of the Maritime University of Szczecin
Akademii Morskiej w Szczecinie
2018, 56 (128), 47–54ISSN 1733-8670 (Printed) Received: 26.03.2018
ISSN 2392-0378 (Online) Accepted: 17.10.2018
DOI: 10.17402/313 Published: 17.12.2018
Mathematical predictions of brass/steel ingot structures
Waldemar Wołczyński
1, Anna A. Ivanowa
2, Piotr Kwapisiński
3 1 Institute of Metallurgy and Materials Science25 Reymonta St., 30 059 Kraków, Poland, e-mail: w.wolczynski@imim.pl
2 Institute of Applied Mathematics and Mechanics
74 Rosa Luxemburg St., 83-114 Donetsk, Ukraine, e-mail: anna.ivanova@ukr.net
3 KGHM – Polish Copper Company
48 Skłodowskiej-Curie St., 59-301 Lubin, Poland, e-mail: Piotr.Kwapisiński@kghm.com
corresponding author
Key words: steel forging ingot, brass continuously cast ingot, structural transformations, crankshaft for ship engines, mathematical prediction of structural zones, numerical calculation of heat transfer
Abstract
Metallographic studies performed on a cross-section of static steel ingot allow the observation of the following morphological zones: a) columnar grains (treated as austenite single crystals), b) zone of the columnar into equiaxed grains transformation (CET), and c) equiaxed grains at the ingot axis. These zones are reproduced theoretically by the numerical simulation. The simulation is based on the calculation of both the temperature field in a solidifying large steel ingot and the thermal gradient field obtained for the same boundary conditions. In particular, a new, innovative method based on the mathematical treatment applied to different functions resulting from both the aforementioned fields, are used in the structural predictions. The method developed, firstly for the massive steel ingot, has subsequently been applied to theoretically predict the structural zones in continuously cast brass ingots. In the case of continuously cast brass ingots three different morphologies were revealed experimentally: a) columnar structures, b) equiaxed structures preceded by the CET (sharp transition), and c) single crystals situated axially. The above model for the structural zones prediction is useful in plastic deformation design for: a) steel forging ingots assigned for the crankshafts applied to the ship engines, and b) continuously cast brass ingots assigned for special applications in the shipbuilding industry.
Introduction
Some structural observations performed for the continuously cast brass ingots confirm that both columnar structures or equiaxed structures can be dominant in these castings. The appearance of a giv-en type of structure during steady state solidifica-tion of the brass ingot depends on the intensity of cooling, height of the crystallizer, and the velocity of the brass ingot translation along the crystallizer (Hunt, 1984). The formation of a given dominant structure is justified since the continuous casting is a stationary process (apart from the initial transient period of this process (Wołczyński et al., 2016). The equiaxed structure forms when the local thermal gradient is negative, whereas the thermal gradient is
locally positive for columnar grains formation (Gan-din, 2000).
The columnar into equiaxed structure transfor-mation (CET) is expected in both continuously cast brass ingots and steel static ingots, since both types of the structure usually co-exist in the ingot mor-phology. However, the CET is rather sharp in the case of continuous casting, whereas the same struc-tural transition occurs over a period of time. It was previously shown by the experimental observations on continuously cast brass ingots (KGHM – Polish Copper Company, Lubin) and for steel forging ingots assigned for crankshafts in ship engines (CELSA – Huta Ostrowiec, Ostrowiec Świętokrzyski). This difference in the CET behavior can result from the fact that the continuous casting is accompanied by
a high solidification rate, and the steel ingots solidify very slowly.
Surprisingly, the morphology of continuously cast ingots, usually, displays the presence of a single crystal situated axially, illustrated in Figure 1. A sin-gle crystal does not appear in the steel static ingot, which is usually a large/massive ingot. In a large steel ingot almost all structural phenomena can be revealed, shown in Figure 2.
The outline of a continuously cast brass ingot shows constrained growth (directional) of the struc-ture, given in Figure 1a. This simplification allows the consideration of the behavior of the thermal gra-dient situated at the solid/liquid interface. When the columnar structure is formed then the thermal gradi-ent is localized askew (almost radially), along a giv-en cell axis. Whgiv-en the single crystal begins to grow axially, then the thermal gradient radically turns its direction to be localized along the single crystal axis (vertically, along the ingot axis). Thus, this kind of structural transformation is also accompanied by a significant change in the temperature field created within the solidifying brass ingot. For this simplified case, the columnar into single crystal transformation (CSCT) occurs, shown in Figure 1a.
