The utility of R-curves for understanding fracture toughness-strength relations in bridging ceramics

The mechanical behavior of four rare earth (RE)-Mg-doped Si3N4 ceramics (RE = La, Lu, Y, Yb) with varying grain-boundary adhesion has been examined with emphasis on materials containing La and Lu (which represent the extremes of RE ionic radius). Fracture-resistance curves (R-curves) for all ceramics rose very steeply initially, giving them exceptional strength and relative insensitivity to flaw size. The highest strength was seen in the Lu-doped material, which may be explained by its steeper initial R-curve; the highest apparent toughness (for fracture from millimeter-scale micronotches) was seen in the lowest strength La-doped material, which may be explained by its slowly rising R-curve at longer crack lengths. Excellent agreement was found between the predicted strengths from R-curves and the actual strengths for failures originating from natural flaws, a result attributed to careful estimation of the early part of the R-curve by deducing the intrinsic toughness, K-0, and the fact that this portion of the R-curve is relatively insensitive to sample geometry. Finally, it was found that RE elements with relatively large ionic radius (e.g., La) tended to result in lower grain-boundary adhesion. This implies that there is a small window of optimal grain-boundary adhesion which can lead to the fastest rising R-curves (for short cracks) and the highest strengths. The importance of this work is that it reinforces the notion that factors which contribute to the early part of the R-curve are critical for the design of ceramic microstructures with both high strength and high toughness.