Spherically isotropic, elastic spheres subject to diametral point load strength test

• Published in: International journal of solids and structures Vol. 36; no. 29; pp. 4473 - 4496
• Main Authors: Chau, K.T., Wei, X.X.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.1999; Elsevier Science
• Subjects: Displacement functions; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fracture mechanics, fatigue and cracks; Fundamental areas of phenomenology (including applications); Measurement and testing methods; Measurement methods and techniques in continuum mechanics of solids; Physics; Point load strength test; Solid mechanics; Spheres; Spherically isotropic; Stress analysis; Structural and continuum mechanics; Stress analysis; Spheres; Displacement functions; Point load strength test; Spherically isotropic; Stress concentration; Rock mechanics; Rupture; Potential theory; Fourier series; Compression test; Modeling; Legendre polynomial; Sphere; Measurement method; Rupture strength; Breaking test; Strength; Point charge
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/S0020-7683(98)00202-9

This paper presents an analytic solution for the stress concentrations within a spherically isotropic, elastic sphere of radius R subject to diametral point load strength test. The method of solution uses the displacement potential approach together with the Fourier–Legendre expansion for the boundary loads. For the case of isotropic sphere, our solution reduces to the solution by Hiramatsu and Oka, 1966 and agrees well with the published experimental observations by Frocht and Guernsey (1953) . A zone of higher tensile stress concentration is developed near the point loads, and the difference between this maximum tensile stress and the uniform tensile stress in the central part of the sphere increases with E/ E′ (where E and E′ are the Youngs moduli governing axial deformations along directions parallel and normal to the planes of isotropy, respectively) , G′/ G (where G and G′ are the moduli governing shear deformations in the planes of isotropy and the planes parallel to the radial direction) , and ν̄/ ν′ (where ν̄ and ν′ are the Poissons ratios characterizing transverse reduction in the planes of isotropy under tension in the same plane and under radial tension, respectively) . This stress difference, in general, decreases with the size of loading area and the Poissons ratio.