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Fatigue crack growth studies in rail steels and associated weld metal
Theoretical and Applied Fracture Mechanics 6 (1986) 75-84 North-Holland
75
FATIGUE CRACK G R O W T H S T U D I E S IN RAIL S T E E L S AND A S S O C I A T E D WELD M E T A L J.H. B U L L O C H Department of Metallurgy, University of the Witwatersran~ Johannesburg, South Africa.
Fatigue crack growth studies in rail steels and associated weld metal have shown that (a) deformed rail steel exhibited fatigue crack growth rates that are slightly faster than undeformed rail steel and (b) weld metal growth data are appreciably faster than rail steel growth results and exhibit growth rate plateaux that reside above the upper bound reported for rail steel fatigue crack growth. In rail steel microstructures at low AK levels fatigue crack extension occurred by a ductile striated growth mechanism. However at Kmax values approaching 40 MPa x/m transgranular cleavage facets initially formed and their incidence increased with Kmax until final fast fracture. The average cleavage facet size agreed well with pearlite nodule dimensions of 60-100 ~m. The weld metal microstructure was much coarser than the rail steel and contained highly directional columnar grain growth. At all AK levels the dominant fracture mode was transgranular cleavage containing small isolated regions of ductile striated fatigue crack growth. The cleavage facet size varied from 150 to 600 rtm; such a large variation was explained by the fact that in general crack extension tended to occur in association with the proeutectoid ferrite phase.
1. Introduction Although the range of microstructures that can be developed in steels is fairly large, the most common structure associated with good tensile properties is that based on pearlite. Pearlite is made up mainly of a ductile ferrite phase containing about 12% by volume of cementite, a hard intermetallic compound. It is generally accepted that in as transformed high carbon steels the interlamellar spacing in the pearlite controls the monotonic strength properties [1,2]. In the case of fatigue crack growth behaviour in predominantly pearlitic microstructures it is unclear which microstructural parameters affect crack growth. Generally the microstructural parameters affect the tensile properties and fatigue characteristics quite differently. Heald et al [3] has shown that in a 1% C steel considerably faster growth rates were found for a pearlitic microstructure on account of differing fatigue crack growth mechanisms. Various other workers [4,5,6] have demonstrated that transgranular cleavage in addition to ductile fracture occurs in pearlitic steels when the cyclic stress intensity, AK, is increased. A common method of increasing the tensile strength properties of pearlitic microstructures it to plastically deform, usually by a wire drawing process. Such microstructures exhibit large in-
creases in strength at modest levels of plastic deformation. Little is known about the effect of plastic deformation on the fatigue characteristics in pearlitic microstructures. One study on a heavily cold rolled eutectoid steel [7] has demonstrated that short subcritical annealing treatments (350500°C) markedly reduced fatigue crack growth behaviour. A recent study [8] on a 0.2% C steel reported that low levels of prestrain reduce the fatigue life while high levels increase it. The present report describes the fatigue crack behaviour of (a) rail steel in the undeformed and deformed (c = 1%) conditions and (b) associated weld metal material. A detailed fractographic study is also reported.
2. Experimental procedure A section of rail steel containing a weld were supplied to the University of the Witwatersrand. The chemical analysis of the rail steel was as follows: C
Mn
Si
S
0.67
1.01
0.54
0.014
P
Cr
Mo
V
Cu
0.013
0.84
0.01
0.11
-
0167-8442/86/$3.50 © 1986, Elsevier Science Publishers B.V. (North-Holland)
76
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
A section of rail 200 m m in length and 10 m m thick was machined from the rail head and was plastically deformed by 1% (c = 1%). Single edge notch (SEN) pin loaded tensile specimens, 5 m m thick and 37 m m in width, were machined from the undeformed rail steel, the deformed rail section and the weld metal material. Two hounsfield tensile specimens, 5 m m diameter, 20 m m gauge length, were machined from the undeformed rail steel in order to assess the tensile properties. Fatigue crack growth tests were carried out in air on a 50 kN capacity servohydraulic fatigue test facility at an R-ratio = 0.1, utilising a sinusoidal stress waveform at a frequency of 30 Hz. Fatigue crack growth was monitored by travelling microscopes (magnification X 7) located on both sides of the SEN specimen. After fatigue testing each test specimen was halved perpendicular to the fatigue crack growth direction. One half was mounted so that crack profile and microstructural details could be determined while the other half was used for a fractographic study of the fatigue fracture surface. The bulk of the metallographic/fractographic studies was carried out on a 620 Hitatchi Scanning Electron Microscope (SEM). Interlamellar pearlite spacing, pearlite colony size and pearlite nodule size were measured for both the rail steel and the weld metal material. For each microstructure 100 random fields were taken, magnification 2000-5000, and the number of lamellae intercepts counted on a linear grid mounted on the screen of the S.E.M. The total length of line divided by the number of cementite lamellae intersected is defined as g, the mean intercept spacing. This value is simply related to both the interface area per unit volume, Sv, and the mean true lamellar spacing X0- It can be shown that 4 sv = 2 '
(1)
and an approximate expression due to Satykov relates the mean true spacing ~0 to ~. By considering a cube of geometrically ideal pearlite of mean true spacing, ~'0, with two of the cube faces parallel to the lamellae it can be seen that the total interfacial area within the cube is 2
Sv = X=-~.
(2)
Combining eqs. (1) and (2) gives •= 2~ 0 .
(3)
More exact forms of eq. (1) have been developed to deal with situations where not all the cementite platelets have a planar orientation and details of the various methods available for measuring peariite interlamellar spacing have been reported by Underwood [9].
3. Experimental results
3.1. Fatigue crack growth data Duplicate tensile tests on the undeformed rail steel gave the following values: 0.2% proof stress = 475 MPa and Ultimate Tensile Strength (U.T.S.) = 955 MPa. The fatigue crack growth results for the undeformed rail steel, deformed rail steel and weld metal material are shown in Fig. 1, together with the upper and lower bound fatigue data for rail steels reported by Steel [10]. These upper and lower bound lines also encompass the recently
LEGEND • 10_5 --
IL / I / I/
Undeformed Rail
•
"In service" Deformed Rail z~ Laboratory Deformed Rail o Weld Metal 10_6
I /I 13000 I
-
Crack Growth Rate (m/cycle)
,Y
10 -7 Upper b o u n d / / ~ rail steels Ref. 10 /
10_a
I 10
I 20
I 30
I 50
I 100
A K (M Pal/'~ )
Fig. 1. Fatigue crack growth data for deformed and undeformed rail steel and weld metal compared with upper and lower bound lines after [10].
