Astm stp 1332 1999

In the third paper, an analysis technique utilizing a coupled micromechanical model of ductile crack growth and cleavage fracture is shown capable of predicting transition toughness and

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ISSN: 1040-3094

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Foreword

This publication, Fatigue and Fracture Mechanics: Twenty-Ninth Volume, contains pa-

pers presented at the Twenty-Ninth National Symposium on Fatigue and Fracture Mechan-

ics, held in Stanford, CA on 24-26 June 1997 The sponsor of the event was ASTM

Committee E8 on Fatigue and Fracture Tina L Panontin, Materials and Failure Analysis

Group, NASA Ames Research Center, Moffett Field, CA, and Sheri D Sheppard, Mechani-

cal Engineering Department, Stanford University, Stanford, CA, chaired the symposium and

served as editors for this publication

D y n a m i c I n i t i a t i o n F r a c t u r e Toughness of a P r e s s u r e Vessel Steel in the

T r a n s i t i o n R e g i o n - - R E LINK AND S M GRAHAM 17

A p p l i c a b i l i t y of S u b - C h a r p y - S i z e B e n d a n d I m p a c t Specimens for E s t i m a t i o n

o f F r a c t u r e T o u g h n e s s in the T r a n s i t i o n R e g i o n ~ T PLANMAN,

F r a c t u r e B e h a v i o r of S u r f a c e C r a c k Tension S p e c i m e n s in the Ductile-Brittle

T r a n s i t i o n P e r i o d m J A JOYCE AND R E LINK 5 5

A New M e t h o d for P r e d i c t i n g Extensive Ductile T e a r i n g Using F i n i t e E l e m e n t

A n a l y s i s - - M L GENTILCORE AND R H ROBERTS 82

E l a s t i c - P l a s t i c C r a c k G r o w t h S i m u l a t i o n a n d R e s i d u a l S t r e n g t h P r e d i c t i o n of

T h i n P l a t e s with Single a n d M u l t i p l e C r a c k s - - c - s CHEN,

A n a l y s e s o f B u c k l i n g a n d Stable- T e a r i n g in T h i n - S h e e t M e t a l s ~ B R SESHADRI

A N u m e r i c a l I n v e s t i g a t i o n of L o a d i n g R a t e Effects in P r e - C r a c k e d CVN

S p e c i m e n s - - K C KOPPENHOEFER AND R H DODDS | 35

Effect of R e s i d u a l Stress on Brittle F r a c t u r e T e s t i n g ~ M R HILL AND

E v a l u a t i o n of S t r e s s - I n t e n s i t y F a c t o r s Using G e n e r a l F i n i t e - E l e m e n t

M o d d s - - s A SMITH AND 1 S RAJU

Effects of F i n i t e E l e m e n t M e s h on N u m e r i c a l P r e d i c t i o n of Ductile T e a r i n g - -

B SKALLERUD AND Z I ZHANG

F u l l y Plastic J - I n t e g r a l s for T h r o u g h - W a l l Axial C r a c k s in P i p e s - -

D O HARRIS AND P J WOYTOW1TZ

A New Theoretical F r a m e w o r k for Inelastic F r a c t u r e ProcessesmM M RASHID

T h e Use of Local A p p r o a c h to F r a c t u r e in Reactor Pressure Vessel S t r u c t u r a l

I n t e g r i t y Assessment: Synthesis of a Cooperative Research P r o g r a m

Between EDF, CEA, F r a m a t o m e a n d A E A T e c h n o l o g y ~ o MOINEREAU,

J M FRUND, J BROCHARD, M P VALETA, B MARINI, P JOLY, D GUICHARD,

S BHANDARI, A SHERRY, C FRANCE, AND D J SANDERSON 2 8 4

E v a l u a t i o n of F r a c t u r e Toughness Results a n d T r a n s f e r a b i l i t y to F r a c t u r e

M i c r o m e c h a n i c a l P r e d i c t i o n of F r a c t u r e Toughness for P r e s s u r e Vessel Steel

O n the G u r s o n M i c r o - M e c h a n i c a l P a r a m e t e r s ~ z L ZHANG AND M HAUGE 364

C o n d i t i o n s C a u s i n g I n t e r g r a n u l a r C r a c k i n g in High S t r e n g t h Nickel-Copper

New Perspectives on the F r a c t u r e of Nicalon F i b e r s m s T TAYLOR, Y T ZHU,

W R BLUMENTHAL, M G STOUT, D P BEFIT, AND T C LOWE 393

F A T I G U E

Stress Ratio Effects on C r a c k O p e n i n g Loads a n d C r a c k G r o w t h Rates i n

Stress-Level-Dependent Stress Ratio Effect o n F a t i g u e C r a c k G r o w t h - -

A Theoretical a n d E x p e r i m e n t a l Investigation of the Influence of C r a c k T i p

Plasticity on F a t i g u e C r a c k C l o s u r e - - o NOWELL, L J FELLOWS, AND

E s t i m a t i o n of C r a c k G r o w t h Behavior in a Residual Stress Field Using the

A n Analytical Model for S t u d y i n g R o u g h n e s s - I n d u c e d C r a c k C l o s u r e - -

O n the C r a c k - T i p B l u n t i n g Model for Fatigue C r a c k P r o p a g a t i o n in Ductile

Influence of Bauschinger Effect on Residual Stress and Fatigue Lifetimes in

Autofrettaged Thick-Walled Cylinders~A e PARKER AND

Fatigue Durability Enhancement by Controlled O v e r l o a d i n g ~ s M TIPTON AND

An Energy Based Critical Plane Approach to Multiaxial Fatigue Analysis

Residual Stress Effects in Railroad Rail Fatigue G T FRY, H L JONES, AND

A Rapid Method for Generation of a Haigh Diagram for High Cycle

Ultrasonic Pulse Transmit-Receiver Method for Detecting and Monitoring of

Fatigue D a m a g e ~ i MOSTAFA, S HAILU, G E WELSCH, D HAZONY, AND

Sustained Fatigue Crack Growth Oblique to an Applied Load Using

Geometric ConstraintmM A M A G I L L AND F J ZWERNEMAN 6 5 8

An Evaluation of the Adjusted Compliance Ratio Technique for Determining

the Effective Stress Intensity F a c t o r ~ J K DONALD, G n BRAY, AND

The Use of Almost Complete Contacts for Fretting Fatigue T e s t s ~

S T R U C T U R A L A P P L I C A T I O N S High-Speed Civil Transport Hybrid Laminate Sandwich Fuselage Panel

Test M MILLER, A C RUFIN, W N WESTRE, AND G SAMAVEDAM 713

Prediction of Fatigue Life Under Helicopter Loading Spectra for Safe Life

and Damage Tolerant Design P E IRVING AND R G BULLER 727

Structural Loading and Fatigue Failure Analysis of Off-Road Bicycle

Mixed-Mode Fatigue Failure in Structural AdhesivesmE SANCAKTAR 764

Microstructure Evolution and Thermomecbauieal Fatigue Life of Solder

JointsmB GOLDSTEIN, K L JERINA, S M L SASTRY 786

Fatigue Life Prediction of Resistance Spot Welds Under Variable Amplitude

Loads~N PAN, S D SHEPPARD, AND J M WIDMANN 802

Residual Strength Predictions for Multiple Site Damage Cracking Using a

Three-Dimensional Finite Element Analysis and a CTOA C r i t e r i o n m

Fracture Analyses of an Internally Pressurized Tube Containing an Axial,

F r a c t u r e Analysis of Ductile C r a c k G r o w t h in Weld Material f r o m a Full-

