METHOD FOR DETERMINING QUALITY AND DESTINATION OF CONTINUOUSLY CAST BLADES, METHOD FOR DETERMINING CONTINUOUS CASTING CONDITIONS, AND METHOD FOR CONTINUOUSLY CASTING STEEL

Abstract

Provided is a technique capable of determining the quality of a slab cast by continuous casting during casting or after casting. The present invention is a method for determining the quality of a product in which, when the quality of a product formed by rolling a slab cast by using a continuous casting machine is to be determined, a prediction model for hydrogen-induced cracking of a product surface layer section is used, and hydrogen-induced cracking of the product surface layer section is predicted using as an input variable at least one value chosen from among actual measurement values in casting performance data obtained by measurement during casting. The present invention is also a method in which, when the quality of a slab cast by using the continuous casting machine is to be determined using the abovementioned method, the prediction model associates the casting performance data and an area ratio of occurrence of hydrogen-induced cracking in the product surface layer section, at least one value chosen from among actual measurement values in the casting performance data obtained by measurement during casting is input to the prediction model, and the area ratio of occurrence of hydrogen-induced cracking in the surface layer section of the product obtained from the slab during casting or after casting is predicted. The present invention is also a method for determining a destination of the slab on the basis of the obtained predicted value.

Description

[Technical Field]

[0001] The present invention relates to a method for determining the quality of a product or a continuously cast slab from the casting conditions and actual values ​​measured during the continuous casting of steel, a method for determining the destination of the continuously cast slab, and a method for determining the continuous casting conditions. 3 kg, and the volume unit "L" is 10 -3 m 3 The "N" attached to the unit of gas volume represents the volume of the gas under standard conditions, which are 0°C and 101325 Pa. [Background technology]

[0002] During continuous casting of steel, gas bubbles injected into the nozzle and nonmetallic inclusions such as deoxidation products and sulfides can become trapped in the solidified shell and remain on the surface of the product. These bubbles and nonmetallic inclusions can degrade the quality of steel products, especially thick steel plates. For example, in line pipes used for transporting oil and natural gas, hydrogen-induced cracking can occur due to the action of sour gas, originating from bubbles and nonmetallic inclusions. Similar problems also occur in offshore structures, storage tanks, and oil tanks. Furthermore, in recent years, steel products are often required to be used in harsh environments, such as at lower temperatures or in more corrosive environments, making it increasingly important to reduce bubbles and nonmetallic inclusions in cast slabs.

[0003] For this reason, sour-resistant linepipe steel undergoes HIC (Hydrogen Induced Cracking) testing before shipping, and only products that do not experience HIC are shipped as sour-resistant. However, it takes several weeks for the results of the HIC test to become known, and if HIC occurs, the product cannot be shipped as sour-resistant, resulting in a significant decrease in yield. Therefore, if HIC performance could be evaluated at the slab stage before plate rolling without conducting HIC testing, it would be possible to shorten manufacturing time and significantly improve yield.

[0004] Patent Document 1 discloses a method for measuring the opening thickness of horizontal cracks and the maximum segregation grain size on the cut surface of a slab, determining a threshold value from the measurement results and the results of an HIC measurement test, and changing the casting destination. Patent Documents 2 and 3 disclose continuous casting methods for steel that satisfy the Ca / S ratio and the relationship between Ca, S, and O, and further compensate for HIC by keeping the Ca decrease below a threshold. Furthermore, Patent Document 4 discloses an evaluation method that can detect center segregation with high accuracy by binarizing an etched print image of the cross section of steel material. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Laid-Open No. 2015-58473 [Patent Document 2] Japanese Patent Application Laid-Open No. 2016-125137 [Patent Document 3] Japanese Patent Application Laid-Open No. 2016-125140 [Patent Document 4] Japanese Patent Application Publication No. 2017-181030 Summary of the Invention [Problem to be solved by the invention]

[0006] However, the above-mentioned conventional techniques have the following problems. The technology disclosed in Patent Document 1 requires measuring segregated grains on the cut surface of the slab, which poses a problem in terms of shortening the manufacturing period. The technologies disclosed in Patent Documents 2 and 3 can handle HIC cracking originating from Ca-based inclusions, but cannot handle other non-metallic inclusions. Furthermore, the technology disclosed in Patent Document 4 simply evaluates center segregation and does not clarify the correlation between bubbles and non-metallic inclusions and HIC cracking.

