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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later on verified experimentally by Filon (1924) with the aid of photo-elasticity. The stress field in a circular ring under diametral compression by radial stresses, uniformly distributed along two opposite symmetric arcs of its peri phery, was given by Jaeger & Hoskins (1966) by means of complex analysis. The ring test was then considered by Hudson (1969) and Hudson et al. (1972), who concluded that the tensile strength obtained by the ring test is not an actual material property but rather it is an experimental or “technological” property depending on the specimen’s geometry. Mellor and Hawkes (1971) carried out an exhaustive study of both the Brazilian disc and the ring-tests taking into consideration almost all parameters influencing their outcomes. Their most valuable suggestion was the use of curved instead of plane loading jaws, in an attempt to reduce the stress concentration at the loading points. Based on this study, ISRM (1978) suggested the familiar device for the standardized implementation of the Brazilian-disc test. Recapitulating, it can be stated that the ring test exhibits some advantages compared to the Brazilian-disc one. Among them the existence of a single tensile stress component at the points of expected failure is, perhaps, the most crucial one. Consequently, it is important to check whether this particular advantage is affected by possible parasitic factors, as for example geometric eccentricities, distorting the actual geometry of the specimens in comparison to the respective one of “mathematical” rings (for which the center of the disc is identical to that of the hole drilled to form the ring). In this context, the role of eccentricity on the displacement field of rings under diametral compression between the jaws of the ISRM device for the Brazilian-disc test is here quantified experimentally using specimens made of PMMA. The displacement field is obtained with the aid of the 3D DIC technique. 2. Experimental protocol 2.1. The material and the specimens All specimens were made of poly-methyl-methacrylate-A (widely known as PMMA or Plexiglas). A preliminary series of standardized direct tension tests was implemented to obtain the material properties of the specific material batch. The modulus of elasticity, E, was found equal to E=3.0 GPa and Poisson’s ratio, ν, equal to ν=0.38. The specimens of the main protocol were circular discs of radius R o =50 mm and thickness t=10 mm. A hole of radius equal to R i =12.5 mm was drilled throughout the thickness of the discs, either centrally or eccentrically (Fig.1), on each disc. Attention was paid to avoid any influence on the mechanical properties of the specimens’ material during mechanical shaping. The specimens were classified into two classes, based either on the angle between the loading axis and the line of centers of the disc and the hole (φ=0 o (Fig.1c) or φ=90 o (Fig.1d)), or according to the distance, d, between the centers of the disc and the hole (d=R o /8, R o /4 and R o /2). The values of the parameters φ and d of each class of specimens tested are presented in Table 1. An additional series of experiments with φ=45 ο is still in progress. One surface of each specimen was painted white and a pattern of black dots was sprayed, fulfilling the needs of the DIC technique. Then some strategic loci were designed on the painted surface of the specimens (to facilitate post processing of the raw DIC data) including: The loading axis and the line normal to it, a circle surrounding the ring’s hole (as close to its periphery as possible), and a circle approaching, as close as possible, to the periphery of the disc.

P

P

P

P

y

y

y

y

φ=0 ο

d φ=90 ο

φ

θ

d

d

x

x

x

x

R i

R o

P

P

P

P

(a)

(b)

(c)

(d)

Fig. 1. The geometric characteristics of the specimens.