Compression testing spherical particles for strength: Theory of the meridian crack test and implementation for microscopic fused quartz

We show that uniaxial compression testing of spherical particles can give unambiguous access to their tensile strength as governed by surface flaws if one uses pairs of elasto-plastic platens, tailoring their hardness in order to control the relative area of particle-to-platen contact during the test. This eliminates the development of contact microcracks that are typically found to govern particle fracture when hard platens are used. We show that, if the platen materials are well chosen, one can probe a range of stress states for which it is known that particle failure was initiated along the surface, under elevated hoop stress within a region situated remote from the points of load application. Specifically, platens must be chosen such that particles tend to fracture when the ratio of projected contact area radius to particle radius exceeds a specific value that depends on the Poisson ratio of the particles. With fused quartz of Poisson ratio 0.17, this specific ratio value equals 0.65. We demonstrate the approach using microscopic fused quartz spheres 40 +/- 20 gm in diameter as a testbench material; with those particles hardened steel serves as an appropriate platen material. Their strength values are statistically distributed; this is addressed using several platen materials. The resulting bank of data is interpreted using established survival-analysis methods, namely the non-parametric product-limit estimator. We also give a maximum likelihood estimation of the particle strength Weibull distribution parameters derived from the ensemble of data after left-truncation and/or right-censoring of data points situated inside of the range of unambiguous surface fracture strength measurement for each platen material. This gives a Weibull modulus of 6.3 and characteristic strength of 890 MPa for the fused quartz particles. These values are significantly lower than what is produced in high-strength fused quartz fibers of comparable diameter; the difference is most likely a result of surface damage caused during powder storage and manipulation in the absence of a protective coating.