„*T L in$! OF STAND 4 TECF r

Reference

A 1 1 1 0 b 2bD5bT

NBSIR 84-3001

NBS

Publications

EFFECT OF CRACK-TIP REGION

CONSTRAINT ON FRACTURE IN THE

DUCTILE-TO-BRITTLE TRANSITION

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

May 1 984

NBSIR 84-3001

EFFECT OF CRACK-TIP REGION

CONSTRAINT ON FRACTURE IN THE

DUCTILE-TO-BRITTLE TRANSITION

T.L. Anderson

Fracture and Deformation Division

Center for Materials Science

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

May 1984

Sponsored by: U.S. Department of Interior Minerals Management Service

12203 Sunrise Valley Drive

Reston, Virginia 22091

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

FOREWORD

The research results and analysis reported here have implications

regarding the evaluation of toughness requirements of structural

materials for offshore platforms.

This study shows that specimen geometry has a significant effect on

the measured fracture toughness in the ductile-to-brittle transition

region. The geometry effects have been attributed primarily to

constraint effects. Both an increase in the specimen thickness and a

decrease in the ligament size result in an increase in contraint at the

crack-tip and therefore raise the ductile-to-brittle transition

temperature.

The crack-tip region constraint (CTRC) decreases with crack blunting

by a relaxation mechanism. In this study a model for the constraint

relaxation has been developed, which can be used to predict the

ductile-to-brittle transition curves for a low-carbon steel as a function

of geometry.

The results of this study can be applied to verification of required

toughness for large structural elements, such as those used in offshore

platforms, through a temperature shift approach, by considering a

required crack tip opening displacement (CTOD) in the structure at the

service temperature versus a measured CTOD in a standard specimen at some

test temperature. The required CTOD at the service temperature, 6 c

, can

be calculated, for example from the CTOD Design Curve developed at the
British Welding Institute (BWI), which provides a relationship between

the allowable crack size and 6 c for a given design stress level, stress

concentration factor and residual stress level. For example, consider a

structural member of EH36 steel 150 mm thick at service temperature

-20 C C, subjected to a stress level of 75% of the yield strength. Also,

assume that full-yield residual stresses are present. Suppose that a

long surface flaw 15 mm deep is present, oriented so that the stress

field has a maximum effect. According to the BWI COD curve, a material

toughness of 6 c

= 0.25 mm would be required in this case. The BWI

procedure requires measurement of the material toughness using

ful 1 -thickness fracture toughness specimens, 150 mm in this case. In

order to be able to test standard-size specimens to verify the adequacy

of the material toughness, such specimens have to be tested at a

temperature of AT below the operating temperature considered. Based on

the model presented in this study a shift in the ductile-to-brittle

transition temperature due to the difference in thickness between the

actual structure and the laboratory specimen can be predicted through an

assumption about the global notch constraint factor, L, for the

structure. The test temperature requirement for laboratory size

specimens, under the assumptions about the service condition listed above

is shown in Figure I as AT versus specimen thickness for two L values.

The theoretical model presented in this report predicts correct

behavior trends for the change in transition curves with geometrical

parameters. However, this model is oversimplified and excessively

IV
conservative. Another limitation of the analysis in the present form is

that statistical effects are not taken into account. Because the scatter

of toughness data in the transition region is known to be large, and

because of the possibly overconservative nature of the predictions of the

present model, this approach to material toughness validation should be

verified further before it is considered for use in practice. Tests of

specimens comparable in thickness to the upper range of actual structural

thicknesses will be crucial to the verification of this temperature-shift

approach

SPECIMEN THICKNESS, mm

Fig. I. Temperature shift, AT, as a function

of specimen thickness, B, for two

global notch constraint factors, L.

v
CONTENTS

Page

FOREWORD iii

NOMENCLATURE vill

ABSTRACT xii

1. INTRODUCTION 1

1.1 Linear Elastic Fracture Mechanics 2

1.1.1 The Stress Intensity Factor 3

1.1.2 Fracture Toughness 4

1.1.3 Crack Tip Plasticity 5

1.1.4 Summary Comments %

7

1.2 Elastic-Plastic Fracture Mechanics 8

1.2.1 The Crack-Tip Opening Displacement 8

1.2.2 J-Integral 13

1.2.3 Summary Comments 15

1.3 Micromechanisms of Crack Extension 17

1.3.1 Cleavage 19

1.3.2 Ductile Tearing (Microvoid Coalescence) 30

1.3.3 The Ductile-to-Brittle Transition 31

1.4 Effect of Specimen Size and Geometry on Fracture Behavior 35

1.4.1 Experimental Observations of the Size Effect 38

1.4.2 The Causes of Size Effects 40

1.4.3 Scaling Fracture Toughness 41

1.5 Statement of the Problem 42

1.6 Objectives 43

1.7 Technical Approach 43

2. EXPERIMENTAL PROCEDURE 46

2.1 Test Materials 46

2.2 Tensile Tests 46

2.3 Charpy V-Notch Impact Tests 48

2.4 Fracture Toughness Tests 50

2.4.1 SENB Specimens 50

2.4.2 SENT Specimens 57

3. RESULTS AND DISCUSSION 61

3.1 Tensile Data 61

vi
Page

3.2 Charpy-Impact Data 64

3.3 Fracture Toughness 66

3.3.1 ABS EH36 Steel 66

3.3.2 Pure Iron 87

3.3.3 Fractography and Metallography 89

3.3.4 Summary Comments 97

3.4 Characterization of Fracture in the Ductile-to-Brittle

Transition Region 97

3.4.1 The Crack-Tip Strain Function 102

3.4.2 Measurement of CTRC 110

3.4.3 A Spring Model for CTRC 114

3.4.4 A Model to Estimate o° 120

3.4.5 Predicting the Relaxation Slope 123

3.4.6 Predicting Transition Curves 129

3.4.7 Application to Structures 136

3.4.8 Application to Other Materials 140

3.5 Constraint Versus Statistical Models 151

3.5.1 Factors that Affect Constraint 152

3.5.2 Factors that Affect Statistical Shifts in Toughness 153

3.5.3 Determining the Cause of Transition Shifts 154

3.5.4 Summary Comments 157

3.6 Discussion of Results 157

3.6.1 Advances 158

3.6.2 Applications 159

3.6.3 Limitations 161

3.6.4 Summary Comments 162

4. SUMMARY AND CONCLUSIONS 163

5. ACKNOWLEDGMENTS 164

6. REFERENCES 165

7. APPENDIX I: ADVANCES IN FRACTURE TOUGHNESS TEST METHODS 171

7.1 The Rotational Factor 171

7.2 Detecting the Onset of Tearing 173

7.3 Estimation of J from CMOD 175

7.4 Relationships Between J and CTOD 178

7.5 The Eta Factor 181

7.6 Crack-Tip Replication 183

8. APPENDIX II: TABULATED DATA 185

vi i
NOMENCLATURE

area

crack length

critical crack length

specimen thickness

ligament length

elastic compliance

carbide thickness or radius

diameter

initial diameter

grain diameter

martensite packet diameter

diamond pyramid hardness number

Young' s modulus

E/0-v2

)

force in the x direction

volume fraction

strain energy release rate

critical G value

J-contour integral

critical J values

critical J which meets ASTM E 813 standards

stress intensity factor

critical K value

critical K which meets ASTM E 399 standards
spring stiffness

Hall-Petch slope

notch constraint factor

characteristic length along the crack front

m factor to relate J to CTOD

plastic m factor

hardening exponent

work hardening exponent ( 1 / N

load

critical 1 oad

limit load

load at net-section yield

load point displacement

plastic component of q

radius

carbide radius

overall rotational factor

plastic rotational factor

arc length along J contour

traction vector

strain energy

plastic area under the load-mouth opening

displacement curve

displacement in the x direction
mouth opening displacement

plastic component of V

specimen width

strain energy density

critical distance ahead of the crack tip

interparticl e spacing

distance from the crack tip or direction

propogation

stress intensity correction factor

knife edge height

displacement

crack-tip opening displacement

critical CTOD values

strai

effective strain

initiation or fracture strain

principle strains

eta factor

elastic eta

overall eta

plastic eta

contour around a crack tip

surface energy or plastic work

Poisson's ratio

stress

effective stress
1J

r fl ow

yy

<^1 jC? 2>^2

T eff

T

i

y

fracture stress

stress tensor

flow stress

yield stress (lower y.s. unless stated otherwise)

stress in the direction of crack propogation

initial lateral stress

yield strength (upper y.s. unless stated otherwise)

stress normal to the crack plane

stress parallel to the crack front

principle stresses

effective shear stress

friction stress

yield shear stress

xi
ABSTRACT

The effect of geometry on fracture toughness of steel in the

ductile-to-brittle transition region has been studied. The critical

crack-tip opening displacement (CTOD) and the critical J-integral have

been measured as a function of temperature for ten fracture specimen

configurations of ABS grade EH36 steel. In addition, two specimen

geometries of commercially pure iron were tested. Thicker specimens

tend to promote a higher degree of tri axial ity near the crack tip,

thereby elevating the flow’ stress and making it easier to reach the

cleavage stress. This causes a shift in the ductile-to-brittle transition to higher temperatures. Decreasing the uncracked ligament length

of bend specimens also tends to shift the transition to higher temperatures. Changing the loading conditions from bending to tension tends

to shift the transition to lower temperatures when the ligament is

relatively short. When the ligament length is large the transitionregion fracture behavior of a bend specimen approaches that of a tension specimen with a similar geometry.

A technique was developed to experimentally measure crack-tip

constraint. Constraint decreased with crack blunting. This relaxation

in constraint was modeled by a simple spring analog. The model was

used to predict ductile-to-brittle transition curves for hypothetical

structures. Some of the applications and limitations of the model are discussed.

Key words: crack-tip opening displacement; crack-tip constraint;

ductile-to-brittle; transition; elastic-plastic fracture; J-integral;

mechanical properties; structural steels; toughness.

xi i
Effect of Crack-Tip Region Constraint on Fracture in

the Ducti 1 e-to-Bri ttl e Transition

T. L. Anderson

1. INTRODUCTION

Fracture mechanics is a fairly new branch of materials science

which seeks to quantify the critical combinations of stress and crack

size for crack extension. There are two main ideas in fracture mechanics.

First, fracture occurs when the driving force for fracture, a function

of stress and flaw size, exceeds the material's resistance to crack

extension referred to as the fracture toughness. Second, fracture

toughness is a geometry-i ndependent material property; i.e., a simple

laboratory specimen and a large structure both fracture at the same

critical value of driving force. Both of these ideas work quite well

for materials that behave in a linear elastic manner; i.e., fracture

occurs prior to extensive plastic deformation. Recent progress in

ductile fracture mechanics suggests that these ideas are also valid for

* materials that fracture in a fully ductile manner [1].

Contrary to common assumptions, there is not a geometry-i ndependent

fracture criterion for the transition region between linear elastic and

f ul ly-ducti 1 e fracture. The fracture toughness of steels which undergo

a ductile-to-brittle transition is dependent on geometry in the

transition region. Thus, one of the main ideas of fracture mechanics,

the applicability of laboratory fracture toughness data to practical

structures, is not valid.

This document summarizes the author's efforts to characterize the

geometry effect on fracture toughness in the transition region. Basic

concepts of fracture mechanics as well as recent research pertinent to

1
this study are summarized below. Following the literature review the

statement of the problem objectives, and technical approach are given.

The experimental procedures, the results and discussion, and the summary

and conclusions are given in Chapters 2, 3, and 4, respectively. New

developments and refinements of fracture toughness test methods which

resulted from this investigation are included as an appendix.

1.1 Linear Elastic Fracture Mechanics*

The physical basis of fracture mechanics stems from the work of

Griffith [3J who demonstrated that the strain energy released upon crack

extension is the driving force for fracture. The strain energy, U, is

the work done by load, P, causing a displacement, a:

o

u = Pa - cp (l)

2 2

where C = p- = elastic compliance.

The loss of elastic energy upon crack extension of unit area, A, is

defined as the strain energy release rate, G:

r = dU | = £

2 dC = dU

b "

| m

dA 1 A 2 dA dA ! P*

*Sections 1.1 and 1.2 are taken from Ref. [2].

2
Irwin and Kies [4] used this relationship to determine the fracture

resistance of structural materials, G

c> by measuring the critical load,

P , in a specimen with a known compliance function, dC/dA.

1.1.1 The Stress Intensity Factor

Irwin [5], who determined the stress distribution near the tip of a

crack located in a linear elastic body, developed a stress analysis

basis for fracture mechanics. The magnitude of the crack tip stress

field, o.., was found to be proportional to a single parameter, K, the

J stress intensity factor:

a

ij

= TTTr

f

ij ( 0 ) = K * f (position) (3)

where, r and e are cylindrical position coordinates; r = 0 at the crack

tip and e = 0 in the crack plane. K is a function of the applied

stress, o, crack length, a, and a factor dependent on structural geometry,

Y(a):

K = Y(a)a/a. (4)

Tada, Paris and Irwin [6] and Sih [7] have published handbooks of K

formulae for various geometries and boundary conditions.

Irwin [5] demonstrated that the strain energy release rate and

stress intensity factor are related:

K

2

= E'G (5)

3
where, for plane stress, E' = E, the elastic modulus; and for plane

2 strain, E' = E/(l-v ), where v is Poisson's ratio. Thus, it is equivalent to attributing the driving force for fracture to the crack tip

stress field, which is proportional to K, or to the elastic strain

energy release rate, G. The stress intensity, K, is used more commonly

than G because K can be computed for different structural geometries

using stress analysis techniques.

1.1.2 Fracture Toughness

Fracture occurs when the crack tip stress field reaches a critical

magnitude, i.e„, when K reaches K

c

, the fracture toughness of the

material. K

c is a mechanical property that is a function of temperature,

loading rate and microstructure, much the same as yield strength is;

however, K

c is also a function of the extent of crack tip plasticity

relative to the other specimen (or structural) dimensions. If the

plasticity is small compared to the specimen dimensions and the crack

size, then K

c approaches a constant minimum value defined as Kj

c

, the

plane strain fracture toughness.

Measurements of fracture toughness based on linear elastic theory

are limited to the case of plane strain testing in accordance with

ASTM Standard E 399.
where B, a, and W are defined in Figure 1. The specimens are precracked

by fatigue cycling to an initial crack length of a/W = 0.5 and

subsequently loaded to failure. Kj

c is calculated from the critical

load, Pq, the measured crack length, the specimen dimensions and the

specimen calibration function, Y(^j, as follows:

K

0

= Y (It) . Q B/W

W

(7)

Kjc = Kg if all the conditions of ASTM E 399 are met, i.e., precracking

procedures, load-displacement record, specimen dimensions, etc.

1.1.3 Crack Tip Plasticity

Applicability of the linear elastic analysis has been extended to

conditions approaching net-section yielding by correcting for the zone

of plasticity that exists at the crack tip [8]. The idea is that the

plastic material at the crack tip strains without carrying the

incremental load; therefore, in the elastic sense, the crack behaves as

if it were slightly longer. The adjustment is made by adding the radius

of the plastic zone, r , to the apparent crack length:

K = Y(a+r

y

) 0 /a+r^

r

- 1

( K)

2 ry

' ST

where, Cy is the yield strength at the crack tip. The

modifies the crack tip stress field to account for the

redistribution due to the localized plasticity.

( 8 )

(9)

r^ correction

elastic stress

5
6

Figure

1.

ASTM

E

399

compact

specimen

for

fracture

toughness

testing.
The extent of crack tip plasticity is influenced by specimen

dimensions. This is particularly true for thickness. As specimen

thickness increases, a

Y increases from a to /3 a due to through-thethickness elastic constraint [9]. The maximum value of is reached

when the plastic zone size is limited to about 5% of the thickness.

Thus, in a given material, the plastic zone size as computed by equation

(9) can vary with thickness by a factor of three -- leading to a strong

dependence of K

c on thickness.

1.1.4 Summary Comments

The crack tip stress field is the driving force for fracture and

the magnitude of this stress field is proportional to the stress intensity

factor, K. K is a function of crack size, applied stress and structural

geometry and can be computed using stress analysis methods. The resistance

to fracture is a material property defined as the fracture toughness,

«

c

; fracture occurs when K = Thus, for a given structural geometry

and material, critical crack sizes can be determined as a function of

applied stress and vice-versa:

a c

= [^rfrr] • (10!

The approach is applicable to conditions of localized crack tip

plasticity, i.e., where o <_ .8a or r <_0.3a, when the r correction

ys y y

is used to account for crack tip plasticity L10]-

7
1.2 Elastic-Plastic Fracture Mechanics

Many of the high toughness structural materials undergo extensive

plastic deformation prior to fracture. Thus, the concepts of linear

elastic fracture mechanics must be extended to account for elasticplastic behavior. The two approaches of interest in the present investigation are the crack-tip opening displacement (CTOD) and the J integral.

1.2.1 The Crack-Tip Opening Displacement

The CTOD concept is a crack tip strain criterion for fracture

stemming primarily from the work of Wells [11,12]. Wells' hypothesis

was that the opening of the crack faces was strictly related to the

crack extension force, G, and the stress intensity factor, K, under

locally plastic conditions. Wells used an energy balance argument to

derive an expression for CTOD [12J:

2 „ K

6 = =

^I_

Ea a y y

(ii)

where 6 is the CTOD.

In 1965 Burdekin and Stone [13] illustrated how the CTOD concept

could be used to extend the capability of conventional fracture

mechanics to the elastic-plastic case. A Dugdale strip-yield model [14]

was used to develop the following equation for plane stress Mode I

crack-tip displacements under monotonic loading.

f aa , / 7i u \ 6 = —p In sec —

Trt c ay

( 12 )

A fracture toughness test method based on the CTOD concept was

developed by investigations at the Welding Institute [15-17]. The CTOD

8
test specimen (Fig. 2) contained a fatigue-precracked notch and was

loaded in three-point bending to fracture. The critical CTOD was

obtained from the load versus clip-gage displacement record. The

clip-gage displacement, V, was measured across the notch mouth as shown

in Figure 2. The V was converted to CTOD using the following

relationship [15].

V

where z = knife edge thickness

a = crack length

W = specimen width

r = rotational factor,

o This equation was derived assuming that the crack faces opened by a

simple hinge mechanism about a center of rotation. The value of rp was

assumed to be 0.5 in early work.

The current British standard for CTOD testing [18] specifies that

the CTOD be calculated from the following relationship.

k2

i 0.4(W-a)Vp

2

1 + 0.4W + 0.6a + z (H)

where the first term is the elastic component of CTOD, 6 , and the

second term is the plastic component, 6 . The plastic component of the

clip-gage displacement, V

p

, is estimated by constructing a line, parallel

to the elastic-loading line, from the critical point on the load9
O X.

10

Figure

2.

Three-point

bend

specimen

used

to

obtain

fracture

toughness

test

results.
displacement curve to zero load. The elastic component of the clip gage

displacement is then subtracted from the total displacement. The stress

intensity factor for the elastic CTOD calculation is obtained from the

following relationship.

K

= YP

BW

1/2

(15)

where P is the applied load and Y is the stress intensity coefficient.

Y is a function of specimen geometry and can be obtained for a given

crack 1 ength-to-width ratio (a/W) from the test standard [18].

The type of critical CTOD reported depends on the nature of the

observed fracture event. This is illustrated schematically in Figure 3

for a steel which undergoes a ductile-to-brittle transition. At low

temperatures the steel fails by cleavage and 6 c is measured experimentally.

