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Creep behaviour of 12Cr12Mo14V steel at engineering stresses
Materials Science and Engineering, 38 (1979) 199 - 210
199
© Elsevier Sequoia S.A., Lausanne - - P r i n t e d in the Netherlands
1 1 Creep Behaviour o f ~1 Cr~-Mo~V Steel at Engineering Stresses K. R. WILLIAMS and B. J. CANE
Central Electricity Research Laboratory, Central Electricity Generating Board, Kelvin Avenue, Leatherhead, Surrey (Gt. Britain) (Received July 6, 1978)
SUMMARY
The effects of microstructural instability in ~1 C r ~1 M o y1V steel on the creep and creep rupture properties at engineering stresses are discussed. A working model describing the creep rate change with time is developed, based on the concept of a time-dependent "friction stress" parameter. This model takes into account the changing material structure during extended c o m p o n e n t service life (= 100 000 h). The advantages of this approach over conventional applied creep rupture extrapolation techniques are outlined.
1. INTRODUCTION
Commercial steels of the C r - M o - V type are widely used in the Electricity Power Generating Industry. Specifically the steel ~1Cry1MoyV1 (subsequently referred to as CMV) is used i-n the construction of components such as main steam pipes, headers, valves, manifolds, bolts, etc. These components typically operate at temperatures in the range 550 -~ 575 °C with occasional excursions above 600 °C. The design stress of such components is formulated on a creep rupture basis and uses BS806. This particular British Standard calculates the allowable working stress aw as mean stress to cause rupture in 105 h aw =
safety factor
(1)
The safety factor is usually in the range 1.45 -~ 2.10 depending on material and working conditions. This standard necessarily suggests that components with mean properties which have operated ostensibly at design stress and temperature conditions will have a creep life > 1 0 5 h. In order to calculate the stress to cause rupture in 105 h, creep rupture extrapolation
techniques must be applied to existing laboratory stress rupture data. Since these data typically exhibit a +20% scatter around the mean rupture stress, creep rupture extrapolation can present considerable problems and it is necessary to consider extremes in the data. The typical working stress of a CMV main steam pipe is of the order 30 ~ 40 MPa. Using existing CMV creep rupture data (current max tr = 65 000 h) and current extrapolative techniques, we can depict the creep life usage of CEGB power station main steam pipe as in Fig. 1. Creep life fraction expired is also shown alongside each point representing a particular power station. Several important points arise from this summary. (1) Large differences appear in the predicted rupture lives depending on whether maximum or minimum properties are assumed. (2) If minimum properties are implicitly accepted (for safety and integrity reasons), then perfectly sound material can be scrapped (current 2 000 MW station lives are expected to be ~ 1 7 0 000 h). (3) If a specific cast of CMV material could be placed within the scatter band of stress rupture data, then we have a basis for the safe and economical use of CMV material. Recent work [1] on service-exposed CMV material (100 000 h at 40 MPa and 571 °C) has indicated a remaining creep life of ----200 000 h. This result suggests that the creep rupture extrapolative rules used for estimating the mean stress to give a life of 105 hours are highly inaccurate. It is now becoming apparent [ 1 ] that creep rupture extrapolative rules can at best be approximate. Most of these rules rely on a t i m e - t e m p e r a t u r e parameter and mathematical manipulation. If the material structure remained constant, then use of a t i m e -
200 DK RU Ct
|.7
(No) (-) I-] 1,,}
Ib
= = =
DRAKELOW'C" [LIFE FRACTION) RUGELEY'B" (,' ] COTTAM (., ) IRONBRIDGE'B'( " )
C.D H.M RAT W.B
(No) (-) (.) (. )
= .__ =
CASTLE DONINGTON (LIFE FRACTION) HIGH MARNHAM ( ,, ,, ) RATCLIFFE [" ) WEST BURTON [ ,, )
MINIMUM DATA
/ F . A N
o HM. 0 . 6 0
/0 H.M 0 - 4 3
O/DK O.28 OzRU 0.23
1.6
DATA
iO DK 0 . 2 0 .e RU O" 17
o C.D. 0.96
MAXIMUM / DATA ®
/
• C.D. 0.62
/
1.5 • (O21' /o W.B
!
1.3
i 1.4
i I. 5
i I. 6
I 1,7
I 1,8 TIME X 16 5
/
0-26
i 1.9 (HOURSI
®
®
/o RAT 0.26 • W.S
O.3S
I
1.2
/
o/Ib 0.20
Ib 0 . 2 8 RAT 0.37
/E)
I 2.0
I 2.1
I 2'2
I 2,3
I
2"4
Fig. 1. Relationship between safety factor and time to rupture for minimum, mean and maximum properties of CMV steam pipe on selected power stations.
temperature parameter would be justified. However, it is clear that the initial particle distribution of multiphase alloys can change markedly during creep at engineering stresses and commensurable long service exposure times [1 - 3]. Major changes in microstructure can therefore take place when CMV steels and other commercial alloys are used for high temperature applications. These changes in the size, spacing and morphology of precipitates inevitably mean that the creep and fracture resistance of multiphase alloys can alter with time at engineering design conditions (i.e. high temperature, low stress). In the present work a creep model is developed for engineering design conditions which takes into account this change in microstructure with time. A time~lependent effective stress, based on this changing microstructure, is formulated. The changing effective stress is then incorporated into a creep fracture process so that realistic stress rupture curves can be calculated where engineering stresses prevail.
2. INTERPRETATION OF MICROSTRUCTURAL INSTABILITY BY A "FRICTION STRESS" PARAMETER The variation of creep rate ~s with applied stress a is usually described by a Norton relationship
~s = Aa" f(T)
(2)
where A and n are constants, with n in the range 4 -~ 6 for pure close-packed metals. Two phased alloys normally exhibit much higher n values (up to 40), and this n value decreases from large values at high stresses to -~4 at lower stress levels [4 - 7]. It has been shown t h a t the wide range of n values can be rationalised by used of the "friction stress" concept [5, 7 - 10]. Thus creep does n o t take place under the full effect of the applied stress o but only under an effective stress (a -- o0), such t h a t is = A* (a -- Oo)r f(T)
(3)
201 where A* and p are constant, with p - 4.0 and f(T) the temperature dependence of creep rate. The "friction stress" o 0 has been identified with the parameter used in the relationship found during creep between the applied stress and p, the density of dislocations not associated with subgrain boundaries, namely o = oo + c~Gbx/p
(4)
where ~ is a constant, G the shear modulus and b the Burgers vector. The stress (o - - o 0 ) then controls the creep rate by determining the mesh size of the three20 000 hours) and the "friction stress" becomes time dependent, o0(t) [16]. The changing structure and time dependent o0 (t) necessarily means that the n values in eqn. (2) fall below 4 [3]. The low n values (<3) frequently observed at low stress in particle-hardened material [3] need not be the result of an alternative creep mechanism such as solute drag [4], grain boundary sliding [6, 17] etc, but simply a consequence of microstructural changes [1, 3]. It is therefore important to recognize that structural instability does occur in commercial steels during service exposure, and that these changes should be incorporated into creep and creep fracture models when considering tests or service at engineering stresses. In the following section a working model of the changing effective stress with time is developed, which relies on the observed Lifshitz-Wagner coarsening kinetics of vanadium carbide [1].
3. THE WORKING MODEL Recovery creep occurs when (o -- oo) controls the creep rate by determining the mesh size (ld) of the three-dimensional dislocation
network [12]. When the initial threedimensional dislocation mesh size (/i) is determined by the initial heat treatment (typically CMV is in a normalised and tempered condition) equilibrium recovery creep is usually not possible because li ~ld, i.e. initially more than one dislocation mesh spacing can exist between the particles, so that the particles in effect stabilise the dislocation mesh [8]. In the absence of particles (i.e. pure iron) such a fine mesh would recover and coarsen rapidly at 40 MPa and 570 °C, leading to fast creep and fast creep fracture [18]. Evidence that the creep rate is extremely slow in CMV at 570 °C and 40 MPa (Fig. 2) indicates the stabilizing effect carbides have on the threedimensional mesh. As particles coarsen during long term exposure (-~105 h) at temperatures of the order 570 °C, their stabilising effect on the interparticle three-dimensional dislocation mesh weakens. When the particles are so large and far apart that the refinement and coarsening of the interparticle three-dimensional mesh is controlled by the current effective stress, (o -- Oo (t)) (where o0 (t) represents the time-dependent change of Oo) then equilibrium recovery creep will have c o m m e n c e d and o -
o0(t)
_
(5)
o~Gb
We can therefore identify two regimes of creep during low stress laboratory creep tests (~40 MPa) or during service of CMV material. (1) The initial regime where particle and commensurate dislocation coarsening is dominant. In this regime the dislocation mesh is too fine for recovery creep at 40 MPa and 570 °C. Since creep strain does accumulate in this regime (Fig. 2), then some other alternative creep mechanism is controlling. This will be dealt with in the next section. (2) An equilibrium recovery creep regime following the coarsening of the particles and dislocation meshes, such that the current effective stress and the current level of dislocation mesh spacing follow eqn. (5). The particles continue to coarsen in this regime, which essentially means the effective stress continues to increase and with it the creep rate. The dependence of dislocation spacing on particle spacing during structural degeneration is implicit to this argument, and is clear from the diagrammatic representation of (a -- a0)
202
Ib
1RONBRIDGE
Ct ,
COTTAM
W.S..
