Astm stp 1406 2002

STP 1406

Fatigue and Fracture Mechanics:

32nd Volume

Ravinder Chona, editor

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Foreword

This publication, Fatigue and Fracture Mechanics: 32nd Volume, contains papers presented at the

symposium of the same name held at ASTM Headquarters, West Conshohocken, Pennsylvania, on

14-16 June 2000. The symposium was sponsored by ASTM Committee E-8 oD Fatigue and Fracture

and was chaired by Dr. Ravinder Chona of Texas A & M University.

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Contents

TRANSITION ISSUES AND MASTER CURVES

Microstructural Limits of Applicability of the Master Curve---M. T. KIRK,

M. E. NATISHAN, AND M. WAGENHOFER ...................................... 3

Correlation Between Static Initiation Toughness Kjc and Crack Arrest Toughness

Kin 2024-T351 Aluminum Alloy--K. WALLIN ............................... 17

NORMALIZATION PROCEDURES

A Sensitivity Study on a Normalization Procedure---w. A. VAN DER SLUYS AND

B. A. YOUNG .......................................................... 37

Separability Property and Load Normalization in AA 6061-T6 Aluminum Alloy--A. N.

CASSANELLI, H. ORTIZ, J. E. WAINSTEIN, AND L. A. DEVEDIA ....................... 49

FATIGUE

Physical Reasons for a Reduced AK as Correlation for Fatigue Crack

Propagation---c. MARCI AND M. LANG ..................................... 75

Influence of Specimen Geometry on the Random Load Fatigue Crack

Growth--J. c. RADON AND K. NIKBIN ....................................... 88

Fatigue Behavior of SA533-B1 Steds--j.-Y. HUANG, R.-Z. LI, K.-F. cnmN, R.-C. KUO,

P. K. LIAW, B. YANG, AND J.-G. HUANG ....................................... 105

Scanning Atomic-Force Microscopy on Initiation and Growth Behavior of Fatigue

Slip-Bands in ~-Brass--Y. NAKAI, T. KUSUKAWA, AND N. HAYASHI ............... 122

DYNAMIC LOADING---PART ]

Compliance Ratio Method of Estimating Crack Length in Dynamic Fracture

Toughness Tests--J. A. JOYCE, P. ALBRECHT, H. C. TJIANG, AND W. J. WRIGHT ........ 139

Dynamic Fracture Toughness Testing and Analysis of HY-100 Welds---s. M. GRAHAM ,. 158

WELDS AND CLADDING

Creep Crack Growth in X20CrMoV 12 1 Steel Weld Joints--K. s. Kn~, N. W. LEE,

Y. K. CHUNG, AND J. J. PARK .............................................. 179

Application of the Local Approach to Fracture in the Brittle-to-Ductile Transition

Region of Mismatched Welds--F. MINAMI, T. KATOU, AND H. JING ............... 195

An X-Specimen Test for Determination of Thin-Walled Tube Fracture

Toughness--H. H. HSU, K. F. CHIEN, H. C. CHU, R. C. KUO, AND P. K. LIAW ........... 214

APPLICATIONS

An Energetic Approach for Large Ductile Crack Growth in

Components---s. CHAPULIOT, S. MARIE, AND D. MOULIN ........................ 229

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vi CONTENTS

Prediction of Residual Stress Effects on Fracture Instability Using the Local

Approach Y. YAMASHITA, K. SAKANO, M. ONOZUKA AND F. MINAMI ..............

