Astm stp 1406 2002

ABSTRACT: ASTM Standard Test Method E 1921-97, "Test Method for the Determination of Refer- ence Temperature, To, for Ferritlc Steels in the Transition Range, addresses determination of

STP 1406

Fatigue and Fracture Mechanics:

32nd Volume

Ravinder Chona, editor

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Each paper published in this volume was evaluated by two peer reviewers and at least on editor The authors addressed all of the reviewers' comments to the satisfaction of both the technical editor(s) and the ASTM Committee on Publications

The quahty of the papers in this publication reflects not only the obvious efforts of the authors and the technical edttor(s), but also the work of the peer reviewers In keeping with long-standing publicatton practices, ASTM maintains the anonymity of the peer reviewers The ASTM Committee on Publications acknowledges wtth appreciation thetr dedicatton and contribution of time and effort on behalf of ASTM

Printed in Brtdgeport, NJ September 2001

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

G r o w t h - - J c RADON AND K NIKBIN 88

F a t i g u e B e h a v i o r o f S A 5 3 3 - B 1 S t e d s - - j - Y HUANG, R.-Z LI, K.-F c n m N , R.-C KUO,

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

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

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

S U R F A C E F L A W S 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

D Y N A M I C L O A D I N G - - P A R T I I 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

Transition Issues and M a s t e r Curves

M a r k T Kirk, 1 MarjorieAnn E Natishan, 2 and M a t t h e w Wagenhofer 3

Microstructural Limits of Applicability of the

Master Curve

REFERENCE: Kirk, M T., Natishan, M E., and Wagenhofer, M., " M i c r o s t r u c t u r a l Limits of

Applicability of the M a s t e r 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 Refer-

ence Temperature, To, for Ferritlc Steels in the Transition Range, addresses determination of To, a frac-

ture 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 veri-

fied 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 sug-

gests 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, ei-

ther 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 disloca-

tion 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 es-

tablished 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 de-

fects, 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 metal-

lurgical 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 understand-

ing provides a theoretical basis to establish, a priori, those steels to which the Master Curve should ap-

ply, and those to which it should not On this basis, the Master Curve should model the transition frac-

ture 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

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 univer-

sal curve shape applicable to all ferritic steels Several investigators have empirically assessed the va-

lidity 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 A S T M Standard Test Method E 1921-97 to estimate the Master Curve index tem-

perature (To) [7], and to adoption of a Code Case (N-629) within A S M E 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 accep-

tance 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 uni-

versal Master Curve shape that would enable one to establish, a priori, those steels to which the Mas-

ter Curve should apply, and those to which it should not [11-13] These investigators employ dislo-

cation-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-to-

atom movement required for a dislocation to change position within the lattice

Long Range Barriers: Long-range barriers include point defects (solute and vacancies), pre-

cipitates (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 mi-

crostructural 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 equi-

librium position in the lattice Since the activation energy for dislocation motion depends on the en-

ergy 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 dis-

location 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 short-

range 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 Mas-

ter 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)

KIRK ET AL ON APPLICABILITY OF THE MASTER CURVE 5 iron lattice structure characteristic of ferritic steels In this study, we use this physical understand- ing 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 Mas- ter Curve beyond its empirical basis by demonstrating that an understanding of the physics under- lying the Master Curve can be used to establish the steels it applies to without the need for empir- ical 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-me- chanics 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 plas-

tic 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 plas- tic work fit experimental KI, values much more accurately than K1,, values calculated using a tem- perature independent %ff value of 14 J/m 2 [14,15] W S T proposed the following empirically moti- vated temperature dependence of wp

Natishan and Kirk [11] proposed that the empiricism represented by Eq 2 is unnecessary, and pro-

vided the following dislocation-mechanics based description of the plastic work term

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 com- puting fracture toughness while simultaneously accounting for the uniform temperature dependence

of fracture toughness for ferritic steels These investigators used the following constitutive model de-

rived by Zerilli and Armstrong based on dislocation mechanics considerations [16]

k

ITZ_ A = mcr~ q- ~ + C 5 e n -]- C 1 e x p [ - C 3 T + C4T" In(k)]

V l

(4)

