Astm stp 463 1970

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AMERICAN SOCIETY FOR TESTING AND MATERIALS

1 916 Race Street, Philadelphia, Pa 1 9103 NATIONAL AERONAUTICS AND

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(~) BY AMERICAN SOCIETY FOR TESTING AND MATERIALS 1970

Library of Congress Catalog Card Number: 72-97728

ISBN 0-8031-0058-2

NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication

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Foreword

The object of this book is to bring together a series of papers which de-

scribe recent experience obtained in the United States and in England with

the application of the ASTM E-24 Proposed Method of Test for Plane Strain

Fracture Toughness of Metallic Materials This information supplements that

which has appeared in ASTM STP 381 on Fracture Toughness Testing and

its Application and in STP 410 on Plane Strain Crack Toughness Testing of

High Strength Metallic Materials This publication is a cooperative effort of

ASTM and NASA NASA research personnel have participated in ASTM

Fracture Committee activities since their inception in 1959 This participation

reflects the strong interest that NASA has maintained in the development

of test methods for evaluation of the fracture resistance of engineering

materials This interest arises from the necessity for the use of high-strength

alloys in critical parts of aerospace structures By cooperation with ASTM

in publication of this book NASA is helping to fulfill its obligation to

provide the widest practicable and appropriate dissemination of results from

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Related ASTM Publications

Fracture Toughness Testing and Its Applications, STP

381 (T965), $19.50 Plane Strain Crack Toughness Testing of High Strength Metallic Materials, STP 410 (1967), $5.50

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Contents

PAGE

I n t r o d u c t i o n t o S T P 4 6 3 - - w F BROWN, JR 1

P r o g r e s s in F r a c t u r e T e s t i n g o f M e t a l l i c M a t e r i a l s - - J G KAUEMAN 3

T h e o r y 4

I n i t i a l R e c o m m e n d a t i o n s 4

T h i c k n e s s a s a P r o b l e m 7

F a t i g u e C r a c k i n g 8

E m p h a s i s o n T h i c k S e c t i o n s 9

E v o l u t i o n o f N o t c h e d B e n d S p e c i m e n s 12

C o m p a c t K~c S p e c i m e n 15

S c r e e n i n g T e s t s 15

T h i n - S e c t i o n P r o b l e m 18

M e d i u m - S t r e n g t h M a t e r i a l s 18

C a u t i o n a r y N o t e s 18

S u m m a r y 2 0 E v a l u a t i o n o f a M e t h o d o f T e s t f o r P l a n e S t r a i n F r a c t u r e T o u g h n e s s T e s t i n g U s i n g a B e n d S p e c i m e n - - R H H E Y E R A N D D E M C C A B E 2 2 P i l o t P r o g r a m 23

I n t e r l a b o r a t o r y T e s t s 23

F a t i g u e C r a c k i n g 2 4 B e n d T e s t i n g 30

A n a l y s i s o f K~c D a t a 33

C o n c l u s i o n s 4 0 B r i t i s h E x p e r i e n c e w i t h P l a n e S t r a i n F r a c t u r e T o u g h n e s s (KIt) T e s t i n g - -

M J MAY 42

C o l l a b o r a t i v e T e s t P r o g r a m 43

F i r s t S t a g e 43

S e c o n d S t a g e 4 4 S t a n d a r d i z a t i o n o f KIc T e s t i n g 47

I n f l u e n c e o f F a t i g u e P r e c r a c k i n g C o n d i t i o n s 47

C r a c k L e n g t h - S p e c i m e n T h i c k n e s s R e q u i r e m e n t s 51

D r a f t B r i t i s h S t a n d a r d 61

S u m m a r y 61

D i s c u s s i o n 62

T h e I n f l u e n c e o f C r a c k L e n g t h a n d T h i c k n e s s in P l a n e S t r a i n F r a c t u r e T o u g h - n e s s T e s t s - - M H JONES AND W F BROWN, JR 63

M a t e r i a l a n d S p e c i m e n P r e p a r a t i o n 66

T e s t P r o c e d u r e 67

A n a l y s i s o f D a t a 68

B e n d S p e c i m e n s 68

S m o o t h S p e c i m e n s 71

R e s u l t s f o r E f f e c t s o f T h i c k n e s s a n d C r a c k L e n g t h 72

S c r e e n i n g T e s t s f o r K~c 77

C o r r e l a t i o n o f K~c w i t h T e n s i l e P r o p e r t i e s 84

P r a c t i c a l S i g n i f i c a n c e o f R e s u l t s 85

A p p e n d i x e s 88

Downloaded/printed by

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

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vi CONTENTS

PAGE

C r a c k T o u g h n e s s Testing o f H i g h - S t r e n g t h Steels E, A STEIGERWALD 102

N o t c h Bend Tests 107

Km D a t a for H i g h - S t r e n g t h Steels 113

S u m m a r y a n d C o n c l u s i o n s 115

Slow B e n d K~c Testing o f M e d i u m - S t r e n g t h H i g h - T o u g h n e s s S t e e l s - - s T R O L F E A N D S R , N O V A K 124

M a t e r i a l s a n d P r o c e d u r e t25 S p e c i m e n G e o m e t r y a n d Analysis 128

R e s u l t s a n d D i s c u s s i o n 131

Kio Values 131

P o p - i n Criteria . 133

S p e c i m e n Size R e q u i r e m e n t s 139

Effects o f Stress Level D u r i n g F a t i g u e C r a c k i n g 144

Effect o f F a c e N o t c h i n g 145

C o r r e l a t i o n Between Krc a n d C V N Values . 145

S u m m a r y a n d C o n c l u s i o n s 147

A p p l i c a t i o n o f F r a c t u r e M e c h a n i c s T e c h n o l o g y to M e d i u m - S t r e n g t h S t e e l s - -

W G C L A R K , J R , A N D E T W E S S E L 160

I n f o r m a t i o n R e q u i r e d in F r a c t u r e M e c h a n i c s T e c h n o l o g y 161

M a t e r i a l P r o p e r t i e s 162

D i s c u s s i o n o f Materials P r o p e r t i e s 172

E x a m p l e P r o b l e m 177

G e n e r a l Stress Analysis 180

C a l c u l a t i o n o f Critical F l a w Sizes 180

Calculation o f Cyclic Life 182

Material Selection 184

D e v e l o p m e n t o f I n s p e c t i o n Criteria a n d Safety F a c t o r s 185