ANALYTICAL ASPECTS

247

Advantages of the Concise K and Compliance Formats in Fracture Mechanics

Calculations--J. R. DONOSO AND J. D. LANDES ............................... 263

Three-Dimensional Analyses of Crack-Tip-Opening Angles and ~5-Resistance Curves

for 2024-T351 Aluminum Alloy--M. A. JAMES, J. C. NEWMAN, JR., AND

W. M. JOHNSTON, JR ..................................................... 279

COMPOSITES AND CERAMICS

Modeling Multilayer Damage in Composite Laminates Under Static and Fatigue

Load--c. SOUTIS AND M. KASHTALYAN ..................................... 301

Development of ASTM C 1421-99 Standard Test Methods for Determination of

Fracture Toughness of Advanced Ceramics--L BAR-ON, G. D. QUINN, J. SALEM, AND

M. J. JENKINS .......................................................... 315

Standard Reference Material 2100: Fracture Toughness of Ceramics---G. o. QUINN,

K. XU, R. GETTINGS, J. A. SALEM, AND J. J. SWAB ............................... 336

SURFACE FLAWS

Use of K1c and Constraint to Predict Load and Location for Initiation of Crack

Growth in Specimens Containing Part-Through Cracks--w. G. REUTER,

J. C. NEWMAN, JR., J. D. SKINNER, M. E. MEAR, AND W. R. LLOYD ................... 353

An Experimental Study of the Growth of Surface Flaws Under Cyclic

Loading--v. MCDONALD, JR. AND S. R. DANIEWICZ ............................ 381

DYNAMIC LOADING--PART II

Development of Mechanical Properties Database of A285 Steel for Structural Analysis

of Waste Tanks--A. J. DUNCAN, K. H. SUBRAMANIAN, R. L. S1NDELAR, K. MILLER

A. P. REYNOLDS, AND Y. J. CHAO ...........................................

Indexes ...................................................................

399

411

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Transition Issues and Master Curves

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Mark T. Kirk, 1 MarjorieAnn E. Natishan, 2 and Matthew Wagenhofer 3

Microstructural Limits of Applicability of the

Master Curve

REFERENCE: Kirk, M. T., Natishan, M. E., and Wagenhofer, M., "Microstructural Limits of

Applicability of the Master Curve," Fatigue and Fracture Mechanics: 32nd Volume, ASTM STP

1406, R. Chona, Ed., American Society for Testing and Materials, West Conshohocken, PA, 2001,

pp. 1-16.

ABSTRACT: ASTM Standard Test Method E 1921-97, "Test Method for the Determination of Reference Temperature, To, for Ferritlc Steels in the Transition Range, addresses determination of To, a fracture toughness reference temperature for ferritic steels having yield strength ranging from 275 to 825

MPa. E 1921 defines a ferritic steel as: "Carbon and low-alloy steels, and higher alloy steels, with the

exception of austenitic stainless steels, martensitic, and precipitation hardened steels. All ferritic steels

have body centered cubic crystal structures that display ductile to cleavage transition temperature. This

definition is not intended to imply that all of the many possible types of ferritlc steels have been verified as being amenable to analysis by this test method." The equivocation provided by the final sentence

was introduced due to lack of direct empirical evidence (i.e., fracture toughness data) demonstrating

Master Curve applicability for all ferritic alloys m all heat treatment/irradiation conditions of interest.

This question regarding the steels to which E 1921 applies inhibits its widespread application for it suggests that the user should perform some experimental confirmation of Master Curve applicability before

it is applied to a new, or previously untested, ferritic steel. Such confirmations are, in many cases, either impractical to perform (due to considerations of time and/or economy) or imposslble to perform

(due to material unavailability).

In this paper we propose an alternative to experimental demonstration to establish the steels to which

the Master Curve and, consequently, ASTM Standard Test Method E 1921 applies. Based on dislocation mechanics considerations we demonstrate that the temperature dependency of fracture toughness

in the fracture mode transition region depends only on the short-range bamers to dislocation motion established by the lattice structure (body-centered cubic (BCC) in the case of ferritic steels). Other factors

that vary with steel composition, heat treatment, and irradiation include grain size/boundaries, point defects, inclusions, precipitates, and dislocation substructures. These all provide long-range barriers to

dislocation motion, and so influence the position of the transition curve on the temperature axis (i.e., To