Usually, the continuously cast brass ingot exhib-its two types of structural transition: CET, and ESCT, Figure 1b. In the case of steel continuously cast ingots a CECT (chilled equiaxed into columnar structure) transition is expected (Lorbiecka & Sarler, 2010). An attempt will be made, in the current anal-ysis, to reveal this type of structural transformation (CECT) in the continuously cast brass ingot under investigation.
Large static steel ingot forms its morphology in two stages separated by a virtual switching point,
Figure 2a(i). At the first stage, due to the activity of the viscosity gradient, the growing equiaxed crys-tals/grains tend towards the ingot axis to form sedi-mentary cones and accompanying the so-called “A” – segregates inside the solid shell consisting of the columnar structure. At the second stage, due to the activity of the thermo-phoretic force, the growing equiaxed crystals/grains tend towards the solid shell consisting of the columnar structure to promote the thickening of the mentioned shell with the accompa-nying “V” – segregates formation, shown in Figure 2a.
The structure formation as well as structur-al transitions appearing in the large steel ingot are significantly complicated by the phenomena of seg-regation. This phenomenon appears because steel contains more than one element in its chemical com-position (Konozsy et al., 2010).
The mentioned CET – transition occurs within a period of time during which equiaxed structure enters into competition with the columnar structure. Hence, the columnar structure formation disappears during CET. When the CET is completed the equi-axed structure exists exclusively in the steel large ingot. However, there is some supplementary phe-nomena accompanying the formation of the equi-axed structure, Figure 2a.
Experimental observations of the steel morphol-ogy were made via a vertical cut at the mid-depth of a 15-ton forging steel ingot serially cast by the CELSA – Huta Ostrowiec steel plant in Ostrowiec Świętokrzyski, Poland. The examined steel ingot contains 0.32 C, 0.79 Mn, 0.28 Si, 0.009 P, 0.007 S, 0.9 Cr, 0.8 Ni and 0.36 Mo [wt.%].
Some samples were selected along the steel ingot radius to reveal: a) the chilled equiaxed grains under
a) b)
Figure 1. Morphology of the continuously cast brass ingot: a) an example of the co-existence of a single crystal (central) and surrounding columnar structure, as shown schematically; b) co-existence of the SC – single crystal surrounded by the E – equi-axed structure and the C – columnar structure, as revealed experimentally
the ingot surface, b) the columnar and columnar branched grains in the zone of constrained solidifi-cation, Figure 2c, c) the equiaxed grains in the zone of unconstrained solidification, Figure 2d, and d) the steel morphology for the CET transition. Addition-ally, significant segregation, over a macro scale, as well as shrinkage phenomena were revealed in the vicinity of the ingot axis, Figure 2b.
Almost all mentioned structural phenomena can be reproduced by the numerical calculation/ simulation of both the temperature field and ther-mal gradient field, and additionally with the correct interpretation of the functions resulting from these simulations, as presented in the current study.
The sequential formation of the large steel ingot morphology consists of: m – chilled fine equiaxed
grains, CFE; l – columnar cells; C; j, h – columnar
dendrites, CD; o – lower sedimentary cone, LSC; n – upper sedimentary cone, USC; k – lower “A”
segregates, LAS; f – upper “A” segregates, UAS; e –
“V” segregates, VS; d – equiaxed grains, E,
coexist-ing with columnar dendrites; g – equiaxed grains, E,
coexisting with the segregates, c – equiaxed grains,
E, coexisting with the b – shrinkage cavity and axial
porosity, given in Figure 2a.
Some structural defects are mainly formed in the vicinity of the ingot axis but within its upper section, Figure 2b. There are: 1 – large carbides
(macro-seg-regation phenomenon), 2 – precipitates of eutectic
carbides (micro-segregation phenomenon), and 3 –
shrinkages, Figure 2b.