Ductile C r a c k G r o w t h from S i m u l a t e d Defects i n Strength O v e r m a t c h e d B u t t

P r e d i c t i n g Extensive Stable T e a r i n g in S t r u c t u r a l C o m p o n e n t s - - R J DEXTER

H y d r o g e n C r a c k i n g D u r i n g Service of High Strength Steel C a n n o n

C o m p o n e n t s m j H UNDERWOOD, E TROIANO, ~ N VIGILANTE, A A KAPUSTA

A N D S T A U S C H E R

Indexes

897

913

STP1332-E B/Feb 1999

Overview

The National Symposium on Fatigue and Fracture Mechanics is a forum for presen- tation and discussion of significant research and its application to life prediction and structural integrity For the 29th symposium, nearly 100 researchers from 14 countries gathered at Stanford University in Stanford, California on June 24-26, 1997 There, they exchanged information on recent developments on modeling and analyzing fatigue and fracture processes; on applications to real structures and new materials; and on directions for future research The symposium was organized toward these goals by a group of leading researchers who work in all aspects of fracture and fatigue The members of this committee were Robert Dodds, Jr., James Newman, Jr., Drew Nelson, Mark Kirk, James Joyce, Robert Dexter, Michael Mitchell, and Walter Reuter, and the success of the symposium is a direct reflection of their efforts

This Special Technical Publication (STP) documents the technical interchange of the 29th Symposium on Fatigue and Fracture Mechanics It contains 51 papers, 27 on fracture mechanics and 24 on fatigue In addition to the fine contributions made directly by the authors of the papers, the quality of the papers is a result of the diligence and commitment of a large number of reviewers The contributions of the editors at ASTM should also be acknowledged

The first paper in the volume is a synopsis of the Twenty-Ninth National Symposium J.L Swedlow Lecture by Professor C Fong Shih Professor Shih's lecture, entitled "Fracture Analysis In The Ductile/Brittle Regime: A Predictive Tool Using Cell Models," described the current state of the art of two-parameter and mechanism-based fracture prediction approaches, with emphasis placed on the development of computational cell models Professor Shih showed that, within their respective regimes of applicability, both approaches correctly correlate constraint effects on fracture toughness

The 50 papers that followed in the symposium are organized in this volume in three main categories: Fracture Mechanics, Fatigue, and Structural Applications These are described below

Fracture Mechanics

In sessions led by M.T Kirk, A R Ingraffea, H Gao, J H Underwood, R.H Dodds, and J.A Joyce, fracture mechanics research concerning fracture in the transition region, computational and analytical techniques, micromechanical modeling, and new materials was presented

Several papers examined the effects of geometry, specimen size, and loading rate

on fracture behavior and toughness in the transition region Dynamic fracture toughness of A533B steel in the ductile-to-brittle transition was investigated at various loading rates Although fracture toughness generally decreased with increased loading rate, this decrease was not as severe at the highest test temperature as previously reported It was also shown for A533B that the reference temperature, T o, used in the Master Curve approach to charac-

2 FATIGUE AND FRACTURE MECHANICS: 29TH VOLUME

specimens provided adequate measures of the reference temperature and of fracture resis-

tance curves on the upper shelf In a third study, pre-cracked Charpy specimen sets were

shown to inaccurately predict the full constraint Master Curve and to be nonconservative

for tension loaded surface crack specimens and bend specimens with short cracks

The session on computational fracture mechanics contained papers describing the

implementation of several different fracture models within the finite element framework;

the study of global loading effects on fracture prediction; and the use of finite element

methods in fracture mechanics A model of localized necking at the crack tip, which utilizes

a critical strain fracture criterion within a finite element analysis, was shown to predict

ductile tearing in high-toughness, thin (plane stress) members Another simulation was

presented for elastic-plastic crack growth and residual strength predictions in thin

aluminum plates containing multiple cracks In this study, a CTOA fracture criterion was

utilized and shown to exhibit constraint effects as experimental and numerical predictions

diverged with increasing specimen width The CTOA criterion was also used in a finite

element analysis in a third paper to study stable tearing in a variety of thin panels under out-

of-plane buckling conditions; a significant influence of specimen geometry and material

properties on buckling behavior was found

Load-type effects on fracture were studied computationally in two papers of this

session The first examined the effect of impact loading on cleavage fracture and ductile

crack growth using the Weibull stress and the computational cell methodologies, respec-

tively Computational results indicate that impact loading up to 1 m/s significantly raises a

material's resistance to ductile tearing and that the Weibull stress is strongly affected by

through thickness constraint The second study examined the effect of weld residual

stresses and different precracking techniques on constraint conditions and subsequent

cleavage fracture in welded fracture specimens Residual stresses and precompression were

shown computationally to affect both the driving force for fracture and the constraint condi-

tions at the crack tip

The finite element method of determining stress intensity factors was examined in

another paper in the session on computational fracture mechanics, with results indicating

that only the Equivalent Domain Integral technique was unaffected by lack of orthogonality

at the crack front In the final paper of the session, the effects of element type and

integration method, mesh refinement and irregularity, and number of void-material layers

on predictions of ductile tearing using the Gurson-Tvergaard void growth model were

shown to be significant

In the area of analytical fracture mechanics, research resulting in new crack

solutions and analysis techniques was presented The first paper presented fully plastic J-

integral solutions for through-wall axial cracks in pressurized pipes made of power law

hardening materials Derivations of crack stress strain fields for materials that exhibit

pressure sensitive dilatation, such as rock, concrete, or ceramics, were described in the next

paper A third research group discussed a new technique for obtaining structural calibration

functions by scaling a load factor and a deformation factor from a fracture toughness

specimen to the structure The final paper in this area presented work on the Exclusion

Region theory, a new construct that attempts to remove difficulties associated with

boundary value solutions for cracked bodies and the extraction from these solutions of a

physically relevant fracture criterion

OVERVIEW 3

in several papers A cooperative research program to study the applicability of the Beremin

model for cleavage fracture to reactor pressure vessels was described The model is shown

capable of correctly predicting the influence of crack tip constraint in fracture specimens

of varying a/W ratios but is sensitive to numerical effects The Beremin model was also

used in a second study to assess the transferability of toughness measured in mismatched

joints with cracks in weld and HAZ metals The model was found particularly useful in this

application because it directly considers the volume of the local brittle zone in which

fracture initiation occurs In the third paper, an analysis technique utilizing a coupled

micromechanical model of ductile crack growth and cleavage fracture is shown capable of

predicting transition toughness and transition temperature shifts as a function of constraint

(i.e., T-stress) Predictions were verified in test specimens and wide plate configurations of

A533B steel over a range of temperatures The final paper in this area reviewed methods

for calibrating the computational parameters used in the Gurson-Tvergaard model for

predicting ductile crack growth A void coalescence criterion based on Thomason's plastic

limit-load model is advocated to facilitate calibration

Fracture research on new materials included studies of nickel-copper alloys and mono-

filament SiC fibers Subcritical intergranular cracking in the Nickel-Copper Alloy

K-500 was the focus of the first study Occurring in this material at temperatures as low as

room temperature, crack growth was postulated to be due to diffusional-creep based on

evidence found from high resolution microscopy In the second study, the fracture behavior

and strength of Nicalon SiC fibers was investigated to identify the effects of fiber diameter,

flaw location, and flaw population It was found that larger fracture toughness was

exhibited by fibers with smaller diameters and that three distinct populations of internal

flaws were associated with fracture initiation in the fibers

Fatigue

Sessions that presented findings on the effects of crack closure, stress ratio, residual

stresses and load-type on fatigue, and on improved fatigue test techniques were chaired by

