Creep crack growth in 12CrMoV steel at 838 K I: Behaviour at a constant load

Materials Science and Engineering, 82 (1986) 59-76

59

Creep Crack Growth in 1/2Cr-Mo-V Steel at 8 3 8 K I: B e h a v i o u r at a Constant Load G. J. NEATE

Scientific Services Department, Central Electricity Generating Board, Midlands Region, Ratcliffe-on-Soar, Nottingham NG11 OEE (Gt. Britain) (Received August 5, 1985;in revised form December 2, 1985)

ABSTRACT

A n investigation has been conducted o f the p h e n o m e n o n o f creep crack growth in ~ Cr12 M 0 - 4i V steel (where the composition is in approximate weight per cent) at 838 K in a range o f material conditions representative o f the extremes likely to be encountered in p o w e r plant components. To test the universality o f any correlations obtained, tests were performed on a n u m b e r o f specimen types with the size and the thickness as variables. In each o f the materials investigated, the initiation o f a creep crack at a notch occurred by a process o f local damage accumulation and ductility exhaustion in a region ahead o f it. The crack growth rates were f o u n d to be well correlated by the C* parameter; the stress intensity factor did n o t provide correlation even in the lowest ductility materials. However, the C* correlations were f o u n d to be dep e n d e n t on both the specimen thickness and the specimen geometry, these effects arising from the influence o f the stress state developed ahead o f a crack on material ductility and the effects o f geometrical constraint Crack growth in the materials with bainitic microstructures occurred whilst material at the crack tip was undergoing primary deformation so that strain rates were considerably greater than those indicated by a steady state creep law.

1. INTRODUCTION

The phenomenon of the growth of cracks in components subject to loading in the creep range has received much attention in recent years. This interest has been stimulated by the requirement to develop methods for predicting the safe working life of components which 0025-5416/86/$3.50

must be presumed to enter service containing defects of a size below that resolvable by the non-destructive inspection technique used or which develop cracking during operation. In power-generating plant, this latter occurrence is not an uncommon circumstance and, given the often high cost of replacement components and long delivery times, there is considerable economic incentive to develop life prediction techniques. A number of reviews of the subject area have been produced in recent years [1-4] and hence only a resum~ of the developments made in the understanding of the factors governing the growth of the creep cracks will be given here. Much of the early work was experimentally based and a number of parameters were suggested as being useful in correlating the data obtained. In summary, under creep brittle conditions (low material creep ductility and high geometrical constraint) the stress intensity factor K was found to be reasonably successful in providing data correlation [5, 6] whereas parameters such as net section stress [7] and rate of change in crackopening displacement [8] appeared to be more appropriate in the creep ductile regime. Under these latter conditions, it was also found that the failure time of the component could be adequately predicted via the reference stress using uniaxial rupture data [9]. More recently, the strain-rate-based C* parameter has been suggested as a useful correlating parameter [10, 11] where 1 dO C* -

Bda

(1)

B is the specimen thickness and dO/da the rate of change in strain energy release rate per increment of crack length. The usefulness of this parameter has subsequently been well © Elsevier Sequoia/Printed in The Netherlands

60 demonstrated by several workers for a wide variety of materials [12-14]. Clarification of the circumstances under which the various parameters are expected to be applicable has recently been provided by theoretical treatments to elucidate the stress and strain rate fields at the tip of a crack in a creeping material [15-17]. These show that, for a material obeying the creep law ~ = A a n, K is expected to describe the near-tip stress field (and hence to be the appropriate parameter for correlating creep crack growth rate data) when the elastic components are dominant and when n = 1-3, whereas C* will be the relevant parameter when n ~ 4 and creep strains at the crack tip are very much greater than the elastic strains. The present investigation was undertaken to determine the parameter most appropriate for describing creep crack growth rates in Cr-~ Mo-~V steel (where the composition is in approximate weight per cent), a material widely used in generating plant components such as headers, steam pipes, steam chests and turbine casings. To investigate any geometry or material property dependence on the correlation obtained, tests were performed on a number of test piece geometries with the material in a range of metallurgical conditions representing the extremes encountered in component bodies and in the heat~affected zones of welds. In the present paper the data obtained from tests performed under static load conditions are presented; in a companion paper, Part II [18], the data obtained under conditions of displacement-controlled loading are discussed.

2. EXPERIMENTALDETAILS Material with a coarse-grained bainitic microstructure, typical of that found in weld heat-affected zones, was obtained by heat treating blanks cut from an unused section of a main steam pipe for ~_h at 1523 K, followed by oil quenching. The average grain size and the Vickers hardness of this material were 250 pm and 250 HV respectively. To provide material representative of that in a fully tempered heat-affected zone, some blanks were tempered for 12 h at 973 K, giving a Vickers hardness of 230 HV. Representative parent material (grain size, 30 #m; Vickers hardness,

153 HV) was obtained from a hot-rolled normalized-and-tempered (for 3 h at 1223-1273 K plus 3 h at 953-993 K) billet. The chemical compositions of the materials are given in Table 1 and the uniaxial creep and rupture properties of the three material conditions investigated (designated CGB, CGBT and NT) are shown in Figs. 1-4. The specimen ~eometries used to determine creep crack growth rates were compact tension, single-edge-notched tension and centrecracked plate; the details of the specimen dimensions are given in Table 2. In all cases the final portion (4 mm minimum) of the notch was produced by spark machining using a wire 0.25 mm in diameter. All testing was carried out at 838 K using dead-loaded or screwdriven machines operating under load control. The crack length was monitored continuously throughout each test using a d.c. potential drop technique, and the specimen displacements across the notch were measured using a capacitance crack-opening displacement gauge [19] mounted on the front face (compact tension, B >/5 mm), edge face (singleedge-notched tension) or load line (centre cracked plate) of the specimens. The majority of tests were interrupted before failure to allow metallography to be done on the samples.