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
77
reported upper and lower bound fatigue crack growth data of Ibabe and Sevillano [11]. From this figure it can be seen that the deformed rail steel fatigue crack growth data is about 2-3 times faster than the undeformed rail steel data while both reside within the upper and lower bound data. Both exhibit straight line Paris law behaviour and can be described by the following equations: (a) Undeformed rail steel da = 1.92 X 10 -17 A K 6"3, d N(M/cycle)
(4)
(b) Deformed rail steel da = 1.41 X 10 -17 A K 6'9. d N(M/cycle)
(5)
The weld metal fatigue crack growth data did not exhibit a Paris law dependence with AK level. In this case crack growth appeared to be locally unstable and exhibited growth rate plateau that were sometimes 5 times faster than the upper bound growth data for rail steels. It is interesting to note that the Paris exponent values of both rail steels were between 6 and 7 which is appreciably above the normal exponent values of 2-4.
b
2
3.2. Microstructural details Fig. 2. General details of rail steel and weld metal microstructures. Magnitude: 30x.
General details of the rail steels microstructures (undeformed and deformed rail steel microstructures were identical) and weld metal microstructure are shown in Fig. 2. The rail steel exhibits a fine fully pearlitic microstructure, average colony size = 50 ~tm, with little evidence of proeutectoid ferrite, Fig. 2 (a) while the weld metal showed extensive ferrite formation that tended to decorate prior austenite grain boundaries. Also much of the proeutectoid ferrite was nucleated along coarse directional columnar grain boundaries, Fig. 2 (b), that were 0.5 to 1 mm in width. The weld metal microstructure was predominantly pearlitic with an average pearlite colony size of 200-300 ~m. Mean true interlamellar pearlite spacings were recorded with the following results (i) undeformed rail steel X0 = 184 nm, (ii) deformed rail steel X0 = 175 nm and (iii) Weld metal ~0 = 136 nm. Micrographs of the pearlite formed in the rail steel and weld metal are shown in Fig. 3.
Details of the nature of the proeutectoid ferrite formed in the weld metal microstructure are illustrated in Fig. 4, i.e., Fig. 4(a) shows the formation of block proeutectoid ferrite along prior austenite grain boundaries while Fig. 4(b) shows the acircular nature of the grain boundary nucleated ferrite. In this case the ferrite is in the form of fine needles protruding into the pearlite phase and are either Widmanstatten ferrite or the initial ferrite laths prevalent in upper bainitic microstructures.
3.3. Fatigue crack profile details General details of the fatigue crack growth behaviour of rail steels showed that crack extension occurred by ductile striated growth in a
78
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
Fig. 3. Detailed views of the nature of the pearlite formed in rail steel and weld metal microstructures.
transgranular fashion through pearlite colonies fracturing the cementite lamellae. The principal crack paths in the lamellar pearlitic microstructures were along ferrite-cementite interfaces and, in a few isolated cases, along prior austenite grain boundaries. These observations are similar to those recorded by Taylor et al [12]. At grnax values approaching 40 M P a v ~ small isolated flat regions, up to 100 rtm in size, were observed to appear in the fatigue crack profile of both the deformed and undeformed rail steels. These were shown to be isolated regions of
transgranular cleavage fracture, i.e., micro-cleavage facets. Crack profile details of the weld metal microstructure were markedly different to the extent that the fatigue crack path followed a rather tortuous route and exhibited large flat areas that in some instances were 150-600 ~m in length. Such flat regions were indeed large transgranular cleavage facets and the majority of the fatigue crack growth profile exhibited this type of fracture mode. General details of fatigue crack profiles in weld metal are shown in Fig. 5. This figure illustrates
Fig. 4. Details of proeutectoid ferrite formation in weld metal.
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
79
Fig. 5. Fatigue crack profile details of weld metal. Note within the columnar grain, 300-600 ~m in width, there are flat regions of fracture, i.e., cleavage facets. Thus, cleavage fracture facet size is not dictated by these coarse columnar grains but by some other microstructural unit.
the rough nature of crack extensions; also the flat transgranular cleavage regions were in some cases somewhat smaller that the width of the coarse columnar grains. A detailed study of the flat transgranular cleavage regions showed that in many instances the failure event occurred along, or was associated with, grain boundary proeutectoid ferrite, see Fig. 6. Many instances of secondary cracking some distance away from the main crack front were recorded in the weld metal microstructure.
3.4. Fractographic details The general nature of the fatigue crack growth process in rail steels at initial AK levels are illustrated in Fig. 7; the failure mode is transgranular ductile striated growth that exhibited marked directionality effects which probably result from the extension of the fatigue crack through adjacent pearlite colonies with differing growth orientations. At Kma x values approaching 40 MPav/-m" the onset of discrete regions of transgranular cleavage occurs in both the deformed and the undeformed rail steel microstructures and an instance is shown in Fig. 8. The individual size of the cleavage facets were 40-100 ~tm. Initiation sites at each facet
Fig. 6. Crack profile details of fatigue crack propagation along grain boundary ferrite regions in weld metal. Note fatigue crack has propagated through a region of grain boundary ferrite, then the main crack front suddenly changed direction and propagated through a pearlite colony leaving a secondary crack (arrowed) in the grain boundary ferrite.
were clearly evident and generally growth spreads out in the direction of macro crack growth. Such isolated cleavage facets occurred mainly at the test specimen centre; similar observations have been made by other workers [13]. This effectively means that the critical strain for fracture is first satisfied at the centre of the crack envelope. As the crack continues to extend cleavage facets occur in groups across the whole crack front. General features of the cleavage facets are: (a) They are fan-shaped in nature and have a definite initiation site. There is no evidence of cleavage initiating from a cracked cementite lamellae but a few instances of facets initiating from non-metallic inclusion sites were recorded, (b) River lines emanate outwards from the initiation site like the ribs of a fan, (c) The usual morphology is fan-shaped with the edge opposite the initiation site being semi-circular in shape. At Kma x values approaching 50 MPafm- the
80
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
Fig. 7. Fractographic details of fatigue crack growth in rail at K levels of 30 M P a / m . Note crack extension occurs by ductile striated growth that has a high degree of directionality. Such directionality probably results from fatigue crack growth following the orientation of the pearlite colonies.
