy" by P S Veers and J A Van

Den Avyle, and "Elevated Temperature Crack Growth in Aircraft Engine Materials" by

T Nicholas and S Mall We congratulate both sets of authors

Finally, the value of establishing and maintaining cross-industrial and cross-disciplinary

forums of this type deserves special mention The complexities of structural fatigue problems

necessitate broad interdisciplinary approaches and much is to be gained from a continuing

dialogue between industry and academia, researchers and practitioners, and the spectrum

of materials, mechanics, and structures specialists This helps assure that the right problems

are being addressed by researchers and provides ready channels for technology transfer It

is hoped that this symposium may have served as a useful step in promoting a broader view

of fatigue lifetime prediction, in establishing a focal point for information dissemination,

and in providing a platform from which to plan future related symposia

Michael R Mitchell

Rockwell International Science Center Thousand Oaks, CA 91360 Symposium Chairman and Editor

Ronald W Landgraf

Virginia Polytechnic Institute & State University Blacksburg, VA 24061

Symposium Chairman and Editor

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J C N e w m a n , Jr., 1 E P Phillips, 2 M H Swain, 3 and

R A Everett, Jr 4

Fatigue Mechanics An Assessment of a

Unified Approach to Life Prediction

REFERENCE: Newman, J C., Jr., Phillips, E P., Swain, M H., and Everett, R A., Jr.,

"Fatigue Mechanics: An Assessment of a Unified Approach to Life Prediction," Advances in

Fatigue Lifetime Predictive Techniques, ASTM STP 1122, M R Mitchell and R W Landgraf,

Eds., American Society for Testing and Materials, Philadelphia, 1992, pp 5-27

ABSTRACT: The separation between fatigue crack initiation and propagation has often been defined as a macrocrack, visible in a low-power microscope However, in the last decade, research on the small-crack effect in numerous materials has indicated that crack propagation from a microstructural defect (5 to 20 ixm in size) consumes a large percentage (50 to 90%)

of the total fatigue life of materials, even near the fatigue limit Thus the initiation of a "fatigue crack" may occur early in life from defects or irregularities, such as inclusions, voids, dislocations, or slip bands In the present paper, an assessment has been made of a total-life analysis based solely on crack propagation The analysis is based on observations of defect sizes at initiation sites and on fatigue-crack-growth rate data for small and large cracks The assessment was based on data from 2024-T3 aluminum alloy, 2090-T8E41 aluminum-lithium alloy, annealed Ti-6A1-4V titanium alloy, and high-strength 4340 steel under either constant-amplitude

or spectrum loading Comparisons made between fatigue lives measured on notched specimens with those computed from the total-life analysis agreed well The computed lives generally fell within the scatterband of experimental fatigue life data

KEY WORDS: metal fatigue, crack propagation, stress analysis, stress intensity factor, cracks, microstructure

Historically, the fatigue failure process in a metallic material has been divided into three phases: crack initiation, crack growth, and fracture The use of fracture-mechanics concepts

to characterize the growth of cracks and fracture is well established in the design of aerospace structures [1] Standard test m e t h o d s have b e e n d e v e l o p e d for the g e n e r a t i o n and analysis

of fatigue-crack-growth rate data using the stress-intensity factor range, AK, to correlate the data ( A S T M E 647, Test for M e a s u r e m e n t of Fatigue Crack G r o w t h Rates) D a t a

g e n e r a t e d h a v e shown that the 2xK similitude concept works very well T h a t is, for a given material, stress ratio, and test e n v i r o n m e n t , a particular AK value produces the same growth rate regardless of applied stress level or crack length T h e test m e t h o d s are restricted by an

u p p e r b o u n d on stress level (through plastic-zone size considerations), but no restrictions are placed on absolute crack size In practice, h o w e v e r , the standard test m e t h o d s all utilize specimens that contain cracks longer than several millimeters This is quite u n d e r s t a n d a b l e since the applications where fracture mechanics have b e e n used in design have only con-

1Senior Scientist, NASA Langley Research Center, Hampton, VA 23665

ZResearch Engineer, NASA Langley Research Center, Hampton, VA 23665

3Material Scientist, Lockhead Engineering and Sciences Co., Hampton, VA 23665

4Research Engineer, U.S Army Aviation Systems Command, Hampton, VA 23665

Copyright 9 1992 by ASTM International www.aslm.org

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sidered large cracks (greater than i mm) Recently, attention has been given to the possibility

of applying 2xK-rate analyses to cracks much smaller than 1 mm

During the past decade, a large amount of experimental data [2-9] has been generated that shows that the 2xK similitude concept breaks down at small crack sizes and that the data exhibit a "small-crack" effect as shown schematically in Fig 1 When small-crack growth rates (da/dN) are plotted against AK, small cracks are shown to generally grow faster than large cracks at the same 2xK level and small cracks also grow at ~ K levels below the large- crack threshold, 2XK~h Small cracks may exhibit a variety of growth rate behaviors depending upon material and applied stress level as indicated in Fig 1 Explanations for the small- crack effect are usually based on the argument that AK is not an appropriate parameter to characterize the crack-driving force for small cracks because either (1) the magnitude of crack-tip shielding (closure) is very different for small and large cracks [4,5] or (2) the basic assumptions of the AK concept regarding plasticity or continuum mechanics are violated at small-crack sizes [6,7] Clearly, as the crack size approaches zero, a crack size must exist below which the assumptions of the 2xK concept are violated, but the transition from valid

to invalid conditions does not occur as a step function For many engineering applications,

a AK-based analysis that extends into the "gray area" of validity may still prove to be very useful Certainly from a structural designer's viewpoint, a single analysis methodology that

is applicable to all crack sizes is very desirable If for no other reason than that the AK analyses are already being used for large-crack problems, the application of AK analyses to small-crack problems should also be thoroughly explored

The separation between fatigue crack initiation and propagation has often been defined

as a macrocrack, visible in a low-power microscope However, research on small (or short) crack behavior in numerous materials [4,8,9] has indicated that crack propagation from microstructural defects or irregularities (5 to 20 #,m in size), such as inclusion particles, voids, dislocations, or slip bands, consumes a large percentage (50 to 90%) of the total fatigue life of materials, even near the fatigue limit Thus the initiation of a fatigue crack from a microstructural defect may occur early in the life of a structure This observation is essential to the development of a total fatigue life prediction methodology based solely on