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 micro-

crack 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

Combining Eqs 5 and 1 eliminates of the size of the critical microstructural feature from the local fail-

ure 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

"~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 popula-

tion 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 con-

sistent temperature dependence of the elastic modulus (E) exhibited by all ferritic steels is well doc-

umented, and is, therefore, not addressed here Several investigators have reported an exponential in-

crease 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 ex-

hibit the same temperature dependency of cent We focus on the flow stress as quantified by the Zer-

illi-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 tempera-

ture dependence of the flow stress [11,16], Eqs 4-5 imply that the temperature dependence of frac-

ture toughness also depends only on the lattice structure This understanding supports the following

KIRK ET AL ON APPLICABILITY OF THE MASTER CURVE 7 proposal:

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

2

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 ma- terials 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

O'f(rej) = O" G "~ C4 e n "~ k d -t/2 + C1 9 exp[-C2Tref + C3Tref" ln(~)] (7) from Eq 5 to produce the following relationship

2

tr s - o-f(rer = CI " e x p [ - C z T + 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 ex- perimental 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 mea- surements reported by Link and Graham [20]

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 main- tained 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 irradia- tion These data are augmented by strength and fracture toughness values taken from the open litera- ture 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 tempera- ture 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

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 depen- dency 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

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/Arm- strong constitutive relation

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

KIRK ET AL ON APPLICABILITY OF THE MASTER CURVE 11

FIG 3 Comparison of 0.2% offset yield strength data for ferritic non-RPV steels to the Zer- illi/Armstrong constitutive relation

FIG 4 Comparison of Kjc data for HSLA steels with the Wallin Master Curve/27-29]

12 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

FIG 5 Comparison of Kjo data for C-Mn steels with the Wallin Master Curve/30,31]

FIG 6~Comparison of K~c data for tempered martensitic steels with the Wallin Master Curve

/32,331

KIRK ET AL ON APPLICABILITY OF THE MASTER CURVE 13

FIG 7 Comparison of 0.2% offset yield strength data for martensitic steels to the Zerilli/Arm- strong constitutive relation

FIG 8 Comparison of Kjc data for HY-130 steel plate reported by two investigators with the Wallin Master Curve/33,34]

14 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

FIG 9 Comparison of Kjc data for 18Ni (250) maraging steel with the Wallin Master Curve [33]

2 All steels having a martensitic microstructure exhibit yield strength values that vary with tem- perature in a substantially different manner than the variation described by the Zerilli-Arm- strung constitutive model (using coefficients for Annco Iron) (see Fig 7) The strength values for HY-1305 fall consistently below Zerilli-Armstrong prediction, while the strength values for the maraging steel consistently exceed the Zerilli-Armstrong prediction These steels also exhibit a variation of fracture toughness with temperature that deviates substantially from that

of the Master Curve (see Figs 8 and 9)

These experimental findings agree with the proposal made in the preceding section based on dislo- cation mechanics considerations Thus, both the theory and the weight of experimental evidence sup port the idea that the existence of a BCC iron lattice structure is the sole factor needed to ensure that the temperature dependency of fracture toughness in fracture mode transition is well represented by the Master Curve proposed by Wallin

Conclusions

Dislocation mechanics considerations, and all available experimental evidence, point to the short- range barriers to dislocation motion as a key factor influencing the temperature dependency of frac- ture toughness in the fracture mode transition of ferritic steels Consequently, the Master Curve can be expected to describe the transition fracture behavior of all steels having a body centered cubic (BCC) iron lattice structure, Other factors that vary with steel composition, heat treatment, and irradiation (e.g., grain size/boundaries, inclusions, precipitates, and dislocation substructures) all provide long range barriers to dislocation motion, and so only influence the position of the transition curve on the temperature axis (i.e., To as determined by E 1921-97), but not its shape The myriad of metallurgical factors that can influence absolute strength and toughness values exert no control on the form of the

5 It should be noted that HY-130 does receive some degree of tempering, albeit much less than the related al- loy HY-80 Even after tempering the microstructure of HY-130 is predominantly martensitic, which is why we have classified it as martensitlc for purposes of this discussion

KIRK ET AL ON APPLICABILITY OF THE MASTER CURVE

TABLE 2 Assessment o f how well the temperature dependency of strength and toughness data can be

predicted for various steel alloys

15

Category Microstructure Conditions Treated # Eq 8, Fits Data # Eq 6, Fits Data RPV Steels

martensite steels

Yield strength equation: try - trf(ref) = C1 " exp[-CzT + C3T In(k)]-C1 9 exp[-CzTr,f + C3Tr~f" In(e)] where CI = 1033 MPa, C3 = 0.00698/~ and C4 = 0.000415/~ [16]