3. RESULTS

3.1. Coarse-grained bainitic untempered material ( CGB) A typical record of the variation with time of crack length and specimen displacement for a compact tension specimen is shown in Fig. 5. Crack initiation, as indicated by an increase in the potential drop signal, occurred soon after loading (Table 3) whilst the specimens were undergoing primary deformation. Cracktip-opening displacements at this stage were in the range 0-13 pm. These values were calculated on the assumption of rigid rotation about a hinge point midway across the ligament but, since this condition was probably not approached, the actual crack-opening displacements are likely to have been considerably smaller. The indicated crack growth increments up to the primary-to-tertiary displacement rate transition were typically in the range 1-2 nun

61 TABLE 1 Chemical compositions of materials A m o u n t (wt.%) o f the following elements

Steam pipe Billet

0"3,

C

Cr

Mo

V

Mn

Si

Ni

Cu

P

S

0.13 0.10

0.45 0.31

0.15 0.60

0.22 0.26

0.44 0.67

0.31 0.22

0.21 0.04

0.19 0.02

0.011 0.019

0.012 0.020

I

I

I

I

I

I

I

I

30

=G B'I"

2O

O',; 0

o

c

9. O')

a. u

Q.

L)

O'11~

0 L--------'~ 0

I0 u

---~

~

I

I

I

I

I

I

i00

200

300

400

soo

600

700

800

0

900

Time, h

Fig. 1. Typical uniaxial curves (material CGB, 175 MPa; material CBGT, 250 MPa; material NT, 150 MPa).

but were as great as 6.5 mm for the large compact tension specimens. Metallographic and fractographic evidence indicated that this stage o f growth could in fact be regarded as an initiation period in that, during this time, disseminated grain b o u n d a r y microdamage accumulated ahead o f the notch which eventually linked with itself and with the notch to form a macroscopic creep crack. This point was reached after life fractions of 20%-70% (Table 3) and the crack-opening displacements were in the range 1 1 - 5 0 pm. No obvious trend with specimen thickness could be discerned in these displacements, although there was some tendency for them to increase with decreasing applied load (Fig. 6).

Subsequent growth of this crack occurred in an intergranular m o d e by a similar process of linking with damage formed on grain boundaries ahead of the tip (Fig. 7). However, complete linkage o f this microdamage did not occur during either the initiation or the growth stages so that bridges of material joining b o t h crack surfaces were l e f t behind the advancing front. The effect of these bridges was to prevent the full opening of the crack under the applied load so that only a small change in elastic compliance (less than that expected theoretically [20]) occurred as growth proceeded (Fig. 8). Crack growth occurred on a b o w e d front such that crack depths at midthickness were generally 2 - 3 mm greater than

62

400

I

'

'

'

' ....

I

'

'

'

' ....

I

i

'

'

' ....

I

I

I

!

i

I

,

,

300

200--

lOOioi

I

10 2

I0 3

I

I

I

i

iOs

10 4

Failure Time ; h

Fig. 2. Uniaxial creep rupture properties: o, material CGB; t), material CGBT; e, material NT.

10 2

I m

J B

m

i

117J. ""

m

i0 i m

._= m

m

~

10G,

0

""-"--' 0 --

I

IO-I IOO

--0 I

300

200

400

Stress, MPQ

Fig. 3. Uniaxial ductility data: o, material CGB; ~), material CGBT; o, material NT.

at t h e o u t e r edges, irrespective o f t e s t piece thickness. No m e a s u r a b l e t h r o u g h - t h i c k n e s s c o n t r a c t i o n o c c u r r e d in a n y o f t h e specimens. T h e r u p t u r e d a t a f o r t h e specimens are s h o w n in Fig. 9. T h e plane stress r e f e r e n c e

stresses Ore~ w e r e calculated f r o m t h e relation [21] or~ =

P mBW

(2)

63

where P is the applied load, m the yield ratio for the cracked and plain specimen geometry, B the specimen thickness and W the specimen width. It can be seen that the specimens exhibited marked notch-weakening behaviour with failure times being up to three orders of

E E

5

O'2

_1

E 15 U

,c~o 2&~o

3~o 4~oo 5Goo 6oo0

(b]

25

/_ /

0"3

E 1=

/

E E

5 ~20

D'2

~

o.i

~5

..J

--

/

~r c

0"3

I

Tim¢,h

/

T IO-'~ - -

/

(o)

IO O

//-

10-3

25 E E

io

o

,~

2Go

3~

4Go

5~

6o0

Tir~,h

2

25

.~ IO-6

Icl

I

E E

I )

2 E E

/ E IO-:

--

o

E 15

U

o

I

,o~o IO"

I 200

I00

I 300

2c~oo

i

30oo

Time ~h 400

Stress, MPo

Fig. 4. U n i a x i a l creep p r o p e r t i e s : o, m a t e r i a l CGB; qD,

material CGBT; e, material NT.

