JPH0673501A - High carbon steel wire rod or high carbon steel wire excellent in wire drawability and its production - Google Patents

Abstract

PURPOSE:To produce a high carbon steel wire rod or a high carbon steel wire excellent in wire drawability. CONSTITUTION:The high carbon steel wire rod or the high carbon steel wire excellent in wire drawability, which has a composition consisting of, by weight, 0.70-1.20% C, 0.15-1.00% Si, 0.30-0.90% Mn, further 0.006-0.100% Al and/or 0.01-0.35% Ti, P and S respectively limited to <=0.02% and <=0.01%, and the balance Fe with inevitable impurities and where the upper bainite structure prepared by means of two stage transformation comprises >=80% by area ratio and also a micro structure of <=Hv450, is produced. The composition can further contain 0.10-0.50% Cr as alloy component. By this method, the high carbon steel wire rod or high carbon steel wire excellent in wire drawability can be produced and the necessity of intermediate heat treatment in the secondary working stage can be obviated, and remarkable cost reduction, shortening of a term of works, and cost equipment reduction can be attained.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a high carbon steel wire rod or steel wire excellent in wire drawing workability and a method for producing the same.

[0002]

2. Description of the Related Art Usually, wire rods or steel wires are subjected to wire drawing according to the use of various final products. Before this wire drawing, wire rods or steel wires suitable for wire drawing are prepared beforehand. There is a need. Conventionally, as a countermeasure against it, Japanese Patent Publication No. 60-5621
As disclosed in Japanese Patent Publication No. 5: 5, C at an austenitizing temperature: 0.2 to 1.0%, Si <0.30%, M
n: 0.30 to 0.90% of a steel wire rod, potassium nitrate-based or sodium nitrate alone or in combination, 3
High strength and strength characterized by heating and melting at a temperature of 50 to 600 ° C. and immersing in a molten salt stirred by a gas body to set a cooling rate between 800 and 600 ° C. to 15 to 60 ° C./sec. There is a heat treatment method for steel wire rods with small variations.

[0003]

However, in the wire rod having a pearlite structure obtained by the heat treatment method described in the above-mentioned patent publication, the ductility is deteriorated at a high area reduction rate in the wire drawing process, and cracks are generated in the twist test ( (Hereinafter referred to as delamination) is a problem. An object of the present invention is to provide a high carbon steel wire rod or steel wire having excellent wire drawing workability and a method for producing the same, which can advantageously solve the above-mentioned problems of the prior art.

[0004]

The subject matter of the present invention is as follows. (1) C: 0.70 to 1.20% by weight%, Si: 0.15 to 1.00%, Mn: 0.30 to 0.90%, and further Al: 0.006 to. 0.100%, Ti: 0.01 to 0.35%, containing any one or two kinds, P: 0.02% or less, S: 0.01% or less, the balance being Fe and High carbon with excellent wire drawability, characterized by having an unavoidable impurity and having a microstructure in which an upper bainite structure obtained by two-step transformation has an area ratio of 80% or more and Hv of 450 or less. Steel wire rod or steel wire.

(2) As an alloy component, Cr:
0.10 to 0.50% is contained, The high carbon steel wire rod or steel wire excellent in wire drawing workability of the preceding clause 1 characterized by the above-mentioned. (3) C: 0.70 to 1.20% by weight%, Si: 0.15 to 1.00%, Mn: 0.30 to 0.90%, and Al: 0.006 to. 0.100%, Ti: 0.01 to 0.35%, containing any one or two kinds, P: 0.02% or less, S: 0.01% or less, the balance being Fe and After rolling a steel slab consisting of inevitable impurities into a wire rod, 350 to 500 at a cooling rate of 60 to 300 ° C./sec from a temperature range of 1100 to 755 ° C.
After cooling to a temperature range of ℃, within this temperature range, within the range where bainite transformation does not start, or after starting bainite transformation and before ending bainite transformation, the temperature is raised for a certain time, and bainite is completely cooled. A method for producing a high-carbon steel wire rod excellent in wire drawing workability, characterized by holding until the transformation is completed.

