In the tube drawing process, different types of plugs are used to adjust the inner diameter, outer diameter, and thickness of the pipe; Figure 1 (a) shows drawing by means of sinking without a plug, Figure 1 (b, c) shows drawing with a fixed plug or floating plug, and Figure 1 (d) shows a drawing with a long plug [7].

Figure 1: 
Types of tube drawing processes

A bilayered tube drawing process is a method that can control the inner diameter, outer diameter, and thickness of a pipe during the simultaneous drawing of two different materials using a stop plug, as shown in Figure 1 (b). Figure 2 shows a schematic diagram of the bilayered materials tube drawing process.

Figure 2: 
Schematics of bilayered materials tube drawing process

Design of Experiments is a technique that efficiently finds the optimum condition of a product by selecting various factors affecting its characteristics and conducting experiments to determine the relationship between those factors [8][9].

The Taguchi method is an optimization technique whose advantage lies in the fact that if there are many factors to consider, the factor that is insensitive to the influence of external noise can be selected by analyzing the factors with a small number of experiments through the orthogonal array table. It uses a loss function to evaluate the performance of characteristic value. When calculating the loss function, the proportional constant k must be determined. The most important information is to determine the Δ₀ (function limit) and the loss value ∆₀ when the function is not performed. Therefore, when the target value of product characteristics is m, and the actual characteristic value of the product is y,

the quality loss factor is k=A0∆0 and Ly=ky-m2

A product of good quality is obtained on minimizing the value of this loss function. In addition, for factors affecting the variation in performance, the controllable and non-controllable factors are divided, and the concept of noise is introduced. The factors that are noise resistant are selected, and the signal to noise (S/N) ratio is introduced to implement a design that is insensitive to noise.

Multiple factors affect the design of drawing dies, but there exists no research concerning the drawing of bilayered materials. According to “Progress in cold roll bonding of metals for the production of bilayered materials” by Long Li, manufacturing by rolling the bilayered materials plate can increase the bonding strength of the material as the area reduces [10]. Therefore, among the important variables in drawing, the angle of entry of the die and the angle of the plug, which have the greatest influence on the cross-section area reduction, are selected as variables [11]. For this purpose, preliminary analyses were conducted to examine the effect of the die and plug angles on the material drawing and determine the level of design variables, using the commercial analysis program FORGE HPC.

The outer pipe of the test material (Carbon steel) is API X65 5L with ∅ = 114.3 mm, and the thickness is 4.65 mm, 4.7 mm, and 4.75 mm, respectively. The inner pipe is a stainless steel-based SUS316L material with ∅ = 101.6 mm, with a thickness of 2 mm. The final dimension after drawing is ∅ = 101.55 mm and a thickness of 6.6 mm.

The flow stress equation was derived, based on the material properties obtained, according to the FORGE HPC manual. The factor of each equation is a calculated constant, a dimensionless number, and an experimental value derived from material properties. Table 1 and Table 2 show the mechanical properties and chemical composition, respectively, including the derived values [12][13].

A : consistency
m₁ : Temperature Term
m₂ : Sensitivity

For the analysis conditions, the modeling was performed with the shape, as shown in Figure 3, and it was assumed that the die, plug, and chuck were rigid bodies, thereby exhibiting no deformation. Since the billet of the material was thin, the size of the mesh grid was rather small, so the number of material points increased, and analysis efficiency decreased, which increased the analysis time. Therefore, a mesh window was used to form for dense elements, as shown in Figure 4, for the region of interest only with an element size 0.7 times the size of the existing element at the molding position. The friction between each material, die and plug is assumed to be in the lubricated state with coulombic friction (μ) 0.2. Through the literature review, for the friction at the interface between the two materials, the static friction coefficient was found to be 0.74 - 0.8 for friction between steel on steel, and the static friction coefficient was set to 0.74 for the experiment [14].

Figure 3: 
5-Degree shape of drawing modeling of materials of bilayered materials

Figure 4: 
Measuring point of stress and residual stress in bearing

The result data was used to determine the design factors and levels. Figures 5 and 6 are the results of stress analysis at the positions indicated in Figure 4. The die boundary conditions of the pre-analysis are shown in Table 3, and the operating condition of the existing steel pipe manufacturing was applied. As shown in the graph, the maximum stress value was obtained with the die radius between 55 and 60 mm and the plug angle measured at 5 °.

