HK1213300B

HK1213300B - Aluminum alloy plate for can body and production method therefor

Info

Publication number: HK1213300B
Application number: HK16101131.0A
Authority: HK
Inventors: 横井洋; 岩村信吾
Original assignee: 株式会社Uacj
Priority date: 2013-02-25
Filing date: 2014-02-14
Publication date: 2018-05-04

Abstract

An aluminum alloy plate for tank body, containing Mg: 1.0-1.5% (mass%, the same below) Mn：0.8-1.2%、Cu：0.20-0.30%、Fe：0.25%-0.60%、Si：0.20- 0.40%， The remaining chemical composition consists of Al and inevitable impurities, with a conductivity of 37.0-40.0% IACS.In addition, the tank body is manufactured by cold rolling aluminum alloy plates through multiple passes. The tensile strength σ B (10) and yield strength σ 0.2 (10) of the material before the final pass of cold rolling after aging treatment at 150 ℃ for 10 hours, and the tensile strength σ B (1) and yield strength σ 0.2 (1) after aging treatment at 150 ℃ for 1 hour, satisfy the following relationship: σ B (10) - σ B (1) ≥ 5 (MPa), and σ 0.2 (10) - σ 0.2 (1) ≥ 1 (MPa).

Description

Aluminum alloy plate for can and method for producing same

Technical Field

The present invention relates to an aluminum alloy sheet for a can body used as a material of a main body portion of an aluminum can and a method for manufacturing the same.

Background

Among can bodies of aluminum beverage cans, there are can bodies formed by applying Drawing and Ironing (DI) work to an aluminum alloy plate. A 3000 series aluminum alloy having good formability in drawing or ironing is used for a can body formed by DI working.

In recent years, there has been a demand for a can body having a thinner wall from the viewpoints of reducing the amount of materials used, reducing transportation costs, and being competitive with the cost of beverage containers other than aluminum cans. In order to make the can body thinner, it is necessary to increase the strength of the aluminum alloy sheet as a raw material. As such an aluminum alloy sheet, for example, an aluminum alloy sheet described in patent document 1 is proposed.

Documents of the prior art

Patent document

Patent document 1 Japanese patent application laid-open No. 2008-248289

Disclosure of Invention

Problems to be solved by the invention

However, in the production process of the aluminum alloy sheet of patent document 1, the ingot is cooled after the homogenization treatment, and then is heated again and rolled. In this way, in order to increase the strength of a 3000 series aluminum alloy having a conventional composition range, an additional heat treatment is required in the production process, and thus it is difficult to reduce the production cost.

In view of the above background, an object of the present invention is to provide an aluminum alloy sheet for can bodies which has high strength and is easy to manufacture.

Means for solving the problems

An embodiment of the present invention provides an aluminum alloy sheet for can bodies, characterized in that,

contains Mg: 1.0 to 1.5% (mass%, the same applies hereinafter), Mn: 0.8-1.2%, Cu: 0.20-0.30%, Fe: 0.25% -0.60%, Si: 0.20-0.40%, and the balance of chemical components consisting of Al and inevitable impurities,

the conductivity of the conductive material is 37.0-40.0% IACS,

the aluminum alloy sheet for can bodies is produced by cold rolling in a plurality of passes, and the material before the final pass of the cold rolling is subjected to aging treatment at 150 ℃ for 10 hours to obtain a tensile strength sigma_B(10)And yield strength sigma_0.2(10)And its tensile strength sigma after 1 hour of aging treatment at a temperature of 150 DEG C_B(1)And yield strength sigma_0.2(1)The following relationship is satisfied:

σ_B(10)-σ_B(1)≥5(MPa)，σ_0.2(10)-σ_0.2(1)≥1(MPa)。

another embodiment of the present invention provides a method for manufacturing an aluminum alloy sheet for can bodies, including:

preparing a magnesium-containing material: 1.0 to 1.5% (mass%, the same applies hereinafter), Mn: 0.8-1.2%, Cu: 0.20-0.30%, Fe: 0.25% -0.60%, Si: 0.20 to 0.40% and the balance of Al and inevitable impurities,

milling two rolling surfaces and two side surfaces of the plate blank,

then, the plate blank is heated for 1-24 hours at 600-620 ℃ to be homogenized,

cooling the homogenized plate blank to 500-550 ℃ at a cooling rate of 40 ℃/h or more, and then carrying out hot rough rolling,

then, carrying out hot finish rolling at the outlet side at the temperature of 330-360 ℃ to obtain a hot rolled plate,

either a cooling treatment of cooling the hot-rolled sheet to 150 ℃ at a cooling rate of 40 ℃/hr or less or a holding treatment of holding the hot-rolled sheet at a temperature of 300 ℃ or higher for 1 hour or more is carried out,

then, cold rolling the hot-rolled sheet at a temperature of 80 ℃ or lower to obtain an intermediate cold-rolled sheet at a temperature of 140 ℃ or higher,

subsequently, the intermediate cold-rolled sheet is kept at a temperature of 120 ℃ or higher for 2 hours or longer,

then, a final pass of cold rolling with a reduction of 48 to 56% is performed to obtain a cold-rolled sheet with a total reduction of 87 to 90% and a temperature of 150 ℃ or higher,

the cold-rolled sheet is cooled to 80 ℃ at a cooling rate of 15-30 ℃/hour.

Effects of the invention

The aluminum alloy sheet for can bodies has the specific chemical composition, the specific electric conductivity range, and the specific aging characteristics range. Therefore, the aluminum alloy sheet for can has formability equivalent to that of a conventional 3000 series aluminum alloy and also has higher strength.

Further, by using the method for producing an aluminum alloy sheet for can bodies, the aluminum alloy sheet for can bodies can be produced more easily, and an effect of further reducing the production cost can be expected.

Drawings

Fig. 1 is a perspective view of a redrawn cup for measuring bottom wrinkle height in example 1.

FIG. 2 is a graph showing measurement of the wrinkle height in example 1.

Detailed Description

The aluminum alloy sheet for can bodies will be described in detail below.

<Mg>

The aluminum alloy sheet for can bodies contains 1.0 to 1.5% of Mg. Mg is solid-dissolved in aluminum, and has an effect of improving the strength of the aluminum alloy sheet by solid-solution strengthening. Further, by allowing Mg to coexist with Cu and Si, a compound of Mg, Cu and Si can be finely precipitated in the course of cold rolling at a temperature of about 150 ℃. The above aluminum alloy sheet is likely to have higher strength because of precipitation strengthening of these fine precipitates.

