JPH11320034A - Method for predicting developing quantity of porosity in continuous casting of al-mg base alloy slab - Google Patents

Abstract

PROBLEM TO BE SOLVED: To easily estimate the developing quantity of porosity in the inner part of an Al-Mg base alloy slab and to surely cast the slab having a little porosity. SOLUTION: In a vertical continuous casting process of the Al-Mg base alloy slab, as a method for obtaining the preset target porosity value, with which the porosity value in the casting slab is beforehand calculated with the combination of each condition value by using an initial stage hydrogen concn., casting velosity, casting temp., molten metal surface height in a mold, cooling water quantity, etc., as parameters, and the optimum combination of the above condition value is set, the following equation is used to the calculation of curvature radius Rp (μm) of the porosity in the cast slab to predict the developing quantity of the porosity in the continuous casting of the Al-Mg base alloy slab. The equation, Rp =0.14×DAS-2, wherein, DAS is dendrite arm spacing.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for predicting the amount of porosity (vacancy), which is a casting defect, in vertical continuous casting of an Al-Mg based aluminum alloy slab.

[0002]

2. Description of the Related Art Al-Mg based alloys are widely used for vehicle body sheets, cans, and thick plates. The surface quality requirement level of such a product is such that the amount of porosity generated in the Al-Mg based alloy slab as the material is 0.3 vol% or less in area ratio. In addition, the magnetic disk (M
In some cases, the content of D) is required to be 0.2 vol% or less.
However, in the conventional vertical continuous casting method, the amount of porosity generated inside the slab may be 0.3% or more due to various restrictions on the parameters of the casting conditions such as the initial hydrogen concentration and the casting speed. There have been problems such as generation of swarf, surface defects of the slab due to the porosity, point defects and swelling at the time of cutting.

[0003]

In order to solve the above problems and reduce the porosity generation amount to, for example, 0.2 vol% or less, the parameters of the above-mentioned casting conditions are actually changed, and individual It is also possible to inductively derive it by casting. However, there is a problem that it is difficult to perform vertical continuous casting according to various casting conditions in advance for each slab quality because it requires cost and time. The present invention relates to Al-
It is an object of the present invention to provide a method for easily and reliably predicting the amount of porosity generated inside a slab without using an actual apparatus in a method of vertically continuous casting an Mg-based alloy.

[0004]

Means for Solving the Problems The present invention has been achieved by carrying out experimental and analytical studies on the above casting process from a fundamental aspect in order to solve the above problems. That is, in order to calculate the porosity generation amount in the Al-Mg alloy slab in advance, in the unsteady heat conduction analysis of the slab casting process, the surface tension of the molten metal using the solidification parameter obtained from the solidification analysis of the ingot. And the local equivalent pressure due to coagulation shrinkage were derived as a calculation formula. In the conventional calculation of the pressure due to the surface tension of a molten metal, the radius of curvature of porosity was generally assumed to be １ ／ of DAS (Dendrite Arm Spacing).

However, in the case of vertical continuous casting, the cooling rate and the temperature gradient are large and the solidification time is short as compared with sand casting or die casting in which the above assumption is valid. It is very small compared to die casting. Therefore, the radius of curvature of the porosity is D
Assuming AS / 2 is unrealistic. Therefore, as a result of various studies, the longest diameter and area of porosity from the slab surface to the center were measured using a porosity observation device such as an image processing device, and based on these, the correlation between the radius of curvature of each porosity and the measured DAS was determined. The relationship was determined by regression analysis. Using this relationship, the pressure due to the surface tension of the molten metal is calculated, and the amount of supersaturation due to discharge from the solid phase to the liquid phase during solidification of hydrogen in the slab can be calculated.

That is, the method of predicting the porosity generation amount in the continuous casting of an Al—Mg alloy slab of the present invention is described in US Pat.
-In the vertical continuous casting process of the Mg-based alloy slab, the amount of porosity generated in the casting slab by a combination of each condition value with parameters such as initial hydrogen concentration, casting speed, casting temperature, molten metal level in the mold, cooling water amount, etc. Is calculated in advance, and as a method of setting an optimal combination of the above condition values to achieve a predetermined target porosity value, the above formula (1) is used to calculate the curvature radius R _P (μm) of the porosity in the casting slab. (5) is used.

