Microstructural instability of 0.5Cr0.5Mo0.25V creep-resistant steel during service at elevated temperatures

Microstructural instability of 0.5Cr0.5Mo0.25V creep-resistant steel during service at elevated temperatures

Materials Science and Engineering, 47 (1981) 151 - 160 151 Microstructural Instability of 0.5Cr-0.5Mo-0.25V Service at Elevated Temperatures Creep-...

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Materials Science and Engineering, 47 (1981) 151 - 160


Microstructural Instability of 0.5Cr-0.5Mo-0.25V Service at Elevated Temperatures

Creep-resistant Steel During


Central Electricity Research Laboratories, Leatherhead, Surrey (Gt. Britain) B. WILSHIRE

Department of Metallurgy and Materials Technology, University College, Swansea (Gt. Britain) (Received July 31, 1979; in revised form July 29, 1980)


A study was made of the microstructures developed after normalizing and tempering O.5Cr-O. 5Mo- O.25 V ferritic steels and of the changes which occur during service in electricity-generating plant. Progressive loss of creep resistance due to changes in carbide dispersion rather than to the development of grain boundary cavities and cracks is shown to determine the creep life under operating conditions.


Low alloy ferritic steels of the 0.5Cr0 . 5 M o - 0 . 2 5 V type are used extensively for the production of steam turbines for electricity generation. Components such as main and reheat steam pipes are required to operate for periods up to 250 000 h at temperatures where creep deformation can occur. The design specified in the relevant British standard [ 1] assumes that the pipework operates at a constant known pressure and temperature and that the creep life is related to uniaxial stress rupture data. For a required design life the operating stress is usually determined by applying a safety factor of a b o u t 1.2 - 1.5 to the uniaxial data in order to allow for interbatch variations in material properties and for minor deviations from the standard operating conditions expected. During plant operation there is often a need to calculate the remaining life of individual components either because the original design life has been reached or because of the wide range of temperatures which can be experienced in service 0025-5416/81/0000-0000/$02.50

[2]. Since it is essential that the remanent life is estimated with reasonable precision, a detailed understanding of the deformation and fracture processes is necessary. For this reason an investigation of the changes in microstructure which occur during creep of 0 . 5 C r - 0 . 5 M o - 0 . 2 5 V steels was made using samples taken both from operating plant after various known times and from laboratory specimens which had been creep tested under service conditions. This study demonstrates (i) the relevance of changes in the size, spacing and type of carbide present in determining the gradual deterioration in creep resistance observed for tests carried out at low stress levels, (ii) the extent to which creep damage is localized during long-term exposure and (iii) the limited importance of grain boundary cavity development in determining the creep life under service conditions.



Several programmes have been aimed at determining the microstructures developed in 0 . 5 C r - 0 . 5 M o - 0 . 2 5 V steels which had been transformed by continuous cooling from the austenitizing temperature followed by tempering [3 - 6]. In these investigations, optical metallography and electron microscopy of carbon replicas were used so that the precise nature of the precipitates developed could not be identified fully. More recently, these techniques have been supplemented by transmission electron microscopy in order that the ferrite morphologies and the carbide precipitate dispersions in this type of steel could be © Elsevier Sequoia/Printed in The Netherlands