WESTBURTON
RU :
RUGELEY
.18
.16
UNIAXIAL CREEP TESTAT :37 MPa AT 570%
RU
t4 UNIAXIAL CREEP TESTAT 30 MPa AT 5-/O °C W.B
,i2
Ib
c,
ws
T
. iO Z
TYPICAL INITIAL ELASTIC STRAIN IN STRESS RANGE 30-,,40 MPa . ~
er
oe
'06 lb
Ct .04
Ct
/
W.B
/d
"02
/ •
,. Ct Ib
WB I
i
I
I
0.2
0.4
O' 6
O.B
I
1.0
'.
'.
-4
TIME x 10
'
i
;.o
'
'
'
'
'.
'
(HOURS)
Fig. 2. Comparison of strain measured on main steam pipes with averaged uniaxial creep strain data.
~//~,
0
J
CMV(NORMALSEDANDTEMPERED)
O--
o . . ~ '// / / / / s " . /. /- " / / " s" / / s "~"
-
/O /
SERV,CESTRESS(o')~S~/."..." ..////....t.'/A.
n l d l - - ~
e'o(CMVAT ] t t =
o)
~'o
*
(t) ~ / ~" (,2)
-~
,
...
~ t'"
( DISLOCATION
,, _ F . O ~
IaON(~'~o)
, ', i
D E N S I T Y )'~
Fig. 3. Diagrammatic representation between (o -- o0) and dislocation density. CMV at time t = 0 represents the initial structure with large value of o 0 and hence low value of Id giving low creep rates (~). As the structure coarsens during service exposure the (o -- o0) vs. x/P line moves towards that for iron, giving increasing equilibrium dislocation densities and hence increasing recovery creep rates. in Fig. 3. This figure describes the relationship b e t w e e n (o - - Oo) and dislocation d e n s i t y in t h e equilibrium recovery creep regime. As the structure coarsens (i.e. particles grow and interparticle spacings increase) the o us. ~/p line m o v e s t o the right towards t h a t relationship for iron (i.e. o o -~ 0). The changing par-
ticle spacing enables the increasing effective stress t o generate a successively increasing equilibrium density of dislocations and with it higher recovery and creep rates. The simple relationship b e t w e e n interparticle spacing (lp) and dislocation d e n s i t y p is therefore R where
203 R =
current particle spacing,/p(t)
Let
(current dislocation density) 1/2, x/p (t) (6)
Thus we have R-
/p(t)
(16)
rSo = K / ~
then
- lp(t)ld(t )
(7)
lp ( t ) / l p ( 0 ) = (~t +
1) 1/3
(17)
Using eqn. (5) and R, or when t = 0 or structure constant during a single test R =/p(0)/d(0)
o -- o0 (t) -
(8)
where l d is the dislocation mesh spacing. This changing structure can be included in the fundamental eqn. (4) to provide the relationship a = %(t) + structure term
(9)
aGb
R
(10)
ill)
where ~ is the number of particles per cubic centimetre, r the mean particle size and lp the particle spacing = (1/~) 1/3. Using the Lifshitz-Wagner theory of particle coarsening, where (12)
r 3 - - r3o = K t
and ro is the initial particle size, r the particle size at time t and K the rate constant, eqns.(11 ) and (12) give the particle spacing at time t at time t ( K t + r03)1/s
(13)
where (14)
When t = 0, lp (0) = initial particle spacing and lp (0) = f r o
a G b l p ( O ) ( ~ t + 1) 1/3
o -- % (t) =
R
(19)
Substituting for R in eqn. (19), where (20)
~ G b ( ~ t + 1) 1/3
/p(t)
4 f = ~?-- ~r 3 3
f' = (41r/3f) 1/s
Then from eqn. (17),
We obtain
Equation (9) is the more general form of eqn. (4) representing a time-dependent structural change through the parameters v ~ , lp(t) and a0(t ). As the particle spacing increases during service or low stress laboratory testing, the dislocation mesh spacing changes by recovery towards equilibrium. The volume fraction of particles (assumed constant during a test or service) is given by
lp(t) = f '
(18)
R
R = lp (0) Id C0)
where the structure term is given by ~ G b x / ~ , which from eqn. (7) is structure t e r m =
aGbtp(t)
(15)
o -- o0 (t) =
(21) Id (0) All the parameters on the right-hand side of eqn. (21) are measurable by microstructural analysis. Thus we can identify the current effective stress at any time during the service life of the c o m p o n e n t when ~, Id(0) a n d ~ Can be measured. Of course o -- oo(t) could be measured directly by stress relaxation or stress drops [9] b u t this technique is necessarily destructive of service components. Given a measure of the effective stress, the value can be used in t w o ways to estimate remaining life. (1) The effective stress can be used in the modified Norton equation (Williams and Wilshire [3] ), = A ( o - - Oo (t)) 4 f(T)
(22)
and creep rates calculated following the onset of equilibrium. When ep/eo -" 50 then fracture is imminent [3], where ~p is the current creep rate in pseudo-tertiary (i.e. tertiary brought a b o u t by degeneration) and ~0 is the minimum creep rate during non-equilibrium creep. (2) Alternatively it is possible to show that equilibrium recovery creep (and with it cavitation and creep fracture) commences when the effective stress has increased to between 15 and 20 MPa (see Section 4). Thus if the parameters on the right-hand side of eqn. (21) are known, it is possible to construct an effective stress vs. time curve as shown in Fig. 4 for CMV material at 570 °C. The constants used in eqn. (21) and hence Fig. 4 are: a = 43 MPa
204 2;~.O 21 .O FRACTURE POINT
20.0
/
19-O 18.O 17.0 '~ 16.0 '-~ 15'0
b'~ 14.o vI~
/
1:3"0 12.0
er ~to li.O
/
uJ I 0 " 0 > 9.0
~ 8'0 7"0
~: 6.0 D u 5.0 4.0 3"0 2.0 1.0
J
I0
i
I
10 2
103
I
10 4
I
I0 s
r,Me (.OURS)
Fig. 4. Current effective stress (o -- Oo(t)) vs. time to rupture. (i.e. typical operating stress); ~Gb/ld(O) ~- 3.4; = 0.1; G =_1.6 X l 0 s MPa; b = 2.5 X 1 0 - s c m ; p = l 0 s cm cm-3;~ = 5 X 10 -4 h -1 (from Sellars [2] by extrapolation to 570 °C). Assuming fracture occurs at (o -- o 0 (t)) 20 MPa we have a basis for the accurate prediction of time to rupture. Figure 4 suggests the time to rupture for CMV material at o = 40 MPa at 570 °C is ---250 000 hours. This answer necessarily relies on accurate values of ~, la (t) and a but is in good agreement with remnant rupture lives determined experimentally for 100000 hours service-exposed material [ 1 ]. It is instructive to analyse the dislocation and carbide coarsening kinetics of CMV at 570 °C and low stresses in order to examine the extent in time of the equilibrium recovery creep regime. Under the circumstances described earlier the inherent dislocation density coarsens by normal recovery events. Lagneborg [19] has described these events using Friedels' dislocation recovery models [20]. Essentially over a significant period of the coarsening behaviour we have
Po - - P o ( t ) = K'po Po (t)t
(23)
where P0 = initial dislocation density; po(t) = dislocation density at time t; K ' = 7.6 × 10 -17 cm 2 s-1 for iron at 570 °C. Deviations from this behaviour occur at longer times [19]. Lagneborg [19] suggested this deviation m a y be a consequence of the impeding effect of particles on dislocation climb. Since all commercial ferritic materials rely on copious precipitation of carbides for strengthening, then clearly we have an analogous situation in CMV service components to that described in [19]. The dislocation mesh recovery is shown in Fig. 5 for iron between • . / dislocation densltms of 108 _~ 1010 cm -2 in the absence of stress. It is felt that the kinetics described by Fig. 5 are relevant at 40 MPa, as Lagneborg [19] found small superimposed stresses had no effect on the dislocation annealing kinetics. Also plotted in Fig. 5 is the measured coarsening behaviour of vanadium carbide (VC) at 570 °C [1] (VC represents the predominant strengthening carbide in CMV steels [ 21]. Several important points emerge from Fig. 5:
205
~YPICAL DISLOCATION SPACING FOR CMV REEP--TEsTED--AT 4 0 M ~ a - AT-57"()-C-- - -
_ ~
po = 2 X 10 8
j
~
-
~
. . . . . . . . .
---
io+
COARSENING po
166 iO 2
I
I0 3
15EHAVIOUR VC AT 570°C
CALCULATED DISLOCATION SPACING IN UNITS OF cm/cm 3
I
I0 4 TIME (HOURS)
10'5
10 6
Fig. 5. Change of dislocation mesh spacing (/d(t)) and interparticle spacing (Ip(t)) with time for idealised material and CMV service exposed material. A typical dislocation spacing for the creep of CMV at 40 MPa at 570 °C is also
indicated.