[0007]

## EQU5 ## R _P = 0.14 × DAS-2

In the above, DAS is a dendrite arm spacing, that is, a center-to-center distance between dendrites. According to this, by using a curvature radius R _P of the porosity in the slab in line with a vertical continuous casting process of Al-Mg-based alloy, the porosity generation amount approximated to porosity values the target be accurately predicted It becomes possible.

The above formula (1) or (5) is obtained by previously measuring the longest diameter and area of a plurality of porosity from the surface layer of the casting slab to the center by using a porosity observation device such as an image processing device, and obtaining the radius of curvature. Assuming that each area where R _P is measured is divided by half of the longest diameter, for example, an average value of a specific number of porosity in a range of 5 to 100 per 1 cm ² cross section is used, and these average values are used. Radius of curvature R _P from the surface layer to the center of the slab and D measured
A method for predicting the amount of porosity generated in continuous casting of an Al-Mg based alloy slab, which is obtained by regression analysis of a correlation of AS (dendritic arm spacing), is included. Thus, by using the curvature radius R _P of porosity in line with a vertical continuous casting process of the slab, it is possible to predict the porosity generation amount with high accuracy.

Further, based on the radius of curvature R _P , the surface tension Pσ of the molten metal received by the porosity surface in the casting slab is calculated by the following equation (6), which is the same as the equation (2). The method includes a method of predicting the amount of porosity in continuous casting of an Al-Mg based alloy slab for predicting the amount of formation. In the equation (6), σ indicates the surface tension of the molten metal.

[0011]

Equation 6: Pσ = 2σ / R _P

Further, a local equivalent pressure P * according to the following equation (7), which is the same as the above equation (3), in which the surface tension Pσ is added to the local pressure P ′ due to the solidification shrinkage of the molten Al-Mg alloy:
Is used to predict the porosity generation amount,
A method for predicting the amount of porosity generated in continuous casting of an Al-Mg alloy slab is also included.

[0013]

## EQU7 ## P * = P.sigma. + P '

Further, together with the local equivalent pressure P *, the supersaturation amount Φ of hydrogen in the casting slab separately calculated according to each condition value serving as the parameter is used, and the same equation (8) as the above equation (4) is used. Calculating the porosity generation amount V _P (%) in the casting slab, and predicting the porosity generation amount,
A method for predicting the amount of porosity generated in continuous casting of an Al-Mg based alloy slab is included.

[0015]

(Equation 8)

In the above, R is the gas constant (J / mol · k), T is the temperature (K) at the final solidification stage, M is the molar volume of hydrogen gas, and ρ is the density (kg / m ³ ) of the Al—Mg alloy. ). According to each of the above-described methods, it is possible to more accurately and easily predict the porosity generation amount approximated to the target porosity value of the Al-Mg based alloy slab by vertical continuous casting.
Therefore, it is possible to cast a slab of stable quality without excess and shortage, and it is also possible to improve the productivity in the vertical continuous casting process.

[0017]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, an analysis method used for carrying out the present invention will be described. Factors that have a significant effect on porosity generation and distribution are the local equivalent pressure and the amount of gas supersaturation in the alloy. The local equivalent pressure includes a negative pressure caused by an increase in viscous resistance in the molten metal replenishment flow due to solidification shrinkage, a pressure due to the surface tension of the molten metal, and an external atmospheric pressure and a head pressure. Of these, the external atmospheric pressure and the head pressure are considered to be substantially constant at a constant location along the casting direction from the molten metal surface. Therefore, at a constant level of local pressure, the change from the surface to the center of the slab is
Pressure due to solidification shrinkage and pressure due to surface tension.

First, a method of calculating the pressure due to coagulation shrinkage will be described. In the calculation of the pressure drop due to solidification shrinkage, in the case of dentite (primary dendritic crystal) solidification, the flow of the residual liquid phase between the dendrites follows the Dalsey theorem. Accordingly, the relationship between the flow velocity V and the pressure P of the liquid phase is expressed by Expression (9).

