Issue 47

S. K. Kourkoulis et alii, Frattura ed Integrità Strutturale, 47 (2019) 247-265; DOI: 10.3221/IGF-ESIS.47.19

the slope of the plot is reduced with increasing c . Moreover, it is to be highlighted that all plots share a common point at about r =0.8 R 2 for all values of c . On the other hand, the point at which the transverse stress, σ θ , is zeroed, appears depend ing (though very slightly) on the value of the parameter c . The influence of c on the magnitude of the maximum tensile stress developed (i.e., the quantity of utmost practical im portance) is more vividly shown in Fig. 14b: At least for the range of c -values studied here, the relation between σ θ ,max ≡ σ θ,Α and c is perfectly linear. From a quantitative point, increasing the value of c by a factor of 2, i.e., by 100% (from 7.5 mm to 15.0 mm), results to a decrease of σ θ ,max from about 31.3 MPa to about 26.5 MPa, or in other words only by about 15%, indicating the rather minor influence of c on the quantity of importance (i.e., on σ θ,Α ). In Fig. 15 the polar distribution of the transverse stress σ θ , along the outer perimeter of the CSR (i.e., along the locus E ΄ ΑΕ, marked green in the sketch embedded in Fig.15) is plotted for four different values of the eccentricity (the same with the ones considered in previous paragraph). All four curves are quite similar to each other with minor differences, of only quantitative nature. These differences are more or less negligible for the major portion of the range of θ considered and only for θ -values approaching ±90 o do these differences increase significantly. All plots share two common points, sym metric with respect to the θ =0 o line, located at about θ =±48 ο .

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Figure 15 : The polar distribution of the transverse normal stress along the outer perimeter of the CSR for various c -values (in mm).

D ISCUSSION AND CONCLUDING REMARKS

n alternative configuration for the laboratory determination of the tensile strength of brittle materials was proposed, consisting of a Circular Semi-Ring (CSR) subjected to diametral compression, either centrally or slightly eccentrical ly. The configuration is proposed as a possible substitute of the familiar standardized Brazilian-disc test (BDT), taking into account severe criticism against it, concerning the validity of its results and the relation of its outcome with the actual tensile strength as it is obtained from a direct tension test [3-5]. An analytic solution was introduced for the stress field developed in the CSR, based on the solution for the cut circular ring, following the approach introduced by Golovin [21] and Muskhelishvili [20]. The solution was checked against experimental data and the agreement was found very satisfactory. A three dimensional numerical model was then designed that permitted parametric exploration of the role of some geometrical and loading parameters on the distribution of stresses and their magnitude along various critical paths and strategic points of the CSR-specimens. The data of the numerical model are here considered in juxtaposition to the respective ones of the analytic solution. This is achieved by plotting the transverse normal stress σ θ along the critical path AB, according to both approaches (numerical and analytical). The plots are implemented for the reference model ( R 1 =25 mm, R 2 =50 mm, 2 h =10 mm) and the results are exhibited in next Fig. 16. It is clear that the two approaches are extremely close to each other all along the locus considered. The maximum discrepancy is observed at r =50 mm (i.e., at point A) and it does not exceed 7%. A

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