PSI - Issue 25

Ch.F. Markides et al. / Procedia Structural Integrity 25 (2020) 214–225 Ch. F. Markides et al., Structural Integrity Procedia 00 (2019) 000 – 000

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3

the Circular Semi Ring (CSR) configurations, under either compression (CSRc) or tension (CSRt), are discussed in parallel (Fig.1c). The critical stress components, standing as the tensile strength of the material, are given as functions of the fracture load P f , its eccentricity c and the ratio ρ of the outer over the inner radius of the CSR. It is worth men tioning that the fracture load of the CSRc test is about 6 times (and that of the CSRt about 11 times) lower than that of the BD test (3 and 5.5 times, respectively, lower with regard to the CR test), reducing significantly the possibility of premature fracture at the supporting parts of the specimen. These new expressions for the tensile strength of brittle materials are in good agreement with existing ones, incorporating all the parameters of the actual experiment and reducing uncertainties (related to the magnitude and the way of application of the fracture load). From a theoretical point of view, CSRt seems to be more advantageous with respect to the CSRc, due to the lower fracture load required, and the fact that the critical tensile stress constantly exceeds in absolute value the respective compressive one.

Nomenclature BD

Brazilian-disc test

CR

circular ring test/uniform circular ring

CSR circular semi ring CSRc circular semi ring compression test CSRt circular semi ring tension test R 1 inner radius R 2 outer radius ρ > 1 = R 2 / R 1 h the CSR thickness λ , μ ≡ G Lamé constants E , ν

Young’s modulus and Poisson’s ratio of the material

P > 0

externally applied load

P f (CSR c ) fracture load P = P P f (CSR t ) fracture load P = P

f in CSRc f in CSRt

(CSRt) / P f

(CSRc)

K

=P f

eccentricity of P

c

M > 0 torque = Pc β > 0

vertical characteristic of dislocation of the displacement angular characteristic of dislocation of the displacement the tensile strength as obtained from the BD, at disc’s center O

ε > 0 (BD)

σ t σ t

(CR) the tensile strength as obtained from the CR, at the intersection point C of the inner periphery of the CR with the loaded diameter σ t (CSR c ) the tensile strength as obtained from the CSRc, at point B σ t (CSR t ) the tensile strength as obtained from the CSRt, at point A k Hobbs correlation factor relating σ t (CR) to σ t (BD) k (CSRc) correlation factor relating σ t (CSRc) to σ t (BD) k (CSRt) correlation factor relating σ t (CSRt) to σ t (BD) κ , κ * Muskhelishvili’s constants for plane strain, generalized plane stress z = r e i θ the complex variable z c fixed point in the case of friction at specimen-loading device contact region z o fixed point in the absence of friction 2. The analytic solution for the CSRc and the CSRt configurations The experimental and the respective theoretical configurations studied, are shown in Fig.2(a,b,c) for the CSRc- and in Fig.3(a,b,c) for the CSRt-tests. In both cases the specimen is subjected to an overall load P . In general, eccentricity c is different from zero and may diversify between CSRc and CSRt, depending on the set-up; e.g., maximum c in CSRt