[0019]

(Equation 9)

In the above, V is the flow rate (m / s) of the liquid between the dendrites, μ
Is the viscosity coefficient of the liquid between the dendrites (Ns / m ² ), f _L is the liquid phase ratio at the final stage of solidification, ρ is the density of the Al-Mg alloy (kg / m ³ ),
P is pressure (N / m ² ), K is transmittance (m ² ), g is gravitational acceleration
(m / s ² ). Here, the following formula is used to calculate the transmittance K.
Use (10).

[0021]

K = 3.75 × 10 ⁻⁴ · f _L ² · d ₂ ²

In the above, d ₂ is a dendrite arm spacing (DAS). According to Fleming's theory, the relationship between dendrite arm spacing and local solidification time is calculated by equation (11).

[0023]

## EQU11 ## d ₂ = C · t _f ⁿ

In the above, C and n are constants of the Al—Mg alloy, and t _f is the local solidification time. It is assumed that the solidification direction in the steady part of vertical continuous casting changes along the normal direction of the sump (solidification interface). Therefore, the equation (9) is decomposed into the X direction and the Y direction, and the equations (12) and (1) are rearranged.
3) is obtained.

[0025]

(Equation 12)

[0026]

(Equation 13)

Actually, g _x does not exist in the X direction. Further, if the gravitational acceleration g _Y is converted to g in the Y direction, the relationship between the flow velocity V and the pressure P is expressed by Expressions (14) and (15).

[0028]

[Equation 14]

[0029]

(Equation 15)

The flow velocity V _x, V _Y of formula (14), (15), the product of the moving speed and the solidification shrinkage rate of solidification, i.e. replaced with -V _s · β. Further, since the local pressure drop is maximum near the final solidification portion in the solid-liquid coexistence region, that is, near the solidus, L is approximately the ratio of the solidification temperature range ΔT to the temperature gradient G, ie, ΔT / G is
Assume (T _L -T _S ) / G. Further, in the microscopic region in the final stage of solidification, ΔP / ΔX is dP / dX, and
P / ∂Y is approximately represented by dP / dY. Based on the above assumptions, the pressure decrease in the X direction and the Y direction can be expressed by the formula (1)
6) and (17).

[0031]

(Equation 16)

[0032]

[Equation 17]

In the above, α is the angle between the normal direction of the sump and the X axis at the point to be determined. Further, the pressure decrease ΔP due to coagulation contraction is obtained by Expression (18).

[0034]

(Equation 18)

On the other hand, the pressure difference ΔP in the vicinity of the solidus is expressed by the formula (1)
9).

[0036]

ΔP = P _o + ρgh−P ′

The above P _o is ρgh in the external atmospheric pressure is the head pressure. From this equation (19), the local pressure P ′ due to coagulation contraction is obtained by equation (20).

[0038]

P ′ = P _o + ρgh−ΔP

Next, a method of calculating the pressure based on the surface tension of the molten metal will be described. In general, the pressure Pσ due to the surface tension of the molten metal applied to the porosity surface is given by the above equation (2),
It is obtained by the same equation (21) as (6).

[0040]

[Equation 21] Pσ = 2σ / R _P

In the above, Pσ is the pressure (N /
m ² ) and σ are the surface tension (N / m) of the molten metal, and R _P is the porosity radius of curvature (μm). By the way, the surface tension σ of the Al—Mg-based alloy is expressed by an approximate formula of Jacques E et al.
(22).

[0042]

(Equation 22)

In the above, ω is the area occupied by one atom, and is calculated by equation (23).

[0044]

(Equation 23)

In the formulas (22) and (23), W _s is the molar volume when the alloy is molten (10.468 × 10 ⁻⁹ m ⁵ / kg ² ), and W is the molar volume (1.122
× 10 ⁻⁵ m ³ / mol), k is Boltzmann's constant (1.38066 × 10 ⁻²³⁾
J / K), E _s is purified energy Al-Mg alloy (2.8035 ×
10 ⁵ J / (m · mol)), R is gas constant (8.31451 J / (mol · K)),
N is Avogadro's constant (6.022137 × 10 ²³ mol ^-1 ), and f is a coefficient
(0.083).

In the casting industry, it is generally assumed that the radius of curvature R _P of porosity is one half of that of DAS (Dendrite Arm Spacing). However, in the vertical continuous casting which is the object of the present invention,
Since the cooling rate and the temperature gradient are large and the solidification time is short as compared with sand casting or die casting, the size of the porosity observed is very small as compared with the above-mentioned die casting. Therefore, the radius of curvature of the porosity is set to DAS / 2.
Is unrealistic. Therefore, as a result of various studies, the longest diameter and area of the porosity from the surface layer to the center of the slab were measured using a real-time image processing / analysis device (measuring, quantifying, and analyzing the input image).