Fig. 8. Isolated incidence of transgranular cleavage facets formed in rail steel microstructures at Kmax values of = 40 MPa~m.
Fig. 9. Details of cleavage facet formation in deformed rail steel.
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
f,;'
100 LEGEND • DEFORMED RAIL STEEL
o/,'./
[3 UNDEFORMED RAIL STEEL 80 (/) I-I.IJ
/,/
FIGURE 10: Effect of Kmax On the incidence of cleavage facets in deformed and undeformed rail steel.
o w 60 < < w _J o rr < 40 _J
/o
u
/
z < rr c5
f
J
t
O3
z < a: 20
o
f
//
O
30
[3
I 35
I 40
I 45
I 50
Kmax (M Pa.v/m) Fig. 10. Effect o f Kma x o n the i n c i d e n c e o f c l e a v a g e facets in d e f o r m e d a n d u n d e f o r m e d rail steel.
Fig. 11. F r a c t o g r a p h y o f f a t i g u e c r a c k g r o w t h region in weld metal.
55
81
82
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
fatigue crack growth, see Figs. ll(a) and ll(b). Details of the nature of the large cleavage facets are illustrated in Fig. 12; note the occurrence of secondary cracking along a prior austenite grain boundary. This probably is the result of the presence of grain boundary proeutectoid ferrite that has been shown in crack profile studies to preferentially harbour cracking in the weld metal microstructure, see Fig. 6.
4. Discussion
Fig. 12. Details of transgranular cleavage facets in weld metal. Note austenite grain boundary secondary crack. This is probably due to the presence of grain boundary polygonal ferrite that preferentially harbours cracking in the weld metal. Again, cleavage facet size = 500 ~m in diameter.
predominant failure node is transgranular cleavage and an indication of the extent of cleavage facet formation is illustrated in Fig. 9. The incidence of cleavage facet formation with increasing K .... level in deformed and undeformed rail steel microstructures is portrayed in Fig. 10. Essentially the critical Kmax value for initial cleavage facet formation in 35 and 37 MPa¢~- for deformed and undeformed rail steel respectively. With increasing K m a x level the incidence increases with fast failure occurs a t g m a x --- 50 MPav~-, i.e., KQ is attained. Unlike the rail steel microstructures that exhibited the initiation and gradual increase in the amount of cleavage facets with increasing fatigue crack length the weld metal microstructure exhibited predominantly large transgranular cleavage facet formation even at the start of fatigue testing. Fractographic details, see Figs. 11 and 12, show that in some regions large cleavage facets, 150-600 ~tm in size, were connected by thin ribbons of material that had failed by ductile striated
The fatigue crack growth characteristics of both the deformed and undeformed rail steels exhibit a certain similarity to the extent that they have similar Paris law exponent values of between 6 and 7. The deformed rail steel data is slightly faster than the undeformed rail steel growth data at any given level of AK. The weld metal crack growth behaviour, however, was vastly different from the rail steels in that unstable localised crack growth, yielding a series of grow rate plateaux occurred. The fatigue crack growth rates at these plateaux reside appreciably above the upper bound rail steel line. Crack extension in the weld metal microstructure occurred by a series of fast unstable growth (extensive cleavage failure) separated by a stable slower growth process (ductile striated growth) which occurs within thin ribbons of material. This description of the fatigue crack growth characteristics of the weld metal microstructure is borne out by fractographic observations, see Fig. 11. The high values of the Paris law exponent ' m ' of 6 - 7 recorded for the rail steels is a result of the formation of subcritical cleavage facets on the fatigue fracture surfaces a t K m a x levels approaching 40 M P a ~ - . Indeed the weld metal microstructure which showed extensive cleavage failure even at initial AK levels exhibited local Paris law exponent values approaching 20. The upper bound growth line for rail steels has an ' m ' value approaching 6, thus it is logical to suppose that this upper bound data portrayed the existence of subcritical cleavage failure during fatigue crack extension. The lower bound data line for rail steels exhibits an 'm' value of = 4 which is common in a fully ductile fatigue crack growth process, i.e., where no static failure modes are prevalent.
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
The formation of isolated transgranular cleavage facets during fatigue at a certain critical Kmax level and their subsequent increasing incidence with increasing K m a x level has been observed in steels by other investigators [3,13,14,151. Aita and Weertman [13] observed that in pearlitic microstructures the size of the cleavage facets formed during fatigue loading was related to the pearlite nodule size and was independent of both the pearlite colony size and the prior austenite grain size. A pearlite colony is an area within which the carbide lamellae have the same orientation whereas a pearlite nodule is a cluster of wedge-shaped colonies that emanate out from the nodule core and this is shown schematically in Fig. 13. In the rail steel microstructures the pearlite colony size varied from 20 to 50 I~m while the prior austenite grain size could not be assessed with any reliability. The pearlite nodule size in the few cases showing clear nodule formation was 60-100 btm in size. This particular size agrees well with the initial isolated cleavage facet dimensions observed a t K m a x levels of 40 M P a ~ - , viz; 40-100 ~tm, and hence tended to confirm the observations of Aita and Weertman, i.e., the microstructural parameter controlling cleavage fracture in fully pearlitic microstructures is the pearlite nodule size. The onset of cleavage facet formation occurs when the critical tensile stress, %y, sufficient to induce cleavage propagation from a cracked carbide lamellae, is attained at some characteristic distance ahead of the crack tip [16]. Taking this characteristic distance as being the size of two pearlite nodules, i.e., 160 ~tm, assuming Oy = 475 MPa and that the critical value of K m a x = 35
N o d u l e core
Fig. 13. Schematic presentation of a pearlite nodule.