S u m m a r y 186

F r a c t o g r a p h i c Analysis o f t h e L o w Energy F r a c t u r e o f a n A l u m i n u m A l l o y - -

J P T A N A K A , C A P A M P I L L O , A N D J R L O W , J R 191

Material 192

F r a c t o g r a p h i c Study 193

Failure o f L a r g e Inclusions 196

T r a n s m i s s i o n E l e c t r o n M i c r o s c o p y 200

I d e n t i f i c a t i o n o f V o i d - N u c l e a t i n g Particles 204

F r a c t o g r a p h i c O b s e r v a t i o n o f B o u n d a r y Between Fatigue C r a c k a n d D i m p l e d R u p t u r e 210

C o n c l u s i o n s 214

A p p e n d i x 214

C o m m e n t a r y o n Present P r a c t i c e - - w F B R O W N , J R , A N D J E S R A W L E Y 216

S p e c i m e n Size R e q u i r e m e n t s 217

F u n d a m e n t a l C o n c e p t s 219

Effects o f Plastic D e f o r m a t i o n in K~c, Tests 221

F a c e G r o o v i n g 226

Specimen P r e p a r a t i o n a n d Test P r o c e d u r e 227

C r a c k Starter C o n f i g u r a t i o n a n d D i s p l a c e m e n t G a g e L e n g t h 227

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CONTENTS vii

P A G E

F a t i g u e Cracking 228

N o n u n i f o r m i t i e s in Fatigue Cracks 228

Fatigue C r a c k Sharpness R e q u i r e m e n t 229

Testing o f Brittle M a t e r i a l 231

C o m p a r i s o n o f Plane Strain F r a c t u r e Toughness o f Various Alloys 232

C o r r e l a t i o n o f KIc with Other Properties 238

C o r r e l a t i o n with Tensile Properties 238

Tensile Ductility in M a t e r i a l Specifications 240

C o r r e l a t i o n with I m p a c t Properties 241

F r a c t u r e Tests with Subsized Specimens (Screening Tests) 243

M a t e r i a l Selection for Particular Applications 244

Acceptance Tests 244

A l l o y D e v e l o p m e n t Tests 246

T e n t a t i v e M e t h o d o f Test for Plane Strain F r a c t u r e T o u g h n e s s of Metallic Materials ( A S T M D e s i g n a t i o n : E 399-70 T) 249

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STP463-EB/Sep 1970

Introduction

This Special Technical Publication brings together a set of papers that were presented at a Panel Session on Plane Strain Crack Toughness sponsored

by the ASTM E-24 Committee on Fracture Testing of Metals during the

1968 ASTM Annual Meeting in San Francisco The main purpose of this Panel Session was to review the practical experience in fracture toughness testing which had developed since ASTM Committee E-24 placed its major efforts in standardization on methods of test for plane strain fracture toughness These efforts were started early in 1965, and the initial developments were described in A S T M S T P 410.1 The paper by Kaufman reviews these developments and gives a brief history of ASTM Committee E-24 activity

In the latter part of 1966 Subcommittee I of ASTM Committee E-24 on High Strength Metallic Materials formulated a Proposed Recommended Practice for Plane Strain Fracture Toughness Testing of High Strength Materials Using a Fatigue-Cracked Bend Specimen Draft copies of this document were made available early in 1967, and during the next year and a half considerable experience was gained in applying the Proposed Practice to a wide variety of metallic materials

During this trial period various practical problems were encountered, some due to tke inherent limitations of elastic crack mechanics and others associated with certain details of specimen preparation and testing The members of the Panel, who all had well-established fracture testing programs, were asked to emphasize these problem areas As a result of this Panel meeting and subsequent discussions among the ASTM E-24 Comimttee members several changes were made in the Recommended Practice, and a revised document was published in the 1969 A S T M B o o k o f Standards This revision incorporated a compact tension specimen as well as the bend specimen, and was designated as a Proposed Method of Test for Plane Strain Fracture Toughness of Metallic Materials This Proposed Method was subsequently further revised as described in the concluding contribution to this STP and was advanced to a Tentative Method (E 399-70T), a copy of which has been bound at the back of this volume

Since the papers which appear in this STP were presented, ASTM Com- mittee E-24 Method of Test has been incorporated into various specifications issued by both the U S Government and by private industry It forms

t Brown, W F., Jr., and Srawley, J E., Plane Strain Crack Toughness Testing of High Strength Metallic Materials, ASTM STP 410, American Society for Testing and Materials,

1966

1

Copyright 9 1970 by ASTM lntcrnational www.astm.org

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a part of the Aerospace Material Document series issued by the Society of Automotive Engineers and is also the basis far qualifying KIe data for in-

aspects of the Test Method which could be improved, but, what is more important, they have shown that there is a strong desire on the part of many investigators to compromise what they consider to be the overly strict specimen size requirements Suggestions that the required crack length or specimen thickness or both could be reduced appear in several of the papers o f this volume This concern about specimen size arises naturally out of attempts

to apply the Test Method to materials having lower strength and higher toughness than those originally intended by the ASTM E-24 Committee This volume contains two contributions that were not part of the Panel Session on Plane Strain Crack Toughness The first is a paper by J R Low, Jr., and his associates describing some recently completed work on the fracto- graphic analysis of the aluminum alloy 2014-T6 This paper is quite pertinent since it provides a plausible explanation for the relatively low plane strain fracture toughness characteristic of this and possibly other high-strength aluminum alloy plate The second is a contribution by J E Srawley and myself entitled " C o m m e n t a r y on Present Practice." This not only summarizes the salient features of the various papers, but also attempts to clarify certain aspects of plane strain fracture toughness testing where there appears to be some confusion

W F Brown, Jr

Chief, Strength of Materials Branch, National Aeronautics and Space Administration Lewis Research Center, Cleveland, Ohio 44135

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to do an acceptable job, and the timing problems in incorporating methods into specification requirements

KEY WORDS: fractures (materials), toughness, test techniques, fatigue precracking, thickness, crack growth measurement, screening, standardization, evaluation, tests

In 1958, A Special ASTM Committee on Fracture Testing, now known

as ASTM Committee E-24, was established for the purpose of developing and writing test methods for the determination of the fracture characteristics

of materials as they involve the susceptibility of the material to what has been commonly called "brittle fracture" or "catastrophic failure" [1] 2 Failures without warning in certain critical missile applications at stresses far below those normally expected based upon conventional design techniques provided the primary stimuli behind the formation of the committee Despite the prolificacy of the committee (or perhaps because of it), some confusion exists with regard to the path which has been followed in developing fracture-test methods in ASTM Committee E-24 It is the purpose of this paper to review the progress of the committee effort, presenting the reasons behind the various actions taken and the shifts in emphasis over the years

