Materials Science and Engineering, A 136 ( 1991 ) 109-119
109
Microstructure and toughness of the simulated heat-affected zone in Ti- and Al-killed steels J. L. Lee and Y. T. Pan Steel and Aluminium R&D Department, China Steel Corporation, Kaohsiung (Taiwan)
(Received May 14, 1990; in revised form October 16, 1990)
Abstract The microstructure, transformation behaviour and toughness of the simulated welding heat-affected zone in titanium- and aluminlum-killed steels were investigated. Over the temperature range studied, the titanium-killed steel exhibited a larger austenite grain than the aluminium-killed steel. At peak temperatures higher than 1200 °C, the larger austenite grain (greater than 50 ~m) and the existence of titanium oxide in titanium-killed steel provided a favourable environment for the formation of intragranular ferrite laths which formed at a temperature slightly higher than the formation temperature of bainite in aluminium-killed steel. The intragranular ferrite originated mainly from titanium oxide and subsequently grew by an edge-on-face sympathetic nucleation mode. The resultant microstructure was characterized by highly interlocked groups of parallel ferrite laths with aligned M-A-C. The interlocked groups of ferrite sectioned the original austenite into small colonies, which were very effective in resisting brittle fracture, and thus possessed a superior toughness to the bainite in aluminium-killed steel. The brittle fracture surface of intragranular ferrite revealed a quasi-cleavage fracture surface with fine facets. A linear relation between the inverse square root of the fracture facet size and the impact transition temperature was obtained. The formation of intragranular ferrite became less pronounced with decreasing peak temperature because of the small original austenite grain size. At peak temperatures below 1100 °C, the absence of intragranular ferrite and the larger final grain size inherited from an initially coarser austenite grain made the toughness of titanium-killed steel inferior to that of aluminium-killed steel. It was concluded that the difference in toughness between titanium- and aluminium-kiUed steels is mainly attributable to the difference in initial austenite grain size and the tendency towards intragranular nucleation.
1. Introduction As energy exploration activities have moved to regions of colder climates, the low temperature toughness of the constructional steels used in these environments (including their welding heataffected zone (HAZ)) has become increasingly important. Efforts have been made to reduce the carbon equivalent and to increase the toughness and weldability of steel by applying controlled rolling [1] or a thermomechanical control process [2, 3]. Many studies have also been carried out to modify the microstructure in the H A Z . A typical example is the development of titanium nitride (TIN) steel [4, 5]. Fine TiN particles dispersed in steel suppress the grain growth of austenite and refine the H A Z microstructure, 0921-5093/91/$3.50
A steel with high aluminium and low nitrogen content has also been developed to increase the intrinsic toughness of steel by reducing the free nitrogen present [6]. It has been reported that the addition of titanium and boron in steel can provide an Fe23(CB)6 substrate on which intragranular ferrite plates can easily nucleate [7]. The intragranular ferrite plates then divide the austenite grain into several small regions and thus increase the toughness of the steel. Recently, a newly developed titanium oxide bearing steel has been used to improve the H A Z toughness [8-10]. The presence of titanium oxide can also promote the formation of intragranular ferrite plates. Since titanium oxide is stable even at very high welding peak temperatures, it can be used for high heat input welding. However, no © Elsevier Sequoia/Printedin The Netherlands
110
extensive investigation of the microstructure and toughness of titanium oxide bearing steel at various peak temperatures is available. The prerequisite for the formation of intragranular ferrite is still not clear, In the present study, titanium- and aluminiumkilled steels were produced to study the microstructure and toughness in the simulated H A Z at various peak temperatures. The formation of intragranular ferrite is also discussed,
2. Experimental details Two steels were prepared by vacuum induction melting and killed by titanium and aluminium respectively. Each melt was cast into a 100 kg ingot. The ingot was heated at 1200 °C for 2 h, then hot rolled to a plate 15 mm thick. The chemical composition of the plate is given in Table 1. Longitudinal specimens with dimensions 10.5 mm x 10.5 mm x 80 mm were cut from the plate and subjected to H A Z simulation using a Gleeble 1500 thermomechanical simulator operated at a vacuum of about 10-1 Pa. The simulated welding peak temperature ranged from 1000°C to 1400 °C. The time taken for cooling from 800 °C tO 500 °C (t8/s)was 20 s. After H A Z simulation, specimens were machined to produce standard Charpy V-notch specimens with dimensions 10 mm x 10 mm x 55 mm and then subjected to impact tests at various temperatures. Hollow cylindrical dilatometric specimens 12 mm in length with 5 mm outside diameter and I mm wall thickness were used to detect the
transformation behaviour in the simulated H A Z using a Theta high speed dilatometer. The microstructure and fracture surface of the simulated H A Z were examined using optical microscopy (OM), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Quantitative measurements of the austenite grain size were carried out using OM under x 500 magnification and the area examined was at least 4 mm 2. The colony size of bainite or intragranular ferrite and the fracture facet of impact specimens were measured using SEM under x 1000 magnification. The area examined was at least 1 mm 2. The apparent lath width was also determined with SEM. An electron probe microanalyser (EPMA) was used to examine the chemistry of inclusions in the titanium-killed steel. All the data obtained from the above experiments are listed in Table 2.
