A probability distribution model for the compressive strength of micro thin-walled hollow glass beads under uniform pressure

Because of their many excellent properties, hollow glass beads (HGBs) are widely used in composite materials; stealth coatings; the aerospace field; the deep-sea field; electrical, thermal and sound insulation materials and military explosives. However, there is currently no method for predicting the strength of HGBs. This paper proposes a probability distribution model for the compressive strength of micro thin-walled HGBs under uniform pressure. The theoretical model was verified by comparing the parameters of 13 types of HGBs. The model showed that compressive strength is inversely proportional to the square root of the radius for the same type of HGBs. Moreover, for different types of HGBs made with identical materials, the compressive strength is only related to the outer diameter and equivalent density. Further study revealed that the particle size of HGBs follows a normal distribution. The failure mode of HGBs under uniform pressure is mode-II. Therefore, the maximum shear stress, which occurs on the inner surface of HGBs, is the dominant factor in the failure process. Furthermore, the shear strength is only inversely proportional to the square root of the radius even for different types of HGBs.