Toughness equation: Kjclmed,a, = 30 + 70" exp[0.019(T - To)]

variation o f toughness with temperature in fracture mode transition The Master Curve and ASTM Standard Test Method E 1921 can, therefore, be applied with confidence to any steel having a BCC lattice structure without any additional need to experimentally demonstrate Master Curve applicabil- ity It is therefore suggested in the next revision of E 1921 the cautionary note stating that the defini- tion of ferritic steel " is not intended to imply that all of the many possible types of ferritic steels have been verified as being amenable to analysis by this test method" may not be necessary

[4] Wallin, K., "Irradiation Damage Effects on the Fracture Toughness Transition Curve Shape for Reactor Vessel Steels," International Journal of Pressure Vessels and Piping, Vol 55, 1993, pp 61-79

[5] Kirk, M., Lott, R., Kam, C., and Server, W., "Empincal Validation of the Master Curve for Irradiated and Unirradiated Reactor Pressure Vessel Steels," Presented at the 1998 ASME/JSME Pressure Vessel and Pip- ing Symposium, July 26 30, 1998 - San Diego, CA

[6] Sokolov, M A., and Nanstad, R K., "Comparison of Irradiation Induced Shifts of Kjc and Charpy Impact Toughness for Reactor Pressure Vessel Steels," ASTM STP 1325, American Society for Testing and Mate- rials, West Conshohocken, PA 1996

[7] Merkle, J G., Wallin, K., and McCabe, D E., "Technical Basis for an ASTM Standard on Determining the Reference Temperature, To, for Ferritic Steels in the Transition Range," NUREG/CR-5504, US Nuclear Regulatory Commission, November 1998

[8] Server, W., Rosmski, R., Lott, R., Kirk, M., Hoffmann, C., Byrne, S., and Yoon, K., "Application of Mas- ter Curve Fracture Toughness Methodology for Femtic Steels," EPRI-TR-108390 (Rev 1), 1999 (in press) [9] Lott, R., Kirk, M., Klm, C., Server, W., Tomes, C., and Wilhams, J., "Application of Master Curve Tech- nology to Estimation of End of License AdJusted Reference Temperature for a Nuclear Power Plant," Pro- ceedings of the 1999 ASME Pressure Vessel and Piping Conference, ASME, July 1999

Analysis," Paper #106, SMIRT Conference, Lyon, France, August, 1997

[11] Natishan, M and Kirk, M., "A Micro-Mechanical Evaluation of the Master Curve," Fatigue and Fracture

Materials, West Conshohocken, PA 1998

16 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

dency of the Master Curve," Fracture Mechanics, 31st Symposium, ASTM STP 1389, K Jerina and J Ga- hallger, Eds., American Society for Testing and Materials, West Conshohocken, PA 1999

Cleavage Fracture of Mild Steel," Metal Science, Vol 10, 1976, pp 1-6

namics Calculations," Journal of Applied Physics, Vol 61, No 5, March 1987, pp 1816-1825

[17] Wagenhofer, M., Natishan, M., and Gunawardane, H., "A Physically Based Model to Predict the Fracture Toughness Transition Behavior of Ferritic Steels," Engineering Fracture Mechanics In press

cal Fracture Stress and Allied Toughness Value," Metallurgical Transactions A, Vol 22A, 1991

pp 2287-2296

[19] Chen, J H., Zhu, L., Wang, G Z., and Wang, Z., "Further Investigation of Critical Events in Cleavage Frac- ture of C-Mn Base and Weld Steel," Metallurgtcal Transactions A., Vol 24A, 1993, pp 659-667

Ductile-Brittle Transition Temperature Region," Journal of Materials Science Engineering, Vol 176, Nos 1-2, 1994, pp 171-175

CR-6512, USNRC, 1997

Westinghouse Energy Systems Business Unit, WCAP-14616, 1996

of A302-B and A533-B Reference Plates from PSF Simulated Surveillance and Through-Wall Irradiation Capsules," NUREG/CR-3295 (Vol 1), USNRC, 1984

