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HARDENING AND

STABLE TEARING EFFECTS IN

FITNESS-FOR-SERVICE ASSESSMENT:

Progress Report

D. T. Read

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

May 1987

-QC

100

- U 5 6

#86-3045

1987

NBSIR 86-3045

Research Information Center

National bureau oi Standards

Gaithersburg, Maryland 20899

STRAIN HARDENING AND

STABLE TEARING EFFECTS IN

FITNESS-FOR-SERVICE ASSESSMENT:

Progress Report

D. T. Read

Fracture and Deformation Division

Institute for Materials Science and Engineering

National Bureau of Standards

Boulder, Colorado 80303

May 1987

Sponsored by

David Taylor Naval Ship Research and Development Center

Annapolis, Maryland 21402

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

1. INTRODUCTION 1

2 . LITERATURE REVIEW ON DUCTILE TEARING AND TEARING INSTABILITY ... 3

2.1 Introduction 3 2.2 Basic Concepts of Tearing Instability 4

2.2.1 Fundamentals 4

2.2.2 Well-Established Aspects 5 2.3 Problems with Tearing Instability Theory 6 2.3.1 Definition and Meaning of the J- Integral During Tearing 6 2.3.2 Local and Global Instability 8 2.3.3 Specimen/Structure Size Effect 10

2.3.4 Treatment of Flaw Size 10

2.3.5 Flaw Assessment Procedures 11

2.4 Material Tearing Properties 11

2.4.1 Geometry Dependence 11

2.4.2 Tearing Properties Modeling 12

2.5 Conclusions of Literature Review 13

2.6 References 14

3. STRENGTH AND DUCTILITY OF CRACKED TENSILE PANELS 21

3.1 Introduction 21

3.1.1 Material and Specimens 22

3.1.2 Measurements, Apparatus, and Procedures 25

3.1.3 Results 27

3.1.4 Discussion 37

3.2 Conclusions 39

3.3 Acknowledgments 39

3.4 References 39

4. APPLIED J-INTEGRAL VALUES IN ASTM A-710 STEEL PANELS 41

4.1 Abstract 41

4.2 Introduction 41

4.3 Theoretical Background 42

4.4 Material 46

4.5 Specimens, Apparatus, Instrumentation, and Techniques 49

4.6 Results and Discussion 55

4.7 Conclusions 6 3 iii
4.8

4.9

4.10

5.

6 . 6.1

6 . 1.1

6 . 1.2

6.2

6.3

6.4

Acknowledgments 64

References 64

Appendix 66

ESSENTIAL WORK OF FRACTURE (we ) VERSUS ENERGY DISSIPATION RATE

(J c ) IN PLANE STRESS DUCTILE FRACTURE 99

Abstract 99

Introduction 99

Specimens and Experimental Procedures 100

Results 100

Discussion 103

Conclusions 108

Acknowledgments 109

References 109

POTENTIAL DROP MEASUREMENTS OF CRACK LENGTH IN TENSILE PANELS ..110

Calibration Formulae 110

Single Pair of Pickups 110

Four Pairs of Pickups Ill

Experimental Techniques 112

Results 114

References 114
STRAIN HARDENING AND STABLE TEARING EFFECTS IN FITNESS -FOR- SERVICE ASSESSMENT:

PROGRESS REPORT

D.T. Read

Fracture and Deformation Division

National Bureau of Standards

Boulder, Colorado 80303

This report describes studies done to provide information on how to

account for material strain-hardening and tearing in fitness-for-service

assessment. Included are a literature review, a study of the strength and

ductility of cracked tensile panels under compliant loading, a report on applied J- integral measurements in an HSLA steel, a study of the relationship of the essential work of fracture to the J- integral, and a description

of potential drop techniques for crack length measurement in double- edge

notched tensile panels.

Key words: assessment curve; ductility; fracture; J- integral; R- curve;

toughness

.

1 . INTRODUCTION

The fitness-for-service concept implies that geometrical flaws in

structural materials are acceptable as long as such flaws do not reduce

structural strength, ductility, or functional capability below tolerable

limits. Accordingly, with regard to tearing, a slight amount of slow stable

ductile tearing at a crack tip does not in itself threaten structural

integrity any more than did the initial existence of the crack. Modern

tough metals prevent catastrophic flaw growth under overstrains, first by

blunting, and then, for severe overstrains, by slow, stable, ductile

tearing. As test techniques improve, ever smaller amounts of tearing are detected at ever lower toughness levels. Sometimes materials that are known

to have excellent toughness in practice show detectable tearing at very low

toughness levels. Fitness-for-service analysis of slow stable ductile

tearing can extend the demonstrable margin of safety of a structure above

the initiation of subcritical tearing, to allow fuller use of real mater' .

1

, toughness and avoid artificial problems from improved test methods that

1
detect very small amounts of tearing. Because unstable tearing is, by

definition, out of control, it must always be avoided. Further, the extent

of stable tearing must be restricted to safe levels that do not threaten

structural fitness for service. Tearing considerations influence the choice

of critical J level, J c , for use in material evaluation, and they can provide guidance on how material tearing resistance should be weighted

against other desirable material properties in material selection.

Tearing and tearing instability in elastic -plastic and ductile fracture

in thick specimens (as opposed to thin sheet) has been an active research

area since the mid-1970s. Instability in thin sheets was studied even

earlier, for aerospace applications. Paris, Hutchinson, and Rice are among

the eminent names in fracture associated with the early studies of stable

and unstable ductile tearing. Their research sought to extend the use of

the J- integral, J, as a fracture parameter beyond the initiation of tearing

at J j c j to finite values of crack extension, Aa. Material resistance to

tearing was expressed as a resistance curve, called the J-R curve, in which

J was plotted against Aa. The slope of the material J-R curve was converted

to a dimensionless tearing modulus Tmat = (E/<7y) (dJ/da) , where E is Young's

modulus and Oy is material flow stress. Once material resistance to tearing

had been characterized, this resistance could be compared to the driving

force for tearing, as produced by specially designed compliant test fixtures. Quantitative characterization of the driving force for fracture in

terms of the applied tearing modulus, Tapp , was developed as the natural

complement to material resistance to tearing, Tmat . Tearing becomes

unstable when Tapp

exceeds Tmat . This report describes studies done to provide information on how to

account for material strain-hardening and tearing in fitness-for-service

assessment. Included are a literature review, a study of the strength and

ductility of cracked tensile panels under compliant loading, a report on applied J- integral measurements in an HSLA steel, a study of the relationship of the essential work of fracture to the J- integral, and a description

of potential drop techniques for crack length measurement in double- edge

notched tensile panels. References and figures are listed at the end of

each chapter.

2
2 . LITERATURE REVIEW ON DUCTILE TEARING AND TEARING INSTABILITY

2.1 Introduction

A literature search was carried out to find reports of previous studies

relevant to the present goal of developing a procedure for applying the

tearing modulus - tearing instability concept to failure prediction and

failure avoidance in naval materials and structures. Such a procedure must

be based on the fundamentals of tearing behavior, must account for dependence of J-R curves on structural, as well as specimen, geometry and size,

and must be adaptable to new materials.

Two indices were searched, the Metals Abstracts Index and the NASA

Index. The key words used were tearing modulus, R-curve, and stability.

A total of 276 references were found after discarding several that were

clearly extraneous. For present purposes, methods applicable to thin

sheets, properties of specific materials measured using only one specimen

geometry, and test methods themselves are not directly relevant. One

hundred and forty references on aspects of fracture not specifically

relevant to the goals of the present study, including sixteen entries on tearing of thin sheets, were excluded from further consideration here.

Thin sheets tend to behave in a more ductile manner than thick plates

of the same material because thin sheets experience less through- thickness

constraint. Treatment of ductile tearing and instability in thin sheets was developed in the 1950 's and 1960's for aerospace applications. Although the

thin-sheet technology cannot be simply adapted for use in thick plates, it

has served as a guide and a precedent for studies of tearing in thick

plates

.

The other excluded studies were largely measurements or estimates of

the J-R curve for a given material using a single specimen size.

The remaining entries included eighteen on fundamentals, thirty-seven

on geometry dependence, and fourteen on modeling of material tearing modulus

based on more basic material properties. After eliminating duplicates,

eighteen remained on fundamentals [1-18], twenty-seven remained on geometrv

dependence [19-45], and eleven remained on modeling [46-56], Several key

papers introducing the current concept of tearing instability are found in

3
the book entitled Elastic-Plastic Fracture- -Special Technical Publication

668 . edited by J. D. Landes, J. A. Begley, and G. A. Clarke, published by

the American Society for Testing and Materials.

2.2 Basic Concepts of Tearing Instability

This report is not intended to be an introduction to the subject, but,

for completeness, some of the fundamental concepts of tearing instability

theory will be reviewed here. Then, the well-established aspects of the

theory will be summarized.

2.2.1 Fundamentals

Recent attempts to understand, describe, and predict the fracture

process of unstable ductile rupture have utilized the well-known R-curve

approach [57-59]. An R-curve is a plot of some fracture resistance parameter against crack growth. Fracture parameters used have included the

derivative with respect to crack length of energy absorbed (reversibly

and/or irreversibly) by the specimen, stress intensity factor, K, Jintegral, J, crack tip opening displacement, CTOD , and so on. Just as applied stress on a tensile specimen can take on any value up to the maximum

capability of the specimen material, an applied fracture parameter can also

take on any value up to the capability of the specimen material. The

denotation "applied fracture parameter" or "fracture driving force" indicates that the fracture parameter is to be understood in this sense. On the

other hand, certain stress levels are correlated with specific material

responses, such as the yield stress and the ultimate stress. These stress

levels are understood as material properties. Likewise, certain fracture

parameter levels are associated with specific material responses, such as brittle fracture, crack blunting, crack initiation, and ductile tearing.

When a fracture parameter is used to measure the fracture driving force

associated with a certain specific material response, it is called a material fracture resistance parameter, or a toughness. The classic example

of a fracture parameter is G, the derivative with respect to crack length of

elastic potential energy contained in the specimen.

4
The relevance of fracture resistance and fracture driving parameters to

tearing can be clarified by an analysis of the tearing process as follows.

Each increment of crack length can change the fracture driving parameter.

If, for a small increment of crack length, the fracture driving parameter

increases more than the fracture resistance parameter, then another, larger

increment of crack length is predicted. If the driving force parameter

continues to increase faster than the material fracture resistance parameter, the process accelerates and catastrophic ductile rupture occurs. By

plotting fracture driving force curves on the same graph with a material

R- curve, the conditions for instability can be identified.

The R- curve concept has been demonstrated to apply when the J- integral

is used as the fracture driving and fracture resistance parameters [8, 14,

60]. It is not surprising that the R-curve approach using the J-integral

(J-R-curve) works when the method is applied to predict instability in the

very same specimen geometry as the material R-curve is measured. Indeed,

this success would be expected from the principles of the mechanics of

linear systems with one nonlinear element for any parameter which increased

monotonically with crack length, as long as it was consistently calculated

and applied [ 61 ]

.

2.2.2 Well-Established Aspects

There is general agreement in the literature that a material tearing

modulus, Tmat , that characterizes material resistance to ductile tearing

under elastic-plastic or fully plastic strain in terms of the J-integral,

can be at least operationally defined. The material tearing modulus is

calculated directly from the measured J-R curve. A standard method for

measuring J-R curves has been written, and verified by a round- robin test

series. It is recognized that the material tearing modulus may depend on specimen size and geometry. It is recognized that the J-R curve is, in

general, curved, so that Tmat depends on J . It has been found convenient to use plots known as J-T plots, which have J on the y-axis and T on the

x-axis, to determine the conditions for equality of Tmat- and Ta pp

(Fig. 1).

On such plots the material property is represented by a Jmat' Tmat curve and

the applied conditions are represented by a J app" Tapp curve . Where these

5
Tapp , so that the necessary and sufficient conditions for fracture are satisfied. The various curves on such a plot can be used to identify safe

and unsafe conditions with respect to fracture by ductile tearing.

2.3 Problems with Tearing Instability Theory

Because the mechanics of elastic -plastic solids has proved to be a difficult field, with analytic solutions rarely available for problems of

interest, especially those involving varying through- thickness stress, a complete solution to the general problem of propagating cracks in elastic

plastic media is not expected to be available soon. Several specific

problems with tearing instability theory have been encountered.

The present obstacles to use of the J-R-curve approach can be con- trasted with the current understanding of static cracks. Methods are cur- rently available for calculating the fracture driving parameter in terms of

the J-integral for all relevant types of geometries [62]. A standard for

measurement of Jj c has been established [63]. It appears that Jj c values

obtained in standard tests are conservative, that is, lower than or equal to

values obtained for other geometries. On the other hand, the ranges of

applicability of present methods of calculating applied J- integrals for cases of growing cracks have not been verified, and the conservatism of

standard- specimen J-R curves is open to question, especially for thin

specimens of ductile material.

2.3.1 Definition and Meaning of the J- Integral During Tearing

The most fundamental of these problems is that the J-integral, as formally defined [64], applies to non-linear elasticity but not to plasticity as found in real metals. Once stable tearing occurs, the original

J-integral no longer gives the amplitude of the strain singularity at the

crack tip, because of the unloading of the plastically strained region

formed at the original crack tip. This implies some ambiguity in the

meaning of the pseudo J- integrals used for tearing instability. Extensions

and modifications of the J-integral are discussed in the literature. A

correction procedure [65] for J for use in J-R curve measurements has gained

6
Integral,

J

Tearing Modulus, T

Figure 1. Schematic J-T diagram.

7
acceptance, but the final significance of the corrected J produced by this

correction is still unclear, although it satisfies the Rice criterion for a valid expression for the J- integral during tearing.

Because the J- integral no longer specifically characterizes the strain

field at the crack tip after tearing has occurred, the geometry- independence

of J-R curves is open to serious question. The question of geometrydependence of R-curves is discussed in a separate section below.

The amount of tearing permissible before J may become inapplicable has

been estimated to be rather small [14]. This problem is avoided in K-R

curves for ultra-high-strength thin sheet materials, because the deformation

is generally linear elastic, and the stress intensity factor K appears to

adequately characterize the stress distribution around the crack tip. This

results in K-R curves which are sufficiently geometry- independent , as long

as the sheet thickness remains constant. However, many modern structural

materials possess so much ductility that the strain fields are no longer

generally linear elastic. These materials, of course, have higher toughness

than those described by K-R curves. But the analytical framework needed to

exploit the toughness of these materials in cases of growing cracks does not

yet exist.

2.3.2 Local and Global Instability

Tearing instability theory can be applied to prediction of global

instability or local instability. Laboratory tests typically involve global

instability, while structures pose problems of local instability.

In ductile fracture, instability has been defined as "a sudden increase

in crack size and deformation of the test specimen" [17]. In J-R curve measurements or in studies of tearing instability using standard testpieces, tearing typically starts after the maximum load is reached. The

first part of a test is always stable. The rate of specimen deformation is

controlled directly by the testing machine. Instability manifests itself

when the deformation rate increases and the load decreases with no change in

the testing machine's rate of travel. The rapid, unstable tearing is

typically clearly distinguishable from the slow stable tearing preceeding

it. This is a global instability, because the limit load of the specimen as

8
a whole is reached and subsequent tearing directly and immediately reduces

the load carrying capacity of the specimen as a whole.

Because of the complexity of most structures, local instability can

occur and must be considered. By definition, such a local instability can

sever only a small part of the structure, at least at first. For instance,

if a part through surface flaw pops through and then arrests, the event

would be a local instability. The damage caused by a local instability may

be acceptable, or, it may be unacceptable in itself, such as a leak in a pressure vessel. Or, the local damage may form a larger crack which

threatens to escalate into a global instability. Local instability can

occur below the limit load of the full structure, for example, at a severe

stress concentrator. In such a case, the structure itself controls Tapp • The situation here is more complex than those covered by the simple theory

where the testing machine compliance controls Tapp up to global instability.

An example was given by Paris et al. in an early paper on tearing instability [14], the example of a deep surface flaw. The compliance of the

testing machine and the overall length of the flawed plate are irrevelant in

this case. The local compliance of the flawed plate controls Tapp

The key features of local and global instabilities are emphasized on

the following table:

Instability type Local Global

Typical example: Complicated structure Simple specimen

Tappcontrolled by: local compliance full specimen and

testing machine

compliance

Load level relative

to global limit load: below identical

9
This table implies that a flaw should be evaluated for stability using

local compliance if the structure as a whole is below its limit load. If

the structure as a whole is at its limit load the full global compliance

must be considered. Of course, a local instability can extend the tearing

far enough to reduce the limit load of the whole structure, causing a potential global instability. This is exactly what consideration of local

instability seeks to avoid.

Development and testing of tearing instability theory is needed to show

how to use concepts proven and data obtained on global instability, the

usual case for material testing, to analyze and predict the occurrence of

local instability in complex structures.

t

2.3.3 Specimen/Structure Size Effect

Use of the J-R curve in design must include by consideration of the

size effect which occurs in the temperature range of the ductile/brittle

transition in steels. In this temperature range, large and small specimens

can have qualitatively different behavior. At a given temperature, cleavage can terminate R-curve behavior at significantly lower values in large

specimens than in small ones. Therefore, one must be assured that the

material is out of the transition range before applying a J-R curve from

small specimens to predictions of the behavior of thick structural sections.

2.3.4 Treatment of Flaw Size

In the first papers describing the fundamentals of tearing instability

theory, simple versions were presented. In these papers, the specimen

stability was independent of flaw size. That is, the flaw size simply

cancelled out. This means that the simple tearing instability theory does

not provide an answer to the question, "How large a flaw can be tolerated?"

The theory must developed further to investigate questions of flaw size.

10
2.3.5 Flaw Assessment Procedures

Tearing instability theory offers a means of assessing structural

stability for J values in excess of Jj c Therefore it can be used in selecting appropriate values of J for use in J-based flaw assessment procedures

such as that embodied in the J- integral estimation curve. One criterion

proposed is that the J value at which Tmat = 50, called J 50 , is appropriate

as a critical J value. Further study of this area is needed. Such studies

are in progress, both in the present program and elsewhere.