TABLE 1 Chemical analyses of the samples Sample a












M1 M2 M3 M4 M5 M6 R1 R2

0.105 0.105 0.13 0.12 0.10 0.105 0.11 0.14

0.19 0.14 0.28 0.30 0.17 0.15 0.25 0.26

0.021 0.024 0.038 0.035 0.018 0.030 0.022 0.012

0.023 0.036 0.018 0.020 0.026 0.028 0.021 0.009

0.48 0.47 0.53 0.55 0.61 0.50 0.67 0.47

0.41 0.35 0.34 0.42 0.44 0.40 0.39 0.42

0.10 0.11 0.10 0.06 0.08 0.11 0.051 0.13

0.53 0.50 0.53 0.54 0.41 0.52 0.63 0.56

0.22 0.24 0.24 0.25 0.26 0.24 0.26 0.24





0.12 0.11

0.006 0.014

aM, main steam pipe; R, reheat pipe. comprehensively examined after isothermal transformation at a number of subcritical temperatures in the ferrite and bainite ranges [7]. The components used in electricitygenerating plant are normally produced by extrusion, followed by normalizing and tempering. The steam pipes are usually held for 2.7 ks at 1223 - 1253 K, are air cooled and are tempered at 948 - 978 K for 10.8 ks. Since this procedure results in complex mixed microstructures, the range of possible structures was examined prior to a study of the changes occurring during service under stress at elevated temperatures. This was accomplished by sampling several casts of commercial 0.5Cr-0.5Mo-0.25V steel during the construction of the main steam pipe of outside diameter 356 mm and wall thickness 61 mm from one power station and of reheat pipe of outside diameter 490 mm and thickness 29 mm from two other stations. The chemical analyses of these samples are given in Table 1 and the average grain diameters and hardness values are included in Table 2. Random samples were obtained in both the axial and the hoop directions. Preliminary examination indicated relatively little microstructural variation between the inside and outside sampling positions of the pipes. The samples were then turned down to rods 3 mm in diameter from which discs 0.75 mm thick were spark machined. The discs were polished to a thickness of 0.15 mm before thinning using a solution of 5% perchloric acid in methanol at 213 K. Approximately five discs were examined for each cast using a Hitachi 1000 or AEI EM7 high voltage electron microscope (1 MeV). In this way, about a hundred different grains were examined for each of the eight samples.

The complex structures observed can be described most easily in terms of their development on cooling from the austenitizing temperatures to form the predominantly ferritic microstructure. Since the bainitic regions were generally found to occupy less than about 8% of the volume, the present investigation was concentrated primarily on the ferrite phase. It has been established that alloy carbides can precipitate concurrently with the direct transformation of austenite to equiaxed ferrite [7]. The ferrite phase develops from the original austenite boundaries. Periodic precipitation of carbide at the 7 - a interface then leads to stepwise movem e n t of the phase front and the generation of a banded dispersion of carbide particles in the ferrite regions. The appearance of this interphase carbide is shown in Fig. 1. This was identified as VC by means of selected area diffraction analysis, energy-dispersive X-ray analysis and particle morphology. As widely reported for vanadium carbide precipitation in ferrite [8], the Baker-Nutting orientation relationship with the matrix was found, namely

(lOO} vc/(lOO}~
aM, m a i n s t e a m p i p e ; R, r e h e a t pipe.


5 x 10- 7 7 X I0 - 3

2 x I 0- 6

2 x 10-6

1.6 x 10- 6

2 x 10-6

5.0 x 10- 6

3 x I 0- 5

1.4 X 10 - 2

7.5 x 10- 7


1.8 x 10-6

2 x 10- 6

1.2 x 10 - 2

6.5 x 10-6

2 x 10- 6

6 x 10- 6

1.6 x 10- 5


1.7 x 10- 6

6.3 × 10- 6

8 x 10- 7

9 × 10- 6

Particle size (cm)



10- 7


6.5 x 10- 6

7.6 x 10-6

<10 -3 maximum


1.6 X 10- 6

6 x 10 - 3

5 x 10- 6


3.5 x I 0 - 6

5 × 10-6

8 x 10 - 3

1.4 x 10- 5

Particle size (cm)

V o lu m e fraction fI

She e t spacing (cm)

Particle size (cm)





Sample a

Microstructural parameters


5.5 × 10- 4

21 x 10- 4

42 x 10- 4

32 x 10- 4

29 x 10- 4

41 x 10- 4

34 x 10- 4

43 × 10- 4


Grain size



















Volume fraction fB o f bainite

1.3 x 10- 5

0.24 x 10- 5

3 × 10- 5

1.6 x 10- 5

1.2 x 10- 5

4.8 x l 0 - 5

0.65 x 10- 5

4.0 x 10- 5


M i n i m u m interparticle spacing


Fig. 1. VC I precipitates present in 0.5Cr-0.5Mo0.25V steel in the normalized and tempered condition. (Magnification, 28 000× .)