(4) Production of a high carbon steel wire rod excellent in wire drawing workability as described in the above item 3, wherein the starting steel slab further contains Cr: 0.10 to 0.50% as an alloy component. Method. (5) After rolling the starting steel strip into a wire rod, 1100 to 755 ° C
3 at a cooling rate of 60 to 300 ° C / sec from the temperature range of
Cool to a temperature range of 50-500 ° C, and
After holding for X seconds or more and for a time of not more than X seconds defined by the following formula (1) within a range where bainite transformation does not start, increase the temperature by 10 ° C or more and 600-T ₁ (T ₁ : holding temperature after cooling) ° C or less. The method for producing a high carbon steel wire rod having excellent wire drawability according to the above item 3 or 4, wherein the bainite transformation is retained until the bainite transformation is completely completed.

X = exp (16.03-0.0307 × T ₁ ) ... (1) T ₁ : retention temperature after cooling (6) After rolling the starting steel piece into a wire rod, 1100 to 755 ° C.
3 at a cooling rate of 60 to 300 ° C / sec from the temperature range of
After cooling to a temperature range of 50 to 500 ° C. and starting the bainite transformation within this temperature range, before the bainite transformation ends,
That is, after being held for a time Y seconds or less defined by the following formula (2), the temperature is raised to 10 ° C. or more and 600-T ₁ (T ₁ : a holding temperature after cooling) ° C. or less and held until the bainite transformation is completed. The method for producing a high carbon steel wire rod having excellent wire drawability according to the above item 3 or 4, characterized in that.

Y = exp (19.83-0.0329 × T ₁ ) ... (2) T ₁ : holding temperature after cooling (7) C: 0.70 to 1.20% by weight, Si: 0.15 to 1.00%, Mn: 0.30 to 0.90%, and further, Al: 0.006 to 0.100%, Ti: 0.01 to 0.35%. A steel wire containing one or two kinds, P: 0.02% or less, S: 0.01% or less, and the balance being Fe and inevitable impurities from the heating temperature range of 1100 to 755 ° C. and 60 to Three
It is cooled to a temperature range of 350 to 500 ° C. at a cooling rate of 00 ° C./sec, and within this temperature range, within a range in which bainite transformation does not start or after bainite transformation starts and before bainite transformation ends, for a certain time. A method for producing a high-carbon steel wire excellent in wire drawing workability, which comprises holding the material and then raising the temperature and holding until the bainite transformation is completed.

(8) The starting steel wire further comprises Cr: 0.10 to 0.50% as an alloy component, which is a high carbon steel wire excellent in wire drawing workability as described in 7 above. Production method. (9) The starting steel wire is heated in the range of 1100 to 755 ° C. to 350 to 50 at a cooling rate of 60 to 300 ° C./sec.
After cooling to a temperature range of 0 ° C. and holding in this temperature range for 1 second or longer and for a time X seconds or shorter defined by the following formula (1) within a range in which bainite transformation does not start, 10 ° C. or higher, 600−
T ₁ (T ₁ : retention temperature after cooling) ° C. or less and hold until complete bainite transformation is completed, high carbon steel having excellent wire drawability according to item 6 or 7 above Wire manufacturing method.

X = exp (16.03−0.0307 × T ₁ ) ... (1) T ₁ : retention temperature after cooling (10) The starting steel wire is heated from the heating temperature range of 1100 to 755 ° C. to 60 to 300. 350-5 at a cooling rate of ° C / sec
After cooling to a temperature range of 00 ° C and starting the bainite transformation within this temperature range, before the bainite transformation ends, that is, after holding for a time Y seconds or less defined by the following formula (2), 10 ° C
As described above, the wire drawing workability described in the above item 6 or 7 is excellent, in which the temperature is raised to 600-T ₁ (T ₁ : retention temperature after cooling) ° C. or less and retained until the bainite transformation is completely completed. Manufacturing method of high carbon steel wire.

Y = exp (19.83-0.0329 × T ₁ ) ... (2) T ₁ : holding temperature after cooling

The present invention will be described in detail below.

[0013]

The reason for limiting the chemical composition of the bainite wire rod and the steel wire in the present invention will be described. C is a basic element that controls the strength and ductility of steel, and the higher the carbon content, the higher the strength. The lower limit is 0 to ensure hardenability and strength.
It was 70%. The upper limit was 1.20% to prevent the occurrence of pro-eutectoid cementite.