1 Section head, Fracture Mechanics and Product Evaluation Section, Mechanical Testing Division, Alcoa Research Laboratories, Aluminum Company of America, New Kensing- ton, Pa Personal member ASTM

The italic numbers in brackets refer to the list of references appended to this paper

3 Copyright 9 1970 by ASTM International www.astm.org

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T o preserve the continuity, it is necessary to present the review in rather

general terms, oversimplifying in a number o f instances and avoiding deep

involvement in technical details Similarly, it is impossible to acknowledge

and comment on every individual contribution along the route; rather, the

progress is reported as a committee action

Theory

Under the guiding hands of J R Low and G R Irwin, it soon was estab-

lished that elastic fracture mechanics was the vehicle by which the resistance

of materials to unstable crack growth could be best described Though not

without considerable complication by the fact that most real materials do

not behave in a purely elastic manner on fracturing, the limitations neverthe-

less did not appear insurmountable It was hoped that, with appropriate

modifications to take into account the finite sizes of structural members and

test specimens, and the crack-tip plasticity, small specimens could be used to

recreate and describe the situation when unstable crack growth develops in

a large structure Developments over the years have sustained this opinion

Initial Procedural Recommendations

The first significant step taken by the committee was the establishment of

some recommendations for the fracture testing of materials using the basic

and convenient model of an axially loaded center-notched or double-edge-

notched panel [1 ] The stress analysis for this stiuation was reasonably well in

hand, and it seemed desirable to proceed with symmetrically loaded specimens

to reproduce the condition of crack growth to fracture The load and crack

length at the onset of unstable crack growth to fracture were determined,

and the critical stress-intensity factor, K,, and critical strain-energy release

rate, G~, were calculated Two modifications of the basic equation were made,

one for the width of the specimen and the other for the expected size of the

zone or plastic deformation at the crack tip Guidelines for making these

tests were laid out in the First Report of the Special Committee on Fracture

Testing [1 ], which we must observe in retrospect has served as one of the

principal guides for fracture testing throughout the intervening years

Broader use of this procedure, particularly the center-notched specimen

soon unearthed some troublesome problems and resulted in some important

refinements One concerned the important part of the test involving the

measurement of the "critical" crack length, that is, the crack length when

unstable crack growth began Originally it was suggested that crack growth

be measured by an ink-staining technique, presuming that the ink would

reliably follow the slow crack growth by capillary action but would not follow

the rapid unstable growth of a crack Although useful measurements were

made when care was taken with choice and quantity of ink (Fig la), the

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FIG 1 Fracture surfaces o f center-notched specimens with which the ink-stain procedure

was used Jot following slow crack growth (a) with relatively good success and (b) without

success because o f spattering and seepage

potential variability in fluidity and spattering was intolerable (Fig lb) The

displacement gage [2] and electrical potential [3,4] means of following crack

growth were developed, followed later by the acoustic [5] and ultrasonic

techniques [6]; in very thin sections, visual observations on the surfaces were

used also [7] Of these, the displacement gage, which relies on the change in

elastic compliance of the specimen with change in crack length to indicate

the extent of crack growth [8], is probably the most widely used The type

used at Alcoa Research Laboratories (ARL) is shown in Fig 2 with some

representative curves [9]; the difference in slope of a line through the origin

to the point of instability from the original slope is the measure of crack

growth, provided it has taken place under essentially elastic conditions Some

investigators prefer to use a combination of techniques, including the dis-

placement gage and the electrical potential or ultrasonic techniques as auxili-

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Thickness Emerges Clearly as a Problem

The broad use of more sensitive devices for following crack growth played

an important role in further refinements of fracture testing, as it made it easier to recognize two things:

(a) The fact that Kc is a thickness-dependent property, as exemplified by the data for 7075-T6 sheet and T651 plate in Fig 3 Over a certain critical range of thickness for each material, the toad and the crack length at instability (and, therefore, Kc) decrease with increase in thickness, reaching a rather constant minimum value when plane strain conditions are approached closely In the near fully plane strain situation, the instability leading to complete fracture almost immediately follows crack initiation This point had been observed earlier [1], but not fully appreciated

(b) The fact that the initial crack growth, whether stable or unstable, took place at about the same level of stress intensity for a given material, regardless

of specimen thickness [2] Thus, it might be possible to learn something about

a plane strain instability, even though complete fracture of the specimen did not take place under plane strain conditions

As a result of these two observations, the concepts of a lower level of critical stress-intensity factor associated with plane strain conditions (Kic) and of the capability to approximate the plane strain stress-intensity factor from the conditions under which stable crack growth initiated were solidified [8] Both of these points were vital and remain with us today, although both have changed complexion somewhat

7O L~ 60

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As a result of the close attention to crack initiation a "pop-in" concept

developed [10], pop-in being defined optimistically as a small initial burst o f

unstable crack growth under plane strain conditions which is arrested because

the crack growth itself caused a departure from plane strain conditions

An important aspect of plane strain fracture testing became the search for

pop-in, a clear example of which is presented in the second curve in Fig 2

More will be said about this later

Fatigue Cracking

One of the next refinements to develop was a logical outgrowth of greater

concern about crack initiation and how it is affected by the stress condition

and stress concentration at the tip of the notch Originally, the only require-

ment on the notch-tip radii was that they be <0.001 in [1], a requirement

readily met by machining many test materials, especially aluminum alloys

Although data for the aluminum alloys suggested that values of Ko for thin

sheet did not depend on sharpening the notch by fatigue cracking, so long as

other requirements (on net section stress, a / W , etc.) were met, the picture

was different with regard to values of K1 c The initial crack growth was found

to take place at l0 to 15 percent lower values of stress-intensity factor in

fatigue-cracked specimens than in even the most sharply machine-notched

specimens, and with a less-clear indication of pop-in, as indicated by the

representative curves in Fig 4 [9] Since fracture-toughness testing was aimed

FIG 4 Representative load-deformation curves from fracture-toughness tests, showing the

clear "'pop-in" with machine-notched specimens contrasted with the gradual development o f

crack growth in the fatigue cracked specimens Note also that crack growth starts at signi-

