JPH1192880A - High chromium ferritic heat resistant steel excellent in oxidation resistance and water vapor oxidation resistance and its production - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve the adhesion between an oxidized coating film and a base metal and to improve the water vapor oxidation resistance of a steel at a high temp. by forming ultrafine oxides with a specified value or below of diameter on the boundaries with the oxidized coating film or the vicinities thereof. SOLUTION: In a high Cr ferritic heat resistant steel, ultrafine oxides of <=1 μm diameter are uniformly formed on the boundaries with a matrix directly below the oxidized coating film or the vicinities thereof, by which the adhesion between the oxidized coating film and the base metal is improved. Namely, when the ultrafine oxides are present, they are made vanishing points of pores in the coating film and are furthermore made barriers to the growth of voids formed on the boundaries. Moreover, by bridging effect, the adhesion between the coating film and the base metal increases to suppress the peeling of the coating film. For the formation of this fine oxides, elements high in affinity with oxygen such as Ti and Y are added in the range of 0.01 to 0.50%. Furthermore, Ti and Y trap oxygen and suppress the inward diffusion of oxygen to remarkably reduce the oxidizing rate.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION The invention of this application relates to a boiler,
Ferrite heat-resistant steel suitable for materials used in high-temperature and high-pressure equipment such as chemical industry equipment and its manufacturing method.Excellent high-temperature oxidation resistance, especially excellent steam oxidation properties, equivalent to conventional steel. The present invention relates to a heat-resistant steel having the above creep strength and a method for producing the same.

[0002]

2. Description of the Related Art Heat-resistant steel used for high-temperature heat-resistant and pressure-resistant members for boilers, nuclear power plants, chemical industries, and the like generally requires high-temperature strength, toughness, high-temperature corrosion resistance, oxidation resistance, and the like. For these applications, JIS-SUS3
Austenitic stainless steels such as 21H and SUS347H steels, JIS-STBA24 (2.1 / 4Cr-
Low-alloy steel such as 1Mo steel) and JIS-STBA
High ferrite steels of 9-12Cr series such as 26 (9Cr-1Mo steel) have been used.

[0003] Among them, high Cr ferritic steel is 500
At temperatures of up to 650 ° C, it is superior to low alloy steels in terms of strength and corrosion resistance, is inexpensive compared to austenitic stainless steel, has high thermal conductivity, and has low thermal expansion, so it is heat resistant. It is widely used because it has advantages such as less fatigue properties and less scale peeling and no stress corrosion cracking.

On the other hand, in recent years, in thermal power plants,
For the purpose of improving thermal efficiency, boiler steam conditions are being increased to high temperatures and high pressures. From the current supercritical condition of 538 ° C. and 246 atm, in the future it will be under super supercritical conditions of 650 ° C. and 350 atm. Driving is planned. As a result, the required properties for boiler steel have become extremely severe, and conventional high Cr ferritic steels cannot respond to oxidation resistance and long-term creep strength properties, especially steam oxidation resistance properties. . If the steam oxidation resistance is not sufficient, an oxide film is formed on the inner surface of the boiler steel pipe through which high-temperature steam flows. When this oxide film grows to some extent, it peels off due to thermal stress caused by a temperature change of the boiler such as starting and stopping, and causes clogging and the like. Therefore, prevention of steam oxidation, especially prevention of peeling of an oxide film, has become an important issue.

An austenitic stainless steel is a material that can meet the above requirements. However, austenitic stainless steel is expensive and the range of use of commercial plants is limited in terms of economy. Further, austenitic stainless steel has a large coefficient of thermal expansion, and a large thermal stress due to a temperature change due to start-up and shutdown, which causes difficulties in terms of plant design or operation. From such a viewpoint, it is required to improve the characteristics of a low-cost ferritic steel having a small coefficient of thermal expansion and being less expensive.

In order to meet such demands, various high Cr ferritic heat resistant steels have been proposed in recent years. For example, JP-A-3-097832 discloses a high Cr heat-resisting steel containing Cu from the viewpoint of increasing the content of W and improving the high-temperature oxidation resistance.
JP-A-371551 and JP-A-4-371552 propose a high Cr heat-resisting steel in which the high temperature strength and the toughness are improved by adding Co and B in addition to the optimization of Mo / W. . However, in these steels, the high temperature creep strength is improved by adding a large amount of W, but W is Mo, Cr
Is a ferrite-forming element together with
-Has the disadvantage that ferrite is formed and toughness is inevitably reduced.