(1) beyond ~105 h the dislocation density P0 (t) is essentially independent of the initial dislocation density; (2) at times >105 h dislocation mesh spacings are larger than the current interparticle spacing lp (t) (i.e. VC spacing); (3) the dislocation mesh spacing lc measured in iron following recovery creep at 570 °C and 40 MPa is indicated; (4) 1¢ is larger than the inherent dislocation mesh size at times <105 h; (5) the inherent dislocation mesh spacing can be either larger or smaller than the particle spacing. Figure 5 conveniently describes the two creep regimes mentioned earlier. At times greater than 105 h the CMV inherent dislocation mesh spacing has become equal to or greater than the equilibrium mesh spacing for recovery creep in iron at 570 °C and 40 MPa. Accordingly we expect equilibrium recovery creep to commence at times near 105 hours where R(t) = 1.0, and subsequent creep rates
at t > 105 h to be controlled by (o -- o0(t)), i.e. eqn. (21). The actual dislocation densities measured from service-exposed material (40 MPa 565 °C) clearly do not change at the rate predicted by eqn. (23). A similar result was also noted by Lagneborg [19] in particle-hardened material, which points to a dislocation-particle reaction which impedes the normal recovery events. This behaviour will result in equilibrium recovery creep setting in at even longer times than 105 hours as indicated in Fig. 5. The creep mechanism is much less clear at times below 105 hours. In this regime we have three possible dislocation-particle interactions. When ld(t) > lp(t), then normal dislocation annealing can be expected (eqn. (23)). We would therefore expect all dislocation mesh sizes above the VC coarsening line to anneal independently of the carbide distribution. Of most relevance is the situation where dislocation meshes are smaller than the current particle spacing. Under these circumstances there
206 TABLE 1 C a l c u l a t e d e in CMV a c c o r d i n g t o eqn. ( 2 4 ) i.e. N a b a r r o - H e r r i n g c r e e p in p r e s e n c e of particles (creep r a t e ) ( h - 1 )
rp (particle size) ( c m ) 10 - 4 10 - 5 10 - 6 10 - 7
3.10 2.8 9.6 1.5
× × × ×
10 - 8 ~ N - H creep, n o particles 10 - s 10-9 10 - 9 ( r e p r e s e n t s l i m i t o f eqn. ( 2 4 ) )
Grain size, d -- 3 × 10 - 3 c m ( t y p i c a l o f N & T CMV). Strain, e = 5 x 10 - 4 . V o l u m e f r a c t i o n o f c a r b i d e s V0 = 0.01 ( m e a s u r e d ) . Stress, o = 4 0 MPa. T e m p e r a t u r e , T = 565 °C. Creep rate f r o m p l a n t , ~ 1.2 × 10 - 8 h -1 ( m e a s u r e d ) . The strain dependence of the s t r a i n rate is given b y ~ × 3 . 6 5 2 / 3 . 6 8 5 i.e. t h e s t r a i n rate is essentially i n d e p e n d e n t of strain above e = 0.001.
is experimental evidence which indicates that the dislocation mesh coarsen much less rapidly in material containing particles [19]. For example, Fig. 5 shows the actual measured dislocation coarsening rate for a commercial CMV main steam pipe which has operated at constant stress (---40 MPa) and temperature 570 °C. The time at which recovery creep commences may now be greatly extended. This confirms recent findings on the remaining creep life of the quoted service-exposed main steam pipe material, which indicate the real creep life is of the order 250 000 h rather than the expected 130 000 h suggested by stress rupture extrapolations (Fig. 1 ). It is important to investigate the mechanism of strain accumulation in the carbide and dislocation coarsening regime (i.e. up to 105 h on Fig. 5). Clearly strain does accumulate in this region, as indicated by actual creep measurements on service components (Fig. 2). Equilibrium recovery creep is not possible, i.e. (a - - a o ¢ ~ G b ~ / p ) and consequently diffusional processes may play a significant role in this region. Nabarro-Herring (N-H) creep rates are too high for the material and service conditions under consideration. However, a modification of the N - H model by Ashby [22] and Burton [23] suggests that grain boundary particles can inhibit diffusional flow. Under such circumstances the creep rate ~ is given by [23]
d2kT
a
55bKT
1 + 4rp e V o
(24)
where b - 10, ~ is the atomic volume, d the grain size, D the lattice self-diffusion coefficient, a the applied stress, rp the particle radius, U the line energy of the defect in the particle-matrix interface, e the strain, v0 the volume fraction particles. When the volume fraction of second phase particles becomes significant diffusion creep rates can be inhibited. Table 1 shows the expected creep rates from eqn. (24). At a typical grain and particle size for virgin CMV steam pipe, the creep rates are of the order 10 -s h -1, which is in good agreement with experimentally measured values. The collection of particles on grain boundaries parallel to the tensile stress during diffusional creep predicts a progressively decreasing creep rate [24] (see Table 1). However, the observed change in creep rate (Fig. 2) cannot be fully accounted for on this basis. Analysis of eqn. (24) for the strains observed (Fig. 2) indicate ~ to be virtually independent of e at strains near 0.001. Nabarro [25] has pointed out that the inherent dislocation mesh can act as vacancy sources and sinks. The inherent three-dimensional distribution of dislocations (i.e. N&T CMV in virgin state) will usually mean that some will climb by emitting vacancies on application of an applied stress and others will climb by absorbing vacancies. This diffusion will allow the stress to achieve work and leads to diffusional strain. This strain is additional to that caused by diffusion of vacancies from grain boundary sources to grain boundary sinks. Nabarro [25] considered dislocations to be created by the Bardeen-Herring mecha-
207 nism. The steady state contribution to creep was then the balance between this dislocation creation rate and their mutual annihilation. The steady state creep rate is then~
iN
Db° 3 - KTG2 t l n ( ~ ) 1 - 1
(25)
This steady state creep rate is usually much less than the boundary controlled creep rate. Burton and Reynolds [26], however, suggested that transient creep by this mechanism can be important. They interpret the transient creep in UO 2 at 0.5 Tm to be the bowing out by climb of the inherent dislocation network. Dislocation multiplication could n o t occur since the applied stress was less than the critical value 2 E/bk to operate a BardeenHerring source. Thus the creep component by climb saturated out as dislocations bowed to an equilibrium radius of curvature. Burton and Reynolds [26] calculated the transient c o m p o n e n t eBR to vary with time as e~
-
°~ ll--exp( 8Eb
16~Eb2Dtlt XaKT ])
e ~ = 10 -4 = ~ × t = 10 -s X eND = 1.95 × ee
=3 ×
10 4
(see Table 1)
10 -4
10 -4
The total creep strain eTo w = 10 -4 + 1.95 X 10 -4 + 3 × 10 -4 = 5.95 × 10 -4 0.06% This total is in excellent agreement with the laboratory and service-exposed creep measurements.
(26)
where E = 0.5 Gb 2, k is the dislocation mesh spacing and t the time. The engineering design conditions for CMV are typically a = 40 × l 0 s d y n cm -2 = 40 MPa and T = 570 °C. From Fig. 5 and measurements, the initial dislocation spacings are in the range 10 -4 -* 10 -5 cm. Using OBH = 2E/bk, where E = 0.5 Gb 2, b = 2 × 10-s cm, k = 10 -5 cm, G = 6.4 × 1011 d y n cm -z. Then the Bardeen-Herring stress for dislocation multiplication is OBH = 1.28 × 109 d y n cm -2. The applied stress is therefore too small to achieve a Bardeen-Herring source. When ~, = 10 -4 cm then OBH = 1.28 × 10 -s cm, cm -2 and the applied stress can operate B - H sources. However, the creep rates would be extremely small (~ 10 -11 h -1 ), well below those levels observed. Since the initial dislocation spacing of virgin CMV material is near 10 -5 cm (Fig. 5, Williams [27] ) then we have to conclude that B - H dislocation multiplication is not possible. We have however a consistent means of explaining creep strain accumulation in virgin CMV at engineering design conditions prior to the onset of equilibrium recovery creep. The total strain eTOT will be given by e T O T ---- eND + CNp -I- e e
where eND is the dislocation bowing contribution t o diffusional creep strain; eNp is the Nabarro-Herring creep in the presence of particles; and ee is the elastic strain. At 10 000 h (i.e. near end of transient, Fig. 2) the creep strain will be made up of the above components. For a typical CMV virgin material (rp = 10 -6 cm, Vo = 0.01, d = 3 × 10 -3 cm, o = 40 MPa, T = 570 °C),
4. CALCULATIONOF STRESS RUPTURE CURVES To calculate a stress rupture curve the model developed must be extended. The following can serve as a basis for creep rupture in normalised and tempered CMV material. (1) Over a substantial fraction of the creep life ( - 1 0 5 h), equilibrium recovery creep is not possible, i.e. (o -- Oo)/aGb ¢ x/p. (2) As particle coarsening occurs the effective stress increases until equilibrium creep becomes possible and normal cavity nucleation, growth and coalescence commences. (3) The structure continues to coarsen and ultimately the structure attained will be equivalent to that of a pure iron matrix with a dispersion of large carbide particles. In reality the matrix will n o t be of pure iron, but this is a reasonable hypothesis as a first approximation. (4) At this late stage of coarsening the failure mode could be considered to be that of pure iron creeping at the current effective stress. (5) Since pure iron obeys the M o n k m a n Grant relationship [28], the stress rupture plots will be straight lines and there is no difficulty in determining times to rupture at stresses of the order 10 -* 40 MPa.
208
160 140
SERVICE MATERIAL X
120 I00
CALCULATED RUPTURE LIVES MEAN rSO
90 ~. SO
" ~ . ~ - - ~ \
•---o
EXTRAPOLATED MEAN ISO
7o •
uJ
~ ~o SO DESIGN STRESS
c~Gb = 3 ' 2
x-f
40
Cd
.~r,...OCGb
30
x\
I04
I0 5
RUPTURE LIFE tR
"7;-
: a.B
IO6
(HOURSI
Fig. 6. Comparison of the calculated, extrapolated mean ISO and service exposed stress rupture behaviour of CMV.