Changes in RPV Steels," NUREG/CR-5493, US-NRC, 1990

Prediction of Neutron Embrittlement in Reactor Pressure Vessel Materials," EPRI NP-2782, EPRI, 1992 [27] Natishan, M E., "Mechanisms of Strength and Toughness in a M~croalloyed, Percipitation Hardened Steel," University of Virginia, Ph.D Dissertation, 1988

DTNSRDC/SME-87-54, 1987

tion, 1991

of a Low-Strength High-Strain Hardening Steel," Ph.D Dissertation, University of Kansas, 1989

Obtain Accurate Lower Bound Toughness Predictions in the Ductile-to-Brittle Transition," Small Speci-

Conshohocken, PA, 1997

Research and Development Center, DTNSRDC/SME-87-20, December 1987

mance of Seven Structural Steels," Engineering Fracture Mechanics, Vol 2, 1971, pp 319-339

sition Temperature of HY Steels," Journal of Engineering Materials and Technology, ASME, 1981, pp 133-141

K i m W a l l i n I

Correlation Between Static Initiation

Toughness Kjc and Crack Arrest Toughness

Kla 2024-T351 Aluminum Alloy

REFERENCE: Wallin, K., "Correlation Between Static Initiation Toughness Kjc and Crack Arrest Toughness Kta 2024-T351 Aluminum Alloy," Fattgue and Fracture Mechamcs: 32nd Volume,

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

2001, pp 17-34

ABSTRACT: The Master Curve method, developed for brittle fracture initiation estimation, has enabled a consistent analysis of fracture initiation toughness data The method has been modified to also describe crack arrest toughness Here, this "crack arrest master curve" is further validated and used to develop a simple, but yet adequately accurate eorrelatton between the two fracture toughness parame- ters The correlation enables the esUmatmn of crack arrest toughness from small Charpy-sized static fracture toughness tests

If a more accurate description of the crack arrest toughness is required, it can either be measured experimentally or estimated from instrumented Charpy-V crack arrest load information

KEYWORDS: crack-arrest, brittle fracture, fracture toughness testing, correlation, master curve

Normally, fracture toughness testing standards require the use of comparatively large specimens to obtain so-called valid fracture resistance values Extreme standards in this respect are the linear-elas-

tic K1c and K~a standards and the CTOD standards that require elastic behavior of the specimen or full

section thickness specimens, respectively Often, as for operational structures, it is impossible or in- appropriate to obtain large material samples for standard fracture toughness determination This is es- pecially the case with irradiation damage assessment of reactor pressure vessels, but also many other applications have the same restrictions The specimen size requirements are a major obstacle for ap- plying fracture mechanics in structural integrity assessment outside aviation, nuclear, and off-shore industries

At VTT, development work has been in progress for 15 years to develop and validate testing and analysis methods applicable for fracture resistance determination from small material samples The VTT approach is a holistic approach by which to determine static, dynamic, and crack arrest fracture toughness properties either directly or by correlations from small material samples

Recently, a new testing standard for fracture toughness testing in the transition region [1] has been published The standard is in a way "first of a kind," since it includes guidelines on how to properly treat the test data for use in structural integrity assessment No standard, so far, has done this The standard is based on the VTT Master Curve approach Key components in the standard are statistical expressions for describing the data scatter [2] and for predicting a specimen's size (crack front length)

effect [3] and an expression (Master Curve) for the fracture toughness temperature dependence [4,5]

The standard and the approach it is based upon can be considered to represent the state of the art of

i Research professor, VTT Manufacturing Technology, P.O Box 1704, FIN-02044 VTT, Finland e-mail: Kim.Wallin@vtt.fi

18 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

TYPICAL RAW DATA

MASTER CURVE ANALYSIS

FIG 1 -Principle of the master curve method for brittle fracture initiation toughness

small specimen brittle initiation fracture toughness characterization The key elements of the Master Curve method are schematically presented in Fig 1

The Master Curve method and the ASTM testing standard allow the use of the elastic-plastic pa- rameter Kjc, which enables the use of small specimens It is possible to characterize the ductile-to- brittle transition region with precracked Charpy specimens as shown in Fig 2, getting the same re- sult as with large Ktc specimens [6]

Unfortunately no elastic-plastic parameter has been found applicable for crack arrest Direct de- termination of K~a is thus only possible with large specimens behaving in a linear-elastic manner In the A S M E pressure vessel code, reference fracture toughness curves are given both for brittle frac- ture initiation and crack arrest Unfortunately, the reference temperature, RTNDT, applied with the

