Issue 50

Ch. F. Markides, Frattura ed Integrità Strutturale, 50 (2019) 451-470; DOI: 10.3221/IGF-ESIS.50.38 467 characteristics of the optical set-up for which of them (double or single) will materialize, thus, a big value for Z o,t would reveal the single transmitted caustic while the small one adopted in the experiment revealed the double one (see also the relevant Fig.5f). Under the above conclusions, the existing formulae [26] for obtaining the contact length by the aid of the contact caustics are completed by including the case of double caustics, and it is shown that in the same way the spans D + f,r,t and elevations H + f,r,t , of single caustics are used to estimate the half contact length ℓ , the values D – f,r,t , and H – f,r,t (Fig. 7) can be similarly used to obtain ℓ in the case of double caustics. In this context, the explicit expressions for both ℓ + D,f,r,t (Eq.(20)) and ℓ – D,f,r,t (Eq.(25)) are here given for the first time, i.e., the half contact length as obtained from the caustic curves’ spans D + f,r,t , in the case of either single or double caustics, and D – f,r,t , in the case of only double caustics, respectively. Figure 9: Experimental caustics for obtaining the contact length: Front and rear single reflected caustics for (a1) P frame =1 kN, (b1) P frame =2.5 kN and (c1) P frame =3 kN; Transmitted double caustics for (a2) P frame =1 kN, (b2) P frame =2.5 kN and (c2) P frame =3 kN In addition, two ways for specifying the X f,t -axes on experimental caustics’ photos are given, in the case of single and double curves, necessary for applying the existing linear formula [26] for obtaining ℓ H,f,r,t , i.e., the half contact length ℓ through the respective elevations. To assess the formulae obtained for the general (double) caustics, an experimental protocol concerning transparent thin circular discs made of PMMA, squeezed in the ISRM’s apparatus for the standardized implementation of the Brazilian- disc test, was carried out. Though it is obvious that the experiments conducted here could not cover the full range of the experimental investigation required for describing the whole subject and revealing all the features regarding the formation and exploitation of double caustics in praxis, at least they showed, at a very first stage, the efficiency of the method and the general formulae. It is to be mentioned, however, that caustics apart from being a highly sensitive and accurate method concerning the results drawn, it is also very sensitive regarding the preparation and implementation of the experiment, and should be used