J.C Newman, Jr., R.E Link, D.A Hills, M.R Mitchell, D.V Nelson, and S.R Daniewicz

Several researchers investigated how crack tip closure and stress-ratio effects can

be incorporated into crack-growth models Two research groups illustrated a dependence

of crack growth rate on stress ratio in aluminum alloys Some of this dependence is due to

crack closure and some to maximum stress intensity factor involved Several research

groups developed strip-based plasticity models to determine the true crack tip stress

intensity factor range based on either a requirement of tensile stresses and strains in the near

crack front region or energy considerations in the crack-tip region These models were able to

correctly predict the shape evolution of a semi-elliptical surface flaw, the measured

crack tip closure, and the dependence of crack growth rate on crack length Another

research group used a modified strip yield model to study crack growth behavior through a

residual stress field Still another model of crack growth behavior included not only the

effects of plasticity-induced crack closure, but also roughness-induced closure The gradual

transition from roughness-induced to plasticity-induced closure was handled naturally by

this model Work that focused on investigating fatigue crack growth in ductile materials

based solely on the effect of local plastic deformation (without introducing any specific

4 FATIGUE AND FRACTURE MECHANICS: 29TH VOLUME

failure criterion or presumed slip behavior) was also presented Crack growth predicted

from finite element analysis compares favorably with experimental data

The influences of residual stress and multiaxial loading on fatigue were addressed

in several papers One research group discussed the influence of the Bauschinger effect

upon residual stresses and associated fatigue crack growth for pressurized, autofrettaged

thick cylinders Furthermore, they discuss the importance of controlled overstrain in

maximizing crack initiation lifetime in these structures Another group took a more general

look at controlled overloading techniques for fatigue-initiation life improvement and

presented a method for predicting optimal proof-load levels in regions of stress concen-

tration A method was also presented for including proportional and nonproportional

loading in predicting multiaxial fatigue damage This method, based on stresses and strains

acting on critical planes in materials demonstrates improved life predictions relative to

other methodologies A critical-plane fatigue analysis that considered the role of residual

stresses in fatigue crack nucleation in railroad rail was also presented The results of the

analysis suggest that nucleation of rail-head defects occur preferentially in a region below

the running surface of the rail a fact borne out by field observations

Techniques for improved fatigue testing were presented by a number of research

groups These included: a rapid testing technique for generating a Haigh diagram for high

cycle fatigue; an ultrasonic pulse transit-receiver method for in-situ detection and

monitoring of fatigue cracks; an experimental set-up for sustained fatigue crack growth

under Model I and II loading; a new analysis technique for estimating the effective stress intensity

range based on an interpretation of crack closure as a stress redistribution; and an analysis of

contact force depth involved in the frequently used bridge-type fretting fatigue tests

Structural Applications

The session dealing with specific applications of predicting or measuring fatigue

performance was chaired by R.J Dexter An experimental study of a hybrid laminate panel,

as might be used in the High-Speed Civil Transport, was presented Results demonstrate at

a subcomponent level the durability of laminates and confirmed the hypothesis that fiber

bridging can significantly retard the rate at which damage progresses from crack-like

defects in these materials In a second paper, the ability to predict fatigue life under the

variable amplitude loading spectra developed from helicopter operation data was studied in

a beta titanium alloy and a 7010 aluminum alloy It was found that load interaction effects

could be ignored in predicting fatigue damage in the titanium alloy, but not in the aluminum

alloy and that the high mean, low amplitude cycles in the spectra caused 80% of the

damage Fatigue of off-road bicycle components was the focus of a third study, in which a

test bicycle was fully instrumented to measure all in-plane structural loads A rainflow

counting algorithm was used to process stress cycles and allow prediction of fatigue

damage using Miner's rule in a classical S-N approach In another study, the fatigue

strength of adhesively bonded joints under combined bending and shear loading was inves-

tigated The shear loading was shown to significantly affect S-N behavior Another group

presented their findings on the thermomechanical fatigue properties of solder joints in

single lap shear configurations, and demonstrated increased fatigue susceptibility with

certain microstructures Finally, the fatigue initiation response of resistance spot welds

OVERVIEW 5

subjected to constant amplitude and durability loading was presented, along with a model

for analytically predicting the response

W.G Reuter led the session on fracture mechanics applications, which included

aircraft fuselages, nuclear reactor shells and piping, cannon components, and ship beams

In the first paper, the CTOA fracture criterion was used to predict the behavior of

specimens containing multiple-site damage representative of that found in aging aircraft

Using a critical CTOA value measured in a single C(T) specimen, the finite element

analyses were able to predict stable tearing, link-up stresses, and maximum stresses

observed in experiments of the multiple-site damage specimens In a second study, fracture

analyses of an internally pressurized tube containing an axial, through-wall crack were

made using a variety of constraint methodologies, including two parameter techniques A

direct correlation between the crack tip stress fields in the compact tension specimen used

to obtain fracture toughness and those in the tube could not be found In another study, the

application of the Gurson-Tvergaard void growth, computational cell methodology to a

full-thickness beam specimen containing weld, plate, and clad materials was investigated

Good agreement between the predictions and experimental results were found Application

of the cell model methodology was also attempted for an overmatched butt weld containing

a buried, lack-of-penetration defect In this experimentally verified study, the methodology

is shown to provide accurate predictions of ductile tearing when calibrated from welded CT

specimens and when weld plate material property differences are modeled In the next

paper, the problems associated with predicting extensive ductile crack growth (e.g., 100's

mm) in thin steel or weld sections using an R-curve approach were investigated Experi-

ments verified that an alternative approach, based on CTOA, provides more accurate

predictions for these applications In the final paper of the session, environmental cracking

of high strength steel cannon components was studied Results were reported from

hydrogen cracking tests, finite element stress analysis, and stress intensity factor

Jerry L Swedlow Memorial Lecture

C F Shih I

FRACTURE ANALYSIS IN THE DUCTILE/BRITTLE REGIME: A PREDICTIVE TOOL

USING CELL MODELS 2

REFERENCE: Shih, C F., " F r a c t u r e Analysis in the Ductile/Brittle Regime: A Predictive Tool

Using Cell Models," Fatigue and Fracture Mechanics: Twenty-Ninth Volume, ASTM STP 1332, T L

Panontin and S D Sheppard, Eds., American Society for Testing and Materials, West Conshohocken, PA,

1999

ABSTRACT: The 29th Symposium Swedlow Lecture described the current state of the art of predicitve

fracture mechanics tools Both two-parameter and mechanism-based approaches were reviewed, with

emphasis placed on the development of computational cell models Within their respective regimes of

applicability, both approaches are shown to correctly correlate constraint effects on fracture toughness

levels

KEYWORDS: two-parameter fracture mechanics, computational cell models, micromechanics, finite

element analysis

The Swedlow Lecture for the 29th Symposium on Fatigue and Fracture Mechanics

was given by Dr C.F Shih The lecture provided an excellent discussion of the state of

fracture assessments methods, particularly those implemented within computational

frameworks

Dr Shih began by showing the regimes of applicability of various assessment ap-

proaches His schematic, shown in Fig I, indicates that characterization parameter ap-

proaches, J-T or J-Q approaches, are best used in the lower transition regime in which

fracture occurs under limited yielding conditions Mechanism-based approaches, the so-

called computational cell models, are applicable in the mid-transition to upper transition

regime, in which plasticity and and stable ductile tearing amplify the effects of constraint

on the fracture process

Two P a r a m e t e r Approach

Discussion of the J-Q approach focused on the evolution of near crack-tip stresses

and how their magnitude is affected by contained and then uncontained plastic flow [1-4]

