PSI - Issue 28

Christos F. Markides et al. / Procedia Structural Integrity 28 (2020) 710–719 Christos F. Markides and Stavros K. Kourkoulis / Structural Integrity Procedia 00 (2019) 000–000

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Nomenclature BD, BDT

Brazilian Disc (uniform circular), Brazilian Disc Test FBD, FBDT Flattened Brazilian Disc, Flattened Brazilian Disc Test R The radius of either the uniform or the flattened disc t Thickness L The circumference (periphery) of the uniform disc λ , μ = G Lamé constants E , ν Young’s modulus and Poisson’s ratio of the material κ Muskhelishvili’s constant P frame Overall external load P The point force (in units of force per unit thickness) z 1,2,3,4 The circumferential points on L of application of P z k , k z

The n pairs of (conjugate) internal points of application of P (for z k on z 1 z 2 , k z is on z 3 z 4 )

z = r e i θ

The complex variable on the actual plane The angle θ subtended by radius Oz 1 and x axis The complex variable on the mathematical plane

Θ

ζ = ρ e i θ

The unit circle

γ

s =e i θ

The variable ζ on the unit ( ρ =1) circle γ

1. Introduction The Brazilian Disc Test (BDT) (Carneiro 1943, Akazawa 1943), a convenient alternative for the indirect determination of the tensile strength of brittle materials (for which direct tension tests are very difficult to be implemented), was warmly embraced by the engineering community, mainly due to its simplicity (concerning both the preparation of the specimens and, also, the experimental protocol itself). In spite of its advantages, the BDT was seriously criticized by many researchers (Fairhurst 1964, Hobbs 1965, Jaeger & Hoskins 1966, Hudson 1969, Hooper 1971, Mellor & Hawkes 1971), almost immediately after it was introduced. The main concern was the reliability of the test’s outcome, in case the point of fracture initiation is not the disc’s center but any point in the vicinity of the disc-loading platen interface. Indeed, it was experimentally verified that, unless certain conditions are fulfilled, fracture can start from the loaded arcs, instead from the disc’s center, independently of whether the BDT is implemented using flat (ASTM 2008) loading platens (with or without indenters/cushions) or curved jaws (ISRM 1978), as it is schematically shown in Figs.1(a-c).

P frame

P frame

P frame

P frame

Indenter

P frame

P frame

P frame

P frame

(a) (d) Fig. 1. Alternative configurations of the standardized BDT: (a) Plane loading platens in direct contact to the disc; (b) Plane loading platens with indenters or cushions between the disc and the platens; (c) Curved loading jaws; (d) The Flattened Brazilian disc. (b) (c)