Astm stp 1244 1995

STP 1244

Constraint Effects in Fracture

Theory and Applicatons:

Second Volume

Mark Kirk and Ad Bakker, Editors

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04-012440-30

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Foreword

This publication, Constraint Effects in Fracture: Theory and Applications, contains papers presented at the symposium of the same name, held in Dallas/Forth Worth, TX on 17-18 Nov. 1993.

The symposium was sponsored by ASTM Committee E-8 on Fatigue and Fracture along with the

European Structural Integrity Society. Mark Kirk of Edison Welding Institute in Columbus, OH

and Ad Bakker of Delft University of Technology Laboratory for Materials Science in the Netherlands

presided as symposium chairs and are the editors of the resulting publications.

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Terry Ingham

The conference chairmen and ASTM Committee E08 on Fatigue and Fracture note with great

sorrow and regret the death of our colleague Terry Ingham. Terry passed away on January 18, 1994,

a short two months after we all enjoyed his presence and discussions at the symposium on which

this STP is based. He will be remembered not only for the quality of his work, but also for his

energy and commitment even in the later stages of his illness.

Terry graduated from the University of Leeds (United Kingdom) with a degree in Metallurgy in

1965. Subsequently, he joined the United Kingdom Atomic Energy Authority (UKAEA). His work

included the development of experimental fracture toughness test methods and their relationship to

structural behavior, irradiation damage in pressure vessel steels, the effect of specimen size on the

fracture toughness transition regime in ferritic steels, and acoustic emission. All of these topics

resulted in noteworthy contributions to the literature, particularly his contributions to an international

study of irradiation damage in steel, and to the pressure vessel materials section of the UK Light

Water Reactor Study Group Report.

Within the European Structural Integrity Society (ESIS) he was a member of the Working Party

on Fracture Mechanics Testing Standards, for which he contributed substantially to the R-curve test

procedure, P1-87D.

In 1985, he joined the UK Nuclear Installations lnspectorate (NII) as a Principal Inspector, where

he was involved in the licensing of gas cooled reactors and nuclear fueled processing plants.

Although this endeavor entailed a departure from his experimental work, his interest in fracture

mechanics continued at both national and international levels. His work at the Nil was recognized

in 1994 by the award of the Order of the British Empire (OBE), an honor for which he was

justifiably proud.

Our sympathy is extended to his wife and two daughters; we will all miss him.

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Contents

Overview vii

TWO PARAMETER CONTRACT THEORIES

Cleavage Fracture Quantified--Y. J. CHAO AND W. JI

Variations of a Global Constraint Factor in Cracked Bodies Under Tension and

Bending Loads--J. c. NEWMAN, JR., J, H. CREWS, JR., C. A. BIGELOW, AND

D, S. DAWICKE

Limits of J-T Characterization of Elastic-Plastic Crack-Tip Fields-- u165 WANG

AND D, M. PARKS

CRACK GROWTH MODELING

A Numerical Study on the Influence of Geometry Variations on Stable Crack

Growth in CT Specimens for Different Materials--G. SHAN, O. KOLEDNIK, AND

D. F. FISCHER

Numerical Simulation of Stable Crack Growth in Fracture Mechanics

Specimens--D. KLINGBEIL, G. M. ZAHED, A. EBERLE, S. FRICKE, AND W. BROCKS

Numerical Modeling of Ductile Tearing Effects on Cleavage Fracture

Toughness--R. H. DODDS, JR,, M. TANG, AND T. L. ANDERSON

The Role of Geometry and Crack Growth on Constraint and Implications for

Ductile/Brittle Fracture--N. v. O'DOWD, C. F. SHIH, AND R, H. DODDS

100

134

MICROMECHANICAL APPROACHES

Modeling Crack Growth Resistance Using Computational Cells with

Microstructurally-Based Length Scales--c. E SHIN AND L. XIA

Prediction of Cleavage Fracture in the Brittle to Ductile Transition Region of a

Ferritic Steel--R. w. J. KOERS, A. H. M. KROM, AND A. BAKKER

The Second Parameter in J-R Curves: Constraint or Triaxiality--w. BROCKS AND

W. SCHMITT

Application of the Gurson Model to Ductile Tearing Resistance--w. BROCKS. D.