2.4 Material Tearing Properties

2.4.1 Geometry Dependence

It has been widely recognized that the geometry- dependence of the

material J-R curve must be understood if tearing instability theory is to

become useful [19-45]. The incentive for using tearing analysis is that a material R-curve measured by standard test procedures can be applied to

predictions of structural instability for geometries different from the test

geometry. The requirements are that the material R-curve must be unique,

that is, the measured curve must actually apply to the other geometries in

question, and that fracture driving parameters can be calculated accurately

as functions of applied stress or strain and crack size for all geometries

of interest, even in the presence of growing cracks.

A precedent for successful treatment of this problem exists. The

R-curve approach has been applied successfully in the aircraft and aerospace

industries for thin sheets of high-strength material of a given thickness.

The fracture driving parameter used is K x , and its applicability is re- stricted to materials where failure occurs at stresses below net section

yielding. The stress intensity factor K x has been found to adequately

characterize the stress distribution around the crack tip, resulting in K-R

curves which are sufficiently geometry- independent , as long as the sheet

thickness remains constant.

11
A crucial test of the method would be the application of an R-curve

measured for one geometry to different geometries. Interesting geometrical

differences would include changes of scale of in-plane dimensions, changes

of loading mode fracture type (for example, predominantly tensile vs predominantly bending), and changes of thickness. Any method which could

handle these three types of geometrical changes, using a single material

R-curve, would have to be judged eminently successful.

The physical causes of R-curve behavior are qualitatively appreciated

at present; however, quantitative methods of calculating material R- curves from specimen geometry and physical, mechanical, and metallurgical properties are not available at present and are unlikely to be available in the near future. Recent studies generally agree that J-R curves for a given

material at a given temperature are independent of in-plane specimen size

and ligament length for compact tensile (CT) specimens of sufficient size

[42]. However, thickness effects have sometimes been found. Changing from

surface -flawed plates to compact tensile specimens was found to have a large

effect on the J-R curve [32]. A round-robin study revealed that J-R curves

in CT specimens differed from those for three-point-bend specimens. On the

other hand, the J-R curve for a pipe in bending agreed with that for CT

specimens when the appropriate equations for J for the pipe were used [62],

Willoughby, Pratt, and Turner [40] have reported that rising R-curves,

that is, J values increasing with crack length, occur because of "an

increase in remote plastic work," rather than changing behavior at the crack

tip. They noted that this work is, in general, geometry- dependent

.

The present status is that the dependence of J-R curves on specimen

size and geometry is a subject of current research. It is not yet known how

to establish conservative limits on R-curves. Therefore empirical checks on

the actual J-R curve for various geometries of interest are needed. Again,

studies are in progress, both within the current program and elsewhere.

2.4.2 Tearing Properties Modeling

Several papers have appeared in the literature in which the J-R curve

is calculated from more fundamental properties [46-56]. The situation is some what analogous to the relationship between an engineering stress-strain

12
curve and a true stress -strain curve. The true curve is the material

property. Different engineering curves are appropriate for different

specimen geometries such as tension, torsion, and shear.

Analogously, the measured J-R curves are taken as specimen- specific

manifestations of more fundamental properties, such as critical strain or critical crack stretch. Such models usually can fit observed J-R curves

quite well. They indicate that J-R curves are probably geometry- dependent

.

But no clear candidate for the fundamental fracture parameter has emerged.

2.5 Conclusions of Literature Review

Based on a literature review on the subject of ductile tearing, the

following conclusions can be drawn: The J-R curve has been established as a measurement of material resistance to tearing. Tearing instability theory

is well-established as a potential means of analyzing the possibility of

unstable ductile tearing, in which the J-R curve quantifies material tearing

resistance. The major obstacles to application of tearing instability

theory are lack of information about Tmat and Tapp

for specific situations.

In order to develop the treatment of tearing to a state where it can be

conveniently and generally used in the evaluation of structural materials,

the following issues must be addressed further:

1 . Identification of appropriate qualitative use of Tmat for predicting

material performance in the presence of cracks and estimating tolerable

crack sizes;

2. Procedures for quantitative use of tearing instability theory for

predicting material performance in the presence of cracks and calculating tolerable crack size and required toughness levels. This issue can be broken down as follows:

a. Proper and workable procedures for determination of Ta pp

from

stress-strain state and configuration, accounting for the

procedure used to determine Tmat and considering other material

properties

.

b. Extension of existing J- integral calculations, especially the

J- integral estimation curve, to calculation of Tap p

.

13
c. Specimen- structure geometry and size dependence of J-R curves,

accounting for the definition of J used.

2.6 References

[1] M. G. Vassilaros and J. A. Joyce, "An Experimental Evaluation of

Tearing Instability Using the Compact Specimen," Report Number

AD-A107633 DTNSRDC- 81/029 , November, 1981.

[2] P. C. Paris and G. I. Zahalak, "Progress in Elastic-Plastic Fracture

Mechanics and Its Applications," Nonlinear and Dynamic Fracture

Mechanics . American Society of Mechanical Engineers, New York, 1979,

pp. 125-134.

[3] H. W. Liu, "On the Fundamental Basis of Fracture Mechanics," Engineering Fracture Mechanics 17 . 424-438, 1983.

[4] S. Aihara, S. Machida, and T. Kanazawa, "A Study on Unstable Ductile

Fracture," Advances in Fracture Research . Vol.5, Pergamon Press,

Oxford, 1982, pp . 2329-2336.

[5] H. Tada, P. C. Paris, and R. M. Gamble, "A Stability Analysis of

Circumferential Cracks for Reactor Piping Systems," Fracture Mechanics: Twelfth Conference. ASTM STP 700 . American Society for Testing

and Materials, Philadelphia, 1980, pp . 296-313.

[6] D. Rhodes, J. C. Radon, L. E. Culver, "Analysis of Combined Static and

Fatigue Crack Growth Data," Fatigue of Engineering Materials and

Structures 4 . 1981, pp. 49-63.

[7] C. E. Turner, "Fracture Mechanics Assessments and Design. Elastic

Plastic Aspects of Fracture Stress Analysis: Methods for Other Than

Standardized Test Conditions," Fracture Mechanics in Design and

Service . Royal Society, London, 1981, pp . 73-92.

[8] J. A. Joyce and M. G. Vassilaros, "An Experimental Evaluation of

Tearing Instability Using the Compact Specimen," Fracture Mechanics:

Thirteenth Conference. ASTM STP 743 . American Society for Testing and

Materials, Philadelphia, 1981, pp . 525-542.

[9] C. E. Turner, "Use of the R-Curve for Design with Contained Yield--In

Relation to Stable and Unstable Crack Growth," in Fracture and

Fatigue: Elasto-Plasticitv . Thin Sheet, and Micromechanisms Problems:

14
Proceedings of the Third European Colloquium on Fracture . Pergamon

Press, Oxford, 1980, pp . 315-328.

[10] A. A. Willoughby, P. L. Pratt, and C. E. Turner, "The Meaning of

Elastic-Plastic Fracture Criteria During Slow Crack Growth, Growth,"

International Journal of Fracture 17 . 1981, pp . 449-466.

[11] C. E. Turner, "Stable Crack Growth and Resistance Curves," in Developments in Fracture Mechanics - 1 . Applied Science Publishers, London,

1979, pp. 107-144.

[12] B. A.Bilby, "Fracture- -Energy Conditions in Macroscopic Cracking," in

Advances in Research on the Strength and Fracture of Materials:

Proceedings of the Fourth International Conference on Fracture . Pergamon Press, New York, 1978, pp . 1-18.

[13] S. Kaiser, "On the Relation Between Stable Crack Growth and Fatigue,"

Report Number TRITA-HFL-0035 PUBL-215 ISSN- 0349 - 1234 , Royal Institute

of Technology, Stockholm, 1983.

[14] P. C. Paris, H. Tada, A. Zahoor, and H. Ernst, "The Theory of Instability of the Tearing Mode of Elastic-Plastic Crack Growth,"

Elastic-Plastic Fracture. ASTM STP 668 . American Society for Testing

and Materials, Philadelphia 1979, pp . 5-36.

[15] J. W. Hutchinson and P. C. Paris, "Stabilty Analysis of J-Controlled

Crack Growth," Elastic-Plastic Fracture. ASTM STP 668 . American

Society for Testing and Materials, Philadelphia 1979, pp . 37-64.

[16] M. F. Kanninen, E. F. Rybicki, R. B. Stonesifer, D. Broek, A. R.

Rosenfield, C. W. Marshall, and G. T. Hahn, "Elastic-Plastic Fracture

Mechanics for Two-Dimensional Stable Crack Growth and Instability

Problems," Elastic Plastic Fracture. ASTM STP 668 . American Society

for Testing and Materials, Philadelphia, 1979, pp . 121-150.

[17] P. C. Paris, H. Tada, H. Ernst, and A. Zahoor, "Initial Experimental

Investigation of Tearing Instability Theory," Elastic - Plastic Fracture. ASTM STP 668 . American Society for Testing and Materials,

Philadelphia, 1979, pp . 251-265.

[18] C. E. Turner, "Description of Stable and Unstable Crack Growth in the

Elastic Plastic Regime in Terms of Jr Resistance Curves," Fracture

Mechanics. ASTM STP 677 . American Society for Testing and Materials,

Philadelphia, 1979, pp . 614-628.

15
[ 19 ] C. E. Turner, "Stable Crack Growth and Resistance Curves," in Developments in Fracture Mechanics . Vol.l, editededited by L. G. Chell,

Applied Science Publishers, London 1979, pp . 107-144.

[20] L. A. Simpson and B.J.S. Wilkins, "Prediction of Fast Fracture in

Zr-2.5 Percent Nb Pressure Tubes Using Elastic-Plastic Fracture

Mechanics , " in Proceedings of the Third International Conference on Mechanical Behavior of Materials . Pergamon Press, Oxford, 1979, pp

.

563-572.

[21] J. D. Landes and D. E. McCabe, "Effect of Specimen Size and Geometry

on Ductile Fracture Characterization," Proceedings of the Third

International Conference on Mechanical Behavior of Materials . Pergamon

Press, Oxford, 1979, pp . 539-547.

[22] J. P. Gudas , J. A. Joyce, and D. A. Davis, "Investigation of Specimen

Geometry Modification of Determine the Conservative Jj-R Curve Tearing

Modulus Using the HY-130 Steel System," Fracture Mechanics . ASTM STP

677 . American Society for Testing and Materials, Philadelphia, 1979,

pp . 474-485.

[23] L. A. Simpson and C. F. Clarke, "An Elastic-Plastic R-Curve Description of Fracture in Zr--2.5Nb Pressure Tube Alloy," Elastic -Plastic

Fracture. ASTM STP 668 . American Society for Testing and Materials,

Philadelphia, 1979, pp . 643-662.

[24] D. E. McCabe and J. D. Landes, "Elastic-Plastic R-Curves - -For Fracture

Toughness Estimation in Steel Plates," Journal of Engineering Materials and Technology 100 . 1978, pp . 258-265.

[25] D. E. McCabe and J. D. Landes, "An Evaluation of Elastic-Plastic

Methods Applied to Crack Growth Resistance Measurements," ElasticPlastic Fracture. ASTM STP 668 . American Society for Testing and

Materials, Philadelphia, 1979, pp . 288-306.

[26] N. J. Adams, H. G. Munro , B. K. Neale, "The Influence of Specimen

Configuration on Yield Zone Formation and Fracture Resistance," in

Advances in Research on the Strength and Fracture of Materials:

Proceedings of the Fourth International Conference on Fracture. Volume

3B . Pergamon Press, New York, 1978, pp. 593-600.

[27] G. R. Irwin and P. C. Paris, "Elasto-Plastic Crack Tip Characterization in Relation to R-Curves, in Advances in Research on the Strength

16
and Fracture of Materials: Proceedings of the Fourth International

Conference on Fracture. Volume 1 . Pergamon Press, New York, 1978, pp

.

93-100.

[28] S. Kaiser, "Experimental Studies of Different Instability Criteria

Based on the J-R Curve," Report Number TRITA-HFL-0034 PUBL-214

ISSN-0349- 1234 , 1983.

[29] H. L. Bernstein, "A Study of the J-Integral Method Using Polycarbonate," Report Number AD-A121170 AFWAL-TR- 82 -4080 , 1982.

[30] W. J. Mills, "Effect of Specimen Size on the Fracture Toughness of

Type 304 Stainless steel," Report Number DE82-012517 HEDL-TME- 81- 52

,

Hanford Engineering Development Laboratory, Richland, Washington, 1981.

[31] S. Banerjee, "A New Basis for the Determination of Fracture Toughness," Report Number NASA-TM-78592 A-7837, National Aeronautics and

Space Administration, Ames Research Center, California, 1979.

[32] S. J. Garwood, "Ductile Crack Instability in Pressurized Components,"

Pressure Vessel Technology. Vol.l . Institution of Mechanical Engineers, Bury St. Edmunds, England, 1980, pp . 93-101.

[33] J. P. Gudas and D. A. Davis, "Evaluation of the Tentative Jj-R Curve

Testing Procedure by Round Robin Tests of HY130 Steel," ASTM Journal

of Testing and Evaluation 10 . 1982, pp . 252-262.

[34] H. -J. Kaiser and K. E. Hagedorn, "Prediction of Maximum Load Values

of Different Sized CT-Specimens Using the J-R Curve Concept," Fracture

and the Role of Microstructure. Vol.l. Fracture and Fracture Toughness . Engineering Materials Advisory Services Ltd. , Cradley Heath,

England, 1982, pp . 76-83.

[35] T. Kodaira, M. Matsumoto, and N. Nakajima, "Application of D. C.

Electrical Potential Method for Measurement of J-R Curve by a Single

Specimen," Journal of the Iron and Steel Institute of Japan 68 . 1982,

pp. 1040-1045.

[36] J. Carlsson, S. Kaiser, K. Markstron, C. Wuthrich, and H. Oberg,

"Experimental Studies of Stable Crack Growth," Advances in Fracture

Research. Volume 2 . Pergamon Press, Oxford, 1982, pp . 863-869.

[37] H. -J. Kaiser and K. E. Hagedorn, "The Influence of Specimen Geometry

on Stable Crack Growth for a High-Strength Steel", Advances in

Fracture Research. Volume 2 . Pergamon Press, Oxford, 1982, pp.855-8^

17
[38] L. A. Simpson, "Effects of Specimen Geometry on Elastic-Plastic

R-Curves for Zr-2.5 Percent Nb , " Advances in Fracture Research. Volume

2, Pergamon Press, Oxford, 1982, pp . 833-841.

[39] M. A. Khan, T. Shoj i , and H. Takahashi, "Characterization of the Crack

Toughness Behavior of Structural Steels by the Tearing Modulus

Parameter and Acoustic Emission," Journal of Testing and Evaluation

10, 1982, pp. 3-11.

[40] A. A. Willoughby, P. L. Pratt, and C. E. Turner, "The Meaning of

Elastic-Plastic Fracture Criteria During Slow Crack Growth," International Journal of Fracture 17 . 1981, pp. 449-465.

[41] M. G. Vassilaros, J. A. Joyce, and J. P. Gudas , "Effects of Specimen

Geometry on the J-R Curve for ASTM A533B Steel," Fracture Mechanics:

Twelfth Conference. ASTM STP 700 . American Society for Testing and

Materials, Philadelphia, 1980, pp . 251-270.

[42] J. P. Gudas, M. G. Vassilaros, J. A. Joyce, D. A. Davis, and D. R.

Anderson, "A Summary of Recent Investigations of Compact Specimen

Geometry Effects on the JI-R Curve of High-Strength Steels," Report

Number NUREG/ CR-1813, David W. Taylor Naval Ship Research and Development Center, Annapolis, 1980.

[43] H. Takahashi, M. A. Khan, and M. Suzuki, "A Simple Test Method for the

Evaluation of Tearing Modulus," Journal of Testing and Evaluation 9 . 1981, pp. 14-23.

[44] K. W. Carlson and J.A. Williams, "The Effect of Crack Length and Side

Grooves on the Ductile Fracture Properties of ASTM A533 Steel," Report

Number NUREG/CR- 1171 , Hanford Engineering Development Laboratory,

Richland, 1980.

[45] K. W. Carlson and J. A. Williams, "A More Basic Approach to the

Analysis of Multiple - Specimen R-Curves for Determination of J c

-- Critical J- Integral Values at Onset of Crack Extension," Fracture

Mechanics: Thirteenth Conference. ASTM STP 743 . American Society for

Testing and Materials, Philadelphia, 1981, pp . 503-524.

[46] I. M. Bernstein, "The Role of Microstructure and Environment on the

Fracture of Iron- -Carbon Alloys," Mechanical Properties of B.C.C.

Metals . Metallurgical Society/AIME , Warrendale , Pennsylvania, 1981,

pp. 173-179.

18
[47] E. Smith, "Plane Strain Crack Instability Under Small-Scale Yielding

Conditions," International Journal of Engineering Science 20 , 1982,

pp . 15-18.

[48] D. Wagner, J. J. Charrier, and D. Francois, "Observations of Ductile

Mechanisms of Stable Crack Growth in Two Phase Alloys," Analytical and

Experimental Fracture Mechanics . Sijthoff and Noordhoff, Alphen Ann

den Rijn, Netherlands, 1981, pp . 199-210.

[49] D. A. Curry, "Estimating a J Resistance Curve for a Perfectly Plastic

Material," International Journal of Fracture 15 . R59-R62, 1979.

[50] M. P. Wnuk, "Occurrence of Catastrophic Fracture in Fully Yielded

Components Stability Analysis," International Journal of Fracture 15 . 1979, pp. 553-581.

[51] H. W. Liu and A. S. Kuo, "Fracture Toughness of Thin and Tough

Plates," International Journal of Fracture 14 . 1978, pp . R109-R112.

[52] M. P. Wnuk and S. Sedmak, "Final Stretch Model of Ductile Fracture,"

Fracture Mechanics: Thirteenth Symposium. ASTM STP 743 . American

Society for Testing and Materials, Philadelphia, 1981, pp . 236-249.

[53] M. Piszczek and M. P. Wnuk, "Subcritical and Fatigue Crack Growth in

Anti-Plane Strain State," International Journal of Solids and Structures 16 . 1980, pp . 1135-1146.