Further, an aluminum alloy containing Mg is likely to be significantly improved in strength by work hardening in cold working such as cold rolling and DI working. Therefore, the above aluminum alloy sheet easily suppresses drawing wrinkles or bottom wrinkles in the DI processing. In addition, the can body formed of the aluminum alloy sheet is also easily improved in wall strength, i.e., puncture strength and bending strength of the can body.

In order to improve the strength of the aluminum alloy sheet, the Mg content is 1.0% or more, and more preferably 1.2% or more. When the Mg content is 1.0% or more, the strength of the aluminum alloy sheet is sufficiently high, and the can body can be more easily thinned. In addition, in this case, since work hardening at the time of DI processing is easily enhanced, the generation of drawing wrinkles or bottom wrinkles is easily reduced.

If the Mg content is less than 1.0%, the strength of the aluminum alloy sheet may be lowered. In this case, work hardening tends to be insufficient during DI processing, and drawing wrinkles or bottom wrinkles tend to occur.

Although the higher the Mg content is, the more easily the strength of the aluminum alloy sheet is increased, when the Mg content exceeds 1.5%, the earing (0 to 180 ℃ earing) in the rolling direction may become too large at the time of press working the aluminum alloy sheet into a cup shape. Therefore, there is a possibility that a problem in conveyance may easily occur when the aluminum alloy sheet after press working or DI working is conveyed to the next step.

In this case, the work hardening at the time of cold working may become excessively large. Therefore, for example, the force applied to the aluminum alloy sheet during the DI processing may become excessively large, and the aluminum alloy sheet may be broken or scratched during the DI processing depending on the case.

In this case, the amount of Mg diffused into the slab surface during the homogenization treatment increases. Therefore, the Mg oxide film formed on the surface of the slab tends to be thick, and there is a possibility that the surface quality is deteriorated such as flow marks. Further, in this case, Mg having a large potential difference with the matrix is likely to be precipitated₂Si phase, and therefore, there is a possibility that the corrosion resistance of the aluminum alloy sheet is lowered.

As described above, the Mg content is 1.0 to 1.5%, more preferably 1.2 to 1.5%, from the viewpoint of both improvement in strength and improvement in formability and corrosion resistance.

<Mn>

The aluminum alloy sheet for can bodies contains 0.8 to 1.2% of Mn. Mn is solid-dissolved in aluminum, and has an effect of improving the strength of the aluminum alloy sheet by solid-solution strengthening. Further, the work structure produced at the time of cold working recovers due to heating in the coating sintering step or the like, and Mn has an action of delaying such recovery and suppressing softening. Further, Mn coexists with Fe and Si to form Al₆Fine crystals of (Mn, Fe) and α phase compounds (Al-Mn-Fe-Si system) have the function of preventing the aluminum alloy sheet from being sintered together with the mold in the DI processing.

In order to improve the strength of the aluminum alloy sheet and to easily obtain the effect of preventing the seizure, the Mn content is 0.8% or more, and more preferably 1.0% or more. When the Mn content is 0.8% or more, the strength of the aluminum alloy sheet tends to be sufficiently high. In addition, in this case, since Al is sufficiently generated₆Fine crystals of (Mn, Fe) and α phase compounds (Al-Mn-Fe-Si system) can be obtainedThe aluminum alloy plate and the mold can be more surely prevented from being sintered together at the time of DI processing.

When the Mn content is less than 0.8%, the strength of the aluminum alloy sheet may be lowered and the effect of preventing the sintering may be lowered.

The Mn content is 1.2% or less in order to improve formability during cold working such as DI working and to easily obtain an effect of delaying recovery after cold working. In the case where the Mn content is 1.2% or less, the amount of Mn solid solution in the aluminum alloy is easily made sufficiently large. Thus, the aluminum alloy sheet can delay the recovery of the worked structure by heating in the coating and sintering step or the like due to the effect of solid solution of Mn, and can be easily inhibited from softening.

In the case where the Mn content exceeds 1.2%, Al₆The (Mn, Fe) crystal is likely to be coarse, and may lower formability in the DI process or formability in the necking/flanging process in the subsequent step of the DI process. In this case, too much Mn content in the aluminum alloy makes Mn easily crystallized or precipitated in the aluminum alloy. When the number of Mn crystals or precipitates increases, the amount of Mn dissolved relatively decreases, and the effect of delaying recovery after cold working is insufficient. Therefore, it is considered that there is a possibility that the recovery sites in the empty burning increase, and the strength is lowered in the can forming process depending on the case. Further, it is considered that, along with the crystallization or precipitation of Mn, Si or Fe having a low solid solution limit is likely to be crystallized or precipitated, and thus the strength of the aluminum alloy sheet may be lowered.

As described above, the Mn content is 0.8 to 1.2%, more preferably 1.0 to 1.2%, from the viewpoint of improving both the strength of the aluminum alloy sheet, and the formability and softening-inhibiting effect at cold working.

<Cu>

The aluminum alloy sheet for can bodies contains 0.20 to 0.30% of Cu. Cu is dissolved in aluminum and has an effect of improving the strength of the aluminum alloy sheet by solid solution strengthening. In addition, Cu coexists with Mg, and Al-Mg-Cu-based fine precipitates are formed during a period of time at a temperature of about 150 ℃ due to heat generation by working during cold rolling. The aluminum alloy sheet described above is likely to have higher strength because of precipitation strengthening of these fine precipitates. In addition, Cu has an action of delaying recovery of a worked structure by heating in a coating sintering step or the like and suppressing softening.

From the viewpoint of improving the strength of the aluminum alloy sheet, the Cu content is 0.20% or more. In this case, the strength of the aluminum alloy sheet can be sufficiently improved by solid solution strengthening or precipitation strengthening.

If the Cu content is less than 0.20%, the effect of improving the strength by precipitation strengthening may be insufficient, and the strength of the aluminum alloy sheet may be lowered.

Although the strength of the aluminum alloy sheet tends to be improved as the Cu content is increased, in the case where the Cu content exceeds 0.30%, the work hardening at the time of cold working may become excessively large. Therefore, it is considered that the force applied to the aluminum alloy sheet needs to be increased at the time of DI processing, and the aluminum alloy sheet may be broken or scratches may be generated at the time of DI processing depending on the circumstances. In addition, when the Cu content exceeds 0.30%, there is a possibility that the corrosion resistance of the aluminum alloy sheet is lowered.