ficantly lower load levels in the fatigue cracked specimens, though the final fracture instability

takes place at nearly the same conditions in the two types o f specimens

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at the behavior of metals in the presence of cracks or metallurgical flaws,

these findings solidified the requirement that specimens must have been

fatigue cracked This brought on one of the most perplexing aspects of

fracture-toughness testing which exists even t o d a y - - t h a t o f providing an

adequate fatigue crack by stressing at a high enough value to obtain reason-

able growth rates, but one which is low enough to avoid stress-history effects

on the fracture test itself

Emphasis Shifts to Thick Sections

Much of the early fracture-toughness testing was directed at relatively

thin sections, and the procedures prescribed in the First and Second Com-

mittee Reports [11] dealt almost entirely with thin-section problems As

additional experience was gained, it became clear that not only was thickness

an important variable, as mentioned previously, but also some other con-

ditions were not quite as simple as was believed originally O f particular

importance, it became clear that a large amount of variation was obtained in

tests of a given thickness of material where different sizes of specimen were

used and there were indications that the elastic response of the testing machine

in which a test was made might be influencing the results significantly In

short, the possibility that Kc, as defined at that time, might not be a single-

valued property even for a given thickness was indicated

In view of the above complications, plus the implication that the ap-

parently thickness-independent plane strain fracture toughness might be a

more fundamental property of materials, effort shifted to concentration

upon methods to determine KI c It is to be stressed that the attention shifted,

not because of less interest in the thin-section problem, but because of the

greater likelihood that this perhaps more fundamental property might

provide a firmer basis for the development and handling of the overall

fracture problem Knowledge that K~ c provided a "conservative" approach

to the fracture problems and that fatigue and stress-corrosion failures even of

relatively thin members seemed controlled by plane strain fracture conditions

added impetus to the shift It was anticipated that once the plane strain

problem was solved, attention could return to the thin-section (plane-stress

or mixed mode) problem

Thus over the next five years, from about 1963 to 1968, attention focused

rather narrowly on the thick section or plane strain problem, and even in this

region we have seen several transitions A variety of specimens have been

considered for determining the plane strain toughness [12], the first perhaps

being the notched round specimen; however, the large amount of material

and large testing machines required for this type of test discouraged its wide

use Center-notched specimens also were used [2], but again material and

testing-system problems governed, and attention was soon focused on what

commonly was called the single-edge-notched (SEN) tension specimen [12];

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is equivalent to 2 ~ times the square of the ratio of KI c to the yield strength

[12] This is a rather severe requirement; while data for some materials sug- gest that this factor may be reduced, 3 there are sufficient data suggesting that

it is none too conservative [13] 4 (Fig 5) and that changes should be made only after careful study

During this same period, considerable attention was focused on the use of face-grooved specimens to improve the likelihood of achieving plane strain conditions [14] However, further study showed that, although the instability point under plane strain conditions appeared to be sharpened a bit by side grooving, the practice does not consistently increase the ability to develop plane strain conditions In fact, it sometimes has the misleading trait of suggesting by the relatively flat fracture appearance that plane strain conditions have been achieved, when in fact they have not, as indicated by the extent of local plasticity (Fig 6) [13] As a result, the practice of side grooving remains outside the firm recommendations of the committee, although it still

is being used as a research tool by some investigators

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Evolution of Notched Bend Specimens

Greater testing experience soon led to the observation that even the use of

single-edge-notched tension specimens for relatively tough materials re-

sulted in problems in loading capacity and gripping The immediate solution

to the problems was simply to rotate the plane of the specimen by 90 deg, and

conduct a bend test [12] Events at the crack tip were identical, and the

differing stress gradients were taken care of in the equations for calculating

K~, With loading requirements at a practical level and specimen size re-

quirements now reasonably developed, the preparation of the first recom-

mended practice for pIane strain fracture-toughness testing was begun

Some problems with fatigue cracking had to be dealt with, and one of the

most perplexing was how to provide the best chance of achieving a straight

crack front With the straight machined notch used over the years with

FIG 7 Fracture surJ&ees to illustrate fatigue crack fronts: (a) satisfactory from straight

notches, (b) unsatiafactory from straight notches, and (c) satisfactory from chevron notches

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SEN specimens, in some cases the fatigue-crack fronts were straight (Fig

7a), but in others they were curved broadly as a result of the crack initiating

at a corner instead of at the middle or across the entire front (Fig 7b) The

introduction of the "chevron" notch improved the situation (Fig 7c), as the

crack invariably started at the center Thus, the crack front was usually

rather straight coming out of the chevron, and, if curvature developed, it was

symmetrical and more readily controlled

Concurrent with the development of the recommended practice, the

problems in determining the load with which to calculate K~c were being

faced Despite early hopes that it would be possible to rely on the occurrence

of a crack pop-in to assure the presence of a plane strain instability, broader

testing experience with fatigue-cracked specimens indicated that this would

not be possible It was clear that if pop-in was required, the usefulness of the

test method would be limited appreciably The large pop-in was usually the

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14 PLANE STRAIN FRACTURE TOUGHNESS TESTING

FIG 7 Continued

result of a blunt crack, and, as mentioned previously (Fig 4), fatigue-

cracked specimens of many materials exhibited only a gradual departure from

linearity

Study was made of other potential criteria for determining the load with

which to calculate a meaningful value of KI c Some investigators expressed a

preference for the use of the initial deviation from linearity, but this had the

obvious shortcoming that the resultant value would vary widely with the

sensitivity of the displacement gages and chart recorders, and so the practice

was discouraged The potential usefulness of a secant offset associated with a

small but specific amount of crack growth evolved Two percent of effective

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] 5

crack extension was selected, which is indicated by a 5 percent secant offset for

the notch-bend specimens

The use of a secant offset instead of an obvious indication of an instability

carries with it the problem of ensuring that crack growth really has taken

place; overtly one cannot be sure whether the departure from linearity on the

load-displacement curve is associated with crack growth or plastic deforma-

tion Therefore, it is necessary to impose some additional requirements on

the test in terms of criteria for validity of the calculated value It can be

shown that the shape of the knee in the curve itself is a clear indication of

whether the offset is largely attributable to plastic deformation (very gradual

curvature) or to cracking (relatively sharp curvature) [15]; examples are

presented in Fig 8 As a result, a requirement was developed that the curva-

ture must be relatively sharp, as indicated by the fact that the offset at 80

percent of the secant-intercept load must be very small compared with (less

than 25 percent of) the offset at the secant intercept load This requirement,

like the offset itself, has the advantage of not being so much a function of

strain gage sensitivity, and of personal interpretation

With this problem resolved, and after study and clarification of the fatigue

cracking techniques, the bend-test method was completed, evaluated via a

The Compact Kic Specimen

Refinement in the capability for the estimation of K~ c measurement capacity

and some farsighted independent research on the fracture toughness of nuclear

vessel materials [17] led to the conclusion that a compact specimen provided

a more efficient use of material than the notched bend specimen (Fig 9)