As the test temperature increases cleavage becomes less favorable and

the fracture toughness increases. Eventually the fracture mode changes

to microvoid coalescence and the crack grows in a stable manner. <5^ is

defined as the value of CTOD at the onset of tearing. At temperatures

slightly above the fracture mode change, stable tearing can be followed

by unstable cleavage. When this occurs, 6 u is measured at the instability

point. On the upper shelf of toughness, the steel reaches a point of

plastic collapse when the work-hardening cannot keep pace with the

decrease in ligament area caused by stable crack growth. 6 m

is then

measured at the point of maximum load in a bend test. 6^ is the total

CTOD, i.e. 6^ plus the portion of CTOD associated with tearing. A plot

11
samvA ao(i)o lvoiimo

f s

* 2

© o>

O) ^

5 5

i ®

o m

0) w

&5S O• OB

o In

Ibb a

a A

o Hi

c 5

1 8 o 0)

0) 9)

(0 (9

> >

<0 <0

O 0)

mma m

O O

a> a) m

A A

(0 <0

4<i

0) 0)

c c 3 3

ii ii o s

60 60 <

12

8

m

=

Plastic

collapse

or

tearing

instability

8j

=

Onset

of

slow

stable

crack

growth

8

r

=

Resistance

curve

value

Figure

3.

Notation

for

critical

CTOD

values.
of 6 d versus Aa is the resistance (R) curve, a measure of a material's

resistance to crack growth. Figure 3 also shows that 6. is not a strong

function of temperature, but it is a function of the inclusion content.

1.2.2 J-Integral

The J-integral is a characterization developed by Rice [19] of the

elastic-plastic field in the vicinity of the crack tip. The use of the

J-integral as a fracture criterion was suggested and experimentally

demonstrated by Begley and Landes L20]. J is defined as the line

integral

0 = f

T [wdy - f (f^dsj (16)

where, r is any contour surrounding the crack tip,

w is the strain-energy density,

f is the stress vector normal to r,

u is the displacement vector, and

s is the arc length along r.

The J-integral is path independent for linear and non-linear elastic

materials [19] and nearly so for most structural materials under monotonic loading conditions [21]. Thus, J can be computed using numerical

methods by analyzing along a contour away from the crack tip, i.e., in a

region where the analysis methods are quite accurate.

An equivalent interpretation is that J is equal to the change of

potential energy U, upon an increment of crack extension A:

13
For the linear elastic case the potential energy equals the strain

energy and, therefore, equation (17) is the same as equation (2) and

J = G. Thus, J appears to be a logical extension of linear elastic

fracture mechanics into the elastic-plastic range. Due to the irreversibility of plastic deformation, the energy interpretation of the

J-integral does not apply to the process of crack extension in elasticplastic materials -- as G is for elastic materials. J is simply an

analytically convenient, measurable parameter that is a characteristic

of the elastic-plastic field at the crack tip. The contribution of

Begley and Landes [20J was to demonstrate that crack initiation under

elastic-plastic conditions occurs at a characteristic value of J, called

Jj

c

» that is related to in the same way G is related to K in

equation (5). Thus, J integral methods can be used to determine Kj

c in

specimens significantly smaller than the size requirements of equation (6).

Methods of measuring Jj

c are covered by ASTM Standard E 813. A

deeply notched specimen of the compact tension or single-edge notch bend

design is precracked to a/W = 0.6. The specimen is loaded incrementally

to a series of J-levels. After each increment of loading, J and the

crack extension, Aa, are measured. The load-displacement curve is

recorded on an X-Y plotter. Displacement is measured along the load

line. J is calculated from the load-displacement record and specimen

dimensions using:

< 18 >

14
where U is the area under the load-displacement record, b is the

ligament length, (W-a), and n is a dimensionless parameter dependent on

specimen geometry. Aa is measured by either the crack marking technique

or the unloading compliance technique described in ASTM E 813. The

results of a test series are plotted as 0 versus Aa, and the Jj

c is

defined as the extrapolation of the best-fit curve to the blunting line

defined byJ J = 2a v Aa. K T is related to J T as follows:

Y Ic 1c

K

Ic

(0) - ^

(19)

The J T test method is limited to measurement of the onset of

ductile tearing. Thus, it is not applicable to the measurement of

fracture toughness when cleavage is the micromode of fracture. Recently

Dawes [23] has proposed the adoption of a critical J notation equivalent

to the CTOD notation of Figure 3. This notation, shown in Figure 4,

would make the J concept applicable to all micromechanisms of fracture.

This proposed notation is used in the present study.

1.2.3 Summary Comments

The CTOD and J-integral concepts are efforts to define single

parameter characterizations of the fracture process that are applicable

to linear elastic and general yielding fracture. In the CTOD concept,

attention is focused at the crack tip; fracture theoretically occurs

when a critical displacement develops at the crack tip. The J-integral

15
£ 5 5 2 2 ®

O) ^ * « « 2

CO

n

&»° i 5 ® 5 w

to k.o <TM sa» 0 »- •“ Q. 6 3 2 i 1 i 0) 0)

o> o>

CO CO > >

CO CO

a) a> o o

a> a> S 3

co co -M

<0 <0 c c 3 3

ii ii _o £

CO

<0 mc

CDCBOD

CO

0) Soo

COo

a) o co

a> co

CD

Q.

jOoo

CD

CO So

0)

<D

CDCO

0)E

o> »-a>

ksco

CDco3c

<D

si

.5 a) 2 £

a>o 3O

"e 'L

a> siS .2

CD

Q 0)

-5"

a

ii ii

samvA

r ivomao

16

Figure

4.

Notation

for

critical J

values.
concept examines the stress-strain conditions along an arbitrary contour

away from the crack tip; fracture theoretically occurs when the potential

energy available for crack extension reaches a critical value defined by

J. For the linear elastic case, 6 c and Jj are consistent with the

linear elastic fracture criteria:

K

Ic

‘t ri - J t - 2o v 6 . Ic E Ic Y c( 20 )

There has been a great deal of research in recent years on ductile

fracture. Models have been developed to predict fracture by tearing

instability using J-integral R-curves and to predict fracture by plastic

collapse using limit-load expressions [22]. This work is not reviewed

here because it is not directly relevant to fracture of structural

steels at low temperatures.

1.3 Micromechanisms of Crack Extension

Fracture usually occurs by one of three mechanisms as illustrated

in Figure 5. Cleavage is rapid, unstable fracture associated with

brittle materials, while ductile tearing (or microvoid coalescence) can

occur in a slow, stable manner. Intergranular cracking can occur in

either a ductile or brittle manner. It is usually associated with a

corrosive environment and/or grain-boundary segregation. Since intergranular cracking did not occur in this investigation, only cleavage and

microvoid coalescence are reviewed in this section.

17
t t f t

III*

Ductile Tearing

t t t t

I I I I

Cleavage

t t t t

1111

Intergranular Cracking

Figure 5. The three basic micromechanisms of fracture.

18
Local plastic flow around the crack tip precedes fracture in both

ductile and brittle materials. For cleavage the plastic zone must

increase in size until sufficient local stress has been generated to

propagate a crack nucleus formed in some microstructural feature. For

microvoid coalescence or ductile tearing, a critical strain must be

reached for the coalescence of voids formed around second phase particles.

Fracture toughness parameters will necessarily differ for different

fracture mechanisms [23].

1.3.1 Cleavage

Plastic flow is necessary to propagate crack nuclei but cracks may

initiate and propagate at very low macroscopic strains because the

initial flow is localized at a stress concentration [24]. Generally, a

material's susceptabil ity to cleavage is promoted by any factor which

increases the yield strength such as low temperature, constraint which

produces triaxiality, radiation damage, prestrain and strain aging.

Refinement of grain size increases the yield strength but improves a

steel's resistance to cleavage fracture because grain-size refinement

also increases the fracture stress [24-27J.

Cleavage is nucleated when a critical value of "effective shear

stress" is attained corresponding to newly created slip dislocations

which fracture carbides, either by the stress induced at the end of a

pile-up L28-30] or by plastically straining the matrix beyond the

fracture strain of the particles. For normalized or furnace cooled

19
steels the effective shear stress is independent of temperature until

such a low temperature is attained that plastic deformation occurs by

twinning rather than slip [24].

The Petch-Hall equation can be written in terms of shear stress:

T y

= T

i + V

- 1/2

( 21 )

where x^ is the shear yield stress, x.. is the friction stress and d is

the grain diameter. The friction stress, x^, increases rapidly with

- 1/2 decreasing temperature while the effective shear stress, k^d , is

relatively constant with temperature. At low temperatures a crack

nucleus can propagate when the plastic zone is small because the yield

stress is high and little elevation by triaxiality and strain hardening

is needed to satisfy critical conditions for propagation. At higher

temperatures the yield stress is smaller so a larger plastic zone is

required to produce the necessary local stress.

Cleavage fracture is propagation controlled and depends on the

level of the local tensile stress. Values of the critical stress, c^,

are only slightly temperature dependent [24].

Models of propagation-controlled, slip-initiated cleavage fracture

were proposed by Knott [31], Cottrell [34], and McMahon and Cohen [30].

The Knott and Cottrell models treat cleavage as the propagation of a

nucleus formed by the interaction of slip dislocations. The McMahon and

Cohen model considers cleavage as the propagation of a small crack in a

grain boundary carbide. A model by Smith [35] which takes into account

20
both the effect of carbide thickness and dislocation interactions gives

the following expression for a

f

.

f

C o\ 2 2

r

l 2(

C

o\l/2 ] 2

> 4Ey

p + T eff [ 2 + 7\Tdj 7^

-

where C

Q

is the thickness of a grain boundary carbide.

T rr = k d

~ K eff y

is the effective shear stress, and y is a surface energy or plastic

P work term. The critical event is taken to be the propagation of a crack /

nucleus formed in a grain boundary carbide into the adjacent ferrite

matri x.

Knott [24] compiled the results of several authors who measured a

in a variety of mild steels as a function of the reciprocal square root

of grain size. These data are shown in Figure 6. The fracture strength

_ 1 obviously increases rapidly with d~ 2 although the scatter is great at

_ 1 high d~ 2 values. The data in Figure 6 were taken at various temperatures

but the effect of temperature on is small. Data of Curry and

Knott [25] which were taken at a constant temperature (-120°C) follow

the common trend.

A problem arises if one attempts to use equation (22) to explain

_ 1 the grain size dependence of o^. If k^d 2 is substituted for in

equation (22) the grain size terms cancel, leaving a relationship whose

only microstructural parameter is the carbide width, C . Knott [24]

suggested that a possible reason for this anomaly is that the ratio of

C

Q

/d remains constant upon cooling from the austenitic range, since both

21
1500

~

I

1 1 1

Mild Steel

1 1 1 1

•

c? » o z m V

A 0 A

fcr • A °A .

Iff 1000 .* * V _

&t- A * A

"In o Z°* +

0) B+

k.D 8 • Knott (1966.19671 o v Wilshow et al (1966.19661 500

o

A Oates (1969) _

Almond et al 119691 o

Low (1963)

L. o 0 Ritchie et al (1973)

Cixry t Knott (19761 V Holzmonn t Mon (1971)

0 till a Fpomehough

i Groom (1971)

1 1 1 0 12 3 4 5

)',/2

.

6 7 8 9

(Grain diameter, d (mm)’

1'2

Figure 6. Variation of critical fracture stress with grain

size; compiled by Knott [24].

22
C Q

and d depend on similar diffusion phenomena. Experimental data of

Curry and Knott [25] show that there is a strong relationship between

the two parameters, although it is not quite linear.

The relative effect of dislocation pile-up on propagation of a

cleavage crack is a function of C

Q

/d [35]. A crack in a thick carbide

particle is large enough to be treated as a Griffith crack and the

stresses from local dislocations are of secondary importance. However,

for thin particles the crack nucleus does not extend far from the tip of

the pile-up and the dislocations have an important effect.

Knott [24] has modified the model for low- and medium-carbon steels

with spherical carbides. The critical event is taken to be the

propagation of a nucleus in the spheroidal carbide into the ferrite

matrix. The dislocation contribution is ignored because pile-ups do not

occur. Instead the dislocations tangle around the carbide and form a

cell structure. The size of the cell structure depends on X , where X o o

is the interparticle spacing, rather than on d. The expression for the

local fracture stress is given by

ttEy . W> 4

(23)

where C is the carbide diameter. Values of v ("for ferrite) inferred

o p

o from equation (23) and experimental data are around 14 J-m” [24]. This

is consistent with values of Yp obtained for mild steels from equation

( 22 ).

Investigations of the cleavage fracture of low-carbon bainite and

martensite have established that the microstructural feature controlling

23
crack propagation is the packet size [36]. Since large misorientations

often occur at packet boundaries the direction of propagation must

change when the crack encounters a packet boundary. Extra work must be

done to allow a crack in a favorably oriented packet to propagate into

the adjacent packet. This is considered the critical event and a

fracture criterion based on packet size has been developed L36]:

a

f

= 4Ev

ir( 1-v 2 )d

(24)

-2

here d

p is the packet diameter. The inferred Yp value is 120 J*m as _2

compared to 14 J*m for ferrite.

It has long been recognized that a critical fracture stress must be

exceeded at a crack tip before the crack can propagate by cleavage

[24-37]. It has been discovered, however, that while this is a

necessary condition it is not sufficient. It is now believed that the

fracture stress must be exceeded over a critical distance which is

characteristic of a given microstructure. This concept is illustrated

in Figure 7. Ritchie, et. al . [38] applied this concept to develop a

model which predicts temperature variations of Kj

c in mild steel.

Figure 8 shows experimental data fitted to their model. Predictions of

Kj

c were made using an experimental value for a^, which was found to be

insensitive to temperature variations in the range studied, and various

assumed values for critical distance. Figure 8 shows that excellent

agreement was attained by assuming a critical distance of 2 grain

diameters

24
CTyv

Crack

DISTANCE FROM CRACK TIP . X

Figure 7. The Ritchie-Knott-Rice model for cleavage fracture

[38]. Fracture occurs when the fracture stress is

exceeded over a critical distance ahead of the crack

tip.

25
T -2741

O Predicted from Or ossuminq dc

« ^

r°'n d>ometer • Predicted oi$umir>q dc

• two qroin diometefJ

Figure 8. Comparison of predicted and experimental K. values

[38].

lc

26
The effect of grain size on critical distance has been studied by

Curry and Knott [25]. For their mild steel the critical distance was

about four times the grain diameter for d above about 50 urn, but was

relatively independent of grain size for finer grain sizes.

The apparent reason for this is that carbides of sufficient thickness

to satisfy the propagation conditions of equation (22) are more abundant

in coarse grains. In the case of finer grains, more grains have to be

sampled to find a sufficiently thick carbide, and the critical distance

increases with respect to grain size.

Curry and Knott [29] proposed a model for predicting fracture

toughness on the basis of finding favorably oriented carbide particles

within the plastic zone. According to this model, crack nucleus size

distribution is some multiple of the carbide particle size distribution.

The probability of finding a crack nucleus subjected to a stress greater

than or equal to a

is estimated for each nucleus radius and is summed

over all nucleus radii. Cleavage occurs when this probability equals

unity.

Curry [39], in a separate publication, argued that the model

proposed by Ritchie, et. al . [38] is compatible with the statistically

based model of Curry and Knott [29], The characteristic distance can be

related to the mean carbide radius or thickness.

Evans and Hutchinson [40] have also developed a statistically based

model for cleavage fracture. This model provides a rationale for the

critical distance. According to the model the critical distance, which

27
depends on the size distribution and volume concentration of grain

boundary carbides, is the distance from the crack tip at which the

probability of cleavage cracking exhibits a maximum. This is illustrated

in Figure 9 where probability of failure is plotted as a function of

distance. The probability approaches zero at the crack tip because the

volume of material containing cracked carbides tends to zero. At

distances greater than X

c the probability decreases with distance

because o is decreasing. Evans and Hutchinson derived the following

yy

expression for X .

where N is the hardening exponent

(N = 1/n, where n is the work hardening exponent)

k is a constant <1

m is a shape parameter characteristic of the carbide size distribution.

Their model also resulted in an equation for as a function of

material properties:

X

c (25)

a (N+U/2 3/2(k+l)

c (26)

(f*) 1/2(k+1)

a

o (N-l)/2

where

f is the volume fraction of carbides at the grain boundary.

r

c is the average carbide radius

28
Figure 9. Probability of failure as a function of distance

: dlstance at which probability is maximized

is defined as the critical distance.

29
a is a characteristic distance along the crack front

A is a function of N, k, m, and i.

It appears from equation (25) that X

c depends on yield strength and

is therefore a function of temperature- However, when the yield

strength dependence of Kj

c from equation (26) is substituted into

equation (25) the o Q

terms cancel; i.e.,

X

c a a 0

° (27)

This observation, that X

c is not temperature dependent, is very

important to the present study as will become evident in the Results and

Discussion chapter.

Rosenfield, et. al . [41,42] have experimentally measured X

c by

finding the fracture-triggering particle with a scanning electron

microscope (SEM) and measuring the distance from the crack tip to the

particle. These particles were either grain boundary carbides or

nonmetalic inclusions. Although the measured X

c values were quite

scattered, the values appear to be independent of temperature and

fracture toughness.

1.3.2 Ductile Tearing (Microvoid Coalescence)

In ferritic steels as the temperature increases and the flow stress

decreases, it becomes more difficult to produce enough constraint in the

plastic zone for the fracture stress to be exceeded. At temperatures

where the conditions become unfavorable for cleavage a ductile fracture

mechanism, microvoid coalescence, operates. This is the dominant

30
fracture mechanism of FCC alloys, even at very low temperatures. The

commonly observed microstructural stages on the initiation and growth of

a fibrous crack are [43]:

a) The formation of a free surface at a second-phase particle or

inclusion by either interface decohesion or particle cracking.

b) Growth of a void around the particle, often under hydrostatic

stress

c) Coalescence of the growing void with the crack tip.

These events are thought to occur almost continuously as the crack

advances; that is, second-phase particles progressively enter the

"process zone" ahead of the crack tip, and progressive void growth and

coalescence produce small increments of crack growth. The microstructural

parameters that control toughness are the spacing, X , of the particles

and the fracture strain of the matrix, [24,44,45].

When voids grow in a hydrostatic tensile stress field an internal

neck is formed between the void and the crack tip, and final separation

occurs along a knife edge in three dimensions to give a fracture surface

composed of cusps and dimples centered on second-phase particles.

1.3.3 The Ductile-to-Brittle Transition

The effect of flow stress on the ducti 1 e-to-bri ttl e transition is

illustrated schematically in Figure 10. Flow stress is highly

temperature dependent while fracture stress is insensitive to

temperature changes. Cleavage occurs when the flow stress exceeds the

31
32

temperature.

Cleavage

occurs

when

the

flow

stress

exceeds

the

fracture

stress.
fracture stress. For the simple schematic in Figure 10 the ductile-tobrittle transition occurs where the flow stress curve crosses the

fracture stress curve. An increase in triaxiality elevates the flow

stress, causing the transition to occur at a higher temperature.

The effect of the flow properties of material near the crack tip on

fracture toughness and micromechanism of fracture is further illustrated

in Figure 11. At a low temperature, represented by curve(a) in Figure 11,

the yield strength is high; only a small degree of plastic flow occurs

before the critical fracture stress is reached. At higher temperatures

(curve(c)) the yield strength is so low that the fracture stress is

never reached, even after significant plastic flow. The crack begins to

grow by ductile tearing when the material ahead of the crack tip reaches

a critical strain. Curve(b) represents an intermediate condition. The

material reaches the critical strain, causing stable crack growth. Upon

further strain hardening the material reaches the fracture stress,

resulting in unstable cleavage.

Curve(a) represents lower-shelf behavior because a small degree of

plastic flow has preceded fracture; small-scale yielding prior to

fracture results in a low toughness value. Curve(c) represents

upper-shelf behavior because fracture is by ductile tearing and a high

degree of plastic flow (corresponding to high toughness) precedes

failure.

33
34

material

near

the

crack

tip,

illustrating

the

effect

of

flow

stress

on

the

micromechanism

of

fracture.

(a)

Cleavage,

(b)

cleavage

preceded

by

ductile

tearing,

and

(c)

stable

crack

growth.
1.4 Effect of Specimen Size and Geometry on Fracture Behavior

Specimen geometry can have a substantial effect on fracture toughness

as illustrated in Figure 12. As thickness, crack length, and uncracked

ligament length become large compared to the plastic zone the fracture

toughness reaches a minimum value defined by Kj

c

. The ASTM E 399

standard is designed to measure this lower bound fracture toughness.