A S M E reference curves is far from accurate and usually over-conservative This is especially the case for brittle fracture initiation toughness The Master Curve method enables the determination of a clearly superior reference temperature, To, based on the actual initiation fracture toughness, but it does not give any information regarding crack arrest The A S M E code has a fixed relation between

the Kzc and Kta reference curves, thus implying a fixed relation between fracture initiation and crack arrest If this were the general case, the reference temperature To could be used similarly for crack ar- rest Unfortunately the relation between fracture initiation and crack arrest is not constant It can vary considerably from one material to the other The difference can be very large (Fig 3) [7] or very small (Fig 4) [7] Sometimes, fracture initiation and crack arrest toughness seem actually to have a com- mon lower bound (Fig 4)

Clearly, the relation between fracture initiation and crack arrest toughness is more complex than depicted by the A S M E pressure vessel code In the following, Kla is investigated based on a modifi- cation of the master curve method, and a simple correlation between crack arrest toughness and static brittle fracture initiation toughness is developed

Master Curve Description of Crack Arrest Toughness

The A S M E K#a reference curve is based on dynamic fracture toughness and crack arrest data The

A S M E Kta reference curve was originally drawn as a "free hand" lower limiting curve to one set of

Kla data (HSST 02) and three sets of dynamic Kid data [8] The Kid data were included due to a lack

of Kla data It appears, from the test results, that dynamic fracture toughness is close to crack arrest, but for a more accurate description it is better to focus only on crack arrest data

WALLIN ON CORRELATION BETWEEN Kjc AND Kla 19

FIG 2 Comparison between ASTM E 399 KIC and its elastic plastic equivalent Kjc for the ASME reference curve baseline material Filled symbols refer to nonfailed, end of test, values The same re-

from large specimens [61

45O

400 F: 350

50

0 -I 2q

2 0 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

The mechanism of arrest differs from that of initiation Thus the scatter and size effects are not ex- pected to be the same as for brittle fracture initiation Mechanistically, arrest occurs when the local crack driving force at the crack tip decreases below the local arrest toughness over a sufficiently large portion of the crack front A single local arrest is not sufficient to arrest the whole crack front, i.e., the scatter should be more a function of the mean properties of the matrix (and not the local) There- fore the scatter should be less than for initiation and there should not be any statistical size effects in the case of crack arrest

Nine different sets of KIa data, including the original Kla data for the HSST 02 plate used for the construction of the A S M E reference curve, were analyzed statistically to obtain a better understand- ing of the K1a reference curve [9] The biggest difference between brittle fracture initiation toughness and crack arrest toughness is that KI~ should not show a statistical size effect Thus, no size adjust- ment was performed on the KI~ data

The analysis of the Kta results was aimed at finding out whether an unified description of the data was possible It was decided to try to describe the temperature dependence of the KI,, data by the equation

KI~ = 30 + 70"exp{0.019 " ( T - Tm.)} (1)

where Tma corresponds to the temperature where the mean Kla is equal to 100 MPaVmm Equation 1

is of the same form as the standard Master Curve used for the description of the brittle fracture initi- ation toughness

The scatter in Kla was for simplicity assumed to be log-normal so that the proportional scatter in Kta is constant The outcome of the analysis is presented in Fig 5 The assumed temperature depen- dence and distribution seem to describe the data quite well Thus it appears possible to normalize the

I(la transition curve, for these materials, based only on Tma Additionally, the same temperature de-

pendence that is used to describe the brittle fracture initiation toughness seems to be applicable, The

WALLIN ON CORRELATION BETWEEN Kjc AND Kta 21

FIG 5 Scatter and temperature dependence of crack arrest toughness [9]

scatter in Kzo appears less than for Kjo The scatter does not seem to be very material dependent, with

the exception of PTSE-1 However, based also on other tests, this material has been found to be

macroscopically inhomogeneous [10] It might be considered proper to exclude PTSE-1 from the

analysis, but, by including it, a slightly more conservative estimate of the Kza scatter behavior is ob-

tained The standard deviation of the total combined dataset is ~r = 18% (compared to ~r = 28% for

brittle initiation toughness [1])