[54] H. Ernst, P. C. Paris, and M. Rossow, "Analysis of Load-Displacement

Relationship to Determine J-R Curve and Tearing Instability Material

Properties," Fracture Mechanics. ASTM STP 677 , American Society for

Testing and Materials, Philadelphia, 1979, pp . 581-599.

[55] W.P.A. Belchar and S. G. Druce , "Micromechanisms of Ductile, Stable

Crack Growth in Nuclear Pressure Vessel Steels," Atomic Energy

Research Establishment, Harwell, England, 1981.

[56] J. A. Blind, "Micromechanisms of Crack Extension in Alloys," Air Force

Institute of Technology, Wright-Patterson AFB , Ohio, Available from

NTIS : SAP: HC A13/MF A01.

[57] D. E. McCabe and H. A. Ernst, "A Perspective on R-Curves and Instability Theory," Fracture Mechanics: Fourteenth Symposium- -Volume I: Theory and Analysis, ASTM STP 791 . J. C. Lewis and G. Sines, Eds.,

American Society for Testing and Materials, Philadelphia, 1983, pp

.

I-561-I-584.

19
[58] David Broek, Elementary Engineering Fracture Mechanics . Third Edition,

Martinus Nijhoff, The Netherlands, 1983, pp . 185-215.

[59] "Standard Practice for R-Curve Determination," 1982 Annual Book of

ASTM Standards, Part 10, Metals - -Mechanical , Fracture, and Corrosion

Testing; Fatigue; Erosion and Wear; Effect of Temperature, American

Society for Testing and Materials, Philadelphia, 1982, pp . 680-699.

[60] P. C. Paris, H. Tada, A. Zahoor, and H. Ernst, "The Theory of Instability of the Tearing Mode of Elastic-Plastic Crack Growth,"

Elastic-Plastic Fracture. ASTM STP 668 . J. D. Landes, J. A. Begley,

and G. A. Clarke, Eds., American Society for Testing and Materials,

Philadelphia, 1979, pp . 5-36.

[61] J. A. Joyce and M. G. Vassilaros, "An Experimental Evaluation of

Tearing Instability Using the Compact Specimen," Fracture Mechanics:

Thirteenth Conference. ASTM STP 743 . Richard Roberts, Ed., American

Society for Testing and Materials, Philadelphia, 1981, pp. 525-542.

[62] M. G. Vassilaros, J. P. Gudas , and J. A. Joyce, "J-Integral Fracture

Toughness and Tearing Instability Behavior of ASTM A106 Steel Pipes"

in, Circumferential Cracks in Pressure Vessels and Piping Vol. II . edited by G.M. Wilkowski, PVP - Vol. 95, American Society of Mechanical Engineers, New York, 1984, pp . 295-307.

[63] "Standard Test for Jj c , a Measure of Fracture Toughness," 1986 Annual

Book of ASTM Standards, Section 3, Metals Test Methods and Analytical

Proceudres, American Society for Testing and Materials, Philadelphia,

1986, pp. 768-786.

[64] J. R. Rice, "A Path Independent Integral and Approximate Analysis of

Strain Concentration by Notches and Cracks," Journal of Applied

Mechanics 35 . 1968, pp. 379-386.

[65] H. A. Ernst, P. C. Paris, and J. D. Landes, "Estimations on J-Integral

and Tearing Modulus T from a Single Specimen Test Record," Fracture

Mechanics: Thirteenth Conference. ASTM STP 743 . Richard Robert, Ed.

,

American Society for Testing and Materials, Philadelphia, 1981,

pps .476-502

.

20
3. STRENGTH AND DUCTILITY OF CRACKED TENSILE PANELS

Measurements of the strength and ductility of cracked tensile panels

of aluminum 5052 -H32 at room temperature were performed to study the effect

of the applied tearing modulus. Very small cracks significantly reduced

tensile panel ductility. Larger cracks were needed to produce comparable

relative reductions in panel strength. The ductility and strength of

cracked tensile panels were independent of the applied tearing modulus.

Applied tearing modulus appeared to control material ability to withstand

artificially produced growing cracks while under compliant loading, implying

that high material tearing modulus would be beneficial in this situation.

3.1 Introduction

The experiments described below were performed in order to clarify the

qualitative aspects of stable and unstable tearing in a strain-hardening

material and to relate this tearing behavior to tearing instability theory

[1], Because in tearing instability theory a steeply- rising J-R curve indicates high resistance to tearing, one might naively assume that a material with a steep J-R curve is superior in every situation to one with a shallower J-R curve. This assumption could be checked by testing a series

of materials with a systematic gradation of J-R curves. However it would be

difficult to vary the J-R curve without varying other material properties as well

.

In tearing instability theory, the slope of the material J-R curve is

normalized to become the material tearing modulus, Tmat . The complementary

driving force for tearing is the applied tearing modulus, Tapp- Tapp

is

controllable by varying testing machine compliance. Therefore one can investigate some aspects of the contribution of Tmat to material performance

in the presence of cracks by varying Tapp . Sensitivity to Tapp

in a certain

situation would indicate that Tmat is probably important in that situation.

The key performance variables for a cracked specimen are strength and

elongation. Although structures are rarely designed to elongate beyond

yield, fracture mechanics theory and experience show that large structures

21
require a certain degree of material ductility in order to achieve their

design strength. Fracture toughness specimens of acceptably ductile

materials nearly always reach their full strength level. The degree of

material toughness is indicated by specimen deformability , not strength.

Low toughness specimens fracture after only slight plastic deformation,

while high toughness specimens can withstand considerable amount.

Therefore, the relationship between strength, elongation, and crack

size in tensile panels under varying Tapp

is explored in this study, by

forcibly elongating to failure specimens prepared with cracks of various

sizes

.

The complement of a measurement of strain-to-failure for a given

initial crack size is a measurement where the specimen is loaded under

displacement control to some initial strain value, and the crack is then

extended until the specimen fails. Such a process is plausible in practical

applications, through stress-corrosion-cracking, or fatigue crack growth

from pulsating loads superposed on large constant loads, for example.

Furthermore, tearing instability theory considers, as a thought experiment,

the response of a specimen under compliant loading to a small increase in

crack length. This consideration of a spontaneous small increment of crack

length is central to the tearing instability theory developed by Paris et

al., as noted above in Chapter 2. An experimental interpretation of the

occurrence of a small increment of crack growth in a specimen under

compliant load was realized as part of this study. Specimens were compliantly loaded to various elongation levels, and then cracks were extended by saw cutting until specimen failure. Surprisingly, the effect of

machine compliance in this case turned out to be different than in the case

of constant crack size with increasing imposed total elongation.

3.1.1 Material and Specimens

The specimen material, chosen for its strain-hardening characteristics,

availability and machinability , was aluminum alloy 5052-H32. This alloy

contains 2.5 percent magnesium and 0.25 percent chromium by weight; it is

designed to have good workability, very good resistance to corrosion, high

fatigue strength, and moderate static strength. Among other applications,

22
it is said to be suitable for "miscellaneous marine and transport

applications." [2] Its tensile properties, determined from a test of a large flat coupon as described below, are listed in Table 1. The measured

properties are in good agreement with the typical values found in [2].

Two specimen types were used in this study: large flat coupons,

referred to from now on as tensile panels; and compact tensile specimens.

The dimensions of the specimens are shown in Figure 1. The ends of the

tensile panels were suitable for clamping in wedge grips, described below.

In most of the tests, double edge notches (DEN) were cut in the tensile

panels at the center of the specimen's length. Except as specifically noted

below, all notches were started with a hacksaw and finished with a jeweler's

saw 0.25 mm in width. Notches of various lengths were used. The compact

tensile specimens had in-plane dimensions standard for 25-mm-thick

specimens, but the actual thickness was only 3.2 mm. About 35 tensile panels and 10 compact tensile (CT) specimens were used

in the course of this investigation.

Table 1. Tensile properties of the aluminum 5052-H32 alloy used in the

present study, as measured with a large coupon specimen.

Yield strength,

0.2 percent offset

Ultimate strength

Uniform elongation

Reduction of area

179 MPa 25.9 ksi

245 MPa 35.6 ksi

10 percent

57 percent

23
— 85.0

Figure 1

55.0 15.0

V

1.0 rad

0.3175 Thick

All dimensions in cm.

Tensile panels (a) and compact (b) specimens used in the present

s tudy

.

24
3.1.2 Measurements, Apparatus, and Procedures

Measurements made in the course of this investigation were:

o J-R curve on CT specimens;

o Strain to failure as a function of crack length and load- train

compliance

;

o Residual strength as a function ofr notch length and load- train

compliance

;

o Artificially- grown crack length at failure as a function of

initial strain and compliance;

o CMOD, load, imposed displacement, and crack length during a constant-extension-rate test to failure, for five crack tip radii.

All tests were performed using servohydraulic test stands with

automatic computer-controlled data acquisition and storage. Applied load

was measured using load cells, instrumented with electrical resistance

strain gages as usual, built into the test stands. Crack mouth opening

displacement (CMOD) was measured using the double -cantilever -beam gages

(clip gages) conventionally used for fracture testing [3]

.

Overall specimen

displacement was measured using the linear variable differential transformer

(LVDT) built into the test stand.

Wedge grips were used to hold the ends of the tensile panels. One end

had insulated micarta or PTFE sheets between the wedge blocks and the wedge

block holder, to provide electrical insulation. The usual fracture

mechanics clevises were used in the tests of the compact specimens.

In the J-R curve measurements, the initiated cracks were finished with

a jeweler's saw, instead of fatigue cracking, in order to reproduce the

crack tip condition used in the tensile panel tests. Single-specimen,

unloading-compliance techniques were used for conducting the tests and

calculating J- integrals.

In the strain- to - failure tests, the remote failure strain was obtained

by measuring the separation of marks scribed on the specimen surface away

from the notch before and after pulling the specimen. Crack mouth opening

displacement was recorded continuously during the test.

25
Variable effective load- train compliance was obtained for these tests

by electronically simulating the presence of a spring in the load train.

The artificial spring circuit adjusted the servohydraulically- imposed

specimen displacement in response to load changes. Load decreases produced

proportional increases in the imposed displacement, just as would be the case if an actual mechanical spring were included in the load train. The

response time of the artificial spring was slower than that of a real

spring, because it was limited by the response time of the testing machine,

a few tenths of a second. This was not a liability for the material tested,

because it is not subject to cleavage and its behavior is practically rateindependent. In fact, it had the advantage that the unstable fracture

process was slowed somewhat, allowing easier qualitative observation.

"Artificial" crack growth in specimens under load was obtained by

sawing with a hacksaw. The simulated spring was used during these tests to

provide a variable load- train compliance. The initial imposed strain was not held constant, but was allowed to evolve during the test, controlled by

the load train compliance and the artificially growing crack. Because the

specimens were thin and the loading was displacement controlled, only small

amounts of energy were released when the specimens failed, so that the

procedure was not hazardous. For thicker or larger specimens, however, the

safety aspects of such a procedure would require careful consideration.

Tests involving artificial crack growth have been conducted previously, as described by Broek [4]

.

Because most of the DEN specimens of the present study had saw-cut

crack tips, a check of the effect of the tip shape was performed. Notches

with tips of various widths were obtained by drilling holes of selected

diameters at the notch tips. The notch tip width was taken to be equal to

the hole diameter. Two of the notches were finished with saws, one with a jeweler's saw and the other with a hacksaw. These notch widths were measured with feeler gages. A fatigue -sharpened notch was also used in this

series; its width was taken to be zero. Notch widths of 0.0, 0.4, 0.8, 1.6,

and 3.2 mm were obtained. Potential drop across the plane of crack

propagation was measured at four locations in these specimens. Applied load

and crack mouth opening displacement (CMOD) were recorded throughout each

test

.

26
Because none of the specimens in this study failed before general

yielding, measurements providing information on the material ductility were

of interest. Two displacement measurements, total specimen displacement (at

the load point) and crack mouth opening displacement, were recorded

continuously during most of the tests. Displacements near maximum load were

of interest as indicators of the material fracture resistance. For

specificity, the lower limit of near-maximum loads was chosen as 0.9 times

P max , the maximum load. The points corresponding to Pmax , 0.9 Pmax before

maximum load, and 0.9 Pmax after maximum load were easily identifiable on plots of load against displacement. From such plots, crack mouth opening or total specimen displacement from the 0.9 Pmax to Pmax , P to 0.9 Pmax (after

maximum), or 0.9 Pmax (before maximum) to 0.9 Pmax (after maximum) points

could be obtained. These displacements, especially the displacement from

0.9 Pmax to Pmax , were used as indicators of specimen ductility.

3.1.3 Results

The experimental results are shown in Figures 2 to 10. The J-R curves obtained for three specimens of the A15052-H32 are shown in Figure 2. The

specimen thickness used was not large enough to produce formally valid

results according to the standard procedure.

Strain- to-failure as a function of crack length is shown in Figure 3.

The relative crack length on the abcissa is the total specimen cross section

intercepted by the crack. If the full width of the double-edge-cracked

specimen is taken as 2W, and each crack has length a, the relative crack

size would be given by a/W. No effect of compliance was found in these

tests. The strain used in Figure 3 is the remote strain. The decrease in

specimen ductility produced by the cracks is confirmed by the plot of

extension near maximum load against crack size, Figure 4. Specimens with

shorter cracks have considerably larger capacity for extension.

Crack length at failure during artificial crack growth is plotted as a function of compliance in Figure 5 for two initial strain values. Ideal

displacement control corresponds to zero compliance, while load control

corresponds to infinite compliance. In contrast, strain- to - failure

measurements of tensile panels with cracks of various sizes (Fig. 6)

,

27
kN/m

Aa, in

0.05 0.10

400 T

0.15

2000

300 -

200

100

cPa

a i°

£> A

cP

on a A

AO

O A o &>

Al 5052-H32

o Specimen 1 Specimen 2

A Specimen 3

1500

1000

500

0.1 0.2 0.3 0.4

Aa, cm

Figure 2. J-R curves for three compact tensile specimens of aluminum

5052-H32

.

28

lb/in
REMOTE

STRAIN

at

FAILURE,

percent

Figure 3

.

RELATIVE INITIAL CUT SIZE

Remote strain to failure plotted against relative initial crack

size for tensile panels of aluminum 5052-H32, tested under

stroke control for low compliance.

29
EXTENSION

AT

MAXIMUM

LOAD,

mm

RELATIVE NOTCH LENGTH, a/W

Figure 4. Extension near maximum load plotted against relative crack size.

Extensions during the load increase from 0.9 to 1.0 times

maximum load Pmax and extensions during the following load

decrease from 1.0 to 0.9 Pmax are shown.

30
RELATIVE

CUT

SIZE

at

FAILURE,

(a/W)

COMPLIANCE, mm/MN

Figure 5. Crack length at failure during artificial crack growth plotted

against compliance imposed by electronically simulated spring,

for two initial strains, in aluminum 5052 -H32.

31
REMOTE

STRAIN

at

FAILURE,

percent

Figure 6

.

0 -

1 1— ++ —— 0 0.1 0.2 0.3 0.4

RELATIVE INTI AL CUT SIZE

Remote strain to failure plotted against relative initial crack

size for tensile panels of aluminum 5052-H32, tested under load

control for high compliance.

32
LULU

,XBU ij

oj*

E

^

6

0

‘NOISN31X3

Figure 7. Plot of total specimen extension near maximum load against notch

tip width.

33
UJUJ

‘

XBUJ d

o\

XBIU d

6

0

'ao^o

1.6

1.2

0.8

0.4 L

0

Figure 8 .

T

—L _ L 1

1 2 3

NOTCH TIP WIDTH, mm

Plot of crack mouth opening displacement (CMOD) near maximum

load against notch tip width.

34
ULTIMATE

STRENGTH,

MPa

250

Figure 9

.

RELATIVE INITIAL CUT SIZE, a/W

Ultimate strength of notched tensile panel plotted against

initial notch size, under stroke control.

35
250 T

oL t 1—

0 0.1 0.2

RELATIVE INITIAL

i 0.3 0.4

CUT SIZE, a/W

Figure 10. Ultimate strength of notched tensile panel plotted against

initial notch size, under load control.

36
obtained with the testing machine in load control, agree with those of

Figure 3, in stroke control.

The measurements on the specimens with varying notch widths yielded a large family of test records. Analysis of these showed that the clearest

effect of notch width occurs in extension between 90 percent of maximum

specimen load and maximum load Pmax The specimens with very narrow notches

possessed the capacity for some extension with near-maximum loads, but the

specimens with wide notches clearly had more. Figure 7 shows specimen

extension between 0.9 Pmax and Pmax plotted against notch width. The same trend for CMOD is evident in Figure 8. The double-edge-notched specimen

with the fatigue -sharpened notches was omitted from this figure because its

notch was longer than those ot the other specimens on the side where CMOD

was measured, although the total notch length for both notches was the same

as for the other specimens.

3.1.4 Discussion

The specimen material chosen for these studies was quite ductile with

substantial strain hardening, as shown by its tensile properties. Its high

ductility was confirmed by the measured J-R curve. Saw- cut crack tips were

used for this curve, for consistency with the crack- tip preparation used in

the tensile panel tests.

The strain- to-failure measurements were suggested by the previously

reported strong effect of crack size on the driving force for fracture [5].

As anticipated, strain- to - failure decreased rapidly with increasing crack

size, Figure 3. The decrease of failure strain with crack size was much

more rapid than that of ultimate strength, Figure 9. The strength declined

in proportion to the remaining net cross-sectional area, as expected for a tough material. These results suggest that even small cracks can compromise

structural ductility, but larger cracks must be present before structural

strength is affected. This result shows the strong detrimental effect on specimen ductility of net section yielding, which increased in this material

as relative crack size increased from 0.0 to 0.3.

If tearing modulus always controls material performance, loading

specimens under high Tapp

must produce failure more readily than loading

37
under low Tapp . This hypothesis was checked by measuring strain to failure

as a function of crack size for two similar sets of specimens, one with the

testing machine in displacement control and one in load control, Figures 3 and 7. In load control, ideally, a very large change in specimen length

produces no change in applied load. Actually, of course, the testing

machine applies loads over finite time spans, and so the effective

compliance is a function of frequency of loading. The testing machine

response time was of the order of half a second. The tests were conducted

at low loading rates (many seconds) , so in load control the effective

compliance was infinite, in the time scale of the test. The total

compliance available in displacement control was 41mm/MN.

