Astm stp 1074 1990

STP 1074

Fracture Mechanics:

Twenty-First Symposium

J. P. Gudas, J. A. Joyce, and E. M. Hackett, editors

AsTM

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Philadelphia, PA 19103

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August 1990

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Foreword

The ASTM Twenty-First National Symposium on Fracture Mechanics was held in

Annapolis, Maryland, on 28-30 June 1988. Its sponsor was Committee E-24 on Fracture

Testing.

The co-chairmen for this symposium were John P. Gudas, David Taylor Research Center;

James A. Joyce, United States Naval Academy; and Edwin M. Hackett, David Taylor

Research Center. They have also served as editors of this volume.

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Contents

Introduction ix

ELASTIC-PLASTIC FRACTURE MECHANICS (I)

An Analytical Comparison of Short Crack and Deep Crack CrOD Fracture

Specimens of an A36 Steel--w.A. SOREM, R. H. DODDS, JR., AND S. T. ROLFE

Direct J-R Curve Analysis: A Guide to the Methodology--R. HERRERA AND

J. D. LANDES

Application of the Method of Caustics to J-Testing with Standard Specimen

Geometries--R. J. SANFORD AND R. W. JUDY, JR.

Extrapolation of C(T) Specimen J-R Curves--G. M. WILKOWSKI, C. W. MARSCHALL,

AND M. P. LANDOW

Application of J-Integral and Modified J-Integral to Cases of Large Crack

Extension--J. A. JOYCE, D. A. DAVIS, E. M. HACKETT, AND R. A. HAYS

DYNAMIC FRACTURE

Impact Fracture of a Tough Ductile Steel--A. s. DOUGLAS AND M. S. SUH

Dynamic Fracture Behavior of a Structural Steel--K. CliO, J. P. SKLENAK, AND

J. DUFFY

Discussion

Dynamic Key-Curves for Brittle Fracture Impact Tests and Establishment of a

Transition Time--w. BOHME

Explosive Testing of Full Thickness Precracked Weldments--L. N. GI~ORD,

J. R. CARLBERG, A. J. WIGGS, AND J. B. SICKLES

Magnetic Emission Detection of Crack Iuitiation--s. R. WINKLER

TRANSITION FRACTURE

Effect of Biaxial Loading on A533B in Ductile-Brittle Transition--s. J. CARWOOD,

T. G. DAVEY, AND Y. C. WONG

109

126

143

144

157

178

195

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Fracture Toughness in the Transition Regime for A533B-I Steel: The Effect of

Specimen Sidegrooving--E. MORLAND

Analysis of Fracture Toughness Data for Modified SA508 C12 in the Ductile-toBrittle Transition Region--M. T. MIGLIN, C. S. WADE, AND

W. A. VAN DER SLUYS

Discussion

Effects of Warm Pre-Stressing on the Transition Toughness Behavior of an A533

Grade B Class 1 Pressure Vessel Steel--r). LIDBURY AND P. BIRKETT

215

238

263

264

ELASTIC-PLASTIC FRACTURE MECHANICS (II)