Table 2 outlines the time to r u p t u r e calculation for an applied stress of 40 MPa, T = 570 °C, ~ = 5 × 10 - 4 h -z and aGb/ld = 3.2. Column 1 shows the test/service time. Column 2 shows the cur r ent level of (o -- Do(t)) at the time shown in column 1. Column 3 shows the time taken for r u p t u r e of pure iron at the current effective stress level. When column 3 - column 1 fracture occurs. It is possible to follow through a similar argument at o t h e r applied stresses near 40 MPa. However, the equilibrium dislocation density (ld) is required at these ot her stresses before a stress r u p tu r e curve can be derived. Since these values are n o t available at engineering stresses (30 - 50 MPa) it has been necessary t o assume a simple relationship between o -- a0 and x/p in deriving Fig. 6. This figure shows the calculated stress r upt ur e curve on the above basis, also the mean ISO data and its ex tr ap o lated value for normalised and tempered CMV, and l a b o r a t o r y tested data of CMV taken f r o m service after 100 000 hours at 571 °C and 43 MPa.
TABLE
2
Calculation of time to rupture at 40 M P a at 570 °C
(MPa)
Pure iron time to rupture at (o - - Do(t)) (h)
0 104 5 × 104 7 × 104
3.2 5.8 9.3 10.9
-*~ >106 ~ 106 ~-106
10 5
11.8
=10 6
13.5 14.2 14.7 15.2
8.7 8.1 2.19 2.0
T i m e t (h)
Current effective stress (o -- Do(t))
1.5 1.75 2.0 2.2
105 × 105 × 105 × 105 ×
× x × x
105 105 105 106
a = 5 x 10 -4 h -I, c~Gb/Id(O ) = 3.2 MPa. Fracture w h e n column 1 ~ column 3, i.e. tR = 2.2 × 105 h.
Several i m p o r t a n t features are shown on this figure. (1) The failure time at 43 MPa is greater than the mean ext rapol at ed ISO value (---130 000 h).
209
(2) The failure time at 43 MPa is approximately the same as that calculated from service exposed material, i.e. ~- 300 00 h [1]. (3) The coarsening eqn. (21) and the failure model described cannot work at applied stresses approachiJ.~g 150 MPa because there is insufficient time available for particle coarsening. Thus at stresses near and above 150 MPa normal three-stage creep curves prevail [1, 29]. This last point is particularly important and worth emphasising. Stress rupture data of engineering ferritic low alloy steels invariably show downward changing slopes up to presently available laboratory creep rupture times. It is this changing slope which is responsible for the current plethora of extrapolative stress rupture rules. A further factor which current extrapolative methods disregard is the changing creep and rupture mechanism along a stress rupture curve. Confining attention to the fracture behaviour of CMV, it is found that at high stresses and short times to failure, ductilities are high and ductile tearing is the rupture mode [1 ]. At low stresses creep rupture ductilities are much lower and reach a minimum as suggested recently [29, 30]. As the stress rupture mode changes, the constant in the Monkman-Grant relationship also changes [1]. Since the Monkman-Grant relationship is implicitly accepted in many currently used extrapolative techniques it is imperative that the available stress rupture data reflects the mode of creep rupture over the total extrapolated range. In order to generate stress rupture data as above, and additionally validate the currently acceptable extrapolative techniques, we must be careful to include rupture data only where creep ductilities are low and reasonably constant. This situation commonly exists at engineering stresses where pseudo-tertiary curves are found [29] (i.e. where particle size and distribution and hence o0 clearly change during the test). For the case of CMV material all high stress short time to rupture data (typically ~<104 h) must be excluded at 570 °C. This applies specifically to all tests at stresses above approximately 150 MPa where the change from transgranular ductile tearing to nucleation and growth of cavities occurs. One method of identifying this change is to observe the shape of the strain-time curve and by metallography [1]. However measurement of
% on the virgin material by methods outlined recently [3] is equally effective.
5. DISCUSSION In the working model proposed it has been shown that equilibrium recovery creep is not possible at 40 MPa and 570 °C in normalised and tempered CMV. This is because the inherent dislocation mesh is fine, so that the applied stress ( - 4 0 MPa) is unable to create Frank-Read sources as required by the recovery creep model [12]. However, as the copious distribution of fine carbides and dislocation meshes coarsen, a time will be reached in the operation of a service component when recovery creep becomes possible. At this point the equilibrium recovery creep rate becomes established at the current effective stress (eqn. (21)). Examination of Fig. 5 suggests this requires - l 0 s h, although dislocation-particle interactions could introduce an impedance effect delaying the onset of recovery creep. Under these circumstances the diffusional processes will play a more important role in contributing to the total strain accumulated. In the region up to 10 s h diffusion creep can occur. The strain accumulated from this source is, however, small and, in the case of the dislocation climb contribution, saturates at a strain approximately equivalent to the elastic strain. However, as the structure coarsens the dislocation climb process can lead quite naturally to dislocation recovery events and hence recovery creep. It is in the recovery creep range where stress sensitivities of creep rate and fracture are high (n - 4 -* 6) that cavitation becomes strain-dependent. Accordingly we need to identify the time at which recovery creep events commence in order to safeguard the future integrity of structures.
6. CONCLUSIONS The model proposed offers the following advantages. (1) By microstructural examination it should be possible to identify the position of a given cast of material within its stress rupture scatter band. This simple criterion has enormous cost-benefit potential to users of
210 large critical c o m p o n e n t s o p e r a t i n g at elevated temperatures. (2) A c c u r a t e creep r u p t u r e e x t r a p o l a t i o n s m a y be possible using the effective stress approach. (3) T h e first t w o p o i n t s enable realistic life f r a c t i o n s t o be calculated o n service-exposed components. (4) T h e effective stress a p p r o a c h does n o t rely on the analysis o f i n a d e q u a t e service operating records. The operational history of t h e c o m p o n e n t is l o c k e d in t h e m i c r o s t r u c t u r e . (5) T h e m o d e l can be applied n o n - d e s t r u c tively t o large, expensive c o m p o n e n t s , i.e. m i c r o s a m p l i n g and TEM analysis are a d e q u a t e . In c o n c l u s i o n , a w o r k i n g m o d e l o f the creep b e h a v i o u r o f CMV at engineering stresses and t e m p e r a t u r e s has b e e n f o r m u l a t e d . F o r t h e m o d e l t o be applied t o real service situations m e a s u r e d values o f (a) a, the dislocationparticle i n t e r a c t i o n c o e f f i c i e n t ; (b) lp (0), the initial particle size; (c) Ip (t), the particle size w i t h time and h e n c e J3; and ( d ) / d (t), the disl o c a t i o n m e s h spacing with t i m e are required. M e a s u r e m e n t o f these p a r a m e t e r s will p e r m i t calculation o f the effective stress and h e n c e calculation o f the c u r r e n t level o f c r e e p rate and time t o fracture.
ACKNOWLEDGMENT This w o r k was carried out at C E G B Midlands Region Scientific Services Department and the Central Electricity Research Laboratories. The paper is published by permission of the Central Electricity Generating Board.
REFERENCES 1 B.J. Cane and K. R. Williams, C E G B Rep. RD/L/ R 1965, 1977. 2 C. M. Sellars,Creep Strength in Steel and High Temperature Alloys, Sheffield, 1972, Metals Society, 1974, p. 20.
3 K, R. Williams and B. Wilshire,Mater. Sci. Eng., 28 (1977) 289. 4 B. Russell, R. K. Ham, J. M. Silcock and G. Willoughby, Met. Sci.J., 2 (1968) 201. 5 P. L. Threadgill and B. Wilshire, Creep Strength in Steel and High Temperature Alloys, Sheffield, 1972, Metals Society, 1974. 6 M. J. Collins, Creep Strength in Steel and High Temperature Alloys; Sheffield, 1972, Metals Society, 1974, p. 217. 7 P. L. Threadgill and B. Wilshire, Met. Sci. J., 8 (1974) 117. 8 P. W. Davies, G. Nelmes, K. R. Williams and B. Wilshire, Met. Sci. J., 7 (1973) 87. 9 K. R. Williams and B. Wilshire, Met. Sci. J., 7 (1973) 176. 10 J. D. Parker and B. Wilshire, Met. Sci. J., 9 (1973) 248. 11 S. K. Mitra and D. McLean, Proc. R. Soc., 'London, Set. A, 295 (1966) 288. 12 P.W. Davies and B. Wilshire, Scr. Metall., 5 (1971) 475. 13 G. Nelmes and B. Wilshire, Scr. Metall., 10 (1976) 697. 14 W. J. Evans and G. Harrison, Met. Sci., 10 (1976) 307. 15 G. J. Neate and K. R. Williams, CEGB Rep. SSD/ MID/R2/78. 16 K. R. Williams, CEGB Rep. SSD/MID/R3/75, 1975. 17 J. M. Silcock and G. Willoughby, Creep Strength in Steel and High Temperature Alloys, Sheffield, 1972, Metals Society, 1974, p. 122. 18 D. McLean, Trans. Metall. Soe. AIME, 242 (1968) 1193. 19 A. Oden, E. Lind and R. Lagneborg, Creep Strength in Steel and High Temperature Alloys, Sheffield, 1972. 20 J. Friedel, Les Dislocations, Gauthier-Villars, Paris, 1956. 21 G. L. Dunlop and R. W. K. Honeycombe, Met. Sci., 11 (1977) 495. 22 M. F. Ashby, Scr. Metall., 3 (1969) 837. 23 B. Burton, CEGB Rep. RD/B/N3225, 1974. 24 B. Burton, CEGB Rep. RD/B/N2245, 1972. 25 F. R. N. Nabarro, Philos. Mag., 16 (1967) 231. 26 B. Burton and G. L. Reynolds, Philos. Mag., 29 (1974) 1359. 27 K. R. Williams, CEGB Rep., 1979. 28 K. R. Williams, Doctoral Thesis, University of Wales, 1969. 29 P. Smith and K. R. Williams, CEGB Rep. SSD/ MID/R75/75, 1975. 30 B. J. Cane, Mater. Sci. Eng., 35 (1978) 229.
