Astm stp 905 1986

ABSTRACT: A fracture mechanics analysis was conducted to establish the fracture toughness of a controllable pitch propeller crank ring material required to prevent a fracture mode in

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FRACTURE MECHANICS"

SEVENTEENTH VOLUME"

Seventeenth National Symposium

on Fracture Mechanics sponsored by

ASTM Committee E-24

on Fracture Testing Albany, New York, 7-9 August 1984

ASTM SPECIAL TECHNICAL PUBLICATION 905

J H Underwood, U.S Army Armament Research & Development Center, R Chait, U.S Army Materials & Mechanics Research Center,

C W Smith, Virginia Polytechnic Institute &

State University, D P Wilhem, Northrop Aircraft, W A Andrews, General Electric Company, and J C Newman, NASA Langley Research Center, editors

ASTM Publication Code Number (PCN) 04-905000-30

1916 Race Street, Philadelphia, Pa 19103

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Library of Congress Cataloging-in-Publicatlon Data

National Symposium on Fracture Mechanics (17th:

1984: Albany, N.Y.)

Fracture mechanics

(ASTM special technical publication; 905)

"ASTM publication code number (PCN) 04-905000-30."

Includes bibliographies and index

1 Fracture mechanics Congresses I Underwood,

John H II ASTM Committee E-24 on Fracture Testing

III Title IV Series

TA409.N38 1 9 8 4 620.1'126 86-8000

ISBN 0-8031-0472-3

Library of Congress Catalog Card Number: 86-8000

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

Printed in Baltimore, Md

July 1986

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Dedication

This publication is dedicated to the following group of individuals

and their pioneering work in fracture testing:

William F Brown, Jr

James E Campbell Roy H Chirstensen John Hodge George R Irwin Joseph M Krafft William T Lankford John R Low, Jr

Richard A Rawe John E Srawley Henry J Stremba Charles F Tiffany

Their important contributions were central to the A S T M Special

Committee on Fracture Testing of High Strength Sheet Materials,

forerunner of Committee E-24 on Fracture Testing

As a tribute to the founders of A S T M Committee E-24 and to the

series of symposia which they helped to establish, the poem on the

following page was offered as a special presentation at the Albany

meeting

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Till Rice and some others showed us the way

To express all the terms by the integral J

And presently users were nothing loath

To use dJ for stable crack growth;

So fracture was thought to be well understood

At the Albany meeting of John Underwood

But then the Symposium, in second day session, Was taught a quite salutary lesson;

As the crucial question was faced by John Srawley That sometimes J would serve us but poorly

But if these complexities seem to confuse us, Just follow the founders' advice on consensus And study the problem until a year older, Then tell us next time in the Conference at Boulder

Dedicated to those founding members

of the original Committee, whom

it was my good fortune to know

Cerdic Renrut

9 August 1984

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Foreword

The Seventeenth National Symposium on Fracture Mechanics was held on

7-9 August 1984 in Albany, New York ASTM Committee E-24 on Fracture

Testing was the sponsor J H Underwood, U.S Army Armament Research

& Development Center, served as symposium chairman and co-editor of this

publication R Chair, U.S Army Materials & Mechanics Research Center,

C W Smith, Virginia Polytechnic Institute & State University, D P

Wilhem, Northrop Aircraft, W A Andrews, General Electric Company, and

J C Newman, NASA Langley Research Center, served as symposium co-

chairmen and co-editors of this publication

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Related ASTM Publications

Fracture Mechanics: Sixteenth Symposium, STP 868 (1985),

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A Note of Appreciation

to Reviewers

The quality of the papers that appear in this publication reflects not only

the obvious efforts of the authors but also the unheralded, though essential,

work of the reviewers On behalf of ASTM we acknowledge with appreciation

their dedication to high professional standards and their sacrifice of time and

effort

A S T M C o m m i t t e e on Publications

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ASTM Editorial Staff

Allan S Kleinberg Janet R Schroeder Kathleen A Greene Bill Benzing

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Contents

Introduction

A P P L I C A T I O N S

A n Application of Fracture Mechanics to a Ship Controllable Pitch

Propeller Crank R i n g - - P D HILTON, R A MAYVILLE, AND

D C P E I R C E

A New W i d e Plate Arrest Test (SCA Test) on Weld Joints of Steels

for Low Temperature A p p l i c a t i o n - - K T A N ~ A , M SATO,

T I S H I K A W A , A N D H T A K A S H I M A

Variable Flaw Shape Analysis for a Reactor Vessel under Pressurized

Thermal Shock L o a d i n g - - c Y YANG AND W H BAMFORD

Growth Behavior of Surface Cracks in the Circumferential Plane of

S o l i d a n d H o l l o w C y l i n d e r s - - R G FORMAN AND

V S H I V A K U M A R

Fracture Toughness of Ductile Iron and Cast Steel w L BRADLEY,

K E M c K I N N E Y , A N D P C G E R H A R D T , J R

Effect of Loading Rate on Dynamic Fracture of Reaction Bonded

Silicon N i t r i d e - - B M LIAW, A S KOBAYASHI, AND

A F E M E R Y

Resistance Curve Approach to Composite Materials

Characterization M M R A T W A N I A N D R B D E O

A Comparison of the Fracture Behavior of Thick Laminated

Composites Utilizing Compact Tension, Three-Polnt Bend,

and Center-Cracked Tension Specimens ¢ E HARRIS

A N D D H M O R R I S

Residual Strength of Five Boron/Aluminum Laminates with

C r a c k - L i k e Notches After Fatigue L o a d i n g - - R A SIMONDS

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SUBCRITICAL CRACK GROWTH Hold-Time Effects in Elevated Temperature Fatigue Crack

Propagatlon T NICHOLAS AND T WEERASOORIYA 155

Interactive Effects of High and Low Frequency Loading on the

Fatigue Crack Growth of Ineonel 718 A PETROVICH,

Creep Crack Growth under Non-Steady-State Condltlons A SAXENA 185

An Application of Stress Intensity Factor to Fatigue Strength

Analysis of Welded Invar Sheet for Cryogenic Use i SOYA,

An Automated Photomicroscopic System for Monitoring the Growth

An Experimental and Numerical Investigation of the Growth and

Coalescence of Multiple Fatigue Cracks at

Notches A F GRANDT, J R , A B THAKKER, AND

Near-Tip Crack Displacement Measurements During

High-Temperature Fatigue w N SUARPE, JR., AND J J LEE 253

Viseoplastlc Fatigue in a Superalloy at Elevated

TemperatureS R W I L S O N AND A PALAZOTTO 265

FRACTURE TESTING Fracture Testing with Arc Bend Speeimens i H UNDERWOOD,

Jk Testing Using Arc-Tension Specimens j A KAPP AND

Investigation and Application of the One-Polnt-Bend Impact

Mode H Fatigue Crack Growth Specimen

Development R I BUZZARD, B GROSS, AND J E SRAWLEY 329

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A Compact Mode I I Fracture Specimen L BANKS-SILLS AND