As a countermeasure against this, it is most effective to use a martensite single phase. For example, Japanese Patent Application Laid-Open No. 5-263195 discloses a method of reducing the amount of Cr. JP-A-5-311342, 5-3
Nos. 11343, 5-31344, 5-
JP-A-311345 and JP-A-5-31346 propose steels in which toughness is improved by adding a large amount of austenite-forming elements such as Ni, Cu, and Co.

[0008] However, the steel proposed in the former JP-A-5-263196 is inferior in steam oxidation resistance because Mo is mixed in the scale mainly composed of Cr and a dense scale structure cannot be maintained. In order to solve this problem, Japanese Patent Application Laid-Open No. 8-85847 proposes a steel in which Mo is added in a small amount or is not added, and W is added as a main strengthening element. However, since this steel contains a large amount of Ni and Cu like the steel disclosed in Japanese Patent Application Laid-Open No. Hei 5-311342, the structure of the oxide mainly composed of Cr203 is changed, and the steam oxidation resistance is changed. Also has the disadvantage that it deteriorates.

As described above, no high-Cr ferritic heat-resistant steel which satisfies sufficient oxidation resistance and steam oxidation resistance under high temperature and high pressure ultra-supercritical pressure conditions has not been found. In view of the above situation, the invention of this application has been developed to provide a new, high Cr alloy having excellent oxidation resistance at 600 ° C. or higher, especially in steam at 630 ° C. or higher (steam oxidation resistance). It aims to provide ferritic heat-resistant steel.

[0010]

Means for Solving the Problems The present invention solves the above-mentioned problems by providing a high Cr-containing ferritic heat-resistant steel in which an oxide film is formed on the surface during use.
An ultrafine oxide having a diameter of 1 micron or less is formed at or near the interface with the oxide film to improve the adhesion between the oxide film and the base material. A heat resistant Cr ferritic steel (claim 1) is provided.

[0011] The invention of the present application also provides, as an embodiment of the heat-resistant steel, a steel containing 8.0 to 13.0% by weight of Cr,
Ferritic heat-resistant steel containing at least one of Ti and Y in an amount of 0.01 to 0.30% by weight in total (Claim 2), and 8.0% by weight of Cr.
-13.0%, C: 0.06-0.18%, S
i: 0.1 to 1.0%, Mn: 0.05 to 1.5%, N
i: 0 to 0.5%, W: 0 to 4.0%, Mo: 0 to 2.
0%, provided that W + 2Mo ≦ 4.0%, V: 0.10-0.
50%, Nb: 0.02 to 0.14%, N: 0 to 0.1
%, B: 0 to 0.010%, O: 0.010% or less, and at least one or more of Ti and Y in the range of 0.01% ≦ Ti + Y ≦ 0.30% or less, Ferritic heat-resistant steel having a composition consisting of Fe and unavoidable impurities in the remainder (Claim 3).

[0012] In addition, at least one of Co, Rh, Ir, Pd and Pt is 5.0% by weight in total.
A ferritic heat-resistant steel (Claim 4) or the like contained in the following range is provided. And also, the invention of this application
As a method for producing the above heat-resistant steel, the material is heated to 1250 ° C. or higher, and subjected to plastic working such as forging or rolling.
After holding at 150 ° C. for 1 hour or more, it is rapidly cooled to the martensitic transformation end temperature or lower, and then 650 to 800 ° C.
The present invention provides a method for producing a heat-resistant ferritic steel, wherein the method is heated to the range described above and tempered.

[0013]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The invention of this application has the above-mentioned features, but the problem with the oxidation resistance is that the pipe is clogged due to the peeling and deposition of the oxide film. That is, erosion is generated in equipment located further behind by the scattering of the film.
From this viewpoint, the invention of this application has been made, and the gist of the invention is that, as described above, an ultrafine oxide of 1 μm or less is uniformly formed at or near the interface with the base metal immediately below the oxide film. The purpose of this is to improve the adhesion between the oxide film and the base material.

