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Analytical and numerical stress field solutions in the Brazilian Test subjected to radial load distributions and their stress effects at the centre of the disk

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Abstract

A new method is developed in order to determine the stress state inside a disk subjected to arbitrary radial compressive distributions along its boundary, obtaining both numerical and closed-form solutions, which is analytically verified through accepted formulations; additionally, alternative expressions for uniform, sinusoidal and parabolic distributions are proposed. Based on the hypothesis of a smooth stress transition along the loaded and unloaded part of the rim, two new distributions (spline and new cosine) are proposed and analysed. Even if closed-form solutions were not feasible, the latter may be accurately solved numerically since the error committed is that of the numerical technique used. Main differences are observed in radial and shear components, whereas hoop ones are relevant on the vicinity of the load application area and the vertical axis. Special attention is paid to the centre of the sample, of which stress state depends on the distribution shape and the contact angle. Finally, it is concluded that there is always a deviation from the values predicted due to the concentrated load as a consequence of the deformation induced by the jaw, which is especially significant in the uniform stress distribution and also influences the determination of the tensile strength in the material.

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Acknowledgements

The authors acknowledge the financial support from PhD fellowship Severo Ochoa Program of the Government of the Principality of Asturias (PA-14-PF-BP14-067) and from the PhD fellowship of the University of Oviedo (modality B) of 2018.

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Authors and Affiliations

  1. Department of Exploitation and Prospecting Mines, Mining Engineering School, University of Oviedo, C/Independencia,13, 33004, Oviedo, Asturias, Spain

    Diego José Guerrero-Miguel, Martina Inmaculada Álvarez-Fernández, Carmen Covadonga García-Fernández & Celestino González-Nicieza

  2. Department of Mathematics, Faculty of Sciences, University of Oviedo, C/Calvo Sotelo s/n., 33012, Oviedo, Asturias, Spain

    Cesar Menéndez-Fernández

Authors
  1. Diego José Guerrero-Miguel
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  2. Martina Inmaculada Álvarez-Fernández
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  3. Carmen Covadonga García-Fernández
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  4. Celestino González-Nicieza
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  5. Cesar Menéndez-Fernández
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Correspondence to Martina Inmaculada Álvarez-Fernández.

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Guerrero-Miguel, D.J., Álvarez-Fernández, M.I., García-Fernández, C.C. et al. Analytical and numerical stress field solutions in the Brazilian Test subjected to radial load distributions and their stress effects at the centre of the disk. J Eng Math 116, 29–48 (2019). https://doi.org/10.1007/s10665-019-10001-1

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  • DOI: https://doi.org/10.1007/s10665-019-10001-1

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