Influence of Partial Unloadings Range on the JrR Curves of ASTM

A106 and 3-Ni Steels G E SUTTON AND M C VASSILAROS 364

Fracture Toughness Testing of Zircaloy-2 Pressure Tube Material

with Radial Hydrides Using Direct-Current Potential

Assessment of J-R Curves Obtained from Precracked Charpy

Specimens J A KAPP AND M I JOLLES

D U C T I L E F R A C T U R E

401

A Single Specimen Determination of Elastic-Plastic Fracture

Resistance by Ultrasonic Method K HIRANO, H KOBAYASHI,

J-Resistance Curve Analysis for ASTM A106 Steel 8-Inch-Diameter

Pipe and Compact Specimens M G VASSILAROS, R A HAYS,

Influence of Crack Depth on Resistance Curves for Three-Point Bend

Specimens in H Y 1 3 0 - - o L TOWERS AND S J GARWOOD 454

An Investigation of the I and dJ/da Concepts for Ductile Tearing

Computation of Stable Crack Growth Using the

J - I n t e g r a l - - I E CARIFO, J L SWEDLOW, AND C.-W CHO 503

Evaluation of Environmentally Assisted Cracking of a High Strength

Steel Using Elastic-Plastic Fracture Mechanics

Technlques E M HACKETT, P J MORAN, AND J P GUDAS 512

Plastic Energy Dissipation as a Parameter to Characterize Crack

Growth T J WATSON AND M I JOLLES

A N A L Y S I S AND M E C H A N I S M S

542

Stress Intensity Factors for a Circular Ring with Uniform Array of

Radial Cracks of Unequal D e p t h - - s L PU 559

Weight Functions of Radial Cracks Emanating from a Circular Hole

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An Empirical Surface Crack Solution for Fatigue Propagation

Extension of Surface Cracks During Cyclic L o a d i n g - - H M M/3LLER,

Comparison of Predicted versus Experimental Stress for Initiation of

Crack Growth in Specimens Containing S u r f a c e

Comparison of Ductile Crack Growth Resistance of Austenitic,

Niobium-Stabilized Austenitic, and Austeno-Ferritic Stainless

A s s e s s i n g the Dominant Mechanism for Size Effects on C T O D

Values in the Ductile-to-Brittle Transition

R e g i o n - - T L A N D E R S O N A N D S W I L L I A M S 715

Dynamic J-R Curve Testing of a H i g h Strength Steel Using the Key

Stress Intensity Factors for Circumferential Surface Cracks in Pipes

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Introduction

STP905-EB/Jul 1986

This volume and the Seventeenth National ASTM Symposium on Fracture Mechanics on which it is based are part of a continuing series These symposia have become clearly the most prestigious in the field of fracture As such, they are the focus and forum for quality work in all areas of the field, and this

is the important purpose of the symposium and volume

If the field can be divided into testing and analysis, the former has been and continues to be the more emphasized in this symposium series This is appropriate, considering the sponsor, ASTM Committee E-24 on Fracture Testing Nevertheless, analysis is a required part of any test, and much of the work reported here is primarily analysis

At least four general topics or categories of work frequently occur in the papers: ductile fracture, test method development, surface cracks and crack shape effects, and high temperature and loading rate effects The prevalence

of these four categories attests to the basic practical nature of the field of fracture and of those who work in it Each of these categories defines an area

of important current concern in the design and use of load-carrying compo- nents and structures It is the hope and belief of all those involved that this symposium and volume have contributed to these and other important areas

in the field of fracture

The National Symposium on Fracture Mechanics is often the occasion at which ASTM awards are presented to recognize the achievements of current investigators At the Seventeenth Symposium two awards were presented The ASTM Committee E-24 Irwin Medal was presented by Dr Irwin to Mr John G Merkle, Martin Marietta Energy Systems, for his outstanding work

in the field of fracture mechanics The ASTM Award of Merit and honorary title of Fellow were given to Mr David P Wilhem, Northrup Corporation, for his distinguished service and leadership in Committee E-24 Dr J Gilbert Kaufman, Arco Metals, past chairman of E-24, made the presentation to Mr Wilhem

We take this opportunity to thank two groups who deserve a significant share of credit for this symposium The first is the combined support staff of all of us listed below The administrative and clerical work of this whole group was essential to the task and is greatly appreciated The second group is made

up of those behind-the-scenes people whose work is nonetheless critical

In particular, we thank Professor Ray Eisenstadt of Union College for his help in administering the symposium, Mr Jim Gallivan of the Army Materi- als and Mechanics Research Center for financial support, the late Dr Fred

1

Copyright* 1986 byASTM International www.astm.org

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2 INTRODUCTION

Schmeideshoff of the Army Research Office for his help in organizing the

symposium, and Professor Jerry Swedlow for his continuing support and

sound advice during the entire process

Army Armament Research & Development

Center, Watervliet, New York; chairman

and co-editor

Richard Chair

Army Materials and Mechanics Research

Center, Watertown, Massachusetts; co-

chairman and co-editor

Virginia Polytechnic Institute & State Univer-

sity, Blacksburg, Virginia; co-chairman

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Applications

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P D Hilton, 1 R A Mayville, 1 a n d D C Peirce 1