Since the radius of curvature R _P of the porosity is proportional to DAS (Dendrite Arm Spacing), the measured area is set to half the value obtained by dividing the measured area by the longest diameter, and n = 40 measured at one location, for example, per 1 cm ² It was decided from the average value of porosity. That is, when n = 5, the reliability of the regression equation becomes 10% or less, which is not practical. On the other hand, when n = 100 or more, the fluctuation of the average value is 10%.
The following is true, and increasing the number n is not effective. Then, n
If about = 40, the reliability is about 95% or more. Using these, the correlation between the radius of curvature R _P (μm) of each porosity and the measured DAS was determined by a regression analysis method. Specifically, this relationship is expressed by the same equation (2) as the above equations (1) and (5).
According to 4), more preferably, it can be expressed by equation (25).

[0048]

## EQU24 ## R _P = 0.14 × DAS-2

[0049]

R _p = 0.1381 × DAS-2.1

The radius of curvature R of the porosity according to the reality
By using _P , it is possible to accurately calculate the porosity generation amount in the slab of the present invention described later. Further, by substituting equation (24) into equation (21), equation (2) is obtained.
6) is obtained.

[0051]

Rσ = 2σ / (0.14 × DAS-2)

By substituting equation (25) into equation (21), more desirable equation (27) is obtained.

Rσ = 2σ / (0.1381 × DAS-2.1)

Next, the calculation of the supersaturation amount of hydrogen gas in the Al-Mg alloy will be described. Generally, most of the gas in aluminum alloys is hydrogen, and the other gases are virtually negligible except for oxygen contained in the form of aluminum oxide. Moreover, approximately 95% or more of the total gas amount is hydrogen gas, and only hydrogen actually matters. Al-M
In the solidification process in the g-based alloy, the hydrogen gas released from the solid phase to the liquid phase as the solidification progresses enriches the hydrogen gas in the residual liquid phase in front of the solidification interface. When the equilibrium solubility is exceeded, the hydrogen gas becomes supersaturated. Therefore, assuming that the hydrogen gas is completely mixed in the liquid phase, the hydrogen gas concentration in the liquid phase and the solid phase before the porosity is formed is calculated by Fang and Granger formulas (28) and (29). Is required.

[0054]

[Equation 28]

[0055]

[Expression 29] H _s = k · H ₁

In the above, K is a hydrogen equilibrium distribution coefficient (0.052),
H ₁ is the hydrogen concentration in the liquid phase (cc / 100g), H _s is the hydrogen concentration (cc / 100 g) of in solid phase H _2, H ₀ is the initial concentration of hydrogen in the molten metal, fs
Is the solid fraction. As shown in the above equation (28), the hydrogen concentration H ₁ in the residual liquid phase is proportional to the initial hydrogen concentration H ₀ in the molten metal. In addition, the equilibrium solubility H _d of hydrogen in the liquid phase is Sieve
Equation (30) is established according to the law of rts.

[0057]

[Equation 30]

In the above, K _H is the equilibrium constant (0.06
cc / 100g · atm ^1/2 ). Therefore, assuming that the difference between the hydrogen concentration H ₁ in the residual liquid phase and the equilibrium solubility H _d is the hydrogen supersaturation amount Φ in the liquid phase, this can be obtained by Expression (31).

[0059]

Φ = H ₁ −H _d

[0060] As shown in equation (31), the hydrogen supersaturation amount Φ of the liquid phase, indicated by the difference between the H ₁ and H _d.

Here, the formation of porosity in the Al—Mg alloy will be described. As schematically shown in FIG. 1 (A), porosity nuclei 1 generally have dendrites 2, 2
Easy to generate on the route between. As the pressure between the dendrites 2 and 2 decreases and the hydrogen gas becomes supersaturated, the porosity core 1 grows and is finally classified into three types of porosity. still,
Dendrite arm spacing (DAS) in Fig. 1 (A)
Is shown. As shown in FIG. 1 (B), the porosity of the first kind is that the nucleus 1 of the porosity grows due to the decrease in the pressure between the dendrites 2 and 2 during the solidification process, but the dendrite 2 (dendrite arm) Since growth suppresses the growth of the nucleus 1, the porosity 4 eventually becomes considerably elongated.