83
M P a ¢ ~ , a value of 1600 MPa for Oyy is calculated for a rail steel microstructure. This value for the critical tensile stress ahead of the crack tip to initiate cleavage facets, Oyy, agrees well with the value reported by Ritchie and Knott [16] (Oyy= 1300 MPa) for a low C steel, the various values of cleavage stress reported by Hahn [17] and recently reported cleavage fracture stress values for a fully pearlitic steel of 1600-1900 MPa [181. With increasing K m a x level both the deformed and undeformed rail steels exhibit an increase in the amount of cleavage facets observed on the fatigue fracture surface until a t K m a x -~ 50 MPav~fast failure occurs. The deformed and undeformed rail steels exhibit initial cleavage facet formation at Kma× levels of 35 and 37 MPav/m- respectively and between K m a x levels of 35-45 MPaCm-, see Fig. 10, the deformed rail steel exhibits measurably more cleavage facets on the fatigue surface: this trend is probably due to the effect of deformation on the flow properties of the rail steel. The weld metal microstructure exhibited long columnar grains, 300-600 jxm in width, the grain boundaries being decorated with proeutectoid ferrite. Such grain growth results from rapid cooling conditions that are prevalent in the weld metal due to the presence of large heat sinks (long lengths of rail steel sections) on either side of the weld metal during cooling. The prior austenite grain size is of the order of 200 ~m and the pearlite colony size varies between 20-120 ~tm while the size of the pearlite nodules in this particular microstructure could not be reliably assessed. The transgranular cleavage facets, which were the dominant fracture mode at all AK levels of fatigue testing, varied in size from 150 to 600 ~tm and were in many cases connected by thin ribbons of ductile striated regions of fatigue crack growth. Thus in the weld metal microstructure no clear indication could be given as to the nature of the microstructural parameter controlling the static cleavage failure mode. A general fractographic observation was that the fracture path tended to reside along the interface or within proeutectoid ferrite regions. The large variation in transgranular cleavage facet size may be explained by the fact that such proeutectoid ferrite regions occurred along (a) prior austenite grain boundaries generally 200 ~tm in size and (b) at columnar
84
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
growth grain boundaries the size of which varied between 300 and 600 ~m in size. Finally, although the weld metal microstructure was the coarser microstructure, mean true interlamellar pearlite spacing measurements, ?'0, showed that the weld metal pearlite was measurably finer than that of the rail steels. Such differences can be explained in terms of the cooling rate through the pearlite transformation; the weld metal being subjected to rapid cooling through the critical transformation temperatures while the rail steels are in the nomalised condition and hence experience somewhat slower air cooling rates.
5. Summary and conclusions Fatigue crack growth studies in rail steels and associated weld metal have shown that the deformed rail steel exhibited slightly faster fatigue crack growth rates than the undeformed rail steel. Fatigue crack growth behaviour in the weld metal microstructure was appreciably faster than the rail steel data and exhibited growth rate plateaux that reside significantly above the upper bound fatigue crack growth data for rail steel. In rail steels at initial AK levels the fatigue fracture mode was ductile striated growth. At Kma x values approaching 40 M P a f m isolated cleavage facets were observed on the fatigue crack surfaces; the incidence of which increased with Kma x until final fast failure occurred at K m a x = 50 M P a f m . The deformed rail steel fatigue fracture surface (a) exhibited cleavage facet formation at a slightly lower Kma× value, and (b) contained more cleavage facets at a given Kma× than the undeformed rail steel. The cleavage facet size in rail steels agreed well with the pearlite nodule dimensions of 60-100 ~m. The weld metal material exhibited a much coarser microstructure and contained large columnar grains, 300 ~m-600 ~m in width. Transgranular cleavage failure was the dominant fracture mode at all AK levels of fatigue testing; the cleavage facets size varied widely from 150 to 600 ~tm. Regions of ductile striated fatigue growth were evident within the dominant cleavage failure mode. The large variation in cleavage facet size in
weld metal may be explained by the following facts (i) crack propagation generally occurred in regions associated with proeutectoid ferrite and (ii) the proeutectoid ferrite preferentially nucleated at both prior austenite grain boundaries and along coarse columnar grains. Differences in cooling rate through the pearlite transformation resulted in the weld metal having a finer mean true interlamellar pearlite spacing than the rail steels.
Acknowledgments The author would like to thank Professor G.G. Garrett and Professor A. Kemp, both of the University of the Witwatersrand, for many helpful discussions. The assistance of Mr A.M. Bissell (Babcock Power Ltd. Renfrew, Scotland) during the fractographic studies is also greatly appreciated.
References [1] D.A. Porter, K.E. Easterling and G.D.W. Smith, Acta. Metall. 26, 1405 (1978). [2] J.M. Hyzak and I.M. Bernstein, Metall. Trans. 7A, 1217 (1976). [3] P.T. Heald, T.C. Lindley and C.E. Richards, Mats. Sci. Eng. 10, 235 (1972). [4] C.E. Richards and T.C. Lindley, Engrg. Fracture Mech. 4, 951 (1972). [5] G.J. Fowler, Ph.D. Thesis, University of California (1976). [6] R.O. Ritchie and J.F. Knott, Mat. Sci. Eng. 14, 7 (1974). [7] C. Nanez and J.G. Byrne, 2nd Internat. Conf. on Fatigue and Fatigue Thresholds, Vol. 1, p. 401 (1984), [8] G. Crespo and D. Pilo, 6th Internat. Conf on Fracture, New Delhi, Vol. 3, p. 1649 (1984). [9] E.E. Underwood, Quantitative Stereologv, Addison Wesley, Reading, MA, p. 73 (1970). [10] R.K, Steel, Mats. Eval. Oct., 33 (1980). [11] J.M.R. Ibabe and J.G. Sevilland. [12] J.G. Taylor, P.E. Narin and P. Watson, Fracture 2 (1977), ICF4, Waterloo, Canada, p. 681. [13] C.R. Aita and J. Weertman, Scripta. Metall. 12 837 (1978). [14] C.J. Beevers, R.J. Cooke, J.F. Knott and R.O. Ritchie, Metal Science 9, 119 (1975). [15] J.H. Bulloch, Ph.D. Thesis, University of Strathclyde, Glasgow (1980). [16] R.O. Ritchie and J.F. Knott, Mats. Sci. Eng. 14, 8 (1975). [17] G.T. Hahn, Metall. Trans. 15A, 947 (1984). [18] J.J. Lewandowski and A.W. Thompson, 6th Internat. Conf. on Fracture, New Delhi, Vol. 2, p. 1515 (1984).