Si is added as a deoxidizing agent for steel in an amount of 0.15% or more. Further, it is an element that strengthens the solid solution of steel and can reduce the relaxation loss of the steel wire. However, it reduces the amount of scale generation, deteriorates the mechanical descaling property, and slightly lowers the bonder lubrication property of the wire. Therefore, the upper limit was made 1.00%. 0.30% or more of Mn is added as a deoxidizing agent. Further, it is an element that forms a solid solution in steel and strengthens it, but if the amount of addition is increased, segregation easily occurs at the center of the wire. Since the segregated portion has improved hardenability and the transformation end time shifts to the long side, the untransformed portion becomes martensite, which leads to disconnection during wire drawing.
Therefore, the upper limit is set to 0.90%.

Al is the most economical element for not only deoxidizing but also fixing N in steel to make fine-grained austenite. The upper limit is 0.10 considering the increase of non-metallic inclusions.
The lower limit is 0%, and the lower limit is 0.006% at which the effect of Al appears. Ti is already used for controlling the austenite grains of Ti deoxidized steel, mainly plain carbon. The upper limit was set to 0.35% in order to suppress the increase of Ti inclusions and to suppress the formation of dissolved carbonitride in the steel. The lower limit was set to 0.01% where these actions are effective.

In the present invention, Al and Ti are used.
One or two of the above can be added. Since S and P precipitate at grain boundaries and deteriorate the properties of steel, it is necessary to keep S and P as low as possible. Therefore, the upper limit of S is set to 0.01% and the upper limit of P is set to 0.02%.

Cr is an element added as necessary to increase the strength of steel, and the strength increases as the amount of addition increases. However, the hardenability is also improved, and the transformation end line moves to the long side. As a result, the time required for heat treatment also becomes longer, so the upper limit was made 0.50%, and the lower limit was made 0.10% to increase strength.

The reasons for limiting the manufacturing method of the present invention are as follows. The cooling start temperature (T ₀ ) after the wire rod is rolled or the steel wire is heated affects the structure after transformation. The lower limit is the austenite transformation point (755
℃) or more. The upper limit was set to 1100 ° C in order to suppress abnormal growth of austenite crystal grains.

The cooling rate (V ₁ ) after rolling the wire or heating the steel wire is an important factor for suppressing the initiation of pearlite transformation. The present inventors experimentally obtained this. When the initial cooling rate is slower than 60 ° C./sec, when the material is slowly cooled, the transformation starts on the higher temperature side than the nose position of the pearlite transformation, and the pearlite structure is generated, so that the complete bainite structure cannot be obtained. Bainite structure formation temperature is 500
Although it is below ℃, it is necessary to cool rapidly at the initial stage of cooling in order to generate a complete bainite structure. Therefore, the lower limit of the cooling rate (V ₁ ) is set to 60 ° C./sec, and the upper limit is set to 300 ° C./sec which is industrially possible.

The isothermal holding temperature (T ₁ ) after cooling is an important factor that determines the tissue to be formed. Holding temperature is 500 ℃
If it exceeds the above range, a pearlite structure is generated in the central part of the wire or steel wire, so that the tensile strength increases and wire drawability deteriorates. When the holding temperature is lower than 350 ° C, the cementite in the bainite structure starts to be granulated, so that the tensile strength increases and the wire drawability deteriorates. Therefore, the upper limit of the isothermal transformation temperature is 500 ° C and the lower limit is 350 ° C.

Hold at 350 to 500 ° C. for a fixed time
As a result, a supercooled austenite structure is obtained. afterwards
Bainite structure that emerges with increasing temperature
Shows that the precipitation of cementite is coarser than that of the isothermal transformation.
It Therefore, the upper bainite structure transformed by two steps is soft
Turn into. In the case of complete two-step transformation, a temperature of 350 to 500 ° C
Degree of required supercooling time (t ₁) Is a supercooled austena
It is more than the time required to generate
Before the start of the bainite transformation. Preferably
It is 1 second or more and X seconds or less shown by the following formula.

X = exp (16.03-0.0307 ×)
T ₁ ) (T ₁ : retention temperature after cooling) The temperature rise range (ΔT) in the case of two-step transformation after supercooling is
The lower limit is set to 10 ° C where the softening effect due to the two-step transformation appears,
Since the upper limit needs to be 600 ° C. or lower after the temperature is raised, it is set to ΔT or less shown in the following formula. ΔT = 600−T ₁ (T ₁ : retention temperature after cooling) The retention time (t ₂ ) after the temperature rise is until the transformation is completely completed.

