Analysis of symmetric and skew-symmetric weight functions for a semi-infinite interfacial crack in transversely isotropic piezoelectric bimaterials
Source abstract
Abstract
This paper presents an analysis of symmetric and skew-symmetric weight functions for in-plane interfacial crack problems in piezoelectric bimaterials. The symmetric weight function matrix is obtained by means of the solution of a Wiener–Hopf functional equation and the skew-symmetric weight function matrix is developed by the construction of a corresponding full field solution. The explicit expressions for the symmetric and skew-symmetric weight functions are given and applied to in-plane deformation problems for a semi-infinite crack between two dissimilar piezoelectric materials. The validity of the present method in the determination of the field intensity factors is demonstrated by illustrative examples, in which both piezoelectric bimaterials and piezoelectric/elastic bimaterials are considered. It is shown that, for the present interfacial crack problem, both symmetric and skew-symmetric weight function matrices are necessary in the general integral formula for the evaluation of field intensity factors, and that the contribution of the skew-symmetric element of the applied load is not negligible in fracture analysis.
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Research context
OpenAlex topics: Numerical methods in engineering · Fatigue and fracture mechanics · Ultrasonics and Acoustic Wave Propagation
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References (38)
Show source-provided references
1. Antipov YA (1999) An exact solution of the 3-D problem of an interface semi-infinite plane crack. J Mech Phys Solids 47:1051–109310.1016/S0022-5096(98)00096-9 ↗
2. Arfken GB, Weber HJ (2005) Mathematical methods for physicists. Elsevier Academic Press, San Diego
3. Beom HG, Atluri SN (1996) Near-tip fields and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media. Int J Fract 75:163–18310.1007/BF00034075 ↗
4. Bueckner HF (1970) A novel principle for the computation of stress intensity factors. Zeitschrift fur Angewandte Mathematik und Mechanik 50:529–546
5. Bueckner HF (1973) Field singularities and related integral representations. Mech Fract 1:239–314
6. Chen YZ (1989) Weight function technique in a more general case. Eng Fract Mech 33:983–98610.1016/0013-7944(89)90113-6 ↗
7. Chen YZ, Hasebe N (1994) Eigenfunction expansion and higher order weight functions of interface cracks. J Appl Mech 61:843–84910.1115/1.2901566 ↗
8. Gao CF, Wang MZ (2001) Collinear permeable cracks in thermopiezoelectric materials. Mech Mater 33:1–910.1016/S0167-6636(00)00033-8 ↗
9. Gao H (1991) Weight function analysis of interface crack: mismatch versus oscillation. J Appl Mech 58:931–93810.1115/1.2897710 ↗
10. Gao H (1992) Weight function method for interface cracks in anisotropic biomaterials. Int J Fract 56:138–15810.1007/BF00015597 ↗
11. Gu B, Yu SW, Feng XQ (2002) Transient response of an interface crack between dissimilar piezoelectric layers under mechanical impacts. Int J Solids Struct 39:1743–175610.1016/S0020-7683(02)00013-6 ↗
12. Herrmann KP, Loboda VV, Govorukha VB (2001) On contact zone models for an electrically impermeable interface crack in a piezoelectric bimaterial. Int J Fract 111:203–22710.1023/A:1012269616735 ↗
13. Hu K, Fu J, Yang Z (2014) Moving Dugdale type crack along the interface of two dissimilar piezoelectric materials. Theor Appl Fract Mech 74:157–16310.1016/j.tafmec.2014.09.004 ↗
14. Labbens RC, Heliot J, Pellisier-Tanon A (1976) Weight functions for three-dimensional crack problems. Cracks Fract. In: ASTM STP, 601. ASTM, Philadelphia, pp 448–46710.1520/STP28658S ↗
15. Labbens RC, Pellisier-Tanon A, Heliot J (1975) Practical method for calculation stress intensity factors through weight functions. Mech Crack Growth. In: ASTM STP, 590. ASTM, Philadelphia, pp 368–38510.1520/STP33957S ↗
