ABAQUS user subroutines for the simulation of viscoplastic - loicz

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24 Fig. 5. Contour plots of direction cosine and of the maximum principal damage for β = 0.1.
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. 25
Page 1 and 2: Technical Note GKSS/WMS/01/5 intern
Page 4 and 5: 0. Nomenclature 3 1. Introduction 7
Page 6 and 7: R ∞ Wi Z I , Z D Zij 6 saturated
Page 8 and 9: W internal variable, eq. (20b) four
Page 10 and 11: where S is the CAUCHY stress tensor
Page 12 and 13: 12 0 for x ≤ xm 1 h(x) = 2 1− c
Page 14 and 15: flow rule: E Ý i = p Ý ˜ S ′
Page 16 and 17: 16 −1 −1 D1 = 0 , L1 = 0, Z i1
Page 18 and 19: parameters of Tables 2 and 3, and t
Page 20 and 21: 20 Fig. 1. Experiments and model pr
Page 22 and 23: 22 Fig. 3. Contour plots of the max
Page 26 and 27: 26 Fig. 6. FE-mesh and loading cond
Page 28 and 29: 28 Fig. 13. FE-mesh and loading con
Page 30 and 31: proove that the model performs well
Page 33 and 34: 6. References AI, S.H.; LUPINC, V.
Page 35 and 36: 7. Appendices: ABAQUS-Inputfiles 7.
Page 37 and 38: ** auflagerung ** *BOUNDARY, OP=NEW
Page 39 and 40: ** E, nu, Do, n, K1, K2, K3, m1 149
Page 41 and 42: ** ====== 2. load ein ** *STEP, INC
Page 43 and 44: 7.3 Appendix 3: Single crystal plat
Page 45 and 46: *NODE FILE, FREQUENCY=0 *EL FILE, F
Page 47 and 48: 7.4 Appendix 4: TiAl turbine blade
Page 49 and 50: *AMPLITUDE, NAME=CYCLEONE, DEFINITI

ABAQUS user subroutines for the simulation of viscoplastic - loicz

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