Astm stp 1020 1989

STP 1020

Fracture Mechanics:

Perspectives and Directions

(Twentieth Symposium)

Robert P. Wei and Richard P. Gangloff, editors

1916 Race Street

Philadelphia, PA 19103

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ASTM Publication Code Number (PCN: 04-010200-30)

ISBN: 0-8031-1250-5

ISN: 1040-3094

NOTE

The Society is not responsible, as a body,

for the statements and opinions

advanced in this publication.

Peer Review Policy

Each paper published in this volume was evaluated by three peer reviewers. The authors

addressed all of the reviewers' comments to the satisfaction of both the technical editor(s)

and the ASTM Committee on Publications.

The quality of the papers in this publication reflects not only the obvious efforts of the

authors and the technical editor(s), but also the work of these peer reviewers. The ASTM

Committee on Publications acknowledges with appreciation their dedication and contribution

of time and effort on behalf of ASTM.

Printed in Ann Arbor, MI

November 1989

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Foreword

The Twentieth National Symposium on Fracture Mechanics was held on 23-25 June 1987

at Lehigh University, Bethlehem, Pennsylvania. ASTM Committee E-24 on Fracture Testing

was the sponsor of this symposium. Robert P. Wei, Lehigh University, and Richard P.

Gangloff, University of Virginia, served as coeditors of this publication. Robert P. Wei also

served as chairman of the symposium.

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Contents

Overview

PART I--Invited Papers

ANALYTICAL FRACTURE MECHANICS

Fracture Mechanics in Two Decades--GEORGE C. SIH

Weight Function Theory for Three-Dimensional Elastic Crack Analysis--

JAMES R. RICE

NONLINEAR AND TIME-DEPENDENT FRACTURE MECHANICS

Softening Due to Void Nucleation in Metals--JOHN W. HUTCHINSON

AND VIGGO TVERGAARD

Results on the Influence of Crack-Tip Plasticity During Dynamic Crack

Growth--L. B. FREUND

MICROSTRUCTURE AND MICROMECHANICAL MODELING

Creep Crack Growth--HERMANN RIEDEL

The Role of Heterogeneities in Fracture--nLi s. ARGON

FATIGUE CRACK PROPAGATION

Mechanics and Micromechanics of Fatigue Crack Propagation--KEISUKE TANAKA

Microstructure and the Fracture Mechanics of Fatigue Crack Propagation--

E. A. STARKE~ JR.~ AND J. C. WILLIAMS

ENVIRONMENTALLY ASSISTED CRACKING

Microchemistry and Mechanics Issues in Stress Corrosion Cracking--

RUSSELL H. JONES, MICHAEL J. DANIELSON, AND DONALD R. BAER

Environmentally Assisted Crack Growth in Structural Alloys: Perspectives

and New Directions---ROBERT P. WEI AND RICHARD P. GANGLOFF

101

127

151

184

209

233

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FRACTURE MECHANICS OF NONMETALS AND NEW FRONTIERS

The New High-Toughness Ceramics--A. G. EVANS 267

PART II--Contributed Papers

ANALYTICAL FRACTURE MECHANICS

Stress-Intensity Factors for Small Surface and Corner Cracks in Plates--

IVATURY S. RAJU, SATYA N. ATLURI, AND JAMES C. NEWMAN, JR.

