Fatigue Crack Paths 2003

SIFs F O RC Y L I N D R I CAANLDS P H E R I CSAHLE L L S

Cylindrical Shell underInternal Pressure

The actual hoop stress distribution, 610,10”), in an unnotched cylinder (R1 = 00, R2 = 25

m m , r = <><>) under an internal pressure p can be written as follows [1 l]:

_ p (R. —02 “WM-R;-(R.-t>2i2

R5

6 (i

“i

For a longitudinal surface flaw, an approximate expression of the dimensionless SIF,

K >kl(p,cu) ’

along the crack front can be determined through the superposition principle

(see Eq.4, [8]) :

1

5

Z Bn(p,cu) K*I(n)

(7)

K

i

*

:

101.611)

%fmcu)H20

where o'reflp’cu) = p R /t is the well-known uniform hoop stress in a thin-walled pipe

under internal pressure (R = meanradius of the cylinder), and the coefficients Bnumu)

(see Eq. 5) are listed in Table 1.

Table 1. Coefficients of series expansion for a cylindrical shell under an internal pressure.

(R2 —02

R2

r (R —02

R2

"P’ > W 1e —(a —02 (R. +w-ar

“W” R; —0. —02 (R. —a)2 i

Bl

: _ 2 P(R2 ‘02 _

R22

_a

B2 = 3P (R2 _t)2 _

R22

_a2

(PM)

R2 —(R2 _I)2 (R, _..)3

W") R; —(R. —02 (R. —a)“

B I L i i w g B = M R? _a4 _

3 (My)

R22 _(R2 ‘02 (R2 _a)5

4 (Wu)

R22 _(R2 _t)2 (R2 _a)6

B ( )_ _6P(R2_t)2_ R22

_a5

5 p,cu _ R 2 _ ( _Rt)2 (R _ a ) 7 2 2 2

In the case of a notched cylindrical shell, the analytical solution for the hoop stress

distribution 610,96) (w) is not available. Therefore, o'1(p’c)(w) must numerically be

computed in order to obtain the coefficients Bnmc). The reference stress can

conveniently be defined as o'ref(p,c) : pR/t', and the dimensionless SIF, K *up’c), can

be obtained from an expression similar to Eq. 7, where the subscript cu is replaced by c.