The columnar structures (austenite grains) are usually surrounded with eutectic carbides precip-itates (arrows), Figure 2c. In the case of equiaxed structure formation, there are: 1 – large carbides
(belonging to “A” and “V” – segregates), and 2 –
precipitates of eutectic carbides (micro-segregation phenomenon), Figure 2d.
Figure 2. Morphology of the static steel, massive ingot: a) outline of the sequential formation of the ingot structures; b) a struc-ture typical for the areas localized along the ingot axis; c) columnar strucstruc-ture within the solid shell formed during the con-strained growth; and d) the equiaxed structure formed inside the solid shell during unconcon-strained growth
a)
b)
The mentioned numerical simulation of the heat transfer performed for the continuously cast brass ingots is based on the outline given in Figure 3.
The above scheme used in the numerical calcula-tion was applied to prediccalcula-tion of the structural zones in the brass ingot subjected to continuous casting. The typical morphologies of such an ingot after con-tinuous casting are shown in Figure 4. The CCFCT transition (chilled columnar into fine columnar) is visible solely at the ingot surface.
Mathematical prediction of the structural transformations in the brass/steel ingots
The simulation of the heat transfer requires mathematical equations to be applied to a computer
program. For the case of the calculation of tem-perature field for the continuously solidifying brass ingot, Figure 3, the following equations (with some boundary conditions) were applied:
a) when the co-ordinate system does not move with the velocity equal to velocity of the ingot translation:
z T T z T T r r T r T r T T r t T T T c 2 ef 1 (1) orb) when the co-ordinate system is moving with a velocity equal to the velocity of ingot transla-tion, along a given crystallizer:
Figure 3. Outline of the system applied to calculation of temperature field for the continuous casting of the brass ingots
Figure 4. Cross-section of a continuously cast ingot: a) with the dominant columnar structure (CC – chilled columnar cells, FC – fine columnar cells); and b) with the E – equiaxed structure as the dominant morphology
r T r T r T T r t T T T c ef (2)additionally, according to the outline shown in Figure 3,
t r r
Rm
T T , , 0, (3)
L b L S S L b S b T T T c T T T T T L T c T T T c T c , , , ef (4)Eq. (1)–(4) is a modified version of the previous mode of the temperature field calculation (Ivanova, 2013), where:
ρ – density;
cb – brass specific heat; λ – thermal conductivity; T – temperature;
r – current radius, Figure 3; TL – liquidus isotherm; TS – solidus isotherm; cef – effective specific heat;
L – latent heat;
r, φ, z – co-ordinates in the cylindrical co-ordinate system.
For the case of the of the calculation of tempera-ture field in the solidifying static steel ingot, Figure 2a, the following equations (with some boundary conditions) are contained in the professional com-puter program, ABAQUS:
V S V V L S q V Ud d d (5) z λ f T (6) where:U – internal energy of the solid/liquid system; V – volume of the solid;
S – surface area;
q – heat flux per unit area of the body;
f – heat flux;
λ – conductivity matrix; z – position,
(notations taken from the Abaqus Theory Manual accessible in the CYFRONET/AGH – University of Science and Technology).
Mathematical functions resulting from the thermal gradient field for the brass ingot solidification
The numerical simulation of the thermal gra-dient field in the solidifying brass ingot allows the
following functions, which are useful in the structur-al zones/transformations prediction, Figure 5.
Unfortunately, the presented functions do not allow for all the structural transitions (structur-al zones) to be distinguished on the brass ingot cross-section. For example: CCFCT, and ESCT, Fig-ure 4a, are not determined in FigFig-ure 5.
Thus, the subsequent function is interpreted on the basis of the calculated temperature field, Figure 6. The v(z) – function is able to predict all the struc-tural zones revealed/shown in Figure 4a.