TABLE1 Chemical composition of the titanium-and aluminium-killed steels
Element
Content(wt.%) Ti-killed
c Si Mn P s
0.059 1.62 0.009 0.0055
Ni Nb
AI Ti
0.059 1.56 0.0084 0.0056
0.016
0.093
0.58 0.018
0.53 0.023
0.0015 0.015
N
Al-killed
0.02 Trace
0.0016
0.0017
TABLE 2 Microstructure, toughness and fracture facet characteristics of the H A Z in titanium- and aluminium-killed steels Steel
Temperature (°C)
Austenite grain size (tim)
Colony size (tim)
Lath width (tim)
Transformation temperature (°C)
FATT (°C)
Fracture facet size (#m)
Ti-killed Al-killed Ti-killed Al-kiUed Ti-killed Al-killed Ti-killed Al-killed Ti-killed Al-killed
1000
24 18 30 26 49 41 92 84 176 140
ND ND 9.9 10.0 9.4 12.8 9.6 12.2 9.1 12.2
ND ND 2.22 2.14 2.12 2.08 2.25 2.14 2.58 1.88
594 605 580 574 600 587 597 575 604 585
-
14.5 13.8 14.9 13.7 13.1 17.8 12.1 18.6 12.2 20.7
1100 1200 1300 1400
ND, not determined.
52 59 46 51 63 33 64 35 64 36
111 "
200
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0
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n
A t - k i l l e d
-ki
llod
1 (J¢}
:
~
<
120
40
o
I 1000
1100 [~o~t k
I 1200
I
I
1300
1400
I'elnperat_
ure.
1500
o(]
Fig. 1. Austenite grain size obtained at various peak temperatures: o, titanium-killed steel; c3, aluminium-killed steel.
3. Results and discussion 3.1. Microstructure Figure 1 shows the austenite grain size in the simulated H A Z of titanium- and aluminiumkilled steels at various peak temperatures. In both steels, the austenite grain size increases with increasing peak temperature. Over the temperature range studied, the titanium-killed steel has a larger austenite grain size than the aluminiumkilled steel. Microstructural observations showed that spheroidal inclusions were frequently found in the titanium-killed steel (Fig. 2(a)) but rarely found in the aluminium-killed steel. The spheroidal inclusions in the titanium-killed steel were examined using the EPMA and found dominantly to be titanium oxide with small amounts of other impurities such as manganese, sulphur and aluminium (Fig. 2(b)). The combination of titanium with oxygen reduces the opportunity for titanium to form TiN. Under such circumstances, titanium does not play an important role in suppressing the grain growth of austenite. In the aluminiumkilled steel, the existence of AIN can inhibit austenite grain coarsening until coarsening of the A1N particles occurs. This is believed to be the reason for the finer austenite grain size obtained in the aluminium-killed steel, The microstructure of steels heated to 1400 °C is as shown in Fig. 3. The typical microstructure of titanium-killed steel consists of interlocked needle-like ferrite laths which frequently stem from spheroidal inclusions within the austenite grain(Fig. 3(a)).Theneedle-likeferritenucleating in the austenite grain has been referred to elsewhere as an intragranular ferrite plate [9, 10]. In
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~ t.
a
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A
tl
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s
w i M,~ W
Fig. 2. (a) Scanning electron micrograph showing ferrite laths nucleating on titanium oxide; (b) E P M A chemical analysis of the titanium oxide.
the aluminium-killed steel, the microstructure is a typical bainite structure with large bainite packets containing numerous parallel bainite laths (Fig. 3(b)). The scanning electron micrograph in Fig. 4(a) shows that the intragranular ferrite in titaniumkilled steel is characterized by packets of parallel ferrite laths associated with aligned second phase particles. The ferrite packets were frequently found in a nearly perpendicular arrangement. A similar microstructural feature can also be seen in the aluminium-killed steel (Fig. 4(b)) although the packet size is larger and the lath width is smaller.
