Impact breakage of semi-brittle spheres

Abstract

Quasi-static compression cracking and low-velocity impact cracking of 12.7 mm diameter spheres of acrylic resin and polymethyl methacrylate (PMMA), both types regarded as semi-brittle, has been investigated using postfracture optical microscopy observations and high-speed framing photography at framing rates of 200,000 frames per second. It has been shown that under both quasi-static and dynamic loading conditions the initial necessary step is the plastic deformation of the compressed/impacted sphere to an a/ R value of greater than ∼0.5, where a and R are the radii of contact and sphere, respectively. The high-speed photography has shown that under critical conditions one or two primary meridional cracks initiate at the circle of contact and propagate into the bulk, reaching velocities up to 0.8 of the Rayleigh surface wave velocity of the material of the sphere. From the growing primary meridional cracks, secondary meridional cracks initiate and propagate at high speeds towards the free surface of the sphere, leading to the formation of orange segment-shaped fragments. High-speed photography has also revealed that during impact loading, primary and secondary meridional cracks grow around approximately conical zones at the contact regions. High-speed framing photography at a higher framing rate of 500,000 frames per second has also been used to investigate the response of 600–750 μm diameter PMMA spheres when they impacted a smooth silica flat at 200 m s −1. Although under these impact conditions, the spheres did not break up, information about their rebound energies has been obtained and used to analyse the integrity of the spheres. These microspheres are shown to develop at and beyond the edge of the plastically deformed circular flat meridional cracks, which are very similar to those produced in the 12.7 mm diameter spheres.