In order to improve the high temperature oxidation characteristics, it is necessary to increase the Cr content and the S content.
It is known that i-ization is effective. A high Cr composition has a problem that δ-ferrite is generated and toughness is reduced. Therefore, austenitic stabilizing elements such as Ni, Co, and Cu are added to conventional steels. However, when these elements are contained, it is difficult to obtain a stable oxide film, and there is a disadvantage that oxidation resistance is deteriorated. Further, although increasing the Si content suppresses the amount of corrosion, there is a disadvantage that the film is easily peeled off.

The inventors have studied the film structure and the interface structure between the film and the base material based on the synthetic composition, and completed the present invention based on the following findings. If a fine oxide is present at or near the interface between the oxide film and the metal base material, particularly in the region immediately below the film, the fine oxide serves as a void disappearance point in the film and serves as a barrier against the growth of voids generated at the interface. In addition, the bridging effect increases the adhesion between the film and the base material, thereby suppressing film peeling.

In order to generate such a fine oxide, it is effective to add an element having a high affinity for oxygen, for example, Ti, Y in the range of 0.01 to 0.50%. In addition, Ti and Y trap oxygen to suppress inward diffusion of oxygen, and the oxidation rate is significantly reduced. If the oxide particles generated in the region immediately below the coating become too large, the resistance to the peeling of the coating will not be obtained, and no significant difference from the case where no oxide particles are present will not be recognized.

Conventionally, in high Cr ferritic heat resistant steel,
With the addition of Ti, coarse carbonitrides (inclusions) are generated, and the amounts of carbides, nitrides and carbonitrides of V and Nb that contribute to strengthening are drastically reduced, and the creep strength is reduced. Therefore Ti
Although addition is not generally performed, by optimizing the conditions of the thermomechanical treatment, the carbonitride can be finely dispersed and the creep strength can be improved.

From these results, according to the present invention, 6
A heat-resistant ferritic steel having both oxidation resistance and creep strength at a high temperature of 00 ° C. or higher is provided. The configuration of the present invention will be described in more detail. <Precipitated oxide> The main factor of peeling of the oxide film is a thermal stress caused by a temperature change, and the thermal stress increases as the oxide film grows (as the thickness of the film increases). If the thermal stress exceeds the adhesion (bonding strength) between the film and the base material, peeling occurs. Therefore, if the adhesion of the film can be increased, peeling of the film can be suppressed.

In general, the adhesion of the film is achieved by making the oxide film dense and making it difficult to form porosity at the interface between the film and the base material. On the other hand, in the present invention, fine particles are present at the interface between the film and the base material so as to hinder the progress of peeling between the film and the base material, and at the same time, suppress the floating of the film. Here, the effect of preventing scale peeling can be described as follows.

That is, in the present invention, for example, an oxide of Ti or Y is generated by internal oxidation, and for example, an outer scale (Fe oxide) (1) and an inner scale (Fe—Cr oxide) as shown in FIG. (2) is the base material (3)
A scale structure is formed on the surface, and a form in which fine oxide particles (4) exist near the scale / base material interface.

Generally, as shown in FIG. 2A, vacancies existing in the scale aggregate at the interface between the scale and the base metal (base material) to form voids (5). It is considered that separation occurs due to the connection of. Here, as shown in FIG. 2B, when fine oxide particles (4) are present near the interface between the scales (1) and (2) and the base material (3), particularly in the region immediately below the scale (2), The particles serve as vanishing points of the vacancy points in the scale and also serve as barriers for the connection of the voids (5). Further, the particles play a role of mechanically joining the scale and the base material, so that the lifting and peeling of the scale can be controlled.

When oxide particles of 1 μm or less, desirably 0.5 μm or less are present, peeling of the oxide film is suppressed, and the above-mentioned effect is exhibited. On the other hand, when the size of the particles is as large as 3 microns or more, the releasability is deteriorated. <Synthetic Composition> Cr: Generally, an oxide film of a ferritic heat-resistant steel has an Fe-based oxide film formed on the outer layer side and a Cr-based oxide film formed on the inner layer side. This dense Cr ₂ O
₍₃₎ Stabilization without peeling off the film is effective for improving oxidation resistance. From this viewpoint, in the present invention, Cr
Is an essential alloying element. Regarding the amount of addition, 8.0% or more is required to obtain a dense oxide film.
If it exceeds 3.0%, the formation of δ-ferrite is promoted and other properties such as toughness are remarkably deteriorated.
The content is preferably 8.0-13.0%.

