ABAQUS user subroutines for the simulation of viscoplastic - loicz

5.2 Plate containing a hole — BODNER-PARTOM model coupled with damage
The material parameters of the BODNER-PARTOM model of IN 738 LC at 850 °C have also been
determined by OLSCHEWSKI et al. [1990], and their values at 850 °C are shown in Table 4. The
material parameters of the damage model are the same as listed in Table 3.
E 149650 MPa ν 0.33 K0 4.18 10 5 MPa
D0
8.82 10 9 h -1
n 0.289 K1 3.76 10 5 MPa
A1=A2 1.65 10 -7 MPa/h m1 0.581 K2 3.07 10 5 MPa
r1=r2 5.4 m2 0.344 K3 1.54 10 5 MPa
Table 4: Material parameters of the BODNER-PARTOM model for IN 738 LC at 850 °C.
In gas turbine blades with cooling channels, stress concentration occurs due at these channels. A
square plate with a central circular hole is therefore chosen as a model representation of the area of
blades where the air cooling channels are located. The FE model used for the calculation is shown in
Fig. 6. First, the plate is subjected to a creep load of σ3 = 180 MPa. After 40000 hours the maximum
damage reaches a value of about 0.1. A second load of σ2 = 180 MPa is then applied. There is only
one element in the thickness direction so that any gradient over the thickness can not be captured. The
three-dimensional 8-node linear brick continuum element with reduced integration, C3D8R, from the
element library of ABAQUS is used, and geometric non-linearity has been considered. Figs. 7 and 8
show the contour plot of the maximum principal damage after 40000 h and 98000 h, respectively. β is
assumed to be 0.5. Distribution of the maximum principal value of the strain and stress, after 40000 h
and 98000 h, are shown in the Figs. 9-12, respectively. The ABAQUS input-file used for the
computation is given in the Appendix 2.
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