Fig. 5. Typical test records for compact tension specimens 20 m m thick: (a) material CGB, oref = 60 MPa; (b) material CGBT, are f = 75 MPa; (c) material NT, Oref =125 MPa.

TABLE 2 Details of specimens

Material condition

Designation

Type

Specimen dimensions Width W

Thickness B

(ram)

(ram)

Initial-crack-lengthto-width ratio ao/W

Coarse-grained bainitic untempered

CGB CGB CGB

Compact tension Compact tension Single-edge-notched tension

40 100 20

1, 2, 5, 20 50 10

0.3 0.3 0.2

Coarse-grained bainitic tempered

CGBT CGBT CGBT

Compact tension Compact tension Single-edge-notched tension

40 100 20

1, 2, 5, 20 50 10

0.3 0.3 0.2

Normalized and tempered

NT NT NT NT

Compact tension Compact tension Compact tension Centre-cracked plate

40 100 200 40

5, 20 50, 100 100 5

0.3 0.3 0.3 0.4

64 TABLE 3

s°t

Crack initiation d a t a

Material

aref

B

(MPa)

(mm)

Life fraction at initiation as indicated by the following Increase in potential drop

,3o ~:~ 2oF 0

Primaryto-tertiary transition

CGB CGB CGB CGB CGB CGB CGB CGB CGB

275 175 175 I00 100 100 100 60 55

5 5 20 2 5 5 20 20 50

0 0.05 0.05 0 -0 0 0.03 0.04

0.21 0.69 0.31 -0.32 0.62 0.43 0.38 0.55

CGBT CGBT CGBT CGBT CGBT CGBT CGBT CGBT CGBT CGBT

300 200 200 150 150 100 100 100 75 60

20 5 20 2 20 5 5 20 20 50

0.29 0.06 0.06 0.03 0.04 0.08 0 0.01 0.12 0

0.29 0.48 0.13 0.67 0.48 0.52 0.59 0.57 0.44 0.45

NT NT NT NT NT NT NT NT NT NT

225 225 175 175 175 125 125 120 120 120

5 20 5 20 100 5 20 50 100 100

0.42 a 0.36 0.26 0.43 0.06 0.23 0.25 0.21 0.30 a 0.11

-----------

(a)

%

_

_

00 Stress, MP¢I

6O

(b) A

~ . 40

o

o

~ 2--.c 20--

.=

"~3

UO--

0

o,

q

260

)0

Stress, MPa 70C

g 6oc ~E ~ ::L5oc

Ic)

O

-~,o 20C IOC

(.3

c

40 A•

,&

'

2&

3oo

Stress ~MI:~

Fig. 6. Crack tip d i s p l a c e m e n t s at t h e p r i m a r y - t o t e r t i a r y d i s p l a c e m e n t t r a n s i t i o n : (a) material CGB (o, B = 5 r a m ; o , B = 20 m m ; A , B = 50 m m ) ; ( b ) material CGBT (/% B = 2 m m ; o, B = 5 m m ; o, B = 20 m m ; A, B = 50 r a m ) ; (c) material NT (0, B = 5 r a m ; o , B = 20 r a m ; A , B = 50, 100 ram).

a U p p e r b o u n d estimate, s p e c i m e n n o t near t o failure.

magnitude smaller than expected from the uniaxial d a t a A dependence of rupture time on specimen geometry was evident but, for a given geometry, no clear effect of specimen thickness was discernible. Similarly, no systematic effect of specimen thickness on crack growth rates was apparent (Fig. 10).

~ 2. Coarse-grained bainitic tempered material (CGBT) Overall, similar behaviour in terms of crack length and specimen displacement was observed as for the untempered material (Fig. 5). An increase in the potential drop signal, indicating the initiation of microcracking, was again detected early in life (Table 3) during

Fig. 7. M i c r o c r a c k i n g a h e a d o f a crack tip in material CGB.

the primary displacement stage. The crack-tipopening displacements at the primary-to-tertiary displacement rate transition were comparable with those found for the untempered

65

60

I

(:l

I

r ....... I

300

I

.......

_ (a)

I

20C

=

.......

•

I

~

.......

I

i

.......

A 00A40

IOC

•

'"

,

rIi

5C

,,,,~ I0 °

I

.......

I

......

X-d~

040 ,,

i

" X ~ x ~ r . .

=-

<3 m

I

I

.......

I01

I

I

.......

I

I02

I

• .......

I0 3

-

ID~ I

I

-

......

[04

105

Failure Time,h

30C

e~ E o U

i

b). . . . . . .

tl

"~'""1

'

....... I

•

'

z~ o AA

P

....... I

....... I

I ......

~ X ~

a~ 2 0 C

g 4O E i5

'

I

x..~

--

x~

•

~INII

Joc

X

-

x~

4AO •

.......

~ 0"1

i0 °

I

IO'

~ .......

I

I .......

to 2

0

D I

= .......

It9

I

t ,,

IO4

IC

Failure Tim¢,h

300

30

IO

t

I

20

...... l

'

....... I

I ....... I

I ....... I

I ....... f

~ ......

c)

t 30

o 200

Crack Length ,mm u

Fig. 8. Compliance curve for compact tension specimens of material CGB: curve a, theoretical curve [ 20 ]; curve b, mean experimental curve.

