A conservative integral for bimaterial notches subjected to thermal stresses

International Journal for Numerical Methods in Engineering

Volumn 60, Issue 6, 2004, Pages 1075-1102

  Banks Sills, Leslie ^a   Ishbir, Chaim ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Bimaterial notch; Conservative integral; Stress intensity factors; Thermal stresses; Wedges

Indexed keywords

DISPLACEMENTS; LINEAR ELASTICITY; LINEAR THEORY; WEDGE ANGLES;

BONDING; EIGENVALUES AND EIGENFUNCTIONS; ELASTICITY; FINITE ELEMENT METHOD; MECHANICAL PROPERTIES; PARAMETER ESTIMATION; PROBLEM SOLVING; STRESS CONCENTRATION; THERMAL LOAD;

THERMAL STRESS;

ELASTICITY; MATHEMATICAL METHOD; STRESS INTENSITY FACTOR;

EID: 1942519096     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.996     Document Type: Article

References (46)

1. Stern M. Soni ML. On the computation of stress intensities at fixed-free corners. International Journal of Solids and Structures 1976; 12:331-337.
2. Stern M, Becker EB, Dunham RS. A contour integral computation of mixed-mode stress intensity factors. International Journal of Fracture 1976; 12:359-368.
3. Hong C-C, Stern M. The computation of stress intensity factors in dissimilar materials. Journal of Elasticity 1978; 8:21-34.
4. Sinclair GB, Okajima M, Griffin JH. Path independent integrals for computing stress intensity factors at sharp notches in elastic plates. International Journal for Numerical Methods in Engineering 1984; 20:999-1008.
5. Sinclair GB. A remark on the determination of mode I and mode II stress intensity factors for sharp re-entrant corners. International Journal of Fracture 1985; 27:R81-R85.
6. Carpenter WC. Calculation of fracture mechanics parameters for a general corner. International Journal of Fracture 1984; 24:45-58.
7. Carpenter WC. Mode I and II stress intensities for plates with cracks of finite opening. International Journal of Fracture 1984; 26:201-214.
8. Carpenter WC. The eigenvector solution for a general corner of finite opening crack with further studies on the collocation procedure. International Journal of Fracture 1985; 27:63-74.
9. Carpenter WC, Byers C. A path independent integral for computing stress intensities for V-notched cracks in a bi-material. International Journal of Fracture 1987; 35:245-268.
10. Carpenter WC. Insensitivity of the reciprocal work contour integral method to higher order eigenvectors. International Journal of Fracture 1995; 73:93-108.
11. Banks-Sills L. A conservative integral for determining stress intensity factors of a bimaterial strip. International Journal of Fracture 1997; 86:385-398.
12. Okajima M, Sinclair GB. A path independent integral for computing singularity participation at a butt joint. In Proceedings of the International Conference on Computational Mechanics, Japan 1986; 1:V-11-V-16.
13. Akisanya AR, Fleck NA. Interfacial cracking from the free-edge of a long bi-material strip. International Journal of Solids and Structures 1997; 34:1645-1665.
14. Banks-Sills L, Sherer A. A conservative integral for determining stress intensity factors of a bimaterial notch. International Journal of Fracture 2002; 115:1-26.
15. Qian ZQ, Akisanya AR. Analysis of free-edge stress and displacement fields in scarf joints subjected to a uniform change in temperature. Fatigue and Fracture of Engineering Materials and Structures 1998; 21:687-703.
16. Mizuno K, Niyazawa K, Suga T. Characterization of thermal stresses in ceramic/metal joints. Journal of the Faculty of Engineering, University of Tokyo 1988; 39:401-412.
17. Suga T, Elssner G. Characterization of strength of ceramic-to-metal joints. In MRS International Meeting on Advanced Materials, Doyama M, Somiya S, Chang RPH (eds). 1989; 8:99-104.
18. Blanchard JP, Ghoniem NM. An eigenfunction approach to singular thermal stresses in bonded strips. Journal of Thermal Stresses 1989; 12:501-527.
