Mechanics of Sheet Metal Forming

This chapter first introduces sheet metal forming processes, including their industrial importance. The principal strain increments in uniaxial loading are analyzed using calculus tools; they are also discussed with reference to isotropy and anisotropy. The plane stress deformation is analyzed, and the terms stress ratio (α) and strain ratio (β) have been defined. Theories of failure/yielding are introduced with reference to the Tresca yield condition and the von Mises yield theory. The deviatoric stresses have been diagrammatically illustrated, and workable mathematical models have been derived. The Levy-Mises flow rule has been applied using integral calculus to establish the mathematical relationship between α and β. The formulae for determining the effective stress \( \left(\overline{\sigma}\right), \) the effective strain \( \left(\overline{\varepsilon}\right), \) and the work of plastic deformation are presented. Finally, the mechanics of a stretch-forming operation is given. This chapter includes 26 worked numerical examples, 10 diagrams, 45 formulae/equations, 15 numerical problems, and 6 MCQs with their answers given at the end of this book.