~ ~ x . .

tO0

I

i

i0 o

. . . . . . .

iO t Failure

i

to 2

I

,

.,,..J

Ic:9

I

, ......

I

=04

I

......

I~

Time ,h

Fig. 9. Rupture data for notched specimens. material and s h o w e d a similar t r e n d w i t h app l i e d load; h o w e v e r , t h e r e was s o m e indicat i o n t h a t t h e c r a c k - o p e n i n g d i s p l a c e m e n t s decreased w i t h increasing s p e c i m e n thickness (Fig. 6). Crack advance again o c c u r r e d b y a process o f linkage o f d a m a g e in t h e f o r m o f grain b o u n d a r y c a v i t a t i o n and m i c r o c r a c k i n g f o r m e d a h e a d o f t h e c r a c k tip (Fig. 11) and t h e phen o m e n o n o f c r a c k bridging was o b s e r v e d as previously. Crack f r o n t s w e r e again b o w e d w i t h t h e d i f f e r e n c e b e t w e e n c r a c k length at mid-thickness a n d at t h e edges varying w i t h s p e c i m e n thickness; in t h e c o m p a c t t e n s i o n specimens this d i f f e r e n c e was t y p i c a l l y 2 - 3 mra f o r t h e samples 5 m m t h i c k and 4 - 5 m m f o r t h e t h i c k e r specimens. H o w e v e r , t h e c r a c k f r o n t profiles in t h e l a t t e r specimens t e n d e d t o b e f l a t t e r o v e r t h e c e n t r a l p o r t i o n , indicating a generally h i g h e r d e g r e e o f c o n s t r a i n t (plane strain) in these t h a n in t h e t h i n n e r specimens. This was n o t so, h o w e v e r , f o r t h e s p e c i m e n 20 m m t h i c k t e s t e d at t h e highest

Symbol

Specimen type

Fig. 9(a) o • z~

Compact tension Compact tension Compact tension

• []

B (ram) 1 2 5

•

Compact tension Compact tension Single-edge-notched tension

X

Uniaxial

Fig. 9(b) o •

Compact tension Compact tension

1 2

A •

Compact tension Compact tension

5 20

[]

Compact tension Single-edge-notched tension Uniaxial

50 10

5 20 50 or 100 5

•

X

20 50 I0

Fig. 9(c) o

Compact tension

•

Compact tension

•

Compact tension

A X

Centre-cracked plate Uniaxial

66 I01

==

I

I

I

I

I

I

I

I

I

I

1

I

i0 °

T,_ .,10 -I

$

~

Id'

10-2

--

10-3_

10 -4 12

I

I

I

J

I

I

I

I

I

I

I

I

13

14

IS

16

17

18

19

20

21

22

23

24

Crock Length

IC~2

.53 25

,turn

Fig. 10. Effect of thickness on crack growth rates in compact tension specimens.

Symbol

Material

B (ram)

oref (MPa)

o

CGB CGB CGB CGBT CGBT CGBT NT NT

1 5 20 1 5 20 5 20

100 100 100 100 100 100 175 175

• • • m

load; in this case, no crack growth occurred at the edges of the specimen, despite the fact t h a t the crack length at mid-thickness reached 14 mm. Overall, the variation in constraint as indicated by the crack f r o n t profile was reflected in the degree of contraction observed in the through-thickness direction. Strong notch-weakening behaviour was again observed (Fig. 9), with specimen rupture times showing a dependence on geometry. However, in contrast with the untempered material, consistent trends were observed for rupture times to decrease and for crack growth rates to increase for a given specimen geometry as the test piece thickness was increased (Figs. 9 and 10).

3.3. Normalized-and-tempered material (NT) In the majority o f tests, no increase in the potential drop signal was detected prior to the primary-to-tertiary transition in displacement rates (Fig. 5). When a change was observed before this point, the variation in the signal with time suggested t h a t the principal cause was developing plasticity at the notch tip. The time at which the primary-to-tertiary transition in displacement rates occurred was therefore taken as corresponding to crack initiation. Using this definition, initiation was f o u n d to occur at life fractions ranging from 6% to 42% with the initiation time (as a proportion of life) tending to decrease with applied load and increase in specimen size (Table 3). Notch

67 little or no growth occurring at the edges of the specimens and appreciable through-thickness contraction was evident on all test pieces. The specimen rupture times agreed well with those expected from uniaxial data, although modest notch weakening was evident at a reference stress of less than 200 MPa. No significant effect o f specimen size or thickness on rupture times was apparent (Fig. 9) and no significant effect of thickness on crack growth rates was observed for a given specimen geometry (Fig. 10).

4. D I S C U S S I O N

4.1. Crack initiation

Fig. 11. Creep cavities ahead of a crack tip in material CGBT.

Fig. 12. Microcracking ahead of a crack tip in material NT.