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NEWMAN ET AL ON UNIFIED APPROACH TO LIFE PREDICTION 7

crack-propagation behavior This approach differs from the equivalent-initial-flaw-size (EIFS) concept [10] in that the "initial" crack size is provided by the material microstructure instead

of by life calculations, and small-crack effects, which are not included in the EIFS approach, are included in the current analysis To develop a unified fatigue-life prediction method, the behavior of small and large cracks, threshold behavior, load-interaction effects, stress- intensity factors for surface and corner cracks, residual stresses, and elastic-plastic stress- strain behavior at stress concentrations must be incorporated into the crack-growth analysis This paper examines the development of a total-life prediction methodology for aerospace structures based solely on crack propagation from a microstructural defect at stress concentrations [11,12] Using this methodology, crack-growth lives were calculated for a given loading condition by integrating the crack-growth-rate-against-AK relationships (established from experimental data) for crack growth from a microstructural defect size to failure Both small- and large-crack growth rate data are used Small cracks are defined as those that do not exhibit the same growth rate as large cracks at the same AK, that is, a breakdown in

AK similitude Small-crack behavior is dependent upon material and loading conditions and

is generally observed for cracks smaller than about 1 ram The significance of the small- crack effect in fatigue-life calculations was assessed by comparing lives computed using only large-crack data to those computed using a combined small- and large-crack data base The fatigue-life prediction method was demonstrated on notched specimens made of the following materials: an aluminum alloy (2024-T3), an aluminum-lithium alloy (2090-T8E41), an annealed titanium alloy (Ti-6A1-4V), and a high-strength steel (4340) A wide range in loading conditions was investigated In addition to constant-amplitude loading, two load spectra (Felix/28 [13] and a Gaussian-type [14] random load spectra) were studied

Small and Large Crack Growth Rate Data

Most of the fatigue crack growth rate data were obtained from Refs 8 and 9 for the four materials analyzed in this study Tests and analyses were conducted under both constant- amplitude and spectrum loading Center-crack tension specimens and standard test methods were used to obtain the large-crack data The small-crack data were obtained from tests of single-edge-notch tension specimens with a semicircular notch (Fig 2a) For the aluminum, aluminum-lithium, and titanium alloy specimens, the stress concentration, KT, was 3.17; for the steel specimen Kr was 3.3 Notch-root stresses were elastic in all small-crack tests except

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those tested under the Gaussian spectrum loading Cracks initiated and grew along the bore

of the notch as small surface cracks The crack length along the bore of the notch is 2a and the crack depth is c (Fig 2b) The full sheet thickness B is also denoted as 2t for convenience

in expressing the stress-intensity factor in terms of a/t ratios Growth of the small cracks in the 2a-direction was recorded using a plastic-replica technique [15] Crack depth was determined from experimental calibrations where relations between a/c and a/t were determined

by fractographic examinations of broken specimens early in life Herein, results are presented

as 2xK against da/dN for small cracks Note that the small-crack data are da/dN while the large-crack data are dc/dN In some materials, the AK-rate relation may be different in the two directions

Microstructural examinations of crack origins using a scanning electron microscope on three of the materials (the titanium alloy was not examined) were conducted to identify and characterize the initiation sites For the materials examined, cracks initiated at inclusion particles or voids at or near the notch-root surface Table 1 gives a summary of the average size (fii, di) of the surface defect where small cracks initiated in these materials To simplify subsequent life analyses, an equivalent area semicircular crack of radius a~ was used to approximate the initial defect This assumption is reasonable because small cracks very quickly approach a semicircular crack front ]8,9] Because information on crack initiation sites was not available for the titanium alloy, a general discussion on crack initiation in Ti- 6A1-4V titanium alloys is presented later Further details on the materials, specimens, test procedures, and data analyses are given in Refs 8 and 9 Table 2 gives the average tensile properties of the materials

The two load spectra analyzed in this study are briefly described in the following sections Felix [13] is a standard load sequence for helicopters with fixed or semirigid rotors The load sequence is composed of 140 flights These flights are constructed for 33 different load levels, and the maximum load level was scaled to 100 On this scale, the minimum load was

- 28 This gives an overall spectrum stress ratio of - 0.28 In Felix, the number of full load cycles is over 2 million To reduce the time required to conduct fatigue tests, a shortened version, Felix/28, was developed [13] This version contains about 160 000 cycles with the majority of alternating cycles at or below level 28 omitted

The Gaussian random sequence [14] has a frequency distribution of level crossings equal

to that of a stationary Gaussian process Sequence length is defined to be about 10 ~' mean level crossings (No) with positive slope The Gaussian spectrum is characterized by an irregularity factor, I The irregularity factor is defined as the ratio of the number of mean level crossings to the number of peaks (NI), 1 = No/N I For the sequence used herein (1 = 0.99), the spectrum shows very little variation in the mean value (nearly zero) and the

TABLE l Average material defect sizes and equivalent area crack sizes

"Average of particle or void sizes at several initiation sites [8,11,27]

bAverage of particle sizes at twelve initiation sites [18]

CNo metallurgical examination of initiation sites was made

aValue selected to fit fatigue data

eAverage of calcium-aluminate particle sizes at thirty~two initiation sites [18]

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spectrum is very close to an R = - 1 variable-amplitude loading The total range of possible

peaks and troughs is divided into 32 intervals

2024-T3 Aluminum Alloy

Small- and large-crack growth rate data for 2.3 mm thick aluminum alloy [8] are plotted

against 21K for constant-amplitude R = - 1 loading in Fig 3 For clarity, only the small-

crack data points are shown The smallest cracks generally measured along the bore of the

notch were about 0.01 mm in total length (2a) To make life calculations, the data in Fig

3 and in the following figures were represented as piece-wise-linear relationships Small-

crack data are shown as solid lines and large-crack data [8,16] are shown as dash-dot lines

The lines were visually fit through the small-crack data for each stress level because piece-

wise-linear curve fitting methods were not available The sensitivity of the visual curve fitting

method on life calculations will be discussed later A lower bound was assumed to exist for

the small-crack data and was defined by an effective (closure corrected) stress-intensity

factor range relation derived as discussed in Ref 11 Thus, if the small-crack data line

intersected the effective AK curve, the small-crack data curve was assumed to follow the

effective curve down to the small-crack threshold This assumption implies that the small

cracks are fully open (no closure in the early stages, 21K = AKeff) For R = - 1 , a stress

level effect was evident for small cracks, with the higher stress levels showing a more

pronounced small-crack effect (higher growth rates at a given AK) The stress-level effect

was shown in Ref 11 to be caused by crack-closure behavior At the high stress levels, the

crack-opening stress levels took a larger amount of crack growth to stabilize than at the

low stress levels The lower crack-opening stresses caused higher effective stress-intensity fac-

tors and higher rates Hence there are three small-crack growth rate relations shown in

Fig 3 From previous studies [11], the small-crack stress-intensity factor threshold was 1.05

FIG 3 1 S m a l l - a n d l a r g e - c r a c k - g r o w t h rate data f o r 2024- T3 a l u m i n u m alloy u n d e r R = - 1 loading

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Small- and large-crack growth rate data for the Gaussian loading [8] are presented in Fig