KLINGBEIL, G. KUNECKE, AND D.-Z. SUN

163

191

209

232

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EXPERIMENTAL VALIDATION

Fracture Toughness Measurements Using Small Cracked Round Bars--

J. H. GIGVANOLA, H. HOMMA, M. LICHTENBERGER, J. E. CROCKER, AND R. W. KLOPP 255

Experimental Investigation of Fracture Toughness Scaling Models--R. E. LINK AND

J. A. JOYCE 286

The Effect of Constraint Due to Out-of-Plane Stress Field on Fracture of Reactor

Pressure Vessel--An Experimental and Numerical Study--D. L. RUDLAND,

R. MOHAN, N. D. GHADIALI, D. DETTY, A. R. ROSENFIELD, AND G. M. WILKOWSKI 316

The Influence of Plasticity and Geometry on the Mixed Mode Fracture of

PMMA--J. c. w. DAVENPORT AND D. J. SMITH 344

Constraint Effects on the Upper Shelf in Cracked Welded Specimens--c. FRANCO,

P. GILLES, C. ERIPRET, AND S. NALLET 363

APPLICATIONS

Constraint Effects in Testing Different Curved Geometries of Zr-2.5Nb Pressure

Tube Material--E H. DAVIES, R. S. W. SHEWFELT, AND A. K. JARVINE 392

A Comparison of J and CTOD as Elastic-Plastic Fracture Characterizing

Parameters--J. R. GORDON, B. K. NEALE, AND Y.-Y. WANG 425

Size and Deformation Limits to Maintain Constraint in Klc and Jc Testing of

Bend Specimens--K. c. KOPPENHOEFER, M. T. KIRK, AND R. H. DODDS, JR.

Constraint and Statistical Adjustment Models Applied to Transition Fracture

Toughness Data--J, D. LANDES

Interpretation of Constraint Effects Under PTS Conditions Based on J-Q Fracture

Methodology--D. K. M. SHUM

Application of J-Q Fracture Methodology to the Analysis of Thermal-Shock

Experiment TSE-SA--D. K. M. SHUM

Validity of Small Specimen Fracture Toughness Estimates Neglecting Constraint

Corrections--K. WALLIN

445

461

479

501

519

Author Index 539

Subject Index 541

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Overview

The Conference

On 17-18 November, 1993, the American Society for Testing and Materials (ASTM) and the

European Structural Integrity Society (ESIS) co-sponsored the Second Symposium on Constraint

Effects in Fracture. This symposium was held in Ft. Worth, TX; it followed on the success of the

first symposium held in May 1991 in Indianapolis, IN (ASTM STP 1171). A total of 24 papers

were presented. Of these, 13 were submitted from North America and 11 were submitted from Europe.

Motivation

The application of conventional fracture mechanics techniques to assess the integrity of a cracked

structure relies on the notion that a single parameter uniquely characterizes the resistance of a

material to fracture. Material resistance to catastrophic brittle fracture is characterized by a critical

value of the stress intensity factor/tic, while resistance to the onset of ductile, or upper-shelf, fracture

is characterized by a critical value of the J-integral J~c.

Testing standards that govern the measurement of Kic and Jlc, ASTM E 399 and ASTM E 813

respectively, require sufficient specimen thickness to produce predominantly plane strain conditions

at the crack tip and sufficient crack depth to position the crack tip in a highly constrained bending

field. These restrictions are designed to insure the existence of severe conditions for fracture as

described by the Hutchinson Rice Rosengren (HRR) asymptotic fields. The requirements of the

testing standards thereby guarantee that Kit and Jic are lower bound, geometry insensitive measures

of fracture toughness. However, cracks in civil, nuclear, and marine structures are seldom this highly

constrained, which makes predictions of structural fracture resistance based on laboratory fracture

toughness values overly pessimistic. Excessive pessimism in structural assessment can lead to the

unwarranted repair or decommissioning of engineering structures to protect the public safety at a

great, often unwarranted, cost and inconvenience.