As described above, the Cu content is 0.20 to 0.30% from the viewpoint of both improving the strength of the aluminum alloy sheet and controlling the work hardening, and from the viewpoint of improving the corrosion resistance.

<Fe>

The aluminum alloy sheet for can bodies contains 0.25 to 0.60% of Fe. Fe coexists with Mn and Si to form Al₆The fine crystals of (Mn, Fe) and α phase compound (Al-Mn-Fe-Si system) have an effect of preventing the aluminum alloy sheet from being sintered with a mold in DI processing.

In order to easily obtain the effect of preventing sintering and improve the formability, the Fe content is 0.25% or less, more preferably 0.40% or more. In the case of containing more than 0.25% of FeUnder the condition, the Al is₆Further, the formation of the intermetallic compound makes it easy to reduce the earing (0 to 180 DEG earing) in the rolling direction when the aluminum alloy sheet is press worked into a cup shape, and as a result, the problem when the aluminum alloy sheet after press working or after DI working is carried to the next step is easily reduced, and in addition, when 0.25% or more of Fe is contained, the occurrence of wrinkles in the necking step is easily suppressed.

If the Fe content is less than 0.25%, the effect of preventing sintering may be difficult to obtain. In this case, the lug formation in the rolling direction becomes excessively large, and there is a possibility that problems during transportation due to the lug formation are easily caused, and wrinkles are easily generated in the necking step. In addition, if the Fe content is less than 0.25%, it is necessary to use a base metal having high purity for the production of the aluminum alloy sheet, which may lead to an increase in cost.

From the viewpoint of controlling the intermetallic compound, the Fe content is 0.60% or less. When the Fe content exceeds 0.60%, coarse intermetallic compounds are likely to be formed with Mn. This intermetallic compound is not preferable because it becomes a starting point of fracture during the forming process.

Thus, in order to satisfy formability, cost, and sintering prevention effect at the time of DI processing, the Fe content is 0.25 to 0.60%, more preferably 0.40 to 0.60%.

<Si>

The aluminum alloy sheet for can bodies contains 0.20 to 0.40% of Si. Si coexists with Mn and Fe to form an alpha-phase compound (Al-Mn-Fe-Si system), and has a function of preventing the aluminum alloy sheet from being sintered with a mold during DI processing. Si, in the coexistence with Mg and Cu, has an effect of precipitating a fine intermetallic compound during cold rolling at a temperature of about 150 ℃, thereby improving the strength of the aluminum alloy sheet by precipitation strengthening.

The Si content is 0.20% or more for improving the strength. When 0.20% or more of Si is contained, a sufficient amount of fine intermetallic compounds with Mg and Cu are precipitated, and therefore the strength of the aluminum alloy sheet is easily improved.

If the Si content is less than 0.20%, precipitation of the intermetallic compound may be insufficient, and the strength of the aluminum alloy sheet may be reduced. In this case, since it is necessary to use a base metal having high purity for the production of the aluminum alloy sheet, there is a possibility that the cost is increased.

Further, although the effect of preventing sintering is more likely to be obtained as the Si content is larger, if it exceeds 0.40%, an Al-Mn-Si phase having a particle size of 0.1 μm or more is likely to be precipitated by Ostwald ripening. Along with this, precipitation of fine intermetallic compounds of Si, Mg and Cu may be insufficient, and the strength of the aluminum alloy sheet may be reduced. In this case, since the amount of solid solution of Mn is also easily reduced, the recovery of the worked structure due to heating such as dry burning is easily caused, and the strength may be reduced in the can forming step.

In addition, when the Si content exceeds 0.40%, there is a possibility that Mg may be formed when the Mg content is further increased₂Coarse crystals of the Si phase. When such coarse crystals are formed, it is difficult to precipitate fine intermetallic compounds of Si, Mg, and Cu. This is not preferable because it may cause a decrease in strength and a decrease in corrosion resistance. Thus, in order to satisfy the strength, cost, sintering prevention effect and corrosion resistance of the aluminum alloy sheet at the same time, the Si content is 0.20 to 0.40%.

< conductivity >

The aluminum alloy sheet for can bodies has an electrical conductivity of 37.0 to 40.0% IACS. The conductivity is a measured value used as an index of the solid solution amount of Mn, and a lower conductivity indicates a higher solid solution amount of Mn. By controlling the electric conductivity of the aluminum alloy sheet measured under the temperature condition of 25 ℃ to be within the above-mentioned specific range, the effect of improving the strength due to the solid solution strengthening of Mn and the effect of preventing sintering due to the precipitation of α -phase compounds and the like are easily obtained.

When the electric conductivity exceeds 40.0% IACS, the strength of the aluminum alloy sheet may be lowered due to insufficient solid solution amount of Mn. On the other hand, when the electric conductivity is less than 37.0% IACS, the solid solution amount of Mn increases, and the strength of the aluminum alloy sheet increases, but the precipitation of the α -phase compound tends to be insufficient, and the effect of preventing the seizure may be difficult to obtain.

For example, the electric conductivity can be controlled within the above-described specific range by adjusting the start temperature of hot rolling and the cooling conditions after homogenization treatment and before the start of hot rolling.

When the conductivity is within the above-specified range, the density and grain size of the Al — Mn — Si precipitates can be further controlled, thereby obtaining a more significant effect of improving the strength. That is, the aluminum alloy sheet preferably contains 10000 pieces/mm³Al-Mn-Si precipitates of 0.1 to 2.0 μm or less. The Al-Mn-Si precipitates have a function of accumulating dislocations during cold working. Therefore, the aluminum alloy sheet contains Al — Mn — Si precipitates controlled to the specific density and grain size, and thereby work-hardens to further improve the strength.

When the grain size of the Al — Mn — Si precipitates is less than 0.1 μm, the effect of improving the strength is difficult to obtain because accumulation of dislocations is difficult to occur at the time of cold rolling or cold working (press working, DI working, etc.). On the other hand, when the grain size of the Al-Mn-Si precipitates is larger than 2.0. mu.m, the effect of improving the strength is difficult to obtain because the recovery of the worked structure is likely to occur by heating in the can forming step.

