Effect of finite size of component

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Effect of finite size of component
The SIF derived earlier is for cracks in an
infinite body. However the finite size, geometry
of the component, loading conditions have effect
on SIF. The shape or configuration effect is
given by a factor Y such that
SIF for some of the standard geometry are shown
below
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What is Fracture Toughness? Fracture toughness is
a measure of the ability of a material to resist
the growth of a pre-existing crack or flaw. The
fracture toughness of a material is characterized
by the energy per unit area which is required to
create new crack surfaces, and thereby propagate
a crack through the material. This value is known
as the critical stress intensity factor. The
critical SIF at plane stress condition is denoted
by KC ( )
In practice we may attain KC by increasing either
s or a. For a defect of fixed length a, sC is the
critical value of the applied stress for
fracture. Alternatively, for a constant applied
stress s, aC is the critical defect size for
fracture.Note that KC is a macroscopic criterion
for failure. It makes no assumptions about the
precise mechanism of fracture. KIC is the
critical SIF at plane strain condition
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Typical Values of Fracture Toughness KIc
pure ductile metals 100--350 pressure vessel
steel 170 high strength steel 50--150
titanium alloys 50--110 GFRP, fibreglass
20--60 aluminium alloys 20--45 cast iron
6--20 reinforced concrete 10--15
polystyrene 2 silicon nitride 4--5 magnesia
3 granite 3 wood 1 glass 0.5 ice 0.2
Units are .
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Application of the Fracture Mechanics Approach
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A plate of width 1.4 m and length 2.8 m is
required to support a tensile load of 4 MN (in
the long direction). Inspection procedures are
capable of detecting through-thickness edge
cracks larger than 2.7 mm. The two titanium
alloys are being considered for this application.
(Alloy (A) KIC 115 MPa.m1/2 and sy910 MPa
alloy (B) KIC 55 MPa.m1/2 and sy1035 MPa. For
a factor of safety of 1.3 against yielding and
fracture, which one of the two alloys will give
the lightest weight solution?
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