An Application of Fracture

Mechanics to a Ship Controllable

Pitch Propeller Crank Ring

REFERENCE: Hilton, P D., Mayville, R A., and Peirce, D C., " A n Applieatlon of

Fracture Meehanlr to a Shlp Controllable Pitch Propeller Crank Ring," Fracture Me-

chanics: Seventeenth Volume, A S T M STP 905 J H Underwood, R Chait, C W

Smith, D P Wilhem, W A Andrews, and J C Newman, Eds., American Society for

Testing and Materials, Philadelphia, 1986, pp 5-21

ABSTRACT: A fracture mechanics analysis was conducted to establish the fracture

toughness of a controllable pitch propeller crank ring material required to prevent a frac-

ture mode in which loss of a propeller blade occurs Loss of the propeller was assumed to

be prevented if fracture instability could not occur before the fatigue crack grew to a size

beyond which crack growth would proceed radially through the flange of the crank ring

and not around the circumference The fracture analysis was conducted by modeling the

cracked crank ring as a plate with a part-through crack in bending Numerical solutions

for part-through cracks in bending were combined with results for large crack length-to-

plate width geometries for through cracks in bending to determine KI for the large crack

size of interest Values of K1 with plastically adjusted crack lengths were converted to

values of Jj and crack driving force curves were generated Estimates of the plastic col-

lapse moment for the crank ring were made as an alternative method of determining frac-

ture conditions The results of the analysis are a minimum acceptable value of yield

strength and curves of yield strength versus minimum acceptable values of Jm and Tm,t at

a crack extension of 1.27 mm as determined by a J-R curve test

KEY WORDS: fracture mechanics, application, bending, ship component

Controllable pitch propellers are commonly found in current ship propul-

sion systems They are used for both small vessels and large ships with power

as great as 40 000 hp All controllable pitch propellers require some mecha-

nism to rotate the propeller blades In the study described in this paper, rota-

tion is brought about by a crank ring to which the propeller blade is attached

by several bolts An illustration of such a crank ring is shown in Fig 1 Not

IArthur D Little, Inc., Acorn Park, Cambridge, MA 02140

5

9

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6 FRACTURE MECHANICS: SEVENTEENTH VOLUME

I

Axis of Rotation

illet

shown in the figure is the protrusion from the underside of the ring to which a

mechanical " c r a n k " is attached for the purpose of rotating the crank ring

On installation, the crank ring is set over a central post which is attached to

the propeller hub Next, a narrow bearing ring is threaded into the hub body

over the crank ring so that if the crank ring were lifted, its flange would con-

tact the underside of the bearing ring Finally, the propeller blade is bolted to

the crank ring Thus, under the action of centrifugal and hydrodynamic loads

during operation of the propeller, significant pressure loads are transferred

between the underside of the bearing ring and the upper surface of the crank

ring flange This in turn causes cyclic stresses in the fillet at the point where

the flange meets the main crank ring body (Fig 1) These high stresses can

lead to cracking at the fillet [1], and there is a possibility that the crank ring

can fracture In fact, one can imagine a scenario in which rapid fracture from

a fillet crack could proceed around the circumference of the crank ring and

lead to separation of the propeller blade from the hub body

The objective of the investigation described in this paper was to establish

through analysis the material fracture toughness for a particular crank ring

such that, in the unlikely event that a fatigue crack does initiate, a fracture

mode leading to loss of the propeller would be avoided Periodic inspection of

crank rings is generally not conducted, so that in this scenario some other

incident, such as excessive deformation, must occur to make the failure de-

tectable There has been one reported failure incident in which a fillet fatigue

crack initially propagated around the circumference of the crank ring but

eventually propagated and broke through the flange The severed piece of the

crank ring then prevented rotation on the next attempt at pitch control and

this led to the discovery of the fracture It is not clear that fatigue cracks in all

crank rings will proceed in this manner and, in fact, results of our analysis,

presented below, show that there is a significant driving force for continued

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HILTON ET AL ON PROPELLER CRANK RING 7

circumferential fatigue crack growth Nevertheless, based on limited evi- dence, it has been assumed that the crack will propagate initially around the circumference and then through the flange, provided the mode of fracture is

by fatigue and not by rapid brittle or ductile fracture Furthermore, loss of the propeller is assumed to be prevented if fracture instability cannot occur before the fatigue crack grows to a size beyond which crack growth by any mode would proceed approximately radially through the flange and not around the circumference

The first problem in establishing the required crank ring toughness is to choose a crack size and geometry from which fracture instability would proceed through the flange Guaranteeing that fracture instability will not occur prior to attaining this crack size is then equivalent to finding the conditions material toughness required for instability to occur at this crack size; this assumes that smaller crack sizes are less severe

Crank Ring and Crack Geometry

A cross section of the single crank ring geometry analyzed in this investigation is shown in Fig 2 A full-scale laboratory test was performed for this crank ring resulting in a fatigue crack, the geometry of which was used in our analyses and is shown in Fig 3 The crack had several initiation sites located

in the fillet on the thrust side of the blade and at discovery extended about 85 ~ around the circumference At its midpoint the crack was inclined approximately 45 ~ to the vertical The crack front extended part way into the flange and to within about 8.9 mm of the crank ring bottom at the center of the

FIG 2 Geometry of the crank ring

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crack front The crack front in its plan view was not parallel to the bending axis but was instead curved somewhat (Fig 3) The geometry of the crack in its plane is unknown Indications are that it grew more to a trapezoidal shape than to an elliptical shape The location, geometry, and orientation of this crack are consistent with the tensile stresses developed in the crank ring fillet

by the hydrodynamically induced bending loads on the propeller

No calculations were performed to establish the radial extent of the crack in the flange required to ensure that fracture would proceed through the flange and not turn in the circumferential direction Instead, it was assumed that if the radial extent of the crack is half-way through the flange, then further crack growth will also be radial

FIG 3 Crack geometry from laboratory-tested crank ring

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peller blades Measurements made with strain gages in the fillet of the crank

ring during ship operation indicate that these forces result in loads on the

flange which can be modeled as the sum of a uniformly distributed load and a

load whose magnitude varies linearly with respect to the y-axis (Fig 3)

Two methods were used to estimate the magnitude of the crank ring flange

loads on the thrust side of the blade: strength of materials calculations based

on strain gage measurements and finite element analysis In both cases it was

assumed that the flange is subjected to a normal line load along its periphery

Strain gage measurements made on a crank ring with the geometry shown

in Fig 2 in a 35 000 hp ship indicate that the most severe radial tensile stress

in the crank ring fillet is approximately 503 MPa This stress, a, is related to

the nominal bending moment, m, per unit circumferential length at the fillet

by

a = K t 6 r n / t 2

Where t is the flange thickness, 49.3 mm from Fig 2, and Kt is a stress con-

centration factor, estimated from Peterson [2] to be 1.5 The load per unit

length on the outer flange circumference causing the bending moment is p =

m ( R i / R o ) / ( R o - - R i ) , where Ri and Ro are the inner and outer radii of the

crank ring flange; Ro = 369 mm and R i z 322 mm Therefore the maximum

flange load estimated from the strain gage readings is

p = 2540 N / m m Estimates for load distribution along the flange based on strain gage readings