The initiation of a creep crack at a notch may be viewed as a process of local damage accumulation and ductility exhaustion in a region ahead of it. This view is supported b y direct observation of creep damage ahead of notches prior to formation of a macrocrack, b y a general relationship between the relative magnitudes of notch tip displacements at initiation and material uniaxial ductilities and by the generally similar dependences of these properties on applied load (Figs. 3 and 6). Also, where any effect of increased specimen thickness was observed, this was to reduce initiation displacements (Fig. 6) consistent with the expected decrease in material ductility with increased stress triaxiality at the notch. Notwithstanding the general insensitivity of potential drop techniques to detecting incipien t creep cavitation, it is evident that, for the bainitic materials CGB and CGBT, microcracking occurred at the notches before stress redistribution was complete (Fig. 5). The crack initiation times t i may in these circumstances be estimated from the relation [15] ti--~ Ccn+1

1

( n+__l 2~E2rc~ n K2 /

EnA(n + 1) \2n~n n+l tip displacements at initiation were in the range 8 0 - 6 8 0 pm and little effect of specimen thickness was apparent, except perhaps at the highest stress level (Fig. 6). However, the notch tip displacement did tend to decrease with reducing initial load (Fig. 6). Crack growth occurred in an intergranular m o d e by a process of linkage of the crack tip with damage formed ahead of it (Fig. 12). In all cases, crack fronts were highly b o w e d with

(3)

where e¢ is a critical equivalent strain at a small structural distance rc from the crack tip, E Young's modulus and aa ( ~ 1) a numerical factor. For typical values of K for the present tests and taking e¢ = 0.003 and re = 1 mm, eqn. (3) yields initiation times of about 10 -9 h. These are very much shorter than those observed, b u t the result is not surprising given that eqn. (3) strictly applies to a pre-existing sharp-tipped crack rather than to blunt

68 4 of observed values for the tests where notchstrengthening behaviour was not observed.

notches. Since observed initiation times were nevertheless small (Table 3), the important practical point to be taken from these results is that integrity assessments for components containing defects located in coarse-grained bainitic microstructures should assume that initiation occurs at zero time. For the case when crack initiation is preceded by extensive creep deformation in a specimen, Ainsworth [22] has shown that the initiation time is given by ti

tr(aref)

_2(n+l)

n31/2~

2n 3n+4

6i

O're~2'~n/(n+l) K-2]

4.2. Correlation of crack growth rate data 4.2.1. Criteria for selection of correlating parameters As noted in Section 1, the parameter describing the stress and strain rate field ahead o f a notch or crack in a creeping material has been shown to depend on both the applied loading and the material creep properties. Before correlation of the crack growth rate data obtained in the present investigation with these parameters is attempted, it is useful firstly to consider the criteria that have been proposed for judging which parameter is likely to be applicable in given circumstances. Ainsworth [23] has defined a non-dimensional crack growth rate parameter k given by

(4)

where tr(oref) is the failure time at the reference stress, 6i the notch displacement at initiation, ~ (= ~tr) the M o n k m a n - G r a n t constant and 77 a constant (which equals 0.75 for plane strain and equals 1 for plane stress). For test pieces with notches of initial width 60, 8i in eqn. (2) must be replaced by an effective initiation crack-opening displacement ~ where =

[6inl(n+l)

-

(5)

60n/(n+l)]("+I)/"

-

(~O.ref3 x

-

-

-

(6)

EK2~o

where fi is the crack growth rate, E Young's modulus and eo the strain rate at the reference stress. For a material with a creep index n, the value of )~ reflects the dominance of creep or elastic strains ahead of a crack and hence indicates the likely applicability of the possible

Predicted initiation times for the NT specimens using ~ values appropriate to the applied reference stress as deduced from the uniaxial test data are shown in Fig. 13. It can be seen that the predicted times are within a factor of

10 4

,o~=

.

' ........ I

I ' ' ..... I

I ....... ~ 4 ~ 1

--

•

_

~ °

~ iO2---

/

"'~

•

.e

"E

,o~ ~

,o °

,

,,,,,,I

I

,

,d

,,

....

I

J

,o ~ Predicted

initiation

,

,,

....

I

,o 3

I

,

, ....

ic~

Time , h

Fig. 13. Comparison of observed and predicted crack initiationtimes for material NT: ~, specimens showed notch-strengthening behaviour.

69

stress field parameters in correlating crack growth rates. In general, three regimes of crack growth behaviour are defined as follows: in the first regime, X >> 1, n < 3 and correlation of the rate data by K is expected; in the second regime, ~ ~ 0 . 0 5 - 1 , n > 3 and correlation of the rate data b y C* is expected; in the third regime, k ~< 0.05, n > 3, crack tip events are unimportant, and failure is controlled by the reference stress. Riedel and Rice [15] have calculated a characteristic time tl which defines the transition from elastic- to creep-dominated deformation ahead of a crack. This is given by K 2 ( 1 __ p2)

tl -

one to t w o orders of magnitude is evident. The slopes o f the data lines for the individual tests are reasonably consistent b u t it should be noted that, had the experimental compliance curve of Fig. 8 been used to calculate K values, these lines would have become nearly vertical and no correlation would have been obtained. Given these findings, it is necessary to reexamine the conclusions of Section 4.2.1 as to the applicability of K to correlating the data for these materials. In calculating values of tl from eqn. (7), C* values were estimated via an approximate relation derived by Ainsworth [23] where

(7)

~0K2 C* ~ -

where p is Poisson's ratio. Thus, if tf is the observed failure time of a specimen, the following hold: when t l / t f > 1, correlation of the rate data by K is expected; when tl/t~ < 1, correlation of the rate data b y C* is expected; when tl/t~ ~ 1, there is widespread deformation in the ligament, and failure is controlled b y the reference stress. Values of the creep index n for the three materials investigated and calculated values for X and tl/t~ are given in Table 4. The values of X and tl/t~ indicate that K might hence be expected to correlate the crack growth rate data for the bainitic materials (CGB and CGBT) and C* the data for the normalized-and-tempered material (NT). It is noted, however, that for all materials the creep index n is 4 or greater.