Unique Elastic-Plastic R-Curves: Fact or Fiction?--M. R. ETEMAD AND

C. E. TURNER

Adhesive Fracture Testing--M. F. MECKLENBURG, C. O. ARAH, D. McNAMARA,

H. HAND, AND J. A. JOYCE

Discussion

Evaluation of Elastic-Plastic Surface Flaw Behavior and Related Parameters

Using Surface Displacement Measurements--w. R. LLOYD AND

W. G. REUTER

289

307

319

322

MICROMECHANICS OF FRACTURE

Effect of Dynamic Strain Aging on Fracture Resistance of Carbon Steels

Operating at Light-Water Reactor Temperatures--c. w. MARSCHALL,

M. P. LANDOW, AND G. M. WILKOWSKI

Prediction of Fracture Toughness by Local Fracture Criterion--T. MIYATA,

A. OTSUKA~ M. MITSUBAYASHI, T. HAZE, AND S. AIHARA

Microscopic Aspects of Ductile Tearing Resistance in AISI Type 303 Stainless

Steel--A. SAXENA, D. C. DALY, H. A. ERNST, AND K. BANE1LII

Microstructure and Fracture Toughness of Cast and Forged Ultra-High-Strength,

Low-Alloy (UHSLA) Steels--J. ZEMAN, S. ROLC, J. BUCHAR, AND J. POKLUDA

339

361

378

396

COMPUTATIONAL MECHANICS

Simulation of Crack Growth and Crack Closure under Large Cyclic Plasticity--

K. S. KIM, R. H. VAN STONE, J. H. LAFLEN, AND T. W. ORANGE

Comparison of Elastic-Plastic Fracture Mechanics Techniques--F. w. BRUST,

M. NAKAGAKI, AND P. GILLLES

421

448

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Treatment of Singularities in a Middle-Crack Tension Specimen--

K. N. SHIVAKUMAR AND I. S. RAJU

Assessment of Influence Function for Elliptical Cracks Subjected to Uniform

Tension and to Pure Bending--M. PORE

Finite Element Meshing Criteria for Crack Problems--w. n. GERSTLE AND

J. E. ABDALLA, JR.

470

490

509

FRACTURE MECHANICS APPLICATIONS

Application of the CEGB Failure Assessment Procedure, R6, to Surface Flaws--

G. G. CHELL

Method and Models for R-Curve Instability Calculations--T. w. ORANGE

525

545

FRACTURE MECHANICS TESTING

Closure Measurements via a Generalized Threshold Concept---G. MARCI,

D. E. CASTRO, AND V. BACHMANN

Use of the Direct-Current Electric Potential Method to Monitor Large Amounts

of Crack Growth in Highly Ductile Metals----c. w. MARSCHALL, P. R. HELD,

M. P. LANDOW, AND P. N. MINCER

Load-Point Compliance for the Arc-Bend/Arc-Support Fracture Toughness

Specimen--F. I. BARATTA, J. A. KAPP, AND D. S. SAUNDERS

Author Index

Subject Index

563

581

594

613

615

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Introduction

The success of the Twenty-First National Symposium on Fracture Mechanics, held on

28-30 June 1988 in Annapolis, Maryland, and sponsored by ASTM Committee E-24 on

Fracture Testing, demonstrated the continued rapid development occurring in this field.

Papers were solicited from all areas of fracture mechanics and its applications. Contributions

representing a wide range of topics came from the United States and six foreign countries.

New work is presented in elastic-plastic fracture, dynamic fracture, transition fracture in

steels, micromechanical aspects of the fracture process, computational mechanics, fracture

mechanics testing, and applications of this technology. Each area poses its own challenges,

and developments proceed somewhat independently. This volume aids the researcher in

keeping abreast of these varied aspects of the discipline of fracture mechanics.

The diligent work of the Symposium Organizing Committee, the authors, and the reviewers is gratefully appreciated. We would particularly like to recognize the efforts of the ASTM

staff including Mr. Hans Greene, Ms. Kathy Friend, Ms. Wendy Dyer, Ms. Kathy Greene,

Ms. Monica Armata, Ms. Rita Harhut, and Mr. Allan Kleinberg. Finally, the assistance of

Mrs. Mary Cropley and Ms. Amanda Ewen of the David Taylor Research Center is gratefully

acknowledged.

J. P. Gudas

J. A. Joyce

E. M. Hackett

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Elastic-Plastic Fracture Mechanics (I)

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IV. A. Sorem, ~ R. H. Dodds, Jr., 2 and S. T. Rolf8 3

An Analytical Comparison of Short Crack and

Deep Crack CTOD Fracture Specimens of an

A36 Steel

REFERENCE: Sorem, W. A., Dodds, R. H., Jr., and Rolfe, S. T., "An Analytical Comparison

of Short Crack and Deep Crack CTOD Fracture Specimens of an A36 Steel," Fracture

Mechanics: Twenty-First Symposium, ASTM STP 1074, J. P. Gudas, J. A. Joyce, and E. M.

