8 1. NATURE AND SOURCE OF RESIDUAL STRESSES
of the temperature at the core is much slower. As cooling proceeds, the imbalance of temper-
atures and associated dimensions between the core and skin results in generally tensile residual
stresses at the core and balancing compressive stresses at the skin. Depending on the material,
temperature ranges and quench medium, residual stresses can approach or exceed the material
yield strength. In extreme circumstances, stresses during the quenching process can exceed the
material yield strength or the ultimate strength resulting in fracture and partial relaxation of the
residual stresses.
Composite materials bring into play a further mechanism for thermal stress development.
In general, the individual materials within a composite structure have different physical proper-
ties. us, differences in thermal properties produce differential expansions among the various
materials, causing dimensional misfits and consequent residual stresses. If large, the stresses can
cause permanent deformations and associated residual stresses. Smaller residual stresses may also
occur in the elastic range and vary approximately linearly with overall temperature. ese latter
stresses are temporary insofar as a temperature cycle that returns to the starting temperature pro-
duces residual stresses that similarly cycle and return to the starting stress state. In some cases,
there may be a particular temperature, perhaps corresponding to the manufacture temperature,
at which the residual stresses become close to zero. is same mechanism occurs on a much
larger scale with the structural stresses previously considered. For thermal stresses in railway
rails, the zero-stress temperature is called the “rail neutral temperature.” Similar behaviors can
occur on a microscopic scale, where residual stresses of significant size can occur in and around
inclusions and crystal grains in metals.
1.3.3 NON-UNIFORM PLASTIC DEFORMATION
Residual stresses are created in nearly all material forming and shaping procedures, for example,
bending sheet metal to make boxes, spin forming (stretching) metal to make bowls, and twisting
wires to assemble into cables. All such processes involve substantial plastic deformation so as to
change the shape of the workpiece permanently. Almost invariably the associated plastic strains
are non-uniform, and so therefore create the localized material misfits that produce residual
stresses.
Figure 1.8 illustrates residual stress formation in a beam that is bent beyond its elastic
range. For simplicity, the material here is assumed to be elastic-perfectly plastic. Figure 1.8a
shows the maximum stress distribution within the material cross-section that can occur in the
linear elastic range. e maximum stresses at the surfaces just reach the yield stress. On further
bending in Figure 1.8b the material near the outer surfaces yields and deforms plastically at con-
stant stress to produce the outer flat areas in the stress profile. e inner linear area remains in
the elastic range. If the beam is then unloaded, elastic stress release corresponding to the dashed
line in Figure 1.8b occurs. A surface stress greater than yield is required to give a linear stress dis-
tribution with equal moment resultant to the plastic stress distribution. is larger elastic stress
change can occur because the available elastic unloading range spans from tensile yield, through