Page 102 - Manufacturing Engineering and Technology - Kalpakjian, Serope : Schmid, Steven R.

Section 2 11 Residual Stresses
Residual Stresses
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When workpieces are subjected to plastic deformation that is not uniform throughout
the part, they develop residual stresses. These are stresses that remain within a part
after it has been formed and all the external forces (applied through tools and dies) are
removed; a typical example is the bending of a metal bar (Fig. 2.30). The bending
moment first produces a linear elastic stress distribution (Fig. 2.30a). As the external
moment is increased, the outer fibers in the bar reach a stress level high enough to
cause yielding. For a typical strain-hardening material, the stress distribution shown
in Fig. 2.30b is eventually reached, and the bar has undergone permanent bending.
Let’s now remove the external bending moment on the bar. Note that this
operation is equivalent to applying an equal but opposite moment to the bar; conse-
quently, the moments of the areas oab and oac in Fig. 2.3()c must be equal. Line oc,
which represents the opposite bending moment, is linear, because all unloading and
recovery is elastic (see Fig. 2.3). The difference between the two stress distributions
gives the residual stress pattern within the bar, as is shown in Fig. 2.30d. Note the
presence of compressive residual stresses in layers ad and oe, and the tensile residual
stresses in layers do and ef Because there are no external forces applied, the internal
forces resulting from these residual stresses must be in static equilibrium. Although
this example involves only residual stresses in the longitudinal direction of the bar,
in most cases these stresses are three dimensional.
The equilibrium of residual stresses in Fig. 2.30d may be disturbed by the re~
moval of a layer of material from the part, such as by machining or grinding. The
bar will then acquire a new radius of curvature in order to balance the internal
forces. Such disturbances of residual stresses lead to warping of parts (Fig. 2.31).
The equilibrium of residual stresses may also be disturbed by relaxation of these
stresses over a period of time (see below).
Residual stresses can also be caused by temperature gradients within a body,
such as occur during cooling of a casting or a forging. The local expansions and con-
tractions caused by temperature gradients within the material produce a nonuni-
form deformation, such as is seen in the permanent bending of a beam.

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a bc 3
d
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e
f
(C) (Ci)

FIGURE 2.30 Residual stresses developed in bending a beam having a rectangular cross
section. Note that the horizontal forces and moments caused by residual stresses in the beam
must be balanced internally. Because of nonuniform deformation, especially during cold-
metalworking operations, most parts develop residual stresses.