The size effect is most pronounced in the ductile-to-brittle

transition region, as illustrated in Figure 13 [46]. The transition

tends to occur at higher temperatures with larger specimens. At a

constant temperature in the transition region, represented by the

vertical line in Figure 13, the small specimen has a higher fracture

toughness than the large specimen.

This represents a potentially dangerous situation when using

fracture toughness data from small specimens to design large structures.

On the upper shelf of toughness, where ductile tearing is the micromode

of fracture, it is permissible to predict the fracture toughness of

large structures from small specimen data because J. and 6.. are not

strong functions of geometry [47,48]. However, in the transition region

where cleavage may be the micromode of fracture, a crack in a small

specimen may grow in a stable and ductile manner while a large structure

could fail catastrophically by cleavage and have much lower toughness

than predicted in the small scale test.

Although a Kj

c test will always give lower-bound results, it is

sometimes not practical or possible to perform a fracture test according

35
CM

c

36

Figure

12.

Effect

of

specimen

geometry

and

plastic

zone

size

on

fracture

toughness.

Specimens

must

lie

to

the

right

of

the

vertical

line

to

meet

ASTM

E

399

specifications

[46].
MVC

C

07 >> E

.a •r— 07 (_7 x: LO 07

4-> r— CL

1/1 o >, 03 -Q <4- 4-> E c

i/l "O c •r—

•r— 07 07 03 c 4-> E U

03 c -r- 4-7 xr. 07 U t/1 u 1/1 07 C

QJ 07 Q. o

£ X i/i u o CL

s- 07 4-7 -C UJ o•1* i~ c ai

cc

E 07

t03 x:

fc- D

a/ 3 4-> aj JO •*-> ID JO H

4-7 IDU co4-7 < c C7 u 07 • o D- f— r—

CC E • I— lO4-7 07 o •§ UJ c -t-> 1—1 a 03

t- 07 -C

07 x:07CD z

4~>

IS)

4-7 4-> OlC

03> UJ

C 4-> 07 r- 03 o c c i- 07 u •r— <D i- <4- • •” 07

4-7 u

o 07 r— >>

i- 03 07 JD

+7 3 <_7 i

u 4-> •i— •r— i/> a O 4-> 4-> *

O- 03 s- U •r—

<4- t- 07 3 03 UJ <4- > T3 ^4-

• CO

r-H

QJ

s-3

CD

ao(i)o jo r ivoiimo

37
to E 399 specifications. For low- and medium-strength steels the size

requirements for a valid Kj test are often excessive; a specimen of

suitable size would be very expensive and would probably exceed the load

capacity of most test machines. Landes [49] has shown that for some

materials a valid Kj

c cannot be obtained, even with an infinitely large

specimen.

A structure which operates in the ductile-to-brittle transition

region will often behave in an elastic-plastic manner. Therefore a Kj

c value, which is based on a linear elastic analysis, would be overly

conservative.

1.4.1 Experimental Observations of the Size Effect

A number of investigators [47-55] have studied the effect of

specimen thickness on the fracture toughness of various materials. In

the transition region, toughness decreases with increasing thickness

until a saturation thicknss (plane strain) is reached; further increases

in thickness have little or no effect on toughness.

The relative crack length and ligament length in bend specimens can

also affect fracture toughness in the transition region. Figure 14

schematically shows the consensus results of a number of investigators

[47-53,56-59], The ductile-to-brittle transition temperature tends to

increase with increasing crack-length-to-width ratio, a/W. For very

deep cracks, fracture toughness can increase due to plastic flow to the

nearest free surface.

38
<0 ©

+* «-> CO (0 o>

39

TEMPERATURE

Figure

14.

Effect

of

notch

depth

on

fracture

behavior

of

SENB

specimens

[46].
1.4.2 The Causes of Size Effects

There are two different explantions for the size effect on fracture

toughness. One explanation is based on the statistical nature of

cleavage fracture [60-63]; the second is related to the crack-tip stress

state [47-53].

Cleavage fracture toughness depends on the size and distribution of

carbides or inclusions which serve as crack initiation sites [24,42]. A

large particle near the tip of the major crack produces a large crack

nucleus which results in a low fracture toughness. According to the

statistical model [60,61], the average fracture toughness of a large

specimen is lower than that of a smaller specimen because the greater

volume of material sampled in the large specimen results in a higher

probability of finding a large, favorably oriented particle near the

crack tip.

An alternative explanation for size effects is that of crack-tip

constraint [47-53]. Due to the stress concentration inherent in a

cracked body, the material near the crack tip, which is highly stressed,

tends to contract perpendicular to the major stress axis. However, this

material is constrained by the surrounding material due to compatibility

requirments. This constraint produces a triaxial stress state near the

crack tip which elevates the flow stress locally. This elevation in

flow stress makes it easier for the material to reach the fracture

stress. In a small fracture specimen a small amount of material

surrounds the crack tip; therefore constraint is relatively low. In a

40
large specimen or structure, constraint is high because a large volume

of material surrounds the crack tip; thus, fracture toughness is lower

because less elevation of flow stress by plastic deformation ( i . e .

strain hardening) is needed to reach the fracture stress. Elevation of

the flow stress due to constraint shifts the ductile-to-brittle

transition to higher temperatures (see Fig. 10).

Most authors who have studied size effects concede that both

statistical and constraint effects can be contributing factors.

However, there is some disagreement as to which of these two factors is

dominant. It is the author's opinion that the dominant factor depends

largely on the material. This point is further discussed in Section 3.5.

1.4.3. Scaling Facture Toughness

Several investigators have tried various methods to predict

lower-bound toughness values from small-scale tests. One of the most

common methods involves empirically correlating Charpy-impact energies

with Kj

c values [64-67]. However, these empirical equations are

generally only valid for the materials used for the correlations. None

of these methods has proven to be accurate for a wide range of materials

[68]. In a recent article, Dawes, et. al . [69] compared critical crack

lengths obtained by these methods with actual wide plate test results.

They found that these empirical correlations can sometimes overestimate

critical crack lengths by a factor of 10 or more.

41
Landes and Shaffer [60] used the statistical concept to predict Kj

values from small specimen results. They applied a Weibull [70]

distribution to various populations of small specimen results to obtain

lower-bound toughness values.

Rosenfield, et al . [41] have recently had success in predicting

large-scale results from small-scale tests. They found that the

critical J for a large pressure vessel, J

c

, was equivalent to the

elastic portion of the critical J, G

c for small specimens. There is,

however, no theoretical basis for the contention that G is a material

c constant. Also, this hypothesis has not been tested for a range of

materials. It may only be a coincidence that the G

c values for the

specimen and the structure agree for a particular material.

All scaling methods known to the author are either purely empirical

or are based solely on statistical considerations. No one has used the

concept of constraint to quantitatively analyze size effects. Several

investigators [71-76] have used two- and three-dimensional

elastic-plastic finite element analyses to observe the crack-tip stress

state. However, none of thse analyses were applied to the scaling

probl em.

1.5 Statement of the Problem

As stated above, fracture toughness in the ductile-to-brittle

transition region is highly dependent on the size and geometry of the

structure or test specimen. At a given temperature in the transition

42
region, a small laboratory specimen may be ductile while a large

structure of the same material at the same temperature may be quite

brittle. In order to obtain a fracture toughness value representive of

the structure at the service temperature, a laboratory specimen must be

tested at some temperature below the service temperature. Typically,

this temperature shift can range from 5° to 50°C, depending on the

material, structure, and specimen. A method to quantify temperature

shifts in the ductile-to-brittle transition must be developed if the

safety of structures that operate in the transition region is to be

assured.

1.6 Objectives

The major objective of this work was to develop a method to predict

fracture toughness in the ductile-to-brittle transition as a function of

specimen (or structure) size and geometry. This method is based on the

concept of constraint at a crack tip which produces varying degrees of

stress triaxiality.

1.7 Technical Approach

A physically-based model for fracture in the ductile-to-brittle

transition region was developed to account for temperature shifts in the

transition with specimen size. It was assumed that upward temperature

shifts were caused by increases in crack-tip stress triaxiality.

43
Most previous attempts to predict temperature shifts or lower-bound

toughness values have been purely empirical. None of these methods are

valid for a wide range of materials. The statistical model of Landes

and Shaffer [60] is more rigorous but it ignores constraint effects.

The present analysis is based on constraint concepts but does not

consider statistical effects. An integrated model which considers both

constraint and statistical effects will be left for future work.

The specific approaches used in this investigation are outlined

bel ow.

1) Experimental data . A relatively large body of experimental

data was obtained in this study. Most of the data consist of fracture

toughness values for various specimen configurations. These data

provided an empirical demonstration of size and geometry effects on

fracture toughness. The data were also useful for assessing the

validity of models developed in this investigation. Fracture toughness

data were obtained for two materials: a C-Mn steel and commercially pure

i ron.

2) Constraint measurements . Previous authors have discussed

constraint in purely qualitative terms [47-53]. In the present study

constraint was quantified. A technique was developed to experimentally

measure crack-tip triaxiality. Fracture toughness data, microhardness

tests, and existing models for cleavage fracture were utilized for this

measurement.

44
3) Spring model for constraint . The triaxial stress state near a

crack tip was modeled by means of springs which act on a volume of

material ahead of a crack.

4. Equation for the ductile-to-brittle transition . The model

yielded an equation for fracture toughness (in the transition region) as

a function of material properties and geometry-dependent parameters.

This expression was used to construct ductile-to-brittle transition

curves which were compared with experimental data.

5. Application to structures . Transition curves for a

hypothetical structure were predicted by assuming worst-case values for

the geometry-dependent parameters in the fracture toughness equation.

6_. Application to other materials . The expression for fracture

toughness in the transition region was applied to both materials, i.e.,

the C-Mn steel and the pure iron.

45
2. EXPERIMENTAL PROCEDURE

2.1 Test Materials

The material used for the majority of the mechanical tests was a

25.4 mm (1.0 in) thick plate of ABS grade EH36 steel, a 350 MPa (51 ksi)

yield strength C-Mn steel. The chemical composition is given in Table

1. The steel was in the normalized condition and had particularly

uniform properties due to sulfide shape control. In addition to the

normalized steel a hot-rolled billet of commercially pure iron was used

for a limited number of tests. The chemical composition of this

material is given in Table 2.

2.2 Tensile Tests

The tensile properties of both materials were determined from round

tensile specimens (6.35 mm diameter and 31.75 mm gage length) with the

tensile axis parallel to the rolling direction. These specimens were

tested at various temperatures ranging from -255°C to 25°C. All tensile

tests were performed in a screw-driven tensile test machine at a

cross-head speed of 0.2 cm/min. The upper yield point, lower yield

stress, ultimate tensile strength, percent reduction in area, percent

elongation and true stress at fracture were measured for each test. All

testing and measurement procedures conformed to the guidelines of ASTM

E 8, the standard for tension testing of metals.

The testing machine was equipped with a fixture designed for

cryogenic testing. Various temperatures were attained by an elaborate

46
Table

1.

Chemical

Composition

of

the

ABS

Grade

EH36

Steel

(Weight

Percent)

OM

(O JD

r-~ oo

ir> o co

scno

go

cooo

cd

s-3

Cl.>0

CC

CJ

s-CD 3O

VOi—

o

GO I

LOooCOCO

LOo

GO I O o +-> <_> c

cu

O) o

_c s-

+-> CD O- 4-O +Jsz C CT> O -i- •r- CD

+-> 3

c/o o

D.Eoo

VOrHo

GO I O

LOoo

LO

t-H oo

oo

CO

<T3 u

CD _co

CXI

CD -O

CO o

Ol o

(XI

47
temperature control system. The specimen was cooled by reservoirs of

liquid nitrogen or liquid helium above and below the specimen. The

specimen grips were equipped with electric heaters which were connected

to controllers. The desired temperature was simply dialed into the

controllers. The combination of heating and cooling the specimen

produced a steady-state temperature.

2.3 Charpy V-Notch Impact Tests

The Charpy-impact transition curve was established for the

normalized steel in the temperature range -196 to 25°C. The notch

orientation with respect to the rolling direction is shown in Figure 15.

The procedures of ASTM E 23, the standard for impact testing, were

followed. Deviations from the standard occurred in some tests. These

deviations are noted in the results and discussion chapter. For each

test the absorbed energy, percent shear and lateral expansion were

measured. The latter two quantities were measured according to the

guidelines which appear in ASTM A 370. The maximum lateral expansion

was measured with a digital micrometer.

The various test temperatures were attained by placing the specimens

in a constant temperature bath (liquid nitrogen or a liquid nitrogen -

methanol mixture) for a minimum of ten minutes. Each specimen was then

removed form the bath and tested within five seconds.

48
Rolling

Direction

OJ c

.c

m 4~> rS3 O

G)i- +J a U 3

OJD.

m

m c

CJ

w

s- E

,C

U

+J

O

1- D. 3 m m +-> c u

O) f3 • E a. e

-i- s.

C

U -r- -r- C +-> c. s: m cl *-> L. C

0^ -C c

s— -c: 3 O S- +J O uc • in

s- c *«- «*- C J=

"I— 1—; 4- +J O a .c

Q) e S- ~t~ c -1- 3

•T—

a c «3 cn o

+->

C i- c *T— l"v c I— c.

"r- r—

a

i- c s- c S- Q.

lDa

s_

49
2.4 Fracture Toughness Tests

The ductile-to-brittle transition curves were established as a

function of constraint for ABS EH36 steel and commercially pure iron.

Constraint was varied by varying the specimen thickness (B), the crack

length (a), the specimen width (W), and the type of' loading (tension vs.

bending). A total of ten fracture specimen configurations of the

normalized steel were tested. This includes seven geometries of singleedge notched bend (SENB) specimens (see Fig. 2) and three geometries of

single-edge notched tension (SENT) specimens (see Fig. 16). Fracture

toughness tests were also performed on two geometries of pure iron SENB

specimens. The fracture toughness test matrix for both materials is

shown in Table 3. All specimens were machined with the notch orientation

shown in Figure 15.

2.4.1 SENB Specimens

All SENB specimens were fatigue precracked at room temperature

according to the specifications in the British standard for COD

testing [19]. The maximum allowable stress intensity for fatigue

loading, Kp(max), is given by:

K

f

(max)=0.63OyB* (28)

where oy

is the yield strength (in MPa) and B is the specimen thickness

(in mm). The British standard states that the minimum stress intensity,

Kfr(min), be at least 10% of Kp(max), so that:

v

50
J-o

4-T3

QJtoC

QJU

QJCl

to

toco

to to C 4-> 0) to

-t-> 0) -o

QJ CO £ to <J QJ

4->

C

O -C C CD3 0) O

CD+J T3

QJ QJ I i- QJ 3

CO

U

C ns

IS) 4-

tO

QJ

i-3

CD

51
Table 3. Test Matrix for Fracture loughness Tests.

I ABS EH36 Steel

12.7 mm 25.4 mm 38.1 mm 76.2 mm

0.2 b b,t b

0.5 b.t b.t

0.75 b

(W = 25.4 mm)

X\B a/W\ 25.4 mm

0.2 b

(W= 15.9 mm)

(W = 25.4 mm)

b - Bend (SENB) specimen

t - Tension (SENT) specimen

52
aK^. <^0.9 Kp(max) (29)

All tests were performed in displacement control on a 100 kN servo

hydraulic test machine. The displacement rate in all tests was

0.80 mm/min. This corresponds to a loading rate (in the elastic range)

for the square section (W = B) specimens of approximately 9.3 kN/ s for

shallow notched (a/W = 0.25) specimens and 375 N/s for the deep notched

(a/W = 0.75) specimens. The experimental setup is shown in Figure 17.

The mouth-opening displacement and the load-line displacement were

measured simultaneously during the test by two clip gages. The

load-line displacement was measured by the comparison bar technique

developed by Dawes L 7 7 ] . The load and the two displacements were

recorded on a two-pen X-Y plotter. The test instrumentation was wired

to a minicomputer through an anal og-to-di gi tal converter. The load,

crosshead displacement, and both clip-gage displacements were recorded

by the computer at approximately 0.3-s intervals and stored on a

magnetic disk. The computer typically collects and stores around 500

sets of data in a 3 to 5 minute bend test.

Low temperatures were attained by attaching a box to the lower

crosshead and filling it with either liquid nitrogen or an alcohol and

dry ice mixture. Intermediate temperatures (between -196 and -70°C)

were attained by pouring liquid nitrogen into the box to a level below

the specimen. The specimen was cooled by heat transfer through the tes

fixture and by the vapor coming off of the boiling nitrogen below the

specimen. The actual specimen temperature was measured by a

thermocouple implanted in the specimen.

53
54

igure

17.

Photograph

of

the

test

machine

and

three

-point

bend

fixture.
In each test, fracture toughness was measured by the two EPFM

parameters, J and CTOD. Figure 3 shows the notation used for critical

values of CTOD. The notation depends on the nature of the fracture

event, i.e. whether the crack extension is brittle or ductile, and

whether or not unstable cleavage is preceded by stable crack growth. A

similar notation was used for reported critical values of the J-integral

(see Fig. 4).

The crack-tip opening displacement (CTOD) was computed from the

following relationship:

K

2 r

D (W " a) Vo

6 = 6 + 6 = P

, e p 2oyE r (W-a) + a + z (30)

where V

p

= the plastic component of the mouth-opening displacement

z = knife edge thickness

r = rotational factor.

P This equation separates CTOD into elastic and plastic components (6 and

6 , respectively). The British standard [18] suggests that a value of

0.4 be assumed for rp in equation (30). However, a more precise value

for the rotational factor can be calculated if the plastic components of

load-line displacement and mouth opening displacement (q and V ,

respectively) are known [78]:

1 r

=

{

V

p W

p W-a q a -nfi-)

- (a - z)j (31)

55
The average value of r^

0.38 for the pure iron.

CTOD calculations.

was found to be 0.5 for the normalized steel and

These values were used in equation (30) for all

The ASTM Standard E 813, the standard for Jj

c testing, recommends

that the following equation be used to estimate the J-integral for an

SENB specimen.

2U (32) d_ bTwti)

where U is the area under the 1 oad/1 qad-1 ine displacement curve.

However, J can also be estimated from an equation derived by Sumpter and

Turner [79]:

J 2u

v r w E_

B(W-a) rp(W-a)+a+z

(33)

where is the area under the load/mouth-opening displacement curve.

Both equation (32) and equation (33) were used to compute values of J.

The results are compared in the Appendix.

The method that is utilized to detect the onset of stable crack

growth is the double displacement method. Both the mouth-opening

displacements, V, and the load-line displacements, q, from each test are

stored on a magnetic disk. A program has been written which computes

2 2

dq/dV and d q/dV , and plots them as a function of V. The critical

displacement is inferred from these plots (see Appendix).

56
2.4.2 SENT Specimens

The SENT specimens (Figure 16) were f atigue-precracked in bending

with a span equal to 8W. The fatigue loads were chosen such that

tension specimens had the same minimum and maximum values as the SENB

specimens

The SENT specimens were tested in a 1000 kN servohydraul ic test

machine. All tests were performed in displacement control at a

displacement rate of 1.60 mm/mi n. Each end was gripped by a pair of

wedges which were held in place by a cylindrical steel collar. The

wedge grip assembly is shown schematically in Figure 18. The specimen

was cooled by spraying liquid nitrogen onto the specimen. The specimen

was insulated by a styrofoam box placed around the specimen. The

temperature was monitored by two thermocouples placed on opposite sides

of the specimen, near the crack tip.

Critical values of crack-tip opening displacement and the J-integral

were measured in the ducti 1 e-to-bri ttl e transition region. Critical

CTOD values were measured by means of two clip gages, one at the crack

mouth and one 6.43 mm above the crack mouth. Figure 19 shows a

schematic of the double clip-gage measurement of CTOD as well as the

equations which were used. This method was verified by replication (see

Appendix)

57
1 1 1

Wedge Grip

Styrofoam

Enclosure

Specimen

Figure 18. Schematic of the experimental setup for SENT tests.

58
Figure 19. The double clip gage measurement of CTOD from SENT

specimens.

