journal article·2008-02

Precise 3D crack growth simulations

W. Weber, P. Steinmann, G. Kuhn

International Journal of Fracture· Volume 149· Issue 2
Publisher page

Abstract

The continuous growth of 3D cracks under cyclic loading conditions is considered within a discrete simulation procedure. It is performed within the framework of linear elastic fracture mechanics. An incremental procedure is applied to consider the non-linear behavior of crack growth within the simulation. In each increment the direction and magnitude of the crack propagation for each point along the crack front are needed to define the new crack front. Within the present context the crack deflection results from the maximum tangential stress criterion and the crack extension is obtained by the evaluation of a crack propagation rate. To simulate the crack propagation as exactly as possible the evolution of the stress field between two consecutive crack fronts is taken into account. The analysis of the changing stress field is utilized for optimization of the predicted crack fronts. The whole procedure is realized in terms of a predictor–corrector scheme. Numerical examples are presented to demonstrate the benefits of this concept.
Source: expertdata · Quality: candidate unverified · Source record ↗

Research context

OpenAlex topics: Fatigue and fracture mechanics · Numerical methods in engineering · High-Velocity Impact and Material Behavior

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (37)

Show source-provided references
1. Dimitrov A, Andrä A, Schnack E (2001) Efficient computation of order and mode of corner singularities in 3D-elasticity. Int J Numer Meth Eng 52: 805–82710.1002/nme.230 ↗
2. Erdogan F, Ratwani M (1970) Fatigue and fracture of cylindrical shells containing a circumferential crack. Int J Fract Mech 6: 379–39210.1007/BF00182626 ↗
3. Erdogan F, Sih GC (1963) On the crack extension in plates under plane loading and transverse shear. J Bas Eng 85: 549–525
4. Forman RG, Mettu SR (1992) Behavior of surface and corner cracks subjected to tensile and bending loads in a Ti-6Al-4V alloy. ASTM STP 1131: 948–953
5. Forman RG, Kearney VE, Engle RM (1967) Numerical analysis of crack propagation in cyclic-loaded structures. J Bas Eng 89: 459–46410.1115/1.3609637 ↗
6. Frangi A, Novati G (2003) BEM-FEM coupling for 3D fracture mechanics applications. Comp Mech 32: 415–42210.1007/s00466-003-0510-8 ↗
7. Frangi A, Novati G, Springhetti R, Rovizzi M (2002) 3D fracture analysis by the symmetric Galerkin BEM. Comp Mech 28: 220–23210.1007/s00466-001-0283-x ↗
8. Griffith AA (1921) The phenomena of rupture and flow in solids. Philos Trans R Soc 221: 163–19810.1098/rsta.1921.0006 ↗
9. Helldörfer B, Kuhn G (2007) An efficient FEM/BEM approach for 3D crack propagation simulation. In: Runesson K, Diet P (eds) Proc of III Int Conf Adapt Mod Sim. Göteborg, 2007, pp 120–123
10. Heyder M (2006) Experimentelle und numerische Untersuchung der dreidimensionalen Ermüdungsrissausbreitung. ibidem-Verlag, Stuttgart
11. Heyder M, Kuhn G (2006) 3D fatigue crack propagation: experimental studies. Int J Fat 28: 627–63410.1016/j.ijfatigue.2005.06.052 ↗
12. Heyder M, Kolk K, Kuhn G (2005) Numerical and experimental investigations of the influence of corner singularities on 3D fatigue crack propagation. Eng Fract Mech 72: 2095–210510.1016/j.engfracmech.2005.01.006 ↗
13. Huber O, Dallner R, Partheymüller P, Kuhn G (1996) Evaluation of the stress tensor in 3-D elastoplasticity by direct solving of hypersingular integrals. Int J Numer Meth Eng 39: 2555–257310.1002/(SICI)1097-0207(19960815)39:15<2555::AID-NME966>3.0.CO;2-6 ↗