Intersection of Surface Flaws with Free Surfaces: An Experimental Study--

C. W. SMITH, T. L. THEISS, AND M. REZVANI

An Efficient Finite-Element Evaluation of Explicit Weight Functions for

Mixed-Mode Cracks in an Orthotropic Material--GEORGE T. SHA,

CHIEN-TUNG YANG, AND JAMES S. ONG

Automated Generation of Influence Functions for Planar Crack

Problems--ROBERT A. SIRE, DAVID O. HARRIS AND ERNEST D. EASON

NONLINEAR AND TIME-DEPENDENT FRACTURE MECHANICS

Fracture Toughness in the Transition Regime for A533B Steel: Prediction of

Large Specimen Results from Small Specimen TestS--TERRY INGHAM,

NIGEL KNEE, IAN MILNE, AND EDDIE MORLAND

Plastic Collapse in Part-Wall Flaws in PlateS--ANTHONY A. WILLOUGHBY

AND TIM G. DAVEY

A Comparison of Crack-Tip Opening Displacement Ductile Instability

Analyses--J. ROBIN GORDON AND STEPHEN J. GARWOOD

MICROSTRUCTURE AND MICROMECHANICAL MODELING

Effect of Void Nucleation on Fracture Toughness of High-Strength

Austenitic Steels--PATRICK T. PURTSCHER, RICHARD P. REED,

AND DAVID T. READ

Dynamic Brittle Fracture Analysis Based on Continuum Damage Mechanics--

ER-PING CHEN

Effect of Loading Rate and Thermal Aging on the Fracture Toughness of

Stainless-Steel Alloys--WILLIAM J. MILLS

FATIGUE CRACK PROPAGATION

Fatigue Crack Growth Under Combined Mode I and Mode II Loading--

STEFANIE E. STANZL, MAXIMILIAN CZEGLEY, HERWIG R. MAYER,

AND ELMAR K. TSCHEGG

297

317

327

351

369

390

410

433

447

459

479

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On the Influence of Crack Plane Orientation in Fatigue Crack Propagation

and Catastrophic Failure--LESLIE BANKS-SILLS AND DANIEL SCHUR 497

Fracture Mechanics Model of Fatigue Crack Closure in Steel--

YOICHI TANAKA AND ISAO SOYA 514

A Finite-Element Investigation of Viscoplastic-lnduced Closure of Short

Cracks at High Temperatures--ANTHONY PALAZOTFO AND E. BEDNARZ

Crack Opening Under Variable Amplitude Loads--FARREL J. ZWERNEMAN

AND KARL H. FRANK

530

548

ENVIRONMENTALLY ASSISTED CRACKING

Strain-Induced Hydrides and Hydrogen-Assisted Crack Growth in a

Ti-6AI-4V AUoy--SHU-JUN GAO, HAN-ZHONG XIAO, AND XIAO-JING WAN

Gaseous-Environment Fatigue Crack Propagation Behavior of a Low-Alloy

Steel--P. K. LIAW, T. R. LEAX, AND J. K. DONALD

569

581

The Crack Velocity-K~ Relationship for AISI 4340 in Seawater Under Fixed

and Rising Displacement--RONALD A. MAYVILLE, THOMAS J. WARREN,

AND PETER D. HILTON 605

Influence of Cathodic Charging on the Tensile and Fracture Properties of

Three High-Strength Steels--VERONIQUE TREMBLAY, PHUC NGUYEN-DUY,

AND J. IVAN DICKSON 615

Threshold Crack Growth Behavior of Nickel-Base Superalloy at Elevated

Temperature--NOEL E. ASHBAUGH AND THEODORE NICHOLAS

FRACTURE MECHANICS OF NONMETALS AND NEW FRONTIERS

628

Strength of Stress Singularity and Stress-lntensity Factors for a Transverse Crack

in Finite Symmetric Cross-Ply Laminates Under Tension--JIA-MIN BAI

AND TSU-TAO LOO 641

Fracture Behavior of Compacted Fine-Grained SoiIS--HSAI-YANG FANG,

G. K. MILROUDIS, AND SIBEL PAMUKCU 659

Fracture-Mechanics Approach to Tribology Problems--YUKITAKA MURAKAMI

AND MOTOHIRO KANETA 668

INDEXES

Author Index 691

Subject Index 693

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STP1020-EB/Nov. 1989

Overview

Fracture mechanics forms the basis of a maturing technology and is used in quantifying

and predicting the strength, durability, and reliability of structural components that contain

cracks or crack-like defects. First utilized in the late 1940s to analyze catastrophic fractures

in ships, the fracture mechanics approach found applications and increased acceptance in

the aerospace industries through the late 1950s and early 1960s. Much of the early work was

spearheaded by Dr. George R. Irwin and his co-workers at the U,S. Naval Research Laboratory and was nurtured through a special technical committee of ASTM, chaired by Dr.

