An adaptive space-time finite element model for oxidation-driven fracture. (English) Zbl 1068.74607
This paper presents an adaptive, space-time finite element model for oxidation-driven fracture. The model incorporates finite-deformation viscoplastic material behaviour, stress-enhanced diffusive transport of reactive chemical species and a cohesive interface fracture criterion. We describe in detail the variational formulation of the coupled system, with particular attention to stabilized discontinuous Galerkin formulations for the chemical diffusion and the material evolution equations.
We describe a new computational approach for simulating fracture that uses space-time finite elements to track continuous crack-tip motion. This provides an accurate representation of the deformation history in ductile fracture, as is required for the reliable integration of the evolution equations for history-dependent materials. The space-time model supports both transient and direct steady-state calculations. It promotes efficient computations by eliminating the need for extensive mesh refinement away from the current crack-tip location and by exploiting the temporal coherence available in problems formulated in a moving crack-tip frame.
An \(h\)-adaptive finite element procedure reveals the potential of the space-time model for controlling element distortion and maintaining solution accuracy. Numerical studies of mode-III fracture, plane-strain mode-I fracture and stress-enhanced diffusion illustrate the importance of stabilization and adaptivity for obtaining accurate and reliable solutions.
We describe a new computational approach for simulating fracture that uses space-time finite elements to track continuous crack-tip motion. This provides an accurate representation of the deformation history in ductile fracture, as is required for the reliable integration of the evolution equations for history-dependent materials. The space-time model supports both transient and direct steady-state calculations. It promotes efficient computations by eliminating the need for extensive mesh refinement away from the current crack-tip location and by exploiting the temporal coherence available in problems formulated in a moving crack-tip frame.
An \(h\)-adaptive finite element procedure reveals the potential of the space-time model for controlling element distortion and maintaining solution accuracy. Numerical studies of mode-III fracture, plane-strain mode-I fracture and stress-enhanced diffusion illustrate the importance of stabilization and adaptivity for obtaining accurate and reliable solutions.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74R20 | Anelastic fracture and damage |
| 74E40 | Chemical structure in solid mechanics |
| 74C20 | Large-strain, rate-dependent theories of plasticity |
References:
| [1] | Babuska, I.; Yu, D., Asymptotically exact a-posteriori error estimator for the biquadratic elements, (Tech. note BN-1050 (1986), Institute for Physical Science and Technology, Laboratory for Numerical Analysis, University of Maryland: Institute for Physical Science and Technology, Laboratory for Numerical Analysis, University of Maryland College Park, Maryland) · Zbl 0619.73080 |
| [2] | Baehman, P. L.; Shephard, M. S.; Flaherty, J. E., A-posteriori error estimator for triangular and tetrahedral quadratic elements using interior residuals, Int. J. Numer. Methods Engrg., 34, 979-996 (1992) · Zbl 0825.73837 |
| [3] | Bain, K. R.; Pelloux, R. M., Effect of environment on creep crack growth in PM/HIP René-95, Met. Trans., 15A, 381-388 (1984) |
| [4] | Barenblatt, G. I., Mathematical theory of equilibrium cracks in brittle fracture, Adv. Appl. Mech., 7, 55-129 (1962) |
| [5] | Berkovits, A.; Nadiv, S.; Shalev, G., Microstructural processes in high temperature low cycle fatigue of MAR-M200 + Hf, Acta Metall. Mater., 45, 2605-2613 (1995) |
| [6] | Bey, K. S.; Oden, J. T., hp-version discontinuous Galerkin methods for hyperbolic conservation laws, Comput. Methods Appl. Mech. Engrg., 133, 259-286 (1996) · Zbl 0894.76036 |
| [7] | Carranza, F. L.; Fang, B.; Haber, R. B., A moving cohesive interface model for fracture in creeping materials, Comput. Mech., 19, 517-521 (1997) · Zbl 1031.74519 |
