Introduction to Fracture Mechanics phần 6 ppt

For Mode I:
Plane Stress:
E
K
I
2


Plane Strain:
16
Plane Strain:
 
2
2
1


E
K
I
For the general 3-D case, plane strain and anti-plane
strain loading:
 
22
22
1
1







K
EE
KK


17
For the plane stress case (combination Mode I and
Mode II):
E
KK
22




K Dominance
Domain of validity
There exists an annular zone where the K solution
is valid:
18
The inner radius is given by r
p
(plastic zone size).
The outer radius, r
0
, is the radial distance at which
the approximate, asymptotic singular solutions
deviate significantly (say, by more than 10%)

from full elasticity solutions which include higher
order terms. It is found that,
19
ar 1.0
0

where is the crack length.
a
Example Problem
Size Requirements
Consider a low strength steel with σ
ys
=350 MPa,
K
Ic
=250 MPa and E = 210 GPa. What are the
Minimum specimen size requirements for a valid
K
Ic
measurement?
m
20
Example Problem
Size Requirements
K
Ic
Test
ASTM standard E399 (1974) for K
Ic
testing (specimen

dimensions large compared to plastic zone):
2
5
.
2
,
,







Ic
K
B
b
a

21
5
.
2
,
,








ys
B
b
a

Substitute the known values for σ
ys
and K
Ic
. Find that


inchesmBba 50!28.1,,