Figure 5: 
Stress of pipe boundary aspect in bearing

Figure 6: 
Residual stress of pipe boundary aspect

Die Radius (mm)	Plug Angle (˚)
50	5
	6
	7
	8
	9
55	5
	6
	7
	8
	9
60	5
	6
	7
	8
	9
65	5
	6
	7
	8
	9
70	5
	6
	7
	8
	9
Conditions	Type
Material of billet(Outer)	API 5L X65
Material of billet(Inner)	SUS316L
Chuck speed	400mm/s
Die on billet friction	0.2
Billet on billet friction	0.74
Node	26,330
Element	86,712

Variables were selected through pre-analysis results, and the level of the design factor was determined to be at three levels considering the process compared to the level applied to the initial design [9]. Table 4 shows the design factors selected and the level of each design factor. These factors are: A (Die radius), B (Plug angle), C (Pipe cross-section area), and D (friction coefficient).

Data that can be investigated by means of finite element analysis are stress, strain, and shape dimensions that can be observed from the materials. Through the above variables, the radial stress values measured at the interface between the two materials are identified, and through this data, the effects on the material according to the shape are analyzed.

As shown in Table 5, the factors and levels used in this study are three design factors with three levels. For the minimum orthogonal array table that can be applied, a model with a total of 8 degrees of freedom L₉(4³) should be applied. In Table 4, A, B, C, and D indicate design factors and the Arabic numerals indicate the level of design factors. That is, the experiment number 1 of Table 5 is expressed as A₁B₁C₁D₁, and experiment number 9 is written as A₃B₃C₂D₁ [8].

Based on the boundary conditions of the pre-analysis, a new model was applied, according to the orthogonal array, to perform a total of nine analyses. The physical properties are the same as those of Table 1 and 2, and the drawing process conditions are also the same as Table 3. However, the die shape (Die Radius, Plug Angle) of Table 3 was changed to the conditions in Table 5 to conduct the analysis.

Experimental conditions were obtained by means of the orthogonal array according to the level between each factor in the orthogonal array table using the Taguchi method, and a finite element analysis was performed nine times using FORGE HPC.

As a result of the analysis, the stress in the radial direction applied at the interface between the outer and inner pipes at the (a) bearing part and the (b) residual stress part of the interface of the material was examined, as shown in Figure 7. As shown in Figure 8, in the cross-section of the bearing part (a), the material is under tensile stress at the interface of the outer pipe of the material, and under compressive stress at the interface of the inner pipe of the material, and the tensile stress at the outer pipe is higher than the compressive stress at the inner pipe. In (b) residual stress part, as in the case of the bearing part, tensile stress is applied at the outer pipe, and compressive stress is applied at the inner pipe. However, unlike the case of the bearing part, the tensile force in the outer pipe is mostly lost, leading to higher compressive stress in the inner pipe than the tensile stress of the outer pipe.

Figure 7: 
Measurement position of (a) bearing part and (b) residual stress

Figure 8: 
Stress direction

Therefore, to increase the bonding strength between the two materials, it is necessary to have high circumferential stress at the interface between the materials.

Table 6 and 7 show the total stresses of the outer and inner pipes at the bearing and residual stress parts. Using the larger-the-better characteristics equation, the S/N ratio by level for each factor was obtained, and these are shown in Table 8 and 9. The tendency, by level, for each better at the bearing part and the residual stress part is shown in Figure 9. In the graph, a similar tendency was observed for the die radius and reduction of area at the (a) bearing part and the (b) residual stress part; however, the tendency of the plug angle is slightly different. S/N Ratio of the-larger-the better characteristics:

Figure 9: 
S/N Ratio of bearing part and residual stress

The reduction of area tended to decrease as the level increased from Level 1 to Level 3. In Figure 10, when the change in the reduction of the area and thickness were examined in the (a) outer pipe and (b) inner pipe, the reduction area, and the thickness change both increased with the level in the inner pipe.

Figure 10: 
S/N Ratio of Inner and Outer Pipe

However, in the case of the outer pipe, with the application of the tensile stress, the material became thicker, the reduction area decreased, and the thickness change increased.