75
FATIGUE CRACK G R O W T H S T U D I E S IN RAIL S T E E L S AND A S S O C I A T E D WELD M E T A L J.H. B U L L O C H Department of Metallurgy, University of the Witwatersran~ Johannesburg, South Africa.
Fatigue crack growth studies in rail steels and associated weld metal have shown that (a) deformed rail steel exhibited fatigue crack growth rates that are slightly faster than undeformed rail steel and (b) weld metal growth data are appreciably faster than rail steel growth results and exhibit growth rate plateaux that reside above the upper bound reported for rail steel fatigue crack growth. In rail steel microstructures at low AK levels fatigue crack extension occurred by a ductile striated growth mechanism. However at Kmax values approaching 40 MPa x/m transgranular cleavage facets initially formed and their incidence increased with Kmax until final fast fracture. The average cleavage facet size agreed well with pearlite nodule dimensions of 60-100 ~m. The weld metal microstructure was much coarser than the rail steel and contained highly directional columnar grain growth. At all AK levels the dominant fracture mode was transgranular cleavage containing small isolated regions of ductile striated fatigue crack growth. The cleavage facet size varied from 150 to 600 rtm; such a large variation was explained by the fact that in general crack extension tended to occur in association with the proeutectoid ferrite phase.
1. Introduction Although the range of microstructures that can be developed in steels is fairly large, the most common structure associated with good tensile properties is that based on pearlite. Pearlite is made up mainly of a ductile ferrite phase containing about 12% by volume of cementite, a hard intermetallic compound. It is generally accepted that in as transformed high carbon steels the interlamellar spacing in the pearlite controls the monotonic strength properties [1,2]. In the case of fatigue crack growth behaviour in predominantly pearlitic microstructures it is unclear which microstructural parameters affect crack growth. Generally the microstructural parameters affect the tensile properties and fatigue characteristics quite differently. Heald et al [3] has shown that in a 1% C steel considerably faster growth rates were found for a pearlitic microstructure on account of differing fatigue crack growth mechanisms. Various other workers [4,5,6] have demonstrated that transgranular cleavage in addition to ductile fracture occurs in pearlitic steels when the cyclic stress intensity, AK, is increased. A common method of increasing the tensile strength properties of pearlitic microstructures it to plastically deform, usually by a wire drawing process. Such microstructures exhibit large in-
creases in strength at modest levels of plastic deformation. Little is known about the effect of plastic deformation on the fatigue characteristics in pearlitic microstructures. One study on a heavily cold rolled eutectoid steel [7] has demonstrated that short subcritical annealing treatments (350500°C) markedly reduced fatigue crack growth behaviour. A recent study [8] on a 0.2% C steel reported that low levels of prestrain reduce the fatigue life while high levels increase it. The present report describes the fatigue crack behaviour of (a) rail steel in the undeformed and deformed (c = 1%) conditions and (b) associated weld metal material. A detailed fractographic study is also reported.
2. Experimental procedure A section of rail steel containing a weld were supplied to the University of the Witwatersrand. The chemical analysis of the rail steel was as follows: C
Mn
Si
S
0.67
1.01
0.54
0.014
P
Cr
Mo
V
Cu
0.013
0.84
0.01
0.11
-
0167-8442/86/$3.50 © 1986, Elsevier Science Publishers B.V. (North-Holland)
76
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
A section of rail 200 m m in length and 10 m m thick was machined from the rail head and was plastically deformed by 1% (c = 1%). Single edge notch (SEN) pin loaded tensile specimens, 5 m m thick and 37 m m in width, were machined from the undeformed rail steel, the deformed rail section and the weld metal material. Two hounsfield tensile specimens, 5 m m diameter, 20 m m gauge length, were machined from the undeformed rail steel in order to assess the tensile properties. Fatigue crack growth tests were carried out in air on a 50 kN capacity servohydraulic fatigue test facility at an R-ratio = 0.1, utilising a sinusoidal stress waveform at a frequency of 30 Hz. Fatigue crack growth was monitored by travelling microscopes (magnification X 7) located on both sides of the SEN specimen. After fatigue testing each test specimen was halved perpendicular to the fatigue crack growth direction. One half was mounted so that crack profile and microstructural details could be determined while the other half was used for a fractographic study of the fatigue fracture surface. The bulk of the metallographic/fractographic studies was carried out on a 620 Hitatchi Scanning Electron Microscope (SEM). Interlamellar pearlite spacing, pearlite colony size and pearlite nodule size were measured for both the rail steel and the weld metal material. For each microstructure 100 random fields were taken, magnification 2000-5000, and the number of lamellae intercepts counted on a linear grid mounted on the screen of the S.E.M. The total length of line divided by the number of cementite lamellae intersected is defined as g, the mean intercept spacing. This value is simply related to both the interface area per unit volume, Sv, and the mean true lamellar spacing X0- It can be shown that 4 sv = 2 '
(1)
and an approximate expression due to Satykov relates the mean true spacing ~0 to ~. By considering a cube of geometrically ideal pearlite of mean true spacing, ~'0, with two of the cube faces parallel to the lamellae it can be seen that the total interfacial area within the cube is 2
Sv = X=-~.
(2)
Combining eqs. (1) and (2) gives •= 2~ 0 .
(3)
More exact forms of eq. (1) have been developed to deal with situations where not all the cementite platelets have a planar orientation and details of the various methods available for measuring peariite interlamellar spacing have been reported by Underwood [9].
3. Experimental results
3.1. Fatigue crack growth data Duplicate tensile tests on the undeformed rail steel gave the following values: 0.2% proof stress = 475 MPa and Ultimate Tensile Strength (U.T.S.) = 955 MPa. The fatigue crack growth results for the undeformed rail steel, deformed rail steel and weld metal material are shown in Fig. 1, together with the upper and lower bound fatigue data for rail steels reported by Steel [10]. These upper and lower bound lines also encompass the recently
LEGEND • 10_5 --
IL / I / I/
Undeformed Rail
•
"In service" Deformed Rail z~ Laboratory Deformed Rail o Weld Metal 10_6
I /I 13000 I
-
Crack Growth Rate (m/cycle)
,Y
10 -7 Upper b o u n d / / ~ rail steels Ref. 10 /
10_a
I 10
I 20
I 30
I 50
I 100
A K (M Pal/'~ )
Fig. 1. Fatigue crack growth data for deformed and undeformed rail steel and weld metal compared with upper and lower bound lines after [10].