199
© Elsevier Sequoia S.A., Lausanne - - P r i n t e d in the Netherlands
1 1 Creep Behaviour o f ~1 Cr~-Mo~V Steel at Engineering Stresses K. R. WILLIAMS and B. J. CANE
Central Electricity Research Laboratory, Central Electricity Generating Board, Kelvin Avenue, Leatherhead, Surrey (Gt. Britain) (Received July 6, 1978)
SUMMARY
The effects of microstructural instability in ~1 C r ~1 M o y1V steel on the creep and creep rupture properties at engineering stresses are discussed. A working model describing the creep rate change with time is developed, based on the concept of a time-dependent "friction stress" parameter. This model takes into account the changing material structure during extended c o m p o n e n t service life (= 100 000 h). The advantages of this approach over conventional applied creep rupture extrapolation techniques are outlined.
1. INTRODUCTION
Commercial steels of the C r - M o - V type are widely used in the Electricity Power Generating Industry. Specifically the steel ~1Cry1MoyV1 (subsequently referred to as CMV) is used i-n the construction of components such as main steam pipes, headers, valves, manifolds, bolts, etc. These components typically operate at temperatures in the range 550 -~ 575 °C with occasional excursions above 600 °C. The design stress of such components is formulated on a creep rupture basis and uses BS806. This particular British Standard calculates the allowable working stress aw as mean stress to cause rupture in 105 h aw =
safety factor
(1)
The safety factor is usually in the range 1.45 -~ 2.10 depending on material and working conditions. This standard necessarily suggests that components with mean properties which have operated ostensibly at design stress and temperature conditions will have a creep life > 1 0 5 h. In order to calculate the stress to cause rupture in 105 h, creep rupture extrapolation
techniques must be applied to existing laboratory stress rupture data. Since these data typically exhibit a +20% scatter around the mean rupture stress, creep rupture extrapolation can present considerable problems and it is necessary to consider extremes in the data. The typical working stress of a CMV main steam pipe is of the order 30 ~ 40 MPa. Using existing CMV creep rupture data (current max tr = 65 000 h) and current extrapolative techniques, we can depict the creep life usage of CEGB power station main steam pipe as in Fig. 1. Creep life fraction expired is also shown alongside each point representing a particular power station. Several important points arise from this summary. (1) Large differences appear in the predicted rupture lives depending on whether maximum or minimum properties are assumed. (2) If minimum properties are implicitly accepted (for safety and integrity reasons), then perfectly sound material can be scrapped (current 2 000 MW station lives are expected to be ~ 1 7 0 000 h). (3) If a specific cast of CMV material could be placed within the scatter band of stress rupture data, then we have a basis for the safe and economical use of CMV material. Recent work [1] on service-exposed CMV material (100 000 h at 40 MPa and 571 °C) has indicated a remaining creep life of ----200 000 h. This result suggests that the creep rupture extrapolative rules used for estimating the mean stress to give a life of 105 hours are highly inaccurate. It is now becoming apparent [ 1 ] that creep rupture extrapolative rules can at best be approximate. Most of these rules rely on a t i m e - t e m p e r a t u r e parameter and mathematical manipulation. If the material structure remained constant, then use of a t i m e -
200 DK RU Ct
|.7
(No) (-) I-] 1,,}
Ib
= = =
DRAKELOW'C" [LIFE FRACTION) RUGELEY'B" (,' ] COTTAM (., ) IRONBRIDGE'B'( " )
C.D H.M RAT W.B
(No) (-) (.) (. )
= .__ =
CASTLE DONINGTON (LIFE FRACTION) HIGH MARNHAM ( ,, ,, ) RATCLIFFE [" ) WEST BURTON [ ,, )
MINIMUM DATA
/ F . A N
o HM. 0 . 6 0
/0 H.M 0 - 4 3
O/DK O.28 OzRU 0.23
1.6
DATA
iO DK 0 . 2 0 .e RU O" 17
o C.D. 0.96
MAXIMUM / DATA ®
/
• C.D. 0.62
/
1.5 • (O21' /o W.B
!
1.3
i 1.4
i I. 5
i I. 6
I 1,7
I 1,8 TIME X 16 5
/
0-26
i 1.9 (HOURSI
®
®
/o RAT 0.26 • W.S
O.3S
I
1.2
/
o/Ib 0.20
Ib 0 . 2 8 RAT 0.37
/E)
I 2.0
I 2.1
I 2'2
I 2,3
I
2"4
Fig. 1. Relationship between safety factor and time to rupture for minimum, mean and maximum properties of CMV steam pipe on selected power stations.
temperature parameter would be justified. However, it is clear that the initial particle distribution of multiphase alloys can change markedly during creep at engineering stresses and commensurable long service exposure times [1 - 3]. Major changes in microstructure can therefore take place when CMV steels and other commercial alloys are used for high temperature applications. These changes in the size, spacing and morphology of precipitates inevitably mean that the creep and fracture resistance of multiphase alloys can alter with time at engineering design conditions (i.e. high temperature, low stress). In the present work a creep model is developed for engineering design conditions which takes into account this change in microstructure with time. A time~lependent effective stress, based on this changing microstructure, is formulated. The changing effective stress is then incorporated into a creep fracture process so that realistic stress rupture curves can be calculated where engineering stresses prevail.
2. INTERPRETATION OF MICROSTRUCTURAL INSTABILITY BY A "FRICTION STRESS" PARAMETER The variation of creep rate ~s with applied stress a is usually described by a Norton relationship
~s = Aa" f(T)
(2)
where A and n are constants, with n in the range 4 -~ 6 for pure close-packed metals. Two phased alloys normally exhibit much higher n values (up to 40), and this n value decreases from large values at high stresses to -~4 at lower stress levels [4 - 7]. It has been shown t h a t the wide range of n values can be rationalised by used of the "friction stress" concept [5, 7 - 10]. Thus creep does n o t take place under the full effect of the applied stress o but only under an effective stress (a -- o0), such t h a t is = A* (a -- Oo)r f(T)
(3)
201 where A* and p are constant, with p - 4.0 and f(T) the temperature dependence of creep rate. The "friction stress" o 0 has been identified with the parameter used in the relationship found during creep between the applied stress and p, the density of dislocations not associated with subgrain boundaries, namely o = oo + c~Gbx/p
(4)
where ~ is a constant, G the shear modulus and b the Burgers vector. The stress (o - - o 0 ) then controls the creep rate by determining the mesh size of the three
3. THE WORKING MODEL Recovery creep occurs when (o -- oo) controls the creep rate by determining the mesh size (ld) of the three-dimensional dislocation
network [12]. When the initial threedimensional dislocation mesh size (/i) is determined by the initial heat treatment (typically CMV is in a normalised and tempered condition) equilibrium recovery creep is usually not possible because li ~ld, i.e. initially more than one dislocation mesh spacing can exist between the particles, so that the particles in effect stabilise the dislocation mesh [8]. In the absence of particles (i.e. pure iron) such a fine mesh would recover and coarsen rapidly at 40 MPa and 570 °C, leading to fast creep and fast creep fracture [18]. Evidence that the creep rate is extremely slow in CMV at 570 °C and 40 MPa (Fig. 2) indicates the stabilizing effect carbides have on the threedimensional mesh. As particles coarsen during long term exposure (-~105 h) at temperatures of the order 570 °C, their stabilising effect on the interparticle three-dimensional dislocation mesh weakens. When the particles are so large and far apart that the refinement and coarsening of the interparticle three-dimensional mesh is controlled by the current effective stress, (o -- Oo (t)) (where o0 (t) represents the time-dependent change of Oo) then equilibrium recovery creep will have c o m m e n c e d and o -
o0(t)
_
(5)
o~Gb
We can therefore identify two regimes of creep during low stress laboratory creep tests (~40 MPa) or during service of CMV material. (1) The initial regime where particle and commensurate dislocation coarsening is dominant. In this regime the dislocation mesh is too fine for recovery creep at 40 MPa and 570 °C. Since creep strain does accumulate in this regime (Fig. 2), then some other alternative creep mechanism is controlling. This will be dealt with in the next section. (2) An equilibrium recovery creep regime following the coarsening of the particles and dislocation meshes, such that the current effective stress and the current level of dislocation mesh spacing follow eqn. (5). The particles continue to coarsen in this regime, which essentially means the effective stress continues to increase and with it the creep rate. The dependence of dislocation spacing on particle spacing during structural degeneration is implicit to this argument, and is clear from the diagrammatic representation of (a -- a0)
202
Ib
1RONBRIDGE
Ct ,
COTTAM
W.S..
WESTBURTON
RU :
RUGELEY
.18
.16
UNIAXIAL CREEP TESTAT :37 MPa AT 570%
RU
t4 UNIAXIAL CREEP TESTAT 30 MPa AT 5-/O °C W.B
,i2
Ib
c,
ws
T
. iO Z
TYPICAL INITIAL ELASTIC STRAIN IN STRESS RANGE 30-,,40 MPa . ~
er
oe
'06 lb
Ct .04
Ct
/
W.B
/d
"02
/ •
,. Ct Ib
WB I
i
I
I
0.2
0.4
O' 6
O.B
I
1.0
'.