Through the analysis of the variance of the S/N ratio, the effects were divided into the input effect of the response values and the remaining effect. We aim to use the ratio of the two effects in the design evaluation. The results of the analysis indicate that, in the residual stress part, the values are significantly affected by the die radius; however, they are not significantly affected by the plug angle and reduction area. On the contrary, for the bearing part, it is assumed that the values were significantly affected by the plug angle and reduction area but not by the die radius. This can be observed in the analysis of variance shown in Table 10 and 11 and can also be confirmed by the contribution ratio expressed as a percentage against the sum of all level differences obtained through the S/N ratio for each level.

Therefore, the level of the die radius in the residual stress part, level of the plug angle and reduction area in the bearing part was selected, which was 55 mm for the die radius, 5 ° for the plug angle, and 11.62% for the reduction of area.

The experiment was conducted under the optimum conditions of the factors obtained through the Taguchi method. As for the experimental materials, for the outer tube (carbon steel), API X65 5L was used, with ∅ = 114.3 mm and thickness = 4.7 mm. For the inner tube (stainless steel), SUS316L was used with ∅ = 101.6 mm and thickness = 2 mm, and the mechanical properties and chemical composition of each material are as shown in Table 1 and 2. The die radius and the plug angle used for the experiment were at 55 mm and 5°, respectively.

Figure 11 shows (a) die and (b) plug fabricated by means of the previous optimization design. As a process to use both materials for the experiment, to draw both the outer and inner pipes at the same time, the two materials are fixed at the same time. Then, the materials were placed on the drawing tool, inserted into the die, and a dry lubricant was used to reduce the friction between the die, plug, and the materials. Once the plug is inserted, the fixed material is pulled to carry out the forming. Furthermore, since the lengths of the initial materials are different, and the tensile length of the two materials are also different, shear processing at the ends is required. Figure 12 presents the drawing process; (a) is the shape in which the dies and the material are bonded with the lubricant applied to the material, and (b) is the process of performing drawing.

Figure 11: 
(a) Die and (b) plug for drawing of a bilayered pipe

Figure 12: 
Drawing process of bilayered pipe

The final target dimension is ∅ = 101.55 mm, and the thickness is 6.6 mm, as indicated above. As the experiment was performed using the optimal value obtained through the Taguchi method, it was found that ∅ = 101.52 mm and the thickness was approximately 6.56 mm. The application of a tensile force on the material was assumed to slightly reduce the cross-section area. As shown in Figure 13, the bonding of the final product was intact or and no other defects were observed.

A prototype was produced, as shown in Figure 13, using the results obtained through optimal design, and indentation strength tests were performed. To measure the indentation strength of the bilayered material pipe, an experiment was conducted by placing the specimen on the lower jig of the universal testing machine and pressing the upper part of the specimen with the upper jig to push the inner pipe inside the outer pipe. The schematic diagram of the indentation strength test, an image while performing the test with the jigs, and the specimen bonded to the universal testing machine is shown in Figure 14. As for the experimental method, the force required in the upper jig was measured to indent 10 mm for each specimen of 20 mm, 30 mm, 38 mm, and 50 mm, respectively. The indentation strength result of the bilayered pipe manufactured through the hydroforming method, which is a product to be compared against for this study, and that of the bilayered pipe fabricated in this study were compared. The dimensions and materials used were the same as those used in the drawing process of this study. Table 12 shows the results of measuring the force that is required to indent 10 mm on the specimen with a height of 50 mm for the bilayered pipe with the specimen fabricated according to the forming pressure of the hydroforming process. Table 13 shows the indentation strength test result according to the material length of the bilayered drawing pipe. When comparing the values at a specimen length of 50 mm, as shown in Figure 15, the maximum indentation strength obtained from the bilayered drawing pipe was almost eight times higher than that obtained through the hydroforming process. At the interface between the inner and outer material, the penetration of the shape is thought to have occurred due to friction between the materials and the reduction of the cross-sectional area, which increased the bonding strength and resulted in a higher indentation strength.

Figure 13: 
Indentation strength test of bilayered material pipe

Figure 14: 
Indentation strength test of bilayered material pipe

Figure 15: 
Comparison of bilayered drawing and hydroforming