A new approach of diametral compressive testing with circular anvils is proposed. The circular anvils are used to select a suitable contact width or to avoid the collapse of the specimen in the contact edge. Furthermore, the statistical corrections on the diametral compressive strength for the effects of the size and stress distribution are explained by the application of Weibull’s statistical theory. The experimental results of the diametral compressive testing are compared with the uniaxial tensile strengths for some kinds of graphite and marble, and the discrepancies between the two strengths are discussed. According to our macroscopic brittle fracture criterion under biaxial stress state, which was proposed recently, the tensile strength can be deduced from the diametral compressive strength $σHC*$ and the uniaxial compressive strength σC as follows,
$σt*=KICKIIC$

$12σCσHC*(1+σx/σH)+σC$

${σHC*(1−σx/σH)−σC}+σC2$
where $σt*$ is the deduced tensile strength, σxH is the ratio of maximum and minimum principal stresses at the center of the disk, and KIC and KIIC are the values of Mode I and Mode II fracture toughness. The deduced values $σt*$ are ascertained experimentally to agree very well with the uniaxial tensile strength in wide range of brittle materials, such as graphite and marble.
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