'.
-4
TIME x 10
'
i
;.o
'
'
'
'
'.
'
(HOURS)
Fig. 2. Comparison of strain measured on main steam pipes with averaged uniaxial creep strain data.
~//~,
0
J
CMV(NORMALSEDANDTEMPERED)
O--
o . . ~ '// / / / / s " . /. /- " / / " s" / / s "~"
-
/O /
SERV,CESTRESS(o')~S~/."..." ..////....t.'/A.
n l d l - - ~
e'o(CMVAT ] t t =
o)
~'o
*
(t) ~ / ~" (,2)
-~
,
...
~ t'"
( DISLOCATION
,, _ F . O ~
IaON(~'~o)
, ', i
D E N S I T Y )'~
Fig. 3. Diagrammatic representation between (o -- o0) and dislocation density. CMV at time t = 0 represents the initial structure with large value of o 0 and hence low value of Id giving low creep rates (~). As the structure coarsens during service exposure the (o -- o0) vs. x/P line moves towards that for iron, giving increasing equilibrium dislocation densities and hence increasing recovery creep rates. in Fig. 3. This figure describes the relationship b e t w e e n (o - - Oo) and dislocation d e n s i t y in t h e equilibrium recovery creep regime. As the structure coarsens (i.e. particles grow and interparticle spacings increase) the o us. ~/p line m o v e s t o the right towards t h a t relationship for iron (i.e. o o -~ 0). The changing par-
ticle spacing enables the increasing effective stress t o generate a successively increasing equilibrium density of dislocations and with it higher recovery and creep rates. The simple relationship b e t w e e n interparticle spacing (lp) and dislocation d e n s i t y p is therefore R where
203 R =
current particle spacing,/p(t)
Let
(current dislocation density) 1/2, x/p (t) (6)
Thus we have R-
/p(t)
(16)
rSo = K / ~
then
- lp(t)ld(t )
(7)
lp ( t ) / l p ( 0 ) = (~t +
1) 1/3
(17)
Using eqn. (5) and R, or when t = 0 or structure constant during a single test R =/p(0)/d(0)
o -- o0 (t) -
(8)
where l d is the dislocation mesh spacing. This changing structure can be included in the fundamental eqn. (4) to provide the relationship a = %(t) + structure term
(9)
aGb
R
(10)
ill)
where ~ is the number of particles per cubic centimetre, r the mean particle size and lp the particle spacing = (1/~) 1/3. Using the Lifshitz-Wagner theory of particle coarsening, where (12)
r 3 - - r3o = K t
and ro is the initial particle size, r the particle size at time t and K the rate constant, eqns.(11 ) and (12) give the particle spacing at time t at time t ( K t + r03)1/s
(13)
where (14)
When t = 0, lp (0) = initial particle spacing and lp (0) = f r o
a G b l p ( O ) ( ~ t + 1) 1/3
o -- % (t) =
R
(19)
Substituting for R in eqn. (19), where (20)
~ G b ( ~ t + 1) 1/3
/p(t)
4 f = ~?-- ~r 3 3
f' = (41r/3f) 1/s
Then from eqn. (17),
We obtain
Equation (9) is the more general form of eqn. (4) representing a time-dependent structural change through the parameters v ~ , lp(t) and a0(t ). As the particle spacing increases during service or low stress laboratory testing, the dislocation mesh spacing changes by recovery towards equilibrium. The volume fraction of particles (assumed constant during a test or service) is given by
lp(t) = f '
(18)
R
R = lp (0) Id C0)
where the structure term is given by ~ G b x / ~ , which from eqn. (7) is structure t e r m =
aGbtp(t)
(15)
o -- o0 (t) =
(21) Id (0) All the parameters on the right-hand side of eqn. (21) are measurable by microstructural analysis. Thus we can identify the current effective stress at any time during the service life of the c o m p o n e n t when ~, Id(0) a n d ~ Can be measured. Of course o -- oo(t) could be measured directly by stress relaxation or stress drops [9] b u t this technique is necessarily destructive of service components. Given a measure of the effective stress, the value can be used in t w o ways to estimate remaining life. (1) The effective stress can be used in the modified Norton equation (Williams and Wilshire [3] ), = A ( o - - Oo (t)) 4 f(T)
(22)
and creep rates calculated following the onset of equilibrium. When ep/eo -" 50 then fracture is imminent [3], where ~p is the current creep rate in pseudo-tertiary (i.e. tertiary brought a b o u t by degeneration) and ~0 is the minimum creep rate during non-equilibrium creep. (2) Alternatively it is possible to show that equilibrium recovery creep (and with it cavitation and creep fracture) commences when the effective stress has increased to between 15 and 20 MPa (see Section 4). Thus if the parameters on the right-hand side of eqn. (21) are known, it is possible to construct an effective stress vs. time curve as shown in Fig. 4 for CMV material at 570 °C. The constants used in eqn. (21) and hence Fig. 4 are: a = 43 MPa
204 2;~.O 21 .O FRACTURE POINT
20.0
/
19-O 18.O 17.0 '~ 16.0 '-~ 15'0
b'~ 14.o vI~
/
1:3"0 12.0
er ~to li.O
/
uJ I 0 " 0 > 9.0
~ 8'0 7"0
~: 6.0 D u 5.0 4.0 3"0 2.0 1.0
J
I0
i
I
10 2
103
I
10 4
I
I0 s
r,Me (.OURS)
Fig. 4. Current effective stress (o -- Oo(t)) vs. time to rupture. (i.e. typical operating stress); ~Gb/ld(O) ~- 3.4; = 0.1; G =_1.6 X l 0 s MPa; b = 2.5 X 1 0 - s c m ; p = l 0 s cm cm-3;~ = 5 X 10 -4 h -1 (from Sellars [2] by extrapolation to 570 °C). Assuming fracture occurs at (o -- o 0 (t)) 20 MPa we have a basis for the accurate prediction of time to rupture. Figure 4 suggests the time to rupture for CMV material at o = 40 MPa at 570 °C is ---250 000 hours. This answer necessarily relies on accurate values of ~, la (t) and a but is in good agreement with remnant rupture lives determined experimentally for 100000 hours service-exposed material [ 1 ]. It is instructive to analyse the dislocation and carbide coarsening kinetics of CMV at 570 °C and low stresses in order to examine the extent in time of the equilibrium recovery creep regime. Under the circumstances described earlier the inherent dislocation density coarsens by normal recovery events. Lagneborg [19] has described these events using Friedels' dislocation recovery models [20]. Essentially over a significant period of the coarsening behaviour we have
Po - - P o ( t ) = K'po Po (t)t
(23)
where P0 = initial dislocation density; po(t) = dislocation density at time t; K ' = 7.6 × 10 -17 cm 2 s-1 for iron at 570 °C. Deviations from this behaviour occur at longer times [19]. Lagneborg [19] suggested this deviation m a y be a consequence of the impeding effect of particles on dislocation climb. Since all commercial ferritic materials rely on copious precipitation of carbides for strengthening, then clearly we have an analogous situation in CMV service components to that described in [19]. The dislocation mesh recovery is shown in Fig. 5 for iron between • . / dislocation densltms of 108 _~ 1010 cm -2 in the absence of stress. It is felt that the kinetics described by Fig. 5 are relevant at 40 MPa, as Lagneborg [19] found small superimposed stresses had no effect on the dislocation annealing kinetics. Also plotted in Fig. 5 is the measured coarsening behaviour of vanadium carbide (VC) at 570 °C [1] (VC represents the predominant strengthening carbide in CMV steels [ 21]. Several important points emerge from Fig. 5:
205
~YPICAL DISLOCATION SPACING FOR CMV REEP--TEsTED--AT 4 0 M ~ a - AT-57"()-C-- - -
_ ~
po = 2 X 10 8
j
~
-
~
. . . . . . . . .
---
io+
COARSENING po
166 iO 2
I
I0 3
15EHAVIOUR VC AT 570°C
CALCULATED DISLOCATION SPACING IN UNITS OF cm/cm 3
I
I0 4 TIME (HOURS)
10'5
10 6
Fig. 5. Change of dislocation mesh spacing (/d(t)) and interparticle spacing (Ip(t)) with time for idealised material and CMV service exposed material. A typical dislocation spacing for the creep of CMV at 40 MPa at 570 °C is also
indicated.
