Determining Solidification Parameters of Alloy Steels

S. N. Lekakh and V. L. Richards Missouri University of Science and Technology, Rolla, MO

Copyright 2011 American Foundry Society ABSTRACT Information concerning solidification parameters of alloy steel such as fraction solid and dendrite coherency point is important to understanding the solidification phenomenon as well as for accurate modeling of melt flow in thin-walled castings and feeding efficiency during solidification. The literature presents several theoretical approaches for estimation of steel solidification parameters based on equilibrium and Scheil thermodynamic models. A computer-assisted, single-thermocouple method has successfully been used for the study of solidification parameters in aluminum alloys. This paper reports application of the method to steel solidification while overcoming the concomitant high-temperature-related problems. The present work analyzes the limitations of using the computer-assisted single-thermocouple method by applying virtual modeling experiments of steel solidification in which the thermal conductivity changes at the time a solid dendrite network develops. A suitable technique for analysis of steel solidification was suggested. Solidification parameters of high strength HY130 steel containing 5.5% Ni were experimentally determined and compared with those predicted from a thermodynamic model. Key Words: steel, solidification, thermal analysis INTRODUCTION Performance of components cast from high strength alloy steels is determined by the level of micro- and macro- features or defects inherited from metallurgical processing. Modern computational fluid dynamic (CFD) programming codes are intensively used for the prediction of metal flow in the mold and casting solidification. In addition, special algorithms and rules were developed for modeling shrinkage porosity and formation of other defects in steel castings1. Modeling with increased accuracy requires a detailed data base of steel solidification parameters. During flow of steel in thin channels and continuing growth of the dendrite, their tips begin to impinge neighboring crystals so that a dendritic network is established throughout the solidifying melt. The term dendrite coherency point (DC) refers to this point. The temperature of DC plays an important role because it demarcates the transition from mass feeding to interdendritic feeding in the solidification process2 and also could be considered as an end of mold filling. Other

parameters, specifically the fraction solid (FS) as a function of temperature in the interval between liquidus and solidus, and the fraction solid at the dendritic coherency point, (FSDC) are used to simulate of casting feeding and riser optimization. The literature presents several theoretical approaches for estimation of steel solidification parameters based on equilibrium and Scheil thermodynamic models. In particular, a special algorithm based on an interdendritic solidification model and thermodynamic data was developed3 to calculate enthalpy and enthalpy-related data (i.e., specific heat capacity and latent heat), density, and thermal conductivity for low-alloy and stainless steels. These data were used for computing feeding and risering of steel castings4. Thermodynamic modeling is a valuable tool for modeling casting solidification but it cannot predict kinetic effects, in particular, heterogeneous nucleation which plays an important role in solidification. Experimental thermal analysis techniques has been used for decades to quantify the major solidification parameters, such as latent heat, critical points of phase transformation and fraction solid during the solidification process. Latent heat (Q) liberation and changing thermal properties of solidified system both affect the cooling curve. The interpretation methods discussed below can be used for validation of phase transformation temperatures and a more detailed study of solidification parameters. Unsteady state Newtonian and Fourier thermal analyses were applied for single- and two-thermocouple techniques respectively5-8. In Newtonian thermal analysis, the rate of heat evolved from a solidifying object (dQ/dτ) can be calculated from the first derivatives from experimental temperature (dTex/dτ) and so called zero line (dTz/dτ):

⎟⎠⎞⎜

⎝⎛ −=

τττ d

dT

d

dTC

d

dQ zexp (Equation 1)

( ) ⎟⎠⎞⎜

⎝⎛=−

τρ

d

dTCVTThA z

pz 0 (Equation 2)

where: h is the heat transfer coefficient, A is surface area, T is the instantaneous temperature of the specimen, T0 is the ambient temperature, V is the volume of specimen, ρ is density, Cp is specific heat.