are probably upper bound predictions, because the strain gage readings were

made in the fillet directly adjacent to the bolts that connect the propeller

blade to the crank ring Stress in this region may be influenced by the local

stress concentration effect of the nearest bolt On the other hand, the load

distribution along the flange will not be as significantly influenced by load

concentrations associated with individual bolts, because the distance from

the bolts to the load transfer region is larger than that from the bolts to the

fillet where the strain gage was located

A simple finite element model of the crank ring was used as an alternative

method to obtain crank ring load distribution estimates The crank ring,

modeled by a ten-element, three-dimensional mesh (Fig 4), was subjected to

a combination of axial load and bending moment to simulate the centrifugal

and hydrodynamically induced bending loads This loading is obtained by the

superposition of two solutions, symmetric and skew symmetric with respect to

an axis, x, that passes through the center of the crank ring and is parallel to

the neutral axis The inner circumference of the flange is held fixed, modeling

its interaction with the stiffer central portion of the crank ring Displace-

ments are prescribed at the upper edge of the outer circumference on the as-

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49.3rnm

Y

sumption of a rigid bearing ring Two calculations are carried out: the first

prescribes a constant downward displacement on the outer circumference

(modeling the centrifugal load), while the second prescribes a set of displace-

ments varying linearly in y (modeling the hydrodynamic load) These two so-

lutions are superposed in such a way that the nodal reaction forces at the

outer edge of the flange balance the centrifugal load and hydrodynamic bend-

ing moment These loads were obtained from the same example used in the

previous strain gage calculations

The maximum load obtained by finite element analysis was approximately

2100 N / m m This differs from the maximum load derived from the strain

gage readings by 17% Both of the methods used to estimate the load distri-

bution along the circumference of the crank ring are approximate, and it is

difficult to establish which of the estimates is more accurate Since the finite

element analysis ensures thai force and moment equilibrium are satisfied and

avoids the complications associated with load (or stress) concentrations, the

finite element analysis results are used to perform the fracture mechanics

analysis to be described later

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A finite element calculation was also performed to quantify the load redis-

tribution which occurs in the presence of a crack The mesh and loading were

exactly the same as for the uncracked case, except nodes on the inner flange

circumference were released to simulate a crack that extends 90 ~ around the

circumference and 75 % through the flange thickness The center of the crack

was symmetric with respect to the y-axis

The load distributions for the uncracked and cracked crank ring models,

as calculated by the finite element analysis, are shown in Fig 5 There is a

substantial redistribution in load in the presence of a crack In particular, the

load at the intersection of the y-axis with the flange periphery, which is the

location of m a x i m u m load in the uncracked crank ring, shows a reduction in

load to about 700 N / m m f r o m 2100 N / m m Figure 5 also shows that the max-

i m u m load in the cracked crank ring occurs at about 50 ~ from the y-axis

This is in part due to the coarseness of the mesh used and the presence of the

crack tip at this point as well as the reduction in load with y which must occur

because of the bending nature of the problem This large load near the crack

tip suggests that there may still be a significant driving force for circumferen-

tial crack growth

Assumed Lood Distribution

ANGLE IN DEGREES AWAY FROM CRACK CENTER

9 0

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 ) ; W e d D e c 2 3 1 8 : 2 8 : 3 5 E S T 2 0 1 5

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12 F R A C T U R E M E C H A N I C S : S E V E N T E E N T H V O L U M E

The finite element mesh of the cracked crank ring (Fig 4) does not simu-

late the actual crack in two important aspects: the actual crack extends into

the flange instead of just around the circumference, and the crack is inclined

over much of its length instead of being vertical everywhere These character-

istics make the cracked portion of the crank ring more compliant than mod-

eled by the finite element analysis Plastic deformation would also increase

the compliance and decrease the load on the cracked flange Therefore the

load distribution for the cracked crank ring shown in Fig 5 is undoubtedly an

upper b o u n d to the actual load distribution

In the next section, a model of a plate containing a part-through crack

subjected to uniform remote bending will be used to approximate the fracture

behavior of the cracked crank ring The crank ring flange load distribution

required to give a constant (uniform) moment per unit length with respect to

the crack plane was calculated and compared with the load distribution from

the finite element analysis Figure 6 shows how the moment arm of the line

load varies along the crack plane The magnitude of the bending moment

used was obtained from Fig 6 with 0 : 0 and p - 700 N/ram The result of

the calculation is included in Fig 5 to enable comparison with the finite ele-

ment predictions The flange load distribution based on the assumption of

constant bending moment per unit length is seen to have nearly the same form

and magnitude as the finite element results for the cracked crank ring over

the 0 range of interest Thus, in the fracture mechanics analysis of the

cracked crank ring to follow, the approximation is made that the moment per

unit length or width when referring to the plate applied remote from the

crack is constant and equal to

FIG 6 Geometry used to estimate flange load distribution for a constant bending moment

per unit width

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This bending moment applies for one crack geometry With continued

cracking tearing and plastic deformation, the compliance of the cracked

flange will increase and the load will decrease No attempt has been made to

quantify this decrease Instead, the conservative assumption is made that the

cracked flange is subjected to a constant load

Calculation of Crack-Driving Force

The fracture mechanics analysis for the cracked crank ring is carried out

using as a model a plate of finite width which contains a part-through crack

subjected to remote bending This geometry and loading are illustrated in

Fig 7 The model includes many of the important aspects of the cracked

crank ring configuration shown in Fig 3: the fatigue crack does not com-

pletely penetrate the flange thickness and is shallower at its ends; bending

caused by the flange load appears to be the driving force for crack growth;

and the crack is close enough to the outer flange edge to experience finite

width effects Finite element analyses show that the remote bending model is

a good approximation even if the moment is produced by a vertical line load

applied close to the crack plane [3] The bending moment used in the model

calculations is the moment per unit width across the cracked section resulting

from the flange load, as described in the previous section The problem is

treated as quasi-static; dynamic effects on the crack driving force and frac-

ture toughness are not included

The finite element calculations for KI by Newman and Raju [4] are used to

obtain the crack-driving force for the cracked crank ring Newman and Raju

conducted analyses to determine K~ for a plate containing a part-through

crack in bending with the geometry shown in Fig 7 Fracture in the cracked

flange under bending is considered to be most critical at or near the surface of

the flange at the ends of the crack Therefore it is convenient to present

II

r 2c

m

FIG 7 Geometry and loading used to simulate crank ring fracture behavior

Trang 26

results for KI at the surface in terms of the nondimensional parameter F de-

fined by 2

F = K i / O b X f ~ c

where ab is the nominal outer fiber bending stress equal to 6 m / t 2 and m is the