Fig. 3. VCD precipitates present in 0.5Cr-0.5Mo0.25V steel in the normalized and tempered condition. (Magnification, 14 000× .)

content of the remaining austenite increases. During isothermal transformation of these steels this effect eventually slows down the rate of transformation and the spacing of the bands of VCI increases because the band spacing is related to the rate of movement of the 7-~ interface [7]. A similar p h e n o m e n o n was found in the present study since the regions of VCI gradually merged into zones with a more " r a n d o m " vanadium carbide (VCR) precipitate dispersion (Fig. 2). Whilst the random carbides in this zone were similar in size and volume fraction to those of the VCI for the same sample (Table 2), these carbides showed no fixed orientation relationship with the matrix. This random VCR precipitation (Fig. 2) usually appeared as a transition zone between the VCI (Fig. 1) and a

more complex structure composed of vanadium carbide particles associated with dislocations (VCD) in the ferrite regions obtained on transformation of the remaining austenite as cooling proceeded (Fig. 3). In addition to these three principal forms of carbide, small regions of fibrous precipitate [7] were occasionally found in some batches of material (Fig. 4). Whilst all the materials examined showed clear areas of VCI, VCR and VCD, the proportion of each constituent structure varied from a b o u t 80% VCI to almost 80% VCD in the individual casts studied. This variation in microstructure could then be a major factor in accounting for the batch-to-batch scatter in the uniaxial creep and stress rupture data reported for this type of steel [9]. The vari-

Fig. 2. V C R precipitates present in 0.5Cr-0.5Mo0.25V steel in the normalized and tempered condition. (Magnification, 28 000x .)

Fig. 4. A region of fibrous carbide precipitate which was occasionally found to be present in 0.5Cr0.5Mo-0.25V steel in the normalized and tempered condition. (Magnification, 14 000× .)



18 .o_----------o----t-











lOO 8C



7,. .J

//' ~ 4C




I 650

I 675

I 700


/ 725

I 775




Fig. 5. (a) Dispersion parameters for VC I developed in 0.5Cr-0.5Mo-0.25V steel at different isothermal transformation temperatures; (b) grain size developed in 0.5Cr-0.5Mo-0.25V steel at different isothermal transformation temperatures [ 7 ].

ability can be explained in terms of the isothermal transformation behaviour recorded for 0.5Cr-0.5Mo-0.25V steels [7]. When samples were quenched from the austenitizing temperature to various temperatures in the range 920 - 1050 K, the size and sheet spacing of the VCI decreased with decreasing transformation temperature (Fig. 5(a)). The average carbide size and sheet spacing were therefore calculated for VCi for each of the present samples. The average size and interparticle spacing k were also determined for the VCR and VCD regions using the expression [ 10] =


temperatures above approximately 973 K. On this basis, because of the slow cooling rates expected with heavy section pipe, a complete ferrite morphology with VC~ precipitates could be anticipated in the normalized and tempered condition. The more complex structures obtained and the interbatch variations in microstructure observed may then have been influenced by differences in chemical composition (Table 1) but more probably appear to reflect small but important differences in cooling rate. Thus for example the greater hardness and higher volume fraction of bainite found for reheat pipework is then compatible with the faster cooling rates expected for the thinner sections employed.

(Nd)- - I / 2

where N is the number of particles per unit volume and d is their average diameter. The results obtained for the VCI regions (Table 2) suggest that the interphase precipitate developed at temperatures in the range 1023 1073 K. A further indication of the transformation temperature was obtained by comparison of the present grain sizes (Table 2) with those reported for various isothermal transformation temperatures (Fig. 5(b)). This comparison again indicated that transformation occurred above 1023 K except for one batch of reheat pipe. Determination of the apparent transformation finish times by isothermal dilatometry suggests that transformation should be complete within about 200 s at

3. MICROSTRUCTURAL CHANGES DURING SERVICE OF 0.5Cr-0.5Mo-0.25V STEELS In order to determine the extent to which the microstructures produced by normalizing and tempering are stable at elevated temperatures, a series of samples was taken from primary and reheat steam pipes, although some further specimens were obtained from headers and manifolds. These components had operated at nominally between 30 and 50 MN m - 2 at 840 K for periods between 20 000 and 100 000 h. The information derived from these samples was then supplemented by the results obtained for specimens tested under uniaxial tension for similar periods under these service conditions. The size, spacing and type of carbides found in the normalized and tempered conditions (Figs. 1 - 4) were found to have changed considerably. The carbides had coarsened gradually in a manner so as to produce a more uniform structure. In particular, the interphase carbide regions which were easily discernible in the original materials (Fig. 1) became progressively more difficult to identify (Fig. 6). In addition to the general increase in size of the vanadium carbide particles, H-type precipitates became increasingly evident (Fig. 7). This type of precipitate was initially reported by Felix and Geiger [11] and subsequently by Murphy and Branch [4]. H-type carbides are composed of a central particle rich in vanadium with M o 2 C wings, suggesting that growth of M o 2 C o c c u r s on pre-existing vanadium carbide particles. This view is sup-