[0007] For HIC cracking caused by non-metallic inclusions, seven days of testing is required even after steel plate production. By the time a quality defect is discovered, a large number of products have already been manufactured, which can result in a large number of defective products being produced. Also, if defects are predicted after casting, it is possible to avoid further processing and simply remelt the product, but since it is not possible to determine whether there are defects at the casting stage, it is necessary to continue manufacturing the product all the way to the final product. Since evaluation is required after production of the final product, and if there are defects, they cannot be converted into good products, this causes increased costs.

[0008] The present invention has been made in consideration of the above circumstances, and its first object is to propose a product quality assessment method that predicts the quality of a product obtained by rolling a slab at the slab stage. Another object is to propose a method that can assess the quality of a slab cast by a continuous casting machine, particularly the HIC characteristics caused by bubbles and non-metallic inclusions, during or after casting. Additionally, the present invention proposes a method for determining the destination of a continuously cast slab, a method for determining continuous casting conditions, and a method for continuously casting steel. [Means for solving the problem]

[0009] The inventors discovered that the area ratio of hydrogen-induced cracks (HICs) caused by bubbles and non-metallic inclusions can be predicted from actual casting data during casting, i.e., parameters such as the cross-sectional size of the slab, its composition, casting speed, electromagnetic stirring conditions, the lead time from secondary refining to the start of casting, the amount of auxiliary raw materials added, the flow rate of the inert gas blown into the nozzle, and the immersion depth of the submerged entry nozzle, and thus completed the present invention.

[0010] That is, it has been found that the above problems can be advantageously solved by the following invention. [1] A method for assessing the quality of a product rolled from a slab cast in a continuous casting machine, using a prediction model for hydrogen-induced cracking in the product surface layer and using one or more input variables selected from the actual values ​​of the casting performance data measured during casting to predict hydrogen-induced cracking in the product surface layer. [2] A method for determining the quality of a slab cast by a continuous casting machine using the product quality determination method described in [1], wherein the prediction model links actual casting performance data with the area ratio of hydrogen-induced cracking in the surface layer of the product, and one or more values ​​selected from the actual casting performance data measured during casting are input into the prediction model to predict the area ratio of hydrogen-induced cracking in the surface layer of a product obtained from the slab during or after casting. [3] In [2], the casting performance data is some or all of the following: cross-sectional size of the slab, component composition, casting speed, electromagnetic stirring conditions, lead time from secondary refining to the start of casting, amount of auxiliary raw materials added, flow rate of inert gas blown into the nozzle, and immersion depth of the submerged entry nozzle. [4] The method for evaluating the quality of a continuously cast slab according to [3], wherein the component composition is at least one selected from the group consisting of C concentration, Mn concentration, S concentration, and C equivalent calculated by the following formula in terms of Ceq (mass%): Ceq=[C]-0.0616[Al]+2.5275[S]-0.2652[P]+0.0023[Si]+0.0344[Mn]-1.525[S][ Mn]+0.021[Si][Mn]+0.02[Cu]-0.02[Mo]+0.06[Ni]+0.02[Cr]-0.04[V]-0.04[Nb] Here, [M] in the formula is the content of element M expressed as mass percentage. [5] A method for assessing the quality of a continuously cast slab in any one of [2] to [4], wherein the predictive model uses principal component analysis and regression using the Random Forest method, and optionally machine-learns the predictive model using actual measurements of the area ratio of hydrogen-induced cracking in the product surface layer. [6] A method for determining a destination of a continuously cast slab, which determines whether the slab can be used as a sour-resistant line pipe steel based on a quality prediction of the slab determined using the method for determining the quality of the continuously cast slab described in any one of [2] to [5]. [7] A method for determining continuous casting conditions, which determines casting conditions by reverse analysis based on the casting performance data and the prediction model, so that the predicted value of the area ratio of hydrogen-induced cracking in the product surface layer asymptotically approaches a predetermined value based on the quality prediction of the slab determined using the method for determining the quality of the continuous cast slab described in any one of [2] to [5]. [8] The method for determining continuous casting conditions according to [7], wherein the predetermined value is 2% or less. [9] A method for continuous casting of steel, which produces cast pieces according to the casting conditions determined by the method described in [7] or [8]. [Effects of the Invention]