0 2 4 6 8 10 Time, t [min] 40 30 20 10 0 Thermal gradient, G [K/cm] 0 0.5 1 1.5 Time, t [min] 77 57 37 17 Thermal gradient, G [K/cm] a) b)
Figure 5. Points of inflection deciding on the structural zones situation: a) CET, and b) FCCT in the brass ingot
continuously cast brass ingot
CC 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4
Distance from meniscus, z [m]
Liquidus velocity , v [m/h] FC SC C E 0 0.8 1.6 2.4 3.2 Figure 6. The velocity of the liquidus isotherm movement/ motion versus distance from the liquid phase meniscus (liq-uid phase surface)
continuously cast brass ingot continuously cast brass ingot E CET FCCT FC C C crystallizer air-cooling
solidus
Mathematical functions resulting from the tempera- ture field for the large steel ingot solidification
The numerical calculation of the temperature field (performed with the use of the ABAQUS pro-gram) performed for the large/massive steel ingot (roll in a simplification) solidification results in the Space – Time – Structure Map, Figure 7.
Figure 2a. The CET – transition is also shown within the solidification time period: tCR ⇔ tER.
Significance of the structural predictions for the shipbuilding industry
The CELSA – Huta Ostrowiec, Ostrowiec Świętokrzyski, specializes in the production of the forging ingots assigned to the shipbuilding industry, Figure 9.
Figure 9. A massive steel ingot accelerated to deformation at the elevated temperature by press forging
The steel ingot production consists of many steps, as shown schematically in Figure 10.
The steel ingot press forging, Figure 10 (step 9) is the most accountable process in crankshaft pro-duction. An example of plastic deformation is pre-sented in Figure 11, together with the final product (a completely forged crank shaft) subjected to heat treatment.
The crankshaft forging (steel ingot plastic defor-mation) depends significantly on the C/E – structural
chilled structure zone solidus s/1 interface
s/1 interface liquidus C→E
quasi stationary state
0.42 0.4 0.3 0.2 0.1 0.0 Roll radius, r [m] Time, t [h] 0 1 2 3 5 6 7 8 9 10tCR t ER tE0
Figure 7. Space – Time – Structure Map for the massive steel ingot (geometrically – roll as a simplification) with the sol-idus and liqusol-idus isotherms localization (Wołczyński et al., 2011) 0 1 2 t [h] 5 6 7 v [m/h] [m/h]vS 0.10 0.06 0.02 0.10 0.06 0.02 tEC tCR tER tmax tAV tV
Figure 8. Interplay between the two velocities: the v – liqui-dus isotherm movement/motion, and vS – s/l interface dis-placement, S = C, E, AV, for the static steel ingot solidifica-tion, 950 [mm] in diameter
The performed calculation/simulation confirms that the CET – transition occurs over a certain peri-od of time and range of the ingot radius, Figure 7. The intersection of both s/l interfaces within the CET zone emphasizes that both structures: columnar and equiaxed enter into competition (dashed lines/ functions).
The competition is completed at the tER time, when the s/l interface of the columnar structure for-mation is extrapolated to zero (is asymptotic to r(tER) – ingot radius), Figure 7. More detailed analysis of the temperature field allows us to show the behavior of two velocities: the v – liquidus isotherm move-ment/motion, and vS – s/l interface displacement, S = C, E, AV, Figure 8.
All the predicted ingot structures such as: the CE – chilled equiaxed (solidification time period: 0 ⇔ tCE); the C – columnar cells/dendrites (solid-ification time period: tEC ⇔ tER); the E – equiaxed (solidification time period: tCR ⇔ tmax); the E –
equiaxed structure accompanied by the “A” – seg-regates (solidification time period: tmax ⇔ tAV); the EV – equiaxed structure mixed with the “V” –
seg-regates (solidification time period: tAV ⇔ tV), repro-duced mathematically in Figure 8, are also visible in
ratio during a given ingot solidification. Thus, the modeling/prediction of structural zones fraction and resultant structural transformations (Mirihanage et al., 2013), as well as modeling of the structure for-mation mode (Zyska et al., 2016) is a fundamental task which can assist the understanding of the subse-quent plastic deformation.
It should be emphasized that the columnar struc-ture, contrary to the equiaxed one, is conducive in removing the insoluble particles from the ingot by pushing them along its s/l interface (Shangguan, Ahuja & Stefan’s, 1992).
This rejection of the insoluble particles, firstly, depends on solidification rate and insoluble par-ticles radius. When the solidification rate is below the threshold rate, typical for a given alloy, then the rejection/pushing is very intensive (Fraś & Olejnik, 2008). The mentioned problem is of great impor-tance in the case of continuous casting of the brass ingots. Usually, the relationship between the thresh-old rate of solidification and particles radius has a parabolic character.