Paper 11-042.pdf, Page 1 of 8AFS Proceedings 2011 © American Foundry Society, Schaumburg, IL USA

Using liquid state as a reference and solving Eq. 2 the zero line Tz(τ) is obtained. Assuming that the heat transfer coefficient as well as the other parameters are constants, this equation is an exponential function and Tz(τ) can be fitted to the experimental temperature Tex(τ) before solidification by the least square method. The single-thermocouple method is more suitable for measurement of solidification parameters of steel when compared to the two-thermocouple method based on Fourier analysis. However, it possesses some problems with accuracy and data interpretation. The first problem relates to correct calculation of the zero line equation because heat flux significantly changes during the solidification process of a steel casting. The second problem relates to specific conditions of the Newtonian analysis of heat transfer which does not take into account the internal thermal gradient in the solidified specimen. Consequently, and this method is limited to Biot numbers9 smaller than 0.1, where the Biot number is defined as: Bi=hL/k (Equation 3) where L=V/A is characteristic length and k is thermal conductivity. In spite of these limitations, the single-thermocouple technique was successfully used for the study of solidification parameters of low melting temperature alloys, such as aluminum alloys10,11. In addition to the determination of solidus and liquidus temperatures, computer-assisted thermal analysis based on the single-thermocouple technique was used for the evaluation of fraction solid (FS) and dendrite coherency point (DC). Upon developing a continuous dendrite network, the thermal conductivity of the system can be changed significantly due to the difference in thermal conductivity of solid and liquid phases. At that moment, the two-thermocouple technique would indicate a large difference of temperatures between the locations near the wall and in the center of specimen10. The single-thermocouple method was also used for the determination of the DC in aluminum alloys through a minimum point on the second derivative. The time or temperature value associated with the minimal point of the second derivative of the cooling curve obtained from single-thermocouple method is also associated with the maximum temperature difference between a point near the wall and one in the center of specimen which would be obtained from to two-thermocouple method11. The present work analyzes the restrictions of using the computer-assisted single thermocouple method for study of alloy steel solidification. To verify the method, virtual modeling experiments of steel solidification with changing thermal conductivity at the moment of solid dendrite network development were performed. A suitable technique for analysis of steel solidification

parameters including FS and DC was suggested and experimentally verified with using high strength HY130 steel containing 5.5%Ni. Data was compared with predictions from a thermodynamic model. MODELING AND EXPERIMENTAL PROCEDURES In this work, the single-thermocouple method with Newtonian heat transfer model was used (Eq. 1 and Eq. 2). Interpretation of the original experimental cooling curve was refined and an experimental procedure suitable for steel was developed. The improvements in interpretation of the cooling curve involved a change of the curve fitting method for the “zero line” (Tz(τ)) to increase the precision of thermal analysis. In the improved method, the zero line was fitted by least squares method. Coefficients were fit to the first derivative from the experimental temperature line before solidification (coefficients A1 and A2) and to the first and second derivatives after solidification (coefficients A3, A4) giving a Tz(τ) function of the form:

44

3321 )()()exp( startstartz AAAAT τττττ −+−+= (Equation 4)

The difference in values of specific heat for the liquid (CP,L) and solid (CP,S) was taken into account when coefficients A3 and A4 were fit to the experimental line after solidification which improved the accuracy of the zero line position (Eq. 2).

The possible limitations and applicability of the single-thermocouple method for steel solidification were analyzed by means of virtual modeling experiments. In these virtual experiments, solidification of specimens of aluminum alloy and steel in different types of mold was modeled using Fluent CFD program (unsteady state solver). It was assumed that upon developing a continuous dendrite network at the dendrite coherency point, the thermal conductivity of aluminum alloy and steel changed as shown in Figure 1. It was assumed in modeling experiments that fraction solid (FS) was proportionally distributed between liquidus and solidus temperatures. Other thermal property data used in these virtual modeling experiments are given in Table 1.

