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Forming Limit Diagram of Auto-body Steel Sheets at High Strain Rates for Sheet Metal Forming and Crashworthiness (박판성형 및 충돌성능 향상을 위한 고변형률속도에서의 차체강판 성형한계도)
Sheet metal formability is generally defined as the ability of metal to deform into desired shape without necking or fracture. Each type of sheet metal can be deformed only to a certain limit that is usually imposed by the onset of localized necking, which eventually leads to the fracture. A well-known method of describing this limit is the forming limit diagram (FLD), which represents the locus of the necked or fractured position of sheet metals in the space of in-plane principal strains, $epsilon1$-$epsilon2$, where $epsilon1$ is the major strain and $epsilon2$ is the minor strain. The locus of the forming limit is called the forming limit curve (FLC), and the FLC is affected by many factors, such as the forming speed, the lubrication condition, the thickness of sheets, the strain hardening, and the anisotropy of the sheet metals. The forming speed for FLC is particularly significant because the dynamic response of sheet metals differs considerably from the static response. This paper is concerned with the dynamic tensile properties and formability of steel sheets in relation to the strain rate effect. The elongation at fracture increases at a high strain rate for CQ; however, the elongation at fracture for DP590 decreases slightly in relation to the corresponding value for a quasi-static strain rate. The uniform elongation and the strain hardening coefficient decrease gradually when the strain rate increases. The r-value of CQ and DP590 was measured with a high-speed camera in relation to the strain rate effect. The r-value is slightly sensitive to the strain rate effect. Because these properties do not show the consistent tendency, the formability cannot be determined with a single tensile property. To properly evaluate the formability of sheet metals, we therefore need to perform a high-speed forming limit test as well as a dynamic tensile test. A static FLC and a high-speed FLC were constructed with the aid of a punch-stretch test with arc-shaped specimens and square-shaped specimens. The arc-shaped specimens provide better results for the fractured strains than conventional rectangular specimens. A high-speed crash testing machine with a specially designed high-speed forming jig was used for the high-speed punch-stretch tests. The forming velocity was decided by finite element analysis of punch-stretch test with relation to the specimen dimension. Compared with the static FLC, the high-speed FLC of CQ is higher in a simple tension region and lower in a biaxial stretch forming region. The high-speed FLC for DP590 decreases in relation to the static FLC throughout the entire region. The elongation at fracture appears to be closely related to the simple tension region of the FLC. The decrease of the high-speed FLC in the biaxial stretch forming region is due to the shear fracture in fracture surfaces. The results confirm that the strain rate has a noticeably influence on the formability of steel sheets. Thus, the forming limit diagram of high-speed tests should be considered in the design of high-speed sheet metal forming processes. In this paper, three theoretical (Hill-Swift, Jun and M-K models) approaches and two empirical (Keeler-Brazier and Raghavan models) approaches were discussed to predict the FLC of sheet metals. The theoretical models are found to be very conservative, especially at plane strain region in FLC. Among the various prediction models, the Raghavan model with NADDRG (North American Deep Drawing Research Group) curve gives better prediction at plane strain region. However, this model still shows some limitation to predict the simple tension region and biaxial stretch forming region of FLC. Therefore, this paper suggested the modified Raghavan model for CQ and DP590, and changed the angle between two lines of NADDRG curve. In the case of the strain rate sensitive steel sheets of CQ, the high-speed FLC is higher than the static FLC in the simple tension region and shows a slight reduction in the biaxial stretch forming region. Although the advanced high strength steel, DP590 is insensitive to the strain rate, the high-speed FLC decreases considerably. Thus, when determining the forming speed of sheet metal forming process, we need to consider how the formability varies in relation to the strain rate effect.