PSI - Issue 13

Ermioni D. Pasiou et al. / Procedia Structural Integrity 13 (2018) 2101–2108 E. D. Pasiou, S. K. Kourkoulis , M. G. Tsousi, Ch. F. Markides/ Structural Integrity Procedia 00 (2018) 000–000

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the validity of the results provided concerning the tensile strength was doubted by many scientists in the engineering community, almost immediately after the test was proposed. Among the most crucial issues, raising doubts about the reliability of the tests’ outcomes, is the point of fracture initiation. Indeed, only in case fracture starts from the center of the disc the results of the Brazilian-disc test are considered representative of the tensile strength of the material tested. However, this is not always the case and it is quite often reported that fracture starts at the immediate vicinity of the disc-loading jaw contact arc, due to the strong stress concentrations inevitably developed in this area (Markides et al. 2010; Markides & Kourkoulis 2012), rendering the results of the respective experiments erroneous. In most early studies, the exact boundary conditions at the disc-jaw interface were not taken properly into account since it was believed that the stress field at the center of the disc is accurately enough described by Hondros’ (1959) approach, according to which the loading scheme consists exclusively of uniform radial distribution of pressure, acting along two “small” symmetric arcs of predefined length. The actual shape of this distribution and the role of friction were completely overlooked. The assumptions of Hondros’ solution were partly justified by full field analytical solutions (Lavrov & Vervoort 2002; Kourkoulis et al. 2013b), which definitely denoted that the role of the actual distribution of radial pressure and that of the friction stresses is indeed negligible at the disc’s center. However, the same solutions indicated that the role of the as above factors (i.e., the exact distribution of the radial pressure and friction) is of paramount importance in a narrow area around the contact arc, in full accordance with experimental observations of premature fractures in the vicinity of the disc-jaws contact areas (Fairhurst 1964; Hooper 1971). The quantification of the role of these factors is still an “open” issue. The main limitation of existing studies is that arbitrary distributions are adopted for both the radial pressure and, also, for the frictional stresses. For example, Addinall & Hackett (1964) as well as Lavrov & Vervoort (2002) assumed sinusoidal distributions for the friction stresses, while Markides et al. (2011) approached the problem adopting either a continuous sinusoidal or a uniform distribution with discontinuity at the axis of symmetry. A solution closer to experimental evidence was recently pro posed by Kourkoulis et al. (2012; 2013b), who solved the contact problem of two elastic cylindrical bodies (disc and jaw), taking into account the different deformability of the disc and jaw materials (as an additional cause of friction stresses) and considering, also, the fact that the contact arc varies depending on the load-level. The results of this analysis are in accordance with the results for the contact length provided analytically by Timoshenko (Timoshenko & Goodier 1970) as well as with experimental results obtained using the method of caustics (Kourkoulis et al. 2013a). The short survey just described indicates that, in spite of the research devoted to the topic, the validity of the outcomes of the Brazilian-disc test is still questionable. In this direction, the ring test, namely the compression of a circular ring by either diametral line forces or by radial pressure exerted along two symmetric finite arcs of its peri phery, was proposed as an improvement of the Brazilian-disc test, almost immediately after the Brazilian-disc test was introduced. The origin of the ring test can be found in an early paper by Ripperger and Davis (1947). Later on, Hobbs (1964; 1965) indicated that the use of ring-shaped specimens instead of solid discs could eliminate some of the weaknesses of the Brazilian-disc test related to the inevitable stress concentration along the disc-jaw interface and the premature fractures that deteriorate the validity of the results obtained by Hondros’ (1959) classic solution for the stress field in the standardized Brazilian-disc test. Hobbs’ analysis indicated that the maximum tensile stress in a circular ring of inner radius R i , outer radius R o and thickness t, subjected to diametral compression by line forces P, is developed at the point where the loading axis intersects the ring’s inner circle. Its magnitude is given as:

o k P k R t       

max,ring  

 

(1)

t,disc

where k is a function of the R i /R o ratio. Recalling now that, according to Hondros’ (1959) pioneering solution, the term in parentheses in Eq.(1) is approximately equal to the tensile stress developed at the center of a compact disc of radius R=R o and thickness t, subjected to diametral compression by line forces P, it can be written that:

max,ring t,Braziliandisc k   

(2)

It is here mentioned that the analytic solution for the stress field in a ring compressed by diametral line forces was introduced by Timoshenko already in 1910 (Timoshenko & Goodier 1951) by means of real analysis. The solution was