112
(a
Fig. 4. Scanning electron micrographs obtained from the HAZ with a peak temperature of 1400 °C: (a) titanium-killed steel; (b) aluminium-killed steel.
"
Fig. 3. Microstructure of the HAZ with a peak temperature of 1400 °C: (a) titanium-killed steel; (b) aluminium-killed steel,
Figure 5(a) shows a T E M bright field micrograph of two conjunctive g r o u p s of intragranular ferrite. T h e ferrite laths in an individual c o l o n y exhibit the same light reflection in a dark field image as s h o w n in Figs. 5(b) and 5(c). This observation indicates that the ferrite laths in a given
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Fig. 5. Transmission electron micrographs: (a) the bright
field imageof two conjunctivegroups of ferrite laths; (b), (c) dark field light reflectionfrom individual groups of ferrite laths, colony have nearly the same crystallographic orientation, while the orientation is different between colonies. This fact will result in an intimate relation between the colony size and the toughness of a steel and will be discussed in the following sections. Through TEM examinations the aligned second phases were found to consist of cementite, martensite and residual austenite. A
similar second phase microstructure has also been reported by Dolby [11] and was referred to as aligned M-A-C [11]. Figures 6(a)-6(c) show that the tendency to intragranular nucleation becomes less pronounced with decreasing temperature. Below l l00°C no obvious ferrite laths depositing on titanium oxide can be seen (Fig. 6(b)). According to the present study, an average grain size of around 50 /~m is the minimum austenite grain size for the formation of intragranular ferrite and the corresponding reheating temperature is 1200 °C (Fig. 6(a)). In aluminium-killed steel the morphology of bainite does not change significantly from 1300°C to ll00°C, although the grain size decreases with decreasing temperature. When the temperature was lowered to 1000 °C, some fine and irregular ferrite appeared in both steels (Figs. 6(c) and 6(d)). Since the interlocked ferrite or bainite laths section the austenite grain into several colonies, it is important to compare the colony size of the two steels. A colony is defined as the region in which all ferrite or bainite laths are aligned parallel. The results of quantitative analysis of the colony size and apparent lath width are given in Table 2. The colony size does not change significantly with peak temperature in both steels. Beyond 1100 °C, titanium-killed steel exhibits a smaller colony size and larger lath width than aluminium-killed steel. The colony size and lath width of specimens with a peak temperature of 1000 °C is difficult to determine because of the formation of irregular ferrite (Figs. 6(c) and 6(d)). In Fig. 7 the average number of colonies in an austenite grain is plotted against the peak temperature. The average colony number within an austenite grain increases with increasing peak temperature in both steels. Comparing the austenite grain sizes listed in Table 2, it is clear that the larger the austenite grain size the larger the number of colonies. This suggests that intragranular nucleation occurs easier in a coarser austenite grain. In addition, titanium-killed steel has a larger number of colonies in an austenite grain than aluminium-killed steel. This is a result of the greater tendency to intragranular nucleation of titanium-killed steel that arises from the inoculation effect of titanium oxide. 3.2. Transformation behaviour Figure 8 shows typical dilatation curves for the transformation of the H A Z microstructures in
114
(b)
Fig. 6. Microstructure in the HAZ of titanium-killed steel heated to (a) 1200 °C, (b) 1100 °C and (c) 1000 °C; (d) microstructure in the HAZ of aluminium-killed steel heated to 1000 °C.
b
25
~
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15
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"l'emperature,
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Fig. 7. Number of colonies of bainite or intragranular ferrite in an original austenite grain for various peak temperatures: o, titanium-killed steel; n aluminium-killed steel,
200
300
I
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400
500
600
l'emperature,
I 700
800
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Fig. 8. Dilatation curves of the H A Z with a peak temperature of 1400°C: curve a, titanium-killed steel; curve b, aluminium-killed steel.
