The Utility of R‐Curves for Understanding Fracture Toughness‐Strength Relations in Bridging Ceramics

Abstract

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, K0, 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.

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“…According to tangency criterion, rising R-curve materials fracturing from the propagation of "short" cracks are not able to develop the whole toughening capability, and fracture at effective toughness levels (K eff ) lower than the intrinsic fracture toughness measured for long cracks [21,22,32,35,36]. Furthermore, Rcurve materials also exhibit stable subcritical crack growth extension before catastrophic failure.…”

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“…the fracture stress, σF, can be deduced from the R-curve with a knowledge of the prevalent flaw sizes, a. As discussed in detail elsewhere, [8] in addition to the peak toughness, it is the early proportion of the R-curve (over the first hundred micrometers or so of crack extension) that is also very important for ceramics as this governs their fracture strength at realistic flaw sizes. Consequently, the resulting strengths depend markedly on the details of the R-curve and of course the initial flaw sizes, such that optimizing strength vs. toughness can once again involve different choices of microstructures.…”

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