Jc data were shown for TPB and CCP specimens of various crack lengths [5] As shown in

Fig 2, all data collapse to a single trend line when the nondimensionalQ-stress expresses

the constraint differences among the crack geometries

Cell Model Approach

Introduction of computational cell models was made by describing the length and

energy scales associated with various fracture mechanisms As shown in Fig 3, five orders

of magnitude separate the work of fracture for atomic decohesion (cleavage fracture) from

that for void growth and coalescence (ductile fracture) This is due largely to differences in

the length scales over which the processes occur Resistance to fracture is a combination of

the work of the fracture process and the amount of background plasticity It is, therefore,

the result of processes occurring at the crack tip as well as the plastic dissipation in the ma-

Formerly Professor, Brown University Currently, Director, Institute of Material Research and

Engineering, National University of Singapore

F I G 2 - - Cleavage fracture data for mild steel tests at -50~ [5]

terial surrounding the crack.To predict accurately the fracture resistance, a model must cap- ture the highly nonlinear coupling between fracture processes and plastic dissipation in the nearby structure that occurs over vastly different length scales

Cell models seek to capture the "local" or "crack tip" processes that contribute to

the work of fracture A cell is defined as a representative volume of material that contains sufficiently complete information about micro-failure or -separation characteristics It em- bodies both microstructural features and the length scale relevant to the fracture mechanism [6] In ductile tearing, fracture proceeds with the nucleation, growth, and coalescence of

voids Hence, for a cell model of ductile fracture, an important microstructural feature is

the void (inclusion) volume fraction and the mean spacing between initial voids is charac- teristic of the length-scale over which coalescence occurs An example cell model repre-

sentation of the ductile tearing process is shown in Fig 4

For computational predictions of ductile tearing, one approach to define cell

response employs the Gurson-Tvergaard model A continuum model, it assumes the

material acts as a homogenous, porous medium and that the material "softens" as it incurs

SHIH ON PREDICTIVE FRACTURE MECHANICS TOOLS 11

o~ (~n~) ~B(m) r,(J/m2) Interface , , ~ ~ ~ atomic 101~ 10 "1~ 1

Interface ~ ~ / / , ~ / /

$eperaUon coalesoanoa 10 8 10-S 10 2

ceramic

FIG 3 Crack bridging mechanisms and their associated energies

FIG 4 Cell model representation of ductile tearing process

damage leading to fracture The yield criterion is a function of the hydrostatic stress and

void volume fraction, as shown in Fig 5a The model also contains a flow law, a criterion

for nucleating voids, and a law for evolution of void volume fraction [6-8]

The Gurson-Tvergaard (G-T) model is implemented within a computational

framework by discretizing the material along the fracture plane into uniform cells of initial

height D, each containing an initial void volume,fo The cell height, D, is representative of

the characteristic spacing of voids, i.e., the process zone over which the damage (void

growth) leading to ductile cracking occurs [6] Because all the cells lie in a single layer

along the crack plane as shown in Fig 5b, this implementation restricts crack propagation

to the plane directly ahead of the crack tip The material surrounding the layer of Gurson

cells responds as conventional Mises plasticity Hence, the cell model captures both the

crack tip processes and the background plasticity that contribute to fracture resistance

Dr Shih next presented a short tutorial on the calibration of the Gurson-Tvergaard

computational cell model [9,10].Three sets of parameters must be supplied to the model:

micromechanics parameters (i.e., void growth and coalescence mechanics), fracture pro-

cess parameters (initial void volume fraction and cell size), and elastic-plastic flow proper- ties of the unvoided material All are material specific; however, the micromechanics

parameters are available from tabulated data as a function of material strength and harden-

1 2 FATIGUE AND FRACTURE MECHANICS: 29TH VOLUME

FIG 5 ( a ) Yield criterion as function of initial void volume fraction in G-T model,

and (b) G-T model implementation

ing, and the flow properties are directly measurable The remaining fracture process param- eters,fo and D must be calibrated by matching predicted and measured R-curve behavior For many steels, D has been found to equal approximately the CTOD for initiation Accu- rate predictions of ductile tearing have been made once the model is calibrated; an example

of experimentally verified predictions are shown in Fig 6 for surface crack geometries

made of Cr-Mo steel [11]

The cell model approach can also be used to predict constraint and prior ductile

crack growth effects on cleavage fracture [ 12] The two effects on cleavage fracture that are associated with ductile crack growth include an increase in crack tip constraint and an in- crease in sampling volume as the crack tears To predict these effects the G-T model is cou- pled with Weibull stress statistical model; the cell model computes the evolving stress

fields during ductile tearing while cleavage fracture is treated probabilistically by a Weibull distribution (Fig 7a) The Weibull parameters, (~u, (~th and m, must now be calibrated, in addition to the parameters that must be calibrated for the G-T model The experimental data

in Fig 7b were shown to demonstrate the accuracy of the calibrated model, which is good

FIQ 6 Cell model predictions compared to experimental measurements.of

ductile tearing in surface cracks [111

SHIH ON PREDICTIVE FRACTURE MECHANICS TOOLS 13

even after a substantial amount of ductile tearing [13] It was noted that computational

problems can arise from the conflict between the differing resolution of the stress fields re-

quired for ductile tearing (low) and for cleavage (high)

750 501) 25~

(]

W=S0mm ao/W -0.6 (20% S.g.) Plane Slrain Model

compared to experimental data [12]

C o n c l u s i o n

In summary, Dr Shih reiterated that the J-Q fracture theory and the cell model ap-

proaches each have their place in describing and/or predicting fracture The J-Q approach

has been shown to correctly correlate constraint effects on fracture resistance for cleavage

fracture without prior ductile crack growth The computational cell model for ductile frac-

ture has been shown to accurately predict fracture resistance for large amounts of ductile

tearing and, when coupled with a statistical model, to correctly assess the competition be-

tween tearing and cleavage fracture

R e f e r e n c e s

[I] N.P O'Dowd and C.F Shih, "Family of Crack-Tip Fields Characterized by a

Triaxiality Parameter: Part I-Structure of Fields," Journal of the Mechanics and

Physics of Solids, 39 (1991), pp.983-1015

[2] N.P O'Dowd and C.F Shih, "Family of Crack-Tip Fields Characterized by a

Triaxiality Parameter: Part II-Fracture Applications," Journal of the Mechanics and

Physics of Solids, 40 (1992), pp.939-963

[3] L Xia, T.C Wang, and C.F Shih, "Higher-Order Analysis of Crack-tip Fields in

Elastic Power-Law Hardening Materials," Journal of the Mechanics and Physics of

Solids, 41 (1993), pp.665-687

FATIGUE AND FRACTURE MECHANICS: 29TH VOLUME

N.P O'Dowd and C.F Shih, "Two-Parameter Fracture Mechanics: Theory and Applications," ASTM STP 1207, American Socistety for Testing and Materials,

West Conshohoken, PA, (1994) pp 21-47

J.D.G Sumpter and A.T Forbes, "Constraint Based Analysis of Shallow Cracks in Mild Steel," Proceedings of the International Conference on Shallow Crack Fracture Mechanics Tests and Applications, TWI, Cambridge, England (1992)