Further, the density of Al-Mn-Si precipitates exceeds 10000 precipitates/mm³In the case of (3), the homogenization treatment is insufficient, and Al-Mn-Si precipitates may segregate. Therefore, it is difficult toAnisotropy necessary for controlling the earing ratio and the formability in the can-making step described later is obtained. In addition, when Al — Mn — Si-based precipitates segregate, although dislocation accumulation occurs during cold working due to the mutual relationship of the compounds, regions where dislocation-accumulated precipitates are densely arranged and regions where dislocation-accumulated precipitates are sparsely arranged are mixed. Therefore, it is considered that the recovery of the processed structure by heating is too large, and the effect of improving the strength may be difficult to obtain.

< aging characteristics >

Further, the aluminum alloy sheet for can bodies has the above-described specific aging characteristics. The above aging characteristics are values used as an index of the strength-improving effect by precipitation strengthening, and are mainly an index of the strength-improving effect due to Al — Cu — Mg precipitates. The Al-Cu-Mg-based precipitates have a property of easily obtaining an effect of improving strength without involving a change in earing ratio in press working and without adding a step such as heat treatment. Therefore, the productivity of the aluminum alloy sheet can be easily improved by utilizing the precipitates.

Tensile strength σ after 10 hours of aging of the material before the final pass of the cold rolling at a temperature of 150 ℃_B(10)And yield strength sigma_0.2(10)And tensile strength σ after 1 hour of aging treatment at a temperature of 150 ℃_B(1)And yield strength sigma_0.2(1)Satisfy sigma_B(10)-σ_B(1)≥5(MPa)、σ_0.2(10)-σ_0.2(1)In the case of the relationship of 1(MPa) or more, the strength of the can body produced using the aluminum alloy sheet can be further improved by various precipitates containing Al-Cu-Mg precipitates.

The yield strength of the aluminum alloy sheet for can bodies in the rolling direction is preferably 300MPa or more. In this case, the can bottom pressure resistance, the bending strength, the can body piercing strength and other various strengths of the can body produced using the aluminum alloy sheet can be further improved. As a result, the use of the aluminum alloy sheet makes it easy to further reduce the thickness of the can body to be obtained.

The work hardening index of the aluminum alloy sheet for can bodies is preferably 0.07 or more. The value of the work hardening index can be obtained by a tensile test in the rolling direction. When the work hardening index is 0.07 or more, the occurrence of wrinkles (opening wrinkles at press working, opening wrinkles at DI working, and can bottom wrinkles) at the time of producing a can body using the aluminum alloy sheet can be further reduced.

That is, in this case, since work hardening in cold working becomes large, cold working can be started in a state where the material strength is low. Wrinkles caused by cold working are often caused by bending of the material due to a force generated between the material and a working tool such as a die, and the lower the strength of the material, the more difficult it is to generate. Therefore, by setting the work hardening index to 0.07 or more, cold working can be performed in a state of low strength, and generation of wrinkles can be further reduced.

In a forming cup having a blank diameter of 55mm and being subjected to drawing under a drawing ratio of 1.67, the earing ratio R calculated by the following formula (1) is preferably 4% or less.

R＝(M₄₅-V₄₅)/((M₄₅+V₄₅)/2)×100 (1)

In the above formula (1), M₄₅Is a value calculated by the following formula (2), V₄₅Is a value calculated by the following formula (3).

M₄₅＝(A+B+C+D)/4 (2)

In the above formula (2), a is a tab making height of 45 ° (an angle when the rolling direction is 0 °, the same applies hereinafter), B is a tab making height of 135 °, C is a tab making height of 225 °, and D is a tab making height of 315 °.

V₄₅＝(E+F+G+H)/4 (3)

In the above formula (3), E is the lowest height of the valley bottom between the 45 ° direction and the 135 ° direction, F is the lowest height of the valley bottom between the 135 ° direction and the 225 ° direction, G is the lowest height of the valley bottom between the 225 ° direction and the 315 ° direction, and H is the lowest height of the valley bottom between the 315 ° direction and the 45 ° direction.

When the earing ratio R exceeds 4%, the earing portion formed after the aluminum alloy sheet is press-worked may be excessively large. It is considered that the lug-forming portion is too large, which is not preferable because it causes inconvenience in transportation, insufficient height of the trimmed edge after DI processing, defective seaming due to variation of the burring portion in the necking step, and other various problems in the can-making step.

The earing ratio R can be controlled by the recrystallization state after hot rolling and the total rolling reduction ratio of cold rolling. When recrystallization after hot rolling is insufficient, a rolling texture tends to remain. In this case, the cold rolled texture after passing is further grown, and therefore the earing ratio R is likely to become excessively large. In addition, from the viewpoint of improving the strength of the aluminum alloy sheet, a high total reduction ratio of the cold rolling is preferable, but if the total reduction ratio is too high, the earing ratio R may be too large.

Next, a method for producing the aluminum alloy sheet for can bodies will be described in detail. First, an aluminum alloy having the above-described specific chemical composition is cast to prepare a slab. As a casting method of the slab, a known method such as continuous casting or semi-continuous casting can be used.

Next, the two rolled surfaces and the two side surfaces of the slab are milled to remove the uneven portions of the surface layer of the slab. The thickness of the uneven portion varies depending on the chemical composition of the aluminum alloy, but is usually about 5 mm. When the uneven portion remains on the surface of the slab, the remaining uneven portion may cause a reduction in surface quality and earing cracks during rolling, which is not preferable.

And then, heating the plate blank at 600-620 ℃ for 1-24 hours for homogenization treatment. By performing homogenization treatment, additive elements such as Mn, Mg, Si, Fe and the like which are crystallized or segregated during casting of the slab are addedAnd (5) solid solution of elements. Further, by the homogenization treatment, Al can be made₆(Mn, Fe) crystal is converted into α -phase compound (Al-Mn-Fe-Si system compound) and Al₆Since the α phase compound has a superior effect of preventing sintering as compared with the (Mn, Fe) crystal, the effect of preventing sintering can be further improved by performing the homogenization treatment at the temperature within the above-specified range, and it is preferable to perform the homogenization treatment at a high temperature for a long time in order to form α phase compound by making the additive element solid-soluble.

When the temperature of the homogenization treatment is less than 600 ℃, the treatment time is increased to reach the center of the slab for homogenization, and the productivity is easily lowered. On the other hand, when the homogenization treatment temperature exceeds 620 ℃, eutectic melting may occur in a part of the slab, and the quality of the slab surface may be degraded. In addition, when the treatment time of the homogenization treatment is less than 1 hour, homogenization is insufficient, and there is a possibility that the strength of the aluminum alloy sheet to be obtained is lowered, the effect of preventing sintering is lowered, and the like. The homogenization treatment is carried out for a treatment time of usually 10 hours or less to achieve a sufficiently homogenized state, and it is difficult to obtain a commensurate effect even if it exceeds 24 hours.

