## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Two interfacial collinear Griffith cracks in thermo-elastic composite media

**ABSTRACT**

The objective of the article is to find the stress intensity factors and crack energy for a pair of collinear Griffith cracks situated at the interface of the two orthotropic materials under steady state temperature field. The problem is reduced to a pair of singular integral equations, which are solved using Jacobi's polynomials. Numerical computations are carried out for two different pairs of orthotropic materials for different particular cases, which are depicted through figures. The effect of material constants and temperature coefficients on the behavior of physical quantities viz., stress intensity factors and crack energy of the interfacial cracks is the key feature of the present article.

**KEYWORDS**

PAPER SUBMITTED: 2015-10-17

PAPER REVISED: 2016-03-16

PAPER ACCEPTED: 2016-08-05

PUBLISHED ONLINE: 2016-09-05

- Sih, G.C., On the singular character of thermal stresses near a crack, ASME Journal of Applied Mechanics, 29 (1962), 3, pp.587-589.
- Sekine, H., Thermal stresses near tips of an insulated line crack in semi-infinite medium under uniform heat flow, Engineering Fracture Mechanics, 9 (1977), 2, pp.499-507.
- Sekine, H., Thermoelastic interaction between two neighboring cracks (in Japanese), Transaction of Japan Society of Mechanical Engineers, 45 (1979), pp.1058-1063.
- Chen, B., Zhang X., Thermoelasticity problem of an orthotropic plate with two collinear cracks, International Journal of Fracture, 38 (1988), 3, pp.161-192.
- Itou, S., Rengen, Q., Thermal stresses around two parallel cracks in two bonded dissimilar elastic half-planes, Archive of Applied Mechanics, 63 (1993), 6, pp.377-385.
- Chen, B., Zhang, X., On plane thermoelasticity problem of an orthotropic strip with two collinear cracks, Journal of Northwestern Polytechnical University, 11 (1993), 2, pp.121-126.
- Itou, S., Thermal stresses around two parallel cracks in an infinite orthotropic plate under uniform heat flow, Journal of Thermal Stresses, 24 (2001), 7, pp.677-694.
- Baksi, A., Das, S. and Bera, R. K., A note on thermo-elastic problem of two collinear Griffith cracks in an orthotropic medium, Int. J. of Pure and Applied Mathematics, 36 (2007), 4, pp.365-374.
- Zhong, X.C., Wua, B., Zhang, K.S., Thermally conducting collinear cracks engulfed by thermo-mechanical field in a material with orthotropy, Theoretical and Applied Fracture Mechanics, 65 (2013), 1, pp.61-68.
- Thakur, P., Steady Thermal stress and strain rates in a rotating circular cylinder under steady state temperature, Thermal Science, 18 (2014) , Suppl. 1, pp.S93-S106.
- Zhu, Z.-W., Ma, Y., Zhang, H.-D. , Song, W.-D. , Gan, Y.-C., Evaluation of thermal effects and strain rate sensitivity in frozen soil, Thermal science, 18 (2014), 5, pp.1631-1636.
- Thakur, P., Steady Thermal Stress and Strain Rates in a Circular Cylinder with homogeneous compressibility subjected to thermal load, Thermal Science, 18 (2014), Suppl.1, pp.S81-S92.
- Sills, L. B., and Dolev, O., The conservative M-integral for thermal-elastic problems, International Journal of Fracture, 125 (2004), 1, pp.149-170.
- Itou S., Thermal stress intensity factors of an infinite orthotropic layer with a crack, International Journal of Fracture, 103 (2000), 3, pp. 279-291.
- Itou S., Thermal stresses around a crack in an adhesive layer between two dissimilar elastic Half-planes, Journal of Thermal Stresses, 16 (1993), 4, pp.373-400.
- Clements, D. L. and, Tauchert, T. R., A thermoelastic crack problem for an anisotropic slab, J. Austral. Math. Soc. 21 (Series B), (1979), 2, pp.243-255.
- Sharma, B., Thermal stresses in transversely isotropic semi-infinite elastic solids, J. Appl. Mech., 2 (1958), pp.86.
- Das, S., and Patra, B., Stress intensity factors for moving interfacial crack between bonded dissimilar fixed orthotropic layers, Computers & Structures, 69 (1998), 4, pp.459-472 .
- Sih, G. C., and Chen, E. P., Cracks in composite materials, Martinus Nijhoff publishers, Hague, Netherland, 1981.