Modeling of threshold strength in cylindrical ceramic structures

Recently, three-dimensional structured ceramic composites with large threshold strengths (i.e., stress below which there is zero probability of failure) have been fabricated utilizing an architecture consisting of relatively stress-free, elongated prismatic domains, separated by thin compressive walls. We build upon prior work on laminate architectures, with the common feature that these structures are all susceptible to fracture. Typically, these three-dimensional structures consist of thin shells of mullite that surround alumina. Cracks, originating from large flaws within the ceramic body, are arrested by the surrounding compressive layers until a specific stress level is attained (i.e., the threshold strength), resulting in a truncation of the strength distribution in the flaw region. A preliminary stress intensity solution has shown that this arrest is caused by a reduction of the crack driving force by the residual compression in the compressive walls. This solution also predicts that the threshold strength is dependent not only on the magnitude of the residual compression in the walls but also on the dimensions of both phases. A finite element model is presented that utilizes a penny-shaped crack in the interior of such a structure or half-penny-shaped crack emanating from the edge of such a structure. Ongoing analytical and experimental work that is needed to more fully understand this arrest phenomenon and its application towards the development of reliable, damage-tolerant ceramic components are discussed.