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Yield Criteria for Ductile Metals
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angle anisotropy assumed bending billet blank circular compression considered constant corresponding Coulomb friction curve dead metal zone deep drawing diagram of figure diameter direction elastic element energy dissipation engineering metals Engrs equilibrium extrusion extrusion pressure forces exerted fractional reduction frictional resistance given Hence hodograph hydrostatic pressure indenter interface isotropic magnitude maximum mech metal forming processes Mises yield criterion Mohr stress circle normal occurs parallel physical diagram plane strain plane strain deformation plane stress plastic bending plastic deformation plastic flow plastic hinge plastic strain increment plastically deforming region platen pressure platens principal stress punch quasi-static radial radius ratio redundant deformation rigid roll shear strain shear stress sheet metal shown in figure slip line field specimen steel strain tensor strain-rate stress components strip tangential velocity discontinuity temperature tensile thickness Tresca yield criterion tube upper bound estimate vector velocity field workpiece yield locus yield stress yield surface zero