[0011] According to the present invention, the quality of a product or slab, particularly the hydrogen-induced cracking area ratio in the product surface layer, is predicted during or after casting by inputting actual values ​​of measured casting performance data into a pre-prepared prediction model. Therefore, it is possible to accurately predict whether a slab is suitable for a specific product, thereby enabling the production of products with a high yield. Furthermore, by determining casting conditions so that the obtained predicted value asymptotically approaches a predetermined value and producing a slab under the determined casting conditions, products can be produced with a high yield, improving productivity and providing industrial utility. For example, the suitability of a product for sour-resistant linepipe steel can be determined from the predicted HIC value without performing time-consuming HIC testing, making it possible to quickly respond to demands for the production of steel products with diverse specifications, providing industrial utility. [Brief explanation of the drawings]

[0012] [Figure 1] 1 is a schematic side view showing a slab continuous casting machine suitable for carrying out the present invention. [Figure 2] 1 is a graph showing the relationship between the measured value and the predicted value of the HIC crack area ratio (CAR) of the surface layer. [Figure 3] FIG. 1 is a flow chart showing an example of a method for predicting the quality of a continuously cast slab. [Figure 4] This is a schematic flow diagram from continuous casting to shipping. [Figure 5]1 is a graph showing the degree of influence of each variable on principal component 1 and principal component 2 in an example. DETAILED DESCRIPTION OF THE INVENTION

[0013] The following is a detailed description of embodiments of the present invention. The following embodiments are intended to exemplify equipment and methods for embodying the technical concept of the present invention, and are not intended to limit the configuration to those described below. In other words, the technical concept of the present invention can be modified in various ways within the technical scope defined in the claims.

[0014] FIG. 1 is a schematic side view showing a continuous slab caster suitable for use in a continuous steel casting method according to one embodiment of the present invention. As shown in FIG. 1, the continuous slab caster 1 is equipped with a mold 5 into which molten steel 9 is poured and solidified to form the outer shell shape of a slab 10. A tundish 2 is installed at a predetermined position above the mold 5 to relay molten steel 9 supplied from a ladle (not shown) to the mold 5. A sliding nozzle 3 is installed at the bottom of the tundish 2 to adjust the flow rate of the molten steel 9, and an immersion nozzle 4 is installed below the sliding nozzle 3. Meanwhile, below the mold 5, multiple pairs of slab support rolls 6, each consisting of a support roll, a guide roll, and a pinch roll, are arranged. A secondary cooling zone, in which spray nozzles (not shown), such as water spray nozzles or air mist spray nozzles, are installed, is formed in the gap between adjacent slab support rolls 6 in the casting direction (FD). In the secondary cooling zone, the slab 10 is cooled as it is drawn out by cooling water (also referred to as "secondary cooling water") sprayed from spray nozzles. Downstream of the final slab support roll 6 in the casting direction, a plurality of transport rolls 7 for transporting the cast slab 10 are installed, and above these transport rolls 7, a slab cutter 8 is located for cutting a slab 10a of a predetermined length from the cast slab 10. The cross-sectional size of the slab is expressed by the slab width Lw (mm) and the slab thickness Lt (mm).

[0015] As shown in FIG. 1, a soft reduction zone 14 consisting of multiple pairs of slab support rolls is installed on both the upstream and downstream sides of the final solidification position (crater end: CE) 13 of the slab 10 in the casting direction. In the soft reduction zone 14, the distance between the opposing slab support rolls sandwiching the slab 10 (this distance is called the "roll gap") is set to gradually narrower toward the downstream side in the casting direction. In other words, a reduction gradient (a roll gap that is set to gradually narrow toward the downstream side in the casting direction) is set. In the soft reduction zone 14, the slab 10 can be soft reduced in its entirety or in selected areas. Spray nozzles for cooling the slab 10 are also arranged between each slab support roll in the soft reduction zone 14. The slab support rolls 6 arranged in the soft reduction zone 14 are also called reduction rolls.

[0016] An electromagnetic stirrer (not shown) is installed between the mold 5 and the slab support rolls 6 to cause the unsolidified molten steel 12 to flow and wash the inner surface of the solidified shell 11. In addition, an inert gas is blown into the molten steel 9 from an upper nozzle (not shown) and a sliding nozzle 3 installed in the tundish 2 to prevent nozzle clogging.