When thermal history in one particular point of the specimen was obtained from unsteady state heat transfer calculations, this data was used as input into the suggested Newtonian thermal analysis model (Eq.1 – Eq.4). The results of calculating liquidus (Tliq) and solidus (Tsol) temperatures, as well as fraction solid at dendrite coherency point were compared with the input values originally used in CFD model. An experimental study was done pouring high strength HY130 steel containing 5.5%Ni (Table 2). Steel was melted in a 100 lbs induction furnace and treated in the ladle at 1650C (3002F) using 0.07% Al and 0.05% Ca-wire addition. Specimen shape and mold materials used

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will be described below. Signal from an S-type thermocouple (protected by a quartz tube) was transferred

into a PC using a 24-bit National Instruments DAQ.

Table 1. Thermal Properties of Alloys Used in Modeling of Specimen Solidification.

Alloy Tliq, °C Tsol, °C Tdc, °C FS at DC Cp, J/kgK L, J/kg ρ, kg/m3 Aluminum 630 570 600 0.5 900 380 000 2600 Steel 1500 1450 1475 0.5 700 220 000 7800

0

50

100

150

200

250

550 570 590 610 630 650

Hea

t co

nd

uct

ivit

y, W

/mK

Temperature, 0C

Tsol TliqTd

a)

0

10

20

30

40

50

1430 1450 1470 1490 1510 1530

Hea

t co

nd

uct

ivit

y, W

/mK

Temperature, 0C

Tsol TliqTdc

b)

Fig. 1. Approximation of heat conductivity coefficient (K) of aluminum alloy (a) and steel (b) with changing the values at the temperature related to dendrite network development.

Table 2. Chemical composition of HY130 steel (wt. %). C Si Mn Cr V Mo Ni S P Fe

.17 .5 .7 .5 .7 .5 5.4 .01 .01 base

RESULTS VIRTUAL MODELING An example of Newtonian solidification analysis based on the cooling curve obtained from virtual CFD model with an aluminum alloy specimen (60 mm diameter and 70 mm height) solidified at the constant value of external heat transfer coefficient (h=1000 W/m2K) is given in Figure 2. The cooling curve obtained from the central point (Tc) of specimen was used for determination of the zero base line Tz while liquidus (Tliq) and solidus (Tsol) temperatures were found from the positions of extreme

points in the first derivative (Figure 2a). The temperature of the dendrite coherency point can be obtained9.10 from the position of maximum value of temperature difference between the thermocouples located in the center and near the mold wall (Tc-Ts). Also, this can be determined from the minimum value of second derivative of Tc. The values obtained in this manner were close to the original values used as input for the virtual experiment (Table 1). At the same time, calculated FSn (Figure 2c) had significant departure from linear distribution of FSm between Tliq and Tsol originally used in the CFD model. Also, the predicted fraction solid at the dendrite coherence point was far away (Δ) from the original value. In the second virtual experiment, with one tenth the external heat transfer coefficient (h=100 W/m2K), the predicted FS and DC values were reasonably close to those used as input to the model (Figure 2d). Coupled specimen/mold boundary conditions were applied in the virtual experiment of cooling the same aluminum alloy specimen in a sand mold. The instantaneous value of heat transfer coefficient was calculated from surface heat flux and difference of surface and reference (room) temperatures. The calculated value of heat transfer coefficient changed significantly from 370 W/m2K at start solidification point to 60-70 W/m2K at full solid because the low thermal conductivity mold accumulated heat from the casting in the surface layer. These changes in heat transfer deformed the fraction solid versus temperature curve obtained from Newtonian analysis (Figure 3b) while dendrite coherence temperature was defined quite accurately (Figure 3a). The conditions of the virtual experiments with an aluminum alloy are shown in Table 3, in which one can observe that acceptable agreement between solidification parameters (FS at DC) used in virtual experiments and calculated from Newtonian analysis of cooling curve was achieved when the Biot number was less than 0.1. At the same time precision of determination of liquidus and solidus temperatures from extreme points on first derivative did not depend on the cooling condition.