Attention then focused now on the development of the details of the test

procedure with this particular specimen, and the latest version of the test

method for determining K~r incorporates the compact specimen as well as

the notched bend specimen 5

Screening Tests

Over the same period of time during which the methods for the determina-

tion of K~c have been developing, attention also has been focused on screen-

ing tests, that is, tests useful for merit rating materials with regard to tough-

ness, but which do not provide a number useful for any design consideration

Some recommendations concerning the use of sharp-notch tension testing as a

useful tool for the relative ranking of materials were made in the initial com-

mittee report [1 ] These recommendations centered on the 1-in.-wide sheet-

type specimen, but because of: (1) the desirability of enlarging upon the

applicability of the test and (2) experience indicating that the larger size of

Trang 24

] 6 PLANE STRAIN FRACTURE TOUGHNESS TESTING

FIG 8 Representative load-deformation curves from notch-bend fracture toughness tests o f

curvature largely associated with crack-tip plastic" deformation, while the lower curves illus-

trate the sharper curvature indicative o f crack extension

Trang 25

FIG 9 Compact tension and notched bend fracture toughness specimen o f equal K t ,

measurement capacity to illustrate greater efficiency o f material use with former

specimen achieved this greater applicability through a reduction in the frac-

ture strength and therefore in the complication of plastic deformation, a 3-in.-

wide specimen finally was selected, and either center or edge-notching was

permitted (Fig 4 of footnote 6) This 3-in.-wide specimen was the basis of the

first Recommended Practice for Sharp-Notch Tension Testing of High-

Strength Sheet Materials developed by the committee, 6 a practice which

soon will evolve into an ASTM and USASI Standard Test Method

This practice provides that the ratio of the sharp-notch strength to the

tensile yield strength, in addition to the sharp-notch strength, should be

calculated and is of significance for screening materials This is in recognition

that this ratio is a better indication of the amount of plasticity that a material

is capable of developing (instead of cracking) in the presence of a severe

notch (which is a meaningful relative measure of fracture toughness) [18]

than is the commonly used ratio of the sharp-notch strength to the tensile

strength

It is appropriate at this point to contrast the screening test with the method s

for determining KIe Contrary to the thoughts of many, an invalid value of

K~ ~ (that is, a value determined by a test which does not meet all of the criteria

for validity), is not a reliable and useful relative measure of toughness

Therefore, while the temptation to use the invalid values "just for screening"

is strong, it may give false information and must be avoided The reason for

this is that there is no way to gage how far away from the true value of K~ c

the invalid number really is, and whether the invalid KQ is larger or smaller

t h a n KI c F o r some materials, an invalid value may be essentially or exactly

equal to K~c, but, for another material, an equally invalid number (that is,

invalid for identical reasons) may be far removed from the real value An

example of this situation was given in Ref 13 by comparing invalid data for

three aluminum alloys for which the invalid values line up the materials in an

unrealistic manner based on all screening criteria and, more important,

6 1968 Book o f A S T M Standards, Part 31, pp 963-971

Trang 26

upon service experience This point is emphasized solely to illustrate that

invalid K ~ numbers can be safely used only for guidance on how to obtain

a valid test

Back to the Thin-Section Problem

Since a substantial amount of progress now has been made on the thick-

section problem, it is appropriate to refocus attention on the thin-section

problem Many of the fracture problems encountered in the aerospace and

missile industry are thin-section problems Thus, in recent action of ASTM

Committee E-24, a new task group on thin sections has been formed; it

represents and will receive a large part of its guidance from the aerospace

industry

Medium-Strength Materials

Although this review has been aimed principally at Subcommittee I on

High Strength Materials, it is appropriate to note that a considerable amount

of attention has been given to the use of elastic fracture mechanics for evalu-

ating the fracture toughness of the medium-strength materials, in which the

simplifications on limited plastic zone formation are not so readily applicable

A review by Subcommittee III of this problem has indicated that, in general,

the same procedures described above can be used, though the specimens have

to be much larger because of the greater toughness; this results in the situa-

tion that: (a) the single-edge notched tension specimen is of little use because

of great load, loading shackle, and material requirements, (b) the notch-bend

specimen is satisfactory from the load and load-application standpoint, but

still requires a lot of material, and (c) the compact K~ c specimen appears to

be the optimum answer Some hope remains for the double-cantilever beam

specimen [19] and for the incorporation of what commonly is referred to as

elastic-plastic analysis [20] in this area, but much development work re-

mains to be done before we put forth any new methods based on these ap-

proaches

Cautionary Notes

Despite the progress which has been made, it has not been fast enough or

all inclusive enough to suit many individuals and organizations To find out

why, it is necessary only to look at several restraints which confront those

involved in the fracture problem

First, it is essential that fracture data which are to be used in the design

and analysis of structure or cross compared from laboratory to laboratory

be developed from standardized test procedures Within the past several years,

we have seen the development of methods for making a variety of types of

C o p y r i g h t b y A S T M I n t ' l ( a l l r i g h t s r e s e r v e d ) ; M o n D e c 7 1 3 : 1 9 : 1 9 E S T 2 0 1 5

D o w n l o a d e d / p r i n t e d b y

U n i v e r s i t y o f W a s h i n g t o n ( U n i v e r s i t y o f W a s h i n g t o n ) p u r s u a n t t o L i c e n s e A g r e e m e n t N o f u r t h e r r e p r o d u c t i o n s a u t h o r i z e d

