Andrew A. Wereszczak

The tensile failure stress of a brittle‐material sphere is important to the survival of the sphere itself but is particularly relevant to systems that employ such spheres for applications in which the sphere exterior is subjected to tension during system fabrication or operation. That maximum hoop or tangential stress can be measured by diametrally compressing a C‐sphere specimen directly machined from such spheres. This combination of specimen geometry and test method was conceived at Oak Ridge National Laboratory around 20 years ago. Although the C‐sphere geometry has been tested with larger spheres, the ease and efficacy of its testing are unknown for submillimeter sphere diameters. To consider this, C‐sphere specimens were machined from yttria‐stabilized zirconia (YSZ) spheres of ∼500 µm diameter. The maximum (hoop or tangential) tensile stress was determined as a function of compressive failure force and specimen dimensions using finite element analysis. Companion effective area and volume as a function of Weibull modulus were computed. Hoop tensile failure stresses were then measured and fractography conducted to examine flaw type and location and to estimate the mirror constant of this YSZ grade. This novel study demonstrates that hoop tensile failure stress can be determined with sub‐millimeter brittle‐material spheres.

Contact of brittle‐material spheres can occur while they are manufactured, handled, or used in operation as roller elements or in deformably processed composite material. Statistically, the directional contact between two spheres will nearly always be oblique or eccentric in an unconfined and mobile sphere population. Although analyses of oblique contact exist, the portrayal of its maximum (tensile) first principal stress ( S ₁ ) field is lacking. This information is needed for improved judgment of the prospect of crack initiation. Given these, the S ₁ due to eccentric contact and subsequent crack initiation was analyzed using finite element analysis (FEA) and corroborative demonstration of c‐crack creation. The FEA shows that an asymmetric S ₁ field is created about the contact patch and is caused by superimposed shear intrinsic to eccentric contact. A crack will initiate if the maximum S ₁ exceeds the material's tensile strength, and its field will cause the crack to propagate and arrest to form a C‐shaped crack, or c‐crack. C‐crack initiation trends with lower applied forces, with greater amount of contact eccentricity, higher coefficient of friction, and smaller spherical radius. These metrics deserve recognition, especially when c‐cracked brittle‐material spheres are used in a system whose functionality or reliability is potentially compromised by the c‐cracks.

The bulk compaction of granular materials has been studied for decades to interpret and manage responses for soils and powder‐based component fabrication, and geophysical, celestial, and ballistic impact. Their bulk or macroscopic compaction response is limited by what occurs at the granular or microstructural scale. Motivation existed to more closely examine that association specific to granular brittle materials (e.g., ceramics and glasses). That examination is offered in a series of three companion papers where Part I describes a new supplemental analysis adopted to bulk compaction response involving relatively high compaction stresses (4000 MPa). Bulk compactions of vitreous silicates and crystalline quartzes were interpreted in three ways, including that of a new analysis that considers the product of void ratio ( e ) and stress ( S ) as a function of S, hereafter referred to as “SeS analysis”. The SeS analysis was found to be an informative supplement to conventional bulk compaction analyses because it provides more consistent higher sensitivity for the identification of bulk density rate increase with increasing compaction (softening); a rate increase that arises from the cumulative effect of the onsets and progression of compaction‐induced yielding, fracture or comminution, densification, phase change, or combinations thereof occurring at the granular or microstructural scale.