[0017] The chemical composition of a slab can be determined using analytical values ​​from samples taken from the molten steel in the ladle or tundish. For example, C and Mn are known to be components that affect the toughness of the product. It is also known that the greater the C equivalent Ceq (mass%), expressed by the formula below, the greater the degree of decline in toughness. Steel toughness affects HIC properties. Furthermore, Mn and S form MnS-based non-metallic inclusions, which affect the HIC properties of the surface layer. Ceq=[C]-0.0616[Al]+2.5275[S]-0.2652[P]+0.0023[Si]+0.0344[Mn]-1.525[S][ Mn]+0.021[Si][Mn]+0.02[Cu]-0.02[Mo]+0.06[Ni]+0.02[Cr]-0.04[V]-0.04[Nb] Here, [M] in the formula is the content of element M expressed in mass %.

[0018] The casting speed Vc (m / min) affects the flow rate of molten steel from the SEN 4 and is an indicator of the penetration depth of bubbles and non-metallic inclusions into the solidification pool. The applied current I (A) of the electromagnetic stirring system influences the cleaning power of the inner surface of the solidified shell 11, thereby affecting the capture of bubbles and non-metallic inclusions. The lead time (time) from secondary refining to the start of casting affects the flotation and separation of deoxidized inclusions. The amount of auxiliary materials added, such as the CaSi consumption rate (kg / t-molten steel) and the FeSi consumption rate (kg / t-molten steel), affects the morphology of sulfur-based non-metallic inclusions and their flotation and separation. The inert gas flow rate QAr (NL / min) injected into the upper nozzle or sliding nozzle is an indicator of the bubbles trapped in the slab. The immersion depth Ld (mm) of the SEN 4, in relation to the direction of the molten steel discharge flow, affects the flotation and separation of bubbles and non-metallic inclusions and their penetration depth into the solidification pool.

[0019] The above-mentioned casting performance data, which affect the amount of bubbles and non-metallic inclusions trapped in the solidified shell, are used as variables to input into a prediction model for the hydrogen-induced crack area ratio (CAR) of the product surface layer. Here, the product surface layer refers to the area from the surface to 0.2 times the plate thickness in the plate thickness direction. For example, the prediction model can accurately predict the HIC crack area ratio (CAR) of the surface layer by reducing the number of variables using principal component analysis and then performing regression using the Random Forest method.

[0020] Principal component analysis (PCA) is a method for compressing data with correlations between variables without reducing the information, thereby simplifying analysis by reducing the number of variables in complex data. In this embodiment, variables such as "slab width (Lw) at casting, slab thickness (Lt), carbon concentration (C), manganese concentration (Mn), sulfur concentration (S), carbon equivalent (Ceq), casting speed (Vc)," applied current (I) for electromagnetic stirring, lead time (time) from secondary refining to the start of casting, amounts of auxiliary materials added (FeSi and CaSi), Ar gas flow rate (QAr) injected into the nozzle, and submerged entry nozzle (SEN) immersion depth (Ld)" are compressed to, for example, five variables. When compressed to five variables, the compressed variables can be expressed using variables such as principal component 1 through principal component 5, allowing data expressed with many variables to be represented with fewer variables without reducing the amount of information. Narrowing down the data variables without using PCA requires discarding some variables. This can sometimes require discarding important variables. Principal component analysis generates principal components in order from the first principal component so as to include as much information as possible about each variable, making it possible to reduce the number of variables more efficiently than usual.

[0021] The Random Forest method is a machine learning algorithm. It is an ensemble learning algorithm that integrates multiple weak learners using decision trees and performs cross-validation and cross-validation to improve generalization ability. In the regression of this embodiment, approximately several hundred decision trees were calculated and integrated using the average value. In other words, by compressing the many explanatory variables to about five using principal component analysis and then performing regression using the Random Forest method, highly accurate regression is possible even with a small amount of data.

[0022] In this embodiment, an example has been shown in which the hydrogen-induced crack area ratio CAR of the product surface layer portion is predicted using all of the above-mentioned casting performance data. However, even when only a portion of the casting performance data is used, it is possible to improve the accuracy of the regression by compressing variables using principal component analysis.

