iter structural design criteria for in-vessel components (sdc-ic)

ITER G 74 MA 8 01-05-28 W0.2
BÊ2550.2 Stress Intensity range - Octahedral shear stress theory
The general procedure for calculating the stress intensity range using the octahedral shear
stress (Von Mises) yield theory is as follows:
1) At each instant (t) of the cycle concerned, calculate the components of the stress
tensor s(t) at the point in question.
2) Calculate the tensor which represents the stress difference s(t, t') for each pair (t),
(t') of the cycle. The components of the tensor s(t, t') are equal to the difference
between the components of the tensors s(t) and s(t'):
s(t, t') = s(t) - s(t')
3) Using ICÊ3224.4.3, calculate the stress intensity s( tt , © ) of tensor s(t, t'):
{
2
[ 11 22 ] + [ 22 ( ) - 33(
) ]
( ) = ( ) - ( )
s tt ,© 12.
s tt ,© s tt ,© s tt ,© s tt ,©
Simplification:
[ s33 tt ,© s11
tt ,© ]
+ ( ) - ( )
6 [ s12 tt ,© s tt ,© s tt ,© ]}
2
2
23 31
2
+ ( ) + ( ) + ( )
2
If the principal directions of the stress tensors s(t) remain fixed with time, the
stress intensity s tt , ©
the stress deviator s(t):
s t s t s t s t s t 3
( ) is expressed as a function of the principal components of
[ ]
( ) = ( ) - ( ) + ( ) + ( )
1 1 1 2 3
[ ]
( ) = ( ) - ( ) + ( ) + ( )
s t s t s t s t s t
2 2 1 2 3
[ ]
( ) = ( ) - ( ) + ( ) + ( )
s t s t s t s t s t
Then
3 3 1 2 3
2
2
( ) = ( ( ) - ( ) ) + ( ( ) - ( ) ) + ( ( ) - ( ) )
s t,© t . s t s t© s t s t© s t s t©
SDC-IC, Appendix B. Guidelines for Analysis page 14
3
3
{ 2 2
3 3 }
32 1 1
12
2
2 12
4) For the cycle concerned, the stress intensity range denoted by Ds is equal to the
greatest of the quantities s( tt , © ) calculated for each pair of instants (t) and (t') of
the cycle:
Ds Max
tt ,©
s
[ ]
= ( tt ,© )
( )
The search for the maximum value can be made easier if one of the two instants
defining the cycle is fixed. If tA is taken as the fixed instant, the stress range is