A new and simple method is presented that enables the estimation of the yield strength ( σ _y ) of brittle materials (e.g., ceramics, glasses). It results from the combination of sufficiently high‐stress compaction of their granular form, postmortem analysis of the crushed particles to identify the critical particle size corresponding to their brittle‐to‐ductile transition, and the use of a developed and simple analytical expression. This method was an outcome from Part I of this three‐paper series. To execute it, a granular brittle material is compacted to a sufficiently high stress, whereby the acting comminution produces both a fraction of particles having a sufficiently small size formed by ductile or plastic‐like deformation and a remaining fraction of larger particles formed from brittle fracture. Postmortem microscopy is then used to identify the smallest particle size whose morphology indicates it formed from brittle fracture ( d _B2D ). The brittle material's σ _y can then be estimated using a combination of the d _B2D , Kendall's and Griffith's theories, a priori knowledge of the material's fracture toughness ( K _Ic ), and a fracture mechanics shape factor constant ( Y ) using σ _y = √((32 π K _Ic ² )/(3 Y ² d _B2D )). The method's development and its use to estimate σ _y for several vitreous silicates, α‐quartzes, and NaCl are provided.

An applied and empirical compaction fracture resistance parameter, K _COMP , was developed to represent the compression‐induced interparticle‐comminution response of granular brittle materials (e.g., ceramic or glass particles). The development of K _COMP is an outcome from Part I of this three‐paper series. The K _COMP represents a continuum response of compaction fracture resistance and was adapted from established Griffith linear elastic fracture mechanics theory. From that, the K _COMP relates macroscopically applied compressive stress to a corresponding inverse‐square‐root representative particle size, where the latter is estimated from an entire particle size distribution or specific surface area measurement. The K _COMP value was not constant over a wide range of stresses for all examined brittle granular materials, and this is indicative of a change in the dominant mode of permanent deformation at higher compaction stresses.

A shear band is a heterogeneous, narrow seam within a solid material whose formation is caused by intense localized shearing when a sufficiently large amount of deformation occurs. If that deformation occurs at a sufficiently rapid rate, with operative friction, then co‐located ephemeral heating will occur in the shear band. In this study, shear bands were produced from dynamic shear‐induced compaction of a granular form of crystalline α‐quartz (SiO ₂ ). The produced shear bands were approximately 25‐µm thick and were examined with scanning electron microscopy/electron backscatter diffraction, transmission electron microscopy, Raman spectroscopy, and nanoindentation. They were found to contain a mixture of vitreous silica and small‐sized crystallites. This finding is significant because the presence of the vitreous silica within the shear band is a postmortem indicator that the localized temperature had reached or exceeded the melting temperature (∼1723°C) of crystalline SiO ₂ during the rapid shear and compaction and then sufficiently rapid cooling quenched in that vitreous state.

Ceramic vat photopolymerization (VPP) is a digital light processing method used to make additively manufactured green ceramic components that are then sintered. Despite the ever‐advancing maturation of this method's green‐state process, some of the material properties of sintered VPP‐processed ceramics are still not well defined or understood. One example is Mode I fracture toughness, K _Ic . In this study, attention was devoted to K _Ic measurement using net‐shape chevron‐notched bend bars that were VPP‐processed and the examination of whether valid K _Ic measurement could occur by testing them. Stable crack propagation was observed in >60% of tested samples, indicated by a smooth nonlinear transition through the measured maximum force prior to final fracture. However, their results cannot yet be responsibly referred to as K _Ic because of continuing violations of other prerequisites needed for valid K _Ic testing.

Conventional static flexural strength testing of brittle cylindrical rods only subjects a small fraction of the entire specimen's area or volume to the maximum tensile stress. Thus, a nonconservative measured strength likely results since most flaws on the surface or in the bulk are not subjected to a sufficiently high tensile stress that can cause fracture. To mitigate this, a rotational flexural tester and corresponding test method were developed whereby rotation and monotonically increasing three‐point flexure were superimposed to investigate fracture response of solid glass cylinders. This combination of rotation and flexure subjects more area and volume of a cylindrical test specimen to tensile stress than a standard static (nonrotating) flexural test. As anticipated, failure stresses were lower for the rotational flexural test. Expressions for effective area and volume are provided for rotating solid rods and tubes subjected to three‐point, four‐point, uniform, and uniformly distributed load bending configurations.

The U.S. Department of Energy's Office of Scientific and Technical Information