Many researchers have long advocated a more pragmatic, engineering approach to assess the

fracture integrity of cracked structures. This approach requires that constraint in the fracture toughness

test specimen approximate that of the structure to provide an "appropriate" toughness for use in an

assessment of structural integrity. The appropriate constraint is achieved by matching thickness and

crack depth between specimen and structure. Experimental studies demonstrate the validity of this

approach. These studies show that use of geometry dependent fracture toughness values allows

more accurate prediction of the fracture performance of structures than is possible using conventional

fracture mechanics. However, the task of characterizing fracture toughness becomes more complex

than is presently the case using ASTM standard test methods. Testing of nonstandard specimens is

required, and different fracture toughness data are needed for each geometry of interest. Further,

this approach cannot be applied economically to thick section structures (e.g., nuclear pressure

vessels). This limitation has motivated the development of theories that extend significantly the

range of deformation over which fracture mechanics can be applied accurately to predict the

performance of structures. Many of the research efforts discussed at the Second Constraint Symposium were undertaken to this end.

vii

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viii OVERVIEW

Overview of the Papers Presented

Considerable advancement in both the understanding and characterization of constraint effects

occurred during the two and a half years between the first and second symposia. Evidence of

advancement is available by contrasting the topics of papers presented at the two meetings. During

the First Symposium, considerable emphasis was placed on the development of appropriate strategies

for characterizing constraint effects on initiation fracture toughness, whether by purely brittle (lower

shelf) or by purely ductile (upper shelf) mechanisms. Both theoretical analysis and experimental

investigations focused on the study of fracture in simple laboratory test specimen geometries. At

the Second Symposium, considerable emphasis was placed on the study of factors whose resolution

will ultimately increase the engineering utility of constraint theories. In specific, the following

topics were addressed.

9 The competition between cleavage and ductile fracture in the transition temperature regime

9 Finite element modelling and theoretical parameterization of crack growth processes

9 The effects of bi-axial loading

Additionally, a number of papers reflected cooperative efforts between different engineering

specialties. Several studies combined aspects of both solid mechanics and metallurgy, or addressed

both experimentation and numerical analysis. These investigations, particularly the former, signal

a fundamental shift of focus in the understanding and characterization of fracture processes in

metals. There was a general recognition among attendees at the symposium that it is necessary, in

certain instances, to incorporate variables that characterize a material at a sub-continuum scale into

fracture theories that are used to assess the safety and suitability of structures for continued service.

This is a major philosophical shift from the tenants of single parameter fracture mechanics (SPFM)

that have been widely viewed as the most rational approach for the last 40 years.

This STP is divided topically into the following five categories:

9 2-Parameter Fracture Mechanics (2PFM) theories, 3 papers

9 Crack Growth Modelling, 4 papers

9 Micromechanical Modelling, 4 papers

9 Experimental Validation of Constraint Models, 6 papers

9 Application of Constraint Models, 7 papers

This distribution of papers indicates that the understanding of constraint effects on fracture is

approaching a critical juncture. There is nearly an even division between efforts aimed at development

of an appropriate and physically defensible characterization of constraint effects (papers in the first

three categories) and efforts aimed at applications or codification (papers in the latter two categories).

Summary of Major Findings

All of the various constraint models presented at the symposium share a common goal: to

extend significantly the validity range of SPFM and thereby facilitate more accurate prediction and

assessment of the conditions that cause fracture in structures. Available constraint models include

the mechanics-based approaches of two-parameter fracture mechanics (2PFM) (that is, J-T, J-Q, JA2, J-etg), statistical techniques based on the Weibull model, and micro-mechanical approaches that

address fracture by both cleavage and ductile mechanisms. At this stage, the following general

statements can be made:

1. In the lower transition regime where cleavage fracture occurs before or just after the onset of

ductile tearing, all of the 2PFM constraint models can be applied to parameterize the variation of

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OVERVIEW ix

critical fracture toughness with constraint. Of the various models available, the J-Q approach of

O'Dowd and Shih applies rigorously to the highest deformation levels and to the broadest range

of materials. Experimental evidence is available, which shows the validity of this approach. All of

the 2PFM approaches, however, suffer from the disadvantage that they complicate considerably the

task of characterizing material toughness because the toughness at a given temperature becomes a

function of constraint rather than a single value.