John R. Low. Over the past 20 years, fracture mechanics has undergone major development

and has become an important subdiscipline in solid mechanics and an enabling technology

for materials development, component and system design, safety and life assessments, and

scientific inquiries. The contributions are now utilized in the design and analysis of chemical

and petrochemical equipment, fossil and nuclear power generation systems, marine structures, bridges and transportation systems, and aerospace vehicles. The fracture mechanics

approach is being used to address all of the major mechanisms of material failure; namely,

ductile and cleavage fracture, stress corrosion cracking, fatigue and corrosion fatigue, and

creep cracking, From its origin in glass and high strength metallic materials, the approach

is currently applied to most classes of materials; including metallic materials, ceramics,

polymers, composites, soils, and rocks.

The first National Symposium on Fracture Mechanics was organized by Professor Paul

C. Paris, and was held on the campus of Lehigh University in June 1967. The National

Symposium has gained prominence and international recognition and serves as an important

international forum for fracture mechanics research and applications under the sponsorship

of ASTM Committee E-24 on Fracture Testing. It has been held annually since 1967, with

the exception of 1977. The growth of the National Symposium has paralleled the development

and utilization of fracture mechanics. Landmark papers and Special Technical Publications

have resulted from this Symposium series. It is appropriate that this, the 20th anniversary

meeting of the National Symposium, be held again at Lehigh University and that the proceedings be archived in an ASTM book.

At this anniversary, following from two decades of intense and successful developments,

it is appropriate and timely to conduct an introspective examination of the field of fracture

mechanics and to define directions for future work. The Organizing Committee, therefore,

set the following goals for the 20th National Symposium on Fracture Mechanics, Fracture

Mechanics: Perspectives and Directions:

1. To provide perspective overviews of major developments in important areas of fracture

mechanics and of associated applications over the past two decades.

Copyright9 by ASTM International

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2 FRACTURE MECHANICS: "I'WENTIETH SYMPOSIUM

2. To highlight directions for future developments and applications of fracture mechanics,

particularly those needed to encompass the nontraditional areas.

To achieve the stated goals, the technical program was organized into the following six

sessions:

(a~ Analytical Fracture Mechanics

(b) Nonlinear and Time Dependent Fracture Mechanics

(d) Fatigue Crack Propagation

(e) Environmentally Assisted Cracking

(f) Fracture Mechanics of Nonmetals and New Frontiers

This Special Technical Publication accurately adheres to the objectives and approach of

the Symposium. The twelve invited review papers, organized topically in the order of their

presentation in one section, provide authoritative and comprehensive descriptions of the

state of the art and important challenges in each of the six topical areas. The worker new

to the field will be able to survey current understanding through the use of these seminal

contributions. The thirty-one contributed papers, organized topically in a separate section,

provide reports of current research. These papers are of particular importance to fracture

mechanics researchers.

Although each manuscript was subjected to rigorous peer reviews in accordance with

ASTM procedures, the authors of invited review papers were encouraged to respond

thoughtfully to the reviewers comments and suggestions, but were granted considerable

latitude to exercise their judgment on the final manuscript. This action was taken by the

Editors to preserve the personal (vis-d-vis, a consensus) perspective of the individual experts,

and to accurately reflect agreements and differences in opinion on the direction of future

research. The invited papers, therefore, need to be read in this context. The opinions

expressed and positions taken by the individual authors are not necessarily endorsed by the

author's peers, the Editors, or the ASTM.

The review papers document the significant progress achieved over the past two decades

of active research in fracture mechanics. Collectively, the authors provide compelling arguments for the need of continued development and exploitation of this technology, and

insights on the challenges that must be faced. Some of the specific challenges are as follows:

1. On the analytical front, we must expand upon the effort to integrate continuum fracture

mechanics analyses with the microscopic processes which govern local fracture at the

crack tip.

2. In the area of advanced heterogeneous materials, fracture mechanics methods must

be further developed and applied to describe novel failure modes. Claims of high

performance for these materials must be supported by quantitative and scalable characterizations of fracture resistance that is relevant to specific applications.