(1) beyond ~105 h the dislocation density P0 (t) is essentially independent of the initial dislocation density; (2) at times >105 h dislocation mesh spacings are larger than the current interparticle spacing lp (t) (i.e. VC spacing); (3) the dislocation mesh spacing lc measured in iron following recovery creep at 570 °C and 40 MPa is indicated; (4) 1¢ is larger than the inherent dislocation mesh size at times <105 h; (5) the inherent dislocation mesh spacing can be either larger or smaller than the particle spacing. Figure 5 conveniently describes the two creep regimes mentioned earlier. At times greater than 105 h the CMV inherent dislocation mesh spacing has become equal to or greater than the equilibrium mesh spacing for recovery creep in iron at 570 °C and 40 MPa. Accordingly we expect equilibrium recovery creep to commence at times near 105 hours where R(t) = 1.0, and subsequent creep rates
at t > 105 h to be controlled by (o -- o0(t)), i.e. eqn. (21). The actual dislocation densities measured from service-exposed material (40 MPa 565 °C) clearly do not change at the rate predicted by eqn. (23). A similar result was also noted by Lagneborg [19] in particle-hardened material, which points to a dislocation-particle reaction which impedes the normal recovery events. This behaviour will result in equilibrium recovery creep setting in at even longer times than 105 hours as indicated in Fig. 5. The creep mechanism is much less clear at times below 105 hours. In this regime we have three possible dislocation-particle interactions. When ld(t) > lp(t), then normal dislocation annealing can be expected (eqn. (23)). We would therefore expect all dislocation mesh sizes above the VC coarsening line to anneal independently of the carbide distribution. Of most relevance is the situation where dislocation meshes are smaller than the current particle spacing. Under these circumstances there
206 TABLE 1 C a l c u l a t e d e in CMV a c c o r d i n g t o eqn. ( 2 4 ) i.e. N a b a r r o - H e r r i n g c r e e p in p r e s e n c e of particles (creep r a t e ) ( h - 1 )
rp (particle size) ( c m ) 10 - 4 10 - 5 10 - 6 10 - 7
3.10 2.8 9.6 1.5
× × × ×
10 - 8 ~ N - H creep, n o particles 10 - s 10-9 10 - 9 ( r e p r e s e n t s l i m i t o f eqn. ( 2 4 ) )
Grain size, d -- 3 × 10 - 3 c m ( t y p i c a l o f N & T CMV). Strain, e = 5 x 10 - 4 . V o l u m e f r a c t i o n o f c a r b i d e s V0 = 0.01 ( m e a s u r e d ) . Stress, o = 4 0 MPa. T e m p e r a t u r e , T = 565 °C. Creep rate f r o m p l a n t , ~ 1.2 × 10 - 8 h -1 ( m e a s u r e d ) . The strain dependence of the s t r a i n rate is given b y ~ × 3 . 6 5 2 / 3 . 6 8 5 i.e. t h e s t r a i n rate is essentially i n d e p e n d e n t of strain above e = 0.001.
is experimental evidence which indicates that the dislocation mesh coarsen much less rapidly in material containing particles [19]. For example, Fig. 5 shows the actual measured dislocation coarsening rate for a commercial CMV main steam pipe which has operated at constant stress (---40 MPa) and temperature 570 °C. The time at which recovery creep commences may now be greatly extended. This confirms recent findings on the remaining creep life of the quoted service-exposed main steam pipe material, which indicate the real creep life is of the order 250 000 h rather than the expected 130 000 h suggested by stress rupture extrapolations (Fig. 1 ). It is important to investigate the mechanism of strain accumulation in the carbide and dislocation coarsening regime (i.e. up to 105 h on Fig. 5). Clearly strain does accumulate in this region, as indicated by actual creep measurements on service components (Fig. 2). Equilibrium recovery creep is not possible, i.e. (a - - a o ¢ ~ G b ~ / p ) and consequently diffusional processes may play a significant role in this region. Nabarro-Herring (N-H) creep rates are too high for the material and service conditions under consideration. However, a modification of the N - H model by Ashby [22] and Burton [23] suggests that grain boundary particles can inhibit diffusional flow. Under such circumstances the creep rate ~ is given by [23]
d2kT
a
55bKT
1 + 4rp e V o
(24)
where b - 10, ~ is the atomic volume, d the grain size, D the lattice self-diffusion coefficient, a the applied stress, rp the particle radius, U the line energy of the defect in the particle-matrix interface, e the strain, v0 the volume fraction particles. When the volume fraction of second phase particles becomes significant diffusion creep rates can be inhibited. Table 1 shows the expected creep rates from eqn. (24). At a typical grain and particle size for virgin CMV steam pipe, the creep rates are of the order 10 -s h -1, which is in good agreement with experimentally measured values. The collection of particles on grain boundaries parallel to the tensile stress during diffusional creep predicts a progressively decreasing creep rate [24] (see Table 1). However, the observed change in creep rate (Fig. 2) cannot be fully accounted for on this basis. Analysis of eqn. (24) for the strains observed (Fig. 2) indicate ~ to be virtually independent of e at strains near 0.001. Nabarro [25] has pointed out that the inherent dislocation mesh can act as vacancy sources and sinks. The inherent three-dimensional distribution of dislocations (i.e. N&T CMV in virgin state) will usually mean that some will climb by emitting vacancies on application of an applied stress and others will climb by absorbing vacancies. This diffusion will allow the stress to achieve work and leads to diffusional strain. This strain is additional to that caused by diffusion of vacancies from grain boundary sources to grain boundary sinks. Nabarro [25] considered dislocations to be created by the Bardeen-Herring mecha-
207 nism. The steady state contribution to creep was then the balance between this dislocation creation rate and their mutual annihilation. The steady state creep rate is then~
iN
Db° 3 - KTG2 t l n ( ~ ) 1 - 1
(25)
This steady state creep rate is usually much less than the boundary controlled creep rate. Burton and Reynolds [26], however, suggested that transient creep by this mechanism can be important. They interpret the transient creep in UO 2 at 0.5 Tm to be the bowing out by climb of the inherent dislocation network. Dislocation multiplication could n o t occur since the applied stress was less than the critical value 2 E/bk to operate a BardeenHerring source. Thus the creep component by climb saturated out as dislocations bowed to an equilibrium radius of curvature. Burton and Reynolds [26] calculated the transient c o m p o n e n t eBR to vary with time as e~
-
°~ ll--exp( 8Eb
16~Eb2Dtlt XaKT ])
e ~ = 10 -4 = ~ × t = 10 -s X eND = 1.95 × ee
=3 ×
10 4
(see Table 1)
10 -4
10 -4
The total creep strain eTo w = 10 -4 + 1.95 X 10 -4 + 3 × 10 -4 = 5.95 × 10 -4 0.06% This total is in excellent agreement with the laboratory and service-exposed creep measurements.
(26)
where E = 0.5 Gb 2, k is the dislocation mesh spacing and t the time. The engineering design conditions for CMV are typically a = 40 × l 0 s d y n cm -2 = 40 MPa and T = 570 °C. From Fig. 5 and measurements, the initial dislocation spacings are in the range 10 -4 -* 10 -5 cm. Using OBH = 2E/bk, where E = 0.5 Gb 2, b = 2 × 10-s cm, k = 10 -5 cm, G = 6.4 × 1011 d y n cm -z. Then the Bardeen-Herring stress for dislocation multiplication is OBH = 1.28 × 109 d y n cm -2. The applied stress is therefore too small to achieve a Bardeen-Herring source. When ~, = 10 -4 cm then OBH = 1.28 × 10 -s cm, cm -2 and the applied stress can operate B - H sources. However, the creep rates would be extremely small (~ 10 -11 h -1 ), well below those levels observed. Since the initial dislocation spacing of virgin CMV material is near 10 -5 cm (Fig. 5, Williams [27] ) then we have to conclude that B - H dislocation multiplication is not possible. We have however a consistent means of explaining creep strain accumulation in virgin CMV at engineering design conditions prior to the onset of equilibrium recovery creep. The total strain eTOT will be given by e T O T ---- eND + CNp -I- e e
where eND is the dislocation bowing contribution t o diffusional creep strain; eNp is the Nabarro-Herring creep in the presence of particles; and ee is the elastic strain. At 10 000 h (i.e. near end of transient, Fig. 2) the creep strain will be made up of the above components. For a typical CMV virgin material (rp = 10 -6 cm, Vo = 0.01, d = 3 × 10 -3 cm, o = 40 MPa, T = 570 °C),
4. CALCULATIONOF STRESS RUPTURE CURVES To calculate a stress rupture curve the model developed must be extended. The following can serve as a basis for creep rupture in normalised and tempered CMV material. (1) Over a substantial fraction of the creep life ( - 1 0 5 h), equilibrium recovery creep is not possible, i.e. (o -- Oo)/aGb ¢ x/p. (2) As particle coarsening occurs the effective stress increases until equilibrium creep becomes possible and normal cavity nucleation, growth and coalescence commences. (3) The structure continues to coarsen and ultimately the structure attained will be equivalent to that of a pure iron matrix with a dispersion of large carbide particles. In reality the matrix will n o t be of pure iron, but this is a reasonable hypothesis as a first approximation. (4) At this late stage of coarsening the failure mode could be considered to be that of pure iron creeping at the current effective stress. (5) Since pure iron obeys the M o n k m a n Grant relationship [28], the stress rupture plots will be straight lines and there is no difficulty in determining times to rupture at stresses of the order 10 -* 40 MPa.
208
160 140
SERVICE MATERIAL X
120 I00
CALCULATED RUPTURE LIVES MEAN rSO
90 ~. SO
" ~ . ~ - - ~ \
•---o
EXTRAPOLATED MEAN ISO
7o •
uJ
~ ~o SO DESIGN STRESS
c~Gb = 3 ' 2
x-f
40
Cd
.~r,...OCGb
30
x\
I04
I0 5
RUPTURE LIFE tR
"7;-
: a.B
IO6
(HOURSI
Fig. 6. Comparison of the calculated, extrapolated mean ISO and service exposed stress rupture behaviour of CMV.
Table 2 outlines the time to r u p t u r e calculation for an applied stress of 40 MPa, T = 570 °C, ~ = 5 × 10 - 4 h -z and aGb/ld = 3.2. Column 1 shows the test/service time. Column 2 shows the cur r ent level of (o -- Do(t)) at the time shown in column 1. Column 3 shows the time taken for r u p t u r e of pure iron at the current effective stress level. When column 3 - column 1 fracture occurs. It is possible to follow through a similar argument at o t h e r applied stresses near 40 MPa. However, the equilibrium dislocation density (ld) is required at these ot her stresses before a stress r u p tu r e curve can be derived. Since these values are n o t available at engineering stresses (30 - 50 MPa) it has been necessary t o assume a simple relationship between o -- a0 and x/p in deriving Fig. 6. This figure shows the calculated stress r upt ur e curve on the above basis, also the mean ISO data and its ex tr ap o lated value for normalised and tempered CMV, and l a b o r a t o r y tested data of CMV taken f r o m service after 100 000 hours at 571 °C and 43 MPa.
