Page 24 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

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PROPERTIES OF STRUCTURAL STEELS AND EFFECTS OF STEELMAKING AND FABRICATION

1.22 CHAPTER ONE

loading conditions. For example, for a through-thickness crack of length 2a in an infinite plate under
uniform stress (Fig. 1.11a),

K = f a p a (1.3)
l
where f a is the nominal applied stress. For a disk-shaped crack of diameter 2a embedded in an infi-
nite body (Fig. 1.11b), the relationship is

a
K = 2 f a (1.4)
l
p
If a specimen with a crack of known geometry is loaded until the crack propagates rapidly and causes
failure, the value of K l at that stress level can be calculated from the derived expression. This value
is termed the fracture toughness K c .
A precracked tension or bend-type specimen is usually used for such tests. As the thickness of
the specimen increases and the stress condition changes from plane stress to plane strain, the frac-
ture toughness decreases to a minimum value, as illustrated in Fig. 1.11c. This value of plane-strain
fracture toughness, designated K lc , may be regarded as a fundamental material property.
Thus, if K lc is substituted for K l , for example, in Eq. (1.3) or (1.4) a numerical relationship is
obtained between the crack geometry and the applied stress that will cause fracture. With this rela-
tionship established, brittle fracture may be avoided by determining the maximum-size crack present
in the body and maintaining the applied stress below the corresponding level. The tests must be con-
ducted at or correlated with temperatures and strain rates appropriate for the application, because
fracture toughness decreases with temperature and loading rate. Correlations have been made to
enable fracture toughness values to be estimated from the results of Charpy V-notch tests.
Fracture-mechanics analysis has proven quite useful, particularly in critical applications.
Fracture-control plans can be established with suitable inspection intervals to ensure that imperfec-
tions, such as fatigue cracks, do not grow to critical size.
(J. M. Barsom and S. T. Rolfe, Fracture and Fatigue Control in Structures; Applications of
Fracture Mechanics, Prentice-Hall, Englewood Cliffs, N.J.)

1.14 RESIDUAL STRESSES

Stresses that remain in structural members after rolling or fabrication are known as residual stresses.
The magnitude of the stresses is usually determined by removing longitudinal sections and mea-
suring the strain that results. Only the longitudinal stresses are usually measured. To meet equilibri-
um conditions, the axial force and moment obtained by integrating these residual stresses over any
cross section of the member must be zero.
In a hot-rolled structural shape, the residual stresses result from unequal cooling rates after
rolling. For example, in a wide-flange beam, the center of the flange cools more slowly and devel-
ops tensile residual stresses that are balanced by compressive stresses elsewhere on the cross section
(Fig. 1.12a). In a welded member, tensile residual stresses develop near the weld and compressive
stresses elsewhere provide equilibrium, as shown for the welded box section in Fig. 1.12b.
For plates with rolled edges (UM plates), the plate edges have compressive residual stresses
(Fig. 1.12c). However, the edges of flame-cut plates have tensile residual stresses (Fig. 1.12d). In a
welded I-shaped member, the stress condition in the edges of flanges before welding is reflected in the
final residual stresses (Fig. 1.12e). Although not shown in Fig. 1.12, the residual stresses at the edges
of sheared-edge plates vary through the plate thickness. Tensile stresses are present on one surface and
compressive stresses on the opposite surface.
The residual-stress distributions mentioned above are usually relatively constant along the length
of the member. However, residual stresses also may occur at particular locations in a member, because
of localized plastic flow from fabrication operations, such as cold straightening or heat straightening.

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