59
The J-integral was estimated form an equation derived by Rice, et.

al. [80]:

, _ K

2

, 1 [2 /*

Vp

PdV - PV 1

J

E' Blfc) L 4) p pJ (34)

where is the plastic component of the clip-gage displacement.

Equation (34) was derived for a cracked plate loaded in tension. It is

assumed in this equation that the specimen is restricted from bending.

This condition was imposed by the wedge grips (Fig. 18).

60
3. RESULTS AND DISCUSSION

3.1 Tensile Data

The tensile properties of the ABS grade EH36 steel for 10 temperature

ranging from -196°C to 25°C are shown in Figure 20 and Table 4. The

data follow the expected trends with a minimal amount of scatter. Both

the yield strength and the ultimate tensile strength increase markedly

with decreasing temperature. All flow curves exhibited an upper and

lower yield point which is characteristic of low-carbon steels. The

yield strength (as plotted in Fig. 20) was defined as the upper yield

point. This definition of yield strength was used to satisfy

requirements of ASTM E 8. However, the lower yield stress is more

indicative of the yielding behavior of a fracture specimen. The

increment of stress between the lower and the upper yield stress is

needed in a uniaxial tension specimen to generate mobile dislocations.

The crack tip of a fracture specimen serves as a dislocation source;

thus, the additional increment of stress is not needed for yielding to

occur. The yield stress, o , which appears in a number of equations and

figures in this document refers to the lower yield stress.

The tensile properties of the commercially pure iron are shown in

Figure 21 and Table 5. When this material was tested at temperatures

above -60°C the resulting flow curves are smooth; i.e., there is not a

yield point. However, at temperatures below -60°C, a knee occurs at

yield in the pure iron flow curves. This knee becomes sharper and more

61
|S)| ‘SS3U1S

I/M ‘SS3U1S

62

function

of

temperature.
700

BdKI ‘SSidlS

63

Figure

21.

Tensile

properties

of

commercially

pure

iron

as

function

of

temperature.
defined as the temperature is decreased. There is only a slight load

drop after initial yielding; i.e. upper yield stress = lower yield

stress. The yield strength (as reported in Fig. 21 and Table 5) was

defined as the 0.2 percent offset stress above -60°C and as the yield

point below -60°C.

3.2 Charpy-Impact Data

The Charpy V-notch impact energy transition curve was established

for the ABS EH36 steel and is shown in Figure 22. The percent shear and

lateral expansion were also measured for each specimen. The Charpy data

are summarized in Table 6. Figure 22 shows that the ductile-to-brittle

transition occurs at about -70°C. Note that the curve is nearly

vertical at this temperature. Most specimens tested at or near this

temperature exhibited either ful ly-bri ttl e (low energy) or fully-ductile

(high energy) behavior. Only a few specimens exhibited intermediate

behavior. Table 6 shows that the transition from low energy to high

absorbed energy corresponds well with the fracture surface transition

(0% shear to 100% shear) and the transition from small to large lateral

expansion.

Because of the high toughness of this material, most of the upper

shelf energy values are invalid according to the ASTM E 23 Standard.

The full-scale energy of the Charpy test machine used in this experiment

is 358 J. According to the ASTM standard the energy absorbed by an

impact specimen should not exceed 80% of the full-scale energy of the

64
400

sainof ‘A0U3N3 XOVdWI AdUVHO

O

UJ

DC

<

DC

UJ

S

UJ

H

65

Figure

22.

Charpy

impact

transition

curve

for

ABS

grade

EH36

steel
test machine. Therefore, all energy values above 268 J do not meet the

requirements of ASTM E 23.

3.3 Fracture Toughness

The fracture toughness data for the ABS EH36 steel and the pure

iron are summarized in Tables 7-9. The critical values of J and CTOD

along with the critical fracture event for each specimen are reported.

Three critical fracture events have been observed. J and 6 are

c c defined at the occurrence of unstable cleavage without prior stable

crack growth. J.. and 6.. are defined at the onset of stable crack

growth. When cleavage is preceded by stable crack growth J

u and 6 u are

measured at the point of instability.

3.3.1 ABS EH36 Steel

Figures 23 and 24 show that the ductile-to-brittle transition

curves shift approximately 30°C as the specimen thickness increases from

13 to 38 mm. These data are consistent with previous results [47-55J.

It is believed that these upward shifts in the transition are due

primarily to increases in crack-tip constraint with thickness.

Constraint causes a triaxial stress state and raises the flow stress

near the crack tip. This increase in flow stress tends to promote

cleavage fracture (i.e., shift the transition curve to the right) since

it is easier to reach the fracture stress.

66
CRITICAL

CTOD,

mm

TEMPERATURE, # C

Figure 23. Critical CTOD for cleavage as a function of

temperature and specimen thickness for ABS grade

EH36 steel. W = 25.4 mm (1.0 in).

67
E

<

o

o

TEMPERATURE, # C

Figure 24. Critical J for cleavage as a function of

temperature and specimen thickness for ABS grade

EH36 steel. W = 25.4 mm (1.0 in).

68
It should be noted that the thickest specimens (B = 38.1 mm) had

slightly deeper cracks than the other two specimen geometries shown in

Figures 23 and 24. The deeper cracks were necessary in order to prevent

the load on the thick specimens from exceeding the capacity of the test

machine. These deeper cracks probably contributed to the shift in the

transition curve to higher temperatures.

The influence of crack length on ducti 1 e-to-bri ttl e transition

curves is shown in Figures 25 and 26. The curves in Figures 25 and 26

tend to shift to higher temperatures with increasing crack length.

These shifts are due entirely to constraint effects, as opposed to

statistical effects. The thickness is constant for these data; thus the

volume of material along the crack front is constant.

Deeper-notched specimens (i.e., shorter ligament length) apparently

have more crack-tip constraint. The data for the deep-notched geometry

(a/VK0.75) behave in a somewhat unusual manner. The curve drawn through

these data (Figs. 25 and 26) crosses the curve representing the a/VKO.5

data. At low values of 6 c and J

c

» where the plastic zone is relatively

small, the deep-notched geometry has more constraint than the a/kK0.5

geometry. At higher temperatures (and higher 6 c and J

c values) the

constraint is apparently relaxed by plastic flow to the nearest free

surface.

The effect of ligament length on the slip patterns in SENB

specimens has been investigated. Two specimens were coated on one side

with a photoelastic material which, when viewed with polarized light.

69
CRITICAL

CTOD,

mm

-200 -160 -120 -80 -40

TEMPERATURE, # C

Figure 25. Critical CTOD for cleavage as a function of

temperature and crack length for ABS grade EH36

steel. W = 25.4 mm (1.0 in).

70
E

E

<

o

p

o

TEMPERATURE, # C

Figure 26. Critical J for cleavage as a function of

temperature and crack length for ABS grade EH36

steel. W = 25.4 (1.0 in).

71
changes color with strain. Figure 27 shows black and white photographs

of the multicolor strain patterns on two SENB specimens at net-section

yield. The slip lines on both specimens emanate from the crack tip at

initial angles of approximately 45° from the crack plane. These slip

lines then deflect inward due to the bending stresses. At the neutral

axis the normal stress changes sign; the portion of the ligament below

the hinge point is in compression. In the deep-notched specimen

(Fig. 27b) the hinge point is closer to the crack tip. The compressive

stress field near the crack tip tends to produce additional constraint.

As ligament length decreases, the compressive stress field moves closer

to the crack tip and constraint increases.

Increasing geometrical constraint causes the load at net-section

yield to increase. This elevation of yield load can be quantified by

the notch constraint factor, L, which is defined by the limit load

expression for SENB specimens:

La (W-a) 2 B

P

= ° y 4W

(35)

where is the load at net-section yield. In the absence of a crack,

L=l.

Dimensionless load (i.e., load normalized for yield stress and

specimen dimensions) is plotted versus mouth-opening displacement in

Figures 28 and 29. Dimensionless load is obtained by solving

equation (35) for L and allowing P to vary; when P = P^, the

dimensionless load is equal to L. The curves in Figure 28, which are

72
(a)

(b)

Figure 27. Photoelastic strain patterns for SENB specimens;

a) a/WO.2, b) a AK0. 5.

73
4PW

MOUTH-OPENING DISPLACEMENT, mm

Figure 28. Nondimensional-load-versus-displacement curves at

various temperatures for constant SENB specimen

geometry.

74
4PW

MOUTH-OPENING DISPLACEMENT, mm

Figure 29. Nondimensional-load-versus-displacement curves as

a function of SENB specimen geometry.

75
for a constant geometry, form a single curve because load is normalized

for yield stress. Figure 29 shows that dimensionless load is elevated

when crack length and/or specimen thickness are increased. The curves

in Figure 29 are evidence for the hypothesis that the observed shifts in

the ductile-to-brittle transition curves (Figs. 23-26) are caused by

increases in triaxiality.

Figure 30 shows critical CTOD values for cleavage for B = 25.4 mm

and B = 76.2 mm (a/W^0.5 for both geometries). Although the scatter is

great for these two geometries it is apparent that, in this case,

increasing the thickness by a factor of three has little effect on

fracture toughness in the transition region. The square-section,

a/WO.5 geometry apparently produces nearly optimum constraint conditions

at the crack tip. Constraint in the square-section, a/W^O.2 geometry is

not optimal. This is why an increase in thickness by a factor of 1.5

causes a significant shift in the transition curve (see Figs. 23 and

24). At a constant temperature and ligament length, increasing specimen

thickness decreases fracture toughness at a decreasing rate. When

constraint is close to maximum (plane strain) further increases in

thickness have little or no effect.

The effect of specimen width (W) at a constant ligament length

(W-a) is shown in Figure 31. The critical CTOD versus temperature

curves represent data from two SENB geometries with nearly identical

ligament dimensions. One would expect these two curves to agree since

the slip patterns in the ligaments are presumably the same. The actual

76
CRITICAL

CTOD,

mm

-200 -160 -120 -80 -40

TEMPERATURE, *C

Figure 30. Critical CTOD for cleavage as a function of

temperature and thickness for deep-notched SENB

specimens of ABS grade EH36 steel

77
CRITICAL

CTOD,

mm

TEMPERATURE, #C

Figure 31. Critical CTOD for cleavage as a function of

temperature and specimen width (ligament length = constant) for ABS grade EH36 steel

78
experimental curves coincide at low toughness values but diverge at high

toughness values. The geometry represented by the solid line and data

points has a relatively short crack length 3 mm). Since the crack

tip is near a free surface plastic relaxation to this surface (i.e.

gross-section yielding) can occur at high CTOD values. This constraint

relaxation due to short cracks causes the transition curve to become

steeper. This phenomena is very similar to that observed in Figures 25

and 26 for the deep-notched geometry (a/l/K0.75). Apparently, for very

short or very deep cracks the constraint is relaxed by plastic

deformation from the crack tip to the nearest free surface.

Figure 32 shows critical CTOD values for three geometries of

single-edge notched tension (SENT) specimens. Data for all three

geometries fall on approximately the same curve. An increase in

thickness from 25 to 76 mm has little effect on fracture toughness. If

smaller thicknesses (<25 mm) were tested the transition curve would

likely shift to lower temperatures . The ligament length has little

effect on fracture toughness when the material is loaded in tension.

Figure 33 shows the slip pattern of an SENT specimen at net-section

yield. The slip lines emanate from the crack tip at 45° angles on

either side of the crack plane. There is no hinge point or stress

reversal. The crack tip experiences virtually the same constraint

conditions regardless of ligament length. For very short or very deep

cracks constraint relaxation would probably occur as in the SENB

specimens

79
CRITICAL

CTOD,

mm

Figure 32. Critical CTOD for cleavage as a function of

temperature for three SENT geometries of ABS grade

EH36 steel

80
Figure 33. Photoelastic strain pattern of an SENT specimen;

a/VKO.2.

81
A comparison of transition curves (critical CTOD vs. temperature)

for SENB and SENT specimens with identical crack and ligament dimensions

are shown in Figures 34 and 35. Data points were eliminated from these

figures for clarity. Figure 35 shows that the bending and tension

curves coincide for the square-section, a/VK0.2 geometry. However,

Figure 35 shows a definite transition shift between bending and tension

for deep-notched (a/WO.5) specimens. Bending produces an additional

increment of constraint in specimens with short ligaments. As the

ligament length of an SENB specimen increases the constraint produced by

bending decreases and the crack-tip constraint conditions approach those

of a tension specimen.

Figures 36 and 37 show values of 6.. and J., respectively, for five

SENB specimen geometries of ABS EH36 steel. These data are presented

here for the sake of completeness, although the major theme of this

thesis is cleavage fracture. Upper shelf fracture toughness testing is

discussed further in Appendix I.

Both lL and 6^. are apparently independent of geometry and 6.. is

approximately independent of temperature. J. increases slightly with

decreasing temperature because the area under a load-displacement curve

at a constant displacement increases with increasing flow stress.

The method for determining these initiation toughness values is

given in the appendix. Owing to the uncertainty in this technique the

point of incipient crack growth is not well defined, contributing to the

scatter seen in Figures 36 and 37.

82
CRITICAL

CTOD,

mm

TEMPERATURE, #C

Figure 34. Comparison of bending and tension transition curves for square-section, shallow-notch specimens of ABS

grade EH36 steel

83
CRITICAL

CTOD,

mm

TEMPERATURE, *C

Figure 35. Comparison of bending and tension transition curves for square-section, deep-notch specimens of ABS grade

EH36 steel

84
CRITICAL

CTOD,

mm

0.80

0.60

0.40

0. 20 -

-120

ABS EH36 Steel

SENB Specimens

B = 12.7 mm a/W~0.2

B = 25.4 mm

B = 38.1 mm

B = 25.4 mm

B = 25.4 mm

a/W-0.2

a/W~0.29

a/W~0.52

a/W~0.75

JL -80 -40 40

TEMPERATURE, # C

Figure 36. Critical CTOD for the onset of tearing as a function

of temperature and SENB specimen geometry for ABS

grade EH36 steel. W=25.4 mm (1.0 in).

85
Figure 37. Critical J for the onset of tearing as a function of

temperature and SENB specimen geometry for ABS grade

EH36 steel. W = 25.4 mm (1.0 in).

86
3.3.2 Pure Iron

A limited number of fracture toughness tests were performed on

commercially pure iron SENB specimens. The pure iron was chosen as a

second material because it has a microstructure that was ideal for the

microhardness/strain correlation presented in Section 3.4.1.

The fracture toughness data for the commercially pure iron is shown

in Table 9 and Figure 38. A plot of critical CTOD (for cleavage) versus

temperature for two thicknesses of SENB specimens is shown in Figure 38.

The ducti 1 e-to-bri ttl e transition of the pure iron is much steeper than

that of the normalized steel. An increase in thickness from 25.4 mm

(1.0 in) to 50.8 mm (2.0 in) results in an upward shift in the

transition curve of about 5°C.

There is a substantial amount of scatter in the data for the

B = 50.8 mm geometry. It is not known why the two square data points on

the far right side of Figure 38 do not follow the same trend as the

other data for this geometry. However, an examination of the

microstructure (Fig. 38b) revealed a number of large inclusions

distributed throughout the material. It is possible that the crack tips

of the two specimens in question were near inclusions which nucleated

large microcracks. This could explain the lower than expected toughness

of these specimens.

87
CRBTICAL

CTOD,

mm

Figure 38. Critical CTOD for cleavage as a function of

temperature and thickness for commercially pure iron

SENB specimens.

88
3.3.3. Fractography and Metallography

The microstructures of ABS grade EH36 steel and pure iron are

compared in Figure 39. Each micrograph shows a fracture specimen which

was sectioned perpendicular to the crack plane after it was deformed to

a CTOD of approximately 0.3 mm. The normalized steel has a relatively

fine ferrite-pearl ite microstructure while the pure iron microstructure

consists of very large ferrite grains. As stated above, a number of

large inclusions can be seen in the commercially pure iron. According

to Tables 1 and 2 the sulfur content of the iron is about three times

higher than that of the normalized steel. The crack faces in the

normalized steel specimen (Fig. 39a) are relatively straight while the

crack faces in the iron are somewhat jagged. This difference in crack

profiles is probably due to the coarser grain structure of the iron.

Figures 40 and 41 show scanning electron microscope (SEM)

fractographs of the normalized steel and pure iron, respectively.

Figures 40a and 41a show the fracture surfaces of SENB specimens which

failed on the lower shelf of toughness. Fracture surfaces of specimens

which failed in the ductile-to-brittle transition region are shown in

Figures 40b and 41b. The major difference between lower-shelf and

transition behavior as seen by fractography is the presence of a stretch

zone on the transition region fracture surfaces. Lower-shelf fractures

occur when the crack is relatively sharp while in the transition region,

fracture occurs after significant blunting of the crack tip. Transition

and lower-shelf fracture surfaces both contain flat, smooth cleavage

89
(b)

Figure 39. Photomicrographs of blunted crack tips which show the

microstructures of a) ABS grade EH36 steel, and b)

commercially pure iron. Magnification = lOOx.

90
*

I Fatigue Crack

v

A

Fracture Surface

I i 0.15 mm

(a)

A

Fatigue Crack

T

Stretch Zone

A

Fracture Surface

(b)

Figure 40. SEM fractographs of ABS grade EH36 steel which compare

lower-shelf and transition region fracture surfaces,

a) SENB spec B-9, 6 = 0.004 mm; b) SENB spec B - 1 1

6 c = 0.371 mm. MagHif ication = 200x.

91
A

Fatigue Crack

A

Stretch Zone

f

Fracture Surface

v

(b)

Figure 41. SEM fractographs of pure iron which compare lower-shelf

and transition region fracture surfaces, a) Spec J-4,

6 = 0.010 mm; b) spec. J-7, 6 = 0.540 mm. Magnification = lOOx. c

92
facets with "river pattern" lines. These "river patterns" are more

visible in the pure iron fractographs because the facets are much larger

than those of the steel

Figures 42 and 43 show high magnification fractographs of the

stretch zones in both materials. There is some ductile tearing in the

stretch zone of the steel specimen (Fig. 42) as evidenced by the

numerous microvoids which have coalesced. One can see spherical

particles (presumably sulfide inclusions) at the bottom of some of the

voids in Figure 42b. The crack in the iron specimen (Fig. 43) did not

tear prior to fracture. However, a high degree of plastic deformation

has occurred in the stretch zone and a number of voids have formed.

The fracture surface of a normalized steel specimen is compared to

that of a iron specimen in Figure 44. The cleavage facets on the iron

fracture surface are almost an order of magnitude larger than the facets

on the steel specimen. This is to be expected from an observation of

the respective microstructures (Fig. 39) since facet size is related to

grain size. The river patterns can be clearly seen in both

fractographs. Some secondary cracking can also be seen, especially in

the iron (Fig. 44b). Several small cracks in the far left portion of

Figure 44b are parallel to each other; i.e., they occur on the same

crystallographic plane.

The fractographs in Figures 40-44 refute a common misconception

about the ductile-to-brittle transition. It is sometimes said that

fracture on the lower shelf occurs by cleavage while fracture in the

93
(b)

Figure 42. SEM fractographs of ABS EH36 specimen B - 1 1 which show a magnified view of the stretch zone, a) 200x; b) lOOOx.

94
(a)

(b)

Figure 43. SEM fractographs of pure iron specimen 0-7 which show a magnified view of the stretch zone, a) 200x; b) lOOOx.

95
(b)

Figure 44. Comparison of fracture surfaces at 500x for a) ABS

grade EH36 steel and b) commercially pure iron.

96
transition region is mixed mode, the fraction of cleavage depending on

how close a fracture is to the lower shelf. However, the fractographs

show that the micromode of fracture can be pure cleavage in the

transition region, even when a high degree of plastic flow has preceded

fracture. The rapid increase in toughness at the transition occurs

because cleavage becomes energetically unfavorable as temperature

increases. The fracture is not mixed mode until the initiation

toughness is exceeded. As illustrated in Figures 3 and 4, the initation

point for a clean steel can be well up the transition curve.

3.3.4 Summary Comments

Fracture toughness data for two materials as a function of specimen

geometry and test temperature have been presented. The data exhibited

the expected size effects in the ductile-to-brittle transition region.

