A two-dimensional finite element method for simulating the constitutive response and microstructure of polycrystals during high temperature plastic deformation. (English) Zbl 1079.74634
Summary: We describe a finite element method designed to model the mechanisms that cause superplastic deformation. Our computations account for grain boundary sliding, grain boundary diffusion, grain boundary migration, and surface diffusion, as well as thermally activated dislocation creep within the grains themselves. Front tracking and adaptive mesh generation are used to follow changes in the grain structure. The method is used to solve representative boundary value problems to illustrate its capabilities.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74E15 | Crystalline structure |
| 74C99 | Plastic materials, materials of stress-rate and internal-variable type |
| 74F05 | Thermal effects in solid mechanics |
Keywords:
A. Grain boundaries; A. Creep; A. Diffusion; B. Polycrystalline material; C. Finite elementsReferences:
| [1] | Chandra, N., Constitutive behavior of superplastic materials, Internat. J. Non-Linear Mech., 37, 641-684 (2002) · Zbl 1346.74018 |
| [2] | Cocks, A. C.F., Interface reaction controlled creep, Mech. Mater., 13, 165-174 (1992) |
| [3] | Cuitino, A.; Ortiz, M., Computational modeling of single crystals, Model. Simul. Mater. Sci. Eng., 1, 255-263 (1992) |
| [4] | Frost, H.; Ashby, M. F., Deformation Mechanism Maps (1982), Pergamon Press: Pergamon Press Oxford |
| [5] | Hinton, E.; Campbell, J., Local and global smoothing of discontinuous finite element function using a least squares method, Int. J. Num. Meth. Eng., 6, 461-480 (1974) · Zbl 0286.73066 |
| [6] | Huang, Y.; Humphreys, F. J., Measurements of grain boundary mobility during recrystallization of a single phase aluminium alloy, Acta Mater., 47, 7, 2259-2268 (1999) |
| [7] | Hull, D.; Rimmer, D. E., The growth of grain boundary voids under stress, Phil. Mag., 4, 673-687 (1959) |
| [8] | Larche, F. C.; Cahn, J. W., The interactions of composition and stress in crystalline solids, Acta Metall., 33, 331-357 (1985) |
| [9] | Leo, P. H.; Sekerka, R. F., The effect of surface stress on crystal-melt and crystal-crystal equilibrium, Acta Metall., 37, 3119-3138 (1989) |
| [10] | Lohner, R., Some useful data structures for the generation of unstructured grids, Comm. Appl. Numer. Methods, 4, 123-135 (1988) · Zbl 0643.65075 |
| [11] | Molodov, D. A.; Czubayko, U.; Gottstein, G.; Shvindlerman, L. S., On the effect of purity and orientation on grain boundary motion, Acta Mater., 46, 2, 553-564 (1998) |
| [12] | Oden, J. T.; Reddy, J. N., Note on approximation method for computing consistent conjugate stresses in finite elements, Int. J. Numer. Methods Eng., 6, 55-61 (1973) · Zbl 0252.73057 |
| [13] | Padmanabhan, K. A.; Vasin, R. A.; Enikeev, F. U., Superplastic Flow: Phenomenology and Mechanics (2001), Springer: Springer Berlin |
| [14] | Pan, J.; Cocks, A. C.F., Computer simulation of superplastic deformation, Comput. Mater. Sci., 1, 95-109 (1993) |
| [15] | Peraire, M.; Vahdati, M.; Morgan, K.; Zienkiewicz, O. C., Adaptive remeshing for compressible flow computations, J. Comp. Phys., 72, 3855-3868 (1993) |
| [16] | Zhu, J. Z.; Zienkiewicz, O. C., Adaptive techniques in the finite element method, Comm. Appl. Numer. Methods, 4, 197-204 (1988) · Zbl 0633.73070 |
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