115
the steels studied. The dilatation curves of the titanium- and aluminium-killed steels are very similar, although the transformation temperature of the titanium-killed steel is slightly higher than that of the aluminium-killed steel. The marked change in dilatation occurring at higher temperatures represents the formation of the bainite lath and the intragranular ferrite lath in aluminiumand titanium-killed steel respectively. After this dominant transformation, a slight deflection occurs in the dilatation curve. This small change in dilatation indicates the post-transformation of aligned M-A-C. An initial dominant transformation followed by a minor second phase transformation has been referred to elsewhere as a multi-stage transformation [12, 13]. The multistage transformation mode has frequently been found in granular bainite [14], which also cornprises a bainitic ferrite and an austenite-martensite second phase. From the microstructure and transformation behaviour point of view, the intragranular ferrite observed in the present work is similar to granular bainite, Figure 9 is a plot of the dominant transformation temperature against peak temperature. In titanium-killed steel, the lowest transformation temperature occurs at a peak temperature of l l 0 0 ° C and corresponds to the formation of bainite (Fig. 6(b)). A rise in the transformation temperature for peak temperatures higher than 1100 °C corresponds to an increasing tendency to intragranular nucleation. In aluminium-killed steel, the transformation temperature does not change significantly beyond 1100 °C since the microstructure is dominantly bainite and does not
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1 led
~-~ 1 l~_d
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6 ,o ~' ,~o 5~o 0
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570
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11011 ,'ca
k
I
1200 I'emp
I
13(.10 . . . . . . . . .
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1400
1500
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Fig. 9. Transformation temperature of the simulated H A Z
for various peak temperatures: o, titanium-killed steel; rT, aluminium-killedsteel,
change too much with temperature. The rise in transformation temperature at 1000 °C for both steels is caused by the formation of irregular ferrite (Figs. 6(c) and 6(d)). In general, the transformation temperature of aluminium-killed steel is lower than that of titanium-killed steel. As discussed in the previous section, beyond 1100 °C titanium oxide particles provide favourable nucleation sites which in turn encourage the transformation to occur at higher temperature. It has also been proposed that MnS tends to deposit on titanium oxide and form a manganesedepleted zone surrounding the titanium oxide [10]. A decrease in the manganese content reduces the hardenability of austenite in the vicinity of titanium oxide and thus elevates the transformation temperature [10]. From the EPMA examination (Fig. 2(b)), it was found that the titanium oxide frequently contains a certain amount of manganese and sulphur. This discovery suggests that MnS plays an important role in promoting the nucleation of intragranular ferrite. Concerning the formation of intragranular ferrite laths in titanium-killed steel, two major factors should be considered: (1) the initial austenite grain size; (2) the nucleation site inside the austenite grain. According to Shewmon [15], in a coarse grain structure the nucleus is formed inside the grain. In the case of higher peak temperatures, the larger austenite grain provides a suitable environment for intragranular nucleation. In addition, the presence of titanium oxide provides heterogeneous nucleation sites and reduces the energy needed to form a nucleus. The combination of these two factors resulted in a high tendency to nucleation inside the austenite. For aluminium-killed steel, the absence of appropriate nucleation sites makes the nucleation of intragranular ferrite less pronounced even in a coarse austenite grain. Figure 2(a) shows an example of ferrite laths originating from a titanium oxide panicle. The ferrite nucleating from the titanium oxide creates a new austenite-ferrite interface. The newlyformed ferrite lath easily deposits on the broad face of the previous ferrite lath. The nucleation behaviour of the new ferrite lath growing on the austenite-ferrite interface has been referred to as sympathetic nucleation [16] and the deposition of one ferrite lath with its narrow face on the broad face of the other ferrite lath has been termed edge-on-face nucleation [16]. Therefore the
116
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25
1 • ed I -I<-i l lod
0
T i - k i
I'!
A
~
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~,~
1 1 OO ['~.a k
1 200
1 300
, l , ¢ ~ n l l ) e z _ a t. l l r e •
l 400 o
1 5OO
C
Fig. 10. Impact absorbed energy for various peak temperatures obtained at a test temperature of - 6 0 °C: o, titaniumkilled steel; n, aluminium-killed steel.
nucleation behaviour of intragranular ferrite can be described in terms of edge-on-face sympathetic nucleation. The consecutive edge-on-face deposition of ferrite laths resulted in a highly interlocked microstructure in the titanium-killed
steel.