The result, shown above in Figures 3 and 6, and 9 and 10, was that

compliance had no effect on remote strain to failure or maximum remote

stress

.

Load- train compliance proved to be more relevant in the next

experiment. In tests on artificial crack growth, compliance had a significant effect on crack growth to failure. As shown in Figure 5, for

initial strains below yield, compliant loading reduced the crack size at

failure by nearly a factor of two. The remaining ligament at failure for

the lowest compliance value was only about one -fortieth of the value at

infinite compliance. This striking effect was repeated for specimens

prestrained to twenty times yield strain. The final crack length in the low

compliance test was fifteen times the final length in the

infinite-compliance test. This result indicates that high material tearing

modulus is likely to contribute to material durability under artificial

crack growth.

The two results discussed above indicate that structural designers

should consider using high- tearing-modulus material especially in situations

where progressive crack growth from causes other than the main structural

load is possible. This conclusion is drawn directly from the observation

that high Tapp produced fracture at lesser notch lengths than low Tapp

under

artificial notch growth, Figure 5. It is assumed that where a high Tapp

promotes fracture, a high Tmat will enhance fracture resistance.

38
The experiments on crack tip radius were consistent with expectations.

Sharp cracks reduced ductility more than blunt cracks, because they

introduced a larger degree of strain concentration.

3.2 Conclusions

The conclusions of the work reported here can be summarized as follows:

1) Very small cracks can significantly reduce tensile panel ductility.

Larger cracks must be present before panel strength is significantly

reduced. A crack so large that only net section yielding occurs reduces the

ductility, measured by post-yield strain remote from the crack, to nil.

2) The relative magnitudes of material and applied tearing modulus do not

control ductility or strength of cracked tensile panels.

3) The value of material tearing modulus relative to applied tearing

modulus does affect resistance to failure at cracks produced artificially

while the main load on the specimen evolves in time as dictated by the

combined compliance of the specimen and load train. Low load train

compliance, and therefore, presumably, high material tearing modulus,

increases the crack size at failure.

3 . 3 Acknowledgments

The technical support of J. D. McColskey and D. P. Vigliotti in

conducting the tests reported here is appreciated. This report was prepared

as part of the Fracture Control Technology Program, under the sponsorship

of Dr. H. H. Vanderveldt, Naval Sea Systems Command (SEA 05R25) . The effort

was directed by Dr. John P. Gudas , David Taylor Naval Ship Research and

Development Center, under Program Element 62761N, Task Area SF-61 -544-504

.

3.4 References

[1] Section 2, this report.

[2] American Society for Metals, Metals Handbook Ninth Edition. Volume ?,

Properties and Selection: Nonferrous Alloys and Pure Metals . America!.

39
[3]

Society for Metals, 1979, p. 101.

American Society for Testing and Materials, "Standard Test Method

E399-81 for Plane-Strain Fracture Toughness of Metallic Materials," in

1982 Annual Book of ASTM Standards. Part 10 . American Society for

Testing and Materials, Philadelphia, 1982, pp . 592-622.

[4] David Broek, Elementary Engineering Fracture Mechanics . Third Edition,

Martinus Nijhoff, The Netherlands, 1983, pp . 185-215.

[5] D. T. Read, "Applied J-Integral Values in Tensile Panels," Ductile

Fracture Test Methods . Proceedings of a CSNI Workshop, Nuclear Energy

Agency, Organization for Economic Cooperation and Development, Paris,

1983, pp. 273-291.

40
4. APPLIED J- INTEGRAL VALUES FOR ASTM A- 710 STEEL PANELS

4.1 Abstract

In a test program motivated by the need for a quantitative relationship

among fracture toughness, flaw size, and applied loading for small flaws, to

be used for fitness-for-service assessment, applied J-integral was measured

as a function of applied strain in eight 14-mm-thick specimens of A710 Gr A

Ci 3 steel plate. All the edge cracks had lengths less than 3 percent

of the specimen width of 82 mm. Six specimens were tested in tension;

two were loaded by four-point-bending in the plane of the plate. One singleedge-cracked, transverse-oriented specimen was tested at -30°C. Electrical

resistance strain gauge and clip-gauge crack mouth opening displacement

measurements were used to obtain quantities inside the J-integral. The

J-integral was calculated by trapezoidal rule integration. Unloading crackmouth compliance measurements were used to obtain crack length values so that

tearing effects could be observed.

Ltiders strains occurring right after yield caused rapid increases in the

applied J-integral values for the tensile specimens. Except for the Liiders

strain effect, the behavior of the applied J-integral in bending was similar

to that in tension. The extra J-integral produced by tearing was ascribed to

two causes: loading of a longer crack in gross -section-yielding, and net

section yielding accompanying the tearing. The initiation toughness

and tearing resistance of the panels with short cracks were greater than

those of conventional three-point-bend specimens of the same thickness. No

effect of temperature on applied J-integral was found from the specimen

tested at -30°C. The present data support Wilson's prediction of the dependence of J on strain for a material with a bilinear stress/strain curve.

4.2 Introduction

This paper describes experimental results of direct evaluations of the

J-integral as a function of applied strain in tensile and bending panels wi - :.

41
small cracks. This test program was motivated by the need for a general,

experimentally verified, quantitative relationship among fracture toughness,

flaw size, and applied loading for small flaws, to be used for fitness -forservice assessment. The cracks used here intercept only up to 3.4 per cent

of the specimen cross-sectional area. This is small enough that attainable

loads are sufficient to cause considerable specimen yielding in locations

remote from the crack plane. Equations that relate J- integral to area under

the specimen's load-displacement curve for deeply cracked specimens are not

applicable to the small cracks used here. The J- integral values for these

small cracks are of interest for studies of fracture at cracks within

elastic -plastic and fully plastic strain fields.

The experimental techniques used have been described in detail

previously [1]. Including the present results, sufficient data now exist on

the small-crack behavior of the J- integral as a function of applied strain

for comparison to theoretical predictions, comparisons of the behavior of

different alloys, comparison of tensile and bending results, and identification of the effect of ductile tearing.

4.3 Theoretical Background

The J- integral has been defined as a path- independent line integral on

a contour surrounding a crack tip [2]; it has also appeared as the amplitude

of the Hutchinson-Rice-Rosengren (HRR) stress/strain singularity [3,4]. A

modified J- integral has been used in tearing studies [5]. The integral used

in this paper is asserted to be the path- independent line integral J [1],

taken on a contour lying far from the crack tip. No claim is intended

regarding the existence or amplitudes of HRR stress - strain fields in the

present specimens, or about any unique correspondence between the J- integral

measured here and the initiation or extent of tearing.

Several theoretical predictions of the behavior of the J- integral in

specimens with small cracks are available [6-10]. Figure 1 displays three of

these, two for cracks in infinite plates calculated from an analysis by

Wilson and one by calculated from an analysis given by Shih, German, and

Kumar [11]. The conversions used in this figure for the normalized

J-integral, j, and the normalized remote strain, e, are

42
NORMALIZED

J-INTEGRAL,

J/7raa

y

€

NORMALIZED REMOTE STRAIN, €

m

/e

y

Figure 1. Three theoretical predictions of the behavior of the J- integral

as a function of remote strain in specimens with small, W/a = 8,

and inf initesinal , W/a = <», cracks.

43
j = JE/ (7rau

y

) ( 1 )

and

e = e/e

y

, (2)

where J is J- integral, E is Young's modulus, a is crack size, cr ys is material

flow strength, ct u is material ultimate strength, ayis material flow strength

(<7 ys + ct u)

/

2 , and e y

is nominal material flow strain, given by cr y/E. The two curves labelled Wilson Bilinear and Wilson Ramberg-Osgood are different

predictions constructed using, respectively, bilinear and Ramberg-Osgood

representations of the stress - strain curve of the specimen material. The

Ramberg-Osgood constants n and a were obtained by fitting the specimen material

true stress - strain curve, which was calculated from the engineering

s tress - strain curve. Figure 2 compares the specimen material true

stress-strain curve its Ramberg-Osgood and bilinear representations. The

Ramberg-Osgood parameters used were n = 14 and a = 4.125. A slope of E/N = E/72 was used for the upper part of the bilinear representation.

The Ramberg-Osgood curve (Figure 1) for J as a function of strain makes

use of upper-bound plane stress h factors calculated by He and Hutchinson [12]

to relate J to strain. To apply this approach to the present specimen

material, the h factors given for a series of work hardening exponents n were plotted against 1/n for extrapolation to n = 14. The Ramberg-Osgood curve plotted in Fig. 1 is thus an extrapolated upper bound. It differs by a factor

of h/(27r) = 2.5 from the curve labelled Wilson Bilinear. The Bilinear curve is an analytical continuation of the linear elastic relationship for J as a function of strain. Similar curves were given previously by Merkle [7] and by

Begley, Landes, and Wilson [6]. Turner [8] has reported curves derived from

finite element analyses that lie generally between Wilson's two curves in

Figure 1. In addition, the relationship between crack tip opening displacement

(CTOD) and strain given originally by Burdekin and described by Dawes [9] can

be converted to give J if the constraint factor m is known. For m values in

the range 1 to 2 the CTOD curve also falls generally between the two curves given by Wilson's analysis.

44
TRUE STRAIN, percent

Figure 2. Engineering stress/strain curve for longitudinal and transverse

round-bar tensile specimens of the ASTM Grade A Class 3 alloysteel specimen material used in the present study.

45
The difference between the Shih et ai. curve and the others in Figure 1

is that only it was derived for a specific finite crack size, namely,

a/W = 1/8. The others all refer to small or infinitesimal cracks compared to

the plate width. The difference between the behavior of small cracks and

cracks of relative size a/W >1/8 has been confirmed experimentally and

related to plate deformation patterns elsewhere [13-15]. Previous experimental results [13-15] indicated that the J-integral for small cracks in a highstrength quenched and tempered nickel steel fell between the two predictions

by Wilson, closer to the upper curve.

4.4 Material

The specimen material used in this investigation was reported by the

manufacturer to be ASTM A710 Grade A Class 3 alloy steel. It was received in

the form of 19-mm- (0.75-in-) thick plate. The chemistry, as supplied by a commercial source, is listed in Table 1. This chemical analysis indicates

less than 0.01 weight per cent of Nb , which violates the specification for

A710 Grade A Class 3 steel. Some unusual behavior of this alloy under heat

treatment, which may be related to its chemistry, have been noted [16]. The

TABLE 1 -Chemical composition, in weight per cent, of the ASTM A710 Grade A

Class 3 alloy steel specimen material used in the present study.

Carbon Manganese Nickel Chromium Silicon Cooper Sulfur

0.042 0.54 0.85 0.65 0.34 1.2 0.010

Phosphorous Niobium Aluminum Iron

less than 0.005 less than 0.010 less than 0.020 balance

46
tensile properties of the specimen material, obtained using replicate round

b.tr tensile specimens 6.4 mm (0.25 in) in diameter, are listed in Table 2.

The engineering stress-strain curve contains a slight yield point, some Liiders

extension, and strain hardening. The tensile properties of the specimen

material at room temperature were essentially the same in the transverse and

longitudinal directions, except for the elongation, as can be seen from Table

2. The Liiders strain after the yield point was present in both longitudinal

and transverse orientations. After its maximum, the load decreased more

rapidly with extension in the longitudinal specimens than in the transverse

ones, leading to the lower elongation values for the longitudinal specimens.

TABLE 2 -Tensile properties, at room temperature, of the ASTM Grade A Class 3 alloy steel specimen material used in the present study.

Longitudinal

Yield Strength,

0.2 percent offset

Ultimate tensile strength

Elongation

Reduction of Area

637

732 MPa

12.0 percent

75.5 percent

Transverse

Yield Strength,

0.2 percent offset

Ultimate tensile strength

Elongation

Reduction of Area

634

727 MPa

17 percent

71 percent

92.4 ksi

106.2 ksi

93.2 ksi

105.5 ksi

47
The fracture toughness of this specimen material at room temperature was investigated using three -point-bend specimens in the LT and TL orientations.

The in-plane dimensions were nominally 50 by 220 mm (2 by 9 in) . Thicknesses

of 14 and 19 mm (0.55 and 0.75 in) were used as noted. Half of the specimens

(as noted) were side-grooved 12.5 percent on each side after fatigue precracking. The tests were performed according to ASTM Standard Test Method

E-813. The Jj c and J-R results are listed in Table 3. Items of non-compliance

with the standard were the differences between compliance-measured and physical

TABLE 3 -Toughness and tearing resistance, in terms of the J- integral, of the

ASTM Grade A Class 3 alloy steel specimen material used in the present

s tudy

.

Orientation Side- grooved Non- side - grooved

J ]> Ic

N/mm lb/in Tmat N/mm lb/in Tmat

TL 118 674 53 183 1046 73

120 686 49 117 669 84

145 829 4_1 —

Average 128 731 48 150 857 78

LT 234 1337 103 371* 2120* 168*

377* 2154* 186*

Average 374 2137 177

*19 mm thick specimen.
crack extension values, Aac and Aap , noted below, and the specimen dimensions.

The higher values of J used to obtain the material tearing modulus failed to

meet the specimen size requirement. The results of the J- integral tests

indicate that the specimen material is quite tough at room temperature, and

that non-side-grooved specimens in the LT orientation (crack grows across the

rolling direction) are the toughest (Jq c = 374 N/mm, Tmat = 177) , while

side-grooved specimens in the TL orientation (crack grows along the rolling

direction) are the least tough (Jjc = 128 N/mm, Tmat = 48). These values were

calculated using T = E • (dJ/da)/a^ , where E is Young's modulus. In the TL

orientation, the side-grooved and non-grooved specimens had similar Jj c values.

However in the LT orientation, the one side -grooved specimen had lower Jj c and

Tmat values that the two non-grooved specimens.

The compliance-measured crack extension values, Aac , differed

from the respective physical crack extension values, Aap, by more than 15

percent. This is attributed to friction in the conventional three-point-bend

fixture used and to crack front curvature. The Aac values were corrected by

linear scaling before data reduction. No pop- ins or other signs of rapid crack

advance were observed in these room temperature tests

.

In the TL orientation, the side-grooved and non-side-grooved specimens

had similar Jj c values. However in the LT orientation, the one side-grooved

specimen had lower Jj c and Tmat values than the two non- side -grooved speci- mens .

4.5 Specimens, Apparatus, Instrumentation, and Techniques

Tensile and four-point-bending panel specimens of the specimen material

were machined with gauge sections measuring 82 mm (3.22 in) wide by 14 mm

(0.55 in) thick by 250 mm (10 in) long. The total specimen lengths were

584 mm (23 in) for the transverse specimens and 850 mm (33 in) for the longitudinal specimens. The transverse specimens were made shorter because of the

size of the plate of specimen material available. The grip sections at each

end of the specimen were 108 mm (4.25 in) wide to confine plastic strain to

the gauge section. Table 4 gives the details of the crack geometries tested

Figure 3 shows the loading methods used for the tension and bending tests.

For the tensile tests, mechanical wedge-grips clamped the specimen grip sec49
LOAD

Tensile Loading

LOAD

Wedge

Block

Wedge Block

Holders

LOAD

Four-Point

Bending

Figure 3

.

Loading methods used for tensile and four-point-bend tests
TABLE 4 -Specimen and test types and for the specimens used on the present

study.

Abbreviation Orientation Crack

Geometry

Loading

Mode

Crack

Length

mm

Relative

Crack

Size

DECT

(saw-cut

crack tips)

LT Double

Edge

Tension 1 .

1

0.014

SECT LT SingleEdge

Tension 1.9 0.023

SECT

(prestrained)

LT SingleEdge

Tension 2.3 0.028

SECT LT SingleEdge

Bending 1.4 0.017

SECT TL Single - Edge

Tension 1.5 0.018

PTST TL PartThrough

Surface

Tension 3.7 x 13 0.034

SECT TL SingleEdge

Bending 1.2 0.015

SECT

(-30 C)

TL SingleEdge

Tension 1.2 0.015

DECT = Double-edge-cracked tensile.

SECT = Single-edge-cracked tensile.

SECB = Single-edge cracked bend.

PTST = Part- through- surface tensile.

51
tions; for the bend tests, four-point loading was used. The outer bending

points were 560 nun (22 in) apart for the transverse specimens and 810 mm

(32 in) apart for the longitudinal specimens. The inner bending points were

250 mm (10 in) apart for the transverse specimens and 300 mm (12 in) apart

for the longitudinal specimens. The bending points were 25 mm (1 in) diameter steel rollers on flat steel holders. The rollers were free to rock as the specimen bent. Loads were supplied by a displacement-controlled servo- hydraulic testing machine with a capacity of 1 MN (225,000 lbs).

Instrumentation as developed previously [1] for direct measurement of the

J- integral was used, including a load cell built into the testing machine,

a crack mouth opening displacement (CMOD) gauge (ring- gauge) , about 35

electrical resistance strain gauges, and up to 3 linear variable differential

transformer (LVDT) gauges for displacement measurement. An array of 5 small

strain gauges was located near the crack mouth to give the strain profile

there, as shown in Figure 4. An additional high- strain- gradient location, such

as the specimen back face opposite a surface flaw, could also be instrumented

with a linear array of 5 closely- spaced small strain gauges. Some gauges were always located away from the crack, for measurement of remote strain.

The strain gauges, load cell, and crack mouth (CMOD) gauge were wired to

conventional signal conditioning circuitry. The LVDTs contained signal con- ditioning circuits within their cases. The conditioned signals from all the

gauges were introduced to the input of a commercially available sixteen-bit

analog to digital (A/D) conversion system. The least significant bit in the

load reading corresponded to a load of 30 N, and the least significant bit in

the CMOD reading corresponded to a displacement of less than 1 x 10" 4 mm. The least significant bit in the strain readings corresponded to a strain of

about 3xl0" 5

. The A/D system was linked to a commercially available microcomputer system for converting voltage readings to physical quantity values

and storing these on floppy discs. The specimens were tested under displacement control. Increments of displacement were imposed. At each increment,

the gauges were scanned and the readings were recorded, printed, and used to

calculate a preliminary J- integral which was plotted along with the strain

gauge strains. Slight relaxations of the load, on the order of 1 percent, were observed after displacement increments imposed at high strains. These

occurred over a period of up to 2 minutes after the displacement increment.

