×

zbMATH — the first resource for mathematics

Modeling mixed-mode dynamic crack propagation using finite elements: Theory and applications. (English) Zbl 0663.73074
Previous work in modeling dynamic fracture has assumed the crack will propagate along predefined mesh lines (usually a straight line). In this paper we present a finite element model of mixed-mode dynamic crack propagation in which this constraint is removed. Applying linear elasto- dynamic fracture mechanics concepts, discrete cracks are allowed to propagate through the mesh in arbitrary directions. The fracture criteria used for propagation and the algorithms used for remeshing are described in detail. Important features of the implementation are the use of triangular elements with quadratic shape functions, explicit time integration, and interactive computer graphics. These combine to make the approach robust and applicable to a broad range of problems.
Example analyses of straight and curving crack problems are presented. Verification problems include a stationary crack under dynamic loading and a propagating crack in an infinite body. Comparisons with experimental data are made for curving propagation in a cracked plate under biaxial loading.

MSC:
74R05 Brittle damage
74S05 Finite element methods applied to problems in solid mechanics
Software:
Hondo
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Achenbach, J. D.; Bazant, Z. P. (1975): Elastodynamic near-tip stress and displacement fields for rapidly propagating cracks in orthotropic materials. J. Appl. Mech. 18/1, 1-22 · Zbl 0313.73084
[2] Atluri, S. N.; Nishioka, T. N. (1985): Numerical studies in dynamic fracture mechanics. Int. J. Fracture 27, 245-261 · doi:10.1007/BF00017971
[3] Barsoum, R. S. (1977): Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements. Int. J. Num. Meth. for Eng. 9, 495-507 · Zbl 0348.73030
[4] Bathe, K.-J. (1982): Finite element procedures in engineering analysis. New Jersey: Prentice-Hall
[5] Belytschko, T.; Hughes, T. R. (eds.) (1983): Computational methods for transient analysis. Amsterdam: North-Holland · Zbl 0521.00025
[6] Broberg, K. B. (1951): The moving griffith crack. Phil. Mag. 42, 739-750 · Zbl 0043.23504
[7] Chen, Y. M.; Wilkins, M. L. (1977): Numerical analysis of dynamic Crack Problems. Elastodynamic crack problems. Leyden: Noordhoff
[8] Dadkhah, M. S. (1984): Dynamic fracture under the influence of biaxial state of stress. Master’s Thesis, Mech. Eng., University of Washington
[9] Freund, L. B. (1972a): Crack propagation in an elastic solid subjected to general loading-I. Constant rate of extension. J. Mech. Phys. Solids 20, 129-140 · Zbl 0237.73099 · doi:10.1016/0022-5096(72)90006-3
[10] Freund, L. B. (1972b): Crack propagation in an elastic solid subjected to general loading-II. Non-uniform rate of extension. J. Mech. Phys. Solids 20, 141-152 · Zbl 0237.73099 · doi:10.1016/0022-5096(72)90007-5
[11] Freund, L. B. (1973): Crack propagation in an elastic solid subjected to general loading-III. Stress wave loading. J. Mech. Phys. Solids 21, 47-61 · Zbl 0265.73080 · doi:10.1016/0022-5096(73)90029-X
[12] Freund, L. B. (1974): Crack propagation in an elastic solid subjected to general loading-III. Stress wave loading. J. Mech. Phys. Solids 22, 137-146 · Zbl 0276.73046 · doi:10.1016/0022-5096(74)90021-0
[13] Freund, L. B.; Clifton, R. J. (1974): On the uniqueness of plane elastodynamic solutions for running cracks. J. Elasticity 4 293-299 · Zbl 0295.73015 · doi:10.1007/BF00048612
[14] Hawong, J. S.; Kobayashi, M. S.; Dadkhah, M. S.; Kang, S. J.; Ramulu, M.: Dynamic crack curving and branching under biaxial loading. Office of Naval Res., Tech. Rpt. No. UWA/DME/Tr-85/50
[15] Henshell, R. D.; Shaw, K. G. (1975): Crack tip finite elements are unnecessary. Int. J. Numer. Meth. in Eng. 12, 93-99 · Zbl 0306.73064
