Fracture of Spherical Particles under Compression

Niranjan D Parab, Purdue University

Abstract

The fracture behaviors of individual and contacting particles are studied using experimental techniques. Six different materials were studied: soda lime glass, silicon dioxide, silicon, barium titanate glass,poly methyl methacrylate, and yttria stabilized zirconia. The fracture mechanisms were studied at quasi-static and dynamic loading rates. Single, two, and multiple contacting particle geometries were studied to investigate the effects of contact conditions on the fracture mechanisms. The experiments were performed for various diameter ranges to assess the effects of size on fracture behavior. The quasi-static fracture behavior of particles was studied using the single particle compression experiments, performed using a servo-hydraulic machine. Two deterministic models based on the tensile stresses at the contact and near the center of the particle and a statistical model based on the Weibull weakest link theory were proposed to identify the fracture modes of the particles. The models provided an upper and lower bounds for the fracture stresses, however, the variability in the experimental data prevented definitive identification of the fracture modes. ^ A modified Kolsky bar apparatus was synchronized with the high speed X-ray phase contrast imaging setup to record the in-situ fracture mechanisms of single, two, and multiple contacting particles under dynamic compression. No significant size effects on the fracture mechanisms were observed. For the single particle experiments, the crack initiation was observed to occur near the center of the particle for all materials. For two particle experiments, the crack initiation occurred near the particle-particle contact in form of angular Hertzian cracks for brittle materials. These angular cracks only separated fragments near the contact and did not ultimately fracture the particle. Angular cracks with resulting contact fragments were also observed in the multi-particle experiments for soda lime glass particles. The elastic-plastic particles did not show any contact cracks. For all particles, the cracks that caused the catastrophic fracture initiated under the particle-particle contact or near the center of the particle. For the single and two particle experiments, the cracks propagated toward the contact, thus forming meridional cracking pattern. For the multi-particle experiments, cracks spanned the contact points with one major meridional crack observed in all experiments. Regardless of the contact conditions, three major catastrophic fracture modes were observed for the particles depending on the material properties: (1) explosive fragmentation or pulverization (soda lime glass), (2) finite number of large cracks or major cracking (silicon, silicon dioxide, and barium titanate glass), and (3) single crack (poly methyl methacrylate, and yttria stabilized zirconia). ^ A new phenomenological model was then proposed to better describe the observed morphological fracture mechanisms under dynamic compression. This phenomenological model was represented by a pulverization parameter that was related to the hardness, elastic modulus, fracture toughness and the size of the particles assuming displacement driven loading conditions. High pulverization parameter values were associated with explosive fragmentation failure, low pulverization parameter values were associated with single cracking failure, and intermediate pulverization parameter values spanned a range of failure modes between explosive fragmentation and single cracking failure. ^ Scanning electron microscopy was then used to image the generated fragments from the dynamic fracture experiments. All particles showed some variant of the prominent brittle fracture features which included hackle lines and Wallaner lines. In some polycrystalline particles, inter-granular crack propagation was observed. The sharpness of the features were observed to be related to the magnitude of the pulverization parameter for the materials.^

Degree

Ph.D.

Advisors

Weinong W. Chen, Purdue University.

Subject Area

Mechanics|Aerospace engineering|Mechanical engineering

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