as determined by E 1921-97), but not its shape. This understanding suggests that the myriad of metallurgical factors that can influence absolute strength and toughness values exert no control over the form

of the variation of toughness with temperature In fracture mode transition. Moreover, this understanding provides a theoretical basis to establish, a priori, those steels to which the Master Curve should apply, and those to which it should not. On this basis, the Master Curve should model the transition fracture toughness behavior of all steels having an Iron BCC lattice structure (e.g., pearlitic steels, ferritic

steels, balnitic steels, and tempered martensitic steels). Conversely, the Master Curve should not apply

to untempered martensitic steels, which have a body-centered tetragonal (BCT) lattice structure, or to

austenite, which has a FCC structure. We confirm these expectatmns using experimental strength and

toughness data drawn from the literature.

KEYWORDS: Master Curve, fracture toughness transition behavior, To, martensitic steel, ferritic steel,

dislocation mechanics, nuclear reactor pressure vessels

1 Semor materials engineer, United States Nuclear Regulatory Commission, Rockville, MD, 20852.

2 Senior materials engineer, Phoenix Engineering Associates, Inc., 3300 Royale Glen Ave., Davidsonville, MD,

21035.

3 Graduate research assistant, Mechanical Engineering Department, Umversity of Maryland, College Park, MD

20742.

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4 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

Background and Objective

The Master Curve concept, as introduced by Wallin and co-workers in the mid-1980s, describes

the fracture toughness transition of ferritic steels [1,2]. The concept includes a weakest-link failure

model that describes the distribution of fracture toughness values at a fixed temperature, and provides

a methodology to account for the effect of crack front length on fracture toughness. Additionally,

Wallin observed that the increase of fracture toughness with increasing temperature is not sensitive

to steel alloying, heat treatment, or irradiation [3,4]. This observation led to the concept of a universal curve shape applicable to all ferritic steels. Several investigators have empirically assessed the validity of a universal curve shape for both unirradiated and irradiated nuclear reactor pressure vessel

(RPV) steels, invariably with favorable results [5,6]. These research and development activities have

led to passage of an ASTM Standard Test Method E 1921-97 to estimate the Master Curve index temperature (To) [7], and to adoption of a Code Case (N-629) within ASME Section XI that uses To to

estabhsh an index temperature (RTro) for the Kic and KI~ curves [8].

The strong empirical evidence supporting a Master Curve for nuclear RPV steels, and it's acceptance into consensus codes and standards, sets the scene for its application to assessment of nuclear

RPV integrity to end of license (EOL) and beyond [9]. However, as with any empirical methodology,

questions arise regarding the appropriateness of the technique beyond its data basis [10]. Favorable

resolution of this question is especially important in nuclear RPV applications, where it is not always

possible to conduct tests on the steel that most hmits reactor operations.

Recent work by Natishan and co-workers has focused on development of a physical basis for a universal Master Curve shape that would enable one to establish, a priori, those steels to which the Master Curve should apply, and those to which it should not [11-13]. These investigators employ dislocation-based deformation models to describe how various aspects of the microstructure of a material

control dislocation motion, and thus the energy absorbed to fracture, and how these effects vary with

temperature and strain rate. The microstructural characteristics of interest include both short- and

long-range barriers to dislocation motion:

Short Range Barriers: The lattice itself provides short-range barriers that effect the atom-toatom movement required for a dislocation to change position within the lattice.

Long Range Barriers: Long-range barriers include point defects (solute and vacancies), precipitates (semicoherent to noncoherent), boundaries (twin, grain, etc.), and other dislocations.

Long-range barriers have an inter-barrier spacing several orders of magnitude greater than the

short-range barriers provided by the lattice spacing.

