Error Propagation Biases in the Calculation of Indentation Fracture Toughness for Ceramics

Indentation fracture toughness models generally share the derived parameter Pc ^−3/2, where P is the indentation load and c the measured crack length. Biases, inherent to error propagation through this nonlinear transformation ( c to c ^3/2), can be introduced into calculated values for K _{I C} , depending upon the amount of averaging of crack length data performed prior to the transformation. This work utilizes Monte Carlo simulations to evaluate the bias in K _{I C} calculated using both mean and linear regression methods. Significant positive biases were demonstrated when using mean-based calculations where coefficients of variation (cv) in c exceeded 10%. Regression methods produced significantly less bias. With cv < 10% or when c is averaged per load, both methods produce essentially unbiased estimates for K _{I C} .