After the homogenization treatment, the slab is cooled to 500-550 ℃ at a cooling rate of 40 ℃/hour or more and then hot rolled. When the starting temperature of hot rough rolling is less than 500 ℃, precipitation of Al — Mn — Si-based compounds is promoted, and the amount of Mn dissolved in the steel decreases, which may reduce the strength of the aluminum alloy sheet obtained. On the other hand, when the start temperature of hot rough rolling exceeds 550 ℃, oxidation of Mg is promoted, which may result in a decrease in surface quality. In addition, the precipitation of Al-Mn-Si compounds is caused even in a high-temperature state after the homogenization treatment is continued for a long time. Therefore, the cooling rate is preferably set to 40 ℃/hr or more, and the cooling is more preferably started as soon as possible after the homogenization treatment. In addition, in order to set the cooling rate to 40 ℃/hr or more, a cooling method such as water cooling or spray cooling may be employed.

After the hot rough rolling, the hot finish rolling was performed with the outlet side temperature set to 330-. When the outlet side temperature of the finish hot rolling is less than 330 ℃, recrystallization may be insufficient. Therefore, when the obtained aluminum alloy sheet is press-worked, the lug formation at 45 ° may become excessively large, or the lug formation may be broken, which may cause inconvenience in transportation. In this case, ear-making defects and the like may occur in the trimming step after the DI processing, and the productivity may be further reduced. On the other hand, when the outlet side temperature exceeds 360 ℃, a part of the material during hot rolling may adhere to the roll. Therefore, the surface quality of the hot-rolled sheet may be degraded and the appearance may be abnormal.

The finish hot rolling can be performed using, for example, a tandem hot rolling mill having 3 stands or more. In this case, it is preferable to set the reduction ratio of the finish hot rolling to 88 to 94%. If the reduction ratio is less than 88%, the amount of strain accumulated in the finish hot rolling is small, and recrystallization after the end of rolling may be insufficient. On the other hand, when the reduction ratio exceeds 94%, a part of the material during hot rolling may adhere to the rolls, which may cause a reduction in the surface quality of the hot-rolled sheet and an appearance abnormality.

Then, the hot-rolled sheet is subjected to either a cooling treatment of cooling the hot-rolled sheet to 150 ℃ at a cooling rate of 40 ℃/hr or less or a holding treatment of holding the hot-rolled sheet at a temperature of 300 ℃ or more for 1 hour or more. These treatments all have the effect of recrystallising the hot-rolled sheet. In other words, by selecting either the cooling treatment of cooling the hot-rolled sheet to 150 ℃ at a cooling rate of 40 ℃/hr or less or the holding treatment of holding the hot-rolled sheet at a temperature of 300 ℃ or more for 1 hour or more, the hot-rolled sheet can be sufficiently recrystallized, and the earing ratio R can be easily controlled within the above-mentioned specific range. When none of the above treatments is performed, recrystallization of the hot-rolled sheet may be insufficient, and it may be difficult to control the earing ratio R.

After any of the above treatments, the obtained hot-rolled sheet was cooled until the temperature became 80 ℃ or less for accurate temperature control at the time of cold rolling. Although the cooling rate is not particularly limited, if the cooling rate is too slow, the time until the next step is prolonged, which may lead to deterioration of productivity. Therefore, it is preferable to perform cooling by a forced cooling means such as fan cooling.

Then, the hot-pressed sheet having a temperature of 80 ℃ or lower is cold-rolled to prepare an intermediate cold-rolled sheet having a temperature of 140 ℃ or higher. Thus, the intermediate cold-rolled sheet contains an Al-Cu-Mg-based compound precipitated during cold rolling. The Al — Cu — Mg based compound is a compound to which a working strain is imparted by cold working and which starts to precipitate in a state of a temperature of 90 ℃ or higher, and has an effect of improving the strength of the aluminum alloy sheet obtained by precipitation strengthening. Further, the Al — Cu — Mg based compound has a property of accumulating the amount of work strain imparted by cold working after the heat treatment, and therefore the strength of the aluminum alloy sheet obtained can be further improved.

In order to sufficiently precipitate the Al — Cu — Mg based compound in the intermediate cold-rolled sheet, it is preferable to set the intermediate cold-rolled sheet to have a temperature of 140 ℃. When the temperature of the intermediate cold-rolled sheet is 140 ℃ or higher, an Al-Cu-Mg-based compound can be precipitated. In the case where the temperature of the intermediate cold-rolled sheet exceeds 170 ℃, there is a possibility that recovery of the worked structure associated with the reduction in strength may be caused.

Then, the intermediate cold-rolled sheet obtained is held at a temperature of 120 ℃ or higher for 2 hours or longer, whereby the intermediate cold-rolled sheet can be sufficiently aged to precipitate the Al-Cu-Mg-based compound. When the holding time of the intermediate cold-rolled sheet at 120 ℃ or more exceeds 10 hours, the intermediate cold-rolled sheet is not preferable because it may cause overaging, which may lower the strength of the aluminum alloy sheet to be obtained and also lower the productivity.

Then, the intermediate cold-rolled sheet obtained was subjected to a final pass of cold rolling with a reduction of 48 to 56%. Thus, a cold-rolled sheet having a total rolling reduction of 87 to 90% and a temperature of 150 ℃ or higher is obtained. By setting the temperature of the cold-rolled sheet to 150 ℃ or higher, the amount of work strain of the aluminum alloy sheet obtained can be appropriately recovered, and the formability in subsequent press working, DI working, or the like can be improved. The temperature of the obtained cold-rolled sheet has no upper limit, and the formability can be further improved without causing a problem in product characteristics at least up to 190 ℃.

Further, by setting the total rolling reduction of the cold-rolled sheet in the cold rolling within the above-described specific range, work hardening can be sufficiently increased, and further, the strength of the aluminum alloy sheet can be improved. If the total reduction ratio is less than 87%, the work hardening may be insufficient, and the strength of the aluminum alloy sheet to be obtained may be reduced. On the other hand, when the total reduction rate exceeds 90%, the earing rate R may increase, which is not preferable.