L Xia, C.F Shih, and J.W Hutchinson, "A Computational Approach to Ductile Crack Growth under Large Scale Yielding Conditions," Journal of the Mechanics and Physics of Solids, 43 (1995), pp.389-413

L Xia and C.F Shih, "Ductile Crack Growth - I A Numerical Study using

Computational Cells with Microstructurally-Based Length Scales," Journal of the Mechanics and Physics of Solids, 43 (1995), pp.223-259

L Xia and C.F Shih, "Ductile Crack Growth - II Void Nucleation and Geometry Effects on Macroscopic Fracture Behavior," Journal of the Mechanics and Physics

of Solids, 43 (1995), pp.1953-1981

J Faleskog, X Gao, and C.F Shih, "Cell Model for Nonlinear Fracture Analysis

I Micromechanics Calibration (1997) Submitted

X Gao, J Faleskog, and C.F Shih, "Cell Model for Nonlinear Fracture Analysis

H Fracture Process Calibration and Verification." (1997) Submitted

X Gao, J Faleskog, R.H Dodds, and C.F Shih, "Ductile Tearing in Part-Through Cracks: Experiments and Cell-Model Predictions." (1997) Submitted

L Xia and C.F Shih, "Ductile Crack Growth - HI Transition to Cleavage Fracture Incorporation Statistics," Journal of the Mechanics and Physics of Solids, 44

(1996), pp 603-639

K Wallin, "Statistical Aspects of Constraint with Emphasis on Testing and

Analysis of Laboratory Specimens in the Transition Region," Constaint Effects in Fracture, ASTM STP 1171, Hackett, et al Eds., American Socistety for Testing

and Materials, West Conshohoken, PA, (1993)

Fracture Mechanics

Richard E Link 1 and Stephen M Graham 2

D Y N A M I C I N I T I A T I O N F R A C T U R E T O U G H N E S S O F A P R E S S U R E V E S S E L

S T E E L IN T H E T R A N S I T I O N R E G I O N

REFERENCE: Link, R E and Graham, S M., "Dynamic Initiation Fracture Toughness of a Pressure Vessel Steel in the Transition Region," Fatigue and Fracture Mechanics: Twenty-

Testing and Materials, West Conshohocken, PA, 1999

A B S T R A C T : The dynamic fracture toughness of an ASTM A533, Grade B steel plate was determined at several temperatures in the ductile-brittle transition region Crack-tip loading rates ranged from approximately 103 to 105 MPax/m/s The fracture toughness was shown to decrease with increased loading rate The dynamic fracture toughness was compared with results from previous investigations and it was shown that the decrease in toughness due to increased loading rate at the highest test temperature was not as severe

as reported in previous investigations It was also shown that the reference temperature,

To, was a better index of the fracture toughness vs temperature relationship than the nil- ductility temperature, RTrqDr for this material

K E Y W O R D S : dynamic fracture, A533B steel, fracture toughness, ductile-brittle transition, reference temperature

Introduction

The fracture toughness of a ferritic steel is a function of temperature and strain rate The toughness can be lowered by decreasing the temperature or increasing the strain rate This behavior has been demonstrated many times and it has been taken into account

in design codes such as the ASME Boiler and Pressure Vessel Code The Km reference

curve in Section Ill was developed from measurements of the dynamic and crack arrest fracture toughness of pressure vessel steels and is assumed to represent a lower bound fracture toughness for pressure vessel steels and weldments Much of the dynamic fracture toughness data that forms the basis of the Kn~ curve was developed by Shabbits at Westinghouse in the late 1960's [1] Shabbits tested A533, Gr B, compact specimens ranging in size from 1T to 8T over a range of loading rates from quasi-static to

l Assistant professor, U.S Naval Academy, Annapolis, MD

2 Consultant, Vector Research Corp., Rockville, MD

1 8 FATIGUE AND FRACTURE MECHANICS: 29TH VOLUME

approximately 105 MPa~/m/s (105 ksi~in/s) in the ductile-to-brittle transition region The

fracture toughness results from Shabbits are plotted in Figure 1 as a function of loading

rate The Nil-Ductility temperature (NDT) for this plate (HSST Plate 2) was -18~ (0~

There is little influence of loading rate on the fracture toughness at temperatures near the

lower shelf for this plate, -46~ (-50~ As the temperature is increased above NDT into

the transition region, there appears to be a noticeable reduction in the toughness with

increased loading rate The trend lines shown by Shabbits for the tests at the two highest

temperatures are somewhat questionable because of insufficient data from which to draw

any conclusions about the variation in toughness with loading rate In addition, there is

considerable variability in the fracture toughness of a material in the transition region

Again, there is insufficient data to quantify the degree of data scatter that could be

expected at the higher temperatures It becomes increasingly difficult to generate linear-

elastic fracture toughness data at temperatures high in the transition region because the

required size of the specimen becomes large very quickly, making testing very costly and

prohibitive Indeed, the KtR curve has been referred to as the million dollar curve due to

the high cost of testing very large specimens

In general, nuclear reactor pressure vessels do not experience crack-tip loading

rates as high as 105 MPa~]m/s (105 ksi~/in/s) However, under some postulated accident

conditions, in particular during the short time interval immediately following a crack

arrest event, the crack-tip loading rates can be in the range of 104 to 105 MPa~]m/s (104 to

105 ksi']in/s) with crack tip temperatures approximately 42~ (75~ above NDT [2] It

is possible under these conditions for the arrested crack to reinitiate and continue to

propagate through the vessel wall The results of computational simulations of these

events depend heavily on the variation in fracture toughness with temperature and strain

rate in the mid to upper transition region where the existing database is relatively sparse

[31

Objective

The objective of this investigation was to characterize the dynamic fracture

initiation toughness, Kid, of an ASTM A533, Grade B, Class 1 steel plate over a range of

crack-tip loading rates from 10 3 to 10 5 MPa~/rn/s (9.1 x 102 to 9.1 x 10 4 ksi~/in/s) and over

a range of temperatures 0 > (T-RTNDr) > 45~ The data from this investigation are

intended to supplement the existing database on dynamic fracture initiation toughness,

particularly at higher loading rates where the existing database is sparse Two reference

temperatures, RTNDr and To, were investigated as indexing parameters for correlating the

results of this investigation with previously published data measured on a different plate

of material RTNDT for a material is defined as the greater of the nil-ductility temperature

or 33~ (60~ below the temperature corresponding to a Charpy impact energy of 67.8J

(50 ft-lb) The reference temperature, To, is the temperature corresponding to a median

fracture toughness, KjOr)=100 MPa-m 1/2, for a deeply cracked specimen with a thickness

of 25 mm

LINK AND GRAHAM ON TOUGHNESS OF PRESSURE VESSEL STEEL 19

Mechanical Properties

Description of Source Plate

The material used in this investigation was a piece of ASTM A533, Gr B, C1 1

steel plate from HSST Plate 14 which was provided by Oak Ridge National Laboratory

from the High Strength Steel Technology Program The piece of plate was approximately

129.5 cm x 94 cm x 23.5 cm thick (51 in x 37 in x 9-1/4 in thick) and was assigned a

three-letter identifying code, HAS The chemical composition of the plate, as reported in

the material certification report is listed in Table 1 The plate had been quenched and

tempered at 690~ (1275~ by the steel manufacturer No subsequent heat treatments

were performed on the plate and all tests were conducted in the as-received condition

All specimens were removed from the mid-thickness of the plate (between the

quarter thickness positions) and were located at a minimum of 2.54 cm (1 in.) from any

flame-cut or as-heat treated surface Specimens were stamped with orientation marks and

identifying codes Tensile strength, Charpy impact toughness and quasi-static fracture

toughness tests were conducted in order to characterize the plate properties

Figure 1 Dynamic fracture toughness as a function of loading rate for A533, Gr B steel

plate determined by Shabbits [ l]