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3.3. HAZ toughness Figure 10 shows the impact absorbed energy of specimens tested at - 6 0 ° C . The absorbed energy of the aluminium-killed steel is very low at peak temperatures beyond l lO0°C, while it is fairly high at 1000°C. A reverse trend occurs in the titanium-killed steel. The micrographs in Fig. 11 were taken from an area slightly below the fracture surface in the broken Charpy specimen. Figure 1 l(a) reveals the straight crack pattern in aluminium-killed steel, with deviations (arrowed) occurring mainly at colony boundaries. This result suggests that the colony boundaries are the main obstacles to crack propagation. The low absorbed energy of the aluminium-killed steel above 1100 °C is a result of its larger colony size (Table 2), while the increase in absorbed energy at a peak temperature of 1000 °C can be attributed to the refinement of the austenite grain size. Figure 1 l(b) shows the crack pattern of titaniumkilled steel. In contrast to the straight crack in aluminium-killed steel, short cracks of somewhat zigzag shape were found to be the major crack pattern in titanium-killed steel. This is because the intragranular ferrite sections the austenite grain into small colonies (Fig. 7). During brittle fracture, the crack front frequently encounters
r ' _ IIh'J ~
.. ~
~s, > ~i
II
~ ' ~ ~
,-.,
~ ,~,-~ ~ ..-, (b) ~,_,
20,urn ~ ....
Fig. 1 1. Optical micrographs taken from an area slightly below the fracture surface in the broken Charpy specimens: (a) aluminium-killed steel; (b) titanium-killed steel.
colony boundaries and deviates from its propagation path. Therefore the effective grain size needed to resist brittle fracture becomes small. Fhe decrease in toughness at l l 0 0 ° C is due to the absence of intragranular ferrite and the
117
-2o
O
'ri
-ki
1 I~d
[] ~ ~- k i • ~ d
-~o ~,l < z ~ 2~
~ ~ -
~
_
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-,, o • '~ ~,, .....
i >
,
, ....
~ , ~,,o
i ,
~,,o
i ' ~'""
' ~ ....
Fig. 12. The 50% FATT of the H A Z for various peak temperatures: ©, titanium-kiiled steel; D aluminium-killed steel.
increase in toughness at 1000 °C is attributed to the resultant fine ferrite structure inherited from the initial fine austenite grain, The change in the fracture appearance transi-
tion temperature (FATT) with peak temperature is shown in Fig. 12. The transition temperature of aluminium-killed steel increases with increasing peak temperature and levels off at 1200°C, whereas in titanium-killed steel the highest FATT occurs at 1100 °C. As mentioned previously, the H A Z toughness is mainly determined by two competing factors: the austenite grain size and the tendency to intragranular nucleation. With increasing peak temperature the coarse austenite grain impairs, while the intragranular ferrite improves, the toughness. The rise in the FATT in aluminium-killed steel with increasing peak temperature occurs because of austenite grain coarsening. Further increase in the peak temperature does not further deteriorate the toughness because of the increasing tendency to intragranular nucleation. In the lower temperature region, the toughness of titanium-killed steel was also impaired by grain coarsening. However, a strong tendency to intragranular nucleation leads to a
Fig. 13. Scanning electron micrographs showing the fracture morphology of the simulated H A Z (peak temperature, 1400 °C): (a) titanium-killed steel, tested at - 6 0 °C; (b), (c) aluminium-killed steel tested at 60 °C: (d) titanium-killed steel tested at - 80 °C,
118
decrease in FATT in the higher temperature region. Consequently a FATT peak occurs at an intermediate temperature, 3.4. Fractography
The fracture surface of Charpy impact specimens tested at - 6 0 °C is shown in Fig. 13. The specimen of titanium-killed steel heated to 1400 °C exhibits a dimple fracture mode (Fig. 13(a)). Since the test temperature is about the transition temperature of titanium-killed steel, the fracture surface contains several large voids in addition to a great number of microvoids indieating a transition from ductile to brittle fracture, The dimple mode fracture permits titanium-killed steel to absorb more energy during fracture. In contrast, aluminium-killed steel reveals a quasicleavage fracture mode and two typical fracture morphologies were observed (Figs. 13(b) and 13(c)). Figure 13(b) reveals a quasi-cleavage fracture surface which is composed of flat facets and tear ridges formed at the interface of adjacent facets. Within the fracture facets, a slight river pattern can be seen stemming from the facet centre. In Fig. 13(c), the nearly parallel heavy ridges divide the fracture surface into small elongated areas. Within the subdivided area, many slightly parallel tear ridges, instead of the river pattern, can be seen. A similar fraciure morphology was recognized previously as an intercrystalline fracture along a bainite lath [17]. The above two fracture morphologies have been reported to be the major characteristics of brittle fracture in tempered lower bainite [17]. For titanium-killed steel, brittle fracture occurs typically with a mixed mode of the two fracture -ao -~°