The temperature of the cold-rolled sheet after the final rolling pass can be controlled by the temperature of the intermediate cold-rolled sheet and the reduction ratio in the final rolling pass of the cold rolling. That is, when the reduction ratio is less than 48%, the heat generation by working is small, and the temperature of the cold-rolled sheet may be less than 150 ℃. On the other hand, when the reduction ratio exceeds 56%, the strain of the rolled surface after rolling becomes too large, which may cause problems such as cracking of the sheet, uneven application of oil, and jamming of the sheet during forming of the cup in the can-making process

In order to satisfy both the requirements of controlling the temperature of the cold-rolled sheet and reducing the strain on the rolled surface, the reduction ratio in the final pass of the cold rolling is 48 to 56%, and more preferably 50 to 54%.

And then, cooling the cold-rolled sheet to 80 ℃ at a cooling rate of 15 to 30 ℃/hr to obtain the aluminum alloy sheet for can bodies. By cooling the cold-rolled sheet under the above conditions, Al-Cu-Mg-based compounds are precipitated by aging, and the work hardening of the aluminum alloy sheet can be further increased. In this case, the processed structure is restored, and therefore, the formability in the subsequent can forming step can be further improved. If the cooling rate is less than 15 ℃/hr, the recovery of the worked structure tends to be excessive, and the strength of the aluminum alloy sheet obtained may be lowered by overaging. On the other hand, when the cooling rate exceeds 30 ℃/hr, the recovery of the processed structure tends to be insufficient, and there is a possibility that the formability is lowered.

The aluminum alloy sheet for can bodies produced by the above method is preferably supplied directly to the can forming step without performing the drawing leveling. As described above, the aluminum alloy sheet for can bodies has a large work hardening caused by the action of Al — Cu — Mg based compounds or the like at the time of cold working. Therefore, if the stretching leveling is performed before the can forming process, the strength of the material to be fed to the press working or DI working may be unexpectedly increased, and wrinkles may be easily generated in these processes.

Examples

Example 1

Examples of the aluminum alloy sheet for can bodies will be described below.

< preparation of slab >

First, a slab was prepared by DC casting using an aluminum alloy (alloy nos. 1 to 9) containing the chemical components shown in table 1, and then both rolling surfaces and both side surfaces of the slab were milled by 10mm and 5mm, respectively. Thereafter, the slab was heated at 605 ℃ for 2 hours to perform homogenization treatment. After the homogenization treatment, the slab was cooled to 515 ℃ at a cooling rate of 45 ℃/hr, and the temperature was maintained for 2 hours to homogenize the temperature of the entire slab.

< Hot Rolling >

Next, from the state where the slab temperature was 515 ℃, hot rough rolling of the slab was started using a reversing mill, and the hot rough rolling was completed in a state where the slab thickness was 30mm through a plurality of rolling passes. The slab temperature at the end of the hot rough rolling was 465 ℃. After the hot rough rolling, hot finish rolling was performed at a reduction of 92% using a 4-stand tandem hot finish rolling mill, thereby preparing a hot-rolled sheet having a sheet thickness of 2.4 mm. The outlet side temperature of the hot-rolled sheet was 340 ℃.

< Cold Rolling >

The hot-rolled sheet obtained as described above was cooled to 150 ℃ at a cooling rate of 25 ℃/hr, and then further cooled to 55 ℃ by a fan. Thereafter, the intermediate cold-rolled sheet was obtained by 2-pass cold rolling using a single stand rolling mill. The intermediate cold-rolled sheet obtained had a sheet thickness of 0.58mm and a temperature of 155 ℃.

Subsequently, the intermediate cold-rolled sheet was kept at a temperature of 120 ℃ or higher for 140 minutes. Thereafter, a final pass of cold rolling with a reduction of 53.4% was performed from the state where the temperature of the intermediate cold-rolled sheet was 118 ℃ by using a single stand rolling mill, to obtain a cold-rolled sheet. The resulting cold-rolled sheet had a sheet thickness of 0.27mm and a temperature of 165 ℃. The total reduction in cold rolling was 88.8%.

< Final treatment >

Thereafter, the cold-rolled sheet was cooled to 80 ℃ at a cooling rate of 22 ℃/hr, and cleaning of rolling oil and coating of lubricating oil were carried out without stretching leveling to obtain aluminum alloy sheets (test materials nos. 1 to 9) shown in tables 2 and 3. Further, the coating of the lubricating oil was carried out by electrostatic coating in an amount of 100mg/m²。

TABLE 1

The test materials obtained as described above were subjected to conductivity measurement and evaluation of the performance characteristics, and the results are shown in table 2. In addition, for the evaluation of the aging characteristics, the values of the tensile strength and the yield strength in the rolling direction measured in accordance with JIS (japanese industrial standards) Z2241 were used. In particular cold rolledThe material before the final pass (intermediate cold-rolled sheet) was subjected to a 10-hour aging treatment at 150 ℃ to determine its tensile strength σ_B(10)And yield strength sigma_0.2(10). Similarly, the material before the final pass of the cold rolling (intermediate cold-rolled sheet) was taken and the tensile strength σ thereof after 1-hour aging treatment at 150 ℃ was measured_B(1)And yield strength sigma_0.2(1). Then, σ is calculated_B(10)And σ_B(1)Difference of sum sigma_0.2(10)And σ_0.2(1)The difference between them. The electric conductivity was measured using an electric conductivity measuring instrument ("SIGMATEST 2.069.069" manufactured by Foerster corporation), and the temperature of the test material was 25 ℃ at the time of the measurement.

TABLE 2

Table 3 shows the mechanical properties and the earing ratios R of the respective test materials evaluated by the following methods.

< mechanical Properties >

Tensile test in the rolling direction was carried out in accordance with JIS Z2241, and the tensile strength σ of each test material was measured_BAnd yield strength sigma_0.2. Yield strength sigma_0.2The value of (B) is preferably 300MPa or more. For yield strength σ_0.2Test materials below 300MPa are underlined in Table 3.

Further, from the tensile test results, the work hardening index (n value) was calculated. The value of n is preferably 0.07 or more. For test materials with n values less than 0.07, underlined in table 3.

< ear formation Rate R >

A blank having a diameter of 55mm was collected from each test material, and drawn at a draw ratio of 1.67 to form a cup shape. The ear-making rate R of this cup was calculated by using the above-mentioned formulas (1) to (3). The earing rate R is preferably 4% or less. For test materials with an ear formation rate R of more than 4%, underlined in Table 3.