4 In the analysis of the Gaussian data, AK was based on the full-load range from maximum load to minimum load in the spectrum The measured growth rate was an average value that included the spectrum-load sequence effects because crack-length measurements were taken at intervals of about 100 000 cycles A stress level effect was also observed in the Gaussian small-crack data [8], but the data shown in Fig 4 were all taken at a maximum stress level of 125 MPa Again, the solid lines were visually fit to the data Based on analyses

in Ref 8, the small-crack data should begin to agree with the large-crack data at rates greater than about 10 -8 m/cycle The large-crack data are represented by the dash-dot line, while the dash line extending to the large-crack threshold was extrapolated The large-crack AK threshold was estimated from constant-amplitude data at R = - 1 by assuming that all cycles in the spectrum were full-range (spectrum maximum to spectrum minimum) cycles

applied stress level of about 95 MPa The smallest cracks measured along the bore of the notch were also about 0.01 mm in length (2a) The small-crack threshold, 1.1 MPa-m 1/=,

f x x I

A K , M P a - m 1/2 FIG 4 Small- and large-crack-growth rate data for 2024-T3 aluminum alloy under Gaussian random loading

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-II I0

was determined by fitting the analysis to fatigue-limit data for similar specimens tested at

lower stress levels This value of threshold also closely corresponds to the lower limit of the

small-crack data

A comparison of small- and large-crack data generated under the Gaussian random loading

[19] is shown in Fig 6 Again, the projected crack lengths on a plane normal to the loading

axis were used to calculate AK Small-crack tests were conducted with a spectrum S Of

190 MPa Here, the small cracks grew at much higher rates than large cracks at the same

AK value Again, small- and large-crack AK threshold values (1.1 and 4.5 MPa-m '/2, re-

spectively) were estimated from constant-amplitude data (R = - 1 )

T i - 6 A I - 4 V T i t a n i u m A l l o y

Small- and large-crack data generated on a titanium alloy (1.5 mm thick) in the mill-

annealed condition under R = - 1 constant-amplitude loading [20] are shown in Fig 7

The small-crack data were obtained from tests at a maximum applied stress of 225 MPa

U n d e r these conditions the notch-root stresses were elastic Cracks initiated as surface cracks

along the bore of the notch and were usually discovered at about 0.01 mm in length (2a)

No metallurgical examinations of initiation sites were made for this material because these

tests were conducted elsewhere In lieu of this, a general discussion on initiation in this class

of material will be given later Although the small-crack data exhibited a large amount of

scatter, small cracks grew much faster than large cracks at low stress-intensity factors but

tended to give slightly slower rates at the higher stress-intensity factors than the large cracks

For titanium alloys, this behavior may have been caused by the fact that growth in the a-

and c-directions may differ The solid and dash-dot lines represents the small- and large-

crack data, respectively The solid line was a visual fit through the mean of the small-crack

data The large-crack AK threshold was 10 MPa-m t j2 The small-crack threshold was obtained

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F I G 7 - - S m a l l- and large-crack-growth rate data for Ti-6AI-4V titanium alloy under R = - 1 loading

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by fitting the analysis to fatigue-limit data The dash line is an estimate for the effective stress-intensity factor relation using a constraint factor of 2 [11]

4340 Steel

Small-crack tests conducted on the 4340 steel showed that cracks initiated mostly at calcium-aluminate inclusion particles, or pits left by these particles during machining, along the notch-root surface [18] Here, the smallest cracks measured along the bore of the notch during fatigue cycling were about 0.02 mm (2a) in length In the steel, cracks initiated at larger inclusion particles than in the aluminum and aluminum-lithium alloys The small- crack data shown in Fig 8 are for constant-amplitude R = 0 loading with a maximum stress level of about 375 MPa The small- and large-crack data agreed quite well, even down to threshold

A comparison of small- and large-crack data gene~'ated under the Felix/28 load spectrum

of about 400 MPa The small-crack data tended to give about the same rates as the limited large-crack data at a given AK value The lack of a small-crack effect for the steel is believed

to be caused by the high constraint (plane strain) behavior for small cracks [18]

Analysis Procedures

To illustrate the total-life analysis and the influence of small-crack effects on these calculations, closed-form life analysis procedures [12] are used The growth-rate data for both small and large cracks, as shown in Figs 3 to 9, are expressed as linear relations on a log- log plot of AK against rate, Because most of the fatigue-crack-growth life of notched specimens is spent while cracks are small surface cracks, the stress-intensity factor for a small semicircular surface crack in a stress-concentration field is used as the crack-driving param-

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NEWMAN ET AL, ON UNIFIED APPROACH TO LIFE PREDICTION 15

eter Closed-form life equations are then given for any initial crack size, ai, using both the

large-crack data base and the combined small- and large-crack data base

Crack-Growth Rate Relations

Simple representations for small- and large-crack growth rate behaviors are shown in Fig

10 The crack-growth rate relation for large cracks (crack lengths greater than 1 ram) is

expressed as

d a / d N = C~ k K " (1) where C~ and n are constants for a particular loading condition (stress ratio or spectrum)

and are independent of stress level Equation 1 is truncated at the large-crack threshold,

AK~, as indicated in Fig 10

Similarly, the crack-growth rate relation for small cracks (point A to B in Fig 10) is

expressed as

where C2 and m are values determined from a visual fit to a particular set of data Because

of the breakdown in the AK-concept for small cracks, C 2 and m are no longer independent

of stress level or crack length Because of the dependence on stress level and crack length,

this region must be established from either tests (as illustrated in this paper) or from the

crack-closure model [11] At point B, the growth rate for the small crack becomes equal to

the rate for a large crack At point A, the growth rate for the small crack intersects the

effective stress-intensity factor range relation if small cracks are fully open (no closure)

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The effective stress-intensity factor range relation is expressed as

where C3 and p are constants that are, again, independent of stress level and crack length

Equation 3 is truncated at the small-crack threshold, AKSh

Stress-Intensity Factor Range

Failure of the single-edge-notched tension specimens was caused by surface cracks that

initiated at material defects or irregularities at or near the notch-root surface [8,9] The

stress-intensity factor range for a small surface crack at a notch root [11] can be expressed

as

where a is the crack half-length along the bore of the notch, c is the crack depth, t is one-

half sheet thickness (B = 20, r is the notch radius, 4) is the parametric angle (~b = ~r/2 is

the intersection of crack front with notch surface), and Q is an elliptical crack shape factor

a/c with a/t [8,9], showed that F at ~b = iT/2 was reasonably constant for a wide range in

surface was approximated by

where G = 0.66 K r for the aluminum, aluminum-lithium, and titanium alloy specimens; G

= 0.71 K r for the steel specimens where KT is the elastic stress concentration factor (The