2. In the lower transition regime it is also possible to predict, without resort to empirical argument,

this variation of toughness with constraint using the results of standard fracture toughness tests

coupled with the micro-mechanics approach of Dodds and Anderson. At this conference the applicability of this model was extended into the upper transition regime where significant stable tearing

may precede the onset of cleavage. Again, experimental evidence is available which shows the

validity of this approach. Certain issues remain with respect to the proper treatment of 3D effects;

these are currently under investigation.

3. A "master curve" approach to the analysis of fracture toughness data in the transition regime

has been proposed in a draft ASTM standard on this topic (ASTM Task Group E08.08.03 on ElasticPlastic Fracture Mechanics Technology in the Ductile-to-Brittle Transition Regime). Combination

of this approach with a statistical correction for thickness effects based on the Weibull model appears

to provide a powerful tool for the predicting toughness of geometrically similar specimens from

one another (e.g. thick C(T)s predicted from thin C(T)s) across a wide range of thicknesses.

4. 2PFM models can be applied on the upper shelf to parameterize constraint effects on R-curve

behavior. However, these approaches lack a rigorous theoretical basis in this application as a

reference infinite body field solution that is self-similar to the solutions for growing cracks in finite

bodies is not available. As a consequence, it can be expected that "size effects" on fracture toughness

will likely reveal themselves in such an application. On the upper shelf the way forward appears

to be through application of some form of local approach wherein sub-continuum material variables

are incorporated into the models to provide a capability to predict accurately structural behavior

from smaller scale fracture toughness test results.

Acknowledgments

The chairmen would like to acknowledge Dorothy Savini of ASTM for her professionalism in

guiding us through the planning and smooth execution of the symposium. Further, Therese Pravitz

and Shannon Wainwright of ASTM are to be commended for their assistance during the peer review

process. We are indebted to our colleagues who assisted us with the abstract review process and

with the conduct of the symposium. These individuals included Ted Anderson of Texas A&M

University, Wolfgang Brocks of the Fraunhofer-Institut fur Werkstoffmechanik, Bob Dodds of the

University of Illinois, Steve Garwood of TWI, Phillipe Gilles of Framatome, Ed Hackett of the

Nuclear Regulatory Commission, Lee James of Westinghouse, Dietmar Klingbell of BAM, Ronald

Koers of Shell Research, Randy Nanstad of the Oak Ridge National Laboratory, MarjorieAnn E.

Natishan of the University of Maryland, and C. Fong Shih of Brown University.

Others to be thanked include the authors who submitted the papers that comprise this publication.

Discussions by the authors and attendees energized symposium atmosphere. Finally thanks go to

the peer reviewers for their critiques and comments, which helped ensure the quality of this STP.

Mark Kirk

Edison Welding Institute, Columbus, Ohio, USA;

symposium cochairman and coeditor.

Ad Bakker

Delft University of Technology, The Netherlands;

symposium cochairman and coeditor.

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Two Parameter Contract Theories

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E~Chao 1 and W. M 1

CLEAVAGE FRACTURE QUANTIFIED BY J AND A 2

REFERENCE: Chao, Y. J., and Ji, W., nCleavage Fracture Quantified

by J and A2, N Constraint Effects in Fracture Theory and Applications:

Second Volume, ASTM STP 1244, Mark Kirk and Ad Bakker, Eds., American

Society for Testing and Materials, Philadelphia, 1995.

ABSTRACT: The analytical asymptotic solutions including higher order terms for

stresses at a crack tip embedded in a power law elastic-plastic material are applied to

the interpretation of cleavage fracture for a mild steel. It is demonstrated that fracture

initiation can be determined by using two parameters J and A 2 -- J represents the level

of loading and A 2 quantifies the level of constraint. Constraint related issues such as

size effect, transferability, and biaxial stress effect are investigated. The predicted

results have the same trend as seen experimentally.