Next, each test material was molded into a DI can, and subjected to dry firing at 205 ℃ for 10 minutes to prepare a can-shaped test piece. Using this test piece, the pot bottom pressure resistance, DI formability and burring formability were evaluated by the following methods, and the evaluation results are shown in Table 3.

< pressure resistance at bottom of can >

The pot bottom shape of the test piece (DI pot) was set to 48mm in pot bottom ground diameter and 9.8mm in arch bottom depth, and the pot bottom pressure resistance at this time was measured. The pressure resistance at the bottom of the can is preferably 600kPa or higher. For test materials with a pot bottom pressure resistance of less than 600kPa, underlined in Table 3.

< DI formability >

100 cans were produced from each of the above test bodies with a target thickness of 0.105mm, and the success rate of can production and the appearance of visual observation were evaluated. In table 3,. circa represents a symbol indicating that all cans (100 cans) were successfully formed and no appearance defects, a symbol indicating that all cans (100 cans) were successfully formed but no appearance defects, a symbol indicating that 1 to 5 cans were broken, and a symbol indicating that 6 or more cans were broken. The DI formability is preferably such that all cans are successfully formed without appearance defects (expressed as ∈). Test materials that had poor appearance (indicated by ≈ o) or had cracks (indicated by Δ and ×) are underlined in table 3.

< Flanging formability >

After 100 cans were formed from each of the above test bodies, the lug-forming portions were trimmed and neck-formed in a smooth die to 204-gauge. Then, a flange having a flange thickness of 157 μm and a flange width of 2.4mm was formed at the open end, and the presence or absence of cracks at the flange end was visually observed. In table 3, a circle indicates that all cans (100 cans) were successful and no burring cracks, and a x indicates that burring cracks occurred in 1 can or more. The flanging formability is preferably such that all cans are successfully formed without flanging cracks (indicated by ∘). For the test materials with vent cracks (indicated by x), underlined in table 3.

Next, redrawn cups 1 (without forming a dome bottom) 5 were prepared from each test material during the DI process shown in fig. 1. Using this redrawing cup 1, the bottom wrinkle height was evaluated by the following method, and the evaluation results are shown in table 3.

< bottom corrugation height >

As shown in fig. 1, a wrinkle height measurement chart was obtained by measuring wrinkles 12 on the bottom edge outer portion 11 of each redrawing cup 1 using a roundness measuring instrument 2 (model EC-1010A, Mitutoyo, ltd.). Fig. 2 shows an example of a wrinkle height measurement chart. The figure is a polar coordinate system with a point O as a pole, and the angle is expressed in the circumferential direction, and the degree of unevenness of the corrugation 12 is expressed in the radial direction. In the obtained graph, a value calculated by (a value of a distance 31 from the point O to the apex of the crest 3-a value of a distance 41 from the point O to the apex of the trough 4) is set as the ridge height H for the adjacent crest 3 and trough 4. Calculating the corrugation height H of each crest 3 on the whole circumference of the bottom edge outer part 11, and taking the maximum value as the maximum corrugation height H_max. Thereafter, the maximum height H of corrugation was calculated for each of 5 cans prepared from the same test material_maxAnd calculating the average value of the values, and taking the value as the bottom wrinkling height H_bShown in table 3. Bottom crinkling height H_bPreferably 200 μm or less. For test bodies with a bottom corrugation height of more than 200 μm, underlined in table 3.

TABLE 3

As is clear from Table 1, the test materials No.1 to No.3 were formed of alloys (alloy Nos. 1 to 3) having the above-mentioned specific chemical compositions. Further, as is clear from Table 2, the test materials No.1 to No.3 exhibited electric conductivities in the above-specified ranges and also exhibited the above-specified aging characteristics. Thus, it is clear from Table 3 that the test materials No.1 to No.3 are excellent in mechanical properties and moldability, and the test pieces prepared by using the test materials are also excellent in product characteristics. On the other hand, as shown in Table 1, the test materials No.4 to No.9 had disadvantages in mechanical properties and the like as shown in Table 3 because at least one additive element in the chemical components was out of the above-specified range.

Example 2

In this example, the aluminum alloy sheet for can bodies was produced by preparing a slab using alloy No.1 in example 1 and then variously changing the production conditions. That is, in this example, the steps of slab preparation, hot rolling, cold rolling and finishing treatment were sequentially performed using various production conditions shown in table 4 instead of the production conditions (production conditions a to M) of example 1, thereby producing aluminum alloy sheets (test materials nos. 11 to 23) shown in tables 5 and 6.

The conductivity measurement and the evaluation of the performance characteristics of each test material were performed in the same manner as in example 1, and the results are shown in table 5.

Ken 5

The mechanical properties and the like of each test material were evaluated in the same manner as in example 1, and the results are shown in table 6.

TABLE 6

The production conditions (production conditions A to C) used for the test materials No.11 to No.13 were within the above-specified ranges. Further, as is clear from Table 5, the test materials No.11 to No.13 exhibited electric conductivities in the above-specified ranges, and possessed the above-specified aging characteristics. Thus, it is clear from Table 6 that the test materials No.11 to No.13 are excellent in mechanical properties and moldability, and the test pieces prepared by using the test materials are also excellent in product characteristics.

Further, according to the manufacturing method of this example, the aluminum alloy sheet for can be manufactured without performing an additional heat treatment step after the plate blank is subjected to the homogenization treatment. Therefore, the aluminum alloy sheet for can bodies can be produced more easily, and an effect of reducing the production cost can be expected.

Although test material No.14 was prepared using the production conditions within the above-described specific ranges, the elongation leveling caused work hardening, which resulted in poor formability. This is considered to be because the correction force for the stretch leveling is too large, and it is presumed that the formability can be improved by adjusting the correction force.

As shown in Table 4, the test materials No.15 to No.23 had disadvantages in mechanical properties and the like as shown in Table 6 because at least one of the respective production conditions was out of the above-specified ranges.

Example 3

This example is an example of an aluminum alloy sheet produced by heat-treating the obtained hot-rolled sheet after the hot finish rolling in example 2. The following describes the production method of this example.

< preparation of slab >

First, a slab was prepared by DC casting using alloy No.1 in example 1. Subsequently, the two rolled surfaces of the slab were milled for 10mm, and the two side surfaces were milled for 5 mm. Thereafter, the slab was heated at 605 ℃ for 2 hours to perform homogenization treatment. After the homogenization treatment, the slab was cooled to 530 ℃ at a cooling rate of 45 ℃/hr, and the temperature was maintained for 2 hours to homogenize the temperature of the entire slab.