Tensile Properties

Test procedure- Longitudinal tensile specimens, 6.4 m m (0.252 in.) in diameter

with an 25.4 m m (1 in.) gage length, were used to determine the tensile properties over

20 FATIGUE AND FRACTURE MECHANICS: 29TH VOLUME

the temperature range -65~ < T < 30~ and strain rates, 10-4/s < drddt < 20Is All testing

was conducted in closed-loop, servo-hydraulic testing machines under actuator

displacement control at constant actuator velocity Elongation measurement on all

specimens except those at the highest strain rate (-20Is) were made with an extensometer

with a 25.4 m m (1 in.) gage length Two sets of springs were used to firmly secure the

extensometer to the specimen for tests conducted at accelerated testing rates Load was

measured with a strain gage-based load cell Both the load cell and the extensometer

were connected to signal conditioning amplifiers having a frequency response up to 25

kHz Load and elongation data were recorded on a 4-channel digital oscilloscope Strain

rates were determined from elongation versus time records of each test The strain rate

that was reported was the average strain rate in the specimen during yield point

elongation of the specimen, prior to the onset of significant strain hardening

TABLE 1 Chemical composition of A S T M A533, Grade B, Class 1 steel plate studied in

this investigation (Values are in weight percent.)

Element HSST Plate 14 ASTM A533,

Copper 0.070 Not specified

Columbium 0.019 Not specified

All tests were conducted in a temperature controlled environmental chamber with

liquid nitrogen used for cooling and electric resistance used for heating The test

temperature was monitored by a thermocouple attached to the surface of the specimen

grip, immediately adjacent to the test specimen The test temperature was maintained

within + I ~ (+2~ during the tests Due to the limited frequency response of the load

cell, a special specimen design was utilized for the tests conducted at a strain rate of

~20Is This specimen, shown in Figure 2, had two sections: a 6.401 m m (0.252 in.)

diameter test section, and a 9.5 mm (0.375 in.) diameter section that was instrumented

with a strain gage to record the remote strain during the test Applied load was calculated

from the remote strain In addition, high elongation strain gages were bonded to the test

section to monitor the strain during the test

LINK AND GRAHAM ON TOUGHNESS OF PRESSURE VESSEL STEEL 21

It is very difficult to conduct a test at a constant strain rate since the strain rate in

the specimen varies considerably during a dynamic tensile test Previous investigators

[4,5] typically calculate the average strain rate based on the crosshead or actuator speed

divided by the specimen gage length This measure of strain rate is invariably greater

than the actual strain rate in the specimen (up to an order of magnitude) The difference

between the strain rate measured on the specimen and that inferred from crosshead

displacement is presumable due to strain in the grips, fixtures and testing machine

Analysts who use the dynamic flow properties in visco-plastic analyses should be aware

of the difference between the actual strain rate in the specimen and that inferred from

crosshead displacement measurements The strain rate reported for each test is the

average strain rate in the specimen, measured with an extensometer or a strain gage, at the

yield point during the test

function of strain rate for the three test temperatures in Figure 3 and Figure 4,

respectively The yield and ultimate strengths increase significantly with increasing strain

rate above 0.Ol/s, with the lowest temperature tests showing the greatest effect The yield

strength increases up to 40% over the quasi-static value while the ultimate strength

increases a maximum of approximately 18% It should be noted that the ultimate

strengths at the higher strain rates reported herein are influenced by specimen heating

during the test For the short test times at the higher strain rates, the test occurs under

nearly adiabatic conditions and the temperature of the specimen increases rapidly during

the plastic deformation phase of the tensile test

There is some uncertainty in the results at the higher strain rates (> l/s) for the

29~ (85~ tests Initially, it appears that the yield and ultimate strengths are increasing

with the increasing strain rate; however, the strength at the highest strain rate falls off

Based on the trends of increasing strength with increasing rate as exhibited by the tests at

the lower temperatures, the strengths measured at the highest strain rate at 29~ (85~

appear suspect

22 FATIGUE AND FRACTURE MECHANICS: 29TH VOLUME

In order to examine this discrepancy further, the yield strength results are plotted

as a function of the parameter RT In [A/(de/dt)] which represents the apparent activation

energy for plastic flow in a model proposed by Bennet and Sinclair [6] In this

expression, T is the absolute temperature, R is the universal gas constant 8312 J/(kg mol

K) (40.377 in-lb/(~ mol)) and A is the frequency factor, assumed to be constant with a

value of 10S/s for iron Bennet and Sinclair have shown that when the yield strength of

many bcc metals is plotted as a function of this parameter, the data tend to fall on a single

curve This is generally true for the data plotted in Figure 5, with the exception of the

results at 29~ (85~ and a strain rate of 17/s This suggests that the yield strength

determined at the highest strain rate and temperature is inaccurate Re-examination of the

test records did not indicate any abnormal behavior, but it is possible that the strain gages

used to record the load for the tests at the highest strain rate were not properly calibrated

Charpy Impact Toughness Tests

Full Charpy impact energy transition curves were determined for specimens

oriented in both the T-L and L-T orientations Standard size specimens were tested in

accordance with ASTM E23 over the temperature range of the ductile-to-brittle transition

The results are plotted in Figure 6 There is little influence of specimen orientation on the

impact toughness The 67.8 J (50 ft-lb) impact energy level for this plate corresponded to

a temperature of 21~ (70~

Drop-weight Nil-Ductility Transition (NDT) temperature tests were conducted in

accordance with ASTM E208 to determine the NDT temperature for the plate Type P3

specimens were tested using an impact energy of 407 J (300 ft-lbs) The NDT

temperature for this plate was - 18~ (0~

According to Section IT[ of the ASME Boiler and Pressure Vessel Code, the

reference temperature, RTNDT, for a material is the greater of either the NDT temperature

determined from drop-weight specimens, or 33~ (60~ below the temperature of the

67.8 J (50 ft-lb) impact energy level determined from a Charpy impact energy curve The

RTNDr for this particular plate was determined to be -12~ (10~ based on the Charpy

impact energy

Fracture Toughness Tests

The quasi-static fracture toughness of the plate was determined over the ductile-

to-brittle transition range using 1T compact specimens oriented in the T-L direction

Tests were conducted using the unloading compliance technique in accordance with

ASTM E1820 "Standard Method for Measurement of Fracture Toughness." In addition,

the procedures of the current draft of the "Test Practice for Fracture Toughness in the

Transition Range, ''3 were employed as well The specimens had an initial crack length of

a/W=0.55 and were sidegrooved Tests were conducted at three temperatures based on

the temperature of the 28J Charpy impact energy level, T28j, which was -20~ (-5~

3"Test Practice for Fracture Toughness in the Transition Range," Draft 8, ASTM Task

Group E08.08.03, ASTM, West Conshohocken, PA

LINK AND GRAHAM ON TOUGHNESS OF PRESSURE VESSEL STEEL 2 3

c

c

_

>,

Figure 3 Yield strength as a function of strain rate for HSST Plate 14, A S T M A533, Gr B,

tested at three different temperatures

LINK AND GRAHAM ON TOUGHNESS OF PRESSURE VESSEL STEEL 25

The test temperatures were -64~ (-84~ -21~ (-5~ and 28~ (83~ (corresponding

to approximately T28J 45~ T28J, T28j-I-45~ Six replicate specimens were tested at each of the lower temperatures where the specimens cleaved with little or no prior ductile tearing At the warmest temperature it was possible to develop full resistance curves, so only three tests were conducted An additional set of six specimens was tested at an intermediate temperature, -4~ (25~ where the specimens cleaved after some significant ductile tearing ( 0.50 m m to 0.76 m m (0.020 to 0.030 in.)) A tabular summary of the test results is given in Appendix A