Oref

(n + 1)EC*

4.2. 2. Data correlation The crack growth rate data for materials CGB and CGBT are shown as a function of the nominal stress intensity factor in Fig. 14(a) and Fig. 14(b) respectively. The correlations are n o t particularly good in that scatter in the crack growth rates o f approximately

(8)

It is noted, therefore, that the values calculated for b o t h tl and X are sensitive to the value chosen for ~0. These latter values were obtained by fitting a law of the form

(9)

~ m = Co"

to the uniaxial data, where ~mm is the minim u m creep rate, C a constant and o the applied stress. However, as already noted (Fig. 1), the creep curves for materials CGB and CGBT exhibit pronounced primary stages so that much of the damage giving rise to eventual failure accumulates at strain rates considerably in excess of the minimum. Similarly, therefore, strain rates ahead o f a growing crack in these materials are likely to be higher for any given reference stress than indicated b y eqn. (9). This view is supported by the observation that crack initiation in the notched test pieces occurred while the specimens (and hence the material ahead of the crack tip) were undergoing primary deformation (Fig. 5). Consequently, values o f tl and X will have been considerably underestimated and over-

TABLE 4 Values o f n, X a n d t l / t f Material

CGB CGBT NT

n

~ 4 4-11 7.7-19.5

~

30-720 3-42 1 0 - 5 - 1 0 -3

(theoretical)

tl / Q (experimental)

16-390 0.9-63 4 x 1 0 - 5 - 6 x 10 -3

0.09-0.38 0.01-0.23 --

tl / t f

70

:L

i

I

(a)

i

i

,

~.

i,o,

m

I U

,o-,[-10-31

I

I

i

I

IO 2

I0 r

Nominal

'°~-

(b~

Stress

Intensity

I

> MPo

Factor

.

.

ml12

.

.

__:-

-

ioo -

-~ ~ Io-2 _ _

~

10-30 J"

I

Nominal

l

Stress

Intensity

J

~

,

,

,

,

i02

Factor,MPa m t/2

Fig. 14. Crack growth rates as a function of stress intensity factor (a) for material CGB and (b) for material CGBT.

Symbol

Specimen type

B (ram)

W (mm)

¢

Compact tension Compact tension Compact tension Compact tension Single-edge-notched tension

2 5 20 50 10

40 40 40 100 10

o •

•

estimated respectively. The possibility hence arises that C* is in fact the most appropriate parameter for correlating creep crack growth rate data for these materials. To test this possibility, C* values were obtained from the measured specimen displacement rates using the relation [24]

C* = f(n)o~t ,~LT.

(10)

where f(n) is a function of geometry (which equals 2n/(n + 1) for compact tension speci-

mens, n/(n + 1) for single-edge-notched tension specimens and (n -- 1)/(n + 1) for centrecracked plate specimens), on, t the net section stress and ~LL the deflection rate at the loading line. The crack growth rate data for the two materials are shown as a function of C* in Fig. 15; it can be seen that overall correlation of the data is achieved within a factor of approximately 5, although a distinct separation of the data for the different test piece geometries and thicknesses is apparent, particularly

71 ,d ~ r ....... l (o) ~o2

I ....... I

i ....... ii

....... i

~ ....... i

I ....... i

r ....... i

i .....

U.

L

"T

= ic~

~ to~ rr

o

162

____

t9

tO--~ z

r i ll,,,,J 4 166

-5

16

f ....... J

16

C*,MPa

,o ~ ~

i

.......

I

i .......

I

J ....... I

~ ....... I

J62

i ....... I

o-

i ...... ,Jo°

,#

m h"I

r ....... I

(b) I01 :

/

ij=

~

10 °

/j

rr

IO-I t9

0 io-2

id j~6

I .......

I

io-s

, .......

I

i ....... I l~

id4

i ....... I io"2

I

i

tl,,,,

I

I

i0-I

i

-

i,,,,

i0°

C '~, M p a fn h -I

Fig. 15. C r a c k g r o w t h r a t e s as a f u n c t i o n o f C* (a) f o r m a t e r i a l C G B a n d ( b ) f o r m a t e r i a l CGBT.

Symbol o • •

Specimen type

B (ram)

W (ram)

Compact tension Compact tension Compact tension Compact tension Single-edge-notched tension

2 5 20 50 10

40 40 40 100 10

for the material CGBT. In the latter case, it is also noted that the data line for the most highly loaded compact tension specimen 20 m m thick, rather than forming a continuance with those for the tests on specimens of similar thicknesses, aligns with those for the test pieces 2 and 5 mm thick. This finding implies that the stress states produced in these specimens were similar and is in agreement with the differences in crack front profiles observed in these test pieces. The load and geometry

dependence of the correlations is discussed further in Section 4.2.3. Finally, it can be seen from Table 4 that the values of tl/t~ calculated using the experimentally determined C* values are consistent with the expectation that C* should be the correlating parameter. The crack growth rate data for material NT are shown as a function of C* (calculated from eqn. (10) using measured specimen displacement rates) in Fig. 16. It can be seen that, whilst the slopes of the individual data lines

72 '°°~_

I

.......

