The Origin of Griffith Cracks
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DUCTION
OUR well-established theories of brittle fracture require a preexisting crack to initiate failure, as proposed elegantly by Griffith in Cottrell.[1,2] Similarly, ductile failure requires a preexisting population of pores or cracks.[3,4] Often, such cracks appear to be associated with a dispersion of brittle second phases or particles decohered from their matrix, so that under tensile stress, the opening voids can initiate either (1) cracking, by link up of cracks of neighboring particles or (2) failure by plastic flow, the matrix shearing to create knife-edged cusps surrounding dimples which contain at their bases the original fractured or decohered particles. It would be problematic to explain fracture if neither pores nor cracks preexisted in a metal. However, the presence of a defect that could constitute a Griffith crack or a pore is not necessarily to be expected. For instance, solidification cannot be expected to create either pores or cracks because the phase transformation involves merely the movement of atoms by only fractions of an interatomic distance, from a randomly close packed site to a regular close packed site. Effectively, the atoms never come apart. This short account draws attention to the fact that interatomic bonds in metals are so strong that pores and cracks in metals can be formed only at stresses close to the theoretical strengths of solids and, thus, in general would not be expected to exist. The decohesion of JOHN CAMPBELL, Emeritus Professor of Casting Technology, is with the Department of Metallurgy and Materials, University of Birmingham, Birmingham B15 2TT, United Kingdom. Contact e-mail: [email protected] Manuscript submitted July 7, 2011. Article published online September 16, 2011. METALLURGICAL AND MATERIALS TRANSACTIONS B
second phases from a matrix or the opening of a grain boundary would be expected to be impossibly difficult as a result of the high strength of the metallic