Approximate structures of thermoelastic fields induced by a penny-shaped thermal-medium crack in a transversely isotropic layer. (English) Zbl 1503.74099
Keywords:
transversely isotropic layer; penny-shaped crack; integral kernel series expansion method; approximate solution; thermoelastic fieldReferences:
| [1] | Nowacki, W., Thermoelasticity (1962), Pergamon Press: Pergamon Press New York · Zbl 0227.73009 |
| [2] | Sih, G. C.; Michaopoloulos, J.; Chou, S. C., Hygrothermoelasticity (1986), Martinus Niijhoof Publishing: Martinus Niijhoof Publishing The Netherland |
| [3] | Abbas, I. A.; Marin, M., Analytical solutions of a two-dimensional generalized thermoelastic diffusions problem due to laser pulse, Iran J. Sci. Technol. Trans. Mech. Eng., 42, 57-71 (2018) |
| [4] | Othman, M. I.A.; Singh, B., The effect of rotation on generalized micropolar thermoelasticity for a half-space under five theories, Int. J. Solids Struct., 44, 2748-2762 (2007) · Zbl 1121.74021 |
| [5] | Othman, M. I.A.; Atwa, S. Y.; Jahangir, A.; Khan, A., Effect of magnetic field and rotation on generalized thermo-microstretch elastic solid with mode-I crack under the Green Naghdi theory, Comput. Math. Model., 24, 4, 566-591 (2013) · Zbl 1308.74122 |
| [6] | Othman, M. I.A.; Sarhan; Atwa, Y., Propagation of plane waves of a mode-I crack for a generalized thermoelasticity under influence of gravity for different theories, Mech. Adv. Mater. Struct., 21, 9, 697-709 (2014) |
| [7] | Othman, M. I.A.; Atwa, S. Y.; Jahangir, A.; Khan, A., The effect of rotation on plane waves in generalized thermo-microstretch elastic solid for a mode-I crack under Green-Naghdi theory, J. Comput. Theor. Nanosci., 12, 11, 4987-4997 (2015) |
| [8] | Hutchinson, J. W.; Suo, Z. G., Mixed mode cracking in layered materials, Adv. Appl. Mech., 29, 63-191 (1992) · Zbl 0790.73056 |
| [9] | Sih, G. C., Thermonechanics of solids: non-equilibrium and irreversiblity, Theor. Appl. Fract. Mech., 9, 175-198 (1988) |
| [10] | Sih, G. C., On the singular character of thermal stress near a crack tip, J. Appl. Mech., 29, 587-589 (1962) · Zbl 0108.37603 |
| [11] | Olesiak, Z.; Sneddon, I. N., The distribution of thermal stress in an infinite elastic solid containing a penny-shaped crack, Arch. Rat. Mech. Anal., 4, 1, 238-254 (1959) · Zbl 0089.42002 |
| [12] | Zhang, X. Y.; Xue, Y. J.; Li, X. F., Transient thermoelastic response in a cracked strip of functionally graded materials via generalized fractional heat conduction, Appl. Math. Model., 70, 328-349 (2019) · Zbl 1462.74049 |
| [13] | Singh, A.; Das, S.; Craciun, E. M., The effect of thermo-mechanical loading on the edge crack of finite length in an infinite orthotropic strip, Mech. Comp. Mater., 55, 3, 285-296 (2019) |
| [14] | Kassir, M. K.; Sih, G. C., Three-Dimensional Crack Problems (1975), Noordhoff International Publishing: Noordhoff International Publishing Leyden · Zbl 0312.73112 |
| [15] | Art. 103472 · Zbl 07375788 |
| [16] | Jin, B.; Zhong, Z., Dynamic stress intensity factor (mode i) of a penny-shaped crack in an infinite poroelastic solid, Int. J. Eng. Sci., 40, 637-646 (2002) |
| [17] | Wang, B., Three-dimensional analysis of a flat elliptical crack in a piezoelectric material, Int. J. Eng. Sci., 30, 6, 781-791 (1992) · Zbl 0756.73076 |
| [18] | Rice, J. R.; Ben-Zion, Y.; Kim, K. S., Three dimensional perturbative solution for a dynamic planar crack moving unsteadily in a model elastic solid, J. Mech. Phys. Solids, 42, 813-843 (1994) · Zbl 0806.73056 |