The plastic deformation of the columnar structure is rather difficult, whilst the equiaxed structure eas-ily yields to the forging (Sztwiertnia et al., 2002).
Therefore, an additional experiment has been per-formed to confirm the above conclusion. Two sam-ples were selected from the small (laboratory scale) ferritic steel ingot. The first sample consisted exclu-sively of the oriented columnar structure, and the second exclusively of equiaxed structure. The mea-surement of the columnar structure orientation con-firmed that the privilege orientation for those grains was {200} (privilege direction of the crystal growth). The obtained pole figures are shown in Figure 12.
It should be noted that the determined orienta-tion, Figure 12, is not the same in the case of the columnar structure growing in the austenitic steel, Figure 2c. Hence, austenitic steel does not yield to the forging, Figure 11, in such a problematic manner as ferritic steel does.
RD RD
TD
200 200
a) b)
Figure 12. Pole figures, {200}, measured for the grains: a) laying parallel to the direction of a plastic deformation, and b) equiaxed, from the middle of the ferritic steel ingot Figure 10. The steps of the steel ingots production: 1 – steel scrap collection, 2 – charging basket, 3 – electric arc furnace, 4 – ladle furnace, 5 – vacuum degassing system, 6 – casting of ingots, 7 – vacuum car, 8 – heat furnace, 9 – press forging (1250, 2000, 3200, 8000 tons), 10 – heat treatment, 11 – machining, 12 – pit furnace, 13 – bogie – type furnace, 14 – quenching tank, and 15 – final machining and painting
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Figure 11. Crankshaft production from the steel forging ingots: a) plastic deformation of the steel ingot by the press forging (in course), b) heat treatment imposed to a complete-ly forged/formed crankshaft (with its final shape) (courte-sy of Mr. Robert Martynowski, CELSA – Huta Ostrowiec, Ostrowiec Świętokrzyski)
a)
Conclusions
Mathematical prediction of structural zones localization as well as structural transformations within the solidifying continuously cast brass, and static steel ingots was developed. A good agreement between theoretical predictions and experimental observations has been confirmed, as complemented by Figure 2a with Figure 8, and Figure 4a with Fig-ure 6.
Modelling of structural zones seems to be very useful in the control of structural zone localization and further plastic deformation of a given ingot. A particular role played by the C/E – structural ratio in the subsequent plastic deformation of the ingots, this was confirmed by the pole figure measurements performed for the ferritic steel ingot, Figure 12. It is evident that in the case of the columnar structure, only one slip system is active during plastic defor-mation, Figure 12a, whereas many slip systems work during plastic deformation of the equiaxed structure, Figure 12b.
Thus, an optimization of the C/E – structural ratio (structural factor, sf = VC/VE; VC – volume fraction of columnar structure, VE – volume fraction of equi-axed structure in an ingot) is necessary for the steel ingots assigned for the press forging, which leads to the production of the crankshafts ultimately used in the shipbuilding industry, Figure 11.
Whether or not both structural zones appear in the ingot morphology depends on the heat transfer rate and resultant velocity of columnar grains growth, thermal gradient at the solid/liquid (s/l) interface and possible presence of grain refiners in the liquid (pos-sibly also imposed ultrasounds).
The unusual role is also played by the CET zone (if it appears in a given ingot), by this structural zone length in space and time, Figure 7. It appears that sharp transition between the C – zone and E – struc-tural zone is not advantageous for plastic deforma-tion. The structural mixture (C+E), can be a buffer remissive for the transition of slip system, active in the columnar grains deformation and the slip sys-tems active in the plastic deformation of the equi-axed grains. Therefore, the continuous casting of the brass ingots should also lead to the appearance of the time consuming structural zone C+E, instead of the sharp transition, as visible in Figure 1b.
Acknowledgments
Support for this research was provided by the National Center for Research and Development under Grant No. PBS3/A5/52/2015. The assistance of the steel plant CELSA – Huta Ostrowiec in Ostro-wiec Świętokrzyski, and in particular, Mr. R. Marty-nowski, and Mr. S. Binek is greatly appreciated.
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