These effects were attributed to variations in crack-tip constraint. In

Section 3.4, the concept of constraint is used to model the size effects

on fracture toughness.

3.4 Characterization of Fracture in the Ducti 1 e-to-Bri ttl e Transition

Region

As stated in Chapter 1, the objective of this work was to

characterize the size effects on fracture toughness and develop a

constraint-based model by which the toughness of large structures can be

estimated from small-scale fracture tests.

97
Thus far, constraint has only been discussed qualitatively. For

size effects to be expressed analytically in terms of constraint, an

experimental measure of constraint is needed. The method by which these

measurements were made is presented below.

Crack-tip region constraint (CTRC) is defined in this investigation

as the degree of stress triaxiality near the crack tip; i.e.,

CTRC = (36)

o

where o is the stress normal to the crack plane (assumed to be equal

to the maximum principal stress, o^) and a is the effective stress.

The effective stress is defined by the von Mises equation:

1 o

= — [(a r

a

2

) 2 + (a

1 -o3

) 2 + (c^-c^) 2

]

2 (37)

/2

a < a o

where a

Q

is the yield stress. The effective stress is equivalent to the

flow stress (at a given strain) in the absence of triaxiality. The

analogous quantity, effective strain, is defined by equation (38):

e n— [(e

1 -e

2

) 2 + U2

, 3

) 2 (e

1 -e3

)^] i (38)

where e 2

and are Principal strains. The a versus e flow curve is

equivalent to the uniaxial true stress/true strain curve. Thus, a

material's yielding and strain hardening behavior obtained from a

98
uniaxial test can be related to triaxial conditions through equations

(37) and (38) [81].

Equation (36) contains three unknowns. One unknown can be

eliminated if e at a given point ahead of the crack tip is known; a can

be inferred the flow curve. Section 3.4.1 describes how the author

measured crack-tip region strain.

A model for cleavage fracture due to Ritchie, et. al . |_38] was used

to solve for o . According to this model, fracture occurs when the

yy

fracture stress, a^, is exceeded over a characteristic distance, X

c

,

ahead of the crack tip (see Fig. 7). Thus, at the moment of fracture,

o is equal to o r at a distance X ahead of the crack tip. The fracture

yy f c stress is taken as the final load divided by the final area in a uniaxial

tensile test in which the fracture mode is cleavage. The critical

distance is inferred from Tracey's finite element crack-tip stress

solutions L82] which are shown in Figure 45. The normal stress, o , on

the ordinate is set equal to o^; K is set equal to a lower-shelf Kj

c value; a

Q

is equal to the yield stress at that lower-shelf temperature.

One can then solve for X in Figure 45 and set it equal to X .

It was assumed that and X

c are material properties which are

independent of temperature and constraint. Figure 46 is a plot of

versus temperature for the pure iron and the ABS EH36 steel obtained

from low temperature tensile tests. The dashed lines are drawn at one

standard deviation above and below the mean. The fracture stress of the

normalized steel is apparently insensitive to temperature. There

99
Figure 45. Finite element solutions for stress ahead of the crack

tip (small-scale yielding); after Tracey [82].

100
FRACTURE

STRESS,

MPa

1600

1200 8

8

800

400

a.A A

'A

o ABS EH36 Steel

A Pure Iron

O'

-260 -220 -180 -140

TEMPERATURE, # C

Figure 46. Cleavage fracture stress versus temperature for ABS

grade EH36 steel and pure iron tensile tests.

100

101
appears to be a downward trend with increasing temperature in the pure

iron data. However, since there are only four data points for this

material it is difficult to tell whether or not this is a real trend.

The assumption that o f

is independent of temperature was used for both

materials. The mean values of in Figure 46 are 1156 MPa for the

normalized steel and 627 MPa for the pure iron. The assumption that X

c is constant for a given material was partially justified in Section

1.3.1 where it was shown that, according to the model of Evans and

Hutchinson [40], X

c is independent of temperature. The Evans and

Hutchinson model in only valid for small-scale yielding; however the

data of Rosenfield, et. al . , [41,42] indicate that X

c remains constant

with large-scale yielding.

3.4.1 The Crack-Tip Strain Function

A knowledge of the strain field ahead of a blunted crack tip is

necessary for constraint measurements. The effective flow stress at a

given point ahead of the crack tip can be inferred from the flow curve

if effective strain is known. Shoji et al . [83] measured strain ahead

of crack tips in a steel with a bainitic microstructure. After

deformation to a given CTOD, the specimen was annealed to nucleate

ferrite grains in the intense strain region at the crack tip. The

recrystall ized ferrite grain size was calibrated with prior plastic

strain. Shoji obtained the following empirical relationship for strain

as a function of 6 and distance from the crack tip.

102
(SCOSG

r

0.65

e = 0.25 ( (39)

where r is the distance from the crack-tip free surface and 0 is the

angle from the crack plane to the point in question.

Other Investigators [84,85] have used microhardness correlations to

determine the crack tip strain distribution. This method was used here

because microhardness seems to be a more direct and sensitive measure of

strain than recrystal ized grain size. Microhardness tests were used in

this investigation to measure crack-tip strain. Initial attempts to

measure strain with crack-tip microhardness tests on the ABS EH36 steel

were unsuccessful. The fine, two-phase microstructure of this steel

made reproducible hardness measurements impossible. The pure iron is

much better suited to this technique because it is an essentially

single-phase material with very large grains.

The microhardness/strain calibration method is outlined in Figure

47. The diameters of two fractured tensile bars were measured (from

enlarged photographs) at various locations in the necked-down region.

The reduction in diameter was used to compute plastic strain:

where D

q is the original diameter of the tensile specimen. The plastic

strain was plotted against distance from the fracture surface. This

plot is shown in Figure 48 for two pure iron tensile specimens. Each

(40)

103
Fractured

Tensile

Specimen

o

104

Figure

47.

Microhardness/strain

calibration.

Strain

is

determined

as

a

function

of

distance

ona

fractured

tensile

bar.

Microhardness

measurements

are

then

taken

at

various

distances

from

the

fracture

surface

and

correlated

with

strain.
TRUE

STRAIN

Figure 48. Plastic strain as a function of distance from the

fracture surface in two pure iron tensile specimens.

105
specimen was then sectioned and microhardness measurements were taken at

various distances from the fracture surface. The diamond pyramid

hardness test with a load of 50 g was used for all microhardness

measurements. Distance was converted to strain from Figure 48 and

microhardness values were plotted against the corresponding strain

-2/3

values. Figure 49 shows a plot of microhardness versus e , which is a

straight line. Each data point in Figure 49 represents the average of

8-10 microhardness measurements at a constant strain. In addition to

the two necked-down specimens, unstrained material and two specimens (#1

and #2) uniformly deformed to different strains were used for the

microhardness/strain calibration. According to Figure 49:

Two pure iron SENB specimens were used to determine the crack-tip

strain function. Each specimen was deformed at room temperature to a

given CTOD and then unloaded. Next, the specimens were sectioned in the

center, perpendicular to the crack plane (see Fig. 39b). After the

specimens were mounted, polished and etched, microhardness measurements

were taken at various points ahead of the crack tip, on the crack plane.

The microhardness indentations were spaced at approximately 100 ym

intervals. These indentations were then removed by grinding so that

additional microhardness measurements could be made. This process was

repeated several times in order to provide enough data to compute

reliable mean values. Figure 50 shows a logarithmic plot of strain

106
MICROHARDNESS

(DPH

Figure 49. Diamond pyramid hardness (load = 50 g) as a function

of plastic strain in pure iron.

107
8/x

Figure 50. Crack-tip region strain as a function of CTOD and

distance from the crack tip. The Shoji [61] strain

function is superimposed for comparison.

108
versus 6/X, where X is the distance from the crack tip. Each data point

in Figure 50 represents the average of 4-6 microhardness measurements.

The strain function from Figure 50 is given below.

The Shoji [83] strain equation is represented by the dashed line in

Figure 50. There is a significant difference between equations (39) and

(42). However, equation (38) was obtained for a steel with a bainitic

microstructure. The materials of interest here have ferritic or

ferri te/pearl i te microstructures.

Although equation (42) was defined for the pure iron, it was

assumed that this equation also describes the strain field ahead of a

crack in ABS grade EH36 steel. The justification for this assumption is

as follows: Cracks in both materials blunt in approximately a

semicircle (see Fig. 39); i.e., blunting cracks in both materials

correspond to the same displacement field. For a given displacement

field, the correpsonding strain field should not be a strong function of

material. Also, the flow characteristics of both materials should be

similar since the primary microstructural constituent in each material

is ferrite, which should dominate the flow properties.

(42)

109
3.4.2 Measurement of CTRC

With the strain function (eq. 42) and experimental values for

fracture stress and critical distance, there is now enough information

to solve for constraint in equation (36). The crack-tip region

constraint was measured for three geometries of normalized steel SENB

specimens: 1) B=0.5W=12.7mm, a/W % 0.2; 2) B=W=25.4mm, a/W ^ 0.2;

3) B=W=25.4mm, a/W ^ 0.5. The average value of a

^ for this material is

1156 MPa (see Fig. 46); a value of 0.215 mm was computed for X

c from

Figure 45. It was assumed that these parameters remain constant with

temperature and geometry variations. The procedure which was used to

measure CTRC is outlined below.

1) A critical CTOD value in the ductile-to-brittle transition

region was taken from Table 7.

2) For a given 6 c value, e at X

c was computed:

where e Q

is the strain at X

c at the moment of fracture; Xc =

constant = 0.215 mm.

3)

The effective stress corresponding to a strain of e c is inferred

form the uniaxial true stress/true strain curve at the temperature

of the corresponding 6 c value. Figure 51 shows that the strainhardening rate of the normalized steel is insensitive to

(43)

no
(cr-cr 0

),

MPa

Figure 51. True stress/true strain curves normalized for

temperature for ABS grade EH36 steel

Ill
temperature in the region of interest. The average of the three

curves in Figure 51 represents a unified flow curve which is valid

over a wide range of temperatures.

4) CTRC was computed from equation (44):

o CTRC = ^

(44)

°c

where a ^

= constant = 1156 MPa.

5) Steps 1 through 4 were repeated for various temperatures and

geometries

Critical crack-tip region constraint is plotted as a function of

critical CTOD in Figure 52. Constraint decreases markedly with CTOD.

Apparently crack-tip blunting causes a relaxation in triaxiality. At a

constant CTOD the constraint tends to be lowest for the thinnest

specimens (B=0. 5W=12. 7mm) . This was expected since this geometry

exhibits a ductile-to-brittle transition in the lowest temperature range

(see Figs. 23 and 24)

It should be noted that critical CTOD values above approximately

| 0.5 mm are 6 u values; i.e., some stable tearing has preceded fracture.

The above analysis is not strictly valid if tearing has occured.

However, critical CTOD values up to 0.8 mm are plotted Figure 41 because

the amount of tearing is small. This small degree of tearing apparently

112
T

2.0

o

D A O

O

1.8

*b

br

o

ccho

-I

<

o

cco

1.6

1.4

A A

*

1.2

ABS EH36 Steel D

SENB Specimens

B = 0.5W = 12.7mm, a/W-0.2

o B=W= 25.4mm,a/W~0.2

a B= W = 25.4mm, a/W~0.52

1.0

0.2 0.4 0.6 0.8

CRITICAL CTOD, mm

Figure 52. Critical crack-tip region constraint as a function of

critical CTOD for three SENB specimen geometries of

ABS grade EH35 steel

113
has little effect since the high toughness data in Figure 52 do not

deviate from the trend established by the other data.

No curves are drawn through the data in Figure 52 because, up to

this point, no functional relationship between CTRC and critical CTOD

has been established. The determination of a functional relationship

requires a model for the observed material behavior. One such model for

the constraint relaxation at a crack tip is proposed below.

3.4.3 A Spring Model for CTRC

Although the physical situation described above is complex (i.e., a

three-dimensional elastic-plastic continuum) the model presented here is

relatively simple. This approach is justified because complex models of

natural phenomena are often preceded by more rudimentary versions.

These simple analyses often provide valuable insights.

The relaxation in constraint with crack blunting was modeled by

means of an elastic spring analog. This is illustrated in Figures 53

and 54 where an element of material which is loaded to the fracture

stress is constrained laterally by linear elastic springs in tension.

The spring in the x direction is assumed to be connected at the crack

tip and the hinge point (in a bend specimen). It is assumed that the

crack is sharp initially; the initial stress in the x direction is o°.

The crack is assumed to blunt in a semicircle, resulting in a relaxation

in the x direction of the spring of 6/2. The force relaxation is given

by

114
Crack Tip

t \ T0-‘

8

i

"

J

rowtnr " 00000000000

^<rx

1

8/2

-k8

2

kS

2A

Figure 53. Spring model for CTRC relaxation. The crack tip

blunts in a semi circle, thereby relaxing the spring

which is causing a lateral tensile stress in the

material element.

115
Figure 54. Constraint relaxation in the thickness and ligament

directions.

116

(W-a)
where k is the spring stiffness.

Thus, the stress in the x direction is given by

o

x

( 46 )

where A is the area over which the spring acts. There is also a

relaxation in the z direction due to lateral constraint (Fig. 54).

The Tresca yield criterion can be used to solve for o:

o=o - o • max min (47)

where o is the maximum principle stress and o . is the minimum

max

r r min

principle stress. If it is assumed that o <o <o f , then

A l. I

o

c (48)

The Tresca criterion was used instead of the von Mises criterion

(eq. 37) in order to simplify equations.

Equation (48) states that the critical effective stress is linearly

dependent on CTOD. These two quantities are plotted in Figure 55;

best-fit straight lines were computed by linear regression analysis.

The experimental values of critical effective stress in Figure 55 were

obtained by means of the first three steps outlined in Section 3.4.3.
CO CL

CO

CO

LU

CCh

CO

LU

>

o

LU

LL

ll

LU

<

o

cro

CRITICAL CTOD, mm

Figure 55. Critical effective stress as a function of critical

CTOD for three SENB geometries of ABS grade EH36

steel

118
These are essentially the same data as were plotted in Figure 52, except

that the fracture stress (which is a constant) was divided by o

c to

obtain the critical CTRC values in Figure 52. Despite the simplicity of

the model, equation (48) correlates well with experimental data. The

coefficients of determination for the three geometries plotted in Figure

55 range from 0.939 to 0.975.

Each specimen geometry in Figure 55 exhibits a different slope and

intercept. According to equation (48) the intercept is at Since

the fracture stress is a material constant the initial laterial stress,

o°, must be geometry dependent. The slope of each of the curves in

Figure 55, which will hereafter be called the relaxation slope, is equal

to k/2A, where k is the spring stiffness.

The relaxation slope and intercept for various specimen

configurations of ABS grade EH36 steel are listed in Table 10. (Data

from Tables 7f and 7g are not included because the large scatter and

small sample population made it impossible to establish meaningful

trends .

The relaxation slope tends to decrease with increasing ligament

length in the bend specimens. This can be explained qualitatively in

terms of the inverse relationship between the length and stiffness of a

spring; i.e., a short spring is stiffer than a long spring. The length

of a spring is related to the ligament length. The relationship between

relaxation slope and ligament length is quantified later.

119
The constraint relaxation behavior for the three tension geometries

is different than that of SENB specimens. Table 10 shows that the

ligament length of an SENT specimen has little effect on the relaxation

slope. However, when the thickness is increased by a factor of three

the relaxation slope decreases significantly. Apparently the

contraction in the thickness direction governs the constraint

relaxation, even if the ligament length is much less than the thickness.

3.4.4 A Model to Estimate o°

A As stated above, the initial lateral stress is geometry dependent.

The spring model has been extended to derive an expression for this

stress. For the purpose of this derivation, the initial lateral stress

which governs constraint was assumed to act in the x direction.

Consider the case where fracture in an SENB specimen coincides with

the onset of net-section yielding. The amount of plastic flow prior to

fracture would be small; the crack would be relatively sharp. The

following assumptions can therefore be made:

Also, since the ligament is on the verge of yielding, the fracture load,

P.f, is equal to the yield load. Thus, according to equation (35)

120
P (49)

f

Lo (W-a) 2 B o4W

Solving3 for o leads to

o

a = a

o c

4P

f

W

One can then solve for a

(W-a) 2 BL

o.

= °f

- a

x (50)

°x

= a

f nom

(51)

where a 4P

f

W nom

(W-a) 2 B

= nominal ligament stress at fracture.

The nominal stress at fracture for the normalized steel is approximately

770 MPa. This quantity seems to be insensitive to geometry. Thus,

a

0 0.67 — = 1 - (52)

Equation (52) is plotted in Figure 56 along with experimental

values for initial lateral stress as a function of notch constraint.

The predicted curve lies above the data but the trends of the data and

the curve are similar. A vertical line is drawn on Figure 56 at L = /3.

This represents the upper limit of elastic constraint. The value of /3

is an approximate upper bound of L although L can exceed /3 slightly

because the specimen behavior is elastic-plastic.

The fact that a

0

and L may be simply related is encouraging because

it means prediction of transition curves as a function of geometry is

possible. While multiple specimens at various temperatures are required

121
0.70

©x

0/

Of

0.60

O B = 0.5W=12.7mm,a/W~0.2

a B = W = 25.4mm ,a/W~0.52

B = 1.5W = 38. 1mm, a/W-0.29

_ o B = W= 25.4mm, a/W~0.2

v B = W= 25.4mm, a/W~0.75

0.50-

0.40-

0.30

L=v^3" = limit of elastic constaint

1.0 1.2 1.4 1.6 1.8

NOTCH CONSTRAINT FACTOR (L)

Figure 56. Comparison of predicted and experimental initial

lateral stress as a function of notch constraint for

ABS EH36 steel SENB specimens.

122
to determine o° for a given geometry (Fig. 55), L can be determined from

a single test at any temperature.

3.4.5 Predicting the Relaxation Slope

According to Table 10, the slope of the relaxation curve, k/2A, is

dependent on ligament length for bend specimens and apparently on

thickness for tensile loading. In the analyses that follow, only the

case of the SENB geometry, where constraint relaxation is primarily in

the x direction, is considered.

In order to obtain estimates of the relaxation slope, it was

necessary at this point to replace the linear elastic spring with a bar

of length r^b, where b is the ligament length, W-a, and r^ is the

rotational factor (eq. 31). This bar is illustrated at the top of

Figure 57. If the bar is displaced a distance 6/2, a strain field will

be introduced into the bar. A uniform strain field will be introduced

if the displacement field is linear along the length of the bar (Fig.

57, center). A displacement field can be applied such that the strain

is infinite at x=0 and zero at x=infinity. This asymptotic strain

field, which is illustrated at the bottom of Figure 57, should be

representative of the real e x field ahead of a blunted crack tip.

The strain field in the bar should have the form:

e x (53)

123
rpb

S/2

Uniform Strain Field

Figure 57. Schematic of a bar displaced by 6/2 with

corresponding uniform and asymptotic strain fields

124
The exponent in equation (53) must be the same as that in equation (42)

because e is simply related to the other principle strains and e

through incompressibility equations. In order to satisfy these

equations at all values of x and 6, the exponents on each of the

principle strains and 1 must be the same.

If the small strain approximation (which is reasonably accurate for

strains up to 0.10) is used, equation (53) can be integrated with

respect to x to determine the displacement field:

A6

0 - 875

X0 - 125

u

= + C (54)

x 0.125

One can solve for the constants A and C by applying the following

boundary conditions (see Fig. 57, bottom).

6 £x

= 16 ( r b)

U ' 125 x°-^

(55)

(56)

If the materials strain hardening behavior is idealized as linear, one

can easily solve for the change in a due to a plastic strain, e : X X

125
(57)

Aa

x

e E x p

E 6 P__

0.125 0.675

16(r

p b)

where Ep is the plastic modulus.