In the case of mixed two-step transformation, 350 to 500 ° C.
Required supercooling time (t ₁) Is bainite
After the start of transformation, it is set to Y seconds or less shown by the following formula. Y = exp (19.83-0.0329 × T₁)
(T₁: Holding temperature after cooling) After supercooling, the temperature rise width (ΔT) in the case of two-step transformation is complete
As with all 2-step transformation, the lower limit is soft due to 2-step transformation
The temperature is 10 ° C, and the upper limit is 60 ° C.
Since it is necessary to keep the temperature below 0 ° C,
To do.

ΔT = 600−T ₁ (T ₁ : retention temperature after cooling) In a pearlite wire or steel wire treated at a constant temperature of more than 500 ° C., a pearlite structure is formed at the center of the wire or steel wire. Since the pearlite structure has a layered structure of cementite and ferrite, it contributes greatly to work hardening, but the decrease in ductility does not prevent it. For this reason, in the high surface area reduction region, the tensile strength increases and the twisting characteristic deteriorates, which causes delamination.

On the other hand, the bainite wire or steel wire transformed in two stages according to the present invention is in a state in which coarse cementite is dispersed in ferrite, so that work hardening can be suppressed. As a result, it is possible to suppress the occurrence of delamination even in a high area reduction ratio area, and it is possible to perform wire drawing. The area ratio of the bainite structure is measured by observing the structure in the cross section by the lattice point method. The area ratio is an important index indicating the formation state of bainite structure and affects the wire drawability.
The lower limit of the area ratio was set to 80% at which the two-step transformation effect remarkably appears.

The Vickers hardness of the upper bainite structure is an important factor for showing the characteristics of the sample. The bainite wire rod or steel wire subjected to the two-step transformation that has undergone the cooling process and the temperature raising process has coarser precipitation of cementite, as compared with the case where the isothermal transformation is performed. For this reason, the upper bainite structure that has undergone the two-step transformation is softened. The upper limit of the Vickers hardness was set to 450 or less considering the influence of the C content.

[0027]

【Example】

Example 1 Table 1 shows the chemical composition of the test steel. A to D in Table 1 are examples of the steels of the present invention, and E to J are examples of comparative steels. The E steel has a C content of at least the upper limit, and the F steel has a Mn content of at least the upper limit.

A slab of 300 × 500 mm was rolled by a continuous casting facility into a steel slab having a 122 mm square cross section. After rolling these steel pieces into a wire rod, the molten salt (D
LP) cooling was performed. The average area reduction rate of these wires is 17
% To 1.00 mmφ and a tensile test and a twist test were performed.

The tensile test was carried out by using the JISZ2201 No. 2 test piece according to the method described in JISZ2241. In the twist test, the test piece was cut to a length of 100d + 100, and then rotated at a distance between chucks of 100d and a rotation speed of 10 rpm until it was broken. d represents the diameter of the steel wire. The characteristic values thus obtained are also shown in Table 2.

No. 1-No. No. 4 is the steel of the present invention. N
o. 5 to No. 10 is a comparative steel. Comparative Example No. In No. 5, since the cooling rate was too slow, a pearlite structure was generated, wire drawability was deteriorated, and wire breakage occurred during wire drawing. Comparative Example N
o. In No. 6, since the temperature rising temperature was too low, a bainite structure transformed into two steps was not generated, wire drawability deteriorated, and wire breakage occurred during wire drawing.

Comparative Example No. In No. 7, since the constant temperature transformation time was not sufficiently secured, martensite occurred, wire drawability was deteriorated, and wire breakage occurred during wire drawing. Comparative Example No. In No. 8, since the supercooling treatment time was long, the proportion of the bainite structure transformed by the two-step transformation was lowered, and the wire drawability was lowered.
A wire break occurred during wire drawing. Comparative Example No. In No. 9, since the C content was too high, pro-eutectoid cementite was generated and the wire drawing workability was deteriorated.

Comparative Example No. In No. 10, since the Mn content was too high, micro martensite was generated due to center segregation, and wire drawability was deteriorated.