The porosity of the second kind is dendrite 2,
As the pressure decrease between the two increases further, the porosity size between them increases, and rises from the route between the dendrites 2 and 2 under the influence of buoyancy and convection between the dendrites 2 and 2, as shown in FIG. As shown, the porosity 6 has a slightly larger diameter.
In addition, the third type of porosity, in the final stage of coagulation,
Since the pressure is significantly reduced and the solidification progress speed is increased, the dendrites 2 adjacent to each other start to collide with each other, as shown in FIG. As a result, it becomes difficult to supply the molten metal, and the typical shrinkage porosity 8 is obtained. The above three types of porosity 4, 6, and 8 are mixed in an actual slab.

Next, the porosity generation conditions and the calculation of the generation amount will be described. The generation of porosity is said to be determined by whether or not the difference between the gas pressure P _g in the nucleus of the porosity and the contraction negative pressure applied to the nucleus is greater than the surface tension of the bubble. That is, if the following formula (32) is satisfied, the porosity is formed stably. If the porosity is not satisfied, even if the porosity is formed, the porosity is crushed by the negative pressure and remains as a solid solution.

[0064]

P _g ≧ P ′ + Pσ ≒ P ^*

In the above, P _g is the gas pressure in the nucleus (N / m ² ), P ^*
Is the pressure P 'due to coagulation shrinkage (calculated by the formula (20))
And the local equivalent pressure which is the sum of the pressure Pσ due to the surface tension. The local equivalent pressure P ^* can also be expressed as in equation (33) by substituting equation (21).

[0066]

P ^* = P '+ Pσ = P' + 2σ / R _P

The generation of porosity is greatly affected by the hydrogen concentration in the residual liquid phase. So, Kao, Chan
According to g assumption, the amount of porosity V _P (%) is the equation (4) is calculated by (8) the same following equation (34).

[0068]

(Equation 34)

R is the gas constant, T is the temperature at the final stage of solidification, and M is the molar volume of hydrogen gas (m ³ / mol). Formula (3
As shown in 4), the amount V _P of porosity in the slab is proportional to gas supersaturated amount [Phi, is inversely proportional to the local equivalent pressure P ^*. As a specific analysis procedure, after performing the unsteady thermal coagulation analysis, the solidification parameters (temperature gradient, cooling rate, solidification progress rate, solidification time, dendrite arm spacing, cooling water amount, etc.) obtained in the solidification analysis Using the above formula
According to (20), the local pressure P ′ due to coagulation contraction is calculated by the equation (2)
The pressure Pσ due to the surface tension is calculated according to 1). When these are summed, the local equivalent pressure P ^* is calculated by Expression (33). Next, the supersaturation amount Φ of hydrogen is calculated by the equation (31).
Is calculated and this is substituted in equation (34) together with the above P ^* value, it can be calculated the amount V _P of porosity.

[0070]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Specific embodiments of the present invention will be described below. First, an Al-Mg based alloy of Al-4.4 wt% Mg was cast into a slab 406 mm wide according to a normal vertical continuous casting method. The casting condition in this case is the level of the molten metal in the mold.
(H): 62 mm, casting speed (V): 58 mm / min, casting temperature
(T) was 730 ° C., the amount of cooling water was 400 l / min, and the initial hydrogen concentration (H ₀ ) in the molten metal was 0.4 cc / 100 g. First,
For thermal analysis, 13 thermocouples were set on the cast slab at a position of about 1 meter in the vertical direction from the start of casting, and 13 places (5, 10, 15, 15) from the surface layer to the center (203 mm) 20,30,
40, 60, 80, 100, 125, 150, 175, 203 mm), the temperature history was measured every 0.5 seconds. In addition, in order to confirm the insertion position of each thermocouple, the slab was cut after casting, and the positions were identified by X-rays.