[0023] Figure 3 shows a flow chart illustrating an example of a method for predicting the HIC crack area ratio (CAR) of a product surface. Casting conditions and online measurements are input into a prediction model (S1), and variables are reduced using principal component analysis (S2). Regression is performed using the reduced variables using the random forest method (S3), and the HIC crack area ratio (CAR) of the product surface due to bubbles and nonmetallic inclusions is predicted (S4). Furthermore, by using the measured values ​​of the HIC crack area ratio (CAR) of the product surface as training data for principal component analysis (S5), it is possible to predict the HIC crack area ratio (CAR) with even greater accuracy. The predicted CAR value can be used to determine whether or not to send the product to the next rolling process. Furthermore, the predicted CAR value can be used to improve the quality of the slab by adjusting the immersion depth (Ld) of the submerged entry nozzle (SEN) or the applied current (I) of the electromagnetic stirring system so that the CAR approaches a predetermined value during casting (S6).

[0024] FIG. 4 is a flow diagram showing the process from continuous casting (S11) to rolling (S12) to shipping (S13). Typically, to determine the quality of a slab cast by a continuous caster, an EPMA is used to analyze the distribution of bubbles and nonmetallic inclusions (S14). This analysis takes one to two weeks. Furthermore, an HIC test is performed to determine whether the product should be shipped after rolling (S15). The HIC test involves immersing a test specimen in hydrogen sulfide and evaluating the crack area ratio (CAR) when hydrogen-induced cracks occur in the center of the thickness or on the surface of the plate (product). This test requires at least one week. The CAR must be below a threshold value to determine whether the product should be shipped. Conventionally, by the time this test revealed a quality defect, a large number of products had already been manufactured, resulting in the production of a large number of defective products. In this embodiment, quality can be predicted during or immediately after casting without performing an HIC test, significantly shortening the lead time and preventing mass nonconformity during this period. [Example]

[0025] Example 1 The present invention will be described in more detail below with reference to examples. The continuous casting machine used in the test was the same as continuous casting machine 1 shown in Figure 1. Low-carbon aluminum-killed steel was cast using this continuous casting machine. Tables 1 to 3 show actual casting data, such as casting conditions, and the measured and predicted values ​​of the HIC crack area ratio (CAR) in the product surface layer using the continuous casting method according to the above embodiment. Here, the product surface layer refers to the area from the surface to 0.2 times the plate thickness in the plate thickness direction. Using the actual casting data shown in Tables 1 and 2 as input, a prediction model for the HIC crack area ratio (CAR) in the product surface layer was used to perform regression using principal component analysis and the Random Forest method. Figure 2 shows a graph of the relationship between the measured and predicted values ​​of the HIC crack area ratio (CAR) in the product surface layer. In this prediction model, the explanatory variables were reduced to five variables using principal component analysis, and regression was performed using the Random Forest method. Figure 5 shows the relationship between principal component 1 and principal component 2 of the principal component analysis and the correlation coefficients of various operating conditions. The operating conditions with the largest sum of the correlation coefficients between principal components 1 and 2 were then determined to be the variables with the greatest influence on the HIC crack area ratio (CAR) in the product surface layer. For example, from Figure 5, the following variables (operational conditions) were extracted as having the greatest influence: "lead time" (the lead time from secondary refining to the start of casting), "amount of auxiliary materials added" (amount of FeSi added, amount of CaSi added), "immersion depth (Ld) of the submerged entry nozzle," "casting speed (Vc)," and "applied current (I) for electromagnetic stirring." Using this method, the measured and predicted values ​​of the HIC crack area ratio (CAR) in the product surface layer showed good agreement, making it possible to predict HIC cracks in the product surface layer during or immediately after casting. Table 3 shows an example of controlling the immersion depth Ld of the submerged entry nozzle and the applied current I of the electromagnetic stirring during casting so that the predicted CAR value approaches 0.00%. This control significantly reduced the area ratio of HIC cracks in the product surface layer. The threshold for the HIC crack area rate CAR of the product surface layer varies depending on the required quality. For example, for a steel product with a target HIC crack area rate CAR of 2% or less, the prediction model for the HIC crack area rate CAR of the product surface layer according to the above embodiment was used to redirect slabs with a predicted CAR value greater than 2%, resulting in a 7% improvement in yield.