Hackett, Eds., American Society for Testing and Materials, Philadelphia, 1990, pp. 3-23.

ABSTRACT: The effect of crack-depth to specimen-width ratio on crack tip opening displacement (CTOD) fracture toughness is an important consideration in relating the results of laboratory tests to the behavior of actual structures. Deeply cracked three-point bend specimens

with crack-depth to specimen-width ratios (a/W) of 0.50 are most often used in laboratory

tests. However, to evaluate specific weld microstructures or the behavior of structures with

shallow surface cracks, specimens with a~ W ratios much less than 0.50 often are required. Laboratory tests reveal that three-point bend specimens with short cracks (a/W = 0.15) exhibit

significantly larger critical CTOD values than specimens with deep cracks (a/W = 0.5) up to

the point of ductile initiation.

In this study, finite element analyses are employed to compare the elastic-plastic behavior of

square (cross-section) three-point bend specimens with crack-depth to specimen-width ratios

(a/W) ranging between 0.50 and 0.05. The two-dimensional analysis of the specimen with an

a/Wratio of0.15 reveals a fundamental change in the deformation pattern from the deep crack

deformation pattern. The plastic zone extends to the free surface behind the crack concurrent

with the development of a plastic hinge. For shorter cracks (a/W = 0. l0 and 0.05), the plastic

zone extends to the free surface behind the crack pnor to the development of a plastic hinge.

For longer cracks (a/W > 0.20), a plastic hinge develops before the plastic zone extends to the

free surface behind the crack.

These results prompted further study of specimens with an a/W ratio of 0.15 using threedimensional, elastic-plastic finite element analyses. Results of the short crack (a/W = 0.15)

analysis are compared to the results of the deep crack (a/W = 0.50) analysis reported previously by the authors. In the linear-elastic regime (characterized by small-scale plastic deformation) the relationship of stress ahead of the crack tip to CTOD is identical for the short crack

and the deep crack specimens. At identical CTOD levels in the elastic-plastic regime (largescale plasticity, hinge formation), the crack tip stress is significantly lower for specimens with

a~ W = 0.15 than for specimens with a~ W = 0.50. Correspondingly, at equivalent stress levels,

the CTOD for the short crack is approximately 2.5 times the CTOD for the deep crack. This

observation has considerable significance in the application of CTOD results to failure analysis

or specification development where the fracture mechanism is cleavage preceded by significant

crack tip plasticity.

KEY WORDS: elastic-plastm fracture mechanics, CTOD, crack depth, short crack, toughness,

finite element, constraint

University of Kansas, Lawrence, KS 66045; currently at Exxon Production Research Company,

Houston, TX 77252.

2 University of Illinois, Urbana, IL 61801.

3 University of Kansas, Lawrence, KS 66045.

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4 FRACTURE MECHANICS: TWENTY-FIRST SYMPOSIUM

The crack-depth to specimen-width ratio (a/W) has a significant effect on the fracture

toughness results in the elastic-plastic regime where brittle fracture is preceded by significant

crack tip blunting but no ductile tearing. Typically, deep cracks (a/W = 0.5) are tested in

laboratory specimens to develop maximum constraint (stress triaxiality) at the crack tip and

therefore provide conservative estimates of material toughness. While this approach may be

appropriate for the general characterization of material fracture toughness, in the evaluation

of existing flaws in structures it is more appropriate to model the actual degree of constraint

present in the structural component. In weldments, for example, the testing of short cracks

becomes particularly important, since the region of lowest toughness does not necessarily

occur at a crack depth halfway through the specimen. With the variation of microstructures

through the heat-affected zone (HAZ) and local brittle zones (LBZs), it is probable that a

deeply cracked laboratory specimen would not produce the conservative fracture toughness

values expected.