Next, in the micro observation of the slab, a sample from the surface layer to the center near the center of the long side of the slab was cut out at a position 1 meter from the casting, and the cross section of the slab in the sample was buffed. The mirror surface was observed. In addition, the observation of porosity
Without corroding each of the polished samples, using a real-time image processing analyzer (trade name: LUZEX),
The shape, size, and area ratio of each porosity having a circle equivalent diameter (diameter) of 6 μm or more observed in the microstructure from the surface layer to the center of the slab were measured. The final measured value of the area ratio was an average value of n = 10 values measured for one sample.

Further, in order to quantitatively evaluate the internal defects of the slab, the density from the surface layer to the center of the slab was measured.
The amount of each porosity generated was calculated by comparing with the density of the standard sample. The Archimedes method was used for measuring the density. The dendrite arm spacing (DAS) was measured from a photograph of the surface of each sample enlarged 100 times using the secondary branch method. and,
Gas content is measured from the surface on the long side of the slab
(203mm) 13 locations (5,10,15,20,25,30,35,40,60,8
(0,125,175,203 mm) by the Landsley method.

As a result, the porosity generation from the surface layer to the center of the slab was roughly as follows. In the vicinity of the surface layer (from the surface layer to 60 mm), the size of each porosity was very small, about several tens of μm, and almost existed within the interval between the secondary dendrite arms. That is, the growth was suppressed by the growth of the dendrite arm, resulting in elongated porosity. This is presumably because the porosity generated was small because the cooling rate and temperature gradient of the surface layer were large and the pressure loss between the branches was small. In the middle layer (8
(0 mm to 140 mm), the pressure drop between the branches increases,
The size of each porosity was larger than the above and the quantity was larger. Most of them were within the spacing of the secondary dendrite arms, and some were distributed along grain boundaries. Furthermore, in the central part (160 mm to 203 mm), the pressure drop between the branches is remarkable, and the size of each porosity is further increased, not only within the interval between the secondary dendrite arms but also within the interval between the primary dendrite arms. Large amounts were present. The shape of such porosity was irregular and typical shrinkage porosity.

Each graph in FIG. 2 shows the distribution of the number and area ratio of porosity having an equivalent circle diameter of 6 μm or more measured from the surface layer to the center of the slab using the image processing and analysis apparatus.
In the vicinity of the surface of the slab (up to 40 mm, illustrated in FIG. 2 (A)), most of the fine porosity with a circle equivalent diameter of 6 to 15 μm
The number of porosity and the area ratio correspond to each other, and the area where the number is large has a large area ratio. In the intermediate layer (60 mm to 120 mm, illustrated in FIG. 2B), the number of porosity was larger than that near the surface layer, and porosity of 15 μm or more began to be recognized. Quantitatively, fine porosity having an equivalent circle diameter of 6 to 15 μm occupied about 75% of the whole, but the area ratio of the whole was less than half. In addition, the center layer (140mm-20
In 3 mm, as shown in FIG. 2 (C)), the number of porosity sharply increased, and coarse porosity having a circle equivalent diameter of 40 μm or more was conspicuous.

The graph of FIG. 3 shows the distribution of the number of porosity having a circle equivalent diameter of 6 μm or more per unit area and the average area ratio based on the above data. According to this, it can be seen that the distribution of the number of generated porosity from the surface layer to the center of the slab corresponds to the distribution of the area ratio. That is, both showed a tendency to temporarily decrease from the surface layer to 20 mm, then increase to 180 mm, and then exceed this and decrease toward 203 mm (center). The area ratio was extremely small, about 0.1% or less, since most of the fine porosity was from the surface layer to 40 mm. The area ratio is a minimum of 0.038% at 20 mm from the surface layer. Between 60mm and 120mm (middle part)
Since the porosity having an equivalent circle diameter of 15 μm or more starts to appear, the area ratio gradually increases. 120mm-203m
Between m (center), the area ratio of porosity increased sharply, reaching a maximum of 1.0% at 180 mm. The average area ratio of the central portion was 0.35% of the average area ratio of the intermediate portion, and was 0.85% or more on average.