applied bending moment per unit width The assumed crank ring crack is

characterized by the ratios a / c : 0.16, a / t = 0.82, and c / W = 0.89 (Fig

3) Newman and Raju's results closest to this case are for a / c = 0.2, a / t =

0.8 and c / W : 0.8, which give a value of F = 0.49 This value is certainly

low because F increases sharply as c / W approaches unity and there is a con-

siderable difference between c / W = 0.8 and c / W = 0.89

Results by Boduroglu and Erdogan [5], who have recently published KI

solutions for plates of finite width containing through cracks and loaded in

remote bending, are used to quantify the effect of a greater crack length-to-

width ratio for the plate containing a part-through crack Results for the

through crack case are given for values of c / W very close to unity The ap-

proach in using these results is to assume that the effect of finite width for the

through crack geometry is the same as the finite width effect for the part-

through crack geometry Table 1 lists the factors F for a number of c / W

values for part-through cracks with a / c = 0.2 and a / t = 0.8 as obtained

from Ref 4 and for through cracks with c / t = 4 [ = ( a / t ) / ( a / c ) ] as obtained

from Ref 5 The ratio of F-factors for the two cases is also listed

The results in Table 1 indicate that for a / c = 0.2 and a / t = 0.8 the factor

F for the part-through crack geometry is approximately one half of the factor

for the through crack geometry Therefore the approach taken to obtain a

value of F for the cracked crank ring geometry is to obtain a value of F from

the through crack analysis for a geometry close to the crank ring geometry

I and to multiply it by 0.5 The value of F for a through crack geometry with

i c ~ W = 0.89 and c / t = 5 is F = 1.6 [6] so that for the part-through crack

F = 0.5(1.6) = 0.8 This is the value used in the fracture mechanics analysis

TABLE 1 Effect of finite width on KI at the surface for plates loaded in remote bending

containing part-through and through cracks

Where F = K i / t r b ~ a/c = 0.2, a/t = 0.8, c / t = 4:

Trang 27

Using the dimensions and loading for the cracked crank ring, m = 88.9

N - m / m m , t 49.3 mm, and c 246 mm, the value of K~ at the free surface,

without correction for plasticity, is equal to 158 MPa ~ One notes immedi-

ately that, according to this analysis, a very tough material is needed to avoid

loss of the propeller in the presence of the assumed fatigue crack

The fracture mechanics analysis of the crank ring will account for a cer-

tain amount of stable crack growth, so it is necessary to quantify the depen-

dence of F o n crack length This is done by employing the dependence of F o n

crack length for the through crack and multiplying by one half The variation

of F with c for the crank ring crack dimensions, c / t - 5, W / t [ ( c / t ) /

( c / W ) ] = 5.64, is approximately [6]

Ft = 2.73c 24.9 Multiplying this expression by one half provides the relation to be used in the

fracture mechanics assessment of the cracked crank ring:

Newman and Raju's results can also be used to estimate the stress intensity

factor at the bottom of the crank ring crack For a / c = 0.2 and a / t = 0.8 the

stress intensity factor at the bottom of the crack is approximately one half of

the value at the surface for 0.2 < c / W < 0.8; data for c / W > 0.8 were not

given Finite element analyses of an elliptical part-through crack in bending,

which model the close proximity of the vertical flange loads to the crack plane

and the short moment arm in comparison to the plate width and surface crack

length, also indicate that K1 at the deepest point of the crack is about 50% of

Kl at the surface [3] This would appear to contradict the possibility of a

fatigue crack in the crank ring growing to the shape shown in Fig 3 Without

attempting to explain this apparent contradiction, it is noted that crack prop-

agation from the top part of the crack is the fracture that would lead to loss of

the propeller and is therefore of greatest interest in this analysis

The large KI value calculated earlier for the crank ring crack shows that

tough materials must be used to avoid loss of the propeller according to this

methodology This implies that the material will be at or near its upper shelf

behavior, that it can experience stable tearing, and that elastic-plastic frac-

ture mechanics techniques are necessary to quantify its resistance to fracture

(at least to characterize the material toughness with small specimens) Conse-

quently, crack driving force curves are calculated in terms of J~, since the

material's fracture resistance is expected to be expressed in terms of J r R

curves

The crack driving force curve is the relation between Ji and crack length or

crack extension and is estimated from values of KI through the relation

Trang 28

where E ' is the effective elastic modulus equal to E for plane stress and

E/(1 ~, 2) for plane strain: E is Young's modulus and u is Poisson's ratio

Plasticity is accounted for in the analysis by making a crack length plastic

zone correction to KI before converting to Jl:

ceff= c + ( l / 6 ~ r ) ( K i / o o ) 2

where K1 on the right-hand side of the equation is calculated using the origi-

nal crack length, c Two-dimensional, plane strain conditions are assumed to

prevail near the flange surface The crack-driving force relation with the plas-

tic zone correction is then given by

where Eq 1 is used to calculate F, and the applied load or stress oh, is assumed

to be constant (load control)

Figure 8 shows a plot of J~ versus crack extension for the crack geometry of

Fig 3 and a material with yield strength equal to 690 MPa The J r R curve for

a Ni-Cr-Mo steel with ao : 690 MPa is shown for comparison

An alternative driving force for unstable fracture is the attainment of the

plastic collapse load A lower bound to the limit moment for a plate with a

part-through crack in bending is obtained by calculating the moment which

arises when the axial stress over the entire net section is equal to the yield

FIG 8 - - Crack-driving force curve f o r the cracked crank ring in comparison to the JI-R curve

f o r a 690 MPa yield strength Ni-Mo-Cr steel

Trang 29

strength [ 7] The idealized cross-sectional geometry shown in Fig 9 was used

to perform this calculation The neutral axis for this section is essentially at

the lower crack front, and the limit moment per unit width (2 W = 556 mm)

is given by

where the units for mlim and Oo are N - m / m m and MPa Therefore, for Oo =

690 MPa, mlim : 117 N-m/mm, which is greater than the applied moment

assumed for the crank ring in this analysis: 88.9 N-m/mm The actual col-

lapse moment would be larger because the crack is probably smaller than the

idealization shown in Fig 9, the material will harden, and the cracked geom-

etry induces some constraint to plastic deformation

Strength and Toughness Requirements for the Crank Ring

It is now possible to determine the strength and toughness of the crack ring

material required to prevent failure from occurring under the assumptions of

this investigation In the section on loads, it was determined that the effective

bending moment per unit width on the cracked section shown in Fig 3 is

approximately equal to 88.9 N-m/mm

A lower bound estimate of yield strength necessary to prevent collapse from

occurring can be calculated from Eq 4 In this case:

