Sub-10-micrometer toughening and crack tip toughness of dental enamel

Abstract

In previous studies, enamel showed indications to occlude small cracks in-vivo and exhibited R-curve behaviors for bigger cracks ex-vivo. This study quantifies the crack tip toughness (K I0, K III0 ), the crack closure stress and the cohesive zone size at the crack tip of enamel and investigates the toughening mechanisms near the crack tip down to the length scale of a single enamel crystallite. The crack-opening-displacement (COD) profile of cracks induced by Vickers indents on mature bovine enamel was studied using atomic force microscopy (AFM). The mode I crack tip toughness K I0 of cracks along enamel rod boundaries and across enamel rods exhibit similar range of values: K I0,Ir =0.5-1.6MPa.m 0.5 (based on Irwin's 'nearfield' solution) and K I0,cz =0.8-1.5MPa.m 0.5 (based on the cohesive zone solution of the Dugdale-Muskhelishvili (DM) crack model). The mode III crack tip toughness K III0,Ir was computed as 0.02-0.15MPa.m 0.5 . The crack-closure stress at the crack tip was computed as 163-770MPa with a cohesive zone length and width 1.6-10.1µm and 24-44nm utilizing the cohesive zone solution. Toughening elements were observed under AFM and SEM: crack bridging due to protein ligament and hydroxyapatite fibres (micro-and nanometer scale) as well as microcracks were identified.

Influence of structural hierarchy on the fracture behaviour of tooth enamel

“…Besides measurements of stress-strain curves at different length scales, there have been contributions in enamel research investigating the submicrometre fracture toughness and toughening mechanisms with small-scale testing methods [25,26]. Apart from these, additional R-curve measurements provided greater insight into the orientation-related factors associated with crack growth resistance of enamel at larger scales.…”

Towards bio-inspired engineering materials: Modeling and simulation of the mechanical behavior of hierarchical bovine dental structure

“…It has to survive millions of chewing cycles under complex-stress state conditions in the oral environment of the host even in the existence of severe internal cracks and flaws [17,18]. In order to meet this functional requirements enamel should possess damage tolerance capability as evidenced in the recent studies [19,20,21,22,23,24], which has been mainly attributed to the complex hierarchical and graded arrangement of its fiber-like mineral crystals and organic constituents.…”

“…More recently, R-curve measurements [20,22] revealed that the fracture resistance of enamel rises up to 4 MPa m 1/2 due to its graded structure and toughening mechanisms operating on all hierarchical levels [19].…”

“…From experimental data [19,21,40], it is known that in bovine teeth failure is dominated by fiber debonding or fiber breaking in the vicinity of the protein layers. Thus, it is reasonable to resort to a cohesive zone model as proposed in the early 1960s by Barenblatt [41] and Dugdale [42] to represent the region where a material may separate.…”

“…The mineral volume fraction is about 90%-95% [47]. The diameter of a single HAP fiber is approximately 50 nm, surrounded by a a protein layer of a few nanometer thickness, [19]. All simulations are done within the commercial finite element code Abaqus.…”