FIG. 4 is a graph showing a comparison between the DAS size distribution in the slab calculated by the transient thermal solidification analysis and the measured values. As shown in this graph, each calculated value and each measured value are in good agreement. Both are 20 mm from the surface of the slab
In the vicinity, the DAS size becomes minimum and increases toward the center (203 mm), and reaches a maximum at a calculated value of about 160 mm and a measured value of about 175 mm. After these, all of them decrease again. Next, the equations (33), (21), (2)
FIG. 5 shows distributions of the local equivalent pressure (P ^* ), the pressure due to surface tension (Pσ), and the pressure (P ′) due to solidification shrinkage from the surface layer to the center of the slab calculated based on (0). As a result, the pressure due to coagulation shrinkage (P ') becomes the pressure due to surface tension (P').
σ), the influence on the local equivalent pressure (P ^* ) can be neglected except for the central part. Therefore, it is considered that the pressure (Pσ) due to the surface tension has a great influence. The local equivalent pressure (P ^* ) is near the surface
(5mm), then decrease, then increase to 30mm, where it reaches its maximum. After this, the pressure (P ^* ) gradually decreases, reaches a minimum at 180 mm, and then increases again toward the center.

FIG. 6 is a graph showing the relationship between the DAS size affecting the pressure (Pσ) due to the surface tension and the local equivalent pressure (P ^* ). According to this, the pressure (P ^* ) decreases as the DAS size increases. This is the formula
As shown in (24), proportional to the DAS size porosity radius of curvature (R _P), since the DAS size increases porosity radius of curvature (R _P) also increases, the pressure due to the surface tension (Pshiguma) is This is because the pressure decreases and the local equivalent pressure (P ^* ) also decreases. Further, as shown in the figure, there is a tendency that the gradient of the pressure decrease decreases as the DAS size increases. FIG. 7 is a graph showing the distribution of hydrogen supersaturation (Φ) in the residual liquid phase in the slab during the solidification process of the slab. As shown in the equation (31), the amount of supersaturation (Φ) is inversely proportional to the equilibrium solubility (H _d ) in the liquid phase. However, the equilibrium solubility (H _d ) in the alloy is proportional to the pressure, and the solubility (H _d ) decreases in a place where the pressure is low, so that the supersaturation amount (Φ) increases on the contrary. Therefore, as shown in this graph, it can be seen that the distribution of the hydrogen supersaturation amount (Φ) is inversely proportional to the local equivalent pressure (P ^* ) and corresponds to the DAS size distribution.

FIG. 8 is a graph showing a comparison between the calculated value of the porosity generation amount (V _P ) from the surface layer of the slab to the center and the measured value. Near the surface of the slab as shown
Except for (~ 20 mm), each calculated value and each measured value agree very well. Porosity generation amount toward the center from the surface layer of Both slabs (V _P) is gradually increased, in measurement 170
The maximum value was 0.4 mm between mm and 180 mm, and the maximum value was calculated at approximately 180 mm (0.37%). This is because the local equivalent pressure (P ^* ) decreases after 30 mm as shown in the graph of FIG. 5, and the hydrogen supersaturation amount (Φ) in the residual liquid phase decreases as shown in the graph of FIG. This is to increase. Beyond 180mm from the surface of the slab, by a decrease in growth and hydrogen supersaturation amount of local corresponding pressure (P ^*) (Φ), porosity generation amount (V _P) decreases. By the graph of FIG. 8, the prediction method of the porosity generation amount according to the present invention (V _P) that is backed valid.

Therefore, the solidification parameters set as targets (temperature gradient, cooling rate, solidification progress rate, solidification time, DAS
, Etc.), the local pressure due to coagulation shrinkage in equation (20).
The (P '), also respectively calculate the pressure (Pshiguma) caused by the surface tension of curvature radius R _P of the porosity calculated above in Equation (24) is substituted into equation (21), the sums of these values The local equivalent pressure (P ^* ) is calculated by Expression (33). next,
The supersaturation amount (Φ) of hydrogen is calculated by the above equation (31), and this is substituted into the above equation (34) together with the above (P ^* ) value,
The amount of porosity in each distance from the slab surface layer (V _P)
The by calculating, accurately predict in advance the amount of porosity to (V _P) before performing the continuous casting. That is, by selecting the coagulation parameters, such as closer to the target value appropriately, Al having based on optimum value, the amount of porosity which approximates the porosity values that target (V _P) in the interior
-The Mg-based alloy slab can be continuously cast accurately.

The formulas (9) to (34) and their calculation order are stored in advance in a ROM of a computer, and the respective casting condition values recorded in the RAM of the computer are appropriately selected and input. The porosity generation amount can be automatically calculated.

