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40
n
Yo
Yo
Yvo
ε
σ
σ
α
ε
σ
σ
⎛
⎞
= + ⎜
⎟
⎝
⎠
1
n
n
e
pl
n
Yo
E
E F
σ
σ
σ
ε
σ
σ
ε
ε
σ
⎛ ⎞
= +
= + = +
⎜ ⎟ ⎜ ⎟
⎝ ⎠
(31)
5.2. Procedure for
J
evaluation using EPRI handbook
J
- integral calculations based on HRR solution is developed for different cases from
General Electric Company and publish in form of Electric Power Research Institute
(EPRI) Handbook in 1981 year. Calculation is based on separate elastic and full plastic
solutions calculation that are than combined to become end results in form
J
tot
=
J
el
+
J
pl
(32)
where the elastic part is based on elastic stress intensity factor for effective crack size
a
eff
:
( )
2
'
eff
I
el
K a
J
E
=
(33)
However, the correction of the crack size based on plastic zone radius is very often
neglected, because of the low difference of only 5 % or less.
For the calculation of plastic part Eqs. (16) and (17) are rewritten to obtain
( )
1 1 ~
,
n n
ij
ij
o o n
o
J
I r
n
σ
αε σ
σ
θ
σ
+ +
⎛ ⎞
=
⎜ ⎟
⎝ ⎠
(34)
Since the nominal stress changes proportional to the load change in a structure, it is
1
n
o o
o
P
J
hL
P
αε σ
+
⎛ ⎞
=
⎜ ⎟
⎝ ⎠
(35)
Here is the parameter
h
dimensionless and depends on the geometry and material
curve exponent
n
;
L
is characteristic length of the structure and
P
0
characteristic loading
of the structure.
L
and
P
0
can be defined arbitrary and
h
is determined based on numerical
analysis in dependence on configuration which is examined. EPRI-Handbook contains
detailed data tables for many characteristic cases.
5.3. Failure assessment diagram (FAD)
Previous assessment methods that consider only fracture mechanics parameters like
J
and
δ
, are independent on yielding conditions and plastic collapse of the structure. For that,
starting from two limiting cases, methods are developed that combine corresponding
criteria of pure brittle and pure ductile failure in form of Failure Assessment diagrams
(FAD). Because of complex behaviour, solutions for real conditions, between these two
limiting cases, are only possible through the interpolation or approximation. Accordingly,
FAD in its classical, simplest form is based on interpolation between two independent
solutions: failure due to the crack, predicted based on LEFM and failure due to the plastic
collapse in critical section that is predicted with plastic analysis.