~ro = m l i m / 0 1 7 = 5 2 3 M P a

Therefore the minimum yield strength for the crank ring material should be

greater than 523 MPa

Two approaches are taken to specify the crank ring material toughness to

avoid ductile tearing instability Both are based on the assumption that the

material does not fail by a cleavage mechanism of fracture for the tempera-

F I G 9 - - I d e a l i z e d crank ring crack geometry used for collapse moment calculation

Trang 30

ture and loading rates characteristic of the crank ring This can be accom-

plished by requiring the minimum upper shelf temperature, say, as deter-

mined by Charpy tests, to be below the operating temperature

In the first approach to specifying required toughness, no crack extension

by tearing is permitted in the engineering sense; that is,

J~ (Ac 0) < J~o where J~c is determined in accordance with a procedure such as ASTM Test

for Jlc, A Measure of Fracture Toughness (E 813)

Equation 3 is used to calculate Ji (Ac = 0) for an arbitrary yield strength

and this becomes the specified minimum value of J~ for the crank ring mate-

rial The required value of J~r for a yield strength of 690 MPa, according to

this procedure, is 159 k J / m 2 The value of J~c for the 690 MPa yield strength

material whose JFR curve is shown in Fig 8 is 131 k J / m 2 Therefore a specifi-

cation permitting no crack extension by tearing in the engineering sense

would eliminate this steel as a candidate material for the crank ring Again,

this is based on the assumption that a large fatigue crack could develop in the

crank ring

A fracture criterion based on Jir alone for a ductile material is conservative,

because it does not take advantage of the increase in resistance to ductile

crack extension which generally accompanies small amounts of tearing A

more realistic approach is to specify toughness so that tearing will arrest and

not become unstable This is accomplished by requiring that the JrAc and

J~-Ac curve is less than the slope of the JFR curve; in other words, Tappe is less

t h a n Tma t where T = (E/oo 2) dJ/dc Such a procedure is illustrated in Fig 8

Quantifying this criterion is difficult, because the JrR curve requires at least

two parameters to be represented This means technically that there are an

infinite n u m b e r of J~-R curves which intersect the J~-Ac curve

A practical implementation of this approach is to specify a minimum value

value of J~ for the same amount of crack extension for the yield strength in

question A value of Ac = 1.27 mm (0.050 in.) has been chosen for this inves-

tigation This amount of crack extension has a negligible effect on the col-

lapse moment and is within the range of crack extension investigated in the

determination of JrR values in accordance with ASTM E 813

The required value of JrR for a yield strength of 690 MPa according to this

criterion as obtained from Fig 8 is 194 k J / m 2 An additional requirement is

that Treat at Ac - 1.27 m m b e greater than Tappe at Ac = 1.27 m m for the

yield strength in question The minimum allowable value of Zma t for Oo = 690

MPa is 13.4 As a comparison, the values of JI-R (Ac - 1.27 mm) and Tm~t

(Ac = 1.27 mm) for the steel whose J1-R curve is shown in Fig 8 are, respec-

tively, 368 k J / m 2 and 68.2 Thus this steel would be considered suitable for

the crank ring

Trang 31

Application to a Full-Scale Laboratory Test

The basis for the fatigue crack geometry used in this analysis was the crack

that occurred in a controllable pitch propeller crank ring assembly The

crank ring was made of 4150H steel which has a quoted yield strength of al-

most 759 MPa This yield strength is greater than the 523 MPa value required

to avoid plastic collapse The corresponding required value of JI-R (Ac =

1.27 mm) is calculated according to the method described in the previous

section to be

J1-R (Ac : 1.27 mm) - 175 k J / m 2 The toughness data generated for the 4150H steel show that it is not in the