Trang 27

KAUFMAN ON FRACTURE TESTING OF METALLIC MATERIALS 19

fracture test These have ranged f r o m the rather thoroughly evaluated fa-

tigue-cracked notch-bend fracture-toughness test proposed by A S T M C o m -

mittee E-24 to tests seemingly picked out of the air to fill a need for " s o m e

kind of test." Some test methods of the latter type have been recognized by

reputable Technical Societies and yet incorporate ambiguous and untried

techniques; there is no testing experience on which to judge the effects of

test variables, such as specimen geometry and loading rate, and there is even

question as to whether the tests are practical I cite these two extremes to call

attention to the fact that there are right ways and wrong ways to go about

developing test procedures for specifications It cannot be done haphazardly

and it is up to the material producers as well as responsible people in the

sponsoring agencies to be certain that it is not done in this way

Development of the test method in the proper way through systematic

investigation by a group such as A S T M Committee E-24 is not an easy

procedure This development process is often a frustrating process for the

people who are doing it and for the people who are waiting for it It is not

nearly as fast as most people would like Nevertheless when a test method is

finally adopted, you can be reasonably certain that: (a) there have been

studies of m a n y of the test variables on the results, (b) the test procedure has

been evaluated in a systematic p r o g r a m involving a m i n i m u m of six different

laboratories (in what c o m m o n l y is called a round-robin test program), and

(c) there is some rather clear indication of the variability of the data and its

significance

Second, and a logical consequence of the first, we cannot become too

deeply involved or diverted by procedures which, though they serve some

individual purpose, are not amenable to standardization or do not provide

the type of design data to further the needs of industry As an example, Alcoa

Research Laboratories has used sucessfully the tear test [9] for almost 15

years to measure the relative resistance of aluminum alloys to fracture The

test has been and still is very useful, because: (a) there are no limits as far as

we know on the applicability of the data because of such things as excessive

plastic deformation, ( b ) t h e data has been correlated with other indexes of

toughness such as Kic, and (c) most important, it has correlated on numerous

occasions with service experience However, the tear test is not suitable for

standardization, because of such things as the dependence of results on test-

ing machine characteristics and the necessity of some judgmental interpreta-

tion of results Some of the other tests which have been proposed fall into

this category Others simply are not sensitive enough or do not provide the

type of data which will materially advance the design of structures

Third, we must not expect that instantly upon the publication of a test

method it will be possible to incorporate a m i n i m u m level of K~c (or what-

ever other property is involved) into specifications It c o m m o n l y is assumed

Trang 28

that once a recommended fracture test procedure has been adopted it is appropriate immediately to write minimum values of some fracture param- eter into specifications Nothing could be further from the truth Actually, after the procedure has been developed, it is necessary to obtain a large number of data showing the amount of scatter in the results and the influence

of product variation (test direction, product dimension, product heat-treatment) on the values, exactly as has been done with tension test specifications Only when this has been done systematically and with sufficient data to justify statistical analyses, can values for specifications even be considered All such tests must be done in a valid manner; it is not satisfactory to consider data developed over the years by procedures perhaps remotely re- sembling those used in the test practice but differing in many details

It is up to the material producers to be certain that no minimum values find their way into specifications before they are justified In these days of such great demand for materials it is irresponsible to establish specification values for any property at levels where vast quantities of acceptable materials would be rejected needlessly, or where unacceptable materials might be used with catastrophic end results F o r this very reason, we have been extremely cautious about what values go into design handbooks

Summary

In summary, a great deal has been accomplished by ASTM Committee E-24, and it has been accomplished in a reasonable time and by a reasonable path considering the complexity of the task Two test methods have been written, a major addition to one will soon be completed Guidance has been given to the use of fracture mechanics in fatigue, stress-corrosion, and high- rate loading Much more will be accomplished in the future

References

[1 ] "Fracture Testing of High-Strength Sheet Materials," A S T M Bulletin No 243, Jan

1960, p 29; also No 244, Feb 1960, p 18

[2] Boyle, R W., Sullivan, A M., and Krafft, J M., "Determination of Plane Strain Fracture Toughness with Sharply Notched Sheets," Welding Journal Research Supple- ment, Vol 41, 1962, p 428s

[3] Anctil, A A., Kula, E B., and DiCesare, E., "Electric-Potential Technique for Deter- mining Slow Crack Growth," Proceedings, American Society for Testing and Materials, Vol 63, 1963, pp 799-808

[4] Steigerwald, E A and Hanna, G L., "Initiation of Slow Crack Propagation in High- Strength Materials," Proceedings, American Society for Testing and Materials, Vol

62, 1962, pp 885-905

[5] Jones, M H and Brown, W F., Jr., "Acoustic Detection of Crack Initiation in Sharply Notched Specimens," Materials Research & Standards, March 1964, pp 118-128

[6] Clark, W G., "Ultrasonic Detection of Crack Extension in the WOL-type Fracture Toughness Specimen," Materials Evaluation, Aug 1967, p 185

Trang 29

[7] ASTM Special Committee on Fracture Testing of High-Strength Metallic Materials,

"Progress in Measuring Fracture Toughness and Using Fracture Mechanics,"

Materials Research & Standards, Vol 4, No 3, March 1964, pp I07-119

[8] Irwin, G R and Kies, J A., "Critical Energy Rate Analysis of Fracture Strength,"

Welding Journal Research Supplement, Vol 33, 1954, p 193s

[9] Kaufman, J G and Holt, Marshall, "Fracture Characteristics of Aluminum Alloys,"

Aluminum Company of America, ARL Technical Paper No 18, 1965

[I0] Fracture Toughness Testing and Its Applications, ASTM STP 381, American Society

for Testing and Materials, 1965

[11] "The Slow Growth and Rapid Propagation of Cracks," Materials Research & Stand-

ards, Vol 1, 1961, p 389

[12] Brown, W F., Jr., and Srawley, J E., Plane Strain Crack Toughness Testing of High

Strength Metallic Materials, ASTM STP 410, American Society for Testing and

Materials, 1967

[13] Kaufman, J G., Nelson, F G., Jr., and Holt, Marshall, "Fracture Toughness of

Aluminum Alloy Plate Determined with Center-Notch Tension, Single-Edge-Notch

Tension and Notch-Bend Tests," presented at the National Symposium on P~acture

Mechanics, Lehigh University, 1967

[14] Freed, C N and Krafft, J M., "Effect of Side Grooving on Measurements of Plane-

Strain Fracture Toughness," Journal of Materials, Vol l, No 4, Dec 1966, pp 770-

790

[15] Srawley, J E., Jones, M H., and Brown, W F., Jr., "Determination of Plane Strain

Fracture Toughness," Materials Research & Standards, Vol 7, No 6, June 1967,

pp 262-266

[16] Heyer, R H., "Evaluation of E-24 Proposed Recommended Practice for K~ Testing,"

presented at 1968 ASTM Annual Meeting in San Francisco, California, June 24, 1968