3. In the area of subcfitical crack growth (for both fatigue and sustained-load crack growth

in deleterious environments and at elevated temperatures), the gains in understanding

from multidisciplinary (mechancis, chemistry, and materials science) research must be

reduced to practical life prediction methodologies. The critical issues of formulating

mechanistically based procedures that enable the extrapolation of short-term laboratory

data in predicting long-term service performance (that is, from weeks to decades) must

be addressed.

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OVERVIEW 3

4. In the area of education, we must better inform engineering students and practitioners

on the interdisciplinary nature and intricacies of the material failure problem, whether

by subcritical crack growth or by catastrophic defect-nucleated fracture. We must also

continue to develop and to communicate governing ASTM standards to the engineering

community.

This volume demonstrates that the existing fracture mechanics foundation is well positioned

to meet these challenges over the next decade.

Professors Paul C. Paris and George R. Irwin provided important insights during the

closing of the symposium and at the Conference Banquet. The banquet provided an opportunity for the awarding of the first ASTM E-24 Fracture Mechanics Medals to Professors

Irwin and Paris.

We gratefully acknowledge the contributions of the Symposium Organizing Committee:

R. Badaliance (NRL), T. W. Crooker (NASA Headquarters), F. Erdogan (Lehigh University) and R. H. Van Stone (GE-Evandale), and of the Session Chairmen: R. Badaliance,

R. J. Bucci (ALCOA), S. C. Chou (AROD), F. Erdogan, J. Gilman (EPRI), R. J. Gottschall

(DOE/BES), D. G. Harlow (Lehigh), C. Hartley (NSF), R. Jones (EPRI), R. C. Pohanka

(ONR), A. H. Rosenstein (AFOSR), A. J. Sedriks (ONR), D. P. Wilhelm (Northrop); the

assistance of the Local Committee: Terry Delph, Gary Harlow, Ron Hartranft, and Gary

Miller; the hospitality of Lehigh University; and especially the skill and devotion of the

Symposium Secretary, Mrs. Shirley Simmons.

We particularly acknowledge the work of our many colleagues who participated as authors,

as speakers, and in the technical review process; the support of the ASTM staff; and the

able editorial assistance provided by Helen Hoersch and her colleagues.

Financial support by the Office of Naval Research is gratefully acknowledged. All of the

funds were used to provide matching support to graduate students across the United States

so that they can participate in this introspective review of fracture mechanics. Nearly 30

students participated, and all of them expressed their appreciation for the opportunity to

attend.

Robert P. Wei

Lehigh University, Bethlehem, PA.

Richard P. Gangloff

University of Virginia, Charlottesville, VA.

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PART I

Invited Papers

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Analytical Fracture Mechanics

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George C. Sih t

Fracture Mechanics in Two Decades

REFERENCE: Sih, G. C., "k'Sracture Mechanics in Two Decades," Fracture Mechanics: Perspectives and Directions (Twentieth Symposium), ASTM STP 1020, R. P. Wei and R. P.

Gangloff, Eds., American Society for Testing and Materials, Philadelphia, 1989, pp. 9-28.

ABSTRACT: A brief historical and technical perspective precedes emphasizing the need to

understand some of the fundamental characteristics of fracture. What the state of the art was

two decades ago is no longer adequate in the era of modern technology. Observed mechanisms

of failure at the atomic, microscopic, and macroscopic scale will continue to be elusive if the

combined interaction of space/time/temperature interaction is not considered. The resolution

of analysis, whether analytical or experimental or both, needs to be clearly identified with

reference to local and global failure. Microdamage versus macrofracture is discussed in connection with the exchange of surface and volume energy, which is inherent in the material

damage process. This gives rise to dilatation/distortion associated with cooling/heating at the

prospective sites of failure initiation. Analytical predictions together with experimental results

are presented for the compact tension and central crack specimens.