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primary difference in the G values between the steel and the other materials was due to the

assumed crack shape in Refs 8 and 9 The initial a/c ratio was 1.0 for the steel; for the other

materials the initial a/c ratio was 1.1.) For simplicity, Eq 5 was used throughout the total

life calculations

Elastic-Plastic Effects

Most of the small-crack data in Refs 8 and 9 were generated at stress levels near the

fatigue limit for each material studied However, for small cracks and high stress levels, the

plastic-zone sizes are no longer small compared to crack size, and linear-elastic analyses are

inadequate To correct the analyses for plasticity effects, a portion of the Dugdale [21,22]

cyclic plastic-zone length (~o) was added to the crack length, like Irwin's plastic-zone cor-

rection [5] Thus the plastic-zone corrected stress-intensity factor range at the intersection

of the crack front with the notch surface is

Again, G is assumed to be constant and is assumed to be the same as the elastic value for

small cracks The term 3' was found to be ~/4 in Ref 23 by equating AKp to ~ under

plane-stress conditions A n approximate expression for ~o was given by

where p is the Dugdale plastic-zone size, R is the stress ratio, S is the applied stress and %

is the flow stress (average between the yield stress and ultimate tensile strength) For small-

scale yielding, Eq 7 reduces to the exact value [22] for various R-ratios Because small cracks

are assumed to be initially fully open, the effects of closure on the cyclic plastic-zone size

has been neglected When S = ~o, the plastic-zone size and AKp goes to infinity and the

cracked configuration fails under plastic-collapse conditions To account for plasticity effects

on crack growth, AKp replaces AK in Eqs 1 to 3 and the multiplier on AK in Eq 6 is a

constant for a given remote stress level and stress ratio (R)

and Kc is the fracture toughness Equation 8 applies for AK greater than AK,~ If the initial

Trang 24

crack size ai and stress level give a stress-intensity factor range less than AK L, then an infinite

life is obtained

S m a l l - C r a c k M e t h o d - - T h e total life using the small-crack and large-crack curves is com-

puted from Eqs 1 to 3 as

Coefficient X and aj are computed from Eqs 9 and 10, respectively Coefficients Y and Z

are given by

and

The crack lengths, aa and ae, are the crack lengths at the intersections of the straight lines

in Fig 10 The crack lengths, a A and aB, are given by

and

a , = ( Y / X ) 2/( ~ (18)

If a~ is greater than or equal to aA, then N1 is equal to zero and the life is equal to the sum

of N2 and N 3 Likewise, if ai is greater than or equal to aB, then N~ and N2 are equal to

zero and the life is equal to N 3 Again, if the initial crack size a~ and stress level give a

stress-intensity factor range less than AKSh, then an infinite life is obtained

R e s u l t s a n d D i s c u s s i o n

The crack-growth rate data generated for small and large cracks were used to evaluate a

total-life prediction methodology In this approach, fatigue life was assumed to be based

solely on crack propagation from a microstructural defect Crack-growth lives were calculated

for a given loading condition by integrating the crack-growth-rate-against-AK relationships

Trang 25

(established from experimental data) from a microstructural defect size to failure The

fatigue-life prediction method was demonstrated on notched specimens made of the four

materials A wide range in loading conditions (constant-amplitude and spectrum loading)

was investigated The significance of the small-crack effect in these calculations was assessed

by comparing lives computed using only large-crack data to those computed using a combined

small- and large-crack data base The fatigue-life ( S - N ) curve was also predicted for some

of the materials and loading conditions

2 0 2 4 - T 3 A l u m i n u m A l l o y

The calculated lives obtained using only large-crack data and using the combined small-

and large-crack data are plotted in Figs 11 and 12 for the R - - 1 and Gaussian loading,

respectively In these tests, the portion of fatigue life attributed to crack growth from a 0.01

mm crack to failure was generally greater than 90% [8] Typical results for each type of

loading are plotted for a particular stress level Life is plotted as a function of the initial

crack size, ai, assumed in the analysis To put the range of initial crack sizes into perspective,

several benchmark sizes are identified on the ordinate scales The band marked "material

defect" represents the range of inclusion particle or void sizes measured on broken specimens

where cracks initiated The initial crack sizes measured in many tests were essentially the

same size as the inclusion particles from which the cracks initiated Also identified is the

grain-size range and the crack sizes considered in airframe damage tolerance analyses The

dashed line represents results obtained using large-crack data and the solid line using the

combined small- and large-crack data bases The horizontal lines represent the respective

thresholds (below which cracks will not grow) The test data shown in Fig 11 are the total

lives to failure of test specimens like those used to generate the small-crack data The test

data are plotted at the midpoint of the material defect size range (6 ~m, see Table 1) The

large scatter in fatigue life may be due to the fact that these tests were quite close to the

Trang 26

fatigue limit However, the average fatigue life for these tests was quite close to the fatigue

life calculated from the "material defect" size crack

At this point, it may be appropriate to discuss the sensitivity of the visual curve fitting

method on life calculations using the 2024-T3 aluminum alloy data as an example In Fig

3, three visual fit lines were drawn between the effective and large-crack stress-intensity

factor curves Each of these lines corresponds to a particular stress level The middle line

was a fit to the 80 MPa test results In this example, the upper and lower solid lines will be

used as the upper and lower bounds for the 80 MPa data Nearly 80% of the small-crack

data fall within these bounds The fatigue life from the test was 207 000 cycles [11] The

predicted life using the middle curve and the material defect initial crack size was 197 000

cycles The predicted lives using the upper and lower bound curves were about 35% lower

and higher, respectively, than the median results These results indicate that the predicted

lives are not very sensitive to the curve fitting procedure; thus a visual fit should be ac-

ceptable In contrast, using the large-crack data (ignoring the large-crack threshold) would

have given a fatigue life nearly an order-of-magnitude greater than the test life

The calculated and test lives for the Gaussian loading (Fig 12) are to breakthrough

conditions, that is, the life required to grow a crack across the thickness of the notch root

(2a = B) The agreement between the six tests was extremely good considering that these

tests were conducted in three different laboratories [8] The calculated fatigue life to break-

through using small-crack data agreed well with the test data

The results shown in Figs 11 and 12 demonstrate that a fatigue life based solely on crack

propagation from a microstructural defect may be a viable fatigue-life prediction method

for aluminum alloys However, to predict the fatigue (S-N) behavior of the 2024-T3 alu-

minum alloy using the current procedures would require the AK-rate relation for each stress

level (as shown in Fig 3) or a method to predict the influence of stress level on small-crack

effects The crack-closure model [5,11] has been able to predict the stress-level effects on

small-crack growth in the aluminum alloy reasonably well

Trang 27

2090- T8E41 A l u m i n u m - L i t h i u m A l l o y

For the aluminum-lithium alloy, tests and analyses were made under both constant-

amplitude and Gaussian spectrum loading For constant-amplitude tests, the portion of

fatigue life attributed to crack growth from the first observed crack ranged from 35 to 90%

[18] However, some of the first observed cracks in the Gaussian tests [19] were late in life

and were quite large (about 0.1 mm)