52
Figure 4. Crack mouth instrumentation, including an array of small strain

gauges and a crack mouth opening displacement gauge.

53
The usual procedure was to impose the displacement increment, wait 2 minutes

for the load to become constant, and then scan all instruments. The scanning

itself took about 10 seconds. After the instrumentation readings had been

recorded, the unloading compliance, CMOD per unit load, was measured during

an unloading of 10 to 20 percent of the load. An approximate crack length

was obtained. These values were corrected by linear scaling after the test to

give the correct initial and final crack depths. These crack depths were used to detect the initiation of tearing and in the calculation of the

tearing modulus. In a typical test, on the order of 100 displacement increments would be used. At some stage, the strain gauges would begin to fail

because of high imposed strains of the order of 2 to 3 percent. From this

point on a different data analysis method had to be used.

In the post- test data analysis, all the measured strain and displacement

quantities were zero-corrected by fitting the linear part of the record for

each quantity to a linear dependence on the stress, then forcing zero strain

or displacement at zero stress by offsetting the measured strain or displacement. The J- integral was calculated using the trapezoidal rule for

displacement and stress -work integrals along both sides of the contour.

Because the contours were chosen along specimen edges so that the stresses at

the contour were uniaxial, an elastic-perfectly-plastic approximation of the

simple round-bar s tress - strain curve was used for calculating stress-work

integral. Integration of strain gauge strains to obtain the displacements

needed for calculation of the traction-bending term of the J- integral gave some error cancellation, which would not have been obtained had the LVDT

displacements been used. The LVDT displacements were used to check the

integrated strain values and for gauge length strain measurement after strain

gauge failure. Good correlations were obtained experimentally between

J- integral and 1.0 x ay x CMOD. This correlation is expected because of low

geometrical constraint of the simple tension and very-short-crack bend

geometries used here. After strain gauge failure, this correlation was used to

obtain J- integral values.

Photoelastic coatings were bonded to the surfaces of the specimens to

allow photographic recording of the strain patterns in the specimens. The

coatings were observed through a polarizing sheet using white light. Colored

fringes corresponding to the difference between longitudinal and transverse

54
principal strains were observed. This allowed observation of the Luders

bands

.

4.6 Results and Discussion

Results on remote strain, gauge length strain, stress, crack mouth

opening displacement, J- integral, and strain as a function of distance from

the crack plane on the cracked and uncracked specimen edges were obtained

over the whole course of all the tests. A complete presentation of these

results is too lengthy for this publication, and is found elsewhere [17].

The key results are the plots of J- integral against remote strain. All the

other results, though interesting and important in themselves, are supportive

of the J- integral results.

Figure 5 shows the measured J- integral as a function of strain for fourpoint-bending with crack length 1.4 mm for a single-edge-cracked longitudinal

specimen. This figure shows the usual parabolic dependence at low strains

followed by an approximately linear dependence above yield. The deviation of

the post-yield dependence from true linearity is believed to be an artifact

of the experimental arrangement; perhaps it is a result of the significant

curvature induced in the specimen by bending by the end of the test. The

important point is the gradual rate of rise of J- integral with imposed strain

above yield. This result is qualitatively similar to the Wilson results in

Figure 1

.

Figure 6 shows the behavior of J- integral as a function of strain

for all the specimens tested. Six of these are tensile panels, two are four-point-bending panels. This plot shows a feature of the tensile tests

not present in the bend results of Figure 5, namely, the step in J- integral

at a fixed value of strain near yield. From the photoelasticity results,

this step in J- integral is associated with an area of high strain that first

extends at an angle from the crack tip to the opposite edge of the specimen,

and then spreads along the specimen gauge section. This behavior is the same

as the Luders band phenomenon in tensile tests, and is associated with the

Luders extension found in the tensile bar stress/strain curves for this

material. This step in the J- integral vs strain behavior was not present in

the bend tests; the photoelastic results for bending confirmed that no

55
300

200

o

L_

O)

CD

100

0

o

ASTM A—710 Steel

Grade A, Class 3

Room Temp.; Longitudinal

Single Edge Crack:

Length = 1.4 mm

Bending

1500

1000

500

0.01 0.02 0.03

Remote Strain

o

0.04

Figure 5. Experimentally measured J- integral as a function of applied

strain for a four-point-bend specimen with crack length of 1.4 mm

.

56

Integral,

Ib/in
120

o

!>_ U)0

o

o

~o

0

~o

100

80

60

C 40 -

L_

o

20

0

0 5 10

Normalized Strain

15 20

Figure 6. Experimentally measured total J- integral as a function of

applied strain for the eight specimens of this study.

57
Liiders -type strains occurred in the bend tests; the measured J- integral

values agree roughly with the Ramberg-Osgood curve shown in Figure 1. This

agreement is believed to be accidental. The agreement with the previous

experimental estimate confirms that behavior of the applied J- integral is the same for different specimen materials.

The results from the tensile specimens with unusual features, one with

sawcut notches, one prestrained, and one tested —30°C, are indistinguishable

from the rest in Figure 6. This is as expected for applied J- integral. The —30°C specimen had a low value of J c , (Table 5); this is consistent with

expectation

.

The bend test results end at strains lower than the tensile test results

because the specimens buckled after strains of several times yield and could

not be strained further. At high strains on the order of 10 times yield,

tearing initiated in the tensile tests, as shown by the unloading compliance

data. Because of the buckling, the bend panels could not be strained enough

to initiate tearing. Tearing produces the upturn in the J- integral data

of Figure 6 at strains of about 10 times yield.

Figure 7 interprets the behavior of the J- integral as a function of

strain for small cracks in tension and bending specimens. Both types have a parabolic region below yield. The tension specimens show a step- like

increase near yield because of Liiders strain, while the J- integral in the

bending specimens increases gradually. The tensile and bending results con- verge after the Liiders strain region ends, and both show gradual increases of

J- integral with strain. At some J- integral level, tearing begins, increasing

the rate of rise of J- integral with strain.

An attempt was made to correct the data of Figure 6 to reflect the

behavior of flaws in infinitely wide plates. The correction procedure

extracted only that part of the J- integral that resulted from gross section

yielding. All net section yielding effects were excluded. The justification

for this procedure is that through cracks in structures would be relatively

much smaller than 1 to 3 percent of the structural element width; therefore

net section yielding effects that may be present in these specimens would be

absent in a real structure. The specific assumption used in the correction

procedure was that contributions to the J- integral from strains on the specimen edge opposite the crack would not be present in a structural element with

58
NORMALIZED

J-INTEGRAL,

Figure 7. Schematic interpretation of the behavior of J- integral as a function of strain for small cracks in tensile and bend::..'

specimens

.

59
a small crack. Therefore only the strain profile in the neighborhood of the

crack mouth was considered in the calculation of the corrected J- integral.

The strains on the specimen edge opposite the crack were assumed to be equal

to the remote strain on the cracked edge. The J- integral values resulting

from this correction were termed gross section yielding (GSY) J- integral

values and are plotted in Figure 8. This plot, when compared to the total

J- integral values of Figure 6, indicates that the GSY part was only about

half the total J- integral value. Although data from a surface-cracked

specimen are included in Figure 8, a more complex correction procedure is

probably needed for this crack geometry because of the presence of ligament

yielding

.

It is the GSY J- integral values that are appropriate for comparison

with the theoretical predictions discussed above for small cracks in infinite

plates. The data are compared to the Wilson bilinear result in for interior

cracks in plane stress Figure 8. This figure shows good agreement between

experiment and theory. As a result of this comparison it is concluded that

the relationship given by Wilson [10] for a bilinear material, which is

similar to expressions given earlier by Begley, Landes, and Wilson [6] and by

Merkle [7], is the correct expression of the dependence of J-integral on flaw

size and applied strain for small through cracks in infinitely wide plates.

The J-integral values at the initiation of tearing in the tensile

panels were considerably higher than those in the side-grooved three-point-bend

fracture toughness specimens, as can be seen from a comparison of Table 3 and

Table 5. The initiation J c values in the tensile panels were slightly above

those in the non-grooved, three -point-bend toughness specimens. The cause of

this discrepancy is believed to be the low geometrical constraint in the

shallow-cracked tensile and bending panels as compared to the deeply cracked

three -point-bend fracture toughness specimens [18]. The effect of specimen

geometry on crack tip strain fields has been pointed out by McMeeking and Parks

[19]. The present results indicate that the use of toughness values from

three-point-bend specimens for predictions of crack initiation in elements with

small cracks is conservative and may be excessively conservative for certain

cases

.

60
60

y—

tn

o

“O

0

# N

~g

c

L_

o

50 -

o

CD

40

30

20 -

10

0

0

A—710 Steel

DECT, a = 1.1 mm

SECT, a = 1.9 mm

SECT, a = 2.3 mm

SECB, a = 1.4 mm

SECT, a = 1.5 mm

PTST, a = 3.7 mm

SECB, a = 1.2 mm

SECT, a = 1.2 mm

Wilson Bilinear

5 10 15

Normalized Strain

20

Figure 8. Data points: experimentally measured J- integral values corrected

to eliminate all except the gross section yielding contribution;

solid curve: theoretical prediction made using Wilson's

equations for a bilinear material.

61
TABLE 5 -Toughness and tearing resistance, in terms of the J- integral, of

tensile and bend specimens with short cracks.

Tensile and bending panel tests

Specimen

Type

Orientation Side-Grooves ? a/W J c , initiation ^mat

DECT

(saw- cut

cracks)

LT no 0.014 NA NA

SECT LT no 0.023 438 400

SECT

(prestrained)

LT no 0.028 NA 66

SECB LT no 0.017 NA NA

SECT TL no 0.018 338 319

PTST TL no 0.036 382 187

SECB TL no 0.015 NA NA

SECT* TL no 0.014 225 119

*-30°C

DECT = Double -edge -cracked tensile

SECT = Single-edge-cracked tensile

SECB = Single-edge-cracked bend

PTST = Part- through- surface tensile

LT = Longitudinal orientation

TL = Transverse orientation

NA = Not available

62
4.7 Conclusions

Experimental results on direct measurement of the J-integral in alloysteel panels with small relative crack sizes loaded in tension and bending

allow the following conclusions to be drawn:

1 . Loading in bending suppresses Luders band effects that influence

J-integral values measured on ASTM A-710 Grade A Class 3 alloy steel

specimens loaded in tension.

2. When remote strain in tension is equated with remote outer fiber strain in

bending, the behavior of the J-integral as a function of remote strain for

panels containing small cracks is the same in bending as in tension,

except for the step associated with Luders strains in the tensile results.

Comparisons of tensile results for two alloys, including a result at —30°C

and results for transverse- and longitudinal-oriented specimens, confirm

the theoretically predicted commonality of behavior of the normalized

J-integral for specimens with small relative crack sizes.

3. The total J-integral measured in panels with relative crack sizes of 1 to

3 percent followed roughly a theoretical prediction made using formulas

given by Wilson [10] for a Ramberg-Osgood material in plane stress,

however this agreement is believed to be accidental.

4. Correction of the J-integral results to include only the

gross - section-yielding contribution reduced the J-integral values by about

a factor of 2. The corrected values agreed approximately with

predictions made using formulas given by Wilson [10] for a bilinear

material in plane stress. The corrected J-integral values are believed to

be more accurate than the uncorrected values for cracks in infinite

panels

.

5. The toughness and tearing resistance, as measured by the J-integral, of

panels with small relative crack sizes were found to be significantly

higher than the toughness and tearing resistance of side-grooved standard

three-point-bend test specimens, and slightly higher than values for non- side-grooved specimens.

63
4.8 Acknowledgments

This work was supported by the Naval Sea Systems Command under project

SEA 05 R 25, and monitored by J . P. Gudas of the David Taylor Naval Ship

Research and Development Center, Annapolis, Maryland. The experimental

assistance of J . D. McColskey and helpful discussions with H. I. McHenry and

J. P. Gudas are appreciated.

4.9 References

[1] Read, D. T., "Experimental Method for Direct Evaluation of the J-Contour

Integral," Fracture Mechanics: Fourteenth Symposium- -Volume II:

Testing and Applications, ASTM STP 791, J. C. Lewis and G. Sines, Eds.,

American Society for Testing and Materials, 1983, pp . II - 199 - II - 213

.

[2] Rice, J. R. , "A Path Independent Integral and the Approximate Analysis

of Strain Concentrations by Notches and Cracks," Journal of Applied

Mechanics, Vol. 35, No., June 1968, pp . 379-386.

[3] Hutchinson, J. W. , "Singular Behavior at the End of a Tensile Crack in a Hardening Material," Journal of the Mechanics and Physics of Solids,

Vol. 16, No. , 1968, pp. 13-31

.

[4] Rice, J. R. and Rosengren, G. F. , "Plane Strain Deformation Near a Crack

Tip in a Power-Law Hardening Material," Journal of the Mechanics and

Physics of Solids, Vol. 16, No. , 1968, pp . 1-12.

[5] Ernst, H. A., "Material Resistance and Instability Beyond J-Controlled

Crack Growth," Elastic-Plastic Fracture: Second Symposium, Volume I- -In

Elastic Crack Analysis, ASTM STP 803, C. F. Shih and J. P. Gudas, Eds.,

American Society for Testing and Materials, 1983, pp . I-191-I-213.

[6] Begely, J. A., Landes, J. D., and Wilson, W. K. , "An Estimation Model

for the Application of the J- Integral," Fracture Analysis, ASTM STP 560,

American Society for Testing and Materials, 1974, pp . 155-169.

[7] Merkle , J. G., "Analytical Relations Between Elastic-Plastic Fracture

Criteria," Technical Report ORNL/NUREG/TM- 27 , Oak Ridge National Laboratory, Oak Ridge, Tennessee, 1976.

[8] Turner, C. E. , "Elastic-plastic aspects of fracture stress analysis:

methods for other than standardized test conditions, in Fracture

64
Mechanics in Design and Service, Philosophical Transactions of the Rural

Society of London, Vol. A299, 1981, pp . 73-92.

[9] Dawes, M. G., "Welding Journal Research Supplement, Vol. 53, 1974,

pp . 369s-379s.

[10] Wilson, W. K. , "J-Integral Estimate for Small Edge and Interior Cracks,"

Engineering Fracture Mechanics, Vol. 20, No. 4, 1984, pp . 655-665.

[11] Shih, C. F. , German, M. D., and Kumar, V., "An Engineering Approach for

Examining Crack Growth and Stability in Flawed Structures," Technical

Report SRD-80-94, General Electric Company, Schenectady, New York, 1980,

pp . A1-A47.

[12] He, M. Y. and Hutchinson, J. W. , "Bounds for Fully Plastic Crack Problems for Infinite Bodies," Elastic-Plastic Fracture," Volume I--

Inelastic Crack Analysis, ASTM STP 803, C. F. Shih and J. P. Gudas

,

Eds., American Society for Testing and Materials, 1083, pp . 1-277-

1-290.

[13] Read, D. T. and McHenry, H. I., "Interim Progress Report: J-Integral

Method for Fitness-for-Service Assessment," Technical Report NBSIR 81-

1648, National Bureau of Standards, Boulder, Colorado, May 1981.

[14] Read, D. T. , "Applied J-Integral in HY130 Tensile Panels and Implications for Fitness for Service Assessment," Technical Report NBSIR 82-

1670, National Bureau of Standards, Boulder, Colorado, July, 1982.

[15] Read, D. T., "Experimental Results for Fitness-for-Service Assessment of

HY130 Weldments," Technical Report NBSIR 84-1699, National Bureau of

Standards, Boulder, Colorado, March, 1984.

[16] Fields, R. J., private communication.

[17] Appendix of this section.

[18] Li, Q.-F., "A Study About Ji and detail in Three-Point Bend Specimens

with Deep and Shallow Notches," Engineering Fracture Mechanics Vol. 22,

No. 1, 1985, pp. 9-15.

[19] McMeeking, R. M. and Parks, D. M. , "On Criteria for J-Dominance of

Crack-Tip Fields in Large-Scale Yielding," Elastic-Plastic Fracture,

ASTM STP 668, J. D. Landes, J. A. Begley, and G. A. Clarke, Eds., Ameri- can Society for Testing and Materials, 1979, pp . 175-194.

65
4.10 Appendix.

AUXILIARY RESULTS FROM DIRECT MEASUREMENT OF APPLIED J- INTEGRAL IN ASTM A- 7 10

STEEL PANELS

Results on the complex relationships among remote strain, gauge length strain,

stress, crack mouth opening displacement, and J- integral are given in this

Appendix. Also included are typical measured strain distributions at three

stages of tension and bend tests. These results were obtained as part of the

direct measurement of the applied J- integral. They are included here because

they are useful in understanding the behavior of the applied J- integral.

66
Figure Ala-g. Dependence of J- integral, stress, and crack mouth opening

displacement on strain for double -edge -notched tensile panel

with crack length of 1.1 mm.

Remote Strain/Yield Strain

CD

a>

400

300

200

100

400

g 200

CD

a)

0 5 10 15

ASTM A-710 Steel Grade A, Class 3

Room Temp.; Longitudinal

- Double Edge Notch:

Length - 1.1 mm q o° Tension o

O

O

o

o

o

o

o

...

o

ooo

o

o

1

0.00 0.01 0.02 0.03 0.04 Remote Strain

0.05 0.

Figure Ala.

Stress, ksi

0 20 40 60 80 100 ASTM A-710 Steel' Grade A, Class 3

Room Temp.; Longitudinal

- Double Edge Notch:

Length = 1.1 mm

Tension

1

oO

O

O

OO

O

- O

oo

o

o - o

o*

- fo

o

o

o

o

2000

1000

0 06

- 2000

- 1000

0 100 200 300 400 500 600 700 800

Stress, MPa

Figure Alb.

