Size effect on the compression breakage strengths of glass particles

• The general Weibull statistics are modified from a physical basis.
• The Weibull stress is introduced to define the breakage strength accurately.
• The effect of finite contact area and breakage mode on the breakage strength is considered.
• The size effect of the breakage strength is consistent with the Weibullian scaling law.

The quasi-static compression-breakage responses of the glass spheres with five different sizes (4–25 mm) are investigated. The breakage strength data are found to be highly scattered. Based on the Weibull model, a statistical approach is proposed to interpret the characteristics in the breakage strength of the glass particles. The Weibull stress concept is introduced to accurately define the breakage stress of the particles considering the effects of finite contact area and breakage modes. It is observed that the relationship between the cumulative survival probability of the particles and the breakage stress follows the Weibull distribution reasonably well. Moreover, the scaling law between the breakage strength and the particle size is consistent with the theoretical predication by the Weibull model. Finally, the energy consumption during the particle breakage process is discussed with a three-parameter Weibull distribution. The relationship of the characteristic energy and the particle size also follows a power law.

The breakage strengths of the brittle particles, though of the same size and material, are highly scattered. However, the breakage strength distributions of the brittle particles satisfy the Weibull distribution reasonably well. The Weibull modulus does not show obvious dependence on the particle size while the characteristic strength of the particles decreases with the increasing particle size.Figure optionsDownload as PowerPoint slide