Correlation between To and TKla for Low Nickel Steels

Based on the success in applying the Master Curve temperature dependence to Kla data, it was de-

cided to try to develop a correlation between the master curve To and TKIa For the purpose, 54 dif-

ferent datasets containing both static brittle fracture initiation data and crack arrest data were col-

lected from various sources, including some of our own data and much data from literature The

datasets are listed in Table 1, where the material type, yield strength, nickel content, To, and Tma are

given The majority of the data refer to pressure vessel steels 15X2MFA, A508, and A533B, but also

many welds and other steels are included The data contain some embrittled (irradiated or heat

treated) materials The materials yield strengths that cover a range from 280 to 1082 MPa All mate-

rials had nickel contents < 1.3% All data sets were analyzed by the Master Curve methods as shown,

for example, in Figs 6a [11] and 6b [12] for the nonirradiated 72W weld (Linde 124) The quality of

the datasets varied from very few specimens to many specimens Generally, the n u m b e r of specimens

per dataset is more than 10

Overall, the Master Curve provided a satisfactory description of all datasets The materials having

the most data were selected for a further study regarding the validity of the scatter and temperature

22 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

T A B L E 1 List of materials used for the correlation

WALLIN ON CORRELATION BETWEEN KjcAND Kla 23

FIG 7 Temperature dependence and scatter for crack arrest toughness of A508 C1.3

In the case of A508 C1.3, 15X2MFA, and 15X2NMFA, the assumed scatter and temperature depen- dence is well verified Also, in the case of A533B C1.1, the assumed temperature dependence is well verified, but the scatter at high crack arrest values appear somewhat larger than assumed These ab- normally high crack arrest values refer to nonstandard tests, and there is some uncertainty of their va-

WALLIN ON CORRELATION BETWEEN KjcAND Kla 25

TKh, with To, it is possible to predict the crack arrest toughness based on static brittle fracture initia- tion toughness, i.e., small specimens can be used simultaneously for determining Kgc and for esti- mating Kla

The difference between TKIa and To is plotted as a function of To for all materials in Fig 10 A trend between the two parameters can be seen For materials where the static To temperature is low, there

is a large difference between fracture initiation and crack arrest, whereas the difference becomes small for materials with a high To temperature No significant differences in the behavior between dif- ferent materials is visible Thus, the relation between fracture initiation and crack arrest does not ap- pear specific to "material type." The data were also ordered by yield strength This is shown in Fig

11 The effects of yield strength are not very clear, but there is an indication that the higher yield strength materials have a tendency to show a larger difference between initiation and arrest The pos- sible effect of the ultimate strength was also investigated, but no additional improvements were found The possible role of ductile tearing resistance (upper shelf properties) on the relation was not investigated, since neither brittle initiation nor arrest should be significantly connected to ductile tear- ing

The data were fitted with several different equations, out of which one was selected as descriptive

of the data The selection was decided based on the technical soundness, simplicity, and goodness of fit, i.e., the equation providing the best fit to the data was not blindly chosen because the form of it was not technically sound The chosen equation had the form

26 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

FIG l O -Relation between TIaa-To and To Data ordered by material type

and the resulting correlation is

The resulting fit is presented in Fig 12 (three-dimensional) and Fig 13 (two-dimensional), and the

calculated relation is compared with the actual in Fig 14 It is seen that the scatter in the AT estimate

WALLIN ON CORRELATION BETWEEN KjcAND Kla 27

FIG 12 Three-dimensional presentation of the relation between To, %, and TKIa

2 8 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

FIG 14 -Accuracy of predicted TK~a-To difference

is 19~ The yield strength is seen to have a significant effect on the relation, but the primary param-

eter appears to be the static transition temperature To For materials with To values below - 3 0 ~ the

relation can be essentially described with a straight line having a slope of - 1 This actually indicates

a constant Trl, for these materials, i.e., no correlation between TI,;I, and To The scatter in Trio is un-

fortunately so large in this temperature region that the relation between TKIa and To could not be im-

proved by accounting for this "lack of correlation" region separately

Correlation Between To and Tra Including Effect of Nickel

The found correlation (Eq 3) is limited only to steels with a low nickel content ( <1.3% Ni) The

correlation is not expected to be applicable, as such, for steels with a higher nickel content, since

nickel is expected to affect the correlation There are indications that the difference between To and