The initial crack size against cycles to failure are plotted in Figs 13 and 14 for constant-

amplitude (R - - 1 ) and Gaussian random loading, respectively The band marked "ma-

terial defect and grain size" represents the initial sizes at which cracks initiated in many of

the tests (see Table 1) and, also, represents the range in grain size across the notch root

Again, in the analysis, the initial crack size was assumed to be equal to the average size of

the inclusion particles The dashed line represents results from using large-crack data, whereas

the solid line was calculated from small-crack data The horizontal lines indicate the re-

spective thresholds The test data shown in Figs 13 and 14 are the total lives to failure of

test specimens like those used to generate the small-crack data The test data are plotted

at the midpoint of the "material defect" size range (6 p~m, see Table 1) The tests at a stress

ratio of - 1, obtained from several laboratories [9], showed a large amount of scatter The

calculated fatigue life from a microstructural defect agreed reasonably well with the test

data considering the unusual crack-surface profiles observed in these tests (plane of the

crack was oriented at an angle of about 35 deg from loading axis) [9,17,18] The calculated

and test lives for the Gaussian loading (Fig 14) also agreed well with the limited test data

[19] As can be seen in Fig 14, nearly 90% of the fatigue life is consumed in crack growth

from 6 ~m to 0.1 ram This explains the low percentage in crack growth portion of life

reported in Ref 19

The behavior of the aluminum-lithium alloy was quite similar to the 2024-T3 aluminum

alloy in spite of the tortuous crack path The initial defect sizes were about the same size,

FIG 13 Calculated and experimental fatigue lives for 2090-T8E41 aluminum-lithium alloy under

R = - 1 loading with S = 100 MPa

Trang 28

and the small-crack effects were similar Further study is needed, however, to see whether

the aluminum-lithium alloy exhibits a strong stress-level effect like that shown for the alu-

minum alloy

T i - 6 A I - 4 V Titanium A l l o y

For the titanium alloy, fatigue tests were conducted on the same specimen configuration

as used to obtain the small-crack data [20] Tests were conducted under R = - 1 loading

at stress levels near the fatigue limit In these tests, the fatigue life attributed to crack growth

from a 0.005 mm crack to failure ranged from 50 to 70% A comparison of fatigue lives

computed for various initial crack sizes using both large- and small-crack data are shown in

Fig 15 for a stress level of 225 MPa For initial cracks smaller than about 0.03 mm, large

differences in calculated lives were observed between the large-crack and small-crack meth-

ods Obviously, large-crack data are inappropriate for fatigue-life calculations Because no

metallurgical examinations were made of initiation sites, the test data in Fig 15 have been

plotted at an initial crack size of 0.0005 mm to agree with calculated life At present, this

crack size should only be considered as an equivalent-initial-flaw size because it was not

determined from any microstructural feature However, the calculated lives using the small-

crack data are not very sensitive to crack size below about 0.01 mm; in fact, the life from

a "grain size" crack (al = 0.006 ram) to failure amounted to about 70% of the average

fatigue life of the four tests

Figure 16 illustrates the influence of the initial crack size on the fatigue (S-N) behavior

under R = - 1 loading conditions The crack-growth lives from various initial crack sizes

to failure have been plotted as a function of stress level A n initial crack size of 0.0005 mm

and a small-crack threshold of AKS,h = 1.1 M P a - m L~ were selected to fit the fatigue life

and fatigue limit, respectively (Results shown in Fig 15 are a subset of this data for 225

MPa.) The calculated results for ai = 0.01 mm gave slightly less life than the test for stress

Trang 29

Trang 30

2 4 ADVANCES IN FATIGUE LIFETIME PREDICTIVE TECHNIQUES

levels above the fatigue limit, but gave a much lower fatigue limit (lower horizontal solid

line) than the results for the smaller crack size These results illustrate the importance of

the small-crack AK-threshold in calculating the fatigue limit The calculated results for a~

greater than or equal to 0.1 mm are basically from large-crack data for stress levels greater

than the fatigue limit The results for the larger initial crack sizes are consistent with Eylon

and Pierce [24] They have shown that the growth of a crack 0.5 mm in length consumes

only about 5% of the total fatigue life

A n attempt was made to relate the assumed initial crack size (2ai = 0.001 mm) to some

microstructural features Because titanium has a relatively high solubility for most common

elements and multiple vacuum arc melting is accomplished with high purity materials, the

occurrence of inclusion-type defects is rare [25] Eylon and Pierce [24] studied the initiation

of cracks in a Ti-6A1-4V alloy and found that cracks preferred to nucleate in the width

direction of alpha needles, or colonies of alpha needles, along a shear band on the basal

plane The size of the alpha needles was not reported but was stated to be considerably

smaller than the size of alpha grains (grains were about 0.008 mm in size) Thus the alpha-

needle size may be close to the initial crack size needed to predict most of the fatigue life

based solely on crack propagation Bolingbroke and King [26] also monitored the initiation

and growth of small cracks in IMI318 (nominal composition Ti-6A1-4V) titanium alloy for

crack lengths (2a) of about 0.006 mm These cracks initiated in alpha grains or at alpha/

alpha grain boundaries In regions of transformed beta grains, the crack growth was tem-

porarily slowed D o microcracks propagate from 0.001 to 0.006 mm in length or do cracks

of 0.006 mm in length develop, after some "initiation" cycles, by slip-band formation within

these alpha grains? The latter appears to fit the general trend for a wide variety of titanium

alloys [26,27] However, the crack sizes necessary to verify the total-life analysis are about

an order-of-magnitude smaller than those that have been monitored to date Results in Refs

26 and 27 indicate the importance of discontinuous crack growth for small cracks In some

titanium microstructures, small-crack growth is slowed down or even stopped by micro-

Trang 31

structural barriers However, in the mill-annealed titanium alloy [20,26] small-crack growth was not greatly influenced by such barriers All of these results clearly indicate the importance

of small-crack behavior on fatigue life in titanium alloys

4340 Steel

The small-crack data under constant-amplitude (R - 0) loading and under the Felix/28 spectrum loading [18] were used to predict the fatigue (S-N) behavior for specimens other than those used to obtain the small-crack data The initial crack size (an equivalent semicircular defect size of 13 ~m radius) used to make these predictions was determined from tests conducted by Swain et al [18] (see Table 1) Everett [28] conducted fatigue tests on the same material with specimens containing a central hole with a hole-diameter-to-width

(D/W) ratio of 0.25 (KT 3.23) Figure 17 shows a comparison of tests and predictions under R = 0 loading The predictions were made using either an elastic (Eq 5) or elastic- plastic (Eq 6) analysis Because 4340 steel cyclically-strain softens, the monotonic flow stress was replaced by a flow stress obtained from a cyclic stress-strain curve for this material [29]