Several methods of laboratory testing for fracture toughness within the elastic-plastic

regime are standardized. The two most widely used are the J-integral and the crack tip opening displacement (CTOD) test procedures. Both procedures could be extended to include

short crack specimens. Currently, the CTOD test procedure (BS 5762, "Methods for Crack

Opening Displacement Testing") has a major advantage in that it is the only standard which

allows testing throughout the entire realm of fracture toughness from linear-elastic to fullyplastic behavior. J-integral standards (e.g., ASTM E 813, "Jic, A Measure of Fracture Toughness") are currently limited to determining the initiation of ductile tearing (J~c), but have

often been extended to quantify brittle fracture (Jc) prior to initiation of ductile tearing.

Recent experimental investigations [I-7] have examined the effect of a/W ratio on the

fracture behavior of three-point bend specimens. Both critical values and ductile initiation

values of CTOD and J-integral were reported. A variety of materials were tested including

low-strength steels, high-strength steels, and weldments. The experimental studies [1-7] have

demonstrated CTOD and J-integral values for short crack specimens (a/W < 0.20) to be

significantly larger than for deep crack specimens (a/W = 0.50).

Most CTOD-based studies have used the BS 5762 CTOD versus crack mouth opening

displacement (CMOD) relation to analyze the behavior of short crack specimens. This relation is based on a small-scale yielding component and a plastic rotation component. A major

difficulty for CTOD testing is assessing the plastic rotation factor for specimens with a~ W

ratios less than 0.2. This rotation factor has been experimentally determined with dual clipgage techniques [3, 5] and rubber crack replication techniques [3, 4, 6, 7]. The rotation factor

for specimens with a~ W ratios of approximately 0.15 has been reported as low as 0.20 to as

high as 0.45.

This investigation focuses on three objectives. The first is to determine the a~ W ratio at

which the plastic zone extends from the crack tip to the free surface behind the crack for a

material with significant strain hardening. This a~ W ratio is expected to define the boundary

between short crack behavior and deep crack behavior. The second objective is to establish

a relationship to calculate CTOD from the measured load-CMOD record or alternative measurement of specimen response. Ideally, this relationship would merely extend the current

BS 5762 equation. The third objective is to determine the effects of the crack depth on

stresses near the crack tip in relation to the CTOD levels.

Finite element analyses are conducted to study the effect of crack depth on the nonlinear

behavior of CTOD fracture toughness test specimens. Two-dimensional (plane-stress and

plane-strain) analyses are conducted using the uniaxial stress-strain properties of an A36

steel. Square cross-section, three-point bend specimens with crack-depth to specimen-width

ratios (a/W) of 0.50, 0.20, 0.15, 0.10, and 0.05 are analyzed. The stress distributions are

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SOREM ET AL. ON SHORT AND DEEP CRACK FRACTURE SPECIMENS 5

straint. A three-dimensional, elastic-plastic analysis is performed on full-size (31.8 by 31.8

by 127 mm (1.25 by 1.25 by 5.0 in.)) and sub-size (12.7 by 12.7 by 50.8 mm (0.50 by 0.50

by 2.0 in.)) three-point bend specimens with a~ W ratios of 0.15. Comparisons of the numerical results demonstrate the effect of crack depth relative to specimen size and also the effect

of absolute crack depth. Results of the short crack (a/W = 0.15) CTOD specimens are compared to numerical results of the deep crack (a/W = 0.50) CTOD specimens previously

analyzed by Sorem et al. [8].

Material Properties

The material properties for the finite element analysis were taken from the corresponding

experimental study on a 31.8 mm (1.25 in.) thick A36 steel plate in its as-rolled condition.

The engineering stress-strain curve obtained from a standard 12.8 mm (0.505 in.) diameter

longitudinal tensile test conducted at a slow loading rate is shown in Fig. 1. The A36 steel

had an ultimate stress to yield stress ratio of 1.86 and a strain hardening exponent of 0.23.