Tma is less for high nickel steels ( > 2 % Ni) In order to examine the effect of nickel more closely, data

with higher nickel content were sought Unfortunately only one such dataset, containing both static

initiation and crack arrest data, was found The material was a HY 80 steel with 2.55% Ni, O-y = 584

MPa, To = - 177~ and TK1 a = - - 116~ [13] The results of the master curve analysis for H Y 80 are

presented in Figs 15a and 15b The KI, data are rather scarce, but 5 data points are sufficient to get

an estimate of T~cI,

The HY 80 data were included with the 54 other datasets, and the data were ordered by nickel con-

tent It was found that there is a weak, but significant, effect of nickel (Fig 16) The trend is that nickel

has a reducing effect on the difference between static initiation and crack arrest This is understand-

able, because nickel toughens the matrix itself and thus affects more the arrest toughness than the ini-

tiation toughness The data were fitted with an equation similar to Eq 2, but including nickel The re-

WALLIN ON CORRELATION BETWEEN KjcAND Kla 29

30 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

WALLIN ON CORRELATION BETWEEN KjcAND K~a 31 improve the crack arrest behavior of the material Only if the toughening is achieved by directly im- proving the toughness properties of the matrix itself (like is done when adding nickel) can the crack arrest properties also be improved significantly Another outcome of the analysis is that crack arrest

is affected less by material embrittlement than cleavage initiation toughness, i.e., the embritflement- induced shift in transition temperature is less for TKZa than for To

The reliability of Eqs 3 and 4 is not very good ( o a r = 19~ but often only a rough estimate of the crack arrest toughness may be necessary The TKI a estimate corresponding to a 85% confidence level can for example be written as

If the material's nickel content is known, it is advisable to use Eq 4 to get AT, but if the nickel con- tent is less than 1%, Eq 3 can be used as well (difference in estimates less than 5%) For higher nickel contents, Eq 3 becomes increasingly conservative (predicts a larger difference between To and Txl,),

so if only a conservative estimate is required Eq 3 can be used generally, but Eq 4 is preferable It should be pointed out that Eq 4 has not been validated for materials with nickel contents clearly in excess of 2.5% and should therefore be used with caution for such steels

If the TKla estimate obtained from To shows crack arrest in the structure being assessed, there is no

need for experimental determination of Ti~o; a determination of To is sufficient both for the assess-

ment of brittle fracture initiation as well as crack arrest This enables the use of small fracture tough- ness specimens also in the case of crack arrest studies However, if the obtained TKI~ estimate is not sufficiently accurate (does not show crack arrest in the structure), the accuracy of the analysis can be improved, either by direct determination of the crack arrest toughness from standard experiments or the crack arrest estimate can be improved by using a parameter determined from the instrumented im- pact test [9]

Instrumented Charpy-V Fracture Arrest Parameter Fa

Figure 18 shows a typical example of an instrumented impact test load trace corresponding to the ductile/brittle transition region [9] Cleavage fracture has initiated at the point F, However, the spec- imen has not fractured completely, but the crack has arrested at point Fa The load Fa shows an in- creasing temperature dependence At low temperatures the cleavage crack will propagate completely through the specimen, whereas at higher temperatures the crack will arrest at increasingly higher load values Thus Fa is connected to the materials crack arrest toughness Kla

It is possible to define a transition temperature based on the fracture arrest parameter Fa The 4

kN arrest load corresponds approximately to a crack jump halfway through the ligament It also corresponds to the rising part of the F,-T curve Therefore, the mean temperature corresponding to

a fixed arrest load, equal to 4 kN (Tva4) , has been selected as a transition criteria for crack arrest and correlated to TK~a [9] The most recent compilation of the correlation is presented in Fig 19 [9], containing the results from 20 different structural steels, some of which are irradiated and/or embrittled The standard deviation of the relation between Tma and TFa4 is 13~ which is clearly less than for the more empirical correlation between TKIa and To Most of the scatter in the relation

is likely to be due to the comparatively high uncertainty in the determined TFa 4 temperature, but,

as such, it must be taken into consideration when applying the correlation to structural integrity as- sessments

If one has the possibility to determine both To and TFa4, the confidence of the Tma estimate can be improved further by determining a combined estimate of TK1 a When doing this, the different accu- racy of both correlations must be accounted for This can be done by calculating a mean value using different weighing for the two correlations

