Abstract
The work deals with the application of the methods of analytic constraints and analytic elements in modeling stress fields near the tips of cracks and V-notches in elastic bodies. Both methods are based on the combined application of some analytic solutions for stress concentrators and the finite-element method. By using the proposed approach, we perform the numerical analysis of singular stresses formed in plates containing cracks or angular notches under the action of loads of various types.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
M. H. Aliabadi and D. P. Rooke, Numerical Fracture Mechanics, Comput. Mech. Publ., Southampton (1991).
S. N. Atluri (editor), Computational Methods in the Mechanics of Fracture, North-Holland, Amsterdam (1986).
K. Y. Lin and P. Tong, “Singular finite elements for the fracture analysis of V-notched plate,” Int. J. Num. Meth. Eng., 15, 1343–1354 (1980).
A. Seweryn, “Modelling of singular stress fields using finite element method,” Int. J. Solids Struct., 39, 4787–4804 (2002).
D. M. Tracey, “Discussion of ‘On the use of isoparametric finite element in linear fracture mechanics’ by R. S. Barsoum”,” Int. J. Num. Meth. Eng., 11, 401–402 (1977).
C. L. Chow and K. J. Lan, “On crack surface displacement approaches of finite-element analysis in evaluating stress intensity factors,” Int. J. Fract., 12, 488–490 (1976).
V. A. Vaishtok, “Comparison of two numerical methods for the evaluation of stress intensity factors,” Probl. Prochn., 9, 80–82 (1977).
T. K. Hellen, “On the method of virtual crack extensions,” Int. J. Num. Meth. Eng., 9, 187–207 (1975).
Z. J. Yang, J. F. Chen, and G. D. Holt, “Efficient evaluation of stress intensity factors using virtual crack extension technique,” Comput. Struct., 79, 2705–2715 (2001).
G. P. Cherepanov, Mechanics of Brittle Fracture, McGraw-Hill, New York (1979).
H. Ishikawa, H. Kitagawa, and H. Okamura, “J-integral of a mixed-mode crack and its application,” in Proc. of the Third Internat. Conf. on the Mechanical Behavior of Materials, 3, Pergamon, Oxford (1980), pp. 447–455.
G. B. Sinclair, M. Okajima, and J. H. Griffin, “Path-independent integrals for computing stress intensity factors at sharp notches in elastic plates,” Int. J. Numer. Meth. Eng., 20, 999–1008 (1984).
G. R. Irwin, “Analysis of stresses and strain near the end of a crack traversing a plate,” Trans. ASME, J. Appl. Mech., 24, No. 3, 361–364 (1957) [Discussion: J. Appl. Mech., 25, No. 2, 299–303 (1958)].
M. L. Williams, “On the stress distribution at the base of stationary crack,” Trans. ASME: J. Appl. Mech., 24, 109–114 (1957).
A. Seweryn and K. Molski, “Elastic stress singularities and corresponding generalized stress intensity factors for angular corners under various boundary conditions,” Eng. Fract. Mech., 55, 529–556 (1996).
A. Seweryn and J. Zwolinski, “Solution for the stress and displacement fields in the vicinity of a V-notch of negative wedge angle in plane problems of elasticity,” Eng. Fract. Mech., 44, 275–281 (1993).
D. Vasilopoulos, “On the determination of higher-order terms of singular elastic stress fields near corners,” Numer. Math., 53, 51–95 (1988).
A. Seweryn, S. Poskrobko, and Z. Mroz, “Brittle fracture in plane elements with sharp notches under mixed-mode loading,” J. Eng. Mech. ASCE, 123, 535–543 (1997).
M. P. Savruk, P. N. Osiv, and I. V. Prokopchuk, Numerical Analysis in Plane Problems of the Theory of Cracks [in Russian], Naukova Dumka, Kiev (1989).
Author information
Authors and Affiliations
Additional information
__________
Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 4, pp. 26–38, July–August, 2005.
Rights and permissions
About this article
Cite this article
Seweryn, A., Adamowicz, A. On Analytic Constraints and Elements Methods in Modeling Stresses near the Tips of Cracks and V-Notches. Mater Sci 41, 462–478 (2005). https://doi.org/10.1007/s11003-006-0004-x
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11003-006-0004-x