FE Assignment C04 - Division of Solid Mechanics

FEM exercises TMHL17 Material Mechanics
IV. Plasticity: viscoplasticity/creep
1. Overview; background theory
Viscoplasticity is important in applications where high temperature can make time-dependent
deformation develop. Examples are components in gas turbines, aeroengines, steam power plants and
components in high-temperature metal processing plants. To name a further, rather extreme example,
glacier ice creeps, causing the glacier movement that can be recorded by observations over decades of
years.
The temperature at which time-dependent deformation starts to become important (usually noted )
depends, of course, on the material. In stainless steel, is of the order of 350 °C and in nickel-based
alloys 500 °C.
2. Description of problem
Fig. 1 2 stage turbine rotor

Fig. 1 shows a drawing of a turbine rotor, consisting of two turbine discs mounted together by 8 bolts
(2 of which can be seen in the drawing). A conceptual study is to be done in order to investigate if it
would be possible to change the design and replace the 8 bolts with one (larger) centre bolt instead and
if the bolt in that case can be made from the material X22CrMoV12-1.
3. Exercise parts
A FE model of the geometry has already been set up (see Fig. 2). The Abaqus .inp file containing the
model can be downloaded from the course homepage.
Fig. 2 FE model of the conceptual centre-bolt design
Tasks
a) Compute the metal temperatures in the turbine rotor during service (steady state). Heat
transfer coefficients and sink temperatures are shown in Fig. 3
b) Make an elastic analysis to compute the stress in the centre bolt in service if the pretension in
the bolt is 60 % of R p0.2 at room temperature. Mechanical boundary conditions and materials
are shown in Fig. 4.
c) Compute how much of the bolt pretension is left after 30 000 h service (after viscoplastic
relaxation in the bolt).
How much are the contact forces between the discs lowered by the bolt relaxation?

Fig 3 Heat transfer coefficients (HTC) and sink temperatures (T)
Table 1 Rp0.2 for X22CrMoV12-1 according to DIN 17240:1976-07:
Table 2 Relaxation and creep data (DIN 17240:1976-07)

Fig4 Mechanical boundary conditions and materials
Modelling notes
If one assumes that the creep strain can be modelled by a Norton equation
A
B
it can be shown that the relaxed stress after t (h) is:
1
1B
E A
Bt1
B
0
1
,
where E is the elastic modulus and σ 0 is the initial stress. Curve fitting for temperatures up to 460º
gives
B 1.6363e2
2.1087e
1*
T 273.15
6.0093e5
ln( A ) 7.5547e2
,
T 273.15
where T is the temperature in ºC. The stress is given in MPa and the time t in h.
(It may happen that a *CREEP routine must be written, since there will be very low values of A,
which the standar Abaqus data routines may not accept)