3 Fundamentals of press design

2 Basic principles of metal forming
2.2 Basic terms
2.2.1 Flow condition and flow curve
Metallic materials may be shaped by applying external forces to them
without reducing their structural cohesion. This property is known as
the formability of metal. Deformation or flow occurs when the rows of
atoms within the individual crystalline grains are able, when stressed
beyond a certain limit, to slide against one another and cohesion
between the rows of atoms takes place at the following atomic lattice.
This sliding occurs along planes and directions determined by the crystalline
structure and is only made possible by, for example, dislocations
(faults in the arrangement of the atomic lattice). Other flow mechanisms
such as twin crystal formation, in which a permanent deformation
is caused by a rotation of the lattice from one position to another,
play only a minor role in metal forming technology.
Flow commences at the moment when the principle stress difference
(� max – � min) reaches the value of the flow stress k f, or when the shear
strain caused by a purely shearing stress is equal to half the flow stress,
given by:
kf =σmax – σmin
By neglecting the principle stress � 2, this mathematical expression represents
an approximate solution of the shearing stress hypothesis with
the greatest principle stress � 1 and the smallest principle stress � 3:
kf =σ1 – σ3
Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998