Flaw Aspect Ratio Affects Uncertainty in Determining Ceramic Fracture Toughness

Objectives: Surface crack in flexure according to ASTM C1421 is a common method of determining the fracture toughness of dental ceramics. This study aimed to determine the relative uncertainty that can be expected in fracture toughness estimates, which measurements contribute most to this uncertainty, and the specimen and flaw dimensions that correspond to minimum uncertainty.
Methods: The fracture toughness (K_Ic) for surface crack in flexure specimens was derived using MathCAD software (Parametric Technology Corporation). Coefficient relations were determined by finding the partial differentials of K_Ic with respect to each measurement: critical flaw depth (a) and half-width (c), specimen thickness (W), specimen width (B), support span (L), and failure load (P). The uncertainty contribution of each measurement to the calculated K_Ic value was taken to be the absolute value of its coefficient relation multiplied by the historic precision of that type of measurement in my laboratory. Relative uncertainty was determined by summing the uncertainty contributions of all measurements and dividing by the true K_Ic value. Failure load was determined by the combination of all other parameters. Baseline measurements were taken from the NIST fracture toughness standard reference material SRM2100, which my team previously reported testing, and the specimen and flaw dimensions were varied to explore the effects on relative uncertainty.
Results: Relative uncertainty was not affected by K_Ic, B, and L. W had negligible effect. Increasing flaw dimensions decreased relative uncertainty. Minimum uncertainty corresponded to a/c<1 with the optimal a/c ratio decreasing with increasing flaw size (a/c=1.24–0.07ln(c), R²=0.95). Baseline relative uncertainty was 8.2%, but this could be reduced by controlling the flaw dimensions. Relative contributions due to imprecision in measurements were: a and c combined (78.4%), W(4.0%), B(1.5%), P(12.1%), and L(3.9%).
Conclusions: Imprecision in measuring critical flaw dimensions and failure load are the primary contributions to uncertainty in determining SCF fracture toughness.