Ti: Ti has a high affinity for oxygen, and when added in a small amount, a fine oxide is generated immediately below the film. Ti easily bonds not only to oxygen but also to carbon and nitrogen, and also to these elements contained in the alloy to form carbides and the like. If the addition amount is as small as 0.01% or less, all of the Ti bonds to the carbon and the like contained in the alloy,
No oxides can be produced during use. Therefore, it is preferable to add 0.01% or more. On the other hand, if the addition amount is too large, coarsening of the Ti oxide occurs remarkably, which has an adverse effect. Therefore, it is appropriate to set the upper limit to 0.3%. Also, Ti traps oxygen.
Inward diffusion of oxygen is suppressed, and the oxidation rate is significantly reduced.

Further, when Ti is added, coarse carbonitrides (inclusions) are generated, and the amounts of carbides, nitrides and carbonitrides of V and Nb which contribute to strengthening are drastically reduced, and the creep strength is lowered. I do. Therefore, Ti addition has not been generally performed until now. However, when heated to 1250 ° C. or more, re-dissolution of Ti carbide starts, and in this temperature range, predetermined plastic working such as forging, rolling, and extrusion is performed, and immediately after 1000 to 11
After maintaining the temperature in the range of 50 ° C. and cooling to the martensitic transformation end temperature or lower, a martensite structure free of coarse Ti carbides can be obtained. Then 65
By performing tempering in the range of 0 to 800 ° C., a structure in which fine M23C6 and MC are precipitated in tempered martensite is obtained, and a creep strength equivalent to the basic composition without adding Ti is obtained. At this time, the processing temperature is aimed at accelerating the solid solution of the Ti carbide. The higher the processing temperature, the more preferable. The solid solution of the Ti carbide starts to occur at 1250 ° C., but it is desirable to heat it to 1300 ° C. or higher.

Y: Like Ti, Y is also an element having a high affinity for oxygen, and can easily exert the effects of the present invention effectively.
As with Ti, the lower limit is 0.01%, and the upper limit is the same as that of Ti, since it is necessary to add an amount larger than that of Ti in order to bond oxygen during use as in the case of Ti. For reasons, it is suitable to be 0.3%. In the case of Y, similarly to Ti, by trapping oxygen,
Suppresses the inward diffusion of oxygen and significantly reduces the oxidation rate.

When the above-mentioned Ti and Y are added and contained, the total weight percentage is 0.01 to 0.01%.
0.3% is appropriate. If the content is less than 0.01%, the effect of the present invention is not sufficient, and if it exceeds 0.3%, the oxide becomes coarse, which is not preferable.
Other elements have been added so far to provide other necessary properties such as creep properties and toughness, and the amount generally added so far is used as a guide.

C: C may be formed as MC [carbonitride M (C, N). Here, M indicates an alloy element, and the same applies hereafter], an element that forms M7C3 and M23C6 type carbides and greatly affects the performance of steel. Especially,
Precipitation of fine carbides such as VC and NbC during use contributes to improvement of the creep strength on the long-time side. However, in order to obtain the effect of strengthening the precipitation, 0.06% or more is necessary. On the other hand, if it exceeds 0.18%, the carbides become coarse and coarse from the initial stage of use, and conversely, the creep on the long-time side This leads to a decrease in strength. Therefore, the C content is 0.0
Suitably, it is in the range of 6 to 0.18.

Si: Si is an element effective as a deoxidizing agent for molten steel and for improving steam oxidation resistance at high temperatures. However, a large amount of Si causes deterioration of toughness. , 0.01 to 1.0%. Therefore, also in the present invention, the upper limit is 1.0
%. Mn: Mn, which is added as a deoxidizing agent and a desulfurizing agent for molten steel, is an element effective for improving short-time creep strength with high stress. However, in order to obtain the effect, it is necessary to use 0.1.
It is known that the content is required to be not less than 05%, while if it exceeds 1.6%, the toughness is deteriorated. For this reason, it is appropriate that the amount of added Mn is 0.05 to 1.5%.