67

Integral,

Ib/in

^

Integral,

Ib/in
D

CL

(/) CD

0)

(7)

Remote Strain/Yield Strain

o 5 10 15 800

700

600

500

400

300

200

100

0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Remote Strain

I

° o

—i i i

0

°

° -

_ o

08

- Oo

o

~oo

-O ASTM A—710 Steel

o Grade A, Class 3

8 Room Temp.; Longitudinal

D Double Edge Notch:

Length = 1.1 mm

Tension

'</)

CO

(/) CD

L. CO

Figure Ale.

c

‘o

CO

CDc

CD _J

CDCD3

O

o

Remote Strain/Yield Strain

o 5 10 15 0.06

0.05

0.04

0.03

0.02

0.01

0.00

0.00 0.01 0.02 0.03 0.04 0.05 0.06

ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal 0 Double Edge Notch: 0 Length - 1.1 mm 0 ° Tension o°

o

o

- 15 c

’a

CO

tj

a; >-

- 10 .

5=

CO

<*> CDc

CD

CDCD3

DO

Remote Strain

Figure Aid.

68
Remote Strain/Yield Strain

o 5 10 15 E 0.6 E

"c

a)E

0)o

72 0.4 CL

IS) b

cnc

'c

0)CL O 0.2 JC

75o

L*o

oa o.o 0.00 0.01 0.02 0.03 0.04 0.05 0.06 Remote Strain

—

ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal o Double Edge Notch: o Length = 1.1 mm qo Tension °

o

20 £

a>o

_o

CL

cn b

CDc

'c

CDCL O

10

l I J— J———

L

ULO

o

0 c'T

Figure Ale.

E

E

c

CDE

a)o

_D

CL

cn b

U)c

'c

QJCL O

LiO

D

L- u

Stress, ksi

0 20 40 60 80 100 ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal O Double Edge Notch: o Length - 1.1 mm o Tension o

0

oo

oo

o

0

o

o io

§

A

0 100 200 300 400 500 600 700 800

_cnE

c

CDE

CDO

_P

CLW

b

CD

_e

'c

CDCL O

J*o

oc_ u

Stress, MPa

Figure Alf

.

69
400

O

CD

0) C

I —>

Crack Mouth Opening Displacement, mils

o 10 20

300

200

100

ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal

- Double Edge Notch:

Length - 1.1 mm o° Tension 0

°

o.o 0.2 0.4

2000

_c

CD 1000 CD

0.6 Crack Mouth Opening Displacement, mm

Figure Alg.

70

/
'-Integral,

kN/m

J-Integral,

kN/m

Figure A2a-h. Dependence of J- integral, stress, and crack mouth opening

displacement on strain, and J-R curve, for single-cracked

longitudinal tensile panel at room temperature crack length

of 1.9 mm.

Remote Strain/Yield Strain

o 5 10

10000

8000

6000

4000

2000

0

0.00 0.01 0.02 0.03 0.04 0.05 Remote Strain

2000

1500

ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal

Single Edge Crack:

Length = 1.9 mm

Tension

1000

500

(SO*)0

'

' ‘

a>

CD

Figure A2a.

20

Stress, ksi 40 60 80

2000

1500

1000

500

ASTM A—710 Steel

Grade A, Class 3

Room Temp.; Longitudinal

Single Edge Crack:

Length = 1.9 mm

Tension

100

> eaU i mrln funTfiif

10000

8000

6000 O

cr> (V

4000

2000

0

100 200 300 400 500 600 700 800

Stress, MPa

Figure A2b.

71
CD

0)

Crack Length, in 0.04 0.06 0.08 0.10 0.12 0.14 2000

ASTM A—710 Steel Grade A, Class 3 10000

1500 Room Temp.; Longitudinal

- Single Edge Crack:

Length = 1.9 mm 8000

1000

Tension

O

O 6000

o

o 8

4000

500 1 of

2000

0

o — 1 0

2 3 Crack Length, mm

c

o

CD

_a>c

I —>

Figure A2c.

D

Q_

800

700

600

500

(A 400

oo

CD tn 300

200

§

0 100 ?

Remote Strain/Yield Strain

5 10

o ctfo ocyp 300000000 O O O o

ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal

Single Edge Crack:

Length = 1.9 mm

Tension

_L _L

100

80

60

40

20

0.00 0.01 0.02 0.03 Remote Strain

0.04

o 0.05

(/)

GO

GO

CD

L_ 00

Figure A2d.

72
Gauge

Length

Strain

Remote Strain/Yield Strain

o 5 10 0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00

0.00 0.01 0.02 0.03 0.04 0.05 Remote Strain

ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal

Single Edge Crack:

Length = 1.9 mm 0 Tension o

d*

20

- 10

C

‘o

00

xs

CD >-c

'o

ooJZ73c

CD

( 1

CDCT> DaO

Figure A2e.

Remote Strain/Yield Strain

o 5 10

c

(DE

CDO

_DCL

00 Q

cr> c

'c

cdCL O

zxoaS- O

2.5

1.5 -

0.5

i ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal

Single Edge Crack:

Length = 1.9 mm

Tension

O O c*0 <m*>°

o 'AP

-L _

100

80

- 60

40

20

0.00 0.01 0.02 0.03 0.04 0 Remote Strain

o 05

CDo

_o

CL

(/) Q

CD

- C

c

CDCL O

JXo

a

uo

Figure A2f.

73
Integral,

kN/m

Crack

Mouth

Opening

Displacement,

20 Stress, ksi 40 60 80 100

2.5 -

2 -

1.5 -

1 -

0.5

ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal

Single Edge Crack:

Length = 1.9 mm

Tension

o _L

- 100

- 80

60

40

20

0

100 200 300 400 500 600 700 800

Stress, MPa

Figure A2g.

Crack Mouth Opening Displacement, mils

0 20 40 60 80 100 2000

1500

1000

500 -

0

ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal

Single Edge Crack:

Length = 1.9 mm

Tension

jP

10000

- 8000 g

>

6000 ~6

i_a>

CDC

4000 |

2000

0 0.5 1 1.5 2 2.5 3 Crack Mouth Opening Displacement, mm

Figure A2h.

Crack

Mouth

Opening

Displacement,

mils
Integral,

kN/m

J-Integral,

kN/m

A ) . 1 - h . Dependence of J- integral, stress, and crack mouth opening

displacement on strain, and J-R curve, for pre-strained

s ingle - edge - cracked longitudinal tensile panel at room

temperature with crack length 2.3 mm.

Remote Strain/Yield Strain

5 10 15 ASTM A—710 Steel

1

8000 * Grade A, Class 3

Room Temp.; Longitudinal

1

Single Edge Crack: 8 6000 Length - 2.3 mm o Tension o

§

4000 o

08

1 2000 ' 0

0 JOO» ..OOQBOOOOOOOO

o.oo o.oi 0.02 0.03 0.04 Remote Strain

50000

40000 c

30000

CD

_0) 20000 j:

I

- 10000

0

0.05 0.06

Figure A3a.

2000

20 T"

Stress, ksi 40 60 80

T

100 —J—

8000 -

6000

4000 - ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal

Single Edge Crack:

Length = 2.3 mm

Tension

8o

CIO l

50000

- 40000

- 30000 —

cr> a) H 20000 C

10000

0

100 200 300 400 500

Stress, MPa

600 700 800

Figure A3b.

75
CT>

CDC

I

8000

6000 -

4000 -

2000

Crack Length, in 0.5 1 1.5 t r ASTM A-710 Steel Grade A, Class 3 ( Room Temp.; Longitudinal

Single Edge Crack: 0°° Length = 2.3 mm ° Tension °

O S

oo

10 20 30 40 Crack Length, mm

50000

40000 c

- 30000

>

CD

CD

- 20000 C

10000

50

Figure A3c.

800

700

600

O 500

400

tn 300 £

200

100 }

Remote Strain/Yield Strain

10 15

io o (* o qs> oooooooo

_L 0.00 0.01

I

- 100

ASTM A-710 Steel Grade A, Class 3

Room Temp.; Longitudinal

Single Edge Crack:

Length = 2.3 mm

Tension ''''

80

60

40

20

0 0.02 0.03 0.04 Remote Strain

0.05 0.06

CO -X

(A

co

CD GO

Figure A3d.

76
Crack

Mouth

Opening

Displacement,

Remote Strain/Yield Strain

0.00 0.01 0.02 0.03 0.04 0.05 0.06 Remote Strain

c

'a

ohT30

>- \c

'a

oh

JZ

~cr> c

0

_l

0

CD

=5O

o

Figure A3e.

12

10 -

Remote Strain/Yield Strain

10 15

1 1 ASTM A—710 Steel

o

o Grade A, Class 3

“ Room Temp.; Longitudinal

Single Edge Crack:

o

o

o Length = 2.3 mm o Tension §

o

.o o «D «EDoa*>00000000

o

oo

9

0 J

'

400

- 300

- 200

100

0.00 0.01 0.02 0.03 0.04 0.05 0.06 Remote Strain

Figure A3f.

77

Crack

Mouth

Opening

Displacement,

mils
E

Ec

CPE

CDO

_oCL

(/)

CD

_C

'c

CPCL o

-Xo

ao

12

10

2 -

20 Stress, ksi 40 60 80 100 —I

8 - 3

6 - ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal

Single Edge Crack:

Length = 2.3 mm

Tension

U4

$>o

M3 A

400

- 300

- 200

- 100

100 200 300 400 500 600 700 800

Stress, MPa

cpo

J3CL

(/> Q

U)

C

'c

CPCl O

o

o

0 o

Figure A3g.

Crack Mouth Opening Displacement, mils

0 100 200 300 400

0

CD

-PC

1 —>

• r~ i i i —

AS1M A-710 Steel 50000

8000 ” Grade A, Class 3 Q

o Room Temp.; Longitudinal Q

o° 40000

6000

Single Edge Crack: D°° Length = 2.3 mm ° Tension °

s'0 30000

4000 O

O o 20000

2000

n <

— 1

—

© 10000

0

0 2 4 6 8 10 12 Crack Mouth Opening Displacement, mm

Figure A3h.

78

-Integral,

Ib/in
Figure A4a-g. Dependence of J-integral, stress, and crack mouth

displacement on strain, and J-R curves, for single

cracked longitudinal bending panel at room tempera

crack length 1.4 mm.

o

o>

a>c

I

300

200

Remote Outer Fiber Strain/Yield Strain

o 2 4 6 8 10 — _— " ASTM A—710 Steel

Grade A, Class 3 0

0 Room Temp.; Longitudinal &

Single Edge Crack: 0 Length - 1.4 mm o Bending

100 -

1500

1000 —

CD

CD

500

0.00 0.01 0.02 0.03 Remote Outer Fiber Strain

Figure A4a.

Outer Fiber Stress, ksi 20 40 60 80 100 300

CT> jD

I

200

ASTM A—710 Steel

ioo h Grade A, Class 3

Room Temp.; Longitudinal

Single Edge Crack:

Length = 1.4 mm

Bending

000,0000 , 0 °°°

1500

iooo —

ct> <D 1z

I 500

100 200 300 400 500 600 700 800

Outer Fiber Stress, MPa

Figure A4b.

79
Remote Outer Fiber Strain/Yield Strain

o 2 4 6 8 10

o

CL.

800

700

600

COw 500

o> 00

CD JO

400

300

a) 3 200

o

100

i i i ! 1

^ZHIHEOOOOO ooooo o o ® o o 8

o

o

8§

- 8

o

8

j

ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal

Single Edge Crack:

Length = 1.4 mm

Bending

1 ' >

- 100

80

60

40

- 20

0.00 0.01 0.02 0.03 Remote Outer Fiber Strain

Figure A4c.

(/) LX

(A

(/) CD 00

CD JO

CD 3

O

Remote Outer Fiber Strain/Yield Strain

0 2 4 6 8 10

- 8

c

'a

00TO

10 a> >-c

‘a3

CD 6 40

CD 4 s

CD

2 C

CD _J

CDCD 0 =3OO

Figure A4d.

80
Remote Outer Fiber Strain/Yield Strain

0.00 0.01 0.02 0.03 Rembte Outer Fiber Strain

15

- 10

- 5

a)o

_oCL

C/5

c

'c

CDCL O

LiO

a

o o

Figure A4e.

c

cdE

<ro

_o

CL

C/5 Q

05C

’c

CDCL O

LiO

D

0.5

0.4

0.3 -

0.2

0.1

Outer Fiber Stress, ksi 20 40 60 80 100 -r

- ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal

. Single Edge Crack:

Length — 1.4 mm

Bending

000.00 0 0 o®'

(j 0.0 OO cooomo oqp

15

10

c

CDE

CDo

_g

CL

c/5

05

_c

'c

CDCL o

Li

CJo

0 100 200 300 400 500 600 700

Outer Fiber Stress, MPa

o O

800

Figure A4f.

81
Crack Mouth Opening Displacement, mils

300

CD

CDc

I

200

100

0

10 T"

15 ASTM A—710 Steel Grade A, Class 3

Room Temp.; Longitudinal

Single Edge Crack: ° Length - 1.4 mm o Bending

1500

1000

500

o

_Q)c

I

0.0 0.1 0.2 0.3 0.4 0.5 Crack Mouth Opening Displacement, mm

Figure A4g.

82
Figure A5a-h. Dependence of J- integral, stress, and crack mouth opening

displacement on strain, and J-R curve for single-edge-crack

transverse tensile panel at room temperature with crack

length 1.5 mm.

Remote Strain/Yield Strain

5 10 15 I”- ——T- 1500 (- ASTM A—710 Steel

Grade A, Class 3

Room Temp.; Transverse 0 Single Edge Crack:

Length - 1.5 mm 0 iooo h Tension Q

CD

_Q)

~c.

I 500 -

_L

- 8000

6000

CD 4000 _a>

I

2000

0.00 0.01 0.02 0.03 0.04 0.05 0 Remote Strain

o 06

Figure A5a.

Stress, ksi 20 40 60 80 100

1500

1000 -

CD

CD

500 -

i r I I

ASTM A—710 Steel

Grade A, Class 3

Room Temp.; Transverse

Single Edge Crack:

Length = 1.5 mm

Tension

- 8000

6000

CD 4000 _0>C

I

2000

100 200 300 400 500 600 700 800

Stress, MPa

Figure A5b.

83
Crack Length, in 0.04 0.06 0.08 0.10 0.12 0.14

1500

1000 -

CT>

a)

500 -

ASTM A—710 Steel Grade A, Class 3

Room Temp.; Transverse ^

Single Edge Crack:

Length = 1.5 mm 0 Tension

fib

2 3 Crack Length, mm

8000

- 6000 \

CD 4000 c

2000

Figure A5c

.

Remote Strain/Yield Strain

800

700 -

600

o 500

</) 400

in

00 300

200

100

0

-Qo

oB

e

o

_L

10 15

3oooooo

-.oooooooocPQ^J

0.00 0.01

- 100

80

ASTM A-710 Steel Grade A, Class 3

Room Temp.; Transverse

Single Edge Crack:

Length = 1.5 mm

Tension

m

60 in

in

a>

s_

40

20

0 0.02 0.03 0.04 Remote Strain

0.05 0.06

Figure A5d.

84
Remote Strain/Yield Strain

o 5 10 15

Figure A5e.

CDOo

Cl

(/) Q

CDC

'c

CDa. o

c*o

D

O

Remote Strain/Yield Strain

0 5 10 15

0.5 -

ASTM A—710 Steel

Grade A, Class 3

Room Temp.; Transverse

1.5 |- Single Edge Crack:

Length = 1.5 mm

Tension

i h

r

_L

60

c

CDE

CDO

_D

CL

V)

40 c

‘c

CDCL o

20

0.00 0.01 0.02 0.03 0.04 0.05 0 Remote Strain

o 06

o

oo

Figure A5f.

85
d)o

_D

Cl

CD Q

CDc

‘c

a)o. O

o

O

i_ o

20

Stress, ksi 40 60 80 100

1.5

0.5

ASTM A—710 Steel Grade A, Class 3

_ Room Temp.; Transverse

Single Edge Crack:

Length = 1.5 mm

Tension

CD

b mmmdt Annnnrnldl^

60

40

0 100 200 300 400 500

Stress, MPa

600 700 800

c

0)E

a>oo

Cl

(/)

a>c

‘c

0)CL o

20

o

D

o O

Figure A5g.

CD

a;

Crack Mouth Opening Displacement, mils

0 20 40 60

1500

1 1 1 - ASTM A—710 Steel Grade A, Class 3 - Room Temp.; Transverse

Single Edge Crack:

Length = 1.5 mm 0

CP

1000 - Tension 0

O

O

o

o

o

o

o o

-

500 o \

J /0 1 1 1—

8000

6000

.g

"dD)

4000 _Q)C

2000

0

0 0.5 1 1.5 2 Crack Mouth Opening Displacement, mm

Figure A5h.

86
Figure A6a-h. Dependence of J- integral, stress, and crack mouth opening

displacement on strain, and J-R curve, for part- throughsurface-cracked transverse tensile panel at room temperature,

with crack depth 3.9 mm and total crack length 13.3 mm.

c*

CJao

Remote Strain/Yield Strain

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. Room Temp.; Transverse

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0.05 0.06

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Figure A6a.

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Stress, ksi 40 60 80 100

1500

1000

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<u

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ASTM A—710 Steel

Grade A, Class 3

Room Temp.; Transverse

Surface Crack:

Length - 13 mm

Depth - 4 mm

Tension nr.r.r

8000

6000

4000

Xl

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I

2000

100 200 300 400 500

Stress, MPa

600 700 800

Figure A6b.

87
Crack Length, in

x 5 6 Crack Length, mm

- 8000

- 6000 c

CD 4000 a)

- 2000

Figure A6c

.

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Q_

Remote Strain/Yield Strain

10 15 800

700 -

600

500

400

in 300

200

100

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- 100

- 80

- 60

- 40

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(/)

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Figure A6d.

88
Gauge

Length

Strain

Remote Strain/Yield Strain

o 5 10 15 0.06

0.05 -

0.04

0.03 -

0.02

0.01 -

0.00

ASTM A—710 Steel

Grade A, Class 3 < Room Temp.; Transverse o Surface Crack: o Length = 13 mm 0

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Figure A6e.

