A Three-Parameter Weibull Distribution Method to Determine the Fracture Property of PMMA Bone Cement

Abstract

Poly (methyl methacrylate) (PMMA) bone cement is an excellent biological material for anchoring joint replacements. Tensile strength ft and fracture toughness KIC have a considerable impact on its application and service life. Considering the variability of PMMA bone cement, a three-parameter Weibull distribution method is suggested in the current study to evaluate its tensile strength and fracture toughness distribution. The coefficients of variation for tensile strength and fracture toughness were the minimum when the characteristic crack of PMMA bone cement was αch∗=8dav. Using the simple equation αch∗=8dav and fictitious crack length Δαfic=1.0dav, the mean value μ (= 43.23 MPa), minimum value ftmin (= 26.29 MPa), standard deviation σ (= 6.42 MPa) of tensile strength, and these values of fracture toughness (μ = 1.77 MPa⋅m1/2, KICmin = 1.02 MPa⋅m1/2, σ = 0.2644 MPa⋅m1/2) were determined simultaneously through experimental data from a wedge splitting test. Based on the statistical analysis, the prediction line between peak load Pmax and equivalent area Ae1Ae2 was obtained with 95% reliability. Nearly all experimental data are located within the scope of a 95% confidence interval. Furthermore, relationships were established between tensile strength, fracture toughness, and peak load Pmax. Consequently, it was revealed that peak load might be used to easily obtain PMMA bone cement fracture characteristics. Finally, the critical geometric dimension value of the PMMA bone cement sample with a linear elastic fracture was estimated.