KEYWORDS: elastic-plastic fracture, constraint, J-integral, cleavage fracture, crack

tip stress fields, J-A 2 methodology, pressure vessels, biaxial stress, brittle-ductile

transition, size effect, size requirement

Introduction

Constraint effect in fracture is qualitatively referred to as the material behavior of

the dependence of fracture toughness upon the specimen thickness, in-plane geometry and

loading configuration. A broader delineation of the constraint effect would include size

effect ( e.g. K c for small CT vs. K c for large CT) and transferability (i.e. applicability of

the data from laboratory test to full scale structures). For specimens thick enough such

that a majority of the material through the thickness in the crack tip region exhibits a plane

strain behavior the constraint effect is due to the in-plane geometry and loading

configuration. As the thickness is reduced, gradually the constraint effect due to the inplane geometry and loading level diminishes and the constraint effect in the thickness

direction becomes apparent. In the theoretical limit, plane stress conditions, the in-plane

constraint effect vanishes [1]. The current paper addresses the constraint effect due to inplane geometry and loading configuration, particularly for fracture under cleavage. As

such, a plane strain fracture mechanics theory suffices.

1Professor and graduate student, respectively, Department of Mechanical Engineering, University of

South Carolina, Columbia, SC 29208

www.astm.org

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4 CONSTRAINT EFFECTS tN FRACTURE THEORY AND APPLICATIONS: SECOND VOLUME

For cleavage fracture, it is generally recognized that fracture event initiates when a

critical tensile stress o c is attained at a critical distance r c ahead of the crack tip. A large

scatter in the toughness data observed in experiment for cleavage fracture could be due to

the combination of statistical sampling effects [2] and constraint effects. In this paper the

constraint effects on the fracture toughness data are investigated. Referring to fig. 1, if the

critical stress o c can be represented by the well known HRR solutions, after Hutchinson

[3,4] and Rice and Rosengren [5], the fracture can well be characterized by a single

parameter J since the strength of the HRR solution is uniquely governed by J. Note that

the HRR solutions are valid as r---~0. Only under stringent conditions, a structure or

specimen can possess a crack tip stress close to the HRR stress at a finite distance r c. This

is indeed the underlying principle for the severe size requirements by ASTM for fracture

toughness testing. In the general case, the critical stress at the finite distance r c deviates a

certain amount from the HRR stress. A single parameter, such as J or CTOD, is thus not

sufficient to characterize the fracture event. This is the fundamental reason for the

presence of constraint effect in fracture.

, A: HRR l

, B: actual stress

FIG. 1 --Opening stress distribution in front of a crack tip

To quantify the stress at a finite distance r c from the crack tip it is quite nature to

look into the asymptotic solutions including higher order terms. Li and Wang [6]

presented a procedure for determining the second term in the asymptotic expansion.

Sharma and Aravas [7] completed the second order analysis using a somewhat different

method than used by Li and Wang [6]. Recent results by Xia, et al. [8] include higher

order terms. O'Dowd and Shih [9-I l] introduced a Q-stress term to collectively represent

all the higher order terms for the stress fields, Note that these analyses [6-11] are for

plane strain, Mode I conditions. A more complete theoretical asymptotic analysis including

higher order terms for the stress and deformation fields at a crack tip embedded in a

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CHAO AND JI ON CLEAVAGE FRACTURE QUANTIFIED 5

Ramberg-Osgood nonlinear material for Mode I and Mode II under either plane stress or

plane strain conditions are developed by Yang, et al. [12,13]. It is shown that the stress

field at a crack tip can be written as

p=L

where crij=crij/cr0, F= r/L, L is a crack characteristic length, 13 is a positive integer, A I~ is

the amplitude, s o is the stress exponent, and ~-v(l~)(0) is the dimensionless angular

distribution of stress of the 13-th term in the series expansion. Note that i,j-1,2,3 in the

above equation and it is understood that they represent r,0,z in a cylindrical coordinate

system with the origin at the crack tip.

