A constitutive description of the inelastic response of ceramics

The objective of the article is to present a unified model for the dynamic mechanical response of ceramics under compressive stress states. The model incorporates three principal deformation mechanisms: (i) lattice plasticity due to dislocation glide or twinning; (ii) microcrack extension; and (iii) granular flow of densely packed comminuted particles. In addition to analytical descriptions of each mechanism, prescriptions are provided for their implementation into a finite element code as well as schemes for mechanism transitions. The utility of the code in addressing issues pertaining to deep penetration is demonstrated through a series of calculations of dynamic cavity expansion in an infinite medium. The results reveal two limiting behavioral regimes, dictated largely by the ratio of the cavity pressure p to the material yield strength σY. At low values of p/σY, cavity expansion occurs by lattice plasticity and hence its rate diminishes with increasing σY. In contrast, at high values, expansion occurs by microcracking followed by granular plasticity and is therefore independent of σY. In the intermediate regime, the cavity expansion rate is governed by the interplay between microcracking and lattice plasticity. That is, when lattice plasticity is activated ahead of the expanding cavity, the stress triaxiality decreases (toward more negative values) which, in turn, reduces the propensity for microcracking and the rate of granular flow. The implications for penetration resistance to high-velocity projectiles are discussed. Finally, the constitutive model is used to simulate the quasi-static and dynamic indentation response of a typical engineering ceramic (alumina) and the results compared to experimental measurements. Some of the pertinent observations are shown to be captured by the present model whereas others require alternative approaches (such as those based on fracture mechanics) for complete characterization. © 2011 The American Ceramic Society.

The breakdown of the viscous regime in riblets

We investigate the mechanisms involved in the breakdown of the viscous regime in riblets, with a view to determining the point of optimum performance, where drag reduction ceases to be proportional to the riblet size. This occurs empirically for a groove cross-section $A_g^+ \approx 120^+$. To study the interaction of the riblets with the overlaying turbulent flow, we systematically conduct DNSes in a ribbed turbulent channel with increasing riblet size. The conditionally averaged crossflow above and within the grooves reveals a mean recirculation bubble that exists up to the point of viscous breakdown, isolating the groove floor from the overlying crossflow, and preventing the high momentum fluid from entering the grooves. We do not find evidence of outside vortices lodging within the grooves until $A_g^+ \approx 400$, which is well past the drag minimum, and already into the drag increasing regime. Interestingly, as the bubble breaks down, we observe that quasi-two-dimensional spanwise structures form just above the riblets, similar to those observed above porous surfaces and plant canopies, which appear to be involved in the performance degradation.