Table 3. Comparison of Solidification Parameters. Conditions H, W/m2K Difference in

fraction solid at DC

Biot numberTliq Tsol Tliq Tsol

Cont. cooling 1000 1000 0.4 0.3 0.15 Cont. cooling 100 100 0.02 0.03 0.015Sand mold 370 60 0.07 0.12 0.01

Paper 11-042.pdf, Page 3 of 8AFS Proceedings 2011 © American Foundry Society, Schaumburg, IL USA

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

500

525

550

575

600

625

650

675

700

0 10 20 30 40

T',

C/s

ec

Tem

pe

ratu

re, 0

C

Time, sec

Tc

Tz

Tc'

6300C

5700C

-120

-100

-80

-60

-40

-20

0

20

40

60

80

520

570

620

670

720

0 5 10 15 20 25 30 35 40

Tc-T

s, 0

C,

Tc"

, 0C

/se

c2

Tem

pe

ratu

re, 0

C

Time, sec

Tc

Ts

Tc-Ts

Tc"

Tliq

Tsol

Tdcp

a) b)

0

0.2

0.4

0.6

0.8

1

530 550 570 590 610 630 650

Fra

ctio

n s

olid

Temperature, 0C

Δ

FSn

FSm

0

0.2

0.4

0.6

0.8

1

530 550 570 590 610 630 650

Fra

ctio

n s

olid

Temperature, 0C

Δ

FSn

FSm

c) d)

Fig. 2. Virtual modeling and Newtonian thermal analysis of solidification of aluminum alloy with 1000 W/m2K (a, b, c) and 100 W/m2K (d) external heat transfer coefficient. Dashed lines on c) and d) represent the distribution of solid fraction between liquidus/solidus used in the initial model.

-0.1

0

0.1

0.2

500

550

600

650

700

0 20 40 60 80 100 120 140

T",

0C

/se

c2

Tem

pe

ratu

re, 0

C

Time, sec

Tn

T"n

6040C

0

0.2

0.4

0.6

0.8

1

530 550 570 590 610 630 650

Fraction solid

Temperature, 0C

?

FSn

FSm

a) b)

Fig. 3. Virtual modeling (a) and Newtonian thermal analysis (b) of aluminum alloy solidified in sand mold. Dashed line represent distribution of solid fraction between liquidus/solidus temperatures used in model.

The cooling rate of a steel specimen was significantly higher when compared to an aluminum alloy having the same geometry when both were solidified in sand mold. High cooling rate and less heat conductivity of increased Biot number for steel specimen in order of magnitude. An

example of Newtonian analysis of two cooling curves (from the central and near wall locations) of steel solidified in sand mold is given in Figure 4. For the central thermocouple, the FS and DC predicted from Newtonian analysis disagreed (indicated by Δ)

Paper 11-042.pdf, Page 4 of 8AFS Proceedings 2011 © American Foundry Society, Schaumburg, IL USA

significantly with values originally used as input for the virtual experiment (Figure 4a). Better results were obtained for a thermocouple located 10 mm from the wall into the metal (Figure 4b), yet it was difficult to identify the time of development of dendrite coherence due to the small extreme on second derivative (Figure 4c).

0

0.2

0.4

0.6

0.8

1

1420 1440 1460 1480 1500 1520

Fra

ctio

n s

olid

Temperature, 0C

ΔFSn

FSm

a)

0

0.2

0.4

0.6

0.8

1

1420 1440 1460 1480 1500 1520

Fra

ctio

n s

olid

Temperature, 0C

FSn

FSm

b)

-0.5

-0.3

-0.1

0.1

0.3

0.5

1200

1300

1400

1500

1600

0 30 60 90 120 150

T"

0C

/se

c2

Tem

pe

ratu

re, 0

C

Time, sec

Tn

Tn"

14710C

c)

