Method of determining the elastoplastic behavior of components consisting of anisotropic material and use of the method
View Patent ↗A method of determining the elastoplastic behavior of components, in particular of gas turbine plants, at high temperatures. First of all, the linear-elastic behavior is determined and the inelastic behavior is taken into account on the basis of the linear-elastic results by using the Neuber rule, the anisotropic characteristics of the components, as occur in particular through the use of single-crystalline materials, are taken into account in a simple manner by using a modified anistropic Neuber rule in the form σ * 2 = σ ep 2 ( 1 + A C α E R ( A σ ep 2 σ 0 2 ) n - 1 ) where A=inelastic anisotropic correction term, A = 1 2 [ F ( D yy - D zz ) 2 + G ( D zz - D xx ) 2 + H ( D xx - D yy ) 2 + 2 L D yz 2 + 2 MD z x 2 + 2 ND x y 2 ] where F, G, H, L, M and N are the Hill constants, C=elastic anisotropic correction term, C= D • E −1 • D σ *=determined linear stress, σ ep =estimated inelastic stress, D =direction vector of the elastic and inelastic stresses E −1 =inverse stiffness matrix, E R =reference stiffness, σ 0 =reference stress, and σ α, n=material constants.
1. A method of determining the elastoplastic behavior of components at high temperatures, the method comprising:
determining the linear-elastic behavior; and
determining the inelastic behavior based on the determined linear-elastic by using a Neuber rule;
wherein, to take into account anisotropic characteristics of the components,, said Neuber rule comprises a modified anisotropic Neuber rule of the form
σ
_
*
dev
ɛ
_
*
(
σ
_
*
dev
)
=
σ
_
*
dev
E
_
_
-
1
σ
_
*
dev
=
σ
_
ep
dev
E
_
_
-
1
σ
_
ep
dev
+
σ
_
ep
dev
·
∂
σ
v
,
ep
2
∂
σ
·
α
E
R
(
σ
v
,
ep
2
σ
0
2
)
n
-
1
wherein
σ *dev =deviator of the determined linear stress
ε ( σ *dev )=determined linear strain
σ dev ep =estimated inelastic stress,
σ v,ep =Hill elastic-plastic equivalent stress,
E −1 =inverse stiffness matrix,
E R =reference stiffness,
σ 0 =reference stress, and
α, n=constants.
2. The method as claimed in claim 1 , characterized in that, for the quantities σ *dev and σ dev ep , the following equations are used:
σ *dev = D ·√{square root over (σ *2 )}
and
σ
_
ep
dev
=
D
_
·
σ
ep
2
where D designates a direction vector of the length l with deviatoric characteristics, and in that the modified Neuber rule is used in the form
σ
*
2
=
σ
ep
2
(
1
+
A
C
α
E
R
(
A
σ
ep
2
σ
0
2
)
n
-
1
)
with the anisotropic inelastic correction term
A
=
1
2
[
F
(
D
yy
-
D
zz
)
2
+
G
(
D
zz
-
D
xx
)
2
+
H
(
D
xx
-
D
yy
)
2
+
2
LD
yz
2
+
2
MD
zx
2
+
2
ND
xy
2
]
and the anisotropic elastic correction term
C = D · E −1 · D
and
wherein the Hill parameters are designated by F, G, H, L, M, and N.
3. The method as claimed in claim 2 , further comprising:
solving the equation according to the modified Neuber rule with an iterative process.
4. The method as claimed in claim 1 , comprising:
determining the service life of gas turbine components under cyclic loading.
5. The method as claimed in claim 1 , wherein said components comprise components of a gas turbine plant.
6. The method as claimed in claim 1 , wherein said components comprise single-crystalline materials.
7. The method as claimed in claim 3 , wherein said iterative process comprises a Newton iteration.