A Microstructure-Based Mechanistic Model for Bone Sawing: Part 1—Cutting Force Predictions

Abstract

This two-part paper is aimed at developing a microstructure-based mechanistic modeling framework to predict the cutting forces and acoustic emissions (AEs) generated during bone sawing. The modeling framework is aimed at the sub-radius cutting condition that dominates chip-formation mechanics during the bone sawing process. Part 1 of this paper deals specifically with the sawing experiments and modeling of the cutting/thrust forces. The model explicitly accounts for key microstructural constituents of the bovine bone (viz., osteon, interstitial matrix, lamellar bone, and woven bone). The cutting and thrust forces are decomposed into their shearing and ploughing components. Microstructure-specific shear stress values critical to the model calculations are estimated using micro-scale orthogonal cutting tests. This approach of estimating the microstructure-specific shear stress overcomes a critical shortcoming in the literature related to high-strain rate characterization of natural composites, where the separation of the individual constituents is difficult. The six model coefficients are calibrated over a range of clinically relevant depth-of-cuts (DOCs) using pure haversian regions (comprising of osteon and interstitial matrix), and pure plexiform regions (comprising of lamellar bone and woven bone). The calibrated model is then used to make predictions in the transition region between the Haversian and plexiform bone, which is characterized by gradient structures involving varying percentages of osteon, interstitial matrix, lamellar bone, and woven bone. The mean absolute percentage error in the force predictions is under 10% for both the cutting and thrust forces. The reality of spatially varied properties in the cortical bone limits the universal use of microstructure-specific shear stress values reported here. Fundamental advancements in the literature associated with both high-strain rate bone mechanics and machining are needed to address this critical limitation.