[17] Manjoine, M J., "Biaxial Brittle Fracture Tests," Paper 64-Met-3, American Society

of Mechanical Engineers, May 1964

[18] Kaufman, J G and Johnson, E W., "The Use of Notch-Yield Ratio to Evaluate the

Notch Sensitivity of Aluminum Alloy Sheet," Proceedings, American Society for

Testing and Materials, Vol 62, 1962, pp 778-791

[19] Mostovoy, S., Crosley, P B., and Ripling, E J., "Use of Crack Line Loaded Speci-

mens for Measuring Plane Strain Fracture Toughness," Materials Research Labora-

tory, Inc., Jan 1966

[20] Hahn, G T and Rosenfield, A R., "Sources of Fracture Toughness: The Relation

Between K~ and the Ordinary Tensile Properties of Metals," Applications Related

Phenomena in Titanium Alloys, ASTM STP 432, American Society for Testing and

Trang 30

R H H e y e r I and D E M c C a b e 1

Evaluation of a Method of Test for

Strain Fracture Toughness Using a

Bend Specimen

Plane

REFERENCE: Heyer, R H and McCabe, D E., "Evaluation of a Method of Test

for Plane Stain Fracture Toughness Using a Bend Specimen," Review o f Develop-

ments in Plane Strain Fracture Toughness Testing, A S T M STP 463, American

Society for Testing and Materials, 1970, pp 22-41

ABSTRACT: A task group of ASTM Committee E-24 conducted an interlabora-

tory test program on determination of K~c using the proposed " R e c o m m e n d e d

Practice for Plane Strain Fracture Toughness Testing of High-Strength Metallic

Materials Using a Fatigue-Cracked Bend Specimen."

Analysis of K~o data for an aluminum alloy and two high-strength alloy steels

showed that laboratory mean values were within 4-10 percent of grand mean

values Replication was generally satisfactory, although not as good as for

smooth specimen tension tests

Information obtained on fatigue cracking and other details of the procedure

will be useful in planned revisions, leading to a standard method of test

KEY W O R D S : interlaboratory tests, fractures (materials), toughness, fatigue

cracked bend specimen, fatigue precracking, plane strain, high strength materials,

aluminum alloys, steels, maraging steel, evaluation, tests

There were several important steps in the development of a linear elastic fracture mechanics based test for plane strain fracture toughness, and these are recorded in Ref 1 to 4 2 Although a number of different specimen types and loading arrangements could be used, the edge notched bend specimen was selected at the 30 June 1966 meeting of ASTM Committee E-24 on Fracture Testing of Metals as the first type to be developed Subcommittee

I appointed a Task G r o u p to draft a recommended practice using a fatigue cracked bend specimen, to organize appropriate cooperative test programs

to help identify problem areas, and finally to evaluate the method by interlaboratory tests

1 Supervising research metallurgist and senior research metallurgist, respectively, Armco Steel Corp., Middletown, Ohio 45042 Mr Heyer is a personal member ASTM

2 The italic numbers in brackets refer to the list of references appended to this paper

22 Copyright* 1970 by ASTM lntcrnational www.astm.org

Trang 31

Pilot Program

I n a pilot p r o g r a m six l a b o r a t o r i e s were supplied five m a c h i n e d specimens

each of a l u m i n u m alloy 7075-3"651, 13/~ b y 3 by 13 in A t the time m a n y of

the p a r t i c i p a n t s did n o t have the necessary fixtures a n d d i s p l a c e m e n t gage,

as p r o p o s e d in N a t i o n a l A e r o n a u t i c s a n d Space A d m i n i s t r a t i o n ( N A S A )

T e c h n i c a l M e m o r a n d u m X-52209, later p u b l i s h e d as A S T M S T P 410 [4]

T h e p u r p o s e of the pilot p r o g r a m was to check o u t the test fixtures, i n s t r u -

m e n t a t i o n , a n d analysis of d a t a before c o n d u c t i n g the m o r e extensive inter-

l a b o r a t o r y e v a l u a t i o n p r o g r a m

T h e average KIo values o b t a i n e d by the i n d i v i d u a l l a b o r a t o r i e s were in the

r a n g e 20.4 to 22.6 ksi in 1/2, or -4-5 percent T o t a l v a r i a t i o n of single values

was in the r a n g e 19.6 to 23.1 ksi in m , or :k8 percent [5]

Interlaboratory Tests

As experience with the practice b r o a d e n e d , changes were m a d e in the

r e c o m m e n d e d fatigue p r e c r a c k i n g p r o c e d u r e a n d in i n t e r p r e t a t i o n o f the

l o a d - d i s p l a c e m e n t records U s i n g the A p r i l 1967 draft of the practice, n i n e

l a b o r a t o r i e s tested five specimens each of f o u r materials These materials a n d

their m e c h a n i c a l properties are listed in T a b l e 1

TABLE 1 Materials and mechanical properties

2219-T851 18Ni Maraging 4340 500 F 4340-800 F Yield strength, ksi 51.2 276

Tensile strength, ksi 66.6 285

2 to 5 l I to 16 0.42 0.42 0.71 0.71 0.010 0.010 0.012 0.012

Trang 32

24 PLANE STRAIN FRACTURE T O U G H N E S S TESTING

The test specimens were machined to the dimensions shown in Fig 1 and

heat treated by three of nine participating laboratories Randomly selected

specimens were supplied to each laboratory for fatigue cracking and testing

Fatigue Cracking

Information on fatigue cracking equipment and procedures is given in

Table 2 Three types of fatigue loading fixtures were used: three-point bending,

cantilever bending, and pure bending by moments applied at the ends

Frequencies ranged from 600 to 8000 cpm Individual laboratories usually

did not vary stress ratio R1 in fatigue cracking the four materials In most

cases the loading was from near zero tension to maximum tension at the

crack Laboratories 1 and 3 used reversed bending, with R1 = 1.0

The ratio R2, of maximum K~ in fatigue cracking to K~c, varied with

material as shown in Table 2, with a range of 0.16 to 0.50 for 2219-T851 and

4340-800 F The 18Ni maraging and 4340-500 F steel specimens were cracked

at higher R2 ratios, in the range 0.25 to 1.06, with most under 0.67 Where a

single average value is given, the range for individual specimens was small

The number of cycles generally varied for each group of specimens

Where variation was small, a single average value is shown

All laboratories encountered problems in meeting fatigue cracking require-

ments These are numbered in Table 3 and appended to individual K~c values

not meeting the requirement Values in parentheses were not included in

statistical treatment of the data because they failed to meet certain of the

FIG 1 Kzc bend test specimen with nom#lal dimensions o f the materials o f the inter-

laboratory test program

Trang 33

HEYER AND McCABE ON A BEND SPECIMEN 2 5

1 Specimens were lost in fatigue cracking (about four percent of the

number tested), and since no spares were available the number of replicate

tests was reduced to three or four in some cases by failure to meet require-

ments [1]