Fig. 4. Newtonian thermal analysis for thermocouples located in the center (a) and near the wall (b and c) of steel specimen solidified in sand mold. For decreasing cooling rate, a virtual experiment was performed for steel solidified in an investment mold with 10 mm shell thickness which had been pre-heated at 800C (1472F). Thermal properties of silica stucco shell were taken from published data12. In addition, the ceramic shell mold was thermally isolated on the outside by a five mm layer of

low thermal conductivity (λ=0.1 W/mK) alumina fiber material. The results showed (Figure 5) that the predicted FS was in good agreement with the linear assumption used in the model. Temperature and time of DC were easily observable from the position of a minimum in the second derivative of the cooling curve. The Biot numbers for these two virtual experiments are given in Figure 6. The pre-heated ceramic mold provided a Biot number less than 0.1.

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

1300

1350

1400

1450

1500

1550

1600

0 100 200 300 400

T"

(0C

/se

c2)

Tem

pe

ratu

re, 0

C

Time, sec

Tn

Tn"

14750C

a)

0

0.2

0.4

0.6

0.8

1

1420 1440 1460 1480 1500 1520

Fra

ctio

n s

olid

Temperature,0C

FSnFSm

b)

Fig. 5. Virtual modeling (a) and Newtonian thermal analysis (b) of steel solidified in 10 mm wall thickness ceramic mold preheated at 800°C with 5 mm Kaowool insulating layer.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Tliq Tsol

Bio

t n

um

be

r

Sand mold

Preheated shell with insulation

Critical number

Fig. 6. Biot number for steel specimen solidified in sand mold and preheated ceramic shell with Kaowool insulated layer. Shaded area presents critical Biot number region in which system must lie for successful measurement.

Paper 11-042.pdf, Page 5 of 8AFS Proceedings 2011 © American Foundry Society, Schaumburg, IL USA

EXPERIMENTAL RESULTS High strength, low alloy steel (HY-130) containing 5.5%Ni was poured into two different molds containing S-type thermocouples (Figure 7). One mold had a rectangular specimen shape (60x60x50mm) with a top riser. This mold was an investment shell which had been preheated to 800C (1472F) and was surrounded by an insulating alumina fiber layer of approximately five mm thickness. The second mold was a no-bake open-top sand mold with the surface preheated to approximately 400C (752F) by a gas torch. It contained a conically shaped specimen with 80 mm top diameter, 40 mm bottom diameter and 50-55 mm height. In the second mold, the thermocouple was located 15 mm into the metal from the bottom.

a) b)

Fig. 7. Specimens for thermal analysis produced in (a) a preheated thermally insulated ceramic mold and (b) an open no-bake sand mold.

-8

-6

-4

-2

0

2

1400

1450

1500

1550

0 20 40 60 80 100 120

T', 0

C/s

ec

Te

mp

era

ture

, 0C

Time, sec

T T'

a)

-1

-0.5

0

0.5

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120

T",

0C

/se

c2

Fra

cti

on

so

lid

Time, sec

Fraction solid

T"

b)

Fig. 8. Thermal curves obtained from HY130 steel cone shape specimen solidified in no-bake mold (FS at DC approximately equals 0.3). The cooling curves and their first derivatives are shown in Figure 8a and Figure 9a as along with the calculated FS and DC values estimated from the second derivatives

(Figure 8b and Figure 9c). In addition, Figure 9b shows zero line Tz calculated by Eq. 1 and Eq. 2 and difference between first derivatives (T’ex-T’z). This difference was near zero before solidification and had a negative value after solidification because variations in the values of coefficient of heat capacities in liquid and solid conditions (Eq. 4). Both types of specimens provided close value of fraction solid at dendrite coherence point: 0.3 for conical specimen in a sand mold and 0.28 for a rectangular specimen solidified in pre-heated investment mold.