[0026] [Table 1]

[0027] [Table 2]

[0028] [Table 3]

[0029] <Example 2> An example of back-analysis of operating conditions will be described using Test No. 21 in Table 2. Under the initial operating conditions for Test No. 21, the predicted value for the HIC crack occurrence area ratio (CAR) of the product surface layer was 5.46%, while the actual value was 4.60%. As a result of the principal component analysis of Example 1, the variables that significantly influence CAR and that can be changed during operation were identified as variables for changing the immersion depth Ld of the submerged entry nozzle and the applied current I of the electromagnetic stirring. By changing these variables and using a prediction model, back-analysis was performed to search for operating conditions that would result in a predicted CAR value of 0.2%. The obtained conditions were then changed: the immersion depth Ld of the submerged entry nozzle from 186 mm to 210 mm, and the applied current I of the electromagnetic stirring from 400 A to 700 A. As a result, the measured value for the HIC crack occurrence area ratio (CAR) of the product surface layer was able to achieve the target of 2% or less. [Explanation of symbols]

[0030] 1. Continuous casting machine 2 tundishes 3 Sliding Nozzle 4 Submerged Entry Nozzle 5. Mold 6. Casting support roll 7 Transport roll 8 Slab cutting machine 9 Molten Steel 10 Castings 10a (Cut) billet 11 Solidified shell 12 Molten steel in the unsolidified phase 13 Coagulation completion position (crater end) 14 Lightly Pressed Zone FD Casting direction

Claims

1. In determining the quality of a slab cast by a continuous casting machine, a method for determining product quality is used in which a prediction model for hydrogen-induced cracking in the surface layer of a product obtained by rolling a slab cast by a continuous casting machine is used, and one or more input variables are selected from the actual values ​​of casting performance data measured during casting to predict hydrogen-induced cracking in the surface layer of the product. The prediction model links actual casting data with the area rate of hydrogen-induced cracking in the surface layer of the product, A method for assessing the quality of a continuously cast slab, comprising inputting into the prediction model one or more values ​​selected from the actual values ​​of the casting performance data measured during casting, and predicting the area ratio of hydrogen-induced cracking in the surface layer of a product obtained from the slab during or after casting.

2. 2. The method for determining the quality of a continuously cast slab according to claim 1, wherein the casting performance data is some or all of the following: cross-sectional size of the slab, component composition, casting speed, electromagnetic stirring conditions, lead time from secondary refining to the start of casting, amount of auxiliary raw materials added, flow rate of inert gas blown into the nozzle, and immersion depth of the submerged entry nozzle.

3. 3. The method for evaluating the quality of a continuously cast slab according to claim 2, wherein the component composition is at least one selected from a C concentration, a Mn concentration, a S concentration, and a C equivalent calculated in terms of Ceq (mass%) by the following formula: Ceq=[C]-0.0616[Al]+2.5275[S]-0.2652[P]+0.0023[Si]+0.0344[Mn]-1.525[S][ Mn]+0.021[Si][Mn]+0.02[Cu]-0.02[Mo]+0.06[Ni]+0.02[Cr]-0.04[V]-0.04[Nb] Here, [M] in the formula is the content of element M expressed in mass percentage.

4. The prediction model uses principal component analysis and Random Forest regression, The method for determining the quality of a continuously cast slab according to any one of claims 1 to 3, wherein the prediction model is machine-learned using an actual measurement value of an area ratio of hydrogen-induced cracking in a surface layer portion of the product.

5. A method for determining a destination of a continuously cast slab, which determines whether the slab can be used as a sour-resistant line pipe steel based on a quality prediction of the slab determined using the method for determining the quality of the continuously cast slab according to any one of claims 1 to 3.

6. A method for determining continuous casting conditions, comprising: determining casting conditions by reverse analysis based on the casting performance data and the prediction model, such that a predicted value of an area ratio of hydrogen-induced cracking in a surface layer portion of a product asymptotically approaches a predetermined value based on a quality prediction of a slab determined using the method for determining the quality of a continuously cast slab according to any one of claims 1 to 3.

7. The method for determining continuous casting conditions according to claim 6, wherein the predetermined value is set to 2% or less.

8. A method for continuous casting of steel, comprising producing a cast piece in accordance with the casting conditions determined by the method according to claim 6.

Images