Remote Strain/Yield Strain

5 10 15

1500 |- ASTM A—710 Steel Grade A, Class 3

Room Temp.; Transverse ( Surface Crack:

Length = 13 mm o iooo |- Depth = 4 mm Q

° Tension °

CD

I 500 -

n fiminp'

J-

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6000

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~c.

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Figure A6f.

89
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1 -

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-rr-T

ASTM A—710 Steel Grade A, Class 3

Room Temp.; Transverse

Surface Crack:

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TeI?Si9J?A^nnl-.nnna QDQQOOOOOPt

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Figure A6g.

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a;o

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- Depth = 4 mm 0

° 1000 Tension

500 - /<9 0

8000

6000

CD 4000 CD

2000

0

0 0.5 1 1.5 2 2.5 Crack Mouth Opening Displacement, mm

Figure A6h.

90
-Integral,

kN/m

J-Integral,

kN/m

Figure A7a-h. Dependence of J- integral, stress, and crack mouth opening

displacement on strain, for single-edge-cracked transverse

bending panel at room temperature with crack length 1.2 mm.

Remote Outer Fiber Strain/Yield Strain

0 2 4 6 8 200

150 -

100

50

ASTM A—710 Steel

Grade A, Class 3

Room Temp.; Transverse

Single Edge Crack:

Length — 1.2 mm

Four Point Bending

/

0.00 0.01 0.02 Remote Outer Fiber Strain

o.

1000

800

600

400

200

0 03

c>

CT> <D

Figure A7a.

Outer Fiber Stress, ksi 20 40 60 80 100 200

150 -

100 -

50

O

O

o

o ASTM A—710 Steel o Grade A, Class 3 § Room Temp.; Transverse o Single Edge Crack:

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Four Point Bending

I

'

1000

800 c

xT

600 "b~u

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<1)

- 200

100 200 300 400 500 600 700 800

Outer Fiber Stress, MPa

Figure A7b.

91
D

Q_W

co

CD

(7)

CD _Q

CD "5o

Remote Outer Fiber Strain/Yield Strain

0 2 4 6 8 800

700

600

500

400

300

200

100

0 0.00 0.01 0.02 0.03 Remote Outer Fiber Strain

1 1 1 1

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8

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o Grade A, Class 3

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to

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(7)c_

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c

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c_ CO

30

i>-c

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(7)i_

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92
Crack

Mouth

Opening

Displacement,

mm

Crack

Mouth

Opening

Displacement,

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0.1

0.0

0.3

0.2

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Remote Outer Fiber Strain/Yield Strain

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Remote Outer Fiber Strain

Figure Ale.

Outer Fiber Stress, ksi

0 20Jill 40 60 80 100 “i

O

o

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o

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o

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- Grade A, Class 3 8 Room Temp.; Transverse

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o

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J

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J 0 100 200 300 400 500 600 700 800

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CD

Crack Mouth Opening Displacement, mils

o 2 4 6 8 10 200

150

100

50

0

1000

800

600

400

200

0

0.0 0.1 0.2 0.3

I

i ASTM A—710 Steel Grade A, Class 3

Room Temp.; Transverse

- Single Edge Crack:

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Four Point Bending °

<$P z

c

a

CD

CDC

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Crack Mouth Opening Displacement, mm

Figure A7g.

94
Figure A8a-h. Dependence of J- integral, stress, and crack mouth opening

displacement on strain, and J-R curve, for single-edgecracked transverse tensile panel at -30°C with crack length

1

.

2 mm .

Remote Strain/Yield Strain

o 5 10 15

z

r*D

cd £IE

I

500

400

300

200

100

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2000 c

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cn

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Figure A8a.

20

j*

”ocn

(D

500

400

300

100

Stress, ksi 40 60 80 100

i i r ! 1

oo

o

o - o

" o

8

o

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0 100 200 300 400 500 600 700

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Crack Length, in 0.04 0.05 0.06

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I

500

400

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cu

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in

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o 5 10 15

100

80

60

40

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0

0.00 0.01 0.02 0.03 0.04 0.05 0.06 Remote Strain

800

700

600

500

400

300

200

100

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o 5 10 15 0.06

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0.01 -

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'-Integral,

kN/m

Crack

Mouth

Opening

Displacement,

20 Stress, ksi 40 60 80

0.6

0.4 -

100

ASTM A—710 Steel Grade A, Class 3

°- 2 1“ —30 C; Transverse

Single Edge Crack:

Length = 1.2 mm

Tension

oWAnnrt nn QQ Q OOP 00 ?°°°°°

o

o

o

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o.o

20

- 10

0

0 100 200 300 400 500

Stress, MPa

600 700 800

Figure A8g.

Crack Mouth Opening Displacement, mils

o 10 20 500

400

300

200

100

0

ASTM A—710 S'eel Grade A, Class 3

. -30 C; Transverse

Single Edge Crack:

Length = 1.2 mm

Tension

C

2000 c

O)

_a>

1000 |

0

0.0 0.2 0.4 0.6 Crack Mouth Opening Displacement, mm

Figure A8h.

98

Crack

Mouth

Opening

Displacement,

mils
International Journal of Fracture 31 (1986) 161 — 1 ~

1

© Martinus Nijhoff Publishers. Dordrecht - Printed in the Netherlands

5. Essential work of fracture ( we ) versus energy dissipation rate

( Jc ) in plane stress ductile fracture

M.P. WNUK * and D.T. READ

Fracture and Deformation Division, National Bureau of Standards, Boulder. CO 80303, USA

(Received 24 July 1984; in revised form 20 February 1986)

Abstract.

Two measures of fracture toughness have been investigated. The first is the Cotterell's essential work of fracture

( u ) which reflects the energy absorbed in the process of localized necking and decohesion occurring within the crack tip region. The second is the familiar critical energy dissipation rate associated with the onset of crack extension and commonly designated by Jc

. Total of 48 fracture tests have been performed on thin aluminum

double-edge-notched panels and thin compact tension specimens with varying crack size-to-ligament ratios. In a simple experimental procedure it has been established that both measures are equivalent, at least under the plane stress conditions, and that they both represent the fraction of energy which is transmitted through the

plastic deformation field into the crack tip region. The ratio “essential work of fracture/total work of fracture" has been suggested as a quantitative measure of the energy transmission process. Certain predictions are made

concerning variations of the energy transmission factor (ETF) during the stable phase of ductile fracture propagation.

Introduction

Energy release rates have been considered fundamental to fracture mechanics since

Griffith’s original work in the field. In elastic materials, whether linear or non-linear,

there is no history dependence associated with the deformation process, and the energ>

released when a crack grows from length a to a + \a is equal to the difference between

the elastic energies stored in the specimen containing crack of length a and the same

specimen with crack of length a + A a\ all at constant imposed displacement. Real

materials, however, are irreversible. They store some amount of strain energy but ihe> absorb much more energy as work. By analogy to the reversible deformation field generated within a cracked body, the critical rate of energy absorption serves as a measure

of fracture toughness. As we intend to show, the critical /-integral and the Cotterell's essential work of fracture may be used interchangeably, as the equivalent measures of

specific work absorption associated with the initiation of fracture in real materials. Final

results of this investigation are in qualitative agreement with the theoretical considerations of Turner [10.11] and Paris et al. [12] which focus on applications of /-integral in the description of ductile failure. More detailed discussion of the “ubiquitous tj factor",

cf. [10], or the /-term (our ve0 ) w-hich represents the true energy release rate for irreversible solids, cf. [11]. are beyond the scope of this research. In recent times, R-curves have been plotted for elasto-plastic materials to describe

changes in apparent fracture toughness or energy dissipation rate with crack growd

* On leave from The University of Wisconsin-Nlilwaukee.

99
M.P. Wnuk and D.T. Read

Attempts have been made to analyze the fracture process by breaking it up into parts that are the same in all specimen geometries and those that depend on specimen geometry.

The former are usually associated with certain local fracture features while the latter encompass fracture parameters of global nature. For example, theoretical predictions of

the geometry dependence of R-curves (global entities) would be of practical significance

in describing failure under various loading conditions. On the other hand, the concept of

the essential work of fracture, which is obviously a local quantity, has been proposed as a geometry-independent and crack-extension-invariant feature of the fracture process. In 1977 Cotterell [1] reported experimental measurements concerned with plane stress situations and intended to differentiate between essential work of fracture and work done

in the outer plastic region, which shields the crack tip region.

Since the concept of “essential work of fracture” we , is not widely known, and since we

consider the quantity we a potentially useful parameter for assessment of material

toughness against ductile failure, we have set up a simple experimental program with an

intention (a) to verify the existence of the essential work of fracture, we , and (b) to find a

relationship between the quantity we and other well established parameters characterizing occurrence of ductile fracture, such as the critical 7-integral value, Jc

.

2. Specimens and experimental procedures

Cotterell’s experiment has been repeated on thin (3.2 mm thick) sheets of a ductile aluminum alloy, 5052-H32. This alloy had a yield strength of 179 MPa and an ultimate

strength of 245 MPa, uniform elongation of 10 percent, and reduction of area of 57

percent. It contained 2.5 percent magnesium and 0.25 percent chromium by weight. Deep

double-edge notches were cut into tensile panels 560 mm long and 82 mm wide, Fig. la. The panels were instrumented with an extensometer of gage length 80 mm spanning the plane of the notches. The specimens were strained to failure in a servo-controlled

hydraulic testing machine under displacement control. Load was plotted continuously

against extension during the test. The same test procedure was repeated using specimens

of the 1TCT compact specimen geometry, Fig. lb. Anti-buckling guides were used to prevent out-of-plane deformation, resulting in some uncertainty in the load. Compact tensile specimens of the same alloy were used to obtain a JR curve. The notch

preparation was the same as in the notched tensile panels. The in-plane specimen

dimensions were as usual for 1TCT specimens, but the thickness was 3.2 mm, as it was for the tensile specimens. The JR curve data for three specimens, Fig. 2, had the usual shape,

with a critical value of 7, of (0.170 ± 0.025) 7/mm2 and a slope, dJ/da, of 50 ± 8N/mm2

. The slight negative values of crack extension, A a, in Fig. 2, are not real, but are an

artifact of the test procedure.

3. Results

According to Cotterell’s procedure, the recorded load-displacement curves were in- tegrated to give work done to failure. The work for each specimen was divided by

specimen thickness and initial ligament length to give the work done per unit area of

fracture surface. These work density values were plotted against ligament length. Fig. 3a

and 3b. Best-fit straight lines were drawn through the data. The zero-ligament intercepts,

which according to Cotterell represent the specific essential work of fracture, were

0.20 + 0.026 7/mm2

, for the DEN specimens, and 0.20 + 0.05 7/mm2 for the compact

specimens.

For the compact specimens, the data were subject to a large uncertainty, as indicated

in Fig. 3b. The uncertainties arose mainly from friction between the specimens and the

100
kN/m

Essential work of fracture (we )

0.3175 Thick

All dimensions in cm.

Figure 1. Tensile panel (a) and compact (b) specimens used in the present study.

Aa, in

0 0.05 0.10 0.15 400

2000

300

200

100

co ° A

A

D

cp

AO

O A

Al 5052-H32

o Specimen 1 o Specimen 2 A Specimen 3

<1500

i1000

-500

-l-IO 0.1 0.2 0.3 0.4

Aa, cm

Figure 2. J-R curve data for aluminum 5052-H32 specimen material

101

lb/in
M.P. Wnuk and D.T. Read

LIGAMENT LENGTH, mm

CME

E

<

UJDC<

DC

UJCL

UJz

O

Q

*

DCo

$

0.5

0.4

0.3

0.2

0.1

1 1

1 /

< r ^ •

s'

s' s'

s'

s'

S'

s' T l's' s' Aluminum ^

5052-H32

Compact

I

1 1 1 0 5 10 15 20

LIGAMENT LENGTH, mm

Figure 3. Specific work to fracture plotted against ligament length for DEN tensile panels (a) and compact

specimens (b).

anti-buckling guide. Loading due to friction was estimated, and was eliminated from the work calculation. The data point with the smallest ligament was not considered in drawing a straight line through the data points.

The specific essential work of fracture for the CT specimens was consistent with that

for the DEN specimens, within experimental uncertainty. More precise experiments are needed to determine the difference, if any, between the specific essential work of fracture

for these two specimen geometries.

102
Essential work of fracture (we )

4. Discussion

The significance of these test results lies in the equality, within experimental error, of the

critical ./ value and the specific essential work of fracture. This agreement is not considered coincidental. This result is interpreted to mean that both the critical /-integral

for initiation of tearing and the specific work to fracture measure the work done in local straining, necking and material separation near the plane of the propagating crack. * A relation between fracture toughness and absorbed energy has been suggested

previously for side-grooved steel bend specimens with shallower cracks than those of the present study [2], This work proposed a functional relationship between work of fracture and toughness, but the function included arbitrary constants which were calculated from

the experimental data. The agreement between critical J value and specific essential work of fracture could be

further interpreted as support for the conclusion of Willoughby, Pratt, and Turner [3] that /^-curves reflect work done remotely from the crack. Even though the work done during

failure of the tensile panels included contributions from the whole iCcurve (whatever the /Tcurve may have been for such specimens), the work done locally near the crack plane

corresponded to the critical J value for initiation of tearing. Figure 5 shows the entire

plastic strain field, and the local plastic strain field within it. The local field is within a distance of approximately t, the specimen thickness, of the fracture surface, and its thickness reduction, by necking, is more severe than the remote thickness reduction within

the uniform plastic strain field. Considerations of local vs. remote straining bring up another interesting feature of

ductile fracture. Work done by the loading system in deforming the specimen must be

stored as strain work density. Consider the plastic part of this work, which is permanently

absorbed as strain work density. The strain work density is increased both locally, near

the fracture plane, and remotely, away from the fracture plane. The work absorbed locally

contributes directly to the fracture process. Load is transmitted from the specimen grips

to the local crack tip region by remote regions of the specimen. Because this load does

CT

<T

(a) (b) (c)

Figure 4. Side view of three stages in failure of tensile panel: (a) unstrained; (b) strained and necked; tu

fractured.

* Figure 4 shows a side view of three stages in the failure process of the tensile panels used here. The agreement between Jc and we implies that the measured work density gives the work needed to go from stage (a) i. stage

(c). If the energy needed to go from stage (b) to stage (c) were sought, more sensitive experimental technique than those used here would be needed.

103
M.P. Wnuk and D.T. Read

a

t M M

ll;i Entire plastic strain field

V////A Local plastic strain field

Figure 5. Entire and local plastic strain fields in double-edge-notched tensile panel.

work, one can view the remote regions of the specimen as conduits of work from the grips

toward the local fracture region. Any work absorbed in remote regions is not available to the crack tip region. The remote energy absorption process can be viewed as a screening

action that prevents some work from reaching the crack tip region where it can contribute

to fracture. This screening action of the plastic deformation field has been considered a primary reason for the existence of the slow stable cracking occurring during the early

stages of ductile fracture, cf. Broberg [4]. This effect can be described using the final stretch model of a slowly growing crack,

Wnuk [5], If we agree to define the so-called ‘’energy transmission factor” (ETF for short)

as the ratio w essential work of fracture ETF = — = (1) Wj total work of fracture

where we , the essential work of fracture, is the specific essential work of fracture multiplied by the ligament area, and uy is the total work done on the fractured specimen,

then we may indeed assign a quantitative measure to the screening phenomenon. It is noted that high screening corresponds to lower transmission, and vice versa. We proceed to show that the quotient ETF is always less than or equal to one, and that

it decreases from its initial value as the stable crack propagates (a decrease in ETF

signifies a more intensive screening action). To demonstrate these effects let us first calculate the ETF at the onset of crack extension. We use only the DEN panel data

because it has less scatter. Dividing the value of the fracture energy obtained at the zero-ligament intercept by the density of the total work of fracture, as given by the experimental points in Fig. 3a, we obtain estimates of the ETF at the onset ‘of crack

extension for various ligament lengths. These numbers are listed in the third column of

Table 1. For the deeply notched tensile specimens used in our experiment, the ligament /

104
Essential work of fracture (

vv , )

I able 1 Screening of fracture energy by the field of plastic deformation generated around the leading edges of deep notches in a tensile specimen. The quantity “ETF' represents the “damping effect” of the plastic zone

developed around the notches prior to fracture. ETF is defined as the ratio of the essential (or local) energy expended in the fracture process to the total (or global) work done in the entire volume of the specimen

Ligament

/(mm)

(R/a) ini ETF ^ 1 A exp ETF (6) Error

5 0.065 0.870 0.959 10%

10 0.139 0.678 0.916 35%

18 0.281 0.556 0.846 52%

27.5 0.505 0.449 0.756 68%

was fully yielded prior to fracture, thus l —2R. Here, the factor 2 is added because of the symmetry of the double edge notch specimen, while R denotes the plastic zone radius

associated with a single crack tip. For a stationary crack the ratio R/a. where crack

length a — (b — /)/2. with b the full specimen width, is calculated as follows

R _ 1/2 =l a ~ (b-l)/2 ~ bl

( 2 )

The R/a ratios obtained from each data point of Fig. 3a. are shown in the second

column of Table 1. The fourth column provides the ETF values calculated from the line plasticity model of ductile fracture [6.7], applied to an infinite width center crack panel.

