Multiple cracks in an elastic half-plane subjected to thermo-mechanical loading

Document Type : Research Paper


1 Faculty of Engineering, University of Zanjan, P. O. Box 45195-313, Zanjan, Iran

2 Department of Mechanical Engineering, Hashtgerd Branch, Islamic Azad University, P.O. Box 33615-178, Alborz, Iran

3 Department of Engineering and Physics, Karlstad University, 65188 Karlstad, Sweden


An analytical solution is presented for the thermoelastic problem of a half-plane with several cracks under thermo mechanical loading using distributed dislocation technique. The uncoupled quasi-static linear thermoelasticity theory is adopted in which the change in temperature, if any, due to deformations is neglected. The stress field in a half-plane containing thermoelastic dislocation is obtained by means of the complex Fourier transform. Then, the problem is reduced to the solution of a set of simultaneous integral equations with Cauchy type singularities for dislocation density functions. Numerical results for the modes I and II stress intensity are presented to illustrate the effects of crack geometry and loading conditions on the stress intensity factors.Finally, the different cases of crack configurations and arrangements are examined.


Main Subjects

[1]   Tyagi, H., Phelan, P., and Prasher, R., “Predicted Efficiency of a Low-temperature Nanofluid – based Direct Absorption Solar Collector”, J. Solar Energy Eng., Vol. 131, No. 4, pp. 410041-410047, (2009).
[2]   Colangelo, G., Favale, E., de Risi, A., and Laforgia, D., “Results of Experimental Investigations on the Heat Conductivity of Nanofluids Based on Diathermic Oil for High Temperature Applications”, Appl. Energy, Vol. 97, pp. 828–833, (2012).
[3]   Luminosu, I., and Fara, L., “Determination of the Optimal Operation Mode of a Flat Solar Collector by Exergetic Analysis and Numerical Simulation”, Energy, Vol. 30, No. 5, pp. 731–747, (2005).
[4]   Farahat, S., Sarhaddi, F., and Ajam, H., “Exergetic Optimization of Flat Plate Solar Collectors”, Renew. Energy, Vol. 34, No. 4, pp. 1169–1174, (2009).
[5]   Kalogirou, S.A., “Exergy Analysis and Genetic Algorithms for the Optimization of Flat Plate Solar Collectors”, the 25th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems, Perugia, Italy, (2012).
[6]   Sagadevan, S., and Pandurangan, K., “Investigations Onstructural and Electrical Properties of Cadmium Zinc Sulfidethin Films”, International Journal of Nano Dimension, Vol. 6, No. 4, pp. 433-438, (2015).
[7]   Faizal, M., Saidur, R., Mekhilef, S., and Alim, M. A., “Energy, Economic and Environmental Analysis of Metal Oxides Nanofluid for Flat-plate Solar Collector”, Energy Conversion and Management, Vol. 76, pp. 162–168, (2013).
[8]   Maxwell, J.C., “A Treatise on Electricity and Magnetism”, 2rd ed., Clarendon Press, Oxford, UK, (1881).
[9]   Batchelor, G.K., “The Effect of Brownian Motion on the Bulk Stress in a Suspension of Spherical Particles”, Journal of Fluid Mechanics, Vol. 83, No. 1, pp. 97–117, (1977).
[10]  Pak, B.C., and Cho, Y.I., “Hydrodynamic and Heat Transfer Study of Dispersed Fluids with Submicron Metallic Oxide Particles”, Exp. Heat Transfer, Vol. 11, No. 2, pp. 151–170, (1998).
[11]    Duffie, J.A., and Beckman, W.A., “Solar Engineering of Thermal Processes”, 3rd ed. New Jersey, Wiley, (2006).
[12]   Klein, S.A., “Calculation of Flat-plate Solar Collector Loss Coefficients”, Solar Energy, Vol. 17, pp. 79-80, (1975).
[13] Xuan, Y., and Li, Q., “Investigation of Convective Heat Transfer and Flow Features of Nanofluids”, J. Heat Transfer, Vol. 125, No. 1, pp. 151–155, (2003).
[14]  Badescu, V., “Optimal Control of Flow in Solar Collectors for Maximum Exergy Extraction”, Int. J. Heat Mass Transfer, Vol. 50, No. 21-22, pp. 4311-4322, (2007).
[15]  Suzuki, A., “General Theory of Exergy Balance Analysis and Application to Solar Collectors”, Energy, Vol. 13, No. 2, pp. 153–160, (1988).
[16]  Suzuki, A., “A Fundamental Equation for Exergy Balance on Solar Collectors”, J. Sol. Energy Eng., Vol. 110, No. 2, pp. 102–106, (1988).
[17]   Kotas, T.J., “The Exergy Method of Thermal Plant Analysis”, Malabar, FL: Krieger Publish Company, (1995).
[18]  Bejan, A., “Advanced Engineering Thermodynamics”, New York, Wiley, Interscience, pp. 462–465, (1988).
[19]  Torres-Reyes, E., Cervantes de Gortari, J.G., Ibarra-Salazar, B.A., and Picon-Nunez, M., “A Design Method of Flat-plate Solar Collectors Based on Minimum Entropy Generation”, Exergy, Vol. 1, No. 1, pp. 46–52, (2001).
[20] Najian, M.R., “Exergy Analysis of Flat Plate Solar Collector”, MS Thesis, Tehran, Iran: Department of Mechanical Engineering, College of Engineering, Tehran University, (2000).
[21]  Yousefi, T., Veysi, F., Shojaeizadeh, E., and Zinadini, S., “An Experimental Investigation on the Effect of Al2O3–H2O Nanofluid on the Efficiency of Flat-plate Solar Collectors”, Renew. Energy, Vol. 39, No. 1, pp. 293–298, (2012).