Tensile tests were conducted at room temperature and thus typify the stress-strain properties

over a temperature range of 0*C (32~ to 2 I*C (70*F). These temperatures corresponded to

the transition region between brittle and ductile behavior of the A36 steel.

Finite Element Analysis Procedure

Elastic-plastic finite element analyses were conducted on square three-point bend specimens with a/W ratios ranging from 0.05 to 0.50. Finite element meshes for two of these

specimens are shown in Fig. 2. The analyses predicted the deformation for both small- and

large-scale plasticity with no simulation of crack growth. The finite element solutions

employed the conventional, linear strain-displacement relations based on small geometry

500,

400

"~" 3oo 13..

~200

100

0.0

e-- FINITE ELEMENT

INPUT MODIFICATION

TEST DATA

, J I , , ~ I , , ,

0.1 0.2

STRAIN (mm/mrn)

FIG. l--A36 steel tensile test showing modification for finite element analysis.

0.3

70.0

0.0

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6 FRACTURE MECHANICS: TWENTY-FIRST SYMPOSIUM

ROLLERS

CENTER. ~ /~ I CENTER ~/~ .,,,'I

I o/w = 0.s0 I o/w = o.ls LOAD POINT LOAD POINT

FIG. 2--Three-dimensional finite element analysis mesh for the three-point bend

specimens

change assumptions. Numerical computations were performed with the POLO-FINITE

structural mechanics system [9, I0]. The analytical procedure was identical to that adopted

for the study of deeply cracked square specimens considered by Sorem et al. [8]. Details of

the finite element procedure are provided in the Appendix.

Finite Element Results

Plastic Zone Distributions

Two-dimensional finite-element analyses (FEA) were performed on the full-size, square

CTOD specimen geometry with crack-depth ratios (a/W) of 0.50, 0.20, 0.15, 0.10, and 0.05.

Plastic zone sizes obtained from the 2-D FEA were compared at various linear-elastic and

elastic-plastic CTOD levels. The plastic zones developed based on the von Mises equivalent

stress for the five plane-strain models at applied CTOD levels of 0.0254, 0.0533, and 0.109

mm (1.00, 2.10, and 4.30 mils) are shown in Fig. 3. Plastic zones for the specimens with

crack-depth ratios of 0.05 and 0.10 extended from the crack tip to the free surface behind

the crack before a plastic hinge formed. For the specimen with a crack-depth ratio of 0.15,

the formation of a plastic hinge coincided with the plastic zone extending back to the free

surface. The specimen with an a~ W ratio of 0.20 developed a plastic hinge well before the

plastic zone extended back to the free surface. The plastic zone of the deep crack specimen

(a/W = 0.50) was contained completely in the plastic hinge region and never reached the

free surface behind the crack. The boundary between short crack and deep crack specimens

apparently occurs at an a~ W ratio of about 0.15 for this structural steel which undergoes

significant strain hardening.

This definition of short and deep crack behavior agrees with the theoretical slip-line field

discussed by Matsoukas et al. [6] and the results of several experimental studies [3-6]. The

crack depth at which the slip-line field first extends to the free surface was found to be

0.177 W (a/W = 0.177) for a rigid-plastic material. This does not imply that specimens with

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SOREM ET AL. ON SHORT AND DEEP CRACK FRACTURE SPECIMENS 7

CRACK

TIP ~

a/W = 0.50 a/W = 0.20 a/W = 0.15

YIELDED REGIONS AT: ~!~./

CTOD = 0.025 mm

(1.0 mils)

CTOD = 0.053 mm

(2.1 mils)

CTOD = 0.109 mm

(4..3 mils)

olW = o.1o a/W = 0.05

FIG. 3--von Mises stress dzstributtons for two-dimensional plane-strain A36 steel

specimens.

a~ W ratios greater than 0.177 behave the same as deep crack (a/W = 0.50) specimens. The

plastic zone for the deep crack specimen was always confined to the hinge region and did

not extend to the back surface. Even though the plastic hinge formed before the plastic zone

reached the back surface in the specimen with a/W = 0.20, continued strain hardening of

the material caused the plastic zone to eventually reach the back surface.