Classifying microstructural features by their inter-barrier spacing is key to establishing the microstructural features responsible for the temperature dependency of the flow behavior, and thus for

the shape of the Master Curve. Thermal energy acts to increase the amplitude of vibration of atoms

about their lattice sites, consequently increasing the frequency with which an atom is out of its equilibrium position in the lattice. Since the activation energy for dislocation motion depends on the energy needed to move one atom past another, this energy is reduced when an atom is out of position.

Increased thermal energy therefore decreases the resistance of these short-range lattice barriers to dislocation motion. Conversely, increased thermal energy is not effective at moving dislocations past

long-range obstacles because no matter how large the amplitude of atomic vibration, the height of the

energy barrier required to move the dislocation past these large obstacles is orders of magnitude

larger. The flow stress of a material includes contributions from both the thermally activated shortrange barriers to dislocation motion, as well as from the nonthermally activated long-range barriers.

In their work, Natishan and co-workers demonstrate that the temperature dependency of the Master Curve depends only on the short-range barriers to dislocation motion. This finding suggests that

the only criterion for Master Curve applicability is the existence of the body-centered cubic (BCC)

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KIRK ET AL. ON APPLICABILITY OF THE MASTER CURVE 5

iron lattice structure characteristic of ferritic steels. In this study, we use this physical understanding to identify steels both at and beyond the bounds of Master Curve applicability. We assemble

fracture toughness and strength data for these steels from the literature to validate these predictions.

The steels examined vary over a large range of composition and heat-treatment relative to that

characteristic of RPV steels. As such, this study addresses concerns about extrapolation of the Master Curve beyond its empirical basis by demonstrating that an understanding of the physics underlying the Master Curve can be used to establish the steels it applies to without the need for empirical demonstration.

Limits of Master Curve Applicability Based on Dislocation Mechanics Considerations

In their 1984 paper, Wallin, Saario, and T~Srrrnen (WST) [3] suggest a link between the micro-mechanics of cleavage fracture and the observation of a "master" fracture toughness transition curve.

WST use a modified Griffith equation to define the fracture stress, i.e.,

( 1 ) 7rE'yeff

t~f~11 = 2(1 - v2)ro

Where

E is the elastic modulus

v is Poisson's ratio

ro is the size of the fracture-cansing microstructural feature, and

Yeff is the effective surface energy of the material, i.e., the sum of the surface energy and the plastic work absorbed to crack initiation (% + Wp). In the transition region, Yeff is dominated by

the plastic work consumed in moving dislocations.

WST showed that values of Kit computed based on a temperature dependent expression for the plastic work fit experimental KI, values much more accurately than K1,, values calculated using a temperature independent %ff value of 14 J/m 2 [14,15]. WST proposed the following empirically motivated temperature dependence of wp

wp = A + B " exp[C " T] (2)

Natishan and Kirk [11] proposed that the empiricism represented by Eq 2 is unnecessary, and provided the following dislocation-mechanics based description of the plastic work term

"~eff = fade 9 e (3)

Here the integrand is a measure of the strain energy density, and f is the length scale ahead of the

crack over which this strain energy density is applied. The choice of a constitutive model based on

dislocation mechanics to define the stress value in Eq 3 establishes a physically based method of computing fracture toughness while simultaneously accounting for the uniform temperature dependence

of fracture toughness for ferritic steels. These investigators used the following constitutive model derived by Zerilli and Armstrong based on dislocation mechanics considerations [16]

ITZ_ A = mcr~ q- ~ + C5e n -]- C 1 . exp[-C3T + C4T" In(k)]

(4)

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6 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

where Ao-b quantifies strengthening due to solute atoms and precipitates, k is the grain boundary

strength specific to a particular material, I is the grain diameter, e is strain, n is the strain hardening

coefficient, and C1, C3, C4, and C5 are material constants.