KEY WORDS: surface and volume energy, change of volume with surface, dilatation and

distortion, cooling and heating, energy dissipation, material damage, space/time/temperature

interaction, thermal/mechanical effects, crack initiation and growth

The rapid advance of technology in the past two decades has substantially altered the

performance limits and reliability objectives dealing with the application of advanced materials. More and more of the conventional metals, whose mechanical and failure behavior

are characterized by macroparameters in an homogeneous fashion, are being replaced by

multi-phase materials such as composites that reflect a complex dependence on their constituents or microstructure. Past methodologies [1-3] which relied on a single-parameter

characterization are no longer adequate as the new materials become more applicationspecific. New concepts are needed to replace the old ones, making this communication on

fracture mechanics quite timely.

Fracture mechanics became a recognized discipline after World War II because of the

inability of continuum-mechanics theories to address failure by unexpected fracture, a situation that occurs less frequently as the trade-off between strength and fracture toughness

is now better understood. Research activities have fallen into two categories: material science

and continuum mechanics. The former seeks to look at damage from a microscopic or

atomistic viewpoint or both, determining what happens to the atoms and grains of a solid,

which is beyond the scope of this discussion. The latter attempts to formalize the results of

macroscopic experiments without probing very deeply into the origin and physics of how

failure initiates. It would be desirable to have a unique approach such that the hierarchy of

the physical damage mechanisms, each dominant over a certain range of load-time history

Professor of mechanics and director of the Institute of Fracture and Solid Mechanics, Packard

Laboratory No. 19, Lehigh University, Bethlehem, PA 18015.

Copyright9 by ASTM International

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10 FRACTURE MECHANICS: TWENTIETH SYMPOSIUM

can be assessed quantitatively when material or geometry or both are changed. This goal

will be emphasized.

The translation of data collected from specimens with or without a crack to the design of

larger structural components has been problematic. It is the common practice to employ

both uniaxial and fracture data for predicting structural behavior. This is an oversupply 2 of

input data and introduces arbitrariness and inconsistency into the analysis. Linear elastic

fracture mechanics (LEFM) based on the toughness parameter Kk or Gic merely addresses

a go and no-go situation. It implies a unique amount of energy release for a small crack

extension that triggers rapid fracture. Such a concept obviously has no room in situations

where a crack grows slowly at first and then rapidly. The irresistible urge to characterize

ductile fracture for the development of small specimen tests without an understanding of

the underlying physics and principles has hindered progress. Among the two leading candidates were the crack opening displacement (COD) [6] and J-integral approach [7]. The

COD measurements, being sensitive to changes in strain rate, triaxiality of stress, specimen

size and geometry, etc., served little or no useful purpose in design. Application of the

J-integral caused a great deal of confusion because the idea applies only to elastic deformation

and the same symbol J has been used [7,8] to represent the variations of areas under the

load-extension versus crack length curve that include the effect of permanent deformation.

What should be remembered is that the formalism of J precludes the distinction 3 of energy

used in permanent deformation and crack extension that are interwoven in the experimental

data. It would, therefore, be totally misleading to interpret J as the crack driving force

except in the elastic case for then it is identically equal to G. The experimental data [8] did

not yield a linear relation between J and crack growth. Alternate forms of dJ/da were

suggested [9] and resulted in nonlinear crack growth resistance curves. 4

The Charpy V-Notch (CVN) impact test is another empirical method for collecting data

on dynamic fracture with no consideration given to rate effect? It has been used for establishing the nil ductility temperature (NDT). The rate at which energy is actually used to

create dynamic fracture must be isolated from other forms of energy dissipation such as

plastic deformation, acoustic emission, etc., in order to obtain a reliable assessment of the

time-dependent failure process. Current research [13] has not yet recognized that dynamic

fracture is inherently load dependent and cannot be characterized by a single parameter

such as/(1o. One of the major shortcomings of the conventional approaches is that they

failed to separate the fracture energy from other forms of energy dissipation. This is why

COD, J, CVN, KID, etc., are all sensitive to change in loading and specimen geometry and

size. In this regard, they can hardly be claimed as fracture toughness parameters; much less,

as material constants. A detailed discussion of their limitations can be found in Refs 14 and

15.