| [19] | Li, Y.; Zhao, M. H.; Qin, Q. H.; Fan, C. Y., Analysis solution method for 3D planar crack problems of two-dimensional hexagonal quasicrystals with thermal effects, Appl. Math. Model., 69, 648-664 (2019) · Zbl 1462.74140 |
| [20] | Sneddon, I. N.; Lowengrub, M., Crack Problems in the Classical Theory of Elasticity (1969), Wiley: Wiley New York · Zbl 0201.26702 |
| [21] | Li, X. F.; Lee, K. Y., Three-dimensional electroelastic analysis of a piezoelectric material with a penny-shaped dielectric crack, ASME J. Appl. Mech., 71, 866-878 (2004) · Zbl 1111.74513 |
| [22] | Wang, B. L.; Noda, N., Exact thermoelectroelasticity solution for a penny-shaped crack in piezoelectric materials, J. Thermal Stresses, 27, 241-251 (2004) |
| [23] | Zhao, M. H.; Dang, H. Y.; Fan, C. Y.; Chen, Z. T., Analysis of an arbitrarily shaped interface cracks in a three-dimensional isotropic thermoelastic bi-material, part 1: Theoretical solution, Int. J. Solids Struct., 97-98, 168-181 (2016) |
| [24] | Zhao, M. H.; Dang, H. Y.; Li, Y.; Fan, C. Y.; Xu, G. T., Displacement and temperature discontinuity boundary integral equation and boundary element method for analysis of cracks in three-dimensional isotropic thermoelastic media, Int. J. Solids Struct., 81, 179-187 (2016) |
| [25] | Dang, H. Y.; Zhao, M. H.; Fan, C. Y.; Chen, Z. T., Analysis of an arbitrarily shaped interface crack in a three-dimensional isotropic thermal elastic bi-material, Part 2: numerical method, Int. J. Solids Struct., 99, 48-56 (2016) |
| [26] | Rao, J. V.S. K.; Hasebe, N., Axially symmetric thermal stress of a penny-shaped subjected to general surface temperature, Arch. Appl. Mech., 64, 481-496 (1994) · Zbl 0833.73041 |
| [27] | Tsai, Y. M., Thermal stress in a transversely isotropic medium containing a penny-shaped crack, ASME J. Appl. Mech., 50, 24-28 (1983) · Zbl 0511.73005 |
| [28] | Chen, W. Q.; Ding, H. J.; Ling, D. S., Thermoelastic field of a transversely isotropic elastic medium containing a penny-shaped crack: exact fundamental solution, Int. J. Solids Struct., 41, 69-83 (2004) · Zbl 1077.74011 |
| [29] | Li, X. Y.; Li, P. D.; Kang, G. Z.; Chen, W. Q.; Müller, R., Steady-state thermo-elastic field in an infinite medium weakened by a penny-shaped crack: Complete and exact solution, Int. J. Solids Struct., 84, 167-182 (2016) |
| [30] | Li, X. F.; Lee, K. Y., Effect of heat conduction of penny-shaped crack interior on thermal stress intensity factors, Int. J. Heat Mass Transf., 91, 127-134 (2015) |
| [31] | Zhong, X. C.; Long, X. Y.; Zhang, L. H., An extended thermal-medium crack model, Appl. Math. Model., 56, 202-216 (2018) · Zbl 1480.74281 |
| [32] | Shail, R., Some thermoelastic stress distributions in an infinite solid and a thick plate containing penny-shaped cracks, Mathematika, 11, 102-118 (1964) · Zbl 0133.18903 |
| [33] | Srivastava, K. N.; Palaiya, R. M., The distribution of thermal stress in a semi-infinite elastic solid containing a penny-shaped crack, Int. J. Eng. Sci., 7, 641-666 (1969) · Zbl 0172.50204 |
| [34] | Srivastava, K. N.; Palaiya, R. M.; Choudhary, A., Thermal stress in an elastic layer containing a penny-shaped crack and bonded to dissimilar half-spaces, Int. J. Fract., 13, 27-38 (1977) |
| [35] | Tsai, Y. M., Penny-shaped crack in a transversely isotropic plate of finite thickness, Int. J. Fract., 20, 81-89 (1982) |
| [36] | Zhong, X. C.; Lee, K. Y., A thermal-medium crack model, Mech. Mater., 51, 110-117 (2012) |
| [37] | Wu, B.; Peng, D.; Jones, R., On the analysis of cracking under a combined quadratic thermal flux and a quadratic mechanical loading, Appl. Math. Model., 68, 182-197 (2019) · Zbl 1481.74680 |