TABLE
2
Calculation of time to rupture at 40 M P a at 570 °C
(MPa)
Pure iron time to rupture at (o - - Do(t)) (h)
0 104 5 × 104 7 × 104
3.2 5.8 9.3 10.9
-*~ >106 ~ 106 ~-106
10 5
11.8
=10 6
13.5 14.2 14.7 15.2
8.7 8.1 2.19 2.0
T i m e t (h)
Current effective stress (o -- Do(t))
1.5 1.75 2.0 2.2
105 × 105 × 105 × 105 ×
× x × x
105 105 105 106
a = 5 x 10 -4 h -I, c~Gb/Id(O ) = 3.2 MPa. Fracture w h e n column 1 ~ column 3, i.e. tR = 2.2 × 105 h.
Several i m p o r t a n t features are shown on this figure. (1) The failure time at 43 MPa is greater than the mean ext rapol at ed ISO value (---130 000 h).
209
(2) The failure time at 43 MPa is approximately the same as that calculated from service exposed material, i.e. ~- 300 00 h [1]. (3) The coarsening eqn. (21) and the failure model described cannot work at applied stresses approachiJ.~g 150 MPa because there is insufficient time available for particle coarsening. Thus at stresses near and above 150 MPa normal three-stage creep curves prevail [1, 29]. This last point is particularly important and worth emphasising. Stress rupture data of engineering ferritic low alloy steels invariably show downward changing slopes up to presently available laboratory creep rupture times. It is this changing slope which is responsible for the current plethora of extrapolative stress rupture rules. A further factor which current extrapolative methods disregard is the changing creep and rupture mechanism along a stress rupture curve. Confining attention to the fracture behaviour of CMV, it is found that at high stresses and short times to failure, ductilities are high and ductile tearing is the rupture mode [1 ]. At low stresses creep rupture ductilities are much lower and reach a minimum as suggested recently [29, 30]. As the stress rupture mode changes, the constant in the Monkman-Grant relationship also changes [1]. Since the Monkman-Grant relationship is implicitly accepted in many currently used extrapolative techniques it is imperative that the available stress rupture data reflects the mode of creep rupture over the total extrapolated range. In order to generate stress rupture data as above, and additionally validate the currently acceptable extrapolative techniques, we must be careful to include rupture data only where creep ductilities are low and reasonably constant. This situation commonly exists at engineering stresses where pseudo-tertiary curves are found [29] (i.e. where particle size and distribution and hence o0 clearly change during the test). For the case of CMV material all high stress short time to rupture data (typically ~<104 h) must be excluded at 570 °C. This applies specifically to all tests at stresses above approximately 150 MPa where the change from transgranular ductile tearing to nucleation and growth of cavities occurs. One method of identifying this change is to observe the shape of the strain-time curve and by metallography [1]. However measurement of
% on the virgin material by methods outlined recently [3] is equally effective.
5. DISCUSSION In the working model proposed it has been shown that equilibrium recovery creep is not possible at 40 MPa and 570 °C in normalised and tempered CMV. This is because the inherent dislocation mesh is fine, so that the applied stress ( - 4 0 MPa) is unable to create Frank-Read sources as required by the recovery creep model [12]. However, as the copious distribution of fine carbides and dislocation meshes coarsen, a time will be reached in the operation of a service component when recovery creep becomes possible. At this point the equilibrium recovery creep rate becomes established at the current effective stress (eqn. (21)). Examination of Fig. 5 suggests this requires - l 0 s h, although dislocation-particle interactions could introduce an impedance effect delaying the onset of recovery creep. Under these circumstances the diffusional processes will play a more important role in contributing to the total strain accumulated. In the region up to 10 s h diffusion creep can occur. The strain accumulated from this source is, however, small and, in the case of the dislocation climb contribution, saturates at a strain approximately equivalent to the elastic strain. However, as the structure coarsens the dislocation climb process can lead quite naturally to dislocation recovery events and hence recovery creep. It is in the recovery creep range where stress sensitivities of creep rate and fracture are high (n - 4 -* 6) that cavitation becomes strain-dependent. Accordingly we need to identify the time at which recovery creep events commence in order to safeguard the future integrity of structures.
6. CONCLUSIONS The model proposed offers the following advantages. (1) By microstructural examination it should be possible to identify the position of a given cast of material within its stress rupture scatter band. This simple criterion has enormous cost-benefit potential to users of
210 large critical c o m p o n e n t s o p e r a t i n g at elevated temperatures. (2) A c c u r a t e creep r u p t u r e e x t r a p o l a t i o n s m a y be possible using the effective stress approach. (3) T h e first t w o p o i n t s enable realistic life f r a c t i o n s t o be calculated o n service-exposed components. (4) T h e effective stress a p p r o a c h does n o t rely on the analysis o f i n a d e q u a t e service operating records. The operational history of t h e c o m p o n e n t is l o c k e d in t h e m i c r o s t r u c t u r e . (5) T h e m o d e l can be applied n o n - d e s t r u c tively t o large, expensive c o m p o n e n t s , i.e. m i c r o s a m p l i n g and TEM analysis are a d e q u a t e . In c o n c l u s i o n , a w o r k i n g m o d e l o f the creep b e h a v i o u r o f CMV at engineering stresses and t e m p e r a t u r e s has b e e n f o r m u l a t e d . F o r t h e m o d e l t o be applied t o real service situations m e a s u r e d values o f (a) a, the dislocationparticle i n t e r a c t i o n c o e f f i c i e n t ; (b) lp (0), the initial particle size; (c) Ip (t), the particle size w i t h time and h e n c e J3; and ( d ) / d (t), the disl o c a t i o n m e s h spacing with t i m e are required. M e a s u r e m e n t o f these p a r a m e t e r s will p e r m i t calculation o f the effective stress and h e n c e calculation o f the c u r r e n t level o f c r e e p rate and time t o fracture.
ACKNOWLEDGMENT This w o r k was carried out at C E G B Midlands Region Scientific Services Department and the Central Electricity Research Laboratories. The paper is published by permission of the Central Electricity Generating Board.
REFERENCES 1 B.J. Cane and K. R. Williams, C E G B Rep. RD/L/ R 1965, 1977. 2 C. M. Sellars,Creep Strength in Steel and High Temperature Alloys, Sheffield, 1972, Metals Society, 1974, p. 20.
3 K, R. Williams and B. Wilshire,Mater. Sci. Eng., 28 (1977) 289. 4 B. Russell, R. K. Ham, J. M. Silcock and G. Willoughby, Met. Sci.J., 2 (1968) 201. 5 P. L. Threadgill and B. Wilshire, Creep Strength in Steel and High Temperature Alloys, Sheffield, 1972, Metals Society, 1974. 6 M. J. Collins, Creep Strength in Steel and High Temperature Alloys; Sheffield, 1972, Metals Society, 1974, p. 217. 7 P. L. Threadgill and B. Wilshire, Met. Sci. J., 8 (1974) 117. 8 P. W. Davies, G. Nelmes, K. R. Williams and B. Wilshire, Met. Sci. J., 7 (1973) 87. 9 K. R. Williams and B. Wilshire, Met. Sci. J., 7 (1973) 176. 10 J. D. Parker and B. Wilshire, Met. Sci. J., 9 (1973) 248. 11 S. K. Mitra and D. McLean, Proc. R. Soc., 'London, Set. A, 295 (1966) 288. 12 P.W. Davies and B. Wilshire, Scr. Metall., 5 (1971) 475. 13 G. Nelmes and B. Wilshire, Scr. Metall., 10 (1976) 697. 14 W. J. Evans and G. Harrison, Met. Sci., 10 (1976) 307. 15 G. J. Neate and K. R. Williams, CEGB Rep. SSD/ MID/R2/78. 16 K. R. Williams, CEGB Rep. SSD/MID/R3/75, 1975. 17 J. M. Silcock and G. Willoughby, Creep Strength in Steel and High Temperature Alloys, Sheffield, 1972, Metals Society, 1974, p. 122. 18 D. McLean, Trans. Metall. Soe. AIME, 242 (1968) 1193. 19 A. Oden, E. Lind and R. Lagneborg, Creep Strength in Steel and High Temperature Alloys, Sheffield, 1972. 20 J. Friedel, Les Dislocations, Gauthier-Villars, Paris, 1956. 21 G. L. Dunlop and R. W. K. Honeycombe, Met. Sci., 11 (1977) 495. 22 M. F. Ashby, Scr. Metall., 3 (1969) 837. 23 B. Burton, CEGB Rep. RD/B/N3225, 1974. 24 B. Burton, CEGB Rep. RD/B/N2245, 1972. 25 F. R. N. Nabarro, Philos. Mag., 16 (1967) 231. 26 B. Burton and G. L. Reynolds, Philos. Mag., 29 (1974) 1359. 27 K. R. Williams, CEGB Rep., 1979. 28 K. R. Williams, Doctoral Thesis, University of Wales, 1969. 29 P. Smith and K. R. Williams, CEGB Rep. SSD/ MID/R75/75, 1975. 30 B. J. Cane, Mater. Sci. Eng., 35 (1978) 229.