3 Fundamentals of press design

28 Basic principles of metal forming
The greatest deformation, which is equal to the sum of the two other
deformations, is designated the principle deformation j g:
The principle deformation must be a known quantity, as it forms the
basis for every calculation, for example of deformation force. It is easy
to determine, as it carries a different sign to the other two. In the compression
of a cubic body, for example, the increase of width (b1 > b0) and length (l1 > l0) results in a positive sign, while the decrease of height
(h1 < h0) produces a negative sign (Fig. 2.2.1). Accordingly, the absolute
greatest deformation is along the vertical axis j1. .
Similar to the sum of deformations, the sum of deformation rates j
must always be equal to zero:
The flow law applies approximately:
with the mean stress s m given by
The material flow along the direction of the stress which lies between
the largest stress s max and the smallest stress s min will therefore be
small and will be zero in cases of plane strain material flow, where
deformation is only in one plane.
2.2.3 Force and work
ϕ1=− ( ϕ2+ ϕ3)= ϕg
ϕ ˙ 1+ j ˙ 2 + ϕ ˙ 3 =0
( ) ( − ) ( − )
ϕ : ϕ : ϕ = σ − σ : σ σ : σ σ ,
1 2 3 1 m 2 m 3 m
σ σ σ
σm
=
+ +
1 2 3
3
In calculating the forces required for forming operations, a distinction
must be made between operations in which forces are applied directly
and those in which they are applied indirectly. Direct application of
force means that the material is induced to flow under the direct appli-
Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998