Influence of the load eccentricity in three-point bending tests: the correction formulas and error analysis

Explicit expressions are derived for the systematic errors in deflection, maximal stresses and strains, strength, fracture strain, and elastic modulus which are caused by the load eccentricity in three-point bending tests and are ignored by standard technique of force-deflection curve treatment. Specimen are supposed to be homogeneous, isotropic and elastic (ceramics, alloys, and dispersion-filled composites with metallic, ceramic or polymer matrices and so on). For any load and load shift, it is proved that the standard formulas give higher stresses, strength and elastic modulus but lower strains (fracture strain in particular). The error bounds allow us to conclude in which case it is possible to neglect the systematic errors caused by a load eccentricity and when it is necessary to use the accurate formulas accounting for an eccentricity (as in the case of a small beam span).
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