[0033]

[Table 1]

[0034]

[Table 2]

Example 2 Table 3 shows the chemical composition of the sample steel. In Table 3, A to D are examples of the steels of the present invention, and E to J are examples of comparative steels. The E steel has a C content of at least the upper limit, and the F steel has a Mn content of at least the upper limit. With a continuous casting facility, a steel slab having a size of 300 × 500 mm was manufactured from a steel slab having a 122 mm square cross section.

After heating these steel wires, direct molten salt (DLP) cooling was performed under the conditions shown in Table 4. These steel wires were drawn to 1.00 mmφ with an average surface reduction rate of 17% and subjected to a tensile test and a twist test. The tensile test was carried out by using the JISZ2201 No. 2 test piece according to the method described in JISZ2241.

In the twisting test, the length of the test piece was cut to 100d + 100, the distance between chucks was 100d, and the rotation speed was 10 rpm.
It was rotated until it broke. d represents the diameter of the steel wire.
The characteristic values thus obtained are also shown in Table 4. N
o. 1-No. No. 4 is the steel of the present invention. No. 5 to No.
10 is a comparative steel.

Comparative Example No. In No. 5, since the cooling rate was too slow, a pearlite structure was generated, wire drawability was deteriorated, and wire breakage occurred during wire drawing. Comparative Example No. In No. 6, since the temperature rising temperature was too low, a bainite structure transformed into two steps was not generated, wire drawability deteriorated, and wire breakage occurred during wire drawing. Comparative Example N
o. In No. 7, since the constant temperature transformation time was not sufficiently secured, martensite occurred, wire drawability was deteriorated, and wire breakage occurred during wire drawing.

Comparative Example No. In No. 8, since the supercooling treatment time was long, the proportion of the bainite structure transformed into the two-stage transformation decreased, the wire drawing workability deteriorated, and wire breakage occurred during wire drawing. Comparative Example No. In No. 9, since the C content was too high, pro-eutectoid cementite was generated and the wire drawing workability was deteriorated. Comparative Example No. 1
In the case of 0, the Mn content was too high, so that micro martensite was generated due to center segregation and the wire drawability was deteriorated.

[0040]

[Table 3]

[0041]

[Table 4]

[0042]

As described above, the high carbon steel wire or steel wire according to the present invention can be drawn to a much higher area reduction rate than the conventional material and the delamination resistance is also improved. . Further, according to the present invention, it is possible to manufacture a high carbon steel wire rod or steel wire having excellent wire drawing workability, omit intermediate heat treatment in the secondary working step, and significantly reduce the cost.
The work period can be shortened and the facility cost can be reduced.

[Brief description of drawings]

FIG. 1 is a diagram showing a heat treatment pattern of the present invention.

 ─────────────────────────────────────────────────── ─── Continuation of front page (72) Inventor Nishida Century 1 Kimitsu, Kimitsu-shi, Chiba Shin Nippon Steel Co., Ltd. Kimitsu Steel Co., Ltd.

Claims (10)

