PSI - Issue 10

Ch.F. Markides / Procedia Structural Integrity 10 (2018) 163–170 Ch.F. Markides / Structural Integrity Procedia 00 (2018) 000 – 000

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y ΄ =0 (Fig. 3b). Introducing that H in Eq. (22), ℓ is exactly obtained. That ℓ should approach the theoretical value predicted by the third of Eqs. (2); if not, the procedure can be repeated as many times as required until ℓ obtained by Eq. (22) will agree with the theoretically predicted one.

6. Conclusions

The determination of the contact length by the method of reflected caustics in a transparent disc, loaded according to the ISRM’s standardized procedure for the implementation of the Brazilian -disc test, is here revisited. Assuming zero refraction within the disc, which is to be of very small thickness, simplified equations of caustics reflected from the rear face are derived. Under these assumptions the initial curves on the front and rear faces of the disc are similar. In other words, the assumption adopted (i.e., that for the two stress-optical constants C r and C f it holds that C r =C f =C ) is a first, perhaps rough, approximation, which will be relieved in a forthcoming paper in preparation. Those simple formulae for the caustics and initial curve for the rear face of the disc in conjunction with the existing ones for the front face are then used to obtain the contact length between the disc and the ISRM’s jaw. Namely, use is made of known expressions due to Theocaris and Stassinakis (1978) and particularly of a linear formula obtained in that study that is not used until now because of the difficulty in specifying the line y ΄ =0 on the experimental caustics photos. In this context, two ways are here proposed to obtain y ΄ =0 line and in turn the elevation H of the end points of the front caustic and eventually the contact length through the aforementioned formula. The procedure also applies to a transparent circular ring (viz. Fig.4 concerning preliminary tests), provided its inner radius is small enough and the laboratory conditions ensure that the linearity limit of the material is not exceeded. The present work is a first step in the experimental and theoretical valuation of the method proposed for the determination of the contact length. The procedure can be extended to the case of finite refraction indexes within the specimen, something which will be done as the next of this ongoing study.

Rear

Front

Rear

Front

Fig. 4. Reflected caustics in a circular ring.

Acknowledgements

The author expresses his deep gratitude to the two anonymous reviewers of the original manuscript for their most valuable contribution in improving the quality of this paper.

References

Badalouka, B., Papadopoulos, G.A., 2011. Experimental evaluation of stress-optical constants by caustics, International Journal of Fracture 171, 85-90. Chunyang Xiong, Xuefeng Yao, Jing Fang, 1999. A study of dynamic caustics around running interface crack tip. Acta Mechanica Sinica 15, 182-192.