I

'

.......

I

.......

I

I

i

.......

I

I

. . . . . .

i ~ ~- -

T=

| -

10_

0

_

_

tO

uE id3 - -

-,, lOld6

,

.......

1 io-S

, ....... 1 id 'i

, ....... 1 id s

C#,MPa

rn

i ....... 1 iO-2

,

.......

iO-J

h"I

Fig. 16. Crack g r o w t h rates as a f u n c t i o n o f C* f o r material NT.

Symbol

Specimen type

o a

Compact tension Compact tension Compact tension

•

Compact

[] •

Compact tension Centre-cracked plate

•

tension

B (ram) 5 20 50

W(mm) 40 40 100

I00

I00

100 5

200 40

are reasonably consistent, overall correlation is n o t particularly good with the scatter in crack growth rate being a factor of a b o u t 20. However, it is apparent that this scatter is a result of shelving of the data produced b y a dependence o f crack growth rate on specimen geometry and thickness and level of applied loading. As in the bainitic materials, crack growth rates tended to increase with the specimen thickness and size with the highest rates being observed in the c o m p a c t tension specimens 50 and 100 m m thick at the lowest applied reference stresses. These observations are also discussed more fully below.

4.2.3. Creep crack growth models The C* parameter has been f o u n d b y a n u m b e r o f workers to provide correlation of crack growth rate data for a wide range of materials [ 1 2 - 1 4 , 25]. The crack growth rate law indicated b y these investigations has the general form da --

dt

=

~C*~

(II)

where da/dt is the crack growth rate, and and ~ are constants for a given material, tern-

perature and applied loading conditions. The value of fl is usually found to be unity or less and for materials obeying a steady state creep law it is expected to be equal to n/(n + 1). As noted previously, the results of the present investigation support the hypothesis that a critical strain must be attained at a notch for the initiation o f a creep crack. Given the observation that crack growth occurs by linkage with the crack of damage formed ahead of it, it is reasonable to assume that this criterion must also be met at the tip of a crack if growth is to be sustained. Models based on this assumption [12, 26, 27] have shown that eqn. (10) may be written in the more explicit general form da dt

-

7C *~ - -

(12)

ee

where 7 is a constant and ec the ductility of the material under the same multiaxial stressing conditions as existing ahead of the crack. The scatter bands encompassing the data for the materials investigated here are shown in Fig. 17. From a comparison of Figs. 3 and 17, it is clear that the present results support the general form of eqn. (12) in that the crack

73

~'o L ~,o' --

J

J

?

id 2 -

,o_,16

I .......

J

"

I I0-e

J

~

i .......

_

.

I Ids

_ f

1

I

. . . . . . .

I

i

.......

id 4

-=

J

~"

I

i .......

10-3

C~, MPa m

I Id 2

I .......

I td'

i .......

I

I ,,--

iO°

Id

g~

Fig. 17. Comparison of crack growth rate data:

, material CGB;--:, material CGBT; ~:--, material NT.

growth rate data tend to converge at low C* values in correspondence to the variation in the uniaxial ductilities with applied stress. It is evident from Figs. 15 and 16 that, rather than C* providing unique correlation of the data for a given material, there is a dependence of crack growth rate on b o t h the specimen thickness and the specimen geometry. Both of these effects may be explained in terms of differences in geometrical constraint and the dependence of material ductility on stress state. Thus an increase in crack growth rate with specimen thickness is expected since a change in stress state ahead o f a notch or crack from plane stress to plane strain (increased triaxiality) will engender a decrease in material ductility. Similarly, a geometry dependence o f crack growth rates is expected from eqn. (12), given that the stress state and constraint developed ahead o f a notch or crack are dependent on specimen geometry and m o d e of loading. A study o f the stress distributions developed ahead of notches in elastic-plastic materials under conditions of small-scale yielding [28] suggests that the degree o f stress triaxiality developed in notched specimens o f different geometries varies in the order compact tension > single-edge-notched tension > centre-cracked plate. The crack growth rates in these geometries at a given C* are hence expected to vary similarly and it can be seen from Figs. 15 and 16 that the present results are in general agreement with this expectation.

4. 3. Application o f data to plant The geometry dependence of the crack growth rate -- C* correlations found for the bainitic materials is n o t great, all the data being contained within a scatter band of about 5 on growth rate. Since some of these data were obtained from reasonably large compact tension specimens (W = 100 mm; B = 50 mm) which are expected to give conditions of high constraint at the crack tip, it is unlikely that growth rates in substantially larger specimens would have been very much greater than those corresponding to the upper b o u n d of the scatter band determined here. It is hence suggested that, for the purposes of defect assessment, a good estimate of the crack growth rate law appropriate to any given material will be obtained simply by applying a suitable correction to the present data as indicated by a comparison of uniaxial ductility data (eqn. (12)). However, given that only a low degree of constraint was apparent in the specimens of the normalized-and-tempered steel, somewhat higher growth rates than measured here might be expected in large components of the same material. The dependence of ductility on stress state for this material can be estimated from the relation [29] e¢ •R

TM - -

(O1/{~)~

(13)

where e ~ and e ~ are the rupture strains under multi and uniaxial loading respectively, al