19. Yang YY. Spannungssingularitäten in zweistoffverbunden bei mechanischer und thermischer belastung. Ph.D. Thesis, University of Karlsruhe, Karlsruhe, 1992.
20. Munz D, Fett T, Yang YY. The regular stress term in bonded dissimilar materials after a change in the temperature. Engineering Fracture Mechanics 1993; 44:185-194.
21. Munz D, Yang YY. Stresses near the free edge of the interface in ceramic-to-metal joints. Journal of the European Ceramic Society 1994; 13:453-460.
22. Munz D, Yang YY. Stresses in ceramic-metal joints under mechanical and thermal loading. In Mismatching of Welds, Schwalbe KH, Kocak M (eds). ESIS 17, Mechanical Engineering Publications: London, 1994; 35-58.
23. Fett T. Determination of stresses in a plate strip of bonded dissimilar materials. Engineering Fracture Mechanics 1994; 47:547-557.
24. Tilscher M, Munz D, Yang YY. The stress intensity factor in bonded quarter planes after a change in temperature. Journal of Adhesion 1995; 49:1-21.
25. Munz D, Yang YY. The stress distribution in a dissimilar materials joint for complex singular eigenvalues under thermal loading. Journal of Thermal Stresses 1995; 18:407-419.
26. Yosibash Z. Numerical thermo-elastic analysis of singularities in two dimensions. International Journal of Fracture 1996; 74:341-361.
27. Yosibash Z. Thermal generalized stress intensity factors in 2-D domains. Computer Methods in Applied Mechanics and Engineering 1998; 157:356-385.
28. Lui XH, Sou Z, Ma Q. Split singularities: stress field near the edge of a silicon die on a polymer substrate. Acta Materialia 1999; 47:67-76.
29. Munz D, Yang YY. Stresses near the edge of bonded dissimilar materials described by two stress intensity factors. International Journal of Fracture 1993: 60:169-177.
30. Banks-Sills L, Sherer A. A path independent integral for computing stress intensity factors of bimaterial V-notches. Tel Aviv University Report, 2000.
31. Dundurs J. Some properties of elastic stresses in a composite. In Recent Advances in Engineering Science (5th edn). Eringen: AC. 1970: 203-216.
32. Munz D, Yang YY. Stress singularities at the interface in bonded dissimilar materials under mechanical and thermal loading. Journal of Applied Mechanics 1992; 59:857-861.
33. Theocaris PS. The order of singularity at a multi-wedge corner of a composite plate. International Journal of Engineering Science 1974; 12:107-120.
34. Yang YY. Solutions of dissimilar material singularity and contact problems. D.Sc. Thesis, University of Karlsruhe, Karlsruhe, 2002.
35. Boley BA, Weiner JH. Theory of Thermal Stresses. Wiley: New York, 1962.
36. MAPLE V. Version 5. Waterloo Maple, Inc.: Waterloo, 1997.
37. Banks-Sills L. Application of the finite element method to linear elastic fracture mechanics. Applied Mechanics Reviews 1991; 44:447-461.
38. Bathe KJ. ADINA-Automatic Dynamic Incremental Nonlinear Analysis System, Version 7.3, Adina Engineering, Inc.: USA, 1999.
39. Fränkle M, Munz D, Yang YY. Stress singularities in a bimaterial joint with inhomogeneous temperature distribution. International Journal of Solids and Structures 1996; 33:2039-2054.
40. Suga T, Elssner G. Schmauder S. Composite parameters and mechanical compatibility of material joints. Journal of Composite Materials 1988; 22:917-934.
41. Dempsey JP, Sinclair GB. On the stress singularities in the plane elasticity of the composite wedge. Journal of Elasticity 1979; 9:373-391.
42. Dempsey JP, Sinclair GB. On the singular behaviour at the vertex of a bi-material wedge. Journal of Elasticity 1981; 11:317-327.
43. Dempsey JP. Power-logarithmic stress singularities at bi-material corners and interface cracks. Journal of Adhesion Science and Technology 1995; 9:253-265.
44. Muskhelishvili NI. Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff: Holland, 1953.
45. Pageau SS, Gadi KS, Biggers Jr. SB, Joseph PF. Standardized complex and logarithmic eigensolutions for n-material wedges and junctions. International Journal of Fracture 1996; 77:51-76.
46. IMSL Math/Library, Version 3, Texas, 1994.