Fig. 6. Microstructure developed after 35 000 h in a uniaxial creep test carried out at 838 K and 49 MN m - 2 , showing coarsening of the original VC I particles and the gradual formation of particle-free zones adjacent to grain boundaries. (Magnification, 18 900X.)

certain types of vanadium carbide plate appear to be effective in nucleating Mo2C. Thus, for example, the early stages of H.type precipitation were detectable in only one of the original samples in the normalized and tempered condition which showed significant areas of large VCD precipitation (Fig. 8). It then appears that the partially coherent carbides formed by interphase precipitation offer limited nucleation sites for the growth of Mo2C whereas more potential sites develop as the vanadium carbide particles grow during long exposure times at elevated temperatures. This suggests that a high incidence of H-type precipitation would be expected only in normalized and tempered material with large VCD precipitates or, more significantly, in samples in which large spherical vanadium carbide particles had developed during service. As changes in the size, spacing and form of the carbide particles occurred, the density of dislocations evident within the grains increased very gradually. The individual dislocations observed within the grains were almost invariably found to be held up at carbides (Fig. 6), suggesting a gradual loss of creep resistance as particle coarsening takes place. Moreover, growth of grain boundary carbides leads to the progressive formation of particlefree zones adjacent to the boundaries (Fig. 6). The high dislocation density generally observed within these zones demonstrates that creep of 0.5Cr-0.5Mo-0.25V steels during

Fig. 7. Development of H-type precipitates (illustrated by regions labelled A) in 0.5Cr-0.5Mo--0.25V steel samples taken from main steam pipe after 64 000 h service at approximately 40 MN m - 2 and 838 K. (Magnification, 18 9 0 0 x . )

ported by the observation that the ratio of vanadium to molybdenum decreases with increasing particle size, indicating continued diffusion of molybdenum to these sites during service. Molybdenum diffuses to and dissolves in the vanadium carbide and, as the molybdenum content of the particle increases toward saturation, nucleation of molybdenum carbide (Mo2C) becomes possible at the periphery of the vanadium carbide plate. Only

Fig. 8. Initial stages of H-type precipitate formation at VC D particles in 0.5Cr-0.5Mo-0.25V steel in the normalized and tempered condition. (Magnification, 38 500x .)


Fig. 9. Dark field micrograph of the microstructure developed in samples of 0.5Cr-0.5Mo-0.25V steel taken from a reheat header after 50 000 h service at approximately 40 MN m - 2 and 838 K, illustrating the high dislocation densities developed in particle-free zones adjacent to grain boundaries. (Magnification, 21 000× .)

Fig. 11. Grain boundary migration occurring in samples of 0.5Cr-0.5Mo-0.25V steels taken from a reheat header after 50 000 h service at approximately 40 MN m - 2 and 838 K. (Magnification, 9100× .)

which were developing along the original grain boundaries (Fig. 12).


A network of dislocations was observed within the grains during creep of samples of ferritic steel taken from components after varying periods of service (Figs. 9 and 11) and for conventional test pieces subjected to uniaxial tensile creep conditions comparable with those experienced during plant operation

Fig. 10. Microstructure developed after 35 000 h in a uniaxial creep test carried out at 838 K and 49 MN m - 2 , showing the gradual formation of a subcell structure within the ferrite grains. (Magnification, 18 900x.)

service at low stress levels occurs in a highly inhomogeneous manner (Fig. 9). This inhomogeneity of deformation leads to the development of poorly formed subgrain boundaries in limited regions within the ferrite grains (Fig. 10). A further feature associated with the gradual formation of particle-free zones is the occurrence of grain boundary migration (Fig. 11). This migration has the important effect of isolating, within grains, the cavities

Fig. 12. Isolation of grain boundary cavities within grains due to the occurrence of migration in samples of 0.5Cr-0.5Mo-0.25V steel taken from main steam pipe after 64 000 h service at approximately 40 MN m - 2 and 838 K. (Magnification, 4900x .)


