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Steel Designers' Manual - 6th Edition (2003)
254 Fracture and fatigue
then knowing two of the three parameters maximum stress, crack size and fracture
toughness will allow the limiting value of the third parameter to be determined.
For example, if the maximum allowable stress is 160 MPa and the maximum
allowable crack size in an edge cracked plate, where Y = 1.12, is 100 mm then
the minimum fracture toughness of the material must be 100 MPa to avoid
fracture. (Remember that it is important to keep track of the units and 1 MPa
= 31.62 N.mm-1.5 m
m
.)
It has been found by experiment that the fracture toughness value measured in
a laboratory is influenced by the dimensions of the specimen. In particular, the
size and thickness of the specimen and the length of the remaining uncracked
section, called the ligament, control the level of constraint at the crack tip. Constraint
is the development of a triaxial stress state which restricts the deformation
of the material. Thick specimens, which generate high constraint or plane strain
conditions, give lower values of the fracture toughness than those found from thin
specimens under low constraint or plane stress conditions. The least dimensions
to give the maximum constraint, and hence the minimum value of toughness, are
when:
Ê K
thickness, width and ligament ≥ 2.5Á
Ë s
Ic
y
(7.3)
This ensures that the localised plasticity at the crack tip is less than 2% of any of
the dimensions of the body and therefore does not disturb the elastic crack tip stress
field.
The size requirement of Equation (7.3) gives rise to practical problems in testing.
For example, steel with a room temperature yield strength of 275 N.mm-2 and a
minimum fracture toughness of 70 MPa needs to be tested using a specimen at
least 160 mm thick to ensure plane strain conditions. In reality, much structural steelwork
is made from sections substantially thinner than this and its fracture toughness
will be significantly higher. It is good practice in many engineering disciplines
to measure fracture toughness values using specimens of similar thickness to the
proposed application.
Tables 3 to 7 in BS 5950: 20007 define, as a function of temperature, the maximum
thickness of steel that should be used to avoid brittle fracture. This is the same as
BS 5400-3: 20008 m
for steel bridge design. Both BS 5400 and BS 5950 are consistent
with, but generally more conservative than, the minimum thickness to ensure plane
strain conditions, as estimated from Equation (7.3). This means that the toughness
of the steel in use should be better than the minimum value achievable in thick
sections.
Linear elastic fracture mechanics is of much greater use on the lower shelf of
the ductile-brittle behaviour of steels than on the upper shelf. At low temperatures,
the yield strength is higher, the fracture toughness much lower and plane strain
conditions can be achieved in relatively thin sections. On the upper shelf, linear
elastic fracture mechanics tends to be inapplicable, and other techniques need to be
used.
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