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.

A New Sine-Based Probabilistic Approach: Theory and Monte Carlo Simulation with Reliability Application

“…We derive diferent mathematical properties of the NWS-G distributions, involving the quantile function (QF), r th moment, moment generating function (MGF), and probability-weighted moments (PWMs). Equation (10) shows that the QF of the NWS-G distributions is not in straightforward form (i.e., explicit form). Tus, for obtaining random numbers from any member of the NWS-G family, we would need to use numerical methods by incorporating computer software.…”

“…Terefore, to capture the complex form of data, numerous updated and fexible modifcations of equation (1) have been studied. For example, Vanem and Fazeres-Ferradosa [4] studied the truncated translated Weibull model, Alotaibi et al [5] considered the alpha power Weibull distribution to deal with the engineering datasets, Tach [6] proposed a three-component additive Weibull distribution and applied it for modeling the reliability datasets, Abd El-Monsef et al [7] analyzed a reliability dataset using the Poisson modifed Weibull model, Dessalegn et al [8] introduced the modifed Weibull model for the bamboo fbrous dataset, Rehman et al [9] analyzed the failure data by using another modifed Weibull model, and Li et al [10] developed a three-parameter Weibull distribution for modeling the fracture datasets.…”