title: Finite element analysis of depth effect on measuring elastic modulus of a core-shell structure for application of instrumented indentation in tooth enamel.
abstract: Tooth enamel is a complex structure, consisting of numerous enamel rods surrounded by a protein-rich sheath. Considering the possible effect of the protein-rich sheath on the indentation deformation of an enamel rod and the limitation of the Oliver-Pharr method in measuring the elastic modulus of the enamel rod, we used a finite element method to analyze the indentation deformation of an elastic-perfectly plastic cylinder surrounded by an elastic-perfectly plastic film. A concept of the threshold indentation depth was proposed, at which the percentage error of the measured modulus of the cylinder is ±10%. For the indentation depth less than the threshold indentation depth, the elastic modulus measured from the indentation test can be approximated as the intrinsic elastic modulus of the cylinder. The normalized threshold indentation depth strongly depends on the modulus ratio of the film to the cylinder and the ratio of the film thickness to the cylinder radius. The results can be used to guide the use of the Oliver-Pharr method in characterizing the mechanical properties of tooth enamel and bio-composites with core-shell structures.
authors.affiliation: Key Laboratory of Pressure System and Safety, MOE, School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, People's Republic of China; Materials Program, Department of Chemical and Materials Engineering, University of Kentucky, Lexington, KY 40506, USA.
authors.forename: Yunfei
authors.initials: Y
authors.lastname: Jia
authors.affiliation: Key Laboratory of Pressure System and Safety, MOE, School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, People's Republic of China. Electronic address: fzxuan@ecust.edu.cn.
authors.forename: Fu-Zhen
authors.initials: FZ
authors.lastname: Xuan
authors.affiliation: Materials Program, Department of Chemical and Materials Engineering, University of Kentucky, Lexington, KY 40506, USA. Electronic address: fyang0@engr.uky.edu.
authors.forename: Fuqian
authors.initials: F
authors.lastname: Yang
mesh_terms: D003743:Dental Enamel / Q000737:chemistry*; D055119:Elastic Modulus; D020342:Finite Element Analysis; D008962:Models, Theoretical
keywords: Dimensional analysis; Indentation; Oliver–Pharr method; Threshold indentation depth