Equation (57) can be substituted into Equation (48) for effective

stress (x=X , 6=6 ): c c

Q

c = a f

Ei

6 c 16(r b) 0,125

X

°’ 875

P p

(58)

Thus, the relaxation slope is given by

E _K =

P (59)

oi\ i ci k \0.125 v 0.875

2A 16(r b) X

c

Experimental values of relaxation slope and equation (59) are

plotted against ligament length in Figure 58. The plastic modulus was

estimated by constructing a line, tangent to the flow curves in Figure

51, which passed through the origin. For the normalized steel, Ep was

approximately 1750 MPa. The downward trend of relaxation slope with

ligament length in Figure 58 is steeper for the data than for the

prediction. All experimental values are within 10-50 percent of the

prediction. This agreement is reasonably good considering the

simplicity of the model and the relatively large scatter in the fracture

toughness data used to compute relaxation slopes.

126
RELAXATION

SLOPE,

MPa-mm"

Figure 58. Predicted and experimental relaxation slope as a function of ligament length for ABS EH36 steel

SENB specimens.

127
It would be wise to pause at this point to further discuss the

physical basis of this model. The picture presented in Figure 53 is one

where an initially sharp crack blunts (at a constant a ) and the stress

in the x direction relaxes by Ao . The physical rationale of the above

derivation is somewhat different from this concept, although the basic

results are the same.

If a specimen containing a sharp crack is loaded (a = at x

=

X ) at a low temperature such that plastic deformation at the crack tip

where minimal, the stress in the x direction would be o° at X . If a

A L* sharp-cracked specimen is monotonical ly loaded at a higher temperature,

the crack tipp blunts before a reaches a* because the material's flow

yy f

stress is too low to maintain the sharp-crack configuration at high

stresses. Therefore a will be less than a

0 and constraint will be

X X lower for the blunt crack. If this blunt-crack configuration is then

plastically deformed in the x direction to produce the sharp-crack configuration, a (at a constant o ) would increase by A o due to strain

hardening. The ratio of principle stresses required to maintain the

sharp-crack configuration should only be a function of specimen geometry

and elastic properties. Therefore the value of x-stress for this

configuration should be constant for o = a f ; i.e., a + Ac = o°,

yy * xxx

regardless of temperature or prior strain history.

Although the above model is a refinement of the initial

linear-elastic spring analog, both analyses predict a linear dependence

of critical effective stress on critical CTOD. In the next section,

128
this linear relationship is used to derive an equation for

ductile-to-brittle transition curves.

3.4.6 Predicting Transition Curves

Equations (52) and (59) allow one to calcuate the slope and

intercept of a material's constraint relaxation curve. This

information, along with material-flow property data, make it possible to

predict fracture toughness (6 ) as a function of temperature in the

ductile-to-brittle transition region.

Figure 59 schematically shows how one can obtain a critical CTOD

value at a given temperature by superimposing material flow curves on

the effective stress-CTOD plot. The stress-strain curve for an element

X

c ahead of the crack tip can be converted to a stress-CTOD curve by

means of equation (42). Critical conditions occur at the point where

the flow curve crosses the relaxation curve. The ductile-to-brittle

transition curve can be constructed by plotting flow curves at the

various temperatures on the relaxation plot and determining the

corresponding 6 c values (see Fig. 59). Varying specimen geometry causes

the relaxation curve to shift up or down (see Fig. 55). A downward

shift of the relaxation curve causes a shift in the ductile-to-brittle

transition to higher temperatures.

The above graphical analysis can be expressed in equation form.

The material's flow behavior is assumed to follow power-law hardening:

129
aoio ivoiiiao

130

Figure

59.

Graphical

determination

of

critical

CTOD

values.

Critical

conditions

occur

at

the

point

where

the

flow

curve

crosses

the

relaxation

curve.
0 ( 60 )

. n

= a + ae

0

Using equation (41) to solve for strain yields

a = a Q

+ B<5 m

(61)

where 6 = —

x 0.875

and m = 0.875n.

For critical conditions, equation (60) is set equal to equation (58):

m

°c

= °o

+ BS

c °f

• °x

E 6 P

c

16(rpb) 0,125Xc

0.875

Thus,

E 6 ELP

16(r b)

0,125

x 0,875

p c

(62)

Equation (62) expresses fracture toughness (in the transition

region) as a function of three stresses. The fracture stress is a

material property, independent of temperature and geometry. The yield

stress is independent of geometry but is temperature dependent. The

geometry dependence is contained in the initial lateral stress, o°.

This stress governs the temperature at which the upturn in the

toughness-temperature curve occurs, i.e., the border between the lower

shelf and the transition region. The factors on the left side of

131
equation (62), such as strain hardening behavior and ligament length,

govern the slope of the transition curve.

Several transition curves for normalized steel SENB specimens were

computed by graphical means (see Fig. 59). These curves are shown in

Figures 60-62. The relaxation slope and intercept used to construct the

computed curves were taken from Table 10. The computed curves in

Figures 60 and 61 are compared with the corresponding experimental data.

These curves can be thought of as best-fit functions through the data.

Figure 62 compares the computed curves for three SENB geometries. These

curves represent the data presented in Figure 25. The deepest notched

geometry experiences the most rapid constraint relaxation because the

ligament is shorter. This results in the steepest transition. That is

why two of the curves cross in Figures 25 and 62.

The predicted curves were obtained by computing the slopes and

intercepts of the corresponding relaxation curves from equations (52)

and (59). The predicted curve in Figure 60 lies about 10-20°C to the

right of the computed curve which passes through the data. This could

be considered a reasonable prediction of the fracture toughness data.

However, the predicted curve in Figure 61 lies well to the right of the

experimental data. This curve yields overly conservative estimates of

fracture toughness.

The reason for the poor agreement in Figure 61 can be understood by

comparing predicted and experimental values of o° in Figure 56. At low

A

L values the agreement is reasonably good but the predicted and

132
CRITICAL

CTOD,mm

TEMPERATURE, °C

Figure 60. Comparison of computed and predicted transition

curves with experimental data; ABS grade EH36 steel

SENB specimens, B = 0.5W = 12.7 mm, a/W = 0.2.

133
CRITICAL

CTOD,

mm

TEMPERATURE, *C

Figure 61. Comparison of computed and predicted transition

curve with experimental data; ABS grade EH36 steel

SENB specimens, B = 1.5W = 38.1 mm, a/W = 0.29.

134
CRITICAL

CTOD,

mm

TEMPERATURE, C

Figure 62. Computed transition curves for SENB specimens as a function of crack length.

135
experiments! values diverge at high L values. That is why the agreement

between prediction and experiment is much better in Figure 60 (Lsl.35)

than in Figure 61 ( L= 1 . 5 )

The predicted transition curve in Figure 61 is much less steep than

the constructed curve. This is mainly due to the fact that the

temperature dependence of flow stress is less steep at higher

temperatures (see Figs. 20 and 21). This results in a more gradual

ductile-to-brittle transition at higher temperatures.

The model in its present form is not suitable for prediction

purposes, as evidenced by the poor agreement between experiment and

prediction in Figure 61. The models which estimate c° and the

relaxation slope apparently need to be refined. The predicted curves

are highly sensitive to variations in the initial lateral stress.

However, these curves are not nearly as sensitive to the relaxation

slope. Therefore, some of the predicitive capability might be salvaged

by resorting to an empirical correlation between o° and L. A linear

regression fit of the data in Figure 56 yielded the following equation.

o — = 0.183L + 0.242 (63)

°f

3.4.7 Application to Structures

With the empirical correlation between o° and L (eq. 63), the above

analysis can be used to predict the ductile-to-brittle transition curves

of a structure. This structural application was essentially the

original objective of this study. In the following example the model is

136
used to predict the transition behavior of s hypothetical structure of

ABS grade EH36 steel

If one is to predict fracture toughness in the transitior ’•ec*:^

for a structure of a given material using equation (62) (c r the

equivalent graphica 1 rethod', the following innervation is r eedec:

1) Yield stress versus temperature data

2) Material flow properties

3) Fracture stress

4) Critical distance

5) Ligament length

6) Initial lateral stress.

The first three items can be obtained from jniax’la' te r s': 's tests

at various temperatures . The critical distance car be obtained fro" a

lower shelf K.

r test and Tracey’s [82] finite element solutions, ’he

last two items in the above list are dependent on the configurat'c cf

the specific structure.

For the purpose of this example a value of 150 mm (5.9 * r ' was

assured for b. The relaxation slope is rot highly sensitive to t^is

value since the exponent on b in equation (62) is small.

For conditions of optimal constraint, the value c

f

_ is

approximately /3 . However, this value may be o\e ,‘'_. co ,'se'' . at' . e *c r a

typical structure. A very deep crack would be required to produce

optimal notch constraint. Typical structural flaws te^d to be

relatively shallow. An L value of 1.5 ray be '"ore realistic.

137
Values of o° for ABS EH36 steel were computed from equation (63)

A

assuming L values of 1.5 and /3. The slope of the relaxation curve was

calculated from equation (59). The ductile-to-brittle transition curves

were constructed by means of the graphical method.

Figure 63 shows the predicted transition curves for the two assumed

L values. A typical computed curve for an SENB specimen is included for

comparison. The predicted temperature shift between the structure and

laboratory specimen is small at low toughness and large at high toughness values. The predicted structural curves are less steep than the

specimen curve for two reasons. First, the relaxation slope for a large

section is lower. Second, as mentioned previously, the temperature

dependence of flow stress is not as steep at higher temperatures.

The structural prediction for an assumed L value of 1.5 looks

reasonable. Unfortunately, there are no large section data available to

compare with this prediction.

Another problem is that the existing model is only applicable for

loading in bending. Most structures undergo tensile loading or a

combination of bending and tension. Since pure bending is the

worst-case situation with respect to constraint, the present analysis

would give conservative results. It remains to be seen whether this

conservatism is reasonable or excessive.

All things considered, the predictive capability of the present

analyses for structures is definitely suspect. Obviously, further

refinements are needed. Predictions have been made in Sections 3.4.6

138
CRITICAL

CTOD,

mm

TEMPERATURE, °C

Figure 63. Predicted transition curves for a hypothetical

structure of ABS EH 36 steel compared with a computed

curve for an SENB specimen.

139
and 3.4.7 simply to demonstrate the potential of a model such as this,

once its accuracy can be assured. Although the model in its present

form does not agree with experimental data as well as one would hope, it

does provide valuable insights into material behavior.

3.4.8 Application to Other Materials

The model for the ductile-to-brittle transition was used to predict

transition curves for the commercially pure iron. It was reasoned that

if this analysis could be successfully applied to both the C-Mn steel

and the pure iron, the analysis could be used to predict the position

and shape of transition curves for most other low-carbon structural

steel s

As stated in Section 3.4.7, six items are needed to predict

transition curves. Since tensile data was obtained for the pure iron,

the first three items on the list in Section 3.4.7 were readily

available. However, it was not possible to determine an accurate value

for critical distance because none of the fracture toughness tests on

this material yielded a valid Kj

c value. Values of 0.15, 0.30, and

0.45 mm were assumed for X

c

; this correpsonds to approximately 1, 2, and

3 grain diameters, respectively. The initial lateral stress was

estimated according to a rationale described below.

Two assumptions were made for the estimation of o° for pure iron.

First it was assumed that L is constant for a constant geometry of the

two materials. The notch constraint factor is insensitive to

140
temperature but is a function of specimen geometry (Figs. 28 and 29).

This suggests that L is primarily controlled by a material's elastic

properties; the flow properties should be of secondary importance. If

this is true, specimens of two materials with the same geometry and

elastic properties should have the same L value. Second, it was assumed

that equation (63) is valid for both materials. Thus, the two specimens

should also have the same a°/cf ratio. The average fracture stress for

the pure iron was 627 MPa (Fig. 46). Thus = 316MPa for B = 25.4 mm

A and a/W = 0.2.

The assumption that L is not material sensitive was investigated.

Figure 64 is a plot of nondimensional load versus displacement for

normalized steel and pure iron SENB specimens with the same geometry.

These two curves agree reasonably well at high displacements but the

agreement is not as good near net-section yield. Much of the difference

is due to the fact that the normalized steel has a sharper yield point

than pure iron. Apparently, the value of L is slightly dependent on

flow properties since a finite amount of plastic deformation usually

precedes ligament yielding. However, the disagreement between the two

curves is not bad considering that the flow properties of these two

materials are vastly different. The notch constraint factor for a given

specimen geometry probably remains relatively constant for a wide range

of steels.

Constraint relaxation curves and transition curves were computed

from experimental fracture toughness results. This was done to compare

141
4PW

MOUTH-OPENING DISPLACEMENT, mm

Figure 64. Nondimensional-load-versus-displacement curves at a constant

SENB specimen geometry for pure iron and ABS

EH36 steel

142
predicted and experimental results. Also, the effect of the assumed X

c value could be assessed. Figure 65 shows that the strain-hardening

behavior of this material is not sensitive to temperature over the range

of interest. The flow curves for pure iron were converted to stress/CTOD

curves corresponding to the three assumed critical distances. These

curves are plotted in Figure 66. Critical effective stress was measured

from experimental data according to the procedure outlined in Section

3.4.2.

The relaxation curves for the three assumed X values are shown in

c Figure 67. Both slope and intercept are functions of the assumed

critical distance. The expected intercept, which is marked on the

ordinate of Figure 67, was determined by assuming that the o°/af ratio

is the same as that of the normalized steel specimens with the same

geometry. This predicted intercept agrees well with the actual

experimental intercepts.

Ductile-to-brittle transition curves were constructed graphically

according to the procedure illustrated in Figure 59. These curves are

shown in Figure 68. The constructed curves are not strongly affectly by

the assumed X

c value. This procedure for computing best-fit curves

through fracture toughness data is apparently not sensitive to errors in

V

The relaxation slope for pure iron was predicted from equation (59)

as a function of distance ahead of the crack tip. The plastic modulus

of this material was approximately 750 MPa. Figure 69 compares the

143
144

temperature

for

pure

iron.
(<r-cr

n

),

MPa

Figure 66. Flow behavior of pure iron ahead of a crack tip as a function of CTOD and distance.

145
CRITICAL

EFFECTIVE

STRESS,

MPa

CRITICAL CTOD, mm

Figure 67. Critical effective stress as a function of critical

CTOD at three assumed values for critical distance

in commercially pure iron SENB specimens.

146
CRITICAL

CTOD,

mm

Figure 68. Computed transition curves at three assumed critical

distances compared with experimental data for

commercially pure iron SENB specimens.

147
Figure 69. Predicted and experimental relaxation slope as a function of distance from the crack tip for

commercially pure iron.

148
predicted curve with actual values of slope obtained from Figure 67. As

in Figure 58, the agreement between experimental and predicted

relaxation slopes is reasonably good.

Using the predicted intercept and relaxation slopes, transition

curves were constructed graphically for the three assumed critical

distances. These predicted curves are compared with experimental data

in Figure 70. The best agreement was obtained for an assumed critical

distance of 0.45 mm although the curve for X

c

= 0.30 mm agrees

relatively well with the data.

A value of 0.15 mm (^1 grain diameter) is probably an underestimate

of the average critical distance in the pure iron. One would expect

that more than one grain ahead of the crack tip would have to be sampled

to find a particle large enough to initiate fracture. However, one data

point in Figure 70 does coincide with the X c = 0.15 mm curve. It is

likely that a large inclusion was near the crack tip in this specimen.

The predicted curves in Figure 70 shift to higher temperatures with

decreasing critical distance. One could thus obtain a lower-bound curve

for a given material by assuming a lower-bound value for X .

The model developed in this investigation seemed to work very well

for predicting ductile-to-brittle transition curves for the pure iron.

The accuracy of the predictions cannot be fully ascertained because an

accurate value for the critical distance was not available. However,

0.30-0.45 mm is certainly a reasonable range for X .

149
CRITICAL

CTOD,

mm

Figure 70. Predicted transition curves at three assumed critical

distances compared with experimental data for

commercially pure iron SENB specimens.

150
Although, as stated previously, the accuracy of prediction from the

model is often unacceptibl e , the model seems to work well for describing

the ductile-to-brittle transition behavior of both materials. Therefore, it can probably be successfully applied to most structural steels.

3.5 Constraint Versus Statistical Models

As stated in Section 1.4.2, there are two explanations given for

size effects on fracture toughness in the transition region. The

traditional explanation is that smaller specimens lose constraint. The

present analysis utilizes this concept. The second explanation for size

effects was recently proposed by Landes and Shaffer [60]. They maintain

that these effects can be explained by a statistical model for cleavage

fracture. In a large specimen, where a larger volume of material along

the crack front is sampled, the probability of finding a region of low

toughness (e.g., a large grain boundary carbide) along the crack front

is higher. Therefore, the toughness of a large specimen should be lower

than the average toughness of a population of smaller specimens.

There is somewhat of a controversy over whether constraint or

statistical effects are the dominant factor in size effects on fracture

toughness. A discussion of this topic in light of the present results

is given here. Both arguments have some validity. It is hoped that

this section will help to put these different approaches into

perspective.

151
Both constraint and statistics could conceivably contribute to size

effects. The relative contribution of each of these factors can be

qualitatively understood by examining the variables that affect their

magnitude.

3.5.1 Factors that Affect Constraint

Constraint is lowest for thin specimens. As specimen thickness

increases, constraint increases until plane strain conditions are

reached. At this point further increases in thickness have little or no

effect on constraint. The thickness at which plane strain is reached

depends upon material flow properties. For a low-strength steel, a

thicker specimen is required for near-plane strain conditions. For a

given applied stress intensity, the plastic zone is larger in a lower

strength material (eq. 9). As seen in Section 3.4, increased plasticity

results in a constraint relaxation.

In addition to thickness, the crack length and type of loading

affect constraint. Deeper cracks produce additional constraint in bend

specimens. For very deep cracks, constraint is initially higher but

when the remaining ligament is short, constraint relaxes quickly with

plastic flow. Also, bending produces more constraint in deep-noteched

specimens than tensile loading.

152
3.5.2 Factors that Affect Statistical Shifts in Toughness

As in the constraint concept, the statistical model dictates that a

material's mean fracture toughness at a given temperature (in the

transition region) must decrease with increasing thickness. The

statistical model is also similar to the constraint argument in that

statistical effects must saturate at a certain thickness. Once a large

enough volume of material is sampled, further increases in sample size

would have no effect because larger samples would not contain any

additional microstructural features.

The major factor which would likely control the saturation

thickness for statistical effects is the microstructure. For example, a

homogenious microstructure would have a small saturation thickness. A

material that contains a low volume fraction of large grain boundary

carbides would exhibit statistically-related size effects up to a

relatively large thickness because a large volume of material would need

to be sampled in order to insure that the process zone ahead of the

crack tip contained at least one of the large particles.

The grain size of a material could affect the saturation thickness

since the number of grain boundary carbides or other fracture-triggering

particles in a given volume of material is related to the number of

grains sampled in that volume. The grain size effect is illustrated in

the following example. Assume for this example that the volume of

material along the crack front that can contribute to fracture

initiation is contained in a circular cylinder with a radius of 0.2 mm

153
and a length equal to the thickness of the fracture specimen. For an

5 average grain diameter of 0.03 mm, approximately 10 grains would be

sampled in a 25 mm thick specimen. If the grain diameter is doubled, a

5 specimen 200 mm thick would be required to sample 10 grains along the

crack front. Thus, the saturation thickness would be smaller for

fine-grained materials.

Unlike constraint, the statistical size effects are not influenced

by crack length. If the crack length is varied at a constant thickness,

the volume of material along the crack front remains constant. Any

shifts in the transition that occur as a result of varying the a/W ratio

must be attributable to constraint effects. Similarly, transition

shifts between bending and tensile loading can be attributed entirely to

constraint effects.

3.5.3 Determining the Cause of Transition Shifts

The material properties that can determine the magnitude of

constraint and statistical effects were outlined above. With this

information it is often possible to determine the dominant cause of size

effects on fracture toughness of a given material.

Landes and Shaffer (60) used an ASTM A471 NiCrMoV rotor steel with

a yield strength of 765 MPa (111 ksi) for their statistical study. They

performed fracture toughness tests on IT and 4T compact tension (CT)

specimens. The 1T-CT and 4T-CT specimens were 25.4 mm (1.0 in) and

102 mm (4.0 in) thick, respectively. For both CT geometries, B=a=2W.

