Forming Limits of Metal Sheets and Tubes: Analysis Method and Experimental Validation Toshihiko Kuwabara 1, a , Kengo Yoshida 2,b and Fuminori Sugawara 3,c 1 Division of Advanced Mechanical Systems Engineering, Institute of Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei, Tokyo 184-8588, Japan 2 Graduate School of Science and Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa, Yamagata 992-8510, Japan 3 Department of Mechanical Systems Engineering, Graduate School of Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei, Tokyo 184-8588, Japan a kuwabara@cc.tuat.ac.jp, b yoshida@yz.yamagata-u.ac.jp , c 50011833003@st.tuat.ac.jp Keywords: strain localization, forming limit curve, yield function, crystal plasticity, biaxial tensile test Abstract. In the first part of the paper, an analysis of strain localization phenomenon in a polycrystalline sheet is demonstrated on the basis of Marciniak and Kuczyński-type imperfection approach. A thin sheet which possesses a band-type initial thickness imperfection is considered, and biaxial stretching is applied to the rolling and transverse directions of the sheet. Hence, plane stress condition with zero thickness stress is assumed. The development of strain concentration into the band is numerically analyzed. Plotting strain levels at the onset of strain localization on strain space, stretchability of the sheet is represented as a forming limit curve (FLC). Firstly, a phenomenological plasticity theory is adopted in the simulation. The influence of material parameters, such as curvature of yield surface, magnitude of initial imperfection, strain-rate sensitivity, work-hardening exponent, and anisotropy is investigated. Secondly, a crystal plasticity theory based on a slip mechanism of plastic deformation is employed, and influence of typical textures generated in the rolling and recrystalization processes of aluminum alloy sheet production is examined. In the second part of the paper, the experimental methods for determining the FLC and forming limit stress curve (FLSC) of sheet and tubular specimens are presented. For sheet specimens a biaxial stretch test using a flat-head punch proposed by Marciniak and Kuczyński is used. For tubular specimens a multiaxial tube expansion test is used; combined axial force and internal pressure are simultaneously applied to a tubular specimen using a closed loop, servo-controlled biaxial stress testing machine. The latter can be utilized as a biaxial tensile testing method for sheet metals by fabricating a tubular specimen from a flat sheet sample, and that it is even useful to measure the forming limits for nonlinear loading paths. Measured results of FLC and FLSC are presented and the calculated results based on the phenomenological and polycrystal plasticity analyses are validated. The strain path dependency of FLSC is also discussed. Introduction In a biaxially stretched sheet metal, the sheet deforms almost homogeneously up to a certain strain level, after which plastic deformation starts to localize into a narrow band region with significant reduction of the thickness and a localized neck is formed. Shortly after, a band with highly localized shear strains emerges in the neck, and is subsequently accompanied by the growth and coalescence of voids, finally leading to fracture. Thus, the onset of the localized neck plays the role of a precursor to breakage in sheet metals. In the present paper, we concentrate our attention on the