The cyclic flow stress was estimated to be about 1000 MPa Both predictions agreed well near the fatigue limit but differed substantially as the applied stress approached the flow stress of the material In these predictions, the AK threshold for small cracks was 4.3

M P a - m ~ (see Fig 8) The predicted fatigue limit using this value and the initial crack size (13 #m) appeared to be slightly too high (about 10%) The solid symbol shows net-section stress equal to the ultimate tensile strength

A comparison between test and predicted fatigue lives under the Felix/28 spectrum is shown in Fig 18 Again, the small-crack data with an initial crack size of 13 p~m was used

to make the predictions The predicted results using the elastic-plastic analysis agreed well with the test data, except at the fatigue-limit condition Again, the AK threshold for small cracks (8 M P a - m ~4) appeared to be too high and caused a predicted fatigue limit that was

Trang 32

about 30% too high (solid curve) A selected value of AKSh = 6 M P a - m v2 gave much better

results (dashed curve)

Overall, the good predictions for the 4340 steel were probably made possible because

small-crack and large-crack data tended to agree over a wide range in AK, and small-crack

data would not be expected to exhibit a stress-level effect, except at the very high stress

levels These limited results indicate that the determination of the small-crack thresholds

for the steel needs further study

Concluding Remarks

A n assessment has been made of a total-life analysis based solely on crack growth from

microstructural defects The analysis is based on observations of defect sizes at initiation

sites and on fatigue-crack-growth rate data for small and large cracks The assessment was

based on data from 2024-T3 aluminum alloy, 2090-T8E41 aluminum-lithium alloy, Ti-6A1-

4V titanium alloy, and 4340 steel under either constant-amplitude or spectrum loading

Basing total-life calculations on crack growth seems reasonable in view of the test results

and analyses presented For most materials studied (aluminum, aluminum-lithium, and

steel), crack growth was actually monitored over a large percentage (from 70 to over 90%)

of the total fatigue life In the titanium alloy, however, the percentage of fatigue life at-

tributed to crack growth by observation was smaller than in the other materials but was still

about 50 to 70% In the total-life analysis, the calculated fatigue lives using an initial crack

size based on an average inclusion-particle size agreed well with test lives for all materials

except the titanium alloy In the titanium alloy, an initial surface crack with a 0.0005 mm

radius was chosen to fit fatigue lives under constant-amplitude loading At present, this

crack size has not been related to any microstructural feature and should be considered an

equivalent-initial-flaw size

It appears that when small-crack effects are taken into account, fatigue-life analyses based

solely on crack propagation may provide a viable alternative to traditional, two-part

initiation-plus-crack-growth life analyses One advantage of a crack-growth-based procedure

is that the measure of damage, crack size, is a physically measureable quantity that can be

used to gain a better understanding and evaluation of life-prediction analyses Another

advantage would be the use of a single analysis procedure for all life calculations rather

than one procedure for initiation and another for crack growth Disadvantages of the crack-

growth-based procedure are that generation of small-crack data is more difficult than S-N

testing and more complex stress analyses would be required However, with continually

improving computerized stress analyses and encouraging results from models to predict

small-crack effects, a continued exploration of crack-growth-based life design is warranted

References

[1] Gallagher, J P., Giessler, F J., Berens, A P., and Engle, R M., Jr., "USAF Damage Tolerant

Design Handbook: Guidelines for the Analysis and Design of Damage Tolerant Aircraft Struc-

tures," AFWAL-TR-82-3073, May 1984

[2] Pearson, S., "Initiation of Fatigue Cracks in Commercial Aluminum Alloys and the Subsequent

Propagation of Very Short Cracks," Engineering Fracture Mechanics, Vol 7, 1975, pp 235-247

[3] Kitagawa, H and Takahashi, S., "Applicability of Fracture Mechanics to Very Small Cracks or

the Cracks in the Early Stage," in Proceedings', 2nd International Conference on Mechanical

Behaviour of Materials, Boston, 1976, pp 627-631

[4] Ritchie, R O and Lankford, J., "Overview of the Small Crack Problem," in Small Fatigue Cracks,

R O Ritchie and J Lankford, Eds., The Metallurgical Society, Warrendale, Pa., 1986

[5] Newman, J C., Jr., "A Nonlinear Fracture Mechanics Approach to the Growth of Small Cracks,"

Trang 33

NEWMAN ET AL ON UNIFIED APPROACH TO LIFE PREDICTION 27

[6] Miller, K J., Mohamed, H J., Brown, M W., and De Los Rios, E R., "Barriers to Short Fatigue Crack Propagation at Low Stress Amplitudes in a Banded Ferrite-Pearlite Structure," in Small

1986, pp 639-656

[7] Leis, B N., Kanninen, M F., Hopper, A T., Ahmad, J and Broek, D., "Critical Review of the Fatigue Growth of Short Cracks," Engineering Fracture Mechanics, Vol 23, 1986, pp 883-898 [8] Newman, J C., Jr., and Edwards, P R., "Short-Crack Growth Behaviour in an Aluminum A l l o y - -

An A G A R D Cooperative Test Programme," A G A R D Report No 732, 1988

[9] Edwards, P R and Newman, J C., Jr., "Short-Crack Growth Behaviour in Various Aircraft Materials," A G A R D Report No 767, 1990

Laboratory, AFFDL-TM-76-83-FBE, Sept 1976

for 2024-T3 Aluminum Alloy," in Small Fatigue Cracks, R O Ritchie and J Lankford, Eds., The Metallurgical Society, Warrendale, Pa., 1986, pp 427-452

tions," Experimental Mechanics, Vol 29, No 2, June 1989, pp 221-225

(Helix and Felix): Part 2 - - F i n a l Definition of Helix and Felix," Royal Aircraft Establishment TR-84085, Aug 1984

Gaussian Type Recommended for General Application in Fatigue Testing," LBF Report No 2909

I A B G Report No TF-570, April 1976

Fatigue Crack Initiation and Early Fatigue Crack Growth," in Advances in Crack Length Meas-

T3 Aluminum Alloy," in Mechanics of Fatigue Crack Closure, ASTM STP 982, J C Newman, Jr., and W Elber, Eds., American Society for Testing and Materials, Philadelphia, 1988, pp 505-515

Lithium Alloy," A G A R D Report No 767, 1990, pp 2.1-2.11

Cracks in 4340 Steel and Aluminum-Lithium 2090," A G A R D Report No 767, 1990, pp 7.1-7.30

7075-T6 under Constant Amplitude and Different Types of Variable Amplitude Loading, Especially Gaussian Eoading," A G A R D Report No 767, 1990, pp 4.1-4.14

Loading," A G A R D Report No 767, 1990, pp 10.1-10.7

pp 247-309

ASTM Symposium on Small-Crack Test Methods, San Antonio, Tex 14 Nov 1990

4V," Metallurgical Transactions, Vol 7A, 1976, pp 111-121

Metallographic Features by Precision Sectioning in Titanium Alloys," Metallurgical Transactions,