< Hot Rolling >

Next, from the state where the slab temperature was 530 ℃, the hot rough rolling of the slab was started using a reversing mill, and the hot rough rolling was completed in a state where the slab thickness was 30mm through a plurality of rolling passes. The slab temperature at the end of the hot rough rolling was 465 ℃. After the hot rough rolling, a hot finish rolling with a reduction of 91.3% was performed using a 4-stand tandem hot finish rolling mill. Thus, a hot-rolled sheet having a sheet thickness of 2.6mm was prepared. The outlet side temperature of the hot-rolled sheet was 335 ℃.

< Heat treatment before Cold Rolling >

The hot-rolled sheet obtained as described above was subjected to a heat treatment at a temperature of 330 ℃ for 2 hours, and then cooled to 75 ℃ by fan cooling. Thereafter, the intermediate cold-rolled sheet was obtained by 2-pass cold rolling using a single stand rolling mill. The intermediate cold-rolled sheet obtained had a sheet thickness of 0.58mm and a temperature of 160 ℃.

Subsequently, the intermediate cold-rolled sheet was kept at a temperature of 120 ℃ or higher for 4.8 hours. Thereafter, a final pass of cold rolling with a reduction of 53.4% was performed by using a single stand rolling mill to obtain a cold-rolled sheet. The resulting cold-rolled sheet had a sheet thickness of 0.27mm and a temperature of 172 ℃. The total rolling reduction in cold rolling was 89.6%.

< Final treatment >

Thereafter, the cold-rolled sheet was cooled to 80 ℃ at a cooling rate of 24 ℃/hr, and without stretching leveling, washing of rolling oil and coating of lubricating oil were performed to obtain aluminum alloy sheets (test material No.24) shown in tables 7 and 8. Further, the coating of the lubricating oil was carried out by electrostatic coating in an amount of 100mg/m²。

The conductivity measurement and the evaluation of the performance characteristics of the test material No.24 were carried out in the same manner as in example 1, and the results are shown in table 7.

TABLE 7

The mechanical properties and the like of the test material No.24 were evaluated in the same manner as in example 1, and the results are shown in Table 8.

TABLE 8

As is clear from tables 7 and 8, by subjecting the hot-rolled sheet to heat treatment at 300 ℃ or higher for 1 hour or longer, the test materials having excellent mechanical properties and formability can be obtained in the same manner as in the case where the hot-rolled sheet is cooled to 150 ℃ at a cooling rate of 40 ℃/hour or lower. In addition, the test piece prepared using the test material was also excellent in product characteristics.

The heat treatment at 300 ℃ or more and 1 hour or more shown in this example can be performed at any time point after the hot rolling and before the cold rolling. That is, for example, after the hot-rolled sheet is cooled at a cooling rate exceeding 40 ℃/hr, the hot-rolled sheet may be heated again to perform the heat treatment, or the heat treatment may be performed after the hot-rolled sheet is prepared.

Claims

1. A method for manufacturing an aluminum alloy sheet for a can body, comprising:

preparing a magnesium-containing material: 1.0 to 1.5 mass%, Mn: 0.8 to 1.2 mass%, Cu: 0.20 to 0.30 mass%, Fe: 0.25 to 0.60 mass%, Si: 0.20 to 0.40 mass% and the balance of a chemical component consisting of Al and unavoidable impurities;

milling two rolling surfaces and two side surfaces of the plate blank;

then, the plate blank is heated for 1-24 hours at 600-620 ℃ for homogenization treatment;

cooling the homogenized plate blank to 500-550 ℃ at a cooling speed of more than 40 ℃/h and then carrying out hot rough rolling;

then, carrying out hot finish rolling at the outlet side at the temperature of 330-360 ℃ to obtain a hot rolled plate;

performing either a cooling treatment of cooling the hot-rolled sheet to 150 ℃ at a cooling rate of 40 ℃/hr or less or a holding treatment of holding the hot-rolled sheet at a temperature of 300 ℃ or more for 1 hour or more;

then, cold rolling the hot rolled sheet with the temperature of below 80 ℃ to obtain an intermediate cold rolled sheet with the temperature of above 140 ℃;

subsequently, the intermediate cold-rolled sheet is kept at a temperature of 120 ℃ or higher for 2 hours or longer;

then, performing a final rolling pass of cold rolling with the reduction rate of 48-56% to obtain a cold-rolled sheet with the total reduction rate of 87-90% and the temperature of more than 150 ℃;

cooling the cold-rolled sheet to 80 ℃ at a cooling rate of 15-30 ℃/hour.

2. The production method according to claim 1, wherein the aluminum alloy sheet for can bodies produced contains Mg: 1.0 to 1.5 mass%, Mn: 0.8 to 1.2 mass%, Cu: 0.20 to 0.30 mass%, Fe: 0.25 to 0.60 mass%, Si: 0.20 to 0.40 mass%, the balance being chemical components consisting of Al and unavoidable impurities;

its conductivity is 37.0-40.0% IACS;

σ_B(10)-σ_B(1)≥5MPa，σ_0.2(10)-σ_0.2(1)≥1MPa。

3. the production method according to claim 1, wherein the aluminum alloy sheet for can bodies has a yield strength of 300MPa or more in a rolling direction.

4. The production method according to claim 1, wherein the work hardening index of the aluminum alloy sheet for can bodies is 0.07 or more.

5. The production method according to claim 1, wherein the earing ratio R of the formed cup obtained by drawing under the conditions of a plate diameter of 55mm and a drawing ratio of 1.67 calculated by the following formula (1) is 4% or less,

R＝(M₄₅-V₄₅)/((M₄₅+V₄₅)/2)×100 (1)

in the formula (1), M₄₅Is a value calculated by the following formula (2), V₄₅Is a value calculated by the following formula (3),

M₄₅＝(A+B+C+D)/4 (2)

in the above formula (2), when the rolling direction is 0 °, a is a tab height of 45 °, B is a tab height of 135 °, C is a tab height of 225 °, D is a tab height of 315 °,

V₄₅＝(E+F+G+H)/4 (3)

in the formula (3), E is the lowest height of the valley bottom between the 45 ° direction and the 135 ° direction, F is the lowest height of the valley bottom between the 135 ° direction and the 225 ° direction, G is the lowest height of the valley bottom between the 225 ° direction and the 315 ° direction, and H is the lowest height of the valley bottom between the 315 ° direction and the 45 ° direction.