| [38] | Hamzah, K. B.; Long, N. M.A. N.; Senu, N.; Eshkuvatov, Z. K., Numerical solution for the thermally insulated cracks in bonded dissimilar materials using hypersingular integral equations, Appl. Math. Model., 91, 358-373 (2021) · Zbl 1481.74660 |
| [39] | Kit, G. S.; Frenchko, Y. S., Influence of the thermal permablility of an arc-shaped crack on the thermoelastic state in its nerghborhood, Mater. Sci., 9, 70-74 (1975) |
| [40] | Lee, K. Y.; Park, S. J., Thermal stress intensity factors for partially insulated interface crack under uniform heat flow, Eng. Fract. Mech., 50, 475-482 (1995) |
| [41] | Zhou, Y. T.; Li, X.; Yu, D. B., A partially insulated interface crack between a graded orthotropic coating and a homogeneous orthotropic substrate under heat flux supply, Int. J. Solids Struct., 47, 768-778 (2010) · Zbl 1193.74135 |
| [42] | Zhong, X. C.; Wu, Y. B.; Zhang, K. S., An extended dielectric crack model for fracture analysis of a thermopiezoelectric strip, Acta Mech. Solida Sinica, 33, 521-545 (2020) |
| [43] | Polyanin, A. A.; Manzhirov, A. V., Handbook of Integral Equations (1998), CRC Press LLC: CRC Press LLC New York · Zbl 0896.45001 |
| [44] | Gradshteyn, I. S.; Ryzhik, I. M., Table of Integrals, Series and Products (2007), Academic Press: Academic Press London · Zbl 1208.65001 |
| [45] | Ashida, F.; Noda, N.; Okumura, I. A., General solution technique for transient thermoelasticity of transversely isotropic solids in cylindrical coordinates, Acta Mech., 101, 215-230 (1993) · Zbl 0783.73007 |
| [46] | Noda, N.; Takeut, Y.; Sugano, Y., On a general treatise of three-dimensional thermoelastic problems in transversely isotropic bodies, ZAMM J. Appl. Math. Mech., 65, 509-512 (1985) · Zbl 0577.73015 |
| [47] | Kumar, R.; Kansal, T., Propagation of lamb waves in transversely isotropic thermoelastic diffusive plate, Int. J. Solids Struct., 45, 5890-5913 (2008) · Zbl 1362.74020 |
| [48] | Kumar, R.; Kansal, T., Three-dimensional free vibration analysis of a transversely isotropic thermoelastic diffusive cylindrical panel, J. Solid Mech., 2, 376-392 (2010) |
| [49] | Atkinson, K. E., The Numerical Solution of Integral Equations of the Second Kind (2009), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1158.65088 |
| [50] | Kachanov, M., Elastic solids with many cracks and related problems, Adv. Appl. Mech., 30, 259-445 (1993) · Zbl 0803.73057 |
| [51] | Chen, Y. Z.; Atkinson, C., The influence of layer thickness on the stress intensity factor of a penny-shaped crack in a sandwiched viscoelastic bimaterial, Int. J. Eng. Sci., 43, 222-249 (2005) · Zbl 1211.74196 |
| [52] | Yang, J. H.; Lee, K. Y., Penny shaped crack in a three-dimensional piezoelectric strip under in-plane normal loadings, Acta Mech., 148, 187-197 (2001) · Zbl 0987.74057 |
| [53] | Gao, H. J.; Zhang, T. Y.; Tong, P., Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic, J. Mech. Phys. Solids, 45, 491-510 (1997) |
| [54] | Li, X. F.; Lee, K. Y., Effects of electric field on crack growth for a penny-shaped dielectric crack in a piezoelectric layer, J. Mech. Phys. Solids, 52, 2079-2100 (2004) · Zbl 1081.74544 |
| [55] | Kaczyński, A.; Kaczyński, B., On 3D problem of vertically uniform heat flow disturbed by an anticrack in a transversely isotropic magnetoelectroelastic space, Eur. J. Mech. A/Solids, 69, 192-200 (2018) · Zbl 1406.74026 |
| [56] | Art. 103434 · Zbl 07314430 |
| [57] | Zhong, X. C.; Li, X. F., Fracture analysis of a magnetoelectroelastic solid with a penny-shaped crack by considering the effects of the opening crack interior, Int. J. Eng. Sci., 46, 374-390 (2008) · Zbl 1213.74275 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