upper shelf at room temperature, which was the temperature for the full-scale

laboratory test The Charpy energy at room temperature is quoted as ranging

from 8 to 15 J The value of KI at fracture varied from 60 to 123 MPax/m Two

of the tests provided valid K~c values, 60 and 82 MPax/-m, in accordance with

ASTM Test for Plane-Strain Fracture Toughness of Metallic Materials

(E 399); the other tests provided invalid values because either too much plas-

ticity or crack growth occurred it was not determined which or the speci-

men dimensions did not satisfy the plane strain requirements In any case, the

criterion proposed in the analysis of this paper, that the fracture mode be

ductile tearing, was violated

The range of critical Ji values converted from the Kc values is 16 to 68

k J / m 2, all of which are considerably lower than the required value of JI-R =

175 k J / m 2 Therefore the methodology developed in this investigation pre-

dicts that the 4150H is not a suitable crank ring material The fact that the

full-scale laboratory tested 4150H crack ring did not experience unstable

fracture shows that the analysis is conservative The degree of conservatism

on the required JFR value in this case is greater than a factor of two

This degree of conservatism arises because of the many assumptions made

in the analysis Loads calculated using finite element analysis for an idealized

crack geometry are undoubtedly too high Since Ji is proportional to the load

squared, a decrease in load will cause a substantial-decrease in required Ji

Summary and Conclusions

The objective of the investigation reported in this paper was to set material

toughness requirements to avoid loss of a ship propeller blade from a control-

lable pitch propeller crank ring that has a fatigue crack Loss of the propeller

was assumed to be prevented if fracture instability could not occur before the

fatigue crack grew to a size beyond which crack growth would proceed radi-

ally through the crank ring flange and not around its circumference Choice

of this crack size and geometry was based on a full-scale crank ring laboratory

test in which a large fatigue crack occurred

Trang 32

The driving force for crack growth is the vertical line load on the flange

periphery induced by centrifugal and hydrodynamic propeller loads The

magnitude and distribution of the flange loads were estimated with finite ele-

ment calculations Account was taken of the significant load redistribution

that occurs in the presence of a crack by simulating a crack in the finite ele-

ment analysis

The fracture mechanics analysis was conducted by modeling the cracked

crank ring as a plate with a part-through crack in bending Numerical solu-

tions for part-through cracks in bending were combined with results for large

crack length-to-plate width geometries for through cracks in bending to de-

termine KI for the large crack size of interest Values of Kl with plastically

adjusted crack lengths were converted to values of J1 and crack driving force

curves were generated

Fracture instability was considered to be avoided if the JrAc driving force

curve intersected the JI-R curve and at the point of intersection the slope of

tical implementation of this criterion was achieved by specifying minimum

values of JI-R and Treat at Ac = 1.27 mm (0.050 in.), as determined from a

increasing resistance to crack growth associated with small amounts of tear-

ing An estimate of the crank ring plastic collapse moment and its depen-

dence on yield strength was made as an alternative for determining fracture

conditions

Application of the toughness requirements to the laboratory-tested crank

ring, whose geometry and loading were the basis for the analysis, indicated

that the crank ring material toughness was inadequate The fact that the

crank ring did not fracture demonstrates the conservatism of the require-

ments This conservatism is believed to arise mainly from an overestimation

of loads, but may also be influenced by the assumption that fracture occurs

from a sharp crack under monotonically increasing load; in the actual case,

high cyclic loads would precede and cause fracture The influence of this lat-

t e r effect on apparent toughness requires further investigation

The analysis of this paper was restricted to a single crank ring geometry,

but it could easily be applied to other crank rings Use of the toughness re-

quirements developed here would represent a significant deviation from cur-

rent material property specifications, in which only tensile properties and

Charpy energy are used to qualify a material It is the authors' hope that one

of the primary results of the investigation is the demonstration that fracture

control technology can be used as an additional design tool to increase the

reliability and safety of structures

References

[1] Wind, J., " H u b Size Selection Criteria for Controllable Pitch Propellers as a Means to En-

sure Systems Integrity," Naval Engineers Journal, Dec 1978, pp 49-61

Trang 33

[2] Peterson, R E., Stress Concentration Factors Wiley, New York, 1974

[3] Unpublished results obtained by Arthur D Little, Inc., Cambridge, Mass., 1983

[4] Newman, J C., Jr., and Raju, I S., "Analyses of Surface Cracks in Finite Plates under Tension or Bending Loads," NASA Technical Paper 1578, National Aeronautics and Space Administration, Washington, D.C., 1979

[5] Boduroglu, H and Erdogan, F., "Internal and Edge Cracks in a Plate of Finite Width under Bending," Lehigh University Report, Bethlehem, Pa., Nov 1982

[6] Private communication with F Erdogan (from additional, unreported calculations)

[ 7] Johnson, W and Mellor, P B., Engineering Plasticity, Van Nostrand, New York, 1973, p

415

Trang 34

K i y o s h i T a n a k a , 1 M i t s u o Sato, 1 T a d a s h i I s h i k a w a , 1 a n d

H i r o n o r i T a k a s h i m a I

A New Wide Plate Arrest Test (SCA

Test) on Weld Joints of Steels for

Low Temperature Application

REFERENCE: Tanaka, K., Sato, M., Ishikawa, T., and Takashima, H., "A New Wide

Plate Arrest Test (SCA Test) on Weld Joints of Steels for Low Temperature Application,"

Fracture Mechanics: Seventeenth Volume, A S T M STP 905 J H Underwood, R Chait,

C W Smith, D P Wilhem, W A Andrews, and J C Newman, Eds., American Society

for Testing and Materials, Philadelphia, 1986, pp 22-40

ABSTRACT: As a realistic and practical criterion for brittle fracture arrest in low tem-

perature storage tanks, the present authors propose the short crack arrest (SCA) concept

This aims at arresting brittle fracture before propagation to a catastrophe In order to

investigate the capability of steel materials from the viewpoint of this concept, two types of

wide plate tests, the SCA tests on weld heat-affected zone (HAZ) and base metal, were

developed These two test methods were designed to simulate the run-and-arrest pheno-

menon of brittle fracture in actual storage tanks

The two types of tests, together with the compact crack arrest (CCA) test, were applied

to base metals and welded joints of a wide range of steels for low temperature application

Efforts were made to clarify the effects of base metal chemical compositions and condi-

tions for welding on the weld HAZ characteristics

The results revealed that addition of about 3% nickel to the base metal significantly

improved the weld HAZ arrest toughness It was also shown that the SCA capability of

steels could be predicted from the K, values obtained by the CCA test

KEY WORDS: low temperature, fracture toughness, crack arrest, brittle fracture propa-

gation, welded joint, weld heat-affected zone, storage tank

In Japan, in 1968, there was a catastrophic fracture accident in a spherical

tank with a diameter of 16.2 m during hydrotest [1] The tank, made of an

800 MPa high tensile strength steel, collapsed after fast fracture in three

fourths of the circumference The fracture surface consisted of shear fracture

in the base metal and brittle fracture along the heat-affected zone (HAZ) of a

1Senior Research Engineer, Research Engineer, Research Engineer, and Chief Research Engi-

neer, respectively, R&D Laboratories II, Nippon Steel Corporation, Sagamihara, Japan

22

9

Trang 35

TANAKA ET AL ON NEW WIDE PLATE ARREST TEST 23

vertical weld joint with a length of 6.2 m It is believed that a weld hydrogen

crack, with a length of 60 m m and a depth of 13 mm, at the toe of the weld

was the cause of the brittle fracture initiation The brittle fracture propagated

in the HAZ along the weld joint and penetrated the entire weld length Al-

though the brittle fracture was arrested by the neighboring base plates, duc-

tile fracture took place and continued to propagate in an unstable manner

until the tank collapsed

In 1977 a disaster occurred in the Middle East in which a gas liquefaction

and storage plant completely collapsed [2] It is believed that the cause of the

disaster was brittle fracture in a liquefied propane gas (LPG) storage tank In

this case, the brittle fracture propagated in the base plates After this acci-

dent, Cuperus [3] questioned the safety of storage tanks for liquefied light

hydrocarbons and proposed the double integrity principle

From these experiences and other examples of failure accidents, the

present authors recognized the necessity of a comprehensive investigation of

the performance of steel plates and their weld joints in terms of brittle frac-

ture initiation and arrest:

1 Stringent evaluation of fracture initiation toughness of weld HAZs as

well as base metals

2 Realistic evaluation of fracture arrest toughness by means of suitable

simulation methods of the brittle fracture run-arrest phenomenon and a con-

venient test method for arrest toughness

This report describes the results of investigations made by the authors for

establishing these evaluation methods and for collecting a body of data for

material selection

Fracture Initiation Characteristics of Welds

It is well known that welded joints are heterogeneous in terms of the micro-

structure and show a large scatter of brittle fracture toughness Figure 1

shows examples of zones in a welded joint where initiation points of brittle

fractures were found after microscopic investigation on specimens which pre-

sented low initiation toughness The reasons for, and the amount of, the em-

brittlement for each of the zones are different depending on the chemical

compositions of the base metals, the weld thermal cycles, and the hot strain

during welding It is therefore quite important to investigate the fracture ini-

tiation toughness of the welded joint carefully by using many specimens hav-

ing their crack tips at various points in the welded joint It is also important to

apply two kinds of specimen geometries having different notching and crack-

ing directions (i.e., side-cracked and face-cracked specimens) The notch tip

in the former specimen can sample a wide range of microstructures but with-

out a long contact with the same microstructure, whereas that in the latter

can sample a specific microstructure with a long contact This difference pro-

Trang 36

K-joint (~) Subcritical HAZ

| Hot strain embrittlement by remote weld passes for all areas

FIG 1 Embrittled regions in weld joints

duces a significant contrast in the results (i.e., a wider scatter and a lower

minimum value of fracture toughness for the face-cracked specimens)