The empirical "4th power law" [16] on relating the crack growth rate da/dN and change

2 There are no difficulties to predict the fracture behavior of cracked specimens by using uniaxial

data only [4,5].

3 The separation of energy dissipated by permanent deformation and crack extension is not additive.

This was not recognized by those who attempted to formally include the so-called plastic deformation

term in the J-integral approach.

4 Data collected on precracked polycarbonate specimens [10] showed that the dJ/da = const, condition was not satisfied. This was pointed out and discussed in Ref 11. The strain energy density factor

S, when plotted against crack growth, did yield a linear relationship such that specimen size and loading

rate effects can then be easily resolved by interpolation.

5 The Charpy impact energy normally specified in foot-pounds is not sufficient to describe dynamic

fracture. The rate of energy used to initiate dynamic fracture as distinguished from that dissipated in

plastic deformation and other forms is the relevant quantity [12].

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SIH ON FRACTURE MECHANICS IN TWO DECADES 11

in Mode I stress-intensity factor AK continues to dominate the literature on fatigue. Such

a correlation was found to be invalid when moisture effects were accounted for [17]. A

multitude of the so-called fatigue crack propagation laws have been proposed to correct

separately for the mean stress, specimen thickness, temperature, crack size, crack opening,

or closure effects. None of them had any theoretical basis. The majority applied elasticity

to a process that is inherently dissipative. Thresholds in AK were found to disappear when

the same crack growth data were replotted against change in energy release rate, AG. The

influence of mean stress on da/dN reversed in trend for some metals. Special treatments

were suggested for "small or short cracks" as data showed considerable scatter on the

da/dN versus AK plot. It was only discovered later that AK was simply the wrong parameter to use [18]. The phenomenon of crack retardation due to occasional overload in fatigue

has not been explained adequately.

Contrived explanation and data gathering in the absence of theoretical support are destined

to fall by the wayside. Unless the basic fundamentals of energy dissipation associated with

material damage are understood and quantified, fracture mechanics will not withstand the

rigors of progress. Verbal or elegant, or both, mathematical descriptions of already known

and observed events cannot be considered original research for they merely serve as a means

of bookkeeping. Predictive capability is needed such that simple test data can be used to

forecast the behavior of more complex systems regardless of whether they are loaded monotonically, repeatedly, or dynamically. A unified approach for addressing material damage

at the atomic, microscopic, and macroscopic scale levels is long overdue. With this objective

in mind, a few selected topics are chosen to illustrate some of the fundamental aspects of

the fracture process that are not commonly known.

Micro- and Macro-Mechanics of Fracture

Fracture 6 is a process that involves the creation of free surface at the microscopic and

macroscopic scale level. It entails a hierarchy of failure modes, each associated with a certain

range of stress, strain rate, temperature, and material type. Examinations are frequently

traced to the ways with which damages are influenced by the microstructure. The empirical

results have been couched in terms of void growth, cleavage failure, brittle fracture, ductile

fracture, etc. Although observations can be made on failure mechanisms, it has been very

difficult to construct a quantitative theory of failure or damage that can relate the microscopic

entities to the useful macroscopic variables. These difficulties can, in retrospect, be identified

with the inability of theories such as elasticity, plasticity, etc., to account for the irreversible

nature of thermal/mechanical interactions that are inherent in the fracture process. These

effects are assumed to be mutually exclusive in classical mechanics that invoke the independence of surface and volume energy or the decoupling of mechanical deformation and

thermal fluctuation. 7 Addition of the different energy forms leaves out coupling effects that

are, in themselves, problematic. Quantitative assessment of the fracture process cannot be

achieved without an understanding of the underlying physics.

Surface Energy Density

Prior to modeling of the fracture process, it would be instructive to specify the resolution

of the analysis with reference to defect size and microstructure detail. Figures la to lc

6 In this communication, fracture pertains to material discontinuities at the microscopic and macroscopic level. Imperfections at the atomic level should be referred to as vacancies, dislocations, etc.

7 Isothermal condition can only be realized conceptually in the limit as disturbances or changes become

infinitesimally small.

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