Forming limit diagram of sheet metal in the negative minor strain region

• Published in: Materials science and engineering 1987-02, Vol.86 (1-2), p.137-144
• Main Authors: Lian, Jianshe, Baudelet, Bernard
• Format: Article
• Language: English
• Subjects: Applied sciences; Deep drawing; Exact sciences and technology; Forming; Metals. Metallurgy; Other forming methods; Production techniques
• ISSN: 0025-5416
• DOI: 10.1016/0025-5416(87)90448-4

The localized necking of sheet metal in the negative minor strain region has been reexamined by a study of both Hill's instability theory and the theory of Marciniak and Kuczynski. It was found that, when an imperfection is along the zero-extension direction, both the homogeneous zone a and the heterogeneous zone b have the same stress states. This important condition greatly simplifies the theory of Marciniak and Kuczynski, enabling the equation of plane stress which they obtained to be expressed in a one-dimensional form: f 0 exp(ε 3 b)(ε 30 + ε 3 b) n (dε 3 b) m = exp(ε 3 a)(ε 30 + ε 3 a) n (dε 3 a) m The present result can be considered as a new development of Hill's instability criterion theory or as a complete mathematical proof of the “critical thickness strain criterion” proposed recently by Chan, Koss and Ghosh.