154
Landes and Shaffer correlated transition shifts between the two

geometries with a weakest-! ink statistical model . They assured that the

deep-notched 1T-CT configuration contained a high degree of constraint

and that the constraint ir this specirrer was equivalent to that in the

4T-CT georetry. This was probably a valid assurptior since the material

had a high yield stress. However, there would likely be a pronounced

constraint difference betwee r IT- and 4T-CT specimens of a low-stre r gth

mild steel

The A471 steel used by Landes and Shaffer exhibited significant

statistical effects but no differences in constraint were observed. I r

contrast, the ABS grade EH36 steel used in the present study exhibited

significant constraint effects and minimal statistical effects. This

material is a fine-grained normalized steel with a yield stress

approximately half that of the A417 steel.

Figures 23-26 and 35 show that the ductile-to-brittl e transition of

the ABS EH36 steel shifts to higher temperatures by: 1) increasing

specimen thickness, 2) decreasing uncracked ligament le r gt r

i r SENB

specimens, and 3) changing loading from tension to bendi r g ir

deep-notched specimens. The two latter transition shifts are due

entirely to constraint effects for reasons discussed earlier. Figure 30

shows fracture toughness data for 25.4 and 76.2 nr (1.0 a

r d 3.C in)

thick SENB specimens with a/W = 0.5. The constraint ir both o f these

geometries is approximately the same because corresponding values for

the notch constraint factor, L, are equal. Thus, any observed

155
transition shifts would be due to statistical effects. However, the

data for the thick specimens all lie well within the scatter band of the

B = 25.4 mm data. Thus, it can be concluded that for ABS EH36 steel,

statistical effects are saturated at or below B = 25.4 mm.

Of all the specimen geometries tested in this study, only one SENB

configuration has a thickness less than 25 mm. Figure 23 shows a

definite transition shift from B = 12.7 to 25.4 mm (a/W = 0.2).

Figure 29 shows that notch constraint is elevated in the thicker

specimen. However, this does not prove that there are no statistical

contributions to the transition shift. Some evidence for the hypothesis

that statistical effects are minimal in the thin specimens is in

Figure 56 where a° is plotted against L for five SENB geometries. In

four out of five geometries, statistical effects are saturated because

B _> 25.4 mm. If statistical considerations significantly affected the

transition shift between B = 12.7 and 25.4 mm, the measured value of o°

X for B = 12.7 mm would be lower than would be expected from constraint

considerations alone; the data point for B = 12.7 mm in Figure 56 would

lie below the trend established by the other data. However, the B

=

12.7 mm data lies on the same trend as the other data, suggesting that

statistical effects are minimal.

Low strength ferritic materials can exhibit significant size

effects due to loss of constraint in smaller specimens. Materials with

inhomogenious or coarse-grained microstructures can experience

statistically related size effects on toughness. The commercially pure

156
iron used in this study falls into both of these categories. It has

very low strength and its microstructure consists of large ferrite

grains with a small volume fraction of large inclusions. Transition

shifts with thickness in this material might be due to both constraint

and statistical effects. Unfortunately, the relative contributions of

each of these factors cannot be readily determined.

3.5.4 Summary Comments

Both constraint and statistical explanations for size effects on

fracture toughness in the transition region have merit. The dominant

factor depends on the material. Constraint effects are most pronounced

in low strength steels. Statistical effects are at a maximum in

materials with coarse-grained and/or inhomogenious microstructures.

Sometimes a low strength material can also have a microstructure that is

susceptible to statistical transition shifts. This was the case for the

pure iron used in this study. Many weldments may also fit into this

category. For these materials, an integrated model which considers

both constraint and statistical effects is needed.

3.6 Discussion of Results

The original objective of this work was to develop a method for

scaling size effects on fracture toughness in the ductile-to-bri ttle

transition region of steels. Although a number of questions remain

unanswered, substantial advances were made in this area. These advances

157
are outlined below, along with the potential applications and

limitations of the analyses developed here.

3.6.1 Advances

The experimental data obtained in this investigation provided a

demonstration of constraint effects on fracture toughness. It is

apparent from the results that, at least for some materials, size

effects on fracture toughness can be attributed to constraint which is

dependent on specimen size and geometry. Statistical effects may play a

role in some materials but constraint is definitely a factor in

low-strength steels.

A technique to experimentally measure crack-tip region constraint

(CTRC) was developed during the course of this investigation. The first

known quantitative measures of CTRC ever made are presented in this

document. At a constant CTOD, constraint is lowest for a thin specimen

with a shallow notch. Although this behavior was expected in light of

prior work, all previous authors discussed constraint in purely

qualitative terms.

The constraint measurements showed that CTRC decreases with crack

blunting. This relaxation was modeled in this investigation. Although

the model is relatively simple, the agreement with experimental data is

quite good.

An equation for fracture toughness as a function of material- and

geometry-dependent properties was derived from the constraint model.

158
This equation can be used to predict ductile-to-brittle transition

curves for low-carbon steels in various configurations. Material flow

data, a lower-shelf fracture toughness value, and an estimate of the

notch constraint in the configuration of interest are the only data

required for this prediction. The accuracy of these predictions was not

as good as one would hope but the analyses provided valuable insights

into the physics of constraint and the ductile-to-brittle transition.

The model works well for describing the transition behavior of both

ABS grade EH36 steel and commercially pure iron. This suggests that

the description of the ductile-to-brittle transition inherent in the

model may be universal. The analysis is probably applicable to most

structural steels.

3.6.2 Applications

As stated above the model can be used to predict the fracture

toughness of a structure if certain material data are available.

However, a number of refinements are needed for the model to be reliable

for predictive purposes. There are several different approaches to

using this analysis for structural applications.

The most reliable approach would be to experimentally obtain

accurate values for all the parameters in equation (62). This would

require uniaxial tensile tests, lower-shelf Kj tests and a realistic

estimate of the notch constraint factor for a typical structural flaw.

One could then compute the entire transition curve for this structure.

159
The temperature shift approach may be suitable for material

selection applications. It has been established that there is a shift

in transition curves between small-scale test specimens and large

structures. This temperature shift can now be quantified for a given

situation. For example, take a structure which will operate at -40°C.

Assume for this example that is has been determined that a critical CTOD

value of 0.2 mm is required for this structure to be safe with respect

to brittle fracture. The fracture toughness is to be measured from

25 mm thick SENB specimens with a/W = 0.2, machined from a weldment of

the candidate material. Equation (62) can be used to determine the

temperature shift between the specimen and the structure at 6 c

= 0.2 mm

and a service temperature of -40°C. If the temperature shift is

determined to be 20°C, the specimens must be tested at -60°C. The

lower-bound toughness of the SENB specimens at -60°C must be greater

than 0.2 mm for the weldment to be suitable for the structural

appl i cation.

The above methods require information about the flow behavior and

lower-shelf toughness which might not be available in many cases.

However, it is still possible to use the constraint model to make

engineering estimates of a material's toughness. With a knowledge of

the chemical composition, microstructure and approximate yield strength

of a material, one can make estimates of the various parameters in

equation (62) and then estimate a transition temperature for the

material. This approach would not yield highly accurate predictions.

160
However, it may be of use for determining whether a material will be

brittle or ductile at a given temperature. For example this type of

analysis, which involves no mechanical testing, could expedite material

selection by screening out materials that are totally unsuitable for a

given application. Expensive, time-consuming mechanical tests can then

be performed on the more promising candidate materials.

3.6.3 Limitations

There is no question that the model developed in this

investigation is an over-simi pi ication of the actual stress-strain

behavior at the crack tip. For example, the model treats the plastic

relaxation in the x-direction as a one-dimensional problem.

Although the analysis which predicts a relationship between initial

lateral stress, a°, and notch constraint, L, yields values that are

A within 10-20 percent of experimental values, the predictions of the

ductile-to-brittle transition curves were far too conservative when o°

X

is computed in this way. The author had to resort to an empirical fit

between and L. Although this correlation seemed to work well for

specimens of both materials, it is not known how well the empirical

relationship will work for larger section sizes.

The estimation of o° for a large structure is just one problem

A that contributes to the uncertainties in structural predictions.

Another problem is that the model in its present form cannot be applied

to tensile loading. Fortunately the analysis, which is applicable to

161
bending, would normally yield conservative predictions because bending

is a worst-case loading condition.

Owing to the uncertainties mentioned above, the accuracy of

structural toughness predictions is questionable. Large-scale

experimental results are needed to compare with predictions.

Unfortunately, large-scale fracture toughness testing is very expensive

and requires an enormous test machine.

Another limitation of the analysis in its present form is that

statistical effects are not taken into account. Although minimal in the

ABS EH36 steel plate used in this study, statistical effects may be

quite pronounced in inhomogenious materials such as weldments.

3.6.4 Summary Comments

Although there are a number of problems remaining, the results of

this study are encouraging. A methodology has been developed that can

be applied to the problem of scaling fracture toughness results.

Several refinements of the analysis are needed to insure its accuracy in

a wide range of applications.

162
4. SUMMARY AND CONCLUSIONS

Specimen geometry has a drastic effect on fracture toughness in the

ductile-to-brittle transition region. Increasing specimen thickness

and/or crack length causes the transition to occur at higher

temperatures. The geometry effects in ABS grade EH36 steel are

attributed primarily to constraint effects. Thicker specimens produce a

greater amount of stress triaxiality near the crack tip, thus elevating

the flow stress locally. A higher flow stress tends to promote cleavage

fracture by making it easier to reach the fracture stress. For

specimens with relatively short ligaments the transition in bend

specimens occurs at higher temperatures than for specimens loaded in

tension. As ligament length is increased the transition behavior

approaches that of tension specimens. For very short cracks or very

short ligaments, constraint can be relaxed by plastic flow from the

crack tip to the nearest free surface.

Crack-tip region constraint (CTRC) can be indirectly measured by

means of the Ritchie-Knott-Rice fracture model and a crack-tip strain

equation. The CTRC decreases with crack blunting. A simple model for

this constraint relaxation predicts a linear relationship between

critical effective stress and critical CTOD. This linear relationship

agrees well with experimental data.

The model for constraint relaxation can be used to predict

ductile-to-brittle transition curves for a low-carbon steel as a

163
function of geometry. This model can be applied to toughness

predictions of large structures by assuming worst-case values for

geometry-dependent parameters in the model.

The analysis in its present form was derived for SENB specimens and

is not valid for tensile loading. However, bending is a worst-case

loading situation; the present analysis should yield conservative (i.e.,

safe) predictions. The model does not take statistical effects into

consideration. Although for many materials the statistical effects are negligible, materials with an inhomogeneous microstructure, such as weldments, may be highly susceptible to statistical size effects.

Future work should include refining the model to include

statistical effects and tensile loading. Also, the accuracy of the

analysis for structural predictions should be investigated

withlarge-scale fracture toughness tests.

5. ACKNOWLEDGMENTS

I would like to express my deepest appreciation to the members of

my doctoral committee, Drs. H. I. McHenry, G. R. Edwards, D. K. Matlock,

S. R. Daniel, M. G. Dawes, S. B. Romberger, and S. D. Foreman. I especially thank Dr. McHenry for the support and guidance he has given

me these past three years. Special thanks are also due Dr. M. G. Dawes

of the British Welding Institute who provided the initial inspiration

for this work and has served as a mentor throughout this program. I am also grateful to the staff members of the Fracture and Deformation

Division of the National Bureau of Standards who have shared their

expertise and offered a great deal of helpful advice. Members of the

NBS support staff who were especially helpful are JoAnne Wilken and

Diane Bieber, who typed the manuscript, and Mr. N. Sanchez, who prepared

most of the drawings. This research was funded by the Minerals

Management Service of the U.S. Department of Interior.

164
6. REFERENCES

[1] L. H. Larson, Ed., "Advances in El asto-Pl asti c Fracture

Mechanics," Applied Science Publishers, London, 1980.

[2] T. L. Anderson and H. I. McHenry, Natonal Bureau of Standards,

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[3] A. A. Griffith, Phil. Trans. Roy. Soc. 221A, 1920, p. 163.

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[6] H. Tada, P. C. Paris, and G. R. Irwin, The Stress Analysis of

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[7] G. C. Sih, Handbook of Stress Intensity Factors for Researchers and

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University, Bethlehem, Pennsylvania (1973).

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[9] G. R. Irwin, Trans. ASME, J. Basic Eng. 82, 1960, p. 417.

[10] P. C. Paris and G. C. Sih, in: Fracture Toughness Testing and Its

Applications, ASTM STP 381, 1965, p. 30.

[11] A. A. Wells, Brit. Welding J., 12, 1965, p. 2.

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[13] F. M. Burdekin and D. W. Stone, J. Strain Anal., 1966.

165
[14]

[15]

[16]

[17]

[18]

[19]

[ 20 ]

[ 21 ]

L22]

[23]

[24]

[25]

[26]

L27]

[28]

D. S. Dugdale, J. Mech. Phys. Solids, 8 (2), 1960, p. 100.

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May 1971.

M. G. Dawes, Advances in Elasto-Plastic Fracture Mechanics, edited

by E. H. Larsson, Applied Science Publishers, London, 1980, p.

279.

British Standard 5762: Methods for Crack Opening Displacement

(COD) Testing, 1979, The British Standards Institution, London.

J. R. Rice, J. Appl . Mech., 35 (2), 1968, p. 379.

J. A. Begley and J. D. Landes, ASTM STP 514, 1972, p. 1.

D. J. Hayes, Ph.D. Thesis, University of London, 1970.

J. G. Blavel, Advances in Elasto-Plastic Fracture Mechanics,

edited by E. H. Larsson, Applied Science Publishers, London, 1980,

p. 65.

M. G. Dawes, The Welding Institute Research Bulletin, 13, 1982,

p. 50.

J. F. Knott, Fracture 1977, vol . 1, ICF4, Waterloo, Canada, June,

1977, p. 61.

D. A. Curry and J. F. Knott, Metal Science, 10, 1976, p. 1.

D. A. Curry, Nature, 276, 1978, p. 50.

N. S. Stoloff, Fracture, An Advanced Treatise, vol. 6, edited by

H. Lebowitz, Academic Press, New York, 1969, p. 2.

J. F. Knott and A. H. Cottrell, JISI, March, 1963, p. 249.

166
[29J D. A. Curry and J. F. Knott, Metal Science, 13, 1979, p. 341.

[30] C. J. McMahan, Jr. and M. Cohen, Acta Met., 13, 1965, p. 591.

[31] J. F. Knott, JISI, 204, 1966, p. 104.

[32] T. R. Wilshaw, C. A. Rau, and A. S. Tetelman, Eng. Frac. Mech., 1,

1968, p. 191.

[33] J. R. Griffiths, and D. R. J. Owen, J. Mech. Phys. Solids, 19,

1979, p. 419.

[34] A. H. Cottrell, Trans. AIMME, 212, 1958, p. 192.

[35] E. Smith, Proceedings of the Conference on "The Physical Basis of

Yield and Fracture," Inst, of Physics and Phys Soc., 1966, p. 36.

[36] R. E. Dolby and J. F. Knott, JISI, 210, 1972, p. 857.

[37] T. C. Lindley, G. Gates, and C. E. Richards, Acta Met., 18, 1970,

p. 1127.

[38] R. 0. Ritchie, J. F. Knott, and J. R. Rice, J. Mech. Phys. Solids,

21, 1973, p. 395.

[39] D. A. Curry, Metal Science, 14, 1980, p. 78.

[40] A. G. Evans and J. W. Hutchinson, to be published.

[41] A. R. Rosenfield and D. K. Shetty, Eng. Fract. Mech, 17, 1983,

p. 461.

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the ASTM Symposium on User's Experimence with Elastic-Plastic

Fracture Mechanics, Louisville, KY, April 1983.

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L44] D. A. Curry and P. L. Pratt, Mat. Science Eng. 37, 1979, p. 223.

167
[45] C. D. Beachem and G. R. Yoder, Met. Trans. 4, 1973, p. 1145.

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Harbor, FL, November 1980

[47] M. G. Dawes, ASTM STP 668, 1979, p. 307.

[48] A. B. Stuber, Ph.D. Thesis, University of Kansas, 1980.

[49] J. D. Landes, Int. J. Fract., 17, 1981, p. R47.

[50] A. Penelon, M. N. Bassim, and J. M. Dorlot, ASTM STP 677, 1979,

p. 449.

[51] I. Milne, Mat. Sci. Eng., 30, 1977, p. 243.

[52] G. G. Chell and G. M. Spink, Eng. Frac. Mech., 9, 1977, p. 101.

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International Symposium on Elastic-Plastic Fracture Mechanics,

Philadelphia, PA, October 1981.

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17, 1981, p 83.

[57] G. G. Chell and A. Davidson, Mat. Sci. Eng., 24, 1976, p. 45.

[58] G. G. Chell and R. S. Gates, Int. J. Fract., 14 (2), 1978, p. 223.

[59] P. M. S. T. deCastro, J. Spurrier, and P. Hancock, ASTM STP 677,

1979, p. 486.

[60] J. D. Landes and D. H. Shaffer, ASTM STP 632, 1980, p. 368.

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p 107.

168
L62] R. A. Hunt ard L. N. McCartney, Int. J. Fract., 15, 1979, p. 36

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Fract., 18, 1982, p. 253.

[64] J. M . Barsor, Eng. Fract. Mech., 7, 1975, p. 605.

[65] B. Marandet ard G. Sa^z, ASTM S~P 631, 1977, p. 72.

[66] J. K. Barsor and S. 7. Rolfe, ASTM S”P 466, 1970, p 181.

[67] R. H. Sailors and H. T. Corten, ASTM S7P 514, 1972, p. 164.

[68J J. F. Sovak, J. Test. Eval . , 10, 1982, p. 102.

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217/1983, June 1983.

[70] W. Wei bull , J . Appl . Mech., 18, 1953.

[71] M. Saka, T. Shoji, h. Takahashi , ard H. Abe, J. Mech. Prys .

Solids, 30, 1982, p. 209.

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[73] L. P. Harrop, Int. J. Fract., 16, 1980, p. R199.

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L75] Y. Inaiand T. Matake, Eng. Fract. Mech., 16, 1982, p. 659.

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Presented at the ASTM Secc r c I r te'* r ati

r a" Sy~ccs'; J

"' cr E'asticPlastic Fracture Mechanics, Philadelphia, PA, October 1981.

[77] M. G. Dav.es, 7

n.e welding Institute Research 5 J ".eti r

, 7, 1976,

p. 185.

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Fract., 20, 1982, p. R3.

169

IO
[79] J.D.G. Sumpter and C. E. Turner, ASTM STP 601, 1976, p. 3.

[80] J. R. Rice, P. C. Paris and J. G. Merkle, ASTM STP 536, 1973,

p. 231.

[81] G. E. Dieter, Mechanical Metallurgy , McGraw Hill, New York, 1976.

[82] D. M. Tracey, Trans. ASME, 98, 1976, p. 146.

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p. 579.

[84] J. F. Knott, Metal Seicne, 14, 1980, p. 327.

[85] 0. A. Onyewuenyi and J. P. Hirth, Metall. Trans., 13, 1982,

p. 2209.

[86] R. 0. Ritchie, R. F. Smith, and J. F. Knott, Metal Science, 9,

1975, p. 485.

L87] 0. L. Towers, Welding Institute Report 136/1981, March 1981.

170
7. APPENDIX I:

ADVANCES IN FRACTURE TOUGHNESS TEST METHODS

New developments and refinements in fracture toughness test

methods which resulted from this investigation are described below.

These results, although important, were not included in the main body of

this report because they are not part of the central theme of this

dissertation.

7.1 The Rotational Factor

The rotational factor, r , is defined as the distance from the

P hinge point (in an SENB specimen) divided by the ligament length. The

rotational factor was previously defined in equation (31) where r

p is

expressed as a function of specimen dimensions and the plastic

components of mouth-opening (V ) and load-line (q ) displacements [57]:

1 V nW Pn

r

n

= L C(l—E-) - (a+z)] (31)

p W-a q

p 16W

The above equation was derived assuming the SENB specimen deforms in

pure bending about a hinge point; the specimen halves are assumed to

remain rigid.

