Atomistic considerations on the fracture toughness of brittle materials
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A simple atomistic approach to the mechanical strength and the fracture toughness of brittle materials is made by the use of a universal expression for binding potential energy versus atomic separation curves. The scaling factors for the atomic separation and for the energy amplitude successfully apply to describing the intrinsic fracture toughness K* in a scaled dimensionless form. It is demonstrated that the intrinsic fracture toughness combined with a stress shielding coefficient (SSC) yields the fracture toughness of real materials. Microfracture mechanisms for crack-tip stress-shielding processes, as well as the interrelationship between the stress intensity- and the potential energy-derived fracture toughness, are addressed.
I. INTRODUCTION The key functions of the present linear elastic fracture mechanics (LEFM) are summarized as follows1: (1) quantitative description of the stress-strain field for a sharp crack or a flaw embedded in an elastic body, and (2) prediction and assessment of strength and lifetime of engineering structures on the basis of a "criterion for fracture". The criterion describing the critical state for an equilibrium crack has its basis on an assumption of a "certain" critical value of the stress intensity factor Kc of the crack. It is assumed that the crack will start propagating once the stress intensity factor K increases to a "certain" critical value Kc (the fracture toughness). The present LEFM by no means addresses the physical processes and mechanisms of this critical state. None of the atomistic and microstructural considerations on fracture toughness have been conducted in the LEFMregime. It is important to recognize that the fracture criterion of LEFM is merely a hypothesis because of the absence of atomistic fracture physics.2 This LEFM criterion introduces serious difficulty and confusion to the fracture analysis of composite materials which exhibit extremely complex fracture behavior, 35 although it is successful and plays an important role in predicting fracture behavior of monolithic materials, where the fracture toughness Kc in the plane strain condition of these materials is "fortunately" a characteristic material parameter. Nothing is answered by LEFM regarding the questions: "What is the physical meaning of fracture toughness?"; "How does the bonding nature between the constituent atoms relate to the fracture toughness?", "What types of microstructures contribute to increased toughening?", etc. The first atomistic considerations on strength are credited to Orowan.6 He gained a good insight into the 668
J. Mater. Res., Vol. 8, No. 3, Mar 1993
http://journals.cambridge.org
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important relation among the strength, surface energy, Young's modulus, and the equilibrium interatomic separation by reverting to a simple atomistic model. However, the principles underlying his derivation are critical in much of what follows, for the essential feature must be dictated by the requisite of global energy balance between the fracture energy required to creat
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