74 the maximum principal stress, 5 the effective stress and ¢ a constant. On the assumption that o l / ~ varies in the range 2 - 3 for specimens and components and if ¢ = 2 [30, 31], the acceleration factor is estimated to have a value of approximately 2. When defects are assessed in plant, this factor will need to be applied before any adjustment is made to the crack growth rate law on the basis o f a comparison of uniaxial ductilities. In the application of relationships of the form o f eqn. (12) to plant to estimate the growth rates of cracks in components, it is of course necessary that the means be available for estimating C* values. Since, in general, displacement measurements will n o t be available for use in conjunction with expressions of the form of eqn. (10), it will usually be necessary, unless recourse is made to finite element methods, to calculate these values analytically. To assess the general accuracy with which C* values may be calculated, values obtained via eqn. (8) (using e0 values obtained by fitting laws of the form of eqn. (9) to the uniaxial creep rate data) were compared with those determined experimentally (eqn. (10)) for the three materials investigated. It can be seen from Fig. 18 that, for material NT, the calculated C* values were generally greater than the experimental values b y a factor of up to 5. This degree of conservatism is n o t large in practical terms, particularly since greater uncertainty can be expected to arise from lack of knowledge as to the actual creep properties

Id-I

of a material, and this result indicates that eqn. (8) may be used with reasonable confidence in the consideration of defects located in ductile parent materials. This is a useful result since an added attractive feature of eqn. (8) is that it allows C* values to be calculated, at least in instances when the stresses are load controlled, from the readily estimable parameters K and aref. However, in b o t h the bainitic materials, eqn. (8) is seen seriously to underestimate the actual C* values so that some further examination of this result is required. It has been noted previously (Section 3.1) that cracking in materials CGB and CGBT initiated whilst the specimens were undergoing primary deformation. This observation indicates that crack growth was proceeding before redistribution of the stresses ahead of the notches was complete. On the assumption that non-steady state conditions similarly prevail ahead of a growing crack, the crack tip strain rates will be generally greater than expected from eqn. (9) at the reference stress so that eqn. (8) will underestimate C* values. In summary, therefore, the present data indicate that C* values calculated analytically m a y be used with some confidence in conjunction with laws of the form of eqn. (12) to estimate growth rates of cracks in ductile material conditions of C r - M o - V steels. Such a procedure should n o t be used for low ductilit y bainitic materials since the growth rates are likely to be seriously underestimated; it appears that, in these cases, C* needs to be de-

....... I i ....... I i ....... I i ....... I I ....... I I ....... I i ....... I i '

~

io°

~" I d l i

"

o

o

id~

®

-

%®

/ 1()6L

,~,~, iO-9

o

....... I L ....... ,LA'~,,,...] i6 8

,G"~

i~ 6

i ....... II ,d s

....... l i ....... l i ....... l i ....... II id 4

Id 3

Id 2

id'

....... I i ,,,7,,, IO°

IO'

C* (thiixlt.) ~MPa m h-I

Fig. 18. Comparison of theoretical and experimental C* values: O, material CGB; il), material CGBT; e, material NT.

75

,

.......

I

' ....... I

' ....... I

' ....... I

16 '~ _

o °°

Id6 _

167

oo/2/o ° • • •

16 6

i~ ~

164

id ]

16 2

C÷:'(theoret) j M P o m h-u

Fig. 19. Comparison of experimental and theoretical C* values calculated on the assumption of a timehardening creep law (compact tension specimens 20 m m thick of material CGB).

fined in terms of general creep laws which allow the inclusion of primary strain rates. This point is well illustrated for the c o m p a c t tension specimens 20 mm thick of material CGB in Fig. 19 whence it can be seen that much better agreement is obtained between experimental and theoretical C* values when a timehardening rather than a steady state creep law is used.

region ahead of the crack tip and the rate data are well correlated by the C* parameter. (4) Correlations of crack growth rate with C* are dependent on b o t h the specimen thickness and the specimen geometry. These dependences arise through the influence of the stress state developed ahead o f a crack on material ductility and the effects o f geometrical constraint. The results hence support the concept of a unified approach to presenting crack growth rate data in terms of a ductility-modified C* parameter (eqn. (12)). (5) Crack growth in low ductility bainitic materials occurs at crack tip strain rates considerably in excess of those indicated by a steady state creep law. (6) For the purpose of practical assessments, analytical expressions for C* which assume steady state behaviour are likely to yield good estimates of the parameter for defects in normalized-and-tempered material. However, for bainitic materials, these are likely to result in serious underestimates of the parameter and consideration should be given to defining C* in terms of general creep laws which incorporate primary strains.

ACKNOWLEDGMENT

This paper is published b y permission of the Central Electricity Generating Board, Midlands Region, Gt. Britain.

5. CONCLUSIONS REFERENCES

The conclusions drawn from the present investigation of creep crack growth in C r - M o - V steels in material conditions with uniaxial creep ductilities in the range 0.2%-30% are as follows. (1) The initiation of a creep crack at a notch occurs by a process of local ductility exhaustion resulting from the accumulation of a critical creep strain or degree of damage in a region ahead of the notch tip. (2) Crack initiation times in the normalizedand-tempered material were estimated to within a factor of approximately 4 via eqns. (4) and (5). (3) In the materials investigated, crack growth occurs b y the formation, growth and linkage of grain b o u n d a r y damage in a discrete

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7

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