| [8] | Chang, K.-M.; Henry, M. F.; Benz, M. G., Metallurgical control of fatigue crack propagation in superalloys, J. Metals Matls., 29-35 (1990) |
| [9] | Dugdale, D., Yielding of steel sheets containing slits, J. Mech. Phys. Solids, 8, 100-108 (1960) |
| [10] | Dwyer, D. J.; Pang, X. J.; Gao, M.; Wei, R. P., Surface enrichment of niobium on Inconel 718 (100) single crystals, Appl. Surf. Sci., 81, 229-235 (1994) |
| [11] | Ericsson, T., Review of oxidation effects on cyclic life at elevated temperature, Canadian Met. Quart., 18, 177-195 (1979) |
| [12] | Gao, M.; Wei, R. P., Grain boundary γ″ precipitation and niobium segregation in Inconel 718, Scripta Metall. Mater., 32, 987-990 (1995) |
| [13] | Gao, M.; Dwyer, D. J.; Wei, R. P., Niobium enrichment and environmental enhancement of creep crack growth in nickel-base superalloys, Scripta Metall. Mater., 32, 1169-1174 (1995) |
| [14] | Govindgee, S.; Simo, J. C., Coupled stress-diffusion: case II, J. Mech. Phys. Solids, 41, 863-887 (1993) · Zbl 0783.73057 |
| [15] | Hughes, T. J.R.; Franca, L. P.; Mallet, M., A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations, Comput. Methods Appl. Mech. Engrg., 73, 173-189 (1989) · Zbl 0697.76100 |
| [16] | Hughes, T. J.R., Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods, Comput. Methods Appl. Mech. Engrg., 127, 387-401 (1995) · Zbl 0866.76044 |
| [17] | Iacocca, R. G.; Woodford, D. A., The kinetics of intergranular oxygen penetration in nickel and its relevance to weldment cracking, Metall. Trans., 19A, 2305-2313 (1988) |
| [18] | Johnson, C., Numerical Solution of Partial Differential Equations by the Finite Element Method (1987), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0628.65098 |
| [19] | Kim, K. S.; Van Stone, R. H., Elevated temperature crack growth, Final Report, NASA CR-189191 (1992) |
| [20] | Lee, E. H., Elastic plastic deformations at finite strains, J. Appl. Mech., 36, 1-6 (1969) · Zbl 0179.55603 |
| [21] | Lee, H. S.; Haber, R. B., Eulerian-Lagrangian methods for crack growth in creeping materials, (Benson, D. J.; Asaro, R. A., Advanced Computational Methods for Material Modeling. Advanced Computational Methods for Material Modeling, PVP, Vol. 268 (1993)), 141-153 |
| [22] | Malvern, L. E., Introduction to the Mechanics of a Continuous Medium (1969), Prentice Hall: Prentice Hall Englewood Cliffs, NJ · Zbl 0181.53303 |
| [23] | Molins, R.; Andrieu, E., Analytical TEM study of the oxidation of nickel based superalloys, Journal de Physique IV, 3, 469-475 (1993) |
| [24] | Moran, B.; Ortiz, M.; Shih, F., Formulation of finite element methods for multiplicative finite deformation plasticity, Int. J. Numer. Methods Engrg., 29, 483-514 (1990) · Zbl 0724.73221 |
| [25] | Pang, X. J.; Dwyer, D. J.; Gao, M.; Valerio, P.; Wei, R. P., Surface enrichment and grain boundary segregation of niobium in Inconel 718 single- and poly-crystals, Scripta Metall. Mater., 31, 345-350 (1994) |
| [26] | Rich, J. R., Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation methanism, (Argon, A. S., Constitutive Equations in Plasticity (1975), MIT Press: MIT Press Cambridge, MA), 23-79 |
| [27] | Tvergaard, V.; Hutchinson, J. W., The relation between crack growth resistance and fracture process parameters in elastic-plastic solids, J. Mech. Phys. Solids, 40, 1377-1397 (1992) · Zbl 0775.73218 |
| [28] | Valerio, P.; Gao, M.; Wei, R. P., Environmental enhancement of creep crack growth in Inconel 718 by oxygen and water vapor, Scripta Metall. Mater., 30, 1269-1274 (1994) |
| [29] | Weber, G.; Anand, L., Finite deformation constitutive equations and a time integration procedure for isotropic hyperelastic-viscoplastic solids, Comput. Methods Appl. Mech. Engrg., 79, 173-202 (1990) · Zbl 0731.73031 |
| [30] | Wilson, R. K.; Aifantis, E. C., On the theory of stress-assisted diffusion, I, Acta Mecanica, 45, 273-296 (1982) · Zbl 0511.73126 |
| [31] | Woodford, D. A.; Bricknell, R. H., (Treatise on Materials Science and Technology, Vol. 25 (1983), Academic Press: Academic Press New York), 157 |
| [32] | Xu, X.-P.; Needleman, A., Numerical simulations of fast crack crack growth in brittle solids, J. Mech. Phys. Solids, 42, 1397-1434 (1994) · Zbl 0825.73579 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