The rotational factor was measured for five geometries of ABS EH36

steel SENB specimens at various temperatures. Figure 71 shows that r

p

171
ROTATIONAL

FACTOR

(r.

0.70

0.60-

O A O

0.50

o B = 0.5W = 12.7mm, a/W 0.2

0.40-

0.30 L_

-120

o B = W= 25.4mm, a/W 0.2

B=1.5W = 38.1mm, a/W 0.29

a B = W= 25.4mm, a/W 0.52

v B = W = 25.4mm, a/W 0.75

I I I -80 -40 0 40

TEMPERATURE, °C

Figure 71. Plastic rotational factor as a function of SENB

specimen geometry and tempterature for ABS grade EH36

steel

172
is insensitive to geometry and test temperature. The near value of the

data in Figure 6a is 0.522; the standard deviation is 0.030.

Equation (64) can be used to determine the sensitivity of C70D

measurements to variations in r^ [57]:

d( sp/Vp) _ (a+z) (W-a) (64)

dr Lr (K-a)+a+z 12 p P

Using r =0.5, W=25.4 mm, a=12.7 mm and z=1.3 mm, the above derivative is

equal to 0.43. A variation in r^ of 0.030 (1 standard deviation)

corresponds to an error in the 6p measurement of approximately 4

percent. Therefore, CT0D calculations are not highly sensitive to r„

variations

7.2 Detecting the Onset of "Tearing

During a fracture test with an SENB specimen the load-line

displacement (q) was plotted continuously against the crack

mouth-opening displacement (V). After net-section yield the a versus v

plot is a nearly straight line. However, as the crack grows this line

gradually decreases in slope because the center of rotation moves during

crack growth. Figure 72 shows a plot of the first derivative of q with

respect to V. The behavior at the far left of this plot represents the

transition from elastic to plastic deformation. During plastic

deformation the first derivative remains relatively constant an: then

173
1.5

1.4

>

TD

O’

o

1.0

Vv/^vw -

\

F

Vj =1.48 mm

— B= 1.5W= 38.1 mm

a/W = 0.29

T = 25°C

1 1 1 1 0 1.0 2.0 3.0 4.0 5.0

MOUTH OPENING DISPLACEMENT, mm

Figure 72. Derivative of q with respect to V. A sharp drop in the

first derivative generally indicates tearing.

174
increases sharply. At V = 1.48 mm there is a sharp drop in the first

derivative. This is taken as the point of incipient tearing. This

behavior is characteristic of fracture tests where tearing was observed.

Observation of fracture surfaces of specimens that fractured prior to

and immediately following the onset of tearing and the corresponding

derivative plots indicate that the sharp drop in the first derivative

coincides with incipient tearing. At higher displacements the curve has

a zig-zag shape. This is believed to be associated with successive

increments of crack growth.

Figure 72 is typical of the first derivative plots from fracture

tests in which tearing was observed. The spike in the curve, which was

taken as the point of incipient tearing, is slighly more pronounced than

the other spikes. Often the initiation point is ill defined because of

the uncertainty of which spike corresponds to the onset of stable crack

growth.

7.3 Estimation of J from CMOD

For deep-notched SENB specimens the J-integral is usually estimated

from equation (32)

175
where U is the total area under the load versus load-line displacement

curve. The value of J can also be estimated from the load versus

mouth opening displacement curve using equation (33):

J

y

Z 2U — n

+ P

E' B(W-a)

W

(W-a)+a+z ) (33)

where is the plastic component of the area under the P/V curve.

Equation (33) is based on the Sumpter and Turner [79] equation, although

they approximated the area by

where P^ is the limit load.

The J-integral has been calculated for a number of tests using

equations (32) and (33) and the agreement is very good. Figure 73 shows

a comparison of estimates from the two equations. The data represent a

single specimen at various displacements. The difference between the

two J estimates for this particular specimen range from 0.5% to 1.5%.

The value of r^ used in equation (33) to generate Figure 73 was

measured from the same specimen using equation (31). The excellent

agreement between equations (32) and (33) as shown in Figure 73 is

evidence that the simple hinge mechanism is an adequate model to

describe the plastic deformation of an SENB specimen. Figure 73 also

176
J

(from

q

meas),

N

-

mm

Figure 73. Comparison of J estimates from equations (32) and (33).

177
shows that the J-integral can be accurately measured from the

mouth-opening displacement if r^ is known. Thus, it is possible to

measure both J and CTOD from an SENB specimen with a single clip gage.

7.4 Relationships Between J and CTOD

Under conditions of small-scale yielding the relationship between J and

CTOD can be estimated by:

J = m o

Q

6 (65)

where m = 1 for plane stress and m = 2 for plane strain [47]. The value

of m for large-scale yielding should lie between 1.0 and 2.0.

The plastic term in equation (33) is similar to the equation for

the plastic CTOD:

6 P

r

p (w- a)vp

r (W-a)+a+z

P

( 66 )

From equations (33) and (66) one can obtain a simple equation for the

ratio of the plastic J to the plastic CTOD

2 U nW

9 . V Br W-a 2 P P

(67)

178
Equation (67) has been incorporated into a computer program which

plots Jp/6p as a function of mouth-opening displacement. A typical plot

is shown in Figure 74. The ratio Jp/6p increases with displacement

because of work hardening. The work hardening can be accounted for by

replacing the yield stress in equation (65) with a nominal flow stress:

J = m Or-, 6 p p flow p

The nominal flow stress can be estimated by

y

where P is the average load defined as

( 68 )

(69)

and Py

P = Hi

Vp

is the load at yield defined previously in equation (35):

p

= Lo (W-a) 2 B

y

(70)

(35)

Combining equations (35) and ( 67 ) - ( 70) yields the following relationship

for m . P

m

P

(71)

For the ABS grade EH36 steel, r

p s0.5; therefore, m

p =L (the notch

constraint factor). Thus, the relationship between plastic components

179
700 r

400 ' 1 1 1 1 0 1.0 2.0 3.0 4.0 5.0

MOUTH-OPENING DISPLACEMENT, mm

Figure 74. The ratio of the plastic components of J and CTOD as

a function of displacement.

180
of J and CTOD (eq. 69) depends on the geometrical constraint of the

specimen and the flow properties of the material.

7.5 The Eta Factor

A more general form of equation (32) is:

i _ nU

J

where n = 2 for deep notched SENB specimens,

divided into elastic and plastic components

(72)

The above equation can be

[79]:

J n U

e e n U

P P B(W-a) B(W-a)

n U

B W-a

(73)

The elastic eta factor, n g5 can be derived from the elastic compliance

and stress intensity coefficient. The solid line in Figure 75 is a plot

of n

g versus notch depth [87].

Since J is defined as the negative of the spatial derivative of

work, the plastic eta factor, n , and the over-all eta factor, n

Q

, can

be computed as follows:

J

n

o

U B(W-a)

-1 dU

B da (74)

181
oa

00

o

<0

o

o

CM

o

o

182

a/W

Figure

75.

The

overall

eta

factor

(n

)

asa

function

of

a/W

and

displacement

for

SENB

specimens

of

ABS

grade

EH36

steel.

The

elastic

eta

curve

[84]

is

superimposed

for

comparison.
hence

(W-a) dU

n o U da (75)

A series of SENB specimens with notch depths ranging from a/W = 0.19 to

0.75 were tested at room temperature. The area under the load versus loadline displacement curve, U, was measured for each specimen at displacements of

1.0, 1.5, and 2.0 mm. These values of U were then plotted versus crack

length and dll/da was measured for various crack lengths by drawing

tangents to the U versus a curves and computing the slopes. The

over-all eta factor, n

Q

, was then computed as a function of crack

length. The results are plotted in Figure 75. According to Figure 75,

n

Q

is relatively independent of crack length down to a/W = 0.19. It

therefore seems reasonable to use a value of n

= 1. 8-2.0 for all J

measurements from SENB specimens with a/W _> 0.2.

7.6 Crack-Tip Replication

The crack tips of three ABS EH36 steel fracture specimens were

replicated with a plastic impression material. These replicas were made

at various CT0D values by pouring the impression material into the crack

mouth. When the impression material hardened the replica was removed

from the crack and later sectioned. The crack-tip opening displacement

183
was measured directly by placing each sectioned replica under a

microscope equipped with a stage micrometer and a measuring eyepiece.

Measured and computed values of CTOD are compared in Table 11. The

agreement is reasonably good although there are discrepancies at high

CTOD values. The computed CTOD is defined at the original crack tip;

when significant blunting and tearing has occurred it is difficult to

determine the location of the original crack tip. This might account

for the differences between computed and measured high CTOD values.

184
8. APPENDIX II

TABULATED DATA

185
Table

4.

Tensile

Properties

of

the

ABS

Grade

EH36

Steel c P O fl C T- OJ

OJ 4-> £- VO CO CO ID VO o o cn CM CTi a U C s- 13 VO O O'! o r— r— *3" CO <X) VO

QJ T3

C CM VO VO VO p«» p-» p«» p^ PO. QJ

C£L C

-M

O

C •!- 0J 4-> U 03 VO 00 LO cn

i- cn co VO CM LO

OJ c CO CO *3“ Q- O

00 LO CM <— p^ p-. LO

CM o Ol oo

CO *3“ CO CO

IO 0J CL

L. S CO CO CM cn

4-> f—=. p*-. cn o U If) r— CM CM CM *3“ 03 </) S- OJ 1 1 1 r~

U. i.

r^ 00 co VO <Ti CO

CM CO o r—

CM r— CM CM CO CO r— I

r— 1

tr— r— r—

go

OJ - r— to I- CL

<S) z: c —<U +J

<11 cn

+j c

fO OJ E i-

•r- +J

+J l/)

cc CO ^3- CM co cn CM LO CO cn

oo 00 co r^ VO r— cn VO CO cn (T) oo C'. VO VO VO LO LO LO LO <3-

a a: r— o_

a; s:

>- o LO CO cn cn CTi p-» 00 CO VO LO

CO co 00 CM CM LD r— co VO VO CM CM

s- to VO VO LO LO «3“ CO CO CO CO CO

oj oj 5 s- o +-> _j oo

-a ' f— 03

<D CL

oj c

CL ‘i— CL O

=0 CL

CO 00 00 cn p^ oo p^ CO «3“ 1 o

'd" VO t— cn p-~ o r— P'* CO CO co VO VO LO *3- CO CO CO

CJo

00

QJ • CL

VO

cn r^

O Ol CVI ^ VO CO r— O o

00 LD I I

in s in i/i CO I— CM OJ I I c

QJ

•i—

O

a z:

OJCL oo

co co ta- rn go vo CM CM

186
Table

5.

Tensile

Properties

of

the

Commercially

Pure

Iron

4-> O fO C *r— QJ

CD --> S- O O <C

=3 1TD C

CL <D -r- CC

cMOOOo^j-cMoocM^j-LOLOtoo'.r-'.

LO SN 03 C000 C00300 O)

o M •>- C +J

at <o o cn

i. c

<u o

CL rLU oooto^^ocooootoLotor-^ CVJ CM

re 03 CL u s:

+-> *

to *

CO *

LO «d" *o 0^ CO C\1 0^ oo OO o

<_> to CO >3- CM LO O CO o LO CO CO *53" LO) O'! 03 1/3 to to to oo LO o o r— r— r— OO Oo O o $- 03 1— 1— i— r— r— i— r—

+jto

a)

•i- 03

to CL C 3E

aj —

.c: 03 +J 1 1 1 to 1 CM r-. oo CO CO CO 03

4-> O) 1 1 1 CO 1 O CO CO co LO CM (

co

03 C 1 1 1 LO 1 LO <3- oo oo OO oo CM E <u

•I- L4-> 4-> i— t/o

03 CL

ai +j

S-

+-> oo

•I- oo LO 1 1 00 CM CO r— LO to to >- c LO | 1 'd' CM LO LO CM OO OO to r—

03 to 1 1 LO LO <3

- *3

" OO OO CM CM

+

*=3

- to +

co

oo

c_> o

+-> to • (13 ClE

03

LO to O O OO OO CM O CM <naor^io«3-«3-oocMi

CM CM

cr> o-.

i i

oo oo lo

LO OO CM

I I

c

03E • •r- o

CJ z03Q. oo

to CO cm oo to co O CM

187

Cleavage

fractures

+

0.2

percent

offset

yield

strength
Table 6. Charpy V-Notch Impact Data for ABS Grade EH36 Steel

Specimen No. Temp (°C)

Absorbed

Energy (J)

Lateral

Expansion (mm)

Percent

Shear

4 -190 1 0.041 0

5 -125 4 0.055 0

6 -95 11 0.145 0

14 -93 106 1 .565 10

15 -85 22 0.345 0

13 -82 323* 1 .800 100

11 -80 9 0.170 0

17 -76 20 0.342 0

16 -75 225 2.395 55

19 -75 355* 1 .483 100

20 -75 41 0.186 0

10 -73 31 5* + 2.293 100

12 -73 315* 1 .843 100

18 -71 233 2.264 58

7 -70 57 0.859 3

9 -63 334* 1 .890 100

8 -49 323* 1 .630 100

3 0 355* + 2.285 100

1 25 336*

+ 2.500 100

2 25 355*

+ 2.220 100

*Exceeds 80% of the full-scale energy

+Specimen did not fracture completely

188
f—

• LO

*—

r^. 03 oo 03 LO o f-H f-H f-H rH r-~. LO LO *3" r— rH CO o 03 CO LO 03 CM c- 03 CO *3- 03 1 CM CM CO CM *3- 03 CM LO CO r-H CM u E

•r— £ il ll II ii II II II II n II II II II ii II f>

•I- z o u o o o O U U 3 3 .p_ 3 3

i_ —

o o o o o ^3 “3 ,-3 ^3 l-3 ^3 ~3 ^3

QJ c_> c a>

CJ 4-> > OO

a> to to

ro c in O Ll'

to O0 o f“H o r-«. 00 LO '3' CM CO O 4-> cr ^

o on o LO CM o o LO O CO f-H r-H o «3" LO

to <r r- E o o t-H CM f-H CO LO *3- LO CO *3- CO LO 03

aj — 03 E

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Table 7f. B = 3W = 76.2 mm

Specimen No.

Test

Temp. (°C) a/W

Critical

CTOD (mm)

Critical

JCN-mm”

1

)

F-2 -110 0.506 0.108 86

F-5 -105 0.519 0.335 260

F-l -101 0.542 0.154 118

F-8 -97 0.535 0.423 320

F-6 -95 0.502 0.200 120

F-3 -93 0.522 0.120 88

F-7 -86 0.507 0.364 250

F-4 -85 0.520

0.800*

* 626

All fractures were by cleavage

* Cleavage preceded by stable crack growth

194
Table 7g. B = 1.60W = 25.4 mm

Specimen No.

Test

Temp. (°C) a/W

Critical

CTOD (mm)

Critical

J ( N• mm"

1

)

G-6 -123 0.215 0.063 52

G-5 -116 0.232 0.572* 433*

G-7 -114 0.206 0.386 285

G-4 -110 0.214 0.094 na

G-8 -105 0.258 0.380 277

G-l -103 0.228 0.046 38

G-3 -95 0.250 0.646* 470

G-2 -87 0.215 0.437 290

All fractures were by cleavage

* Cleavage preceded by stable crack growth

195
Table 8. Summary of Fracture Toughness Tests on Three

Geometries of SENT Specimens (ABS EH36 Steel)

W = 25.4 mm

Specimen No.

Test

Temp. (°C) a/W B/W

Critical

CT0D (mm)

Critical

J ( N • mm"

1

)

H-4 -133 0.203 1 0.050 na H-l -123 0.246 1 0.184 94

H-2 -115 0.235 1 0.184 82

H-3 -106 0.217 1 0.503* 282

H-5 -89 0.203 1 0.630* 366

1-4 -120 0.527 1 0.208 234

1-1 -111 0.544 1 0.101 58

1-6 -110 0.532 1 0.370 266

1-3 -101 0.534 1 0.540* 444

1-2 -96 0.532 1 0.370 348

1-5 -84 0.533 1 0.666* 521

L-2 -120 0.540 3 0.240 153

L-l -105 0.537 3 0.374 391

L-4 -100 0.522 3 0.418 240

L-5 -92 0.533 3 0.588 242

L-3 -83 0.521 3 0.706 551

All fractures were by cleavage

* Cleavage preceded by stable- crack growth

196
Table 9. Summary of Fracture Toughness Tests on Two

Geometries of Pure Iron SENB Specimens

W = 25.4 mm

Specimen No.

Test

Temp. (°C) a/W B/W

Critical

CT0D (mm)

Critical

J ( N • mm’

1

)

J-4 -93 0.223 1 0.010 6.6

J-5 -84 0.216 1 0.092 45

J-6 -79 0.229 1 0.217 115

J-9 -76 0.228 1 0.199 97

J-3 -76 0.200 1 0.438 209

J-7 -72 0.230 1 0.540 288

J-8 -69 0.201 1 0.185 85

K-8 -90 0.197 2 0.029 13

K-7 -84 0.187 2 0.046 20

K

-74 0.207 2 0.140 70

K-9 -69 0.195 2 0.426 209

K-6 -67 0.187 2 0.628 310

K-2 -63 0.205 2 0.159 68

K-4 -58 0.222 2 0.308 136

All fractures were by cleavage

197
Table

10.

Constraint

Relaxation

Properties

of

ABS

Grade

EH36

Steel

Fracture

Specimens

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198
Table 11. Comparison of Computed CTOD Values with Crack-Tip

Replica CTOD Measurements (T = 25°C, B = W = 25.4 mm)

Table 11a. SENB Specimen B-17, a/W = 0.226

CTOD (mm)

Replica No. Measured Computed From Eqn. (30)

1 0.250 0.297

2 0.540 0.547

3 0.400 1.041

Table lib. SENB Specimen B- 17, a/W = 0.550

CTOD (mm)

Replica No. Measured Computed from Eqn. (30)

4 0.230 0.238

5 0.500 0.490

6 0.760 0.774

Table 11c. SENT Specimen H-6, a/W = 0.222

CTOD (mm)

Replica No. Measured Computed from Fig. 19

7 0.290 0.264

8 0.495 0.563

9 0.850 1.085

199
NBS-1T4A (REV. 2-8C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 8A-3001

2. Performing Organ. Report No. 3. Publication Date

May 1984

4. TITLE AND SUBTITLE

Effect of Crack-Tip Region Constraint on Fracture in the Ductile-toBrittle Transition

5. AUTHOR(S)

T. L. Anderson

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

U.S. Department of Interior, Minerals Management Service

12203 Sunrise Valley Dr.

Reston, VA 22091

10. SUPPLEMENTARY NOTES

Q2) Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT ( A 200-word or less factual summary of most significant information. If document includes a significant

bi bl iography or literature survey, mention it here) The effect of geometry on fracture toughness of steel in the ductil e-to-brittl

transition region has been studied. The critical crack-tip opening displacement

(CTOD) and the critical J-integral have been measured as a function of temperature

for ten fracture specimen configurations of ABS grade EH36 steel. In addition,

two specimen geometries of commercially pure iron were tested. Thicker specimens

tend to promote a higher degree of triaxiality near the crack-tip, thereby elevating

the flow stress and making it easier to reach the cleavage stress. This causes a shift in the ductil e-to-brittl e transition to higher temperatures. Decreasing the

uncracked ligament length of bend specimens also tends to shift the transition to

higher temperatures. Changing the loading conditions from bending to tension tends

to shift the transition to lower temperatures when the ligament is relatively short.

When the ligament length is large the transition-region fracture behavior of a bend speci- men approaches that of a tension specimen with a similar geometry. A technique

was developed to experimental ly measure crack-tip constraint. Constraint decreased

with crack blunting. This relaxation in constraint was modeled by a simple spring

analog. The model was used to predict ductile-to-brittle transition curves for

hypothetical structures. Some of the applications and limitations of the model are discussed

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) crack-tip opening displacement; crack-tip constraint; ductile-to-brittle; transition;

elastic-plastic fracture; J-integral; mechanical properties; structural steels; toughness.

13. AVAILABILITY

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[ | Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

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PRINTED PAGES

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15. Price

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