(Figs. 6 and 10). Dislocation creep theories can be classified into two main groups, those in which dislocation glide processes are considered to be rate controlling and those that depend on dynamic recovery by climb. It has previously been established that, immediately after small stress reductions during creep of ferritic steels, incubation periods of zero creep rate were recorded before creep recommenced at the reduced stress level [12]. This behaviour indicates that dislocation glide mechanisms cannot be rate controlling since, with these processes, a small decrease in stress should be followed immediately by a new slightly lower creep rate and not by an incubation period of zero creep rate. Instead, the occurrence of incubation periods suggests that the flow stress of the material must decrease by recovery before creep can begin again after the stress reduction, i.e. creep of ferrite steels is recovery controlled. The absence of piled-up arrays within t h e ferrite grains suggests that the creep rate is not determined by recovery processes such as the climb and annihilation of edge dislocations from pile-ups of opposite sign on parallel slip planes [13]. Similarly, since the dislocations pinned between carbide particles were invariably found to be bowed o u t along the slip planes in the ferrite (Figs. 9 and 11), the dislocation arrangements are incompatible with the model proposed by Nabarro [14] in which deformation occurs by the operation of Bardeen-Herring sources. The present observations are interpretable, however, in terms of a recovery model for creep [15] in which diffusion-controlled growth of the network leads to the development of link lengths sufficiently long to act as dislocation sources, allowing slip to occur. Even though the dislocations emitted by a source would be expected to rearrange themselves rapidly, the local increase in dislocation density necessitates that the next slip event occurs elsewhere. In this way, a balance between recovery and strain-hardening processes leads to the gradual formation of a roughly constant distribution of link lengths in the network during creep. The occurrence of incubation periods would then be anticipated since, immediately after a small stress reduction, even the longest links present would be t o o small to act as sources so that creep cannot recommence until t h e network size grows by recovery.

At high stress levels the dislocations emitted by a source can b o w between or cut through the particles depending on their size and spacing [16]. In low stress tests the dislocations generated would have to climb over the particles in order that deformation can continue [17]. Alternatively, it has been proposed that the creep rate of two-phase alloys at low stresses is mainly determined by t h e rates of deformation in regions of the grains adjacent to grain boundaries [16]. The extensive development of particle-free zones (Figs. 6 and 9) supports the view that this localized deformation in the grain boundary zones controls the creep behaviour of ferritic steels under service conditions. However, the rate of source generation and the strain resulting from the operation of a source during creep of ferritic steels would depend not only on the carbide spacing but also on the effects of alloying elements present in solid solution. Although dislocations were almost invariably found to be held up at carbides, indicating the relevance of particle hardening under the conditions studied, indirect evidence suggests t h a t the matrix characteristics are also important. This was inferred from measurements of the interparticle spacing in relation to the hardness of the present range of as-received samples in the normalized and tempered condition (Table 2) and for similar materials after service. For both groups of materials the hardness increased with decreasing particle spacing as expected for particle-strengthened alloys (Fig. 13). Even so, for the same interparticle

2O0 190 100 170 160

r 150



o ~


A o



Fig. 13. The relationship between the interparticle spacing o f vanadium carbide precipitates and the room temperature hardness for a range of samples (curve A) in the normalized and tempered condition prior to service and (curve B) in similar samples of 0 . 5 C r - 0 . 5 M o - 0 . 2 5 V steel after service at approximately 40 MN m - 2 and 838 K for periods within the range 20 000 - 100 000 h.


spacing the lower hardnesses of the materials after service indicates a decreased contribution of solid solution strengthening to the room temperature strength. Several investigations have demonstrated that the creep resistance of ferritic steels is affected by the level of m o l y b d e n u m in the matrix [9, 18]. The loss of m o l y b d e n u m from solid solution due to the growth of H-type precipitates during service (Figs. 7 and 8) would be compatible with the decrease in strength after long-term exposure (Fig. 13). Examination of the creep curves recorded for 0 . 5 C r - 0 . 5 M o - 0 . 2 5 V steels tested in tension at low stress levels reveals that the creep rate increases steadily throughout the major portion of the creep life [12]. This continuous acceleration in creep rate is a result of the gradual loss of creep strength due to the changing size and type of the carbides present and the formation of particle-free zones near grain boundaries rather than a consequence of the progressive development of intergranular cavities and cracks. Indeed, cavity development does n o t appear to play a significant role either in causing this acceleration in creep rate or in the determination of the rupture life. Few cavities were discernible by metallographic examination until the late stages of the creep life in tests carried out at low stress levels [12]. However, the transmission electron microscopy did reveal several examples of the isolation of small cavities within grains due to the occurrence of migration in the precipitate-free zones (Fig. 12). Cavities so isolated will not continue to grow during subsequent creep. On this basis, fracture occurs only when the loss of creep strength proceeds to a stage at which the rapid development of cavities and cracks can occur late in the creep life. The marked changes in carbide dispersion occurring during long-term exposure of 0 . 5 C r - 0 . 5 M o - 0 . 2 5 V steels are consistent with the fact that extrapolation of conventionally derived short-term data 1.eads to serious overestimation of the expected life so that only when data are available to approximately 30 000 h are the 100 000 h predictions reasonably accurate [19]. Furthermore, the detection of intergranular cracks only just prior to fracture suggests that estimates of rupture times by calculation of the expected rates of growth and link-up of cavities to form