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
77
reported upper and lower bound fatigue crack growth data of Ibabe and Sevillano [11]. From this figure it can be seen that the deformed rail steel fatigue crack growth data is about 2-3 times faster than the undeformed rail steel data while both reside within the upper and lower bound data. Both exhibit straight line Paris law behaviour and can be described by the following equations: (a) Undeformed rail steel da = 1.92 X 10 -17 A K 6"3, d N(M/cycle)
(4)
(b) Deformed rail steel da = 1.41 X 10 -17 A K 6'9. d N(M/cycle)
(5)
The weld metal fatigue crack growth data did not exhibit a Paris law dependence with AK level. In this case crack growth appeared to be locally unstable and exhibited growth rate plateau that were sometimes 5 times faster than the upper bound growth data for rail steels. It is interesting to note that the Paris exponent values of both rail steels were between 6 and 7 which is appreciably above the normal exponent values of 2-4.
b
2
3.2. Microstructural details Fig. 2. General details of rail steel and weld metal microstructures. Magnitude: 30x.
General details of the rail steels microstructures (undeformed and deformed rail steel microstructures were identical) and weld metal microstructure are shown in Fig. 2. The rail steel exhibits a fine fully pearlitic microstructure, average colony size = 50 ~tm, with little evidence of proeutectoid ferrite, Fig. 2 (a) while the weld metal showed extensive ferrite formation that tended to decorate prior austenite grain boundaries. Also much of the proeutectoid ferrite was nucleated along coarse directional columnar grain boundaries, Fig. 2 (b), that were 0.5 to 1 mm in width. The weld metal microstructure was predominantly pearlitic with an average pearlite colony size of 200-300 ~m. Mean true interlamellar pearlite spacings were recorded with the following results (i) undeformed rail steel X0 = 184 nm, (ii) deformed rail steel X0 = 175 nm and (iii) Weld metal ~0 = 136 nm. Micrographs of the pearlite formed in the rail steel and weld metal are shown in Fig. 3.
Details of the nature of the proeutectoid ferrite formed in the weld metal microstructure are illustrated in Fig. 4, i.e., Fig. 4(a) shows the formation of block proeutectoid ferrite along prior austenite grain boundaries while Fig. 4(b) shows the acircular nature of the grain boundary nucleated ferrite. In this case the ferrite is in the form of fine needles protruding into the pearlite phase and are either Widmanstatten ferrite or the initial ferrite laths prevalent in upper bainitic microstructures.
3.3. Fatigue crack profile details General details of the fatigue crack growth behaviour of rail steels showed that crack extension occurred by ductile striated growth in a
78
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
Fig. 3. Detailed views of the nature of the pearlite formed in rail steel and weld metal microstructures.
transgranular fashion through pearlite colonies fracturing the cementite lamellae. The principal crack paths in the lamellar pearlitic microstructures were along ferrite-cementite interfaces and, in a few isolated cases, along prior austenite grain boundaries. These observations are similar to those recorded by Taylor et al [12]. At grnax values approaching 40 M P a v ~ small isolated flat regions, up to 100 rtm in size, were observed to appear in the fatigue crack profile of both the deformed and undeformed rail steels. These were shown to be isolated regions of
transgranular cleavage fracture, i.e., micro-cleavage facets. Crack profile details of the weld metal microstructure were markedly different to the extent that the fatigue crack path followed a rather tortuous route and exhibited large flat areas that in some instances were 150-600 ~m in length. Such flat regions were indeed large transgranular cleavage facets and the majority of the fatigue crack growth profile exhibited this type of fracture mode. General details of fatigue crack profiles in weld metal are shown in Fig. 5. This figure illustrates
Fig. 4. Details of proeutectoid ferrite formation in weld metal.
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
79
Fig. 5. Fatigue crack profile details of weld metal. Note within the columnar grain, 300-600 ~m in width, there are flat regions of fracture, i.e., cleavage facets. Thus, cleavage fracture facet size is not dictated by these coarse columnar grains but by some other microstructural unit.
the rough nature of crack extensions; also the flat transgranular cleavage regions were in some cases somewhat smaller that the width of the coarse columnar grains. A detailed study of the flat transgranular cleavage regions showed that in many instances the failure event occurred along, or was associated with, grain boundary proeutectoid ferrite, see Fig. 6. Many instances of secondary cracking some distance away from the main crack front were recorded in the weld metal microstructure.
3.4. Fractographic details The general nature of the fatigue crack growth process in rail steels at initial AK levels are illustrated in Fig. 7; the failure mode is transgranular ductile striated growth that exhibited marked directionality effects which probably result from the extension of the fatigue crack through adjacent pearlite colonies with differing growth orientations. At Kma x values approaching 40 MPav/-m" the onset of discrete regions of transgranular cleavage occurs in both the deformed and the undeformed rail steel microstructures and an instance is shown in Fig. 8. The individual size of the cleavage facets were 40-100 ~tm. Initiation sites at each facet
Fig. 6. Crack profile details of fatigue crack propagation along grain boundary ferrite regions in weld metal. Note fatigue crack has propagated through a region of grain boundary ferrite, then the main crack front suddenly changed direction and propagated through a pearlite colony leaving a secondary crack (arrowed) in the grain boundary ferrite.
were clearly evident and generally growth spreads out in the direction of macro crack growth. Such isolated cleavage facets occurred mainly at the test specimen centre; similar observations have been made by other workers [13]. This effectively means that the critical strain for fracture is first satisfied at the centre of the crack envelope. As the crack continues to extend cleavage facets occur in groups across the whole crack front. General features of the cleavage facets are: (a) They are fan-shaped in nature and have a definite initiation site. There is no evidence of cleavage initiating from a cracked cementite lamellae but a few instances of facets initiating from non-metallic inclusion sites were recorded, (b) River lines emanate outwards from the initiation site like the ribs of a fan, (c) The usual morphology is fan-shaped with the edge opposite the initiation site being semi-circular in shape. At Kma x values approaching 50 MPafm- the
80
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
Fig. 7. Fractographic details of fatigue crack growth in rail at K levels of 30 M P a / m . Note crack extension occurs by ductile striated growth that has a high degree of directionality. Such directionality probably results from fatigue crack growth following the orientation of the pearlite colonies.