For two independent estimates of a parameter X(Xl and x~) with different accuracy (~rl and ~r2), a

32 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

FIG 18 Definition of fracture arrest parameter Fa [9]

WALLIN ON CORRELATION BETWEEN KjcAND Kla 3 3 combined estimate of x(Y) has the form

"2 X 1 + 0 " 2 X2

In the case of Tma the combined estimate has a standard deviation of 11~ compared to 13~ and

19~ for the individual estimates

Summary and Conclusions

The Master Curve method, developed for brittle fracture initiation estimation that enables a con- sistent analysis of fracture initiation toughness data, has been modified to be able to describe crack arrest toughness In this work the modified "crack arrest Master Curve" has been further validated and used to develop a simple correlation between the two fracture toughness parameters It can be concluded that:

1 The correlation enables the estimation of crack arrest toughness from small Charpy-sized static fracture toughness tests

2 The basic correlation is valid for low nickel steels ( - 1.2% Ni)

3 High nickel steels have a different correlation, and another correlation including also nickel was therefore developed This correlation is valid for steels having -2.5% Ni

4 The reliability of the correlations is not better than 0-~r = 19~ but often only a rough esti- mate of the crack arrest toughness is necessary

5 If a more accurate description of the crack arrest toughness is required, it can either be mea- sured experimentally or estimated from instrumented Charpy-V crack arrest load information

6 If one has the possibility to determine both To and TFa4kN, the confidence of the TKI a estimate can be improved further by determining a combined estimate of Tma W h e n doing this, the different

accuracy of both correlations must be accounted for

Acknowledgments

This work is a part of the Structural Integrity Project (STIN) belonging to the Finnish Research Program on Nuclear Power Plant Safety (FINNUS), performed at VTT Manufacturing Technology and financed by the Ministry of Trade and Industry in Finland, the Technical Research Centre of Fin- land (VTT), and the Finnish Centre for Radiation and Nuclear Safety (STUK)

References

[1] ASTM E 1921-97, Standard Test Method for Determination of Reference Temperature, To, for Ferritic Steels in the Transition Range, Annual Book of ASTM Standards, Vol 03.01, American Society for Test-

ing and Materials, West Conshohocken, PA, 1998, pp 1068-1084

[2] Wallin, K., "The Scatter in Kic-Results," Engineering Fracture Mechanics, Vol 19, 1984, pp 1085-1093

[3] Wallin, K., "The Size Effect in Klc Results," Engineering Fracture Mechanics, 1985, Vol 22, pp

M R Mitchell, Eds., American Society for Testing and Materials, West Conshohocken, PA, 1997

[7] Wallln, K., "Descriptive Characteristic of Charpy-V Fracture Arrest Parameter with Respect to Crack Ar- rest Kla," Evaluating Material Properties by Dynamic Testing, ESIS 20, E van Walle, Ed., Mechanical En-

gineering Publications, London, 1996, pp 165-176

34 FATIGUE AND FRACTURE MECHANICS: 32ND VOLUME

[8] "Flaw Evaluation Procedures Background and Application of ASME Section XI Appendix A," EPRINP-

[9] Planman, T., Wallin, K., and Valo, M., "Method of Evaluating Crack Arrest Fracture Toughness Kia from

Instrumented Charpy-V Test Data," to be published

Nanstad, R K., Robinson, G C., Thoms, K R., and Whitman, G D., "Pressurized-Thermal-Shock Test of 6-in.-Thick Pressure Vessels PTSE-I: Investigation of Warm Prestressing and Upper-Shelf Arrest," NUREG/CR-4106, ORNL-6135, Oak Ridge National Laboratory, Oak Ridge, TN, 1985

diation Effects on Fracture Toughness of Two High-Copper Submerged-Arc Welds, HSSI Series 5: Main Report and Appendices A, B, C, and D," NUREG/CR-5913, ORNL/TM-12156/V1, Vol 1, Oak Ridge Na- tional Laboratory, Oak Ridge, 1992

Two High-Copper Welds," Effects of Radiation on Materials: 15th Inwrnational Symposium, ASTM STP

Conshohocken, PA, 1992, pp 251-269

Two High-Strength Steels," Nonlinear Fracture Mechanics: Volume II Elastic-Plastzc Fracture, ASTM

Philadelphia, 1989, pp 497-536

Normalization Procedures