More recently, Wagenhofer, Natishan, and Gunawardane proposed that, given the local nature of

Eq 1, the appropriate length scale by which to multiply the strain energy density of Eq 3 to determine

the plastic work value for final fracture is the dimension of the microstructural feature that produces

the critical microcrack [17]. Consequently, Eq 3 represents the plastic work per unit area of microcrack surface created when ~ is approximately the size of a carbide or of a ferrite grain, depending on

which microstructural feature controls cleavage fracture. Based on this idea, Eq 3 becomes

"v~ff = f ~z-ade 9 ro (5)

Combining Eqs 5 and 1 eliminates of the size of the critical microstructural feature from the local failure criteria. Making this substitution, and further modifying Eq 5 to account for the combination of

triaxialit ~, strain, and stress needed to promote cleavage fracture based on a model proposed by Chen,

et al. [18-20] (see [16] for the full details of this derivation), produces the following physically-based

criteria for cleavage failure in fracture mode transition

~ 7rE'YsED

trfa,l = 2(1 - v 2) (6)

where

YSED = _~_ fad IO .... O'z-Adep

E is Young's modulus

v is Poisson's ratio

"~SED is the strain energy density

O" m is the mean stress

is the von Mises effective stress in plane strain

emt is the strain at crack initiation

e e is the plastic strain

The temperature dependency of the Master Curve is captured by the temperature dependency of Eq

6, which contains the following three temperature dependent terms: E, cent, and O'Z-A. The population of steels to which a single Master Curve shape applies can, therefore, be assessed by examining

the population of steels that share a common variation orE, ecnt, and O'Z-A with temperature. The consistent temperature dependence of the elastic modulus (E) exhibited by all ferritic steels is well documented, and is, therefore, not addressed here. Several investigators have reported an exponential increase in the strain at crack initiation (e~nt) with temperature [20, 21]. The microstructural dependency

of ecnt is a topic of continuing investigation, but due to the relationship between stress and strain, we

use the Zerilli-Armstrong constitutive model to define ecnt. Consequently, all ferritic steels will exhibit the same temperature dependency of cent. We focus on the flow stress as quantified by the Zerilli-Armstrong constitutive relation (O-Z-A) as a property that can distinguish the population of steels

to which a single Master Curve shape applies. Since the lattice structure alone controls the temperature dependence of the flow stress [11,16], Eqs 4-5 imply that the temperature dependence of fracture toughness also depends only on the lattice structure. This understanding supports the following

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KIRK ET AL. ON APPLICABILITY OF THE MASTER CURVE 7

proposal:

1. The Master Curve proposed by Wallin, i.e.,:

Ks,, Imed,an : 30 + 70" exp[0.019(T - To)] (6)

should model the temperature dependence of fracture toughness for pearlitic, ferritic, bainitic,

and tempered martensitic steels because all of these steels have a BCC matrix phase lattice

structure.

The Master Curve should not apply to untempered martensite, which has a body-centered

tetragonal (BCT) lattice structure, or to austenite, which has a FCC lattice structure. BCT materials will also exhibit a common Master Curve, albeit a different one that was proposed by

Wallin for BCC materials. FCC materials cannot have a "master" variation of toughness with

temperature because strain history influences the temperature dependency of the flow curve

for these materials [16].

This proposal is assessed in the following section.

Experimental Validation of the Proposed Limits of Master Curve Applicability

Methodology

We make the following comparisons to demonstrate that the BCC lattice structure common to all

ferritic steel provides a physical basis for a universal fracture toughness transition curve:

1. The measured temperature dependency of the yield strength of a wide range of steels is compared with that predicted by the constitutive model proposed by Zerilli and Armstrong, Eq 5,

using the coefficients for Armco iron. Since the lattice structure alone controls the temperature dependence of the yield stress, use of the coefficients for Armco iron in Eq 5 should represent the temperature dependency of all ferritic steels. To compare this prediction to experimental data, the thermal terms are isolated by subtracting the strength at a fixed temperature,

