Fracture of Brittle Solids

Abstract

This is an advanced text for higher degree materials science students and researchers concerned with the strength of highly brittle covalent–ionic solids, principally ceramics. It is a reconstructed and greatly expanded edition of a book first published in 1975. The book presents a unified continuum, microstructural and atomistic treatment of modern day fracture mechanics from a materials perspective. Particular attention is directed to the basic elements of bonding and microstructure that govern the intrinsic toughness of ceramics. These elements hold the key to the future of ceramics as high-technology materials - to make brittle solids strong, we must first understand what makes them weak. The underlying theme of the book is the fundamental Griffith energy-balance concept of crack propagation. The early chapters develop fracture mechanics from the traditional continuum perspective, with attention to linear and nonlinear crack-tip fields, equilibrium and non-equilibrium crack states. It then describes the atomic structure of sharp cracks, the topical subject of crack-microstructure interactions in ceramics, with special focus on the concepts of crack-tip shielding and crack-resistance curves, and finally deals with indentation fracture, flaws, and structural reliability.

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

“…The measured half crack opening profiles (u) versus crack length behind the crack tip (X) are shown in Fig 2(a) and are used to calculate K I0,Ir by the following equation that describes the near-tip COD profile for a straight crack (Irwin, 1958;Lawn, 1993) [Irwin, 1958;Lawn, 1993], and the crack closure stress near the crack tip, the width and length of the cohesive zone and the corresponding crack tip toughness based on cohesive zone solutions developed for Dugdale-Muskhelishvili crack model by Goodier and Field [Dugdale, 1960;Goodier and Field, 1963;Hahn and Rosenfeld, 1965;Hahn, 1976 ( )…”

“…The crack opening up to 10µm behind the crack tip are not associated with observable ligament bridges and are used in the calculation. A key assumption in utilizing the Irwin's 'near-field' solutions is that the crack walls behind the tip remain free of traction (Irwin, 1958;Lawn, 1993). u versus X 1/2 was plotted ( Fig.…”

“…2(b) Similar to Eq. (1), the mode III crack tip toughness, K III0,Ir can be described by the following equation (Irwin, 1958;Lawn, 1993), with u z being the height difference of two crack walls (Fig. 1(e) (C) Cohesive zone: The u versus X plot ( Fig.…”

“…With this information Irwin's crack tip solution (Irwin, 1958;Lawn 1993) is applied to evaluate K I0 .…”

“…AFM is used as a high spatial resolution tool for COD measurement to calculate K I0 (Irwin, 1958;Lawn 1993). The information is also used to apply a cohesive zone models developed by Goodier and Field (Goodier and Field, 1963;Hahn, 1976;Hahn and Rosenfeld, 1965) for the Dugdale-Muskhelishvili crack model (Dugdale, 1960;Muskhelishvili, 1953) to compute the closure stresses at the crack tip, the cohesive zone width and length, as well as the corresponding crack tip toughness.…”