[Claims] 1. C: 0.70 to 1.20% by weight%, Si: 0.15 to 1.00%, Mn: 0.30 to 0.90%, and Al: 0. 006 to 0.100%, Ti: 0.01 to 0.35%, and any one or two of them are contained. P: 0.02% or less, S: 0.01% or less, and the balance is An upper bainite structure obtained by two-step transformation having an area ratio of 80% or more and Hv of 450 or less, which consists of Fe and unavoidable impurities, has a microstructure and is excellent in wire drawing workability. High carbon steel wire rod or steel wire. 2. As an alloy component, Cr: 0.10 is further added.
% Of 0.50%, The high carbon steel wire rod or steel wire excellent in wire drawing workability according to claim 1. 3. By weight%, C: 0.70 to 1.20%, Si: 0.15 to 1.00%, Mn: 0.30 to 0.90%, and Al: 0. 006 to 0.100%, Ti: 0.01 to 0.35%, and any one or two of them are contained. P: 0.02% or less, S: 0.01% or less, and the balance is After rolling a steel slab composed of Fe and inevitable impurities into a wire rod, 350 to 500 at a cooling rate of 60 to 300 ° C./sec from a temperature range of 1100 to 755 ° C.
After cooling to a temperature range of ℃, within this temperature range, within the range where bainite transformation does not start, or after starting bainite transformation and before ending bainite transformation, the temperature is raised for a certain time, and bainite is completely cooled. A method for producing a high-carbon steel wire rod excellent in wire drawing workability, characterized by holding until the transformation is completed. 4. The starting steel billet further contains C as an alloy component.
r: 0.10 to 0.50% is contained, The manufacturing method of the high carbon steel wire rod excellent in wire drawing workability of Claim 3 characterized by the above-mentioned. 5. After rolling the starting steel strip into a wire rod, 1100 to 7
From the temperature range of 55 ° C. to the temperature range of 350 to 500 ° C. at a cooling rate of 60 to 300 ° C./sec, and within this temperature range for 1 second or more and within the range where bainite transformation does not start, the following formula (1) is used. After holding for less than X seconds, 10
The wire drawing workability according to claim 3 or 4, wherein the temperature is raised to not less than 600 ° C and not more than 600-T ₁ (T ₁ : holding temperature after cooling) ° C, and held until the bainite transformation is completely completed. Excellent high carbon steel wire manufacturing method. X = exp (16.03-0.0307 × T ₁ ) ... (1) T ₁ : holding temperature after cooling 6. After rolling the starting slab into a wire rod, 1100 to 7
After cooling from the temperature range of 55 ° C. to the temperature range of 350 to 500 ° C. at a cooling rate of 60 to 300 ° C./sec, after the bainite transformation starts in this temperature range, before the bainite transformation ends, that is, by the following formula (2). After holding for a predetermined time of Y seconds or less, the temperature is raised to 10 ° C. or more and 600-T ₁ (T ₁ : a holding temperature after cooling) ° C. or less and held until the bainite transformation is completely completed. 3. The method for producing a high carbon steel wire rod according to 3 or 4 which is excellent in wire drawing workability. Y = exp (19.83-0.0329 × T ₁ ) ... (2) T ₁ : holding temperature after cooling 7. The composition contains C: 0.70 to 1.20%, Si: 0.15 to 1.00%, Mn: 0.30 to 0.90% in weight%, and Al: 0. 006 to 0.100%, Ti: 0.01 to 0.35%, and any one or two of them are contained. P: 0.02% or less, S: 0.01% or less, and the balance is A steel wire composed of Fe and unavoidable impurities is heated from a heating temperature range of 1100 to 755 ° C. to 60 to 3
It is cooled to a temperature range of 350 to 500 ° C. at a cooling rate of 00 ° C./sec, and within this temperature range, within a range in which bainite transformation does not start or after bainite transformation starts and before bainite transformation ends, for a certain time. A method for producing a high-carbon steel wire excellent in wire drawing workability, which comprises holding the material and then raising the temperature and holding until the bainite transformation is completed. 8. The starting steel wire further comprises C as an alloy component.
r: 0.10 to 0.50% is contained, The manufacturing method of the high carbon steel wire rod excellent in the wire drawing workability of Claim 7 characterized by the above-mentioned. 9. The starting steel wire is heated from a heating temperature range of 1100 to 755 ° C. to 350 at a cooling rate of 60 to 300 ° C./sec.
After cooling to a temperature range of 500 ° C to 500 ° C and holding in this temperature range for 1 second or more and for a time X seconds or less defined by the following formula (1) within a range in which bainite transformation does not start, 10 ° C or more,
The temperature is raised to 600-T ₁ (T ₁ : retention temperature after cooling) ° C. or less, and retention is carried out until the bainite transformation is completely completed. Manufacturing method of carbon steel wire. X = exp (16.03-0.0307 × T ₁ ) ... (1) T ₁ : holding temperature after cooling 10. The starting steel wire is heated from a heating temperature range of 1100 to 755 ° C. to 35 ° C. at a cooling rate of 60 to 300 ° C./sec.
After cooling to a temperature range of 0 to 500 ° C., after starting the bainite transformation in this temperature range, before the bainite transformation ends, that is, after holding for a time Y seconds or less defined by the following formula (2),
10 ° C or higher, 600-T ₁ (T ₁ : retention temperature after cooling)
The method for producing a high carbon steel wire excellent in wire drawing workability according to claim 7 or 8, wherein the temperature is raised to not higher than 0 ° C and the temperature is maintained until the bainite transformation is completed. Y = exp (19.83-0.0329 × T ₁ ) ... (2) T ₁ : holding temperature after cooling