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A NUMERICAL PROCEDURE FOR CALCULATION OF STRESS
INTENSITY FACTORS AND ITS USE FOR LIFE ASSESSMENT OF
STEAM TURBINE HOUSING OF THERMAL POWER PLANT
G. Jovičić, M. Živković, M. Kojić, S. Vulović
Faculty of Mechanical Engineering, Kragujevac, Serbia and Montenegro
INTRODUCTION
Studies of fracture mechanics emerged in the early twentieth century. Among a num-
ber of researchers, Griffith’s idea of “minimum potential energy” provided a foundation
for all later successful theoretical studies of fracture, especially for brittle materials. But it
was not until after World War II that fracture mechanics developed as a discipline.
Derived from Griffith’s theorem, the concept of energy release rate,
G
, was first intro-
duced by Irwin, in a form more useful for engineering applications. Irwin defined an
energy release rate or the crack extension force tendency which can be determined from
stress and displacement fields in the vicinity of the crack tip rather then from an energy
balance for elastic solid as a whole, as Griffith suggested.
Conservation integrals in elasticity have been widely applied to fracture mechanics,
among which the
J
integral is the most popular one. The
J
integral is path independent for
elastic solids, and can be shown that the integral is identical to Irwin’s energy release rate
associated with the collinear extension of a crack in elastic solid [1].
1. DETERMINATION OF FRACTURE PARAMETERS IN THE PAK PROGRAM
1.1. Equivalent domain integral method (EDI)
Rice [1] defined a path-independent
J
-integral for two-dimensional crack problems in
linear and nonlinear elastic materials. As shown in Fig. 1,
J
is the line integral surround-
ing a two-dimensional crack tip and is defined as
1
1
,1
0
lim (
)
S
S
j
ij i
j
J
W u n
δ
σ
Γ → Γ
=
−
∫
d
Γ
,
i
,
j
= 1,2
(1)
where
W
is the strain energy density given by
1
1
2
2
ij ij
ijkl kl ij
W
C
σ ε
ε ε
=
=
(2)
and
n
j
is the outward normal vector to the integration contour
Γ
g
around the crack tip
(Fig. 1),
σ
ij
is the stress tensor,
ε
ij
is the strain tensor,
C
ijkl
is the constitutive tensor and
u
i
are components of the displacement vector.
Knowles and Stenberg [2] noted that this can be considered as the first component of a
vector
,
0
lim (
)
S
S
k
kj
ij i k j
J
W u n
δ
σ
Γ → Γ
=
−
∫
d
Γ
,
i
,
j
,
k
= 1,2
(3)
which is also path independent.
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