Modeling the Forming Limit Diagram of Anisotropic Copper Tubes with Non-Classical Yield Criterion

The application of forming limit curves (FLCs) is essential for estimating the formability of metallic tubes, serving as a crucial parameter for predicting limit strains. Experimentally determining the FLC, however, is time-consuming and requires specialized and costly equipment. In such cases, the finite element method (FEM) offers a practical alternative for predicting the FLC. One of the most accurate methods for obtaining FLCs is based on the Marciniak–Kuczynski (M-K) theory. In this study, the M-K model was incorporated into the finite element framework of ABAQUS to derive the FLC of an anisotropic copper tube using the Hill۴۸ and BBC۲۰۰۳ yield criteria. The input data for the simulations were obtained from uniaxial tensile tests performed in three directions. Subsequently, the influence of key parameters—such as imperfection factor, strain hardening exponent, normal stress, and anisotropy—on the FLC of the copper tube was investigated. The finite element modeling results revealed that increasing the imperfection factor, strain hardening exponent, and normal stress elevates the FLC, indicating improved formability. However, an increase in groove angle reduces formability.

کلیدواژه ها:

Forming Limit Diagram ، Anisotropic Copper Tubes ، Non-Classical Yield Criterion ، Marciniak–Kuczynski Model ، Finite Element Analysis