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

1400

1450

1500

1550

0 100 200 300 400

T'e

x,

0C

/se

c

Te

mp

era

ture

, 0C

Time, sec

Tex

T'ex

a)

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

1250

1300

1350

1400

1450

1500

1550

0 100 200 300 400 500 600

(T' e

x-T

' z),

0C

/se

c

Te

mp

era

ture

, 0C

Time, sec

Tex

Tz

T'ex-T'z

b)

-0.02

-0.01

0

0.01

0.02

0

0.2

0.4

0.6

0.8

1

0 100 200 300 400

Tex", 0C/sec

2

Fraction solid

Time, sec

Fraction solid

T"ex

c)

Fig. 9. Thermal curves obtained from HY130 steel rectangular specimen solidified in pre-heated ceramic shell.

Paper 11-042.pdf, Page 6 of 8AFS Proceedings 2011 © American Foundry Society, Schaumburg, IL USA

DISCUSSION The experimental results on HY130 steel solidification obtained from these two different molds are presented showing fraction solid as a function temperature (Figure 10). The experimental data was also compared to equilibrium solidification obtained from FACTSAGE software for the same steel composition (Table 2). The calculated results of Newtonian single-thermocouple analysis significantly depend on the sampling techniques which were applied. Virtual modeling experiments showed that a high cooling rate could artificially deform the FS versus temperature curve that is experimentally obtained. This prediction was experimentally confirmed. The specimen from the sand mold showed increasing solidification rate at high temperatures (near the liquidus). This result was influenced by the thermal gradient and latent heat release at different points of specimens. Steel solidified near the wall influenced the shape of the cooling curve in the central region of specimen. Data obtained from the specimen produced in pre-heated ceramic shell with an outside insulation layer more closely fitted the calculated solidification curve. In the foundry experiments, real HY130 steel solidified with under-cooling relative to equilibrium. In application, this under-cooling could affect metal flow in mold as well as the time and temperature at which dendrite coherency develops. It is also apparent from Figure 9b that the start of solidification corresponds to the first zero of the T’ex - T’z curve. The second zero is slightly delayed, probably due to solute segregation causing the final liquid to have a lower solidus than equilibrium.

0

0.2

0.4

0.6

0.8

1

1440 1450 1460 1470 1480 1490 1

Fra

cti

on

so

lid

Temperature , 0C

Equilibrium

Sand mold

Shell mold

Fig. 10. Comparison of experimental and equilibrium fraction solid versus temperature for HY130 steel. CONCLUSIONS The applicability of computer-assisted single-thermocouple thermal analysis technique was analyzed using virtual computing and real experiments with cast

steel. It was shown in the virtual experiment, that cooling rate and mold materials used had a minimal effect on determination of dendrite coherence temperature and time. At the same, calculated fraction solid obtained from a single-thermocouple Newtonian thermal analysis could has significant departure from the value used in the model when the specimen cooled at high Biot number. To increase analytical precision, the special technique of thermal analysis of cast steel by casting the specimen into a pre-heated thermally insulated ceramic mold was suggested and verified. The fraction solid thus obtained was plotted against temperature and data was compared to equilibrium solidification. Solidification parameters were determined including fraction solid and dendrite coherency point and these can be used for understanding the solidification phenomenon. Also these results are useful for accurate modeling of melt flow in thin-walled castings and feeding efficiency during steel casting solidification. REFERENCES

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6. Upadhya, K.G., Stefanescu, D.M., Lieu, K., and Yaeger, D.P., "Computer-aided Cooling Curve Analysis: Principles and Application in Metal Casing", AFS Trans., v.97, p.61 (1989).

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Alloys”, v.2: Foundry Alloys, co-published by the American Foundry Society (US) and Scanaluminium, (Sweden) (1990).

11. Jiang, H., Kierkus, W.T., and Sokolovski, J.H., “Determining Dendrite Coherency Point Characteristics of Al Alloys Using Single-Thermocouple Technique”, AFS Trans, v. 103, p.169 (1999).

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