[0081]

According to the present invention, it is possible to easily predict a desired porosity value by combining an Al-Mg-based aluminum alloy slab with an optimum casting condition value in advance and to obtain a target porosity value. Slabs of stable quality can be accurately and continuously cast. In addition, it is possible to efficiently and reliably provide a cast product using the slab.

[Brief description of the drawings]

FIGS. 1A to 1D are schematic views schematically showing a general form of porosity.

FIGS. 2A to 2C are graphs each showing the distribution of the number of porosity and the area ratio in the slab of the embodiment.

FIG. 3 is a graph showing the distribution of the number of porosity and the average area ratio in a slab of an example.

FIG. 4 is a graph showing the distribution of measured and calculated DAS sizes in a slab of an example.

FIG. 5 is a graph in which the local equivalent pressure, the pressure due to surface tension, and the pressure due to solidification shrinkage calculated according to the present invention are distributed from the surface layer of the slab toward the center.

FIG. 6 is a graph showing a relationship between a measured DAS size and a calculated local equivalent pressure.

FIG. 7 is a graph showing the distribution of the amount of hydrogen supersaturation in the residual liquid phase in the slab.

FIG. 8 is a graph showing a distribution of measured and calculated porosity generation amounts in a slab.

[Explanation of symbols]

 4,6,8… porosity DAS …… Dendrite arm spacing

 ────────────────────────────────────────────────── ─── Continued from the front page (72) Inventor Watasugi Hagisawa 1-34-1 Kambara, Kambara-cho, Anbara-gun, Shizuoka Prefecture Nippon Light Metal Corporation Group Technology Center

Claims (5)

[Claims] In the vertical continuous casting process of an Al-Mg based alloy slab, casting is performed by a combination of respective condition values using parameters such as an initial hydrogen concentration, a casting speed, a casting temperature, a level of a molten metal in a mold, and a cooling water amount as parameters. As a method of calculating the porosity generation amount in the slab in advance and setting the optimal combination of the above condition values to achieve a predetermined target porosity value in the continuous casting slab, a curvature radius R _P of porosity in the slab ( μm) is calculated using the following equation (1): A method for predicting the amount of porosity generated in continuous casting of an Al—Mg alloy slab. ## EQU1 ## R _P = 0.14 × DAS-2 DAS is the dendrite arm spacing. 2. The equation (1) is obtained by previously measuring the longest diameter and area of a plurality of porosity from the surface layer to the center of the casting slab, and dividing each area where the radius of curvature R _P is measured by each longest diameter. As a half of the value, the average value of the porosity of a specific number within a range of 5 to 100 is determined, and the correlation between the radius of curvature R _P from the surface layer to the center of the slab and the measured DAS using these average values. The method according to claim 1, wherein the relationship is obtained by a regression analysis method. 3. A molten metal surface tension Pσ received by a porosity surface in the casting slab based on the radius of curvature R _P is represented by the following equation:
The calculation according to (2), and the porosity generation amount is predicted based on the calculation result.
A method for predicting the amount of porosity generated in continuous casting of an l-Mg alloy slab. [Number 2] Pσ = 2σ / R _P above σ is the surface tension of the molten metal 4. The following equation, which is obtained by adding the surface tension Pσ and a local pressure P ′ due to solidification shrinkage of a molten Al-Mg alloy.
2. The porosity generation amount is predicted by using a local equivalent pressure P * according to (3).
4. A method for predicting a porosity generation amount in continuous casting of an Al-Mg based alloy slab according to any one of claims 3 to 3. ## EQU3 ## P * = P.sigma. + P ' 5. A method for generating porosity in a casting slab according to the following equation (4), using not only the local equivalent pressure P * but also the supersaturation amount Φ of hydrogen in the casting slab separately calculated according to each of the parameter values. claim calculates the amount V _P (%), to predict the porosity generation amount, and wherein the 1
A method for predicting the amount of porosity generated in continuous casting of an Al-Mg alloy slab according to any one of claims 1 to 4. (Equation 4) In the above, R is a gas constant, T is the temperature of the final solidification stage, M is the molar volume of hydrogen gas, and ρ is the density of the Al—Mg alloy.