Fig. 8. Isolated incidence of transgranular cleavage facets formed in rail steel microstructures at Kmax values of = 40 MPa~m.
Fig. 9. Details of cleavage facet formation in deformed rail steel.
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
f,;'
100 LEGEND • DEFORMED RAIL STEEL
o/,'./
[3 UNDEFORMED RAIL STEEL 80 (/) I-I.IJ
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FIGURE 10: Effect of Kmax On the incidence of cleavage facets in deformed and undeformed rail steel.
o w 60 < < w _J o rr < 40 _J
/o
u
/
z < rr c5
f
J
t
O3
z < a: 20
o
f
//
O
30
[3
I 35
I 40
I 45
I 50
Kmax (M Pa.v/m) Fig. 10. Effect o f Kma x o n the i n c i d e n c e o f c l e a v a g e facets in d e f o r m e d a n d u n d e f o r m e d rail steel.
Fig. 11. F r a c t o g r a p h y o f f a t i g u e c r a c k g r o w t h region in weld metal.
55
81
82
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
fatigue crack growth, see Figs. ll(a) and ll(b). Details of the nature of the large cleavage facets are illustrated in Fig. 12; note the occurrence of secondary cracking along a prior austenite grain boundary. This probably is the result of the presence of grain boundary proeutectoid ferrite that has been shown in crack profile studies to preferentially harbour cracking in the weld metal microstructure, see Fig. 6.
4. Discussion
Fig. 12. Details of transgranular cleavage facets in weld metal. Note austenite grain boundary secondary crack. This is probably due to the presence of grain boundary polygonal ferrite that preferentially harbours cracking in the weld metal. Again, cleavage facet size = 500 ~m in diameter.
predominant failure node is transgranular cleavage and an indication of the extent of cleavage facet formation is illustrated in Fig. 9. The incidence of cleavage facet formation with increasing K .... level in deformed and undeformed rail steel microstructures is portrayed in Fig. 10. Essentially the critical Kmax value for initial cleavage facet formation in 35 and 37 MPa¢~- for deformed and undeformed rail steel respectively. With increasing K m a x level the incidence increases with fast failure occurs a t g m a x --- 50 MPav~-, i.e., KQ is attained. Unlike the rail steel microstructures that exhibited the initiation and gradual increase in the amount of cleavage facets with increasing fatigue crack length the weld metal microstructure exhibited predominantly large transgranular cleavage facet formation even at the start of fatigue testing. Fractographic details, see Figs. 11 and 12, show that in some regions large cleavage facets, 150-600 ~tm in size, were connected by thin ribbons of material that had failed by ductile striated
The fatigue crack growth characteristics of both the deformed and undeformed rail steels exhibit a certain similarity to the extent that they have similar Paris law exponent values of between 6 and 7. The deformed rail steel data is slightly faster than the undeformed rail steel growth data at any given level of AK. The weld metal crack growth behaviour, however, was vastly different from the rail steels in that unstable localised crack growth, yielding a series of grow rate plateaux occurred. The fatigue crack growth rates at these plateaux reside appreciably above the upper bound rail steel line. Crack extension in the weld metal microstructure occurred by a series of fast unstable growth (extensive cleavage failure) separated by a stable slower growth process (ductile striated growth) which occurs within thin ribbons of material. This description of the fatigue crack growth characteristics of the weld metal microstructure is borne out by fractographic observations, see Fig. 11. The high values of the Paris law exponent ' m ' of 6 - 7 recorded for the rail steels is a result of the formation of subcritical cleavage facets on the fatigue fracture surfaces a t K m a x levels approaching 40 M P a ~ - . Indeed the weld metal microstructure which showed extensive cleavage failure even at initial AK levels exhibited local Paris law exponent values approaching 20. The upper bound growth line for rail steels has an ' m ' value approaching 6, thus it is logical to suppose that this upper bound data portrayed the existence of subcritical cleavage failure during fatigue crack extension. The lower bound data line for rail steels exhibits an 'm' value of = 4 which is common in a fully ductile fatigue crack growth process, i.e., where no static failure modes are prevalent.
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
The formation of isolated transgranular cleavage facets during fatigue at a certain critical Kmax level and their subsequent increasing incidence with increasing K m a x level has been observed in steels by other investigators [3,13,14,151. Aita and Weertman [13] observed that in pearlitic microstructures the size of the cleavage facets formed during fatigue loading was related to the pearlite nodule size and was independent of both the pearlite colony size and the prior austenite grain size. A pearlite colony is an area within which the carbide lamellae have the same orientation whereas a pearlite nodule is a cluster of wedge-shaped colonies that emanate out from the nodule core and this is shown schematically in Fig. 13. In the rail steel microstructures the pearlite colony size varied from 20 to 50 I~m while the prior austenite grain size could not be assessed with any reliability. The pearlite nodule size in the few cases showing clear nodule formation was 60-100 btm in size. This particular size agrees well with the initial isolated cleavage facet dimensions observed a t K m a x levels of 40 M P a ~ - , viz; 40-100 ~tm, and hence tended to confirm the observations of Aita and Weertman, i.e., the microstructural parameter controlling cleavage fracture in fully pearlitic microstructures is the pearlite nodule size. The onset of cleavage facet formation occurs when the critical tensile stress, %y, sufficient to induce cleavage propagation from a cracked carbide lamellae, is attained at some characteristic distance ahead of the crack tip [16]. Taking this characteristic distance as being the size of two pearlite nodules, i.e., 160 ~tm, assuming Oy = 475 MPa and that the critical value of K m a x = 35
N o d u l e core
Fig. 13. Schematic presentation of a pearlite nodule.