14. Irwin GR (1948) Fracture dynamics. In: Irwin GR, Kies JA (eds) Proc of ASM symposium on fracturing of metals. Cleveland, 1948, pp 147–166
15. Irwin GR (1957) Analysis of stresses and strain near the end of a crack traversing a plate. J Appl Mech 24: 361–36410.1115/1.4011547 ↗
16. Kolk K (2005) Automatische 3D-Rissfortschrittssimulation unter Berücksichtigung von 3D-Effekten und Anwendung schneller Randelementformulierungen. VDI-Verlang, Düsseldorf
17. Kolk K, Kuhn G (2005) A predictor–corrector scheme for the optimization of 3D crack front shapes. Fat Fract Eng Mater Struct 28: 117–12610.1111/j.1460-2695.2004.00838.x ↗
18. Kolk K, Kuhn G (2006) The advanced simulation of fatigue crack growth in complex 3D structures. Arch Appl Mech 76: 699–71010.1007/s00419-006-0092-y ↗
19. Kolk K, Weber W, Kuhn G (2005) Investigation of 3D crack propagation problems via fast BEM formulations. Comp Mech 37: 32–4010.1007/s00466-005-0695-0 ↗
20. Leblond JB, Torlai O (1992) The stress field near the front of an arbitrarily shaped crack in a three–dimensional elastic body. J Elast 29: 97–13110.1007/BF00044514 ↗
21. Li S, Mear ME, Xiao L (1998) Symmetric weak-form integral equation method for three-dimensional fracture analysis. Comp Meth Appl Mech Eng 151: 435–45910.1016/S0045-7825(97)00199-0 ↗
22. Mews H, Kuhn G (1988) An effective numerical stress intensity factor calculation with no crack discretization. Int J Fract 38: 61–7610.1007/BF00034276 ↗
23. Murakami Y (1987) Stress intensity factors handbook, Vol 1. pergamon press, Oxford
24. Nuismer RJ (1975) An energy release rate criterion for mixed mode fracture. Int J Fract 11: 245–25010.1007/BF00038891 ↗
25. Orowan E (1950) Fatigue and fracture of metals. MIT press, Cambridge, p 139
26. Paris PC, Erdogan F (1963) A critical analysis of crack propagation laws. J Bas Eng 85: 528–53410.1115/1.3656900 ↗
27. Paris PC, Gomez MP, Anderson WP (1961) A rational analytic theory of fatigue. Trend Eng 13: 9–14
28. Partheymüller P (1999) Numerische simulation der 3D-Rißausbreitung mit der randelementmethode. VDI-Verlang, Düsseldorf
29. Partheymüller P, Haas M, Kuhn G (2000) Comparison of the basic and the discontinuity formulation of the 3D-dual boundary element method. Eng Anal Bound Elem 24: 777–78810.1016/S0955-7997(00)00060-6 ↗
30. Plank R, Kuhn G (1999) Fatigue crack propagation under non-proportional mixed mode loading. Eng Fract Mech 62: 203–22910.1016/S0013-7944(98)00097-6 ↗
31. Pook LP (1995) On fatigue crack paths. Int J Fat 17: 5–1310.1016/0142-1123(95)93045-4 ↗
32. Portella A, Aliabadi MH, Rooke DP (1992) The dual boundary element method: effective implementation for crack problems. Int J Numer Meth Eng 33: 1269–128710.1002/nme.1620330611 ↗
33. Richard HA, Fulland M, Sander M (2005) Theoretical crack path prediction. Fat Fract Eng Mater Struct 28: 3–1210.1111/j.1460-2695.2004.00855.x ↗
34. Rungamornrat J (2006) Analysis of 3D cracks in anisotropic multi-material domain with weakly singular SGBEM. Eng Anal Bound Elem 30: 834–84610.1016/j.enganabound.2006.05.005 ↗
35. Russwurm S, Kuhn G (1991) Behandlung nichtlinearer Rißprobleme mittels BEM. ZAMM Zeitschrift für angewandte Mathematik und Mechanik 71(6): 608–611
36. Schillig R, Kuhn G (1992) Ermüdungsrißausbreitung bei gleichphasiger Mixed-Mode I+II Belastung. Materialwissenschaft und Werkstofftechnik 23: 139–14410.1002/mawe.19920230411 ↗
37. Smith DJ, Ayatollahi MR, Pavier MJ (2001) The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading. Fat Fract Eng Mater Struct 24: 137–15010.1046/j.1460-2695.2001.00377.x ↗