Mo, W: Mo not only provides solid solution strengthening, but also stabilizes M23C6 and improves high-temperature strength. If it exceeds 2%, the formation of δ ferrite is promoted, and at the same time, the precipitation and aggregation of M6C and Laves phase are promoted, so the upper limit is made 2%. W contributes to solid solution strengthening like Mo, and also contributes to fine precipitation of M23C6,
Suppresses coarsening of carbides. With these effects,
Significantly improves creep strength at high temperature and long time. 4%
If δ exceeds δ, δ ferrite and a coarse Laves phase are likely to be formed, and the toughness is reduced. Therefore, it is appropriate to set the upper limit to 4%. When Mo and W are added simultaneously, W +
Suitably, the sum of 2Mo is 4%.

V: V is an element that forms fine carbonitrides and contributes to improvement in creep strength. However, 0.10% or more is necessary to obtain the effect,
Since the effect is saturated even if it is added in excess of 0.50%, the V content is suitably set to 0.10 to 0.50%. Nb: Nb precipitates as carbonitride, and at the same time, it is required to have a minimum content of 0.02% in order to increase the high-temperature strength and to improve the toughness by the action of refining the structure. However, 0.
If it is added in an amount of 15% or more, it is considered that the solidification does not completely occur in the matrix at the normalizing temperature and a sufficient strengthening effect cannot be obtained. Therefore, it is appropriate to set the content to 0.02 to 0.14%. .

N: N is an element that forms nitride and carbonitride to improve creep strength. However, in general, when the content exceeds 0.1%, the coarsening of the nitride proceeds, and on the contrary, a remarkable decrease in toughness is caused.
%. Ni: Ni is an austenite forming element, has an effect of suppressing the formation of δ ferrite, and is known to be effective in improving toughness. However, the addition of 1% or more causes a decrease in creep strength, so the upper limit is preferably set to 1%.

B: B is known to be effective for strengthening grain boundaries and for finely dispersing M23C6 carbides, contributing to high-temperature strength and effective for improving hardenability. 0.01
%, It is known that a coarse B-containing precipitate is formed and embrittlement is caused. Therefore, the upper limit is 0.01%
Is appropriate. Co, Rh, Ir: In addition to the above, Co is an element having an effect of suppressing the formation of δ ferrite.
The study of addition of o is underway. However, it is known that excessive addition causes a reduction in strength and embrittlement, and generally the upper limit is 5%. Rh and Ir
Is also effective like Co. Co, Rh and Ir are
It is appropriate that the total weight is 0.3 to 5.0% even when two or more kinds are added at a ratio of 0.3 to 5.0%.

Of course, the present invention is intended to suppress the peeling of the film by generating a fine oxide of 1 micron or less immediately below the film and exhibiting a bridging effect of the oxide particles. Therefore, it is not limited to the synthetic components exemplified above. Hereinafter, the present invention will be described in more detail with reference to Examples.

[0034]

EXAMPLES Example 1 Various steels having the chemical compositions shown in Table 1 were melted in a 50 kg vacuum induction melting furnace. Hot forging the obtained ingot,
Hot rolling was performed to obtain a plate having a thickness of 20 mm, and various test pieces were collected from these plates. In addition, the comparative example 1 of Table 1,
2, 3 are ASTM T91, T92, T12, respectively.
It is a 2 standard steel.

[0035]

[Table 1]

Prior to various tests, 1050 ° C. × 1 hour →
After the AC normalizing treatment, 780 ° C. × 1 hour → AC tempering treatment was performed, and the steam oxidation resistance was investigated. In the steam oxidation test, test environment: steam atmosphere, test temperature: 7
Evaluation of the scale thickness by continuous heating at 00 ° C. for a test time of 1000 hours, and evaluation of the amount of detached scale when the process of heating for 96 hours at the same temperature and then air-cooling to room temperature was repeated 10 times was performed. Table 2 shows these results.
In the same table, the presence or absence of the oxide immediately below the coating and the size thereof are also shown.