The resistance curves for the tests conducted at 28~ (83~ are plotted in Figure

7 Only specimen HAS-1 yielded a valid Jic value (25J~/(~v = 0.824), the other specimens were marginally of insufficient size to yield fully qualified results (25JQ/av = 1.10 for HAS-2 and 1.13 for HAS-3) The average fracture toughness, JQ, of all three specimens tested at 28~ (83~ was 521.5 kJ/m 2 (2980 in-lb/in2) Results for the tests which failed

by cleavage fracture are plotted in Figure 8 The results are plotted as Kjc values, where Kjc = ~/(JcE) Median fracture toughness values were determined for the series of tests conducted at -64~ (-84~ and -21 ~ (-5~ following the procedure outlined in the draft Standard Practice for Fracture Toughness in the Transition Region These median toughness values were used to calculate the reference temperature, To, in the following expression describing the median fracture toughness as a function of temperature:

2 6 FATIGUE AND FRACTURE MECHANICS: 29TH VOLUME

where Kjc IT is the median fracture toughness in MPa~lm of a 1T specimen tested at a

temperature, T (~ and To is the reference temperature at which a 1T specimen has a

median fracture toughness of 100 MPax/m The median toughness at -64~ (-85~ was

89 MPa~/m (81.4 ksix/in ) and To was -56~ (-68.8 ~ The median toughness at -21~

(-5~ was 153 MPax/m (139 ksix/in ) and To was -50~ (-58.0 oF) The average To was -

53~ (-63.4 oF) The median fracture toughness curve is also plotted in Figure 8 Notice

that above RTNDT the scatter in the toughness data increases considerably This is typical

behavior in the ductile-brittle transition region

Dynamic Fracture Toughness Testing

The test matrix for the dynamic fracture toughness tests is shown in Table 2 The

specimen identification, size and orientation are listed in the matrix These conditions

were established in an attempt to locate data points at appropriate rates and temperatures

with respect to the Shabbits data set in order to better establish the trend of toughness

with temperature and rate, particularly in the 105 MPa~m region The testing and analysis

procedure followed the recommendations for rapid-load plane-strain fracture toughness

testing of Annex A7 in ASTM E399

The dynamic fracture toughness tests were conducted in a 2 224 kN (500 kip),

MTS Systems Corp servo-hydraulic testing machine This machine has a high-rate mode

of operation that was designed to achieve a maximum actuator speed of 508 cm/s (200

in./s) with a load capacity of 979 kN (220 kips) The machine is under open-loop control

during high-rate operation and the actuator speed is controlled by the position of a throttle

valve which restricts the flow of oil from two high pressure accumulators to the actuator

Slack grips were installed in the load train to allow the actuator to accelerate before

applying load to the specimen and the specimen grips were preloaded to maintain

specimen alignment while the actuator was accelerating

An environmental chamber was designed and fabricated for cooling and heating

the specimens and grips to the test temperature Cooling was accomplished by spraying

liquid nitrogen into the moving air stream and heating was via finned strip heaters in the

air stream A digital temperature controller was used to control the specimen temperature

within + I ~ (+2~ of the desired test temperature This system provided excellent

control and stability of the specimen temperature The 2T and 4T compact specimen

designs were similar and the 4T C(T) is shown in Figure 9 The specimens have the

standard W/B=2 The notch is cut by wire EDM and the initial notch length is a/W=0.45

to permit precracking the specimens to an initial crack length of a/W=0.50 The crack

mouth has a non-standard configuration that is designed to accommodate a custom-

designed dual-element displacement gage The capacitance-based displacement gage has

a sensing element positioned at the specimen load-line and at the front face of the

specimen Specimen precracking was initiated at a maximum of 27.5 MPa~]m (25 ksi-

~]in) and reduced gradually under K-control to a level of 19.8 MPa~/m (18 ksi-~/in) for at

least the final 1.27 mm (0.050 in.) of crack extension The precracks produced in this

manner were uniform and met the crack front straightness requirements of E399 The 2T

LINK AND GRAHAM ON TOUGHNESS OF PRESSURE VESSEL STEEL 27

C(T) specimens were sidegrooved 10% of the specimen thickness on each side after

precracking and the 4T C(T) specimens were tested without sidegrooves

Figure 8 Fracture toughness, KjclT as a function of temperature and the master

curve for quasi-static fracture toughness tests on HSST Plate 14

TABLE 2 Dynamic fracture toughness test matrix, including specimen size, orientation

2T (LT) HAS107 2T (LT) HAS 112 2T (TL) HAS116A 2T (TL) HAS117A 4T (TL) HAS103 4T (TL) HAS105

[ 42 (75)

4T (TL) HAS100 4T (TL) HAS 102 4T (TL) HAS 104

4T (TL) HAS055 4T (TL) HAS057 4T (TL) HAS058 4T (TL) HAS056

2 8 FATIGUE AND FRACTURE MECHANICS: 29TH VOLUME

Instrumentation for the dynamic fracture toughness tests consisted of:

9 The actuator-mounted LVDT for monitoring actuator position during the test

9 A dual-element, capacitance-based displacement gage for measuring the specimen load-line and crack-mouth opening displacements

9 Strain gages mounted on the specimen arms in haif-bridge configurations for measuring the load applied to the specimen

9 Signal conditioners associated with each of the transducers

9 A digital oscilloscope for recording the dynamic signals during the test

9 A streaming FM tape recorder as a backup recording device

9 A strip chart recorder for recording the specimen temperature prior to the test

Two precision strain gages (350 ohm) oriented at 90 ~ to each other were mounted

on each specimen arm and configured in a half bridge Each half bridge was amplified and recorded separately Each strain gage bridge was calibrated under quasi-static load with the load cell in the 2 224 kN (500 kip) MTS machine The maximum calibration load was limited to the final maximum precracking load for each specimen

LINK AND GRAHAM ON TOUGHNESS OF PRESSURE VESSEL STEEL 29

Results

A typical test record from a 4T C(T) specimen (HAS105) is plotted in Figure 10

The analysis followed the procedure given in A7.7.2 of E399 Note that the load signals

start to increase from the pre-load level, which was established prior to starting the test to

minimize the effect of impact loading on the measured load and displacement The load

signal from the lower strain gage bridge starts to rise before the upper bridge After

approximately 450 Ixs the upper bridge signal crosses the lower Beyond this point, the

load measured by the upper bridge is slightly higher than that from the lower bridge This

behavior was observed for almost all of the tests conducted at rates in the vicinity of 105

MPa~/m/s (105 ksi~/in/s) and it is believed to be a dynamic effect which has diminished by

the time the specimen fails The difference between the individual signals and the

average load was less than 3% at failure for most of the tests, with only four showing a

difference between 3 and 6%

The load vs COD record for HAS105 is shown in Figure 11 There is some slight

non-linearity towards the end of the test, but in general, the load vs COD trace is linear

and falls within the envelope defined in the High Rate Annex of ASTM E399 For 9 of

the 19 tests, PQ = Pm~x and the load-displacement trace falls within the -+5% bounds

specified in A7.7.2 of E399 There is a lot of judgment required in determining the slope

of the "initial portion of the test record." For this analysis, the theoretical compliance was

used as a guide in selecting the initial slope In some cases the measured compliance was

slightly different than the theoretical In these cases, judicious choice of the slope could

mean the difference between falling within or outside the -+5% bounds The critical load,