It is further demonstrated by Chao, et al. [12,14] that for Mode I under plane

strain conditions the first three terms from the series solution can be used to characterize

the stress aij(r,0 ) in the crack tip region well beyond r/(J/o0)=5. The first three terms

from the infinite series eqn.(1) are sufficient because of the similarity of the angular

distributions of each stress component for 13_>3. Consequently, a third term (13=3) alone

can collectively represent several higher order terms in the series expansion. Thus, using

more than three terms in (1) is redundant and using two terms is not sufficient to

characterizing the stress fields in the range l<r/(J/cr0)<5 as discussed in [7,13]. The threeterm solution for the stress in the 0 direction is written as

% aeoaoI,,

(2)

where

_ A2 X 2

A2 _ .~.. =

A1 (ac0tr0inL / j)S1

, n is the strain hardening exponent, <x is a material constant used in the Ramberg-Osgood

constitutive modeling, (o0,e0) is a reference stress-strain state and I n is a tabulated

function [15]. The first term in eqn.(2) is the HRR solution and the rest represent the

higher order terms in the asymptotic expansion. Note that eqn.(2) has two amplitudes, J

and A2, while J represents the level of loading A 2 is generally a function of loading level

(i.e. J ), material constants (i.e. cZ,Oo,~ o, n), and geometry and loading configuration, or

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6 CONSTRAINT EFFECTS IN FRACTURE THEORY AND APPLICATIONS: SECOND VOLUME

A 2 =f( J ; cx, o0,e0, n ; geometry and loading configuration ) (3)

It appears that for common fracture test specimen geometries both the second and the

third term in eqn.(2) are negative, i.e. A 2 is a negative quantity, ~-00(2) is positive, and

&000) is negative. Since the first term is always positive, the opening stress in front of a

crack tip is thus in general lower than the HRR stress as shown schematically in fig. 1. In

addition, since the critical distance r e is believed [16,17] within the range 1< rc/(J/ao) <5

for cleavage fracture and the critical stress ~c in this range can be represented by eqn.(2),

fracture event can thus be characterized by the two parameters J and A 2 . The three-term

solution combined with the critical stress criterion for cleavage fracture can therefore be

written as

= ( J ~ ro ,, (ro),, (ro)s, 800(3)(o)] C'o aeo~LZ ) [(L) a~~176 a~(2~(0)+(A~)~'L"

(4)

Note that the magnitude of A 2 directly determines the amount of departure of the stress

from the HRR stress. For specimens having A 2 =0, the critical stress is uniquely

characterized by the HRR stress. As a consequence, fracture of such specimens is

controlled by a single parameter, such as J, 55, or CTOD. For general specimen geometry

or structures, A 2 provides a quantitative measure of the level of constraint, e.g. small

(large) value of] A 2 1 corresponds to high (low) constraint or high (low) stress triaxiality.

In this paper A 2 is determined by a point matching technique [12], i.e. the stress

value oij(r,0 ) determined from a finite element analysis (FEA) at a point (r,0) near the

crack tip is set equal to the three-term analytical result, e.g. eqn.(2), for that stress

component to yield the A 2 value. It is shown that A 2 calculated using any stress

component at any angle in the range ro0/J = 0.5 to 4 is nearly independent of the location.

Specifically, we used o00 at r=2(J/o0) or (J/o0) at 0=0 ~ to determine A 2 in this paper.

Table 1 lists the stress exponents of higher order terms and Table 2 provides the

dimensionless values of ~-oe(P) at 0=0 ~ for several hardening exponents to use with

eqns.(2) and (4).

Table 1 Stress exponents of higher order terms, Mode I, plane strain

n s 1 =-1/(n+1) s 2 s 3

(HRR values)

3 -0.25 -0.01284 0.2243

4 -0.2 0.03282 0.2656

5 -0.1666 0.05456 0.2758

10 -0.0909 0.06977 0.2304

13 -0.07143 0.06468 O. 2008

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