Stress intensity factors for the Brazilian disc with a short central crack: Opening versus closing cracks |
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Authors: | ChF Markides DN PazisSK Kourkoulis |
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Institution: | Department of Mechanics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, 5 Heroes of Polytechnion Avenue, Theocaris Bld., Zografou Campus, 157 73 Athens, Greece |
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Abstract: | Closed form expressions are obtained for the stress intensity factors (SIFs) in case of a Brazilian disc with a short central crack, the length of which does not exceed one fifth of the disc radius. The disc is loaded by uniform radial pressure along two finite symmetric arcs of its periphery. The solution is achieved using the method of complex potentials introduced by Kolosov and Muskhelishvili. The advantage of the expressions obtained is that they are valid both for cracks under opening mode as well as for closing cracks. For the first case (opening cracks) the results of the present study are compared with existing approximate solutions and it is concluded that the agreement is excellent as long as the length of the crack remains relatively small compared to the radius of the disc. Regarding the case of a closing mode crack the procedure proposed here (based on a recent alternative approach of the cracked Brazilian disc) leads to a physically acceptable deformed crack shape instead to an unnatural crack with overlapped lips. At the same moment the dependence of the SIFs on the properties of the material is eliminated. |
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Keywords: | Cracked Brazilian disc Stress intensity factors (SIFs) Linear elasticity Complex potentials Closing cracks Overlapping |
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