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Summary
and conclusions
~ )
Fig. 14. Relation between the F A T T and the size of the frae-
turefacet,
where d is the size of the fracture facet in millimetres. The results are consistent with the concept of effective grain size proposed by Matsuda et al. [17]. Comparing the fracture facet size and colony size (Table 2), it is found that the larger the colony size, the larger the fracture facet size. However, in the same specimen the fracture facet size is larger than the colony size. It has been reported that, for a continuously cooled bainite or acicular ferrite structure, laths in a given colony have almost the same crystallographic orientation, while the orientation is different from colony to colony [12]. Similar observations were also made in the intragranular ferrite illustrated in Fig. 5. Therefore a crack of brittle fracture is not likely to change direction across the low angle lath boundaries, whereas major deviation tends to occur at the high angle colony boundary. Naylor and Blondeau [18] have also proposed that colony boundaries are the major obstacles to crack propagation. Therefore the absorbed energy or transition temperature should be closely related to the number of colony boundaries that a cleavage has passed. However, some colonies contain only one or two laths. These small colonies may not be able to absorb enough energy and result in a tear ridge between two adjacent colonies. This may be the reason that the fracture facet is always larger than the colony size.
I
8 Facet
morphologies mentioned above (Fig. 13(d)). The quasi-cleavage fracture surface contains many small facets which are somewhat elongated in shape. Within a facet either a river pattern or an intercrystalline tear pattern can be seen. The special fracture mode and fine facet are believed to arise from the highly interlocked microstructure. As has been reported by Matsuda et al. [17], the transition temperature of heat-treated steel is closely related to the effective grain size which can be determined from the size of the fracture facet in the brittle fracture surface. The relation between transition temperature and facet size is plotted in Fig. 14 and a regression expression is obtained as follows: FATT(°C) = 80.9-16d-1/2
This study was carried o u t t o investigate the microstructure, transformation behaviour and
119
toughness of the simulated H A Z in titanium- and aluminium-killed steels. The major conclusions are as follows. (1) Over the temperature range 1000-1400 °C, the austenite grain size of titanium-killed steel was larger than that of aluminium-killed steel. (2) At peak temperatures beyond 1200°C, the relatively large austenite grain and the presence of spheroidal titanium oxide inclusions promote the formation of intragranular ferrite which is characterized by interlocked groups of parallel ferrite laths with aligned M - A - C . The dominant structure in the aluminium-killed steel w a s bainite. (3) The intragranular ferrite, which formed at a temperature slightly higher than the formation temperature of bainite in aluminium-killed steel, stemmed mainly from titanium oxide and grew continuously with an edge-on-face sympathetic nucleation. (4) The intragranular ferrite divided the initial austenite into small colonies which were found to be very effective in resisting brittle fracture and thus resulted in a very low transition temperature for the titanium-killed steel. The fracture surface of the intragranular ferrite was composed of fine facets within which both a river pattern and intercrystalline tear ridges were observed. A relation similar to the Hall-Petch equation was obtained between the FATT and the fracture facet size. (5) At peak temperatures below l l00°C, the absence of intragranular ferrite and the coarser grain inherited from the larger original austenite grain made the toughness of the titanium-killed steel inferior to that of the aluminium-killed steel. (6) The difference in toughness at various peak temperatures between the titanium- and aluminium-killed steels was mainly attributable to the
differences in initial austenite grain size and the ability of intragranular ferrite to nucleate.
Acknowledgment The authors are grateful to the China Steel Corporation for permission to publish this paper.
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