2 and 3 To minimize plastic deformation at the crack front " the

maximum load of the fatigue cycle shall be no greater than necessary to cause

the final 0.050 in of crack extension to occur in 50,000 cycles, with a load

range not less than three fourths of the maximum toad ''~ The load range

limitation is expressed in terms o f the stress ratio R~ defined in the footnotes of

Table 2 Only one laboratory failed to meet the load range requirement [3]

and on only one material However, 27 percent of the specimens were cracked

using less than 50,000 cycles to produce the last 0.05 in of crack length

Some laboratories reported only the total number of stress cycles; hence,

there may have been more who did not meet requirements [2]

Fatigue cracking is still under consideration in the committee, and new

information indicates that the 50,000 cycle requirement could be relaxed

somewhat; therefore, it was not used as a basis for rejection of K~c values in

this program

4 " A fatigue crack is to be extended from the root of the notch for a

length of at least 0.050 in on each side, as measured at the specimen sur-

faces ''4 This requirement was not met in 10 percent of the specimens Two

specimens of Laboratory 4 had cracks which did not extend beyond the

machined notch at the outside surfaces of the specimen Data for these two

specimens (in parentheses in Table 3) were considered invalid and were not

included in further evaluations Data for other specimens with cracks which

were slightly short but did extend to the outside surfaces were accepted for

analysis

5 "Measurements of the crack length shall be made at the most advanced

point of the crack front and at each surface of the specimen: all three values

shall be recorded F o r calculating K~ c, the sum of the two surface values plus

twice the value at the most advanced point, all divided by 4, shall be used

if the difference between any two readings is greater than 10 percent of

the thickness, the test is invalid ''4 This requirement was not met by 7 percent

of the specimens The problem was principally with the 4340 steel specimens

which tended to have the crack leading near the outside edges rather than at

the midthickness, Fig 2 Also, some specimens had internal flaws which

resulted in an irregular crack front, as in specimen E2461 of Fig 2 The

aluminum alloy and the maraging steel had crack fronts leading at the center

and with crack dimensions within limits

See sections 6.5.2 and 6.5.3 of Ref 8 for revised fatigue precracking requirements

4 See section 7.2.3 of R e f 8 for revised crack measurement requirements

Trang 38

FIG 2 Photographs of crack fronts in 4340 steels

In several cases where the crack front was dimensionally out of limits the

resulting KIe value was obviously out of line All specimens which did not

meet the crack front requirement were excluded in the data analysis

6 " T h e crack length, a, shall be from 0.45 to 0.55 times depth, W." This

requirement was not met by 4 percent of the specimens However, the require-

ment was intended primarily to optimize the specimen, and no data were dis-

carded for failure to meet it

Bend Testing

There were relatively few problems in carrying out the bend test and inter-

preting the load-displacement record A typical fixture design is shown in

Fig 3 In Table 3, deviations f r o m the following bend test requirements are

noted:

7 " T h e initial slope of the load-displacement record shall be not greater

than 2 and not less than one half ''~ This requirement was not met by 8 per-

cent of the records Variance outside the recommended limits was minimal

See section 7.5 of Ref 8 for revised requirement

Trang 39

9

l FIG 3 Bend test fixture design

in all cases, and since the requirement was intended as a guideline to aid in accurate determination o f the displacement ratio it was n o t used as a basis for rejection o f data

8 This requirement is described in the following sections f r o m the 1967

m e t h o d 6 Figure 8 o f the 1969 p r o p o s e d m e t h o d is r e p r o d u c e d as Fig 4

in this report Typical records for the test materials are shown in Fig 5

Draw the secant line OP5 through the origin with slope 5 percent less than the slope of the tangent OA to the initial part of the record P5 is the load at the inter- section of the secant with the record Next, determine the load Po, which will be used to calculate Ko, as follows: if the load at every point on the record which precedes P5 is lower than Ps, then Po is equal to P5 (Fig 4, Type I); if, however, there is a maximum load preceding P5 which exceeds it, then this maximum load is

PQ (Fig 4, Types II and III)

Draw a horizontal line representing a constant load of 0.8 Ps Measure the distance X1 along the horizontal line from the tangent OA to the record, and measure the corresponding horizontal distance to Ps If the ratio of the deviation from linearity at 0.8 P5 to that at P5 is greater than 0.25, then the test is not a valid K~c test (for reasons explained in Ref 4) Proceed to calculate KQ in order to estimate a revised specimen size, but do not report Ke as a valid Kx,

Failure to meet the 0.25 ratio (called displacement ratio in this report) occurred in three a l u m i n u m alloy specimens and in two 4340-800 F specimens, a total o f 3 percent In Table 3, specimens having displacement ratios

o u t o f limits, R e q u i r e m e n t 8, are rejected N o t e that two 4340-800 F specimens are rejected f r o m analysis for out-of-limits crack fronts, R e q u i r e m e n t 5,

as well as for Requirement 8

9 " S p e c i m e n size requirements: I n order for a result to be considered valid according to this r e c o m m e n d e d practice, it is required that both the

6 See sections 8.1.1 and 8.1.2 of Ref 8 The wording has been changed, primarily to provide for the compact tension specimen

Trang 40

DISPLACEMENT GAGE OUTPUT

NOTE: SLOPE OP s IS EXAGGERATED FOR CLARITY

F I G 4 Principal types of load-displacement records

specimen thickness, B, and the crack length, a, shall exceed 2.5 (K~r ~,

and where avs is the 0.2 percent offset yield strength of the material." The following tabulation shows that the four materials all met the size limit requirements

Tiêu đề	Review of Developments in Plane Strain Fracture Toughness Testing
Người hướng dẫn	W. F. Brown, Jr., Editor
Trường học	University of Washington
Thể loại	Special Technical Publication
Năm xuất bản	1970
Thành phố	Lutherville-Timonium

Định dạng
Số trang	277
Dung lượng	5,62 MB