The work-of-fracture of brittle materials: Principle, determination, and applications
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M. Sakai Department of Materials Science, Toyohashi University of Technology, Tempaku-cho, Toyohashi 441, Japan (Received 9 November 1993; accepted 10 January 1994)
Theoretical and empirical considerations of the work-of-fracture, yWOf, of brittle materials are reviewed. The energy principle of the work-of-fracture provides a modified Irwin similarity relationship in the nonlinear fracture mechanics regime. Various microscopic deformation and fracture processes in the crack wake and the crack-face contact regions contribute to the rising ^?-curve behavior of brittle materials, and then significantly affect the work-of-fracture, resulting in the work-of-fracture that is dependent on the dimension and geometry of test specimens as well as test methods. The requisite for the work-of-fracture to be a material characteristic resistance to failure is discussed in relation to the R-curvc behavior. Some examples of the work-of-fracture test results demonstrate the usefulness of the work-of-fracture for designing brittle materials with improved toughness.
I. INTRODUCTION According to the Griffith theory, the critical stress for fracturing brittle solids through the mode I crack propagation can be described by the initial crack length, #0, elastic modulus, E', Poisson's ratio, v, and the surface energy, y. 1 The surface energy y is defined by the energy per unit surface area required to cut an infinite body and separate it into halves.2 If the fracture process is conducted in a completely "reversible" manner, the work to cleave the material is equal to the "intrinsic surface energy, yo-"2 However, the fracture processes of real solids including even the "most brittle" covalent crystals and inorganic glasses are actually accompanied by "irreversible" processes at the crack tip, which may substantially increase the work for creating new surfaces, if it is compared with the intrinsic surface energy.3 A number of additional energy absorbing processes may occur during primary crack extension. Microscopic examination of the fracture surface of polycrystalline ceramics, refractories, and ceramic composites, as well as various types of cement-based materials and rocks, reveals quite complex fracture processes.4'5 Even in the fracture surface of single crystals there are numerous imperfections including dislocations, twin deformation, cleavage steps and lines, etc.3 In some materials, not only is crack branching evident in the frontal process zone, but also the zone shielding by microcracking and/or compressive residual stresses in the following crack wake region, as well as crack-face bridging.6"9 All 1412 http://journals.cambridge.org
J. Mater. Res., Vol. 9, No. 6, Jun 1994 Downloaded: 14 Mar 2015
of these fracture processes add increments of energy consumption to the intrinsic surface energy, y 0 . These irreversible processes in the crack-wake and crack-face contact regions may be developed progressively with crack extension, leading to an increased fracture resistance prior to the transition to unstable fracture.6"9 Accordin
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