Vol 7A, 1976, pp 1477-1480

IMI550 and IMI318," in Small Fatigue Cracks, R O Ritchie and J Lankford, Eds., The Met- allurgical Society, Warrendale, Pa., 1986, pp 129-143

in a Ti-8.6A1 Alloy," in Small Fatigue Cracks, R O Ritchie and J Lankford, Eds The Metal- lurgical Society, Warrendale, Pa., 1986, pp 117-127

NASA TM-102759, Dec 1990

Amplitude Load History," Final Report on NASA Grant NAG1-822, July 1990

Trang 34

M V o r m w a l d , 1 P Heuler, 2 a n d T Seeger 3

A Fracture Mechanics Based Model for

Cumulative Damage Assessment as Part of

Fatigue Life Prediction

R E F E R E N C E : Vormwald, M., Heuler, P., and Seeger, T., " A Fracture Mechanics Based

Model for Cumulative Damage Assessment as Part of Fatigue Life Prediction," Advances in

Fatigue Lifetime Predictive Techniques, A S T M STP 1122, M, R Mitchell and R W Landgraf,

Eds., American Society for Testing and Materials, Philadelphia, 1992, pp 28-43

ABSTRACT: Most fatigue life prediction concepts are based on the transfer of some char-

acteristic material data to the component under consideration The implicitly assumed equiv-

alence can be limited by various factors including different surface conditions, sizes, residual

stress fields, and cumulative damage-related items such as transient endurance limit and load-

dependent failure mechanisms This paper concentrates on aspects related to cumulative dam-

age and presents a model for cumulative damage assessment It allows prediction of crack

initiation life where crack initiation means the occurrence of cracks of an engineering size

( = 1 mm) Though formulated in terms of a cumulative damage calculation, it is based on the

consideration of short crack growth behavior The main features are:

9 Consideration of load sequence dependent crack opening and closing levels controlled by

the elasto-plastic strain history

9 Damage sum (i.e., crack length) dependent decrease of the fatigue limit

9 Derivation of a crack-driving parameter based on elasto-plastic fracture mechanics

An experimental test program including two steels and an aluminum alloy and several types

of loading spectra revealed the improved accuracy of the model in comparison with previous

approaches The improvement can be attributed to the consideration of the most important

aspects determining the physical process of the formation and growth of short cracks under

variable amplitude loading

KEY WORDS: fatigue life prediction, damage accumulation, variable amplitude loading, elasto-

plastic fracture mechanics, short cracks, crack closure, endurance limit, threshold

1IABG, Munich, formerly with Technical University, Darmstadt, Germany

2IABG, Munich, Germany

3Technical University, Darmstadt, Germany

28

Trang 35

VORMWALD ET AL ON CUMULATIVE DAMAGE ASSESSMENT 29 K' Cyclic hardening coefficient

K, Stress concentration factor

m Exponent in crack growth law

n' Cyclic hardening exponent

N Number of cycles to initiation of cracks of technical size

~0 Average yield stress = 1/2(~; + ~u)

% Ultimate tensile strength

~y Monotonic yield stress (0.2% offset)

% Cyclic yield stress (0.2% offset)

Introduction

Designing of components and structures in regards to fatigue is generally a very complex

process that includes aspects of general shape, choice of materials and manufacturing routes,

and estimation of loading environment Fatigue life prediction as part of this process must

consider two main problems if it is assumed that the other items (e.g., loading parameters)

are sufficiently known: (1) transferability and (2) cumulative damage assessment The former

addresses the fact that generally fatigue life is controlled by the unique state and strength

of the material and the surface at highly stressed areas of the component under consideration

It appears to be very difficult to determine fatigue-relevant data for these localized areas

from conventional tests on simple specimens Notch and size effects, surface roughness, and

residual stresses must be properly evaluated Frequently, a fatigue notch factor (Ky) is used,

but this might be too simplistic an approach for such a complex matter The second problem

arises from the fact that the basic data of materials and components are determined under

constant amplitude cycling Under this type of loading, some properties can be determined

(e.g., endurance limit) that might undergo a marked decrease under variable amplitude or

spectrum loading To derive improved fatigue life prediction procedures it appears necessary

to separate the governing factors as far as possible and to assess their relative importance

This paper concentrates on cumulative damage related phenomena and presents a model

for fatigue life prediction in the crack initiation stage To separate the cumulative damage

and transferability problems, simple unnotched specimens were employed as test articles

Essential features and results obtained by this model are presented

Problems of Fatigue Life Prediction Related to Cumulative Damage

Two main classes of fatigue life prediction concepts can be distinguished:

9 Cumulative damage assessment based on some type of S-N data (stress or strain life

curves) (Type A approach)

9 Fracture mechanics based approaches for cumulating crack increments (Type B

approach)

Both crack initiation or total life (Type A) and crack propagation life (Type B) related

concepts must address the cumulative damage problem This arises mainly because fatigue

Trang 36

behavior under constant amplitude (CA) loading can be markedly different to that under

variable amplitude (VA) or spectrum loading Type B (i.e., fracture mechanics based con-

cepts) appear to be more useful, since the measure of damage, the crack (length), can be

physically assessed, whereas Type A concepts are based on relative life consumption that

do not allow for direct measurement of damage and damage increments Relevant phenom-

ena and engineering approaches are discussed below

Endurance Limit and Threshold

Omission tests with increasing gate or filter levels show that load cycles well below the

endurance limit contribute a considerable amount of damage (Type A) [1] Microstructural

barriers that lead to an endurance limit under C A loading can be overcome by microcracks

or persistent slip bands due to higher loads in a V A loading sequence [2], thus producing

a gradual decrease of the original long-life fatigue strength Attempts to consider this effect

by use of strain-life curves with initial or periodic overstrain [3] are, in the authors' opinion,

not generally successful

Residual Stress Fields

In general, the beneficial effects of compressive residual stress fields determined under

high cycle C A loading can not be observed equally under V A loading because of overload-

induced local plasticity producing a shift of local mean stress In principle, prediction concepts

that take into account the local state of stress are able to model these phenomena; this has

been shown by use of the local strain concept (Type A) as well as by crack growth predictions

(Type B) [4] using a superposition of load and residual stress induced stress intensities

Crack Closure

It has been recognized that crack closure contributes considerably to load interaction

effects leading to, respectively, overload or underload induced crack growth retardation or

acceleration Several mechanisms have been identified that contribute to crack closure (e.g.,

plastic deformations ahead of the crack producing crack face contact after some growth,

rough fracture surfaces, and oxide debris)

Crack closure is more pronounced in plain stress than in plain strain situations and has

been successfully implemented into advanced empirical or analytical crack growth prediction

models (e.g., [5,6]) These models represent, of all the predictive approaches presently

available, the most powerful and reliable fatigue life prediction concepts [7,8]