[0037]

[Table 2]

As shown in Table 2, Ti and Y are added.
As a result, fine oxides are formed under the coating, resulting in
As a result, it was confirmed that the amount of the dropped scale was reduced.
At the same time, the scale thickness during continuous heating
Therefore, it is determined that the oxidation rate is also suppressed at the same time. Si
Reduced film thickness during continuous heating in the added comparative steel
However, formation of an oxide was also observed immediately below the film. However, S
The oxide in the case of i addition is relatively large,_TwoO_ThreeFilm
Judged that it promoted peeling because it exists in a layer on the inner surface
Is done. Example 2 About the steel of the invention example 2 in Table 1, 1100-1400 degreeC
Forging is performed within the range described above, and immediately after forging, it is inserted into a furnace at 1050 ° C.
After putting the mixture and keeping it for 1 hour, the mixture was cooled with water. After this, 780 ° C x
1 hour → Perform tempering treatment of AC, 650 ° C, 100
A creep rupture test was performed at Mpa. Table 3 shows the results.
It was shown to.

[0039]

[Table 3]

As shown in Table 3, the creep rupture time was prolonged by heating to 1250 ° C. or more and working.
The breaking time is longer than that of T91 steel of o1. Further, by setting the working temperature to 1400 ° C. or higher, the rupture time was almost the same as that of the T92 (Comparative Example 2) steel or the T122 (Comparative Example 3) steel, and it was determined that the steel had sufficient creep strength.

[0041]

As described above in detail, according to the invention of this application, high-temperature heat-resistant and pressure-resistant members, such as steel pipes, used in a wide range of industrial fields such as boilers, nuclear power and chemical industries.
Provided is a high Cr ferritic heat-resistant steel having excellent steam oxidation resistance, which is useful as a steel plate for a pressure vessel, a material for a turbine, and the like, and which has a creep characteristic equal to or higher than that of a conventional steel.

[Brief description of the drawings]

FIG. 1 is a schematic cross-sectional view illustrating a relational structure between formation of oxide particles and scale in the present invention.

FIGS. 2A and 2B are schematic cross-sectional views illustrating a conventional structure for peeling by voids and a structure for preventing peeling according to the present invention.

[Explanation of symbols]

 1 outer layer scale 2 inner layer scale 3 base material 4 oxide particles 5 void

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Fujio Abe 1-2-1, Sengen, Tsukuba, Ibaraki Pref., National Institute for Metals Science and Technology (72) Inventor, Masaaki Igarashi 1-2-1, Sengen, Tsukuba, Ibaraki, Japan (72) Inventor Takehiko Itagaki 1-2-1 Sengen, Tsukuba, Ibaraki Pref.

Claims (5)

[Claims] 1. High carbon which forms an oxide film on the surface during use
In r-containing ferritic heat-resistant steel, an ultrafine oxide having a diameter of 1 micron or less is formed at or near the interface with the oxide film, and the adhesion between the oxide film and the base material is improved. High Cr ferritic heat resistant steel with excellent steam oxidation resistance. 2. Cr is contained in a content of 8.0 to 13.0% by weight, and at least one of Ti and Y is added and contained in a total weight of 0.01 to 0.30%. Claim 1
Ferritic heat-resistant steel. 3. Cr is contained in an amount of 8.0 to 13.0% by weight, C: 0.02 to 0.18%, Si: 0.1 to 1.0%,
Mn: 0.05 to 1.5%, Ni: 0 to 0.5%, W:
0 to 4.0%, Mo: 0 to 2.0%, provided that W + 2Mo ≦
4.0%, V: 0.10 to 0.50%, Nb: 0.02
０．１0.14%, N: 0０．１0.1%, B: 0０〜0.010
%, O: 0.010% or less, and at least one kind of Ti and Y in the range of 0.01% ≦ Ti + Y ≦ 0.30% or less, with the balance being Fe and unavoidable impurities. 3. The heat-resistant ferritic steel according to claim 1 having the following composition. 4. The heat-resistant ferritic steel according to claim 3, wherein at least one of Co, Rh, Ir, Pd, and Pt is contained in a total weight% of 5.0% or less. 5. The method for producing a heat-resistant ferritic steel according to claim 1, wherein the steel is heated to 1250 ° C. or higher, and subjected to plastic working such as forging or rolling.
After holding at 1150 ° C for 1 hour or more, the steel is rapidly cooled to the martensitic transformation end temperature or lower to form a martensite structure, and then heated to a temperature of 650 to 800 ° C and tempered. Manufacturing method.