PQ, was equal to Pmax based on the load-displacement curves for most of the tests There

were problems with the COD gage on several of the remaining tests, either erratic

behavior of the gage prior to the test or gage failure during the test Therefore, the

measured displacements for these test were not considered reliable, and KQ was calculated

using PO=Pm,x

The results for the dynamic fracture toughness tests are listed in Table 3 None of

the tests resulted in fully qualified Kid values in accordance with ASTM E 399 All but

two of the tests (HAS 115 and HAS 111) did not qualify because of insufficient specimen

size Even HAS115 and HAS111 did not qualify because the time to PQ was less than the

minimum required time of 1 ms The results are plotted as a function of temperature in

Figure 12 Also plotted in Figure 12 are the quasi-static fracture toughness results from

this study and the dynamic fracture toughness results for HSST 02 from Shabbits [1]

The dynamic fracture toughness transition curve is shifted to higher temperatures

compared to the quasi-static curve as expected; however, it is not shifted as far as the

Shabbits data

All but two of the 2T C(T) specimens were oriented in the LT direction and all of

the 4T C(T) specimens were oriented in the TL direction The effect of specimen

orientation can be seen by comparing the results for specimens HAS107 and 112 (LT

LINK AND GRAHAM ON TOUGHNESS OF PRESSURE VESSEL STEEL 31

orientation) with specimens HAS116A and 117A (TL orientation) which were tested at

similar rates and the same temperature The two specimens in the TL orientation

exhibited a slightly higher toughness than the LT specimens This is somewhat contrary

to the expected trend since the TL orientation is usually considered to be the "weak"

direction Given the large scatter normally associated with fracture toughness in the

transition region, there is insufficient data to support a general conclusion regarding the

effect of crack orientation on the fracture toughness

The fracture toughness is plotted as a function of loading rate in Figure 13 along

with the Shabbits data In this figure, it appears that the fracture toughness of HSST Plate

14 (this study) is higher than for HSST Plate 02 when the temperature is expressed in

terms of (T - RTNDT) It also appears that at the higher temperatures the rate of change in

toughness with loading rate is lower than what Shabbits observed

An alternative reference temperature for indexing the fracture toughness based on

the "master curve" [7] was used in an attempt to relate the current results with those of

Shabbits The master curve is an empirical function which is used to describe the

temperature dependence of the median fracture toughness of a IT specimen in the

transition range The expression for the master curve was given previously in equation

(2) A specimen size adjustment is applied to the measured fracture toughness to account

for the statistical size effect on fracture toughness in the transition range The fracture

toughness of a specimen is adjusted to an equivalent IT specimen size using the

relationship:

9 B ~I14

where Kjc B1 is the toughness (in MPa~/m) of a specimen with thickness, B1 (in mm) and

Kjc lr is the adjusted toughness Eq (3) was derived by Wallin [8] from a weakest-link

model which assumed that the fracture toughness follows a three-parameter Weibull

distribution with a fixed Weibull slope of 4 and Kmin=20 MPa-m u2 The reference

temperature for HSST plate 14 was determined to be To = -53~ from the quasi-static

fracture toughness results of 1T C(T) specimens presented earlier Wallin [9] reported an

average reference temperature of To = -27~ for HSST plate 2, determined from three sets

of fracture toughness data on this plate The static fracture toughness for HSST Plates 02

(from Shabbits [10]) and 14 are compared in Figure 14, where the toughness is adjusted

to a 1T specimen size and the temperature is plotted relative to the reference temperature,

To, for each plate The plates exhibit very similar toughness when characterized in this

manner The data for HSST Plate 14 at the highest temperature all lie above the master

curve Since the specimens tested at that temperature exhibited substantial stable crack

growth prior to cleavage fracture, they would be expected to lie above the median line

The dynamic fracture toughness for HSST Plates 02 and 14 are again compared in

Figure 15, except that the toughness is plotted with respect to the reference temperature,

To, and all toughness data are adjusted to a 1T specimen size The data from each plate

fall in the same band when plotted in terms of (T-T0) A reference temperature was

calculated for the dynamic fracture toughness data determined from the 4T specimens

from plate 14 In this case, the procedure for calculating To described in the Draft

32 FATIGUE AND FRACTURE MECHANICS: 29TH VOLUME

Standard could not be used since the tests were conducted at several temperatures An

alternative procedure described by Wallin [9] was used to iteratively determine the

maximum likelihood estimate of To The reference temperature for the dynamic initiation

fracture toughness at a loading rate of -1 x 105 MPa~/m/s was -25~ corresponding to a

shift of +28~

The dynamic fracture toughness is plotted in terms of the loading rate in Figure

16 The isothermal lines shown in the figure are expressed in terms of (T-To), where the

solid lines are an approximate fit to the Shabbits data (HSST 02) and the dashed lines

represent the trend in the NSWC data (HSST 14) The dynamic fracture toughness data

from the two plates are in much better agreement after accounting for the difference in the

reference temperatures of the two plates The dynamic fracture toughness still decreases

with increasing loading rate, but the effect at the highest test temperature is not as

dramatic as initially reported by Shabbits

Conclusions

The dynamic fracture initiation toughness of ASTM A533, Grade B, Class 1 steel plate,

HSST plate 14, was measured in the ductile-to-brittle transition region at loading rates

from 103 to 105 MPa~m/s The toughness decreased as the loading rate increased at a

given temperature, and the toughness increased as the temperature was increased The

results of this investigation were compared with previously published results for a similar

plate, HSST plate 02 When expressed in terms of T-RTNDT, the toughness of HSST plate

14 was greater than that of HSST plate 02 The toughness of the plates as a function of

temperature and loading rate was very similar when the temperature was expressed in

terms of the quasi-static reference temperature, To There was a shift in To of +30~

when the loading rate was increased from quasi-static to 105 MPa~/rn/s The reduction in

fracture toughness with increased loading rate at the highest test temperature was not as

severe as postulated in previous investigations

Figure 12 Comparison of (a) static and dynamic fracture toughness of HSST plate 14 and

(b) dynamic fracture toughness of HSST Plates 02 and 14, as a function of T- RTNDT

LINK AND GRAHAM ON TOUGHNESS OF PRESSURE VESSEL STEEL 3 5

Figure 13 Dynamic fracture toughness as a function of loading rate for HSST Plates 02

and 14, with temperature relative to the RTNDT

Acknowledgment

The work reported herein was performed at the Naval Surface Warfare Center,

Carderock Division under the "Dynamic Fracture Initiation Toughness of Reactor

Pressure Vessel Steels Program." The program was sponsored by the Heavy-Section

Steel Technology (HSST) Program at the Oak Ridge National Laboratory under

Interagency Agreement DE-A105-940R22337 Mr W.E Pennell is the HSST Program

Manager The HSST Program is sponsored by the Office of Nuclear Regulatory Research

of the U.S Nuclear Regulatory Commission The Technical Program Monitor at the

USNRC is Dr Shah Malik This work was performed at NSWCCD under the

supervision of Mr T.W Montemarano, Head, Fatigue and Fracture Branch (Code 614)

The authors would like to acknowledge the contributions of Mr Stanford Womack,

Mechanical Engineering Technician, of the Fatigue and Fracture Branch for his valuable

contributions to the planning and conduct of the experimental work