83
M P a ¢ ~ , a value of 1600 MPa for Oyy is calculated for a rail steel microstructure. This value for the critical tensile stress ahead of the crack tip to initiate cleavage facets, Oyy, agrees well with the value reported by Ritchie and Knott [16] (Oyy= 1300 MPa) for a low C steel, the various values of cleavage stress reported by Hahn [17] and recently reported cleavage fracture stress values for a fully pearlitic steel of 1600-1900 MPa [181. With increasing K m a x level both the deformed and undeformed rail steels exhibit an increase in the amount of cleavage facets observed on the fatigue fracture surface until a t K m a x -~ 50 MPav~fast failure occurs. The deformed and undeformed rail steels exhibit initial cleavage facet formation at Kma× levels of 35 and 37 MPav/m- respectively and between K m a x levels of 35-45 MPaCm-, see Fig. 10, the deformed rail steel exhibits measurably more cleavage facets on the fatigue surface: this trend is probably due to the effect of deformation on the flow properties of the rail steel. The weld metal microstructure exhibited long columnar grains, 300-600 jxm in width, the grain boundaries being decorated with proeutectoid ferrite. Such grain growth results from rapid cooling conditions that are prevalent in the weld metal due to the presence of large heat sinks (long lengths of rail steel sections) on either side of the weld metal during cooling. The prior austenite grain size is of the order of 200 ~m and the pearlite colony size varies between 20-120 ~tm while the size of the pearlite nodules in this particular microstructure could not be reliably assessed. The transgranular cleavage facets, which were the dominant fracture mode at all AK levels of fatigue testing, varied in size from 150 to 600 ~tm and were in many cases connected by thin ribbons of ductile striated regions of fatigue crack growth. Thus in the weld metal microstructure no clear indication could be given as to the nature of the microstructural parameter controlling the static cleavage failure mode. A general fractographic observation was that the fracture path tended to reside along the interface or within proeutectoid ferrite regions. The large variation in transgranular cleavage facet size may be explained by the fact that such proeutectoid ferrite regions occurred along (a) prior austenite grain boundaries generally 200 ~tm in size and (b) at columnar
84
J.H. Bulloch / Fatigue crack growth studies in rail steels and associated weld metal
growth grain boundaries the size of which varied between 300 and 600 ~m in size. Finally, although the weld metal microstructure was the coarser microstructure, mean true interlamellar pearlite spacing measurements, ?'0, showed that the weld metal pearlite was measurably finer than that of the rail steels. Such differences can be explained in terms of the cooling rate through the pearlite transformation; the weld metal being subjected to rapid cooling through the critical transformation temperatures while the rail steels are in the nomalised condition and hence experience somewhat slower air cooling rates.
5. Summary and conclusions Fatigue crack growth studies in rail steels and associated weld metal have shown that the deformed rail steel exhibited slightly faster fatigue crack growth rates than the undeformed rail steel. Fatigue crack growth behaviour in the weld metal microstructure was appreciably faster than the rail steel data and exhibited growth rate plateaux that reside significantly above the upper bound fatigue crack growth data for rail steel. In rail steels at initial AK levels the fatigue fracture mode was ductile striated growth. At Kma x values approaching 40 M P a f m isolated cleavage facets were observed on the fatigue crack surfaces; the incidence of which increased with Kma x until final fast failure occurred at K m a x = 50 M P a f m . The deformed rail steel fatigue fracture surface (a) exhibited cleavage facet formation at a slightly lower Kma× value, and (b) contained more cleavage facets at a given Kma× than the undeformed rail steel. The cleavage facet size in rail steels agreed well with the pearlite nodule dimensions of 60-100 ~m. The weld metal material exhibited a much coarser microstructure and contained large columnar grains, 300 ~m-600 ~m in width. Transgranular cleavage failure was the dominant fracture mode at all AK levels of fatigue testing; the cleavage facets size varied widely from 150 to 600 ~tm. Regions of ductile striated fatigue growth were evident within the dominant cleavage failure mode. The large variation in cleavage facet size in
weld metal may be explained by the following facts (i) crack propagation generally occurred in regions associated with proeutectoid ferrite and (ii) the proeutectoid ferrite preferentially nucleated at both prior austenite grain boundaries and along coarse columnar grains. Differences in cooling rate through the pearlite transformation resulted in the weld metal having a finer mean true interlamellar pearlite spacing than the rail steels.
Acknowledgments The author would like to thank Professor G.G. Garrett and Professor A. Kemp, both of the University of the Witwatersrand, for many helpful discussions. The assistance of Mr A.M. Bissell (Babcock Power Ltd. Renfrew, Scotland) during the fractographic studies is also greatly appreciated.
References [1] D.A. Porter, K.E. Easterling and G.D.W. Smith, Acta. Metall. 26, 1405 (1978). [2] J.M. Hyzak and I.M. Bernstein, Metall. Trans. 7A, 1217 (1976). [3] P.T. Heald, T.C. Lindley and C.E. Richards, Mats. Sci. Eng. 10, 235 (1972). [4] C.E. Richards and T.C. Lindley, Engrg. Fracture Mech. 4, 951 (1972). [5] G.J. Fowler, Ph.D. Thesis, University of California (1976). [6] R.O. Ritchie and J.F. Knott, Mat. Sci. Eng. 14, 7 (1974). [7] C. Nanez and J.G. Byrne, 2nd Internat. Conf. on Fatigue and Fatigue Thresholds, Vol. 1, p. 401 (1984), [8] G. Crespo and D. Pilo, 6th Internat. Conf on Fracture, New Delhi, Vol. 3, p. 1649 (1984). [9] E.E. Underwood, Quantitative Stereologv, Addison Wesley, Reading, MA, p. 73 (1970). [10] R.K, Steel, Mats. Eval. Oct., 33 (1980). [11] J.M.R. Ibabe and J.G. Sevilland. [12] J.G. Taylor, P.E. Narin and P. Watson, Fracture 2 (1977), ICF4, Waterloo, Canada, p. 681. [13] C.R. Aita and J. Weertman, Scripta. Metall. 12 837 (1978). [14] C.J. Beevers, R.J. Cooke, J.F. Knott and R.O. Ritchie, Metal Science 9, 119 (1975). [15] J.H. Bulloch, Ph.D. Thesis, University of Strathclyde, Glasgow (1980). [16] R.O. Ritchie and J.F. Knott, Mats. Sci. Eng. 14, 8 (1975). [17] G.T. Hahn, Metall. Trans. 15A, 947 (1984). [18] J.J. Lewandowski and A.W. Thompson, 6th Internat. Conf. on Fracture, New Delhi, Vol. 2, p. 1515 (1984).