Comparison of Numerical and Experimental Results

Load versus crack mouth opening displacement (CMOD) records from the plane-strain,

plane-stress, and three-dimensional finite element analyses for the square (W = 31.8 mm

(1.25 in.)) CTOD model are compared to a measured load versus CMOD record in Fig. 4.

The measured load versus CMOD record is typical of specimens tested in a temperature

range between 0~ (32~ and 21 ~ (70~ At these temperatures, the stress-strain properties

of the A36 material are similar to the room temperature tensile properties input to the finite

element model.

At equivalent CMOD levels, the plane-strain analysis provides an upper bound and the

plane-stress analysis provides a lower bound to the experimentally measured load. The

CMOD at the center plane of the three-dimensional model is plotted versus load, since it

matches the location of the CMOD measurement in the test specimen. The load-CMOD

record of the 3-D finite element model accurately predicts the experimental load-CMOD

record.

Although very good agreement is achieved between the finite element and the experimental load-CMOD records, this "global" agreement does not necessarily verify the accuracy of

predicted response in the crack tip region, specifically the CTOD. A procedure was developed

to provide a comparison between the crack opening profile predicted by the 3-D finite element analysis and the actual crack profile.

A short crack (a/W = 0.15) test specimen was loaded well beyond plastic hinge development to a CMOD of approximately 0.427 mm (16.8 mils) and then the load was removed.

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8 FRACTURE MECHANICS: TWENTY-FIRST SYMPOSIUM

0.0 5.0 CMOD (mils) 30.0

100.0

80.0

60.0

4.0.0

20.0 o-- 3-D centerline

~-- EXPERIMENTAL

20.0

.ar

5.0

O.C , I L I a I A I = I , I ~ I , 0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

CMOD (mm)

FIG. 4--Load versus CMOD for square (31.8 by 31.8 ram) A36 steel specimens with a/W

= 0.15.

The residual plastic component of CMOD was approximately 0.366 mm (14.4 mils) as illustrated in Fig. 5. The specimen was cut in half longitudinally through the center plane, polished, and etched. Micrographs were taken of the crack profile at the center plane of the

unloaded specimen (Fig. 5a). These micrographs show the residual plastic displacement of

the crack profile in the unloaded specimen. The specimen was then reloaded in a special

fixture to the original CMOD of 0.427 mm (16.8 mils). Micrographs of the crack profile of

the reloaded specimen were taken and compared to the predicted crack profile (superimposed) at the equivalent CMOD level (Fig. 5b). The crack profile of the test specimen is

predicted very accurately by the finite element model. This comparison provides the needed

validation of the 3-D finite element modeling procedures.

CMOD-CTOD Relation

The CMOD-CTOD relation for the short crack specimen is developed from the finite element results. Variations of the CTOD and CMOD through the thickness clearly demonstrate

the three-dimensional character of the short crack specimen. The CTOD values are taken

directly from the deformed finite element mesh using the 90* intercept method [11] at six

positions through the half-thickness of the specimen.

The CMOD-CTOD results for the full-size square specimen are shown in Fig. 6. Load step

20 and load step 24 designated on the figure show the relationship of CTOD levels and

CMOD levels through the thickness of the specimen. The CTOD remains nearly constant

over the center 70% of the specimen and then decreases significantly near the outside free

surface. The CMOD exhibits the opposite behavior. Unlike the deep crack specimen, which

has no variation of CMOD over the thickness of the specimen, the CMOD for the short crack

specimen is smallest at the center plane and increases as the outside free surface is

approached. Similar CMOD variations are observed in the laboratory specimens.

The CMOD-CTOD results of the sub-size square specimen are shown in Fig. 7. Again,

load steps 20 and 24 designated on the figure show the through-thickness relationships of

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