[16] Jung, J.; Ahmad, J.; Kanninen, M. F.; Popelar, C. H. (1981): Finite element analysis of dynamic crack propagation. Failure prevention and reliability, Proc. of the design engineering technical conference sponsored by the reliability stress analysis and failure prevention committee, the design engineering division of ASME, Hartford, Conn.
[17] Key, S. W.; Beisinger, Z. E.; Krieg, R. D. (1978): Hondo II ? A finite element computer program for the large deformation dynamic response of axisymmetric solids. SAND78-0422, Sandia National Laboratories, Alburquerque, NM.
[18] Kobayashi, A. S.; Emery, A. S.; Mall, S. (1976): Dynamic-finite-element and dynamic-photoelastic analyses of two fracturing homalite-100 plates. Exper. Mech. 16/9, 321-328 · doi:10.1007/BF02330248
[19] Koh, H. M.; Haber, R. B. (1986): A mixed Eulerian-Lagrangian model for the analysis of dynamic fracture. UILU-ENG86-2003, University of Illinois, Urbana, Ill. · Zbl 0607.73016
[20] Metcalf, J. T.; Kobayashi, T. (1986): Comparison of crack behavior in homalite 100 and araldite B. Crack arrest methodology and applications, ASTM STP 711, Hahn, G. T.; Kanninen, M. F. (eds.), Amer. Soc. of Testing and Materials, 128-145
[21] Nilsson, F. (1972): Dynamic stress-intensity factors for finite strip problems. Int. J. Fracture Mechanic 8/4, 403-411
[22] Nishioka, T.; Atluri, S. N. (1980a): Numerical modeling of dynamic crack propagation in finite bodies, by moving singular elements-part 1: Formulation. J. Appl. Mech. 47, 570-576 · Zbl 0441.73131 · doi:10.1115/1.3153733
[23] Nishioka, T.; Atluri, S. N. (1986b): Numerical modeling of dynamic crack propagation in finite bodies by moving singular elements ? part 2: Results. J. Appl. Mech. 47, 577-582 · Zbl 0441.73132 · doi:10.1115/1.3153734
[24] Nishioka, T.; Atluri, S. N. (1983): Path-independent integrals, energy release rates and general solutions of near-tip fields in mixed-mode dynamic fracture mechanics. Eng. Frac. Mech. 18/1, 1-22 · doi:10.1016/0013-7944(83)90091-7
[25] Radok, J. R. M. (1956): On the solution of problems of dynamic plane elasticity. Q. Appl. Mathem. 14, 289-298 · Zbl 0072.41203
[26] Rosakis, A. J.; Duffy, J.; Freund, L. B. (1984): The determination of dynamic fracture toughness of AISI 4340 steel by the shadow spot method. J. Mech. Phys. Solids 31/3, 251-260
[27] Rossmanith, H.P. (1983): How mixed-mode crack propagation? A dynamic photoelastic study. J. Mech. Phys. Solids 31/3, 251-260 · doi:10.1016/0022-5096(83)90025-X
[28] Sih, G. C.; Chen, E. P. (1977): Cracks moving at constant velocity and acceleration. Elastodynamic crack problems. Leyden: Noordhoff
[29] Shaw, R. D.; Pitchen, R. G. (1978): Modifications to the Suhara-Fukuda method of network generation. Int. J. Numer. Meth. Eng. 12, 93-99 · Zbl 0367.73074 · doi:10.1002/nme.1620120110
[30] Swenson, D. V. (1986): Derivation of the near-tip stress and displacement fields for constant velocity crack without using complex functions. Tech. note in Eng. Fract. Mech. 18/1, 1-22
[31] Swenson, D.V. (1985): Modeling mixed-mode dynamic crack propagation using finite elements. Dept. Struct. Eng. Rpt. No. 85-10, Civil and Environmental Engineering, Cornell University, Ithaca, NY
[32] Swenson, D. V. (1986): On using combined experimental/analysis to generate dynamic critical stress intensity data. Presented at 19th national symposium on fracture mechanics, June 30?July 2, San Antonio, Texas. ASTM STP (to be publ.)
[33] Thau, S. A.; Lu Tsin-Ywei (1971): Transient stress intensity for a finite crack in an elastic solid caused by a dilatational wave. Int. J. Solids and Struct. 7, 731-750 · Zbl 0227.73166 · doi:10.1016/0020-7683(71)90090-4
[34] Valliappan, S.; Marti, V. (1985): Automatic remeshing technique in quasi-static and dynamic crack propagation. Proc. of the NUMETA 1985 Conference, Swansea, January 7-11
[35] Yoffe, E. H. (1951): The moving griffith crack. Philosophical Magazine 42, 739-750 · Zbl 0043.23504
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.