T,er i.e.,

O'f(rej) = O" G "~ C4 en "~ kd -t/2 + C1 9 exp[-C2Tref + C3Tref" ln(~)] (7)

from Eq 5 to produce the following relationship

tr s - o-f(rer = CI " exp[-CzT + C3T" In(k)] --C1 9 exp[-CzTref + C3Tref" ln(e)] (8)

where a strain rate of 0.0004/S 4 and the coefficients reported by Zerilli and Armstrong for

Armco Iron (C1 = 1033 MPa, C3 = 0.00698/~ and Ca = 0.000415/~ are used [16]. We

compare Eq 8 with experimentally determined 0.2% offset engineering yield strength values

for a reference temperature of T,~f = 27~ + 8~ By encompassing ambient temperature in

most laboratory environments, this selection of Tref admits the largest possible quantity of experimental data to further analysis. The 0.2% offset engineering yield strength at Tref, or Sy~ree),

is taken as the average of all measurements made within this temperature range.

The measured temperature dependence of fracture toughness of these same steels is compared

with that predicted by the Master Curve proposed by Wallin, Eq 6.

4 This rate is typical of that used in quasi-static tension tests of metallic materials. It is the average value of measurements reported by Link and Graham [20].

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8 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

If the BCC lattice structure alone controls the temperature dependence of fracture toughness, then

steels having a variation of yield strength with temperature that matches that predicted by Eq 8 should

also have a fracture toughness transition behavior matching that described by the Master Curve,

Eq 6.

Database

The data used is composed primarily of strength data extracted from RPVDATA, a database maintained by the commercial nuclear power industry [23]. RPVDATA summarizes the mechanical and

compositional properties of nuclear RPV steels and welds both before and after exposure to irradiation. These data are augmented by strength and fracture toughness values taken from the open literature. Literature data were used to broaden the scope of the database by including additional data on

RPV steels, data on other ferritic steels of considerably different compositions, and data on higher

strength and martensitic steels. Table 1 summarizes the chemical composition and ambient temperature strength properties of the various steels included in this analysis. These steels include the

following:

1. Ferritic RPV steels

a. Plates (irradiated and not)

b. Forgings (irradiated and not)

c. Welds (irradiated and not)

2. Ferritic Non-RPV steels

a. Lower strength C-Mn steels

b. High Strength Low Alloy (HSLA) steels

c. Tempered martensitic steels

3. Martensitic steels

a. HY-130 (a high-strength Naval construction steel)

b. Maraging steels

Assessment of Data

In the following sections we compare available data on the variation of yield strength with temperature to the variation predicted by Eq 8 for various steels. To make this comparison we first plot

the yield strength data versus the prediction of Eq 8. We also compare the variation of Kjc with temperature of these steels to the variation predicted by the Master Curve proposed by Wallin, Eq 6.

These comparisons are presented in Figs. 1-9 and are summarized in Table 2. The following general

observations can be made:

All steels having either a ferritic, pearlitic, bainitic, or a tempered martensitic microstructure

exhibit yield strength values that vary with temperature as described by the Zerilli-Armstrong

constitutive model (using coefficients for Armco Iron) (see Figs. I and 3). These steels also

exhibit toughness values that vary with temperature as described by the Master Curve (see

Figs. 2, 4, 5, and 6). None of the following factors appear to influence the temperature dependency of either strength or toughness of these steels:

a. Product form (thermo-mechanical processing, cold/hot work schedule)

b. Irradiation

c. Alloying

Each of these factors influences the flow strength only through the athermal terms ofEq 5 (i.e.,

2xo'~ + k/~l + C5~"), and is therefore not expected to influence the temperature dependency

of either strength or toughness.

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KIRK ET AL. ON APPLICABILITY OF THE MASTER CURVE 9

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1 0 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

FIG. 1--Comparison of 0.2% offset yield strength data for nuclear RPV steels to the Zerilli/Armstrong constitutive relation.

FIG. 2--Comparison of Kjc data for an irradiated RPV steel (A302B) with the Wallin Master

Curve at various fluences (E > 1 MeV) [24--26].

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