ABAQUS user subroutines for the simulation of viscoplastic - loicz

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W internal variable, eq. (20b) fourth order tensors < 4> Ai < 4> I < 4> P , ε Pεe < 4> R < 4> S < 4> T operations ab = a i b j e i e j a ⋅ b = a ib i 8 material tensors (i = 1, 2, 3, 4, 5), eqs. (21a-e) identity tensor positive spectral projection operator for total and elastic strain tensor, eqs. (10a,b) lattice tensor, eq. (5) damage characteristic tensor, eq. (3a) positive projection operator, eq. (12) AB = A ij B kl e ie ke je l A ⋅ B= A ijB jk e ie k A : B= A ij B ji tensor product of two vectors scalar product of two vectors tensor product of two (second order) tensors scalar product of two (second order) tensors double scalar product of two (second order) tensors A = A 2 = A ij A ji EUKLIDean norm of second order tensor < 4> C : A = C A e e ijkl kl i j double scalar product of a fourth and a second order tensor
1. Introduction A CDM (continuum damage mechanics) based anisotropic damage model has been established by QI and BERTRAM to describe the anisotropic development of material damage in single crystals [QI & BERTRAM, 1997; QI, 1998; QI & BERTRAM, 1999; QI, BROCKS & BERTRAM, 2000] and in isotropic material [QI & BROCKS, 2000a, b, c]. Using the effective stress concept of CDM, this model can be coupled with any continuum mechanics model by introducing an adequately defined "effective stress tensor". The resulting model is then able to describe the deformation behaviour with respect to anisotropic material damage including lifetime predictions. The unified viscoplastic model proposed by BODNER & PARTOM [1975] and by CHABOCHE [CHABOCHE & ROUSSELIER, 1983] for polycrystal alloys and the creep model suggested by BERTRAM & OLSCHEWSKI [1996] for single crystal alloys, respectively, are chosen for coupling with the damage model. The resulting models have been implemented into subroutines of the FE-code ABAQUS as "user-defined material models" (UMAT) and can be used to perform FE computations on structural components of poly and single crystals. This report gives a brief description of the models and presents some results of FE-analyses using the respective UMATs. Materials used for the analyses are the Ni-based superalloy IN738 LC, the Ni-based single crystal SRR99 and a TiAl intermetallic alloy. 2. The CDM-based anisotropic damage model Damage of materials is a progressive process ending in final fracture. A natural characteristic of material damage is that the damage generally develops anisotropically. A second-order symmetric tensor D is chosen in the present models as damage variable for the description of the anisotropic damage. According to the effective stress concept of CDM, the effect of stresses and damage on the deformation behaviour can be represented by an adequately defined effective stress. This effective stress tensor is defined as ˜ S = (I − D) −1 2 ⋅S⋅ (I − D) −12 , (1) 9
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 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 24 and 25: 24 Fig. 5. Contour plots of directi
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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