Although crack closure seems to be closely connected to fracture mechanics based (Type

B) life prediction concepts, it can be assumed to be relevant also for Type A approaches

where nominally crack-free material volumes are considered This is based on an interpre-

tation of the damage accumulation process as nucleation and growth of (small) cracks The

consequences of overloads, however, show some typical differences at short and long crack

lengths For long cracks with low nominal stresses, overloads tend to increase the closure

level and to decelerate growth rates A t high stress levels, typical for notches, a decrease

of closure level and hence an increase in growth (or damage accumulation) rate can be

observed

Load-Dependent Deforrnation and Failure Mechanisms

There is wide evidence that deformation and failure mechanisms can depend on the

magnitude of the applied load (e.g., load-dependent dislocation structures, densities of

Trang 37

VORMWALD ET AL ON CUMULATIVE DAMAGE ASSESSMENT 31 microcracks, crack surface topography, buildup of shear lips, and failure sites) Often several regions can be identified along an S - N curve or a crack growth rate curve with different failure mechanisms and failure modes which control fatigue behavior When fatigue life under V A amplitude loading is to be predicted, damage or crack increments must be read across according to the different load ranges occurring within the load sequence In reality, however, the failure-driving mechanisms may be controlled by either the highest load (range)

or the majority of small cycles This would inevitably lead to erroneous estimates of damage (crack) increments in one or the other case

"Kinking" in the crack rate curve is typical for load-dependent failure mechanisms and their macroscopic consequences For the titanium alloy shown in Fig 1 it was not possible

to predict the crack growth behavior under T U R B I S T A N loading on the basis of the original crack rate curve [9] A fictitious extension of the upper part of the C A curve in Fig 1 down

to smaller crack growth rates, however, produced good predictions The kink in the C A curve indicates a load (AK) level where the cyclic plastic zone size reaches the average grain size and the fracture topography changes to a smoother surface with decreasing roughness and crack deflections

It is concluded that due to the aforementioned phenomena fatigue data obtained under

C A loading might be of limited use for assessment of V A fatigue behavior It is not surprising,

10 -3

|

d w"

10 -6

STRESS INTENSITY FACTOR RANGE, AK, MPoV'm'

FIG 1 - - C r a c k growth rate curve for Ti-6Al-4V showing a "kink" at AK = 16 MPa ~ [9]

Trang 38

therefore, that many advanced crack closure based models, such as the O N E R A crack

growth prediction model [5], require some simple VA tests for derivation of input data

Benchmark testing (i.e., calibration of prediction techniques versus relevant test results)

should be a prerequisite of a practical application of numerical life prediction concepts

Fracture Mechanics Based Model for Uniaxial Cumulative Damage Assessment

Work during the last decade revealed that the fatigue life to initiate a crack of technical

size ( = 1 ram) is dominated by the growth of short cracks [10] Consequently the proposed

model is based on a fracture mechanics approach for short cracks, because it offers the

opportunity to explicitly consider crack opening and closure as well as the progressive decay

of the original endurance limit under VA loading Both phenomena are believed to be main

drivers for load interaction effects that very often are predicted with poor accuracy by

conventional life prediction methods Though derived by fracture mechanics consideration,

the model is presented in terms of a cumulative damage model Its basic features and

functions are outlined below

Crack Opening and Closure of Short Cracks

The opening and closure of short cracks have recently been investigated [11] using uni-

axially strained unnotched steel and aluminum specimens of 6 mm diameter at high and

intermediate strain levels Results are shown in Fig 2 together with literature data [12-14]

plotting crack opening stress versus maximum applied stress normalized by an average yield

stress defined as

1

The differences in crack opening stress result not only from different material behavior

but from differences of the definition of the crack opening stress level (for details see [/I])

The ez~perimental trends indicating a decreasing crack opening stress level with increasing

stress range are predicted reasonably well by a formula proposed by Newman [15] on the

basis of analytical assessment of long crack behavior Therefore it is adopted for the present

Trang 39

O Rie and Schubert, 10[rMo910 I l t * ] [ ]

[] Dowling and lyyer, AISI ~31,0 [ 13 ]

- - Newman's model [15]

NORHALIZED HAXIHUH STRESS, Omox Io0

FIG 2 Normalized crack opening stress for small cracks (a < 2 mm)

A second important result of the short crack closure examination (crack depth of 0.2 to

2 ram) was that, under elasto-plastic cycling, closure and opening approximately coincide

in terms of strain and not in terms of stress (Fig 3) This led to the following strain-driven consideration of opening and closure levels:

1 The crack opening and closing levels are completely described by the same global strain value (Fig 3)

Ego= Ecl

E

FIG 3 Crack opening and closure levels for elasto-plastic loading (schematic)

Trang 40

2 This crack opening strain is calculated on a cycle-by-cycle basis A cycle is defined by

a closed hysteresis loop of stress versus global strain

3 The crack opening strain remains unchanged when the upper strain of the loop is lower

than the previously fixed crack opening strain

4 A change in the crack opening strain always depends on the CA crack opening strain

(eop,~), which is the corresponding C A opening level of the cycle under consideration

%p.c~ is the strain level on the ascending hysteresis loop branch (Fig 3) corresponding

to the C A crack opening stress (Crop,~,) according to Eq 2 For completely compressive

cycles (R -> 1) the crack opening strain (eop,~,) is set to the strain value at the upper

reversal point

5 If new absolute maxima within the course of a load sequence are reached, the next

complete cycle fixes eop to the C A crack opening strain of this cycle

6 If the C A crack opening strain of a cycle is higher than the crack opening strain that

previous cycles have left, the effective stress and strain ranges are computed with the

old crack opening strain After suffering the actual cycle a new crack opening strain

has developed according to

eop = eop,c~ - (eoo,~ - eop.o,d) 9 exp ( - 1 5 9 D ,) (3)

7

where Dactua~ is the contribution of the actual cycle to the damage sum Equation 3 has

been derived empirically and was checked by a number of two-level tests (Fig 4)

Details are given in Ref 11

If the crack opening strain of a cycle is lower than the crack opening strain that previous

cycles have left, two cases are to be distinguished:

(a) A large cycle (~ra > 0.4~0) resets the crack opening strain to its C A value

(b) The influence of small cycles (~r~ < 0.4or0) is expressed by Eq 3

NUMBER OF POST OVERLOAD CYCLES N

Tiêu đề	Advances in Fatigue Lifetime Predictive Techniques
Tác giả	M. R. Mitchell, R. W. Landgraf
Trường học	University of Washington
Chuyên ngành	Engineering
Thể loại	Special Technical Publication
Năm xuất bản	1992
Thành phố	Philadelphia

Định dạng
Số trang	495
Dung lượng	10,05 MB