16. Lazarus V, Leblond J (1998) Three-dimensional crack-face weight functions for the semi-infinite interface crack-I: variation of the stress intensity factors due to some small perturbation of the crack front. J Mech Phys Solids 46:489–51110.1016/S0022-5096(97)00073-2 ↗
17. Ma LF, Chen YH (2001) Weight functions for interface cracks in dissimilar anisotropic piezoelectric materials. Int J Fract 110:263–27910.1023/A:1010805704212 ↗
18. Ma LF, Chen YH (2004) Weight functions for interface cracks in dissimilar anisotropic materials. Acta Mech Sin 20:82–8810.1007/BF02493576 ↗
19. McMeeking R, Ricoeur A (2003) The weight function for cracks in piezoelectrics. Int J Solids Struct 40:6143–616210.1016/S0020-7683(03)00366-4 ↗
20. Morini L, Piccolroaz A, Mishuris G, Radi E (2013) Integral identities for a semi-infinite interfacial crack in anisotropic elastic bimaterials. Int J Solids Struct 50:1437–144810.1016/j.ijsolstr.2013.01.021 ↗
21. Morini L, Radi E, Movchan AB, Movchan NV (2012) Stroh formalism in analysis of skew-symmetric and symmetric weight functions for interfacial cracks. Math Mech Solids 18:135–15210.1177/1081286512462299 ↗
22. Narita F, Yoshida M, Shindo Y (2004) Electroelastic effect induced by electrode embedded at the interface of two piezoelectric half-planes. Mech Mater 36:999–100610.1016/j.mechmat.2003.04.003 ↗
23. Ou ZC, Wu XJ (2003) On the crack-tip stress singularity of interfacial cracks in transversely isotropic piezoelectric bimaterials. Int J Solids Struct 40:7499–751110.1016/j.ijsolstr.2003.08.021 ↗
24. Ou ZC, Chen YH (2004) Interface crack problem in elastic/piezoelectric bimaterials. Int J Fract 130:427–45410.1023/B:FRAC.0000049502.54417.1c ↗
25. Paris PC, McMeeking RM (1975) Efficient finite element methods for stress intensity factors using weight function. Int J Fract 11:R354–35610.1007/BF00038904 ↗
26. Paris PC, McMeeking RM, Tada H (1976) The weight function method for determining stress intensity factors. Cracks Fract. In: ASTM STP, 601. ASTM, Philadelphia, pp 471–48910.1520/STP28659S ↗
27. Parks DM, Kamenetzky EM (1979) Weight functions from virtual crack extension. Int J Numer Methods Eng 14:1693–170610.1002/nme.1620141110 ↗
28. Piccolroaz A, Mishuris G, Movchan AB (2007) Evaluation of the Lazarus–Leblond constants in the asymptotic model of the interfacial wavy crack. J Mech Phys Solids 55:1575–160010.1016/j.jmps.2007.02.001 ↗
29. Piccolroaz A, Mishuris G, Movchan AB (2009) Symmetric and skew-symmetric weight functions in 2D perturbation models for semi-infinite interfacial cracks. J Mech Phys Solids 57:1657–168210.1016/j.jmps.2009.05.003 ↗
30. Piccolroaz A, Mishuris G (2013) Integral identities for a semi-infinite interfacial crack in 2D and 3D elasticity. J Elast 110:117–14010.1007/s10659-012-9385-2 ↗
31. Rice JR (1972) Some remarks on elastic crack-tip stress fields. Int J Solids Struct 8:751–75810.1016/0020-7683(72)90040-6 ↗
32. Sham TL (1989) The theory of higher order weight functions for linear elastic plane problems. Int J Solids Struct 25:357–38010.1016/0020-7683(89)90053-X ↗
33. Sham TL, Zhou Y (1989) Weight function in two-dimensional bodies with arbitrary anisotropy. Int J Fract 40:13–4110.1007/BF01150864 ↗
34. Suo Z (1990) Singularities, interfaces and cracks in dissimilar anisotropic media. Proc R Soc A Math Phys 427:331–358
35. Suo Z, Kuo CM, Barnett DM (1992) Fracture mechanics for piezoelectric ceramics. J Mech Phys Solids 40:739–76510.1016/0022-5096(92)90002-J ↗
36. Vanderglas ML (1978) A stiffness derivative finite element technique for determination of influence functions. Int J Fract 14:R291–294
37. Wang BBL, Sun YG, Han JC, Du SY (2009) An interface electrode between two piezoelectric layers. Mech Mater 41:1–1110.1016/j.mechmat.2008.07.006 ↗
38. Willis J, Movchan A (1995) Dynamic weight functions for a moving crack. I. Mode I loading. J Mech Phys Solids 43:319–34110.1016/0022-5096(94)00075-G ↗