Identifying the essential work of fracture. we , per unit area, with the energy absorption

rate 7C

. and then dividing Jc by the total specific work of fracture, wy, (w'hich consists of

the specific elastic strain energy, w0 , and the plastic energy dissipation per unit area. >vp ) we obtain the theoretical energy transmission factor

ETF =

7

wo + WP (3)

The numerator of this expression represents energy dissipation rate measured by the

7-integral which for the D-BCS [6.7] model of a stationary' crack can be readily obtained

from the know'n crack tip opening displacement. 8r We have

7 = ov8, =

Sao? j ln ( sec £)’ or

vEy H1 +

f)-

(4)

The symbol (5 denotes the nondimensional loading parameter. /3 = 'tto/2o . As usual, o

indicates applied stress, a, indicates flow strength, and E} is the effective modulus for plane stress or plain strain, as is appropriate. Here we use the plane stress value. In numerous instances it is convenient to use the extent of the plastic zone R as a measure of

the external field intensity. In such a case the loading parameter /? should be replaced bv

cos

-1 [a/(a + i?)] according to the Dugdale equation. The denominator of the expression

(3) has been evaluated by Wnuk [8], and for the configuration considered here it reads

8 aol

itE-,

2 j yS tan /? + ln(cos j3), or

lv

2 f

+

(fl C0S "lFnri + ln tTnri

105
M.P. Wnuk and D.T. Read

When we divide (4) by (5), the following theoretical estimate of the energy transmission

factor follows

' In sec P

P tan P + In cos P

’ ETF = ln(l + R/a)

{l(R/a) + {R/af)

/ cos_1 (^^ a + R I These two expressions can be used to obtain quantitative predictions for the ETF both for a stationary and a quasi-static crack. The important difference in application of (6) to a quasi-static crack case consists in the evaluation of the quantity “7?” which for a stationary crack is given by the well-known Dugdale expression, so that the ratio R/a

( = sec P — 1) does not depend on the crack length (at least for an infinite width CCP

geometry), while for a moving crack the extent of plastic zone R must be treated as an R- curve quantity, i.e. it has to be thought of as a certain function of the current crack

length, R = R(a). This function may be determined through one of Wnuk’s equations

derived from the final stretch model of a quasi-static crack [5,9]

d R

d a

(M-\-\\o%(4R/p), R^a

\ - \ \og(2R 2/ap)\, R^>a.

(7a)

(7b)

Here, M denotes Wnuk’s tearing modulus, directly proportional to the ratio of the final stretch p and the process zone size p. M differs from Shih’s modulus based on the CTOA

model of quasi-static mode / crack Tp by a constant factor of 7t/8, i.e. M = {it/S)Tp

. Equation (7a) applies to the small scale yielding case regardless of crack configuration,

while the expression (7b) is valid * for the large scale yielding situation encountered in an

infinite width center cracked panel (CCP). In both instances the state of plane stress is presumed. For an intermediate range of the R/a ratios the following equation should be

used, cf. [9] dR/da =

a + R

a

2eR(2a + R)

ap

(7c)

It is readily seen that both (7a) and (7b) result as limiting cases from the expression (7c). When R exceeds the initiation threshold, i? jni , the function R = R(a ) must be

obtained by numerical integration of (7). Finally, when these results are substituted for R

in the second expression in (6), it yields the three steeper curves for the ETF vs. R/a

shown in Fig. 6 as curves 1, 2 and 3. As expected, the expressions in (6) approach one for the case of brittle fracture when

the effects of ductile screening disappear (/? —> 0, R —> 0), while in the other extreme case of material behavior under the large scale yielding situation (R » a), the ETF predicted

by (6) drops to zero. Of course, before this may happen the crack opens up. The ensuing

stable growth and the associated energy transmission factor are governed by the equations

pertaining to a quasi-static, rather than stationary, crack.

Note that (7b) may be written in an alternative form

dJ_ da

so,.

7tE

4a,2 M — lim

7tE

2e — (Aa + a 0 ) (?d)

which for small increments of crack extension, 4a/a 0 « 1 agrees with the well known result of Paris, dJ/da = constant, suggested for metallic alloys of significant ductility. The “constant” becomes then ( o}./E)Tj

or simply Ts ( = 5/e,.p), in which e, denotes strain at the onset of yield.

106

i
Essential work of fracture (we ) AMOUNT OF STABLE CRACK EXTENSION

Figure 6. Initiation locus and the variation of the energy transmission factor due to stable crack extension. Note

that both an increasing ductility and the subsequent stable crack growth tend to intensify the screening action of

the plastic deformation field, which is represented by a lower ETF. Two horizontal scales are used: R /a for the upper curve valid for a stationary crack; and A a/R ml for the three curves concerning a growing quasi-static crack in an infinite width center crack panel curves 1-3. The i?-curves used to draw' curves 1-3 were obtained from the final stretch model [9].

Variation of the theoretical ETF with the extent of yielding preceding fracture, as measured by the ratio R/a, is depicted in Fig. 7. The experimental values of the ETF are

also shown for comparison. Only a qualitative agreement is to be expected because

different configurations were used, double edge notch for the experiment, and CCP of

infinite width for the theory. Another source of error is lack of strain hardening in the

Figure 7. Comparison of experimental and theoretical variations of the energy transmi"i.>n i.ai. r > the ductility of fracture specimen.

107
M. P. Wnuk and D. T. Read

theoretical model, which in its present form describes only the behavior of an ideally

elastic-plastic material. Thus the plastic energy dissipation, w in (3), is underestimated.

Despite all the differences in the conditions of the test and the assumptions underlying

the mathematical model, both curves shown in Fig. 7 exhibit the same trend. The

screening action of the plastic deformation field increases with higher ductility, while it vanishes in the limit of brittle fracture.

It should be noted that at a certain threshold value of the plastic zone size R, say R = R ini , the crack enters into the propagation phase. Description of the variations of the ETF vs. the amount of crack growth, A a, is still possible through the use of (6), but now

the entire /Ccurve has to be substituted for the symbol “/?” appearing in (6). Since in the course of stable cracking the ratio R/a tends to increase from its initial value of R ini /a0 , we observe a more pronounced drop in the energy transmission factor as depicted in Fig.

6. The TTcurves employed in drafting Fig. 6 obey the differential equation derived by one

of the authors (MPW) from his final stretch model of a quasi-static crack propagating in a

ductile material. It is noteworthy that one of those equations, namely (7a) valid for a small scale yielding plane stress situation is virtually identical to (6.9) in [13] derived more

recently through an entirely different approach for the case of small scale yielding in plane strain.

5. Conclusions

Our conclusions are drawn from the total of 48 data points, in which 20 points were

obtained in testing five DEN specimens of varying ligament size, 25 points were derived

from tests performed on five CT specimens with various a/w ratios, while additional 3 CT specimens were used to determine the critical value of /-integral by the conventional

ASTM-approved, experimental procedure as specified by the Standard E813-81. The

essential findings are as follows.

1. The critical /-integral for initiation of tearing and the specific work of fracture as defined by Cotterell both measure work done in local straining, necking, and

material separation near the plane of the propagating crack.

2. An energy transmission factor (ETF), which is the ratio of the essential work of

fracture (that is, the strain work absorbed in regions near the plane of crack

propagation) to the total work of fracture, has been defined.

3. The ETF was shown to decrease during stable crack propagation based on the final stretch model of quasi-static crack propagation applied to an infinitely wide center- cracked-panel. This trend is confirmed by the data points derived from the set of

experiments performed on the finite-width double-edge panel. Obviously, the intention is to compare only the gross features in the ETF variations during the stable crack growth phase, see Fig. 7 and Table 1. The ETF found experimentally was shown to decrease with decreasing initial crack size. In other words, small initial cracks ' tend to enhance the screening effect of the plastic deformation field.

4. It is noted that while the slopes of lines shown in Figs. 3a and 3b differ, reflecting the geometry dependence of the global fracture characteristic such as total work

done per unit area (wy) for DEN and CT specimens respectively, the intercept points

of these two lines are identical. They both converge on the value of 0.2 //mm

2

for the essential work of fracture, or the critical /-integral. This agreement is a manifestation of an important property of the tested fracture parameters ( we and

Jc ), namely, their geometry-invariance.

5. The simple test procedures presented here should perhaps be extended so that they

include plane strain situations. If proven successful, they would offer a novel and

108
Essential work of fracture (we )

unique method of determining JIC without a measurement of A a during the test. This would allow one to avoid the difficult problem of judgment when the crack

initiates, as the experimental technique described in this report would automatically

yield JiC .

Acknowledgements

This work was sponsored in part by the Naval Sea Systems Command (SEA 05R25).

Experimental assistance was provided by J.D. McColskey.

References

[1] B. Cotterell, in Fracture Mechanics and Technology, Vol. 2, Ed. G.C. Sih and C.L. Chow, Sijthoff and

Noordhoff International Publishers (1977) 785-795.

[2] V.L. Gel’miza and D.M. Shur, Problemy Prochnosti , No. 5 (1974) 85-87 (in Russian).

[3] A. A. Willoughby, P.L. Pratt and C.E. Turner, International Journal of Fracture 17 (1981) 449-465.

[4] K.B. Broberg, ibid (1977) 837-859.

[5] M.P. Wnuk, in Proceedings of International Conference on Dynamic Crack Propagation Ed. G.C. Sih, Noordhoff, Leyden, The Netherlands (1972) 273-280.

[6] D.S. Dugdale, Journal of the Mechanics and Physics of Solids 8 (1960) 100-104.

[7] B.A. Bilby, A.H. Cotterell, K.H. Swinden, Proceedings Royal Society, A., 279 (1963) 1-9.

[8] M.P. Wnuk, International Journal of Fracture Mechanics 7 (1971) 383-407.

[9] M.P. Wnuk, International Journal of Fracture Mechanics 19 (1979) 553-581.

[10] C.E. Turner, in Fracture Mechanics: Twelfth Conference, ASTM STP 700 (1980) 314-337.

[11] C.E. Turner, in Fracture Mechanics, ASTM STP 677 (1979) 614-628.

[12] P.C. Paris, H. Ernst and C.E. Turner, in Fracture Mechanics: Twelfth Conference, ASTM STP 700 (1980) 338-351.

[13] W.J. Drugan, J.R. Rice and T.L. Sham, Journal of the Mechanics and Physics of Solids 30 (1982) 447-473.

Resume

On etudie deux mesures de la tenacite a la rupture. La premiere est le travail essentiel de rupture de Cotterell (we ) qui represente l’energie absorbee au cours du processus de striction et de decohesion localisees qui se produit dans la region de l’extremite d’une fissure. La deuxieme est la notion familiere de vitesse critique de

dissipation d’energie associee au demarrage de l’extension d’une fissure, qui est couramment representee par Ji. On a precede a un total de 48 essais de rupture sur des panneaux minces d’ aluminium presentant une double

entaille de bord, et sur des eprouvettes minces de traction compactes presentant divers rapport de longueur de

fissure sur longueurs de ligaments. Par une procedure experimental simple, on a etabli que les deux mesures de

la tenacite sont equivalentes, du moins en etat plan de tension, et qu’elles representent toutes deux la fraction d’6nergie qui est transmise au travers du champ de deformation plastique dans la zone de l’extremite de la fissure. On suggere comme mesure quantitative du processus de transmission d’energie d’utiliser le rapport

“travail essentiel de rupture/travail total de rupture”. Diverses predictions sont faites en ce qui concerne les variations du facteur de transmission d’energie au cours de la phase stable de propagation d’une rupture ductile.

109
6 . POTENTIAL DROP MEASUREMENTS OF CRACK LENGTH IN TENSILE PANELS

Several authors have investigated the use of measurement of electrical

potential difference (PD) as an indirect measurement of crack length [1,2].

The PD technique was investigated for this study. A calibration function for

the double -edge -notched (DEN) tensile panel for one pair of pickup leads was derived and tested. With only one PD value, no information about differences

in crack length between the two cracks in a DEN specimen can be obtained.

Therefore a four- PD technique, involving PD measured at four locations across

the specimen was tried. A calibration function was derived and checked

briefly. This method was found to be potentially useful. However, because PD

for the thin aluminum 5052 H-32 sheets used appeared to be sensitive to local

necking in the crack plane as well as to tearing, the technique was not used in

experiments on tearing in this material. It may prove useful on thicker steel

specimens, which should have a smaller relative thickness reduction in the

crack plane.

6.1 Calibration Formulae

Standard textbooks on electrostatics should be consulted for the methods

of deriving relationships between conductor geometry and the electric field

within the conductor. Here only results will be presented. From now on,

calculated and measured PD values will be referred to as voltages.

6.1.1 Single Pair of Pickups

For a DEN specimen with two coplanar slit- like edge cracks of equal

length, with pickups located symmetrically about the crack plane on the

specimen centerline, the calculated voltage V is:

V = VQ arc sinh (sinh(7ry/2W)/cos (7ra/2W) ( 1 )

110
where V is voltage, VQ is a constant to be determined, y is distance of

pickup above crack plane, W is specimen half width, and a is crack length.

The constant VQ can be determined experimentally, by measuring V for a known

crack length a.

6.1.2 Four Pairs of Pickups

Because the situation for four pairs of pickups is more complex, an intermediate step will be given. The pickup locations are shown in

figure 1. In the theory of complex potentials, each location on the

specimen is associated with a complex number z = x + iy , where (x,y) is the

position in the usual Cartesian coordinates with the origin at the

intersection of the specimen centerline with the crack plane. A complex set

of voltages V exists, such that V = Vr + iV^, where Vr

is the real part of V

and is its imaginary part. The component sought in the following is Vj_.

The following expression was derived:

V = VQ arc sin (sin(^/2W - AB)/B) (2)

where VQ is a real constant, B = 0.5 (sin(jrb /2W) + sin(7rb 2 /2W) ) , AB= 0.5

(sin(7rb 1 /2W) - sin(7rb 2 /2W) ) , b x = W-a x , b 2 = W-a2 , and a x and a 2 are the

lengths of the two edge cracks. If we let x = ?rx/2W, and y = 7ry/2W, the

equation above has the solution

B

2 + AB(2 sin x cosh y/cosh2 V^) - (AB) 2 /cosh2 V^ =

sin2 x cosh2 y/sinh2 V^ + cosh2 x sin2 y/sinh2 V^ (3)

While this equation could be solved for V-j_, the result would be complicated

and would not be useful for calculating B and BA from four measured values

of Vj_ at four (x,y

)

locations. The present form is more useful for this

purpose. Equation 3 can be rewritten in the form

a + bXj_ + cY-l = Zj_ (4)

111
where a, b, and c correspond to the unknowns B

2

, AB and AB 2, and the X^,

and Zi are known functions of the pickup coordinates and the measured values

of V^, taken term by term from Equation (3), and the index i ranges from 1 to 4 when four pickup-pairs are used to obtain values of at four

locations (x,y) . This is simply a system of four linear equations with

three unknown constants, which can be solved by regression techniques. Or,

nonlinear least squares methods can be used. The constant VQ can be

evaluated from a specimen with a known average crack length, so that B is

known, and both crack lengths the same, so that AB is 0.

Both of the equations given above assume that the cracks are infinitely narrow, like slits, that the specimen thickness and resistivity are independent of position, and that "far away" from the crack tip the current

flowing along the specimen length is uniform across the specimen width. In

order to use either of these equations, further understanding of the effects

of necking and crack tip blunting on measured PD would be needed.

6.2 Experimental Techniques

Direct current, magnitude 40 amp, was passed through the aluminum

tensile panel specimen described in Chapter 3. Potential drop was measured

across a high-current-capacity resistor in series with the specimen, to

verify that the current remained constant. The current was introduced into

the specimen near the gripped ends, using heavy brass electrodes clamped

with springs across the full width of the specimen. The voltage was monitored at one location (one-pair) in some tests and at four locations

(four-pair) in others. In all cases, terminals were attached to the

specimen with small screws. Each terminal therefore covered an area several

millimeters square. These terminal contacts should be made smaller in

future tests. The terminals were located opposite one another along the

axial centerline of the specimen 3 cm from the transverse centerline, for

the one-pair case, and opposite one another at distances of 0.8 and 2.4 cm on both sides of the axial centerline (Fig. 1), for the four-pair case. The

specimen terminals were connected through shielded cables to the input

terminals of differential- input analog- to-digital converters with a resolution of 1 part in 65536 over a range of ± 80 mv. Therefore, the least-

112
+ , - Potential drop measurement

contact points, for the

four-pair technique

Figure 1. Location of voltage probes for four-pair measurement of crack

length in a double -edge -notched tensile panel.

113
significant bit represented a change of about 2.5 ^V. All instrumentation

could be sampled about twice per second throughout the course of the test,

with all results stored on floppy disk for later analysis and plotting.

6.3 Results

Results: Single-Pair

Figure 2 shows measured and calculated values of V for a series of

saw-cut notches in a DEN tensile panel. The agreement between calculated

and measured values is quite adequate.

Results: Four-Pair

Good results were found in a check at a single crack length, before

straining. However, because of the previously mentioned problems with

necking and tearing, this method was not tested thoroughly, and was not used

in actual tearing studies.

6.4 References

[1] H. Tada, P. Paris, G. Irwin, The Stress Analysis of Cracks Handbook . Del Research, Providence, RI , 1973, p. 2.35.

[2] C. J. Beevers , ed.

,

The Measurement of Crack Length and Shape During

Fracture and Fatigue . Engineering Materials Advisory Services, London,

1980, pp. 85-272.

114
POTENTIAL

DROP,

V,

mV

CUT LENGTH, a, cm

Figure 2. Measured and calculated value of single-pair pickup voltage as a function of crack length produced by saw-cutting in a double-edge

notched panel.

115
NBS-1 14A (REV. 2-6C) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBSIR 86-3045

2. Performing Organ. Report No. 3. Publication Date

May 1987

4. TITLE AND SUBTITLE

Strain Hardening and Stable Tearing Effects in Fitness-for-Service Assessment:

Progress Report

5. AUTHOR(S)

D.T. Read

6. PERFORMING ORGANIZATION (If joint or other than N BS. see in struction s) 7. Contract/Grant No. national bureau of standards

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

David Taylor Naval Ship Research and Development Center

Annapolis, Maryland 21402

10. SUPPLEMENTARY NOTES

i Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

This report describes studies done to provide information on how to account for

material strain-hardening and tearing in f itness-for-service assessment. Included

are a literature review, a study of the strength and ductility of cracked tensile

panels under compliant loading, a report on applied J-integral measurements in an HSLA steel, a study of the relationship of the essential work of fracture to the

J-integral, and a description of potential drop techniques for crack length measurement in double-edge-notched tensile panels.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitali ze only proper names; and separate key words by semicolons)

assessment curve; ductility; fracture; J-integral; R-curve; toughness

13. AVAILABILITY

C^u n I i mi ted J For Official Distribution, Do Not Release to NTIS

] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

[ X 1 Order From National Technical Information Service (NTIS), Springfield, VA. 22161

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PRINTED PAGES

120

15. Price

U.S. GOVERNMENT PRINTING OFFICE: 1987—776-003/65,196 REGION NO 8 USCOMM-DC 6043-P80