cracks [ 20] cannot provide a realistic prediction of the service life of this type of material. The present observations are directly compatible, however, with the life assessment method that we suggested previously [12] which is based on the recognition of the continuous strength degradation associated with microstructural instability during creep of ferritic steels.


(1) The vanadium carbide precipitates developed in 0 . 5 C r - 0 . 5 M o - 0 . 2 5 V ferritic steels after normalizing and tempering existed predominantly as regions of VCI, VCR or VCD. The proportion of each of these forms of precipitate observed in different batches of material appeared to depend primarily on minor variations in cooling rate during normalization. (2) During service under low stresses at elevated temperatures, the vanadium carbide particles coarsened and H-type carbides formed as wings of Mo2C developed on the original vanadium carbide particles. The distinctly different carbide dispersions present initially in different regions of the normalized and tempered materials became increasingly less apparent with increasing service times. (3) The deformation behaviour was consistent with a recovery model for creep in which diffusion-controlled growth of the dislocation network generated link lengths sufficiently long to act as dislocation sources. At the low stress levels considered, growth of grain boundary carbides resulted in deformation occurring predominantly in particle-free zones adjacent to the boundaries. These changes in carbide dispersion led to a progressive loss of creep resistance, giving the continuously increasing creep rate recorded in uniaxial tensile tests. (4) The limited numbers of grain boundary cavities developed early in the creep life were found to become isolated within grains owing to the occurrence of migration in the precipitatefree zones. Intergranular cracks therefore became discernible only late in the creep life when the gradual loss of creep strength proceeded to a stage at which rapid crack development could occur.


This p a p e r is published with the permission o f the Central Electricity G e n e r a t i n g Board.

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9 V. Foldyna, A. Jakobova, T. Prnka and J. Sobotka, Proc. Conf. on Creep Strength in Steel and High Temperature Alloys, Sheffield, 1972, Metals Society, London, 1973, p. 230. 10 K. H. Westmacott, C. W. Fountain and R. J. Stirton, Acta Metall., 14 (1966) 1628. 11 W. Felix and T. Geiger, Sulzer Tech. Rev., 3 (1961) 37. 12 K. R. Williams and B. Wilshire, Mater. Sci. Eng., 28 (1977) 289. 13 J. Weertman, J. Appl. Phys., 26 (1955) 1213. 14 F. R. N. Nabarro, Philos. Mag., 16 (1967) 231. 15 P. W. Davies and B. Wilshire, Ser. Metall., 5 (1971) 475. 16 P. L. Threadgill and B. Wilshire, Met. Sci., 8 (1974) 117. 17 G. S. Ansell and J. Weertman, Trans. Metall. Soc. AIME, 215 (1959) 383. 18 J. D. Baird, A. Jamieson, R. R. Preston and R. C. Cochrane, Proc. Conf. on the Creep Strength in Steel and High Temperature Alloys, Sheffield, 1972, Metals Society, London, 1973, p. 207. 19 R. F. Johnson and J. Glen, Proc. Conf. on the Creep Strength in Steel and High Temperature Alloys, Sheffield, 1972, Metals Society, London, 1973, p. 37. 20 G. W. Greenwood, in D. M. R. Taplin (ed.), Proc. 4th Int. Conf. on Fracture, University o f Waterloo, Ontario, June 19 - 24, 1977, Vol. 1, Pergamon, Oxford, 1978, p. 293.