# Production Optimization of Premium Food Can with Distortion Printing under Waving Requirement
## 3 Material Parameter Identification
### Material Tests  
The material used is a TFS sheet known as SPTFS MR DR-8 (JIS G 3315). This material offers superior performance in terms of resource conservation, energy efficiency, and environmental protection. The doubly reduced (DR) temper is produced to achieve extremely high-yield strength in chromium-coated TFS, as indicated by the Rockwell superficial hardness values (HR3 TSm). Using the DR method, the base metal's thickness is reduced a second time on a temper mill after annealing, increasing material strength while decreasing elongation. This TFS sheet has a thickness of 0.16 mm and a hardness of DR-8. It is laminated on both sides with PET film, with a thickness of 13 microns on the outside and 20 microns on the inside. In this application, there are two types of low-carbon steels: (1) aluminum-killed steel (Al-killed), which is deoxidized with aluminum during production to remove carbon monoxide, resulting in lower oxygen content and improved surface finish, and (2) super ultra-low-carbon (SULC) steel. The cost of SULC is approximately 2% higher than Al-killed steel. The main difference between these steels, based on the chemical composition of tin mill black plate (TMBP), is the carbon content. Al-killed steel has a higher carbon content (max 1600 ppm), while SULC steel has a lower carbon content (max 60 ppm). Other elements are largely the same, with Si = 400, P = 200, S = 500, and Mn = 6000 (max). The mechanical properties are not uniform in all directions (anisotropy). Consequently, distortion printing results in waving, leading to a relatively high scrap rate in production. Tensile tests of those materials are conducted in three directions (RD (0\({}^{\circ}\)), DD (45\({}^{\circ}\)), and TD (90\({}^{\circ}\))) at a speed of 5 mm/min using a Shimadzu Model Autograph AG-X plus 50 kN (Lab3) at 25 \({}^{\circ}\)C and 51% RH. The test results are averaged from five samples per direction. Both Al-killed and SULC steels have similar yield points and tensile strengths, as shown in Table 1. SULC offers better earning than Al-killed, as illustrated in Figure 11. Therefore, Al-killed steel is suitable for lacquering, while SULC is more suitable for distortion printing. Further investigation of SULC is necessary within the context of distortion printing. The elongation observed in the test results presented in Table 1 is notably low, at less than 2%. Additionally, some of the test outcomes deviate from standard expectations, including unusually low \(R\)-values. According to ASTM E517, the appropriate strain level for determining the \(R\)-value is typically around 20%. To address this discrepancy, additional tests are conducted in collaboration with two laboratories. The averaged results from all three laboratories, across three directions, are presented in Table 2.  
The yield point and tensile strength values obtained from the three laboratories (Lab 1: ASTM E8, Lab 2: DIN 50114, and Lab 3: JIS No. 5) exhibit a significant discrepancy. The yield point determined by Lab 3 is selected for subsequent analysis due to its alignment with the industrial specification indicated in the datasheet. It is hypothesized that the thinness of the steel sheet may have contributed to these variations, as most testing apparatus are designed for materials with a thickness of approximately 1 mm. The quality of the cut edge may also contribute to the observed discrepancies, as the samples are produced using a punch press, which can induce minor edge deformations. Employing a more precise cutting method could potentially mitigate this issue. Figure 12 displays the samples subjected to tensile tests in three directions from the three laboratories. The breakage exhibits minimal elongation, and necking is negligible, raising concerns about the accuracy of these tests, particularly \(R\)-value at 5% strain. The subsequent sections address the material parameter identification method proposed in this study.