In order to simplify the investigation, the present authors proposed the ap-

plication of the fatigue crack tip opening displacement (CTOD) test method

[4,5], the basis of which comes from the fatigue wide plate test by Nibbering

et al [6] and the fatigue fracture toughness test by Yokobori et al [7] The

characteristics of this method, when compared with the ordinary fracture

toughness test method, are as follows:

1 Specimens are cyclically loaded at the test temperature, and the fatigue

crack develops scanning the various microstructures in the crack line

2 When the toughness, or the critical CTOD, 8c, of a microstructure is

lower than the working CTOD, or applied CTOD, brittle fracture takes

place

3 With several specimens, the minimum 6c value of the welded joint tested

can be determined The reliability of this value is high because microstruc-

tures in the area where the fatigue crack passed are all tested by each of the

cyclic loads

When the crack line is misaligned a little from the weld line (Fig 2) the

reliability of the test results increases further It was found, however, that a

small cyclic range of the stress intensity factor, AK, preferably smaller than

30 MPa~fm, has to be maintained during the whole period of the low temper-

ature fatigue loading in order to achieve results consistent with the monotonic

CTOD test [5]

Trang 37

I Weld / IV /Fatigue crack 1

metal ~L ~ development / ~80~85~ during the

b Face cracked specimen

FIG 2 - - F a t i g u e C T O D test on weld joints

Table 1 lists examples of the monotonic and fatigue CTOD test results for

weld HAZs for three kinds of low temperature steels Numerous monotonic

CTOD tests were conducted on each of the weld joints The results are shown

in the form of the coefficients in the Weibull distribution equations; these fit

well the test results For comparison, 6~ values for 2% cumulative probability

were taken as the minimum ~ values of the weld joints The fatigue CTOD

test showed results conforming to those for the monotonic CTOD test This

fact indicates the possibility of economization of fracture toughness tests by

means of the new test method without losing, or instead with increasing, relia-

bility Fracture initiation points in the fatigue CTOD test were also the grain-

coarsened HAZ close to the fusion line Moreover, it is surprising to find that

the low-carbon grain-refined steels showed 6~ values of 0.04 mm or lower

when some unfavorable combinations of metallurgical and testing conditions

were met, since these steels have showed satisfactory performance in all con-

ventional tests and notched wide plate tests as well as in actual application to

L P G storage tanks for more than 20 years

Significance of Local Brittle Zones

In small-scale tests for fracture initiation toughness, such as the CTOD

and Kic tests, the first incident which leaves a discontinuity in the load versus

displacement record is taken as the critical point for investigation With these

tests, however, it is difficult to clarify the significance of the incident with

regard to the total safety of the structures In order to assess the low ~c values

Trang 39

found in the monotonic or fatigue CTOD test, therefore, surface-cracked

wide plate tests were carried out on one of the welded joints that showed low 6r

values Two specimens were prepared from the welded joint described in the

fourth line of Table 1 A full breadth surface crack was produced by cyclic

bending so that the fatigue crack tip lay in the same brittle zone as in the

CTOD specimens One of the two specimens, when tested at 50~ by a

20 MN capacity tension test rig, showed brittle fracture with the stress lower

than the yield stresses of the base and weld metals; the other specimen showed

brittle fracture with a high stress Analysis on the crack tip location of the

latter specimen showed that the initial fatigue crack was too long and had its

tip in the grain-refined HAZ The fracture surface of the former specimen

and its data are shown in Fig 3 There was no indication of brittle fracture

arrest Subsequent study revealed that the fracture initiation point of this

specimen was the same grain-coarsened region as in the CTOD specimens

with the low 6r result The linear elastic fracture mechanics (LEFM) calcula-

tion for this wide plate specimen led to a 6r value of 0.032 mm, which is almost

consistent with the values from the monotonic and fatigue CTOD tests

Agreement of 6r values from CTOD tests and the wide plate test suggests

that the results from the small-scale fracture toughness tests can be applied to

prediction of the fracture initiation stresses of fatigue-cracked wide plate test

specimens that simulate actual structures with fatigue crack defects How-

ever, an infinite surface crack such as that used in the wide plate test is not

expected in actual structures It is important to investigate whether or not

brittle fracture can propagate in the unnotched weld HAZs

Development of the Short Crack Arrest (SCA) Test

The ESSO test has been used widely for the evaluation of brittle fracture

arrest capability of steel materials including base plates and welded joints

The present authors, however, had quite often unexpected results from tests

on welded joints in the as-welded condition Figure 4 illustrates examples of

fracture paths of as-welded joints It is considered at the present time that the

compressive weld residual stress, in the direction transverse to the weld line,

at the specimen edges must be the cause of this deviation, since it is not ob-

served in welded and center notched wide plate tests This compressive weld

residual stress at the edge is considerably high (Fig 4) Since this situation is

not expected in actual structures, modification of the test method is neces-

sary

The basic idea for the approach taken here is that the brittle fracture has to

be initiated at the center of the specimen width to eliminate the effect of the

compressive residual stress The present authors recognize the importance of

the concept proposed by an ASTM committee [8] in 1960 In this concept the

arrest of a brittle fracture becomes possible, when it propagates just beyond

the initial surface crack, due to the higher toughness associated with plane

Trang 40

2 8 FRACTURE MECHANICS: SEVENTEENTH VOLUME

Tiêu đề	Fracture Mechanics
Tác giả	J. H. Underwood, R. Chait, C. W. Smith, D. P. Wilhem, W. A. Andrews, J. C. Newman
Trường học	Virginia Polytechnic Institute & State University
Chuyên ngành	Fracture Mechanics
Thể loại	Bài báo kỹ thuật
Năm xuất bản	1986
Thành phố	Albany

Định dạng
Số trang	837
Dung lượng	15,47 MB