Probabilistic Fracture Strength of High-Aspect-Ratio Silicon Carbide Microspecimens Predicted

Single-crystal silicon carbide (SiC) microsized tensile specimens were fabricated with deep reactive ion etching (DRIE) in order to investigate the effect of stress concentration on the room-temperature fracture strength. This was of interest because microsized turbomachinery that are being developed for power and propulsion applications rotate at very high revolutions per minute and, hence, operate with very high stresses. SiC is an excellent material choice for these harsh environment applications because of its ability to maintain strength, resist creep, and resist oxidation at gas turbine operating temperatures. At the NASA Glenn Research Center, researchers developed SiC microfabrication technology as well as characterization and life-prediction design methodology.

Our testing program had three purposes:

1. Demonstrate the fabrication of simple structures--microtensile specimens in this case--that have high aspect ratios (vertical dimension or etch depth divided by lateral feature size) with sufficient strength, surface finish, and dimensional tolerance suitable for PowerMEMS (microelectromechanical systems for electrical power generation). A highly directional DRIE process was used to fabricate the specimens.
2. Correlate process improvements with fracture strength response, where the fracture strength is defined as the level of stress at the highest stressed location in the structure at the instant of specimen rupture.
3. Test how well the Weibull probabilistic distribution predicts the strength of miniature SiC components. This was done with specimen geometries with various levels of stress concentration and tested a fundamental premise of Weibull theory--that strength increases as the area (or volume) under the highest stress decreases.

Basic schematic of the dogbone microtensile specimens (not to scale). The gauge section is 1.3 mm long. Left: Curved, without a central hole feature. Center: Circular hole. Right: Elliptical hole.

Cross section of a single-crystal SiC test specimen with a circular hole etched to a depth of 140 μm, as observed using a scanning electron microscope. The nickel mask is at the top. Notice the through-the-thickness variation in width of the circular hole.

Specimens without a hole (and hence, with no stress concentration), with a circular hole, and with an elliptical hole were fabricated (see the preceding drawing). The microtensile specimens had significant specimen-to-specimen variations and through-the-thickness variations in dimensions because of the fabrication process (see the photograph). To account for the specimen-to-specimen variation in strength due to the variable severity of flaws from the etching process and for specimen-to-specimen through-the-thickness variations in dimensions (each specimen had different dimensions, and the dimensions changed from the top to the bottom of each specimen), researchers used the Glenn-developed Ceramics Analysis and Reliability Evaluation of Structures--Life (CARES/Life) code with the ANSYS Probabilistic Design System (PDS) to predict the strength response of the specimens with stress concentration. Several hundred trials were run with ANSYS PDS with varying specimen dimensions (see the following grid and plot for an example of a finite element mesh and stress solution of a specimen from ANSYS PDS), and CARES/Life was used to predict fracture strength from each trial.

Left: Example quarter-symmetry mesh. Right: Principal stress solution for the circular-hole specimen. Minimum stress, -43 MPa; maximum stress, 1250 MPa.

The following graph shows the results from the CARES/Life and ANSYS PDS simulations. Simulation results that used the curved specimen geometry strength response as a baseline to predict the strength of the specimens with stress concentration showed good correlation for the circular-hole specimen geometry and some overprediction of the strength of the elliptical-hole specimens. The overprediction of strength for the elliptical hole specimens was likely due to inaccuracies of the stress solution for the highly localized stresses near irregular surfaces. Overall, these results tend to support using the Weibull distribution for the design and analysis of SiC microelectromechanical systems (MEMS) if an accurate stress solution can be obtained. Furthermore, the use of CARES/Life with ANSYS PDS demonstrated that component-level life prediction can be performed in a fully probabilistic design space.

Cumulative distribution plot of CARES/Life and ANSYS PDS Monte-Carlo simulation results for the circular-hole and elliptical-hole specimens compared with experimental data. The Weibull parameters estimated from the curved specimen data were used as a baseline to predict the strength response of the other specimen geometries.

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Last updated: October 10, 2006

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