Towards an accurate, back-of-napkin mathematical model of the whole ceramic armor plate I: The BE equation

In other words, lower-density ceramics, being thicker at an equal weight, perform better because the fracture conoids they form are more massive.

At a glance, this result explained just about everything we knew of the performance gap between common armor ceramics such as boron carbide, silicon carbide, and aluminum oxide. Or so we thought.

Years later, in reviewing large libraries of ballistic data alongside our in-house R&D reports, it became apparent that the Inertia Method tended to overestimate the performance of boron carbide and, simultaneously, underestimate the performance of silicon carbide. The actual performance discrepancy between them, on a weight basis, was slightly but durably less than a pure conoid-based analysis predicts. For e.g., in Level IV plates, a B4C tile will perform roughly 17% better than a SiC tile on a weight basis, though the difference in conoid mass is on the order of 60%.

Needless to say, this called for further investigation. Fracture conoid side angles proved difficult to measure empirically, and predictive equations and models were equivocal at best. Besides, it’s not entirely clear that the projectile interacts very much with ceramic material on the margins of the conoid — a major failure mode for AP projectiles is erosion, and only ceramic material in direct contact with the projectile can contribute to erosion — so it didn’t seem likely to me that increased conoid volume necessarily translates to improved performance in a linear fashion.

So then the question became: “Is there a difference in mechanical properties that can explain why the relative performance gap is narrower than expected?” The two ceramic types were of similar, if not practically identical, hardness; the samples we tested ourselves measured at ~2600HV1 (SiC) and ~2650HV1 (B4C). Hardness was therefore dismissed as a significant factor. But, as it turned out, SiC had a tremendous advantage in compressive strength — a measure of resistance to bulk deformation that is in many respects similar to a hardness test, yet one that takes place on a larger scale and is more sensitive to grain size, defect density, and other large-scale and microstructural features. In fact, SiC’s compressive strength was consistently nearly 35% greater than boron carbide’s.

As a general rule, ceramics fail in compression because, under a uniaxial compressive load, they experience tensile stresses perpendicular to the applied force due to Poisson’s effect. These tensile stresses act on pre-existing microcracks within the ceramic, causing them to propagate and eventually link up to form a crush zone. Unlike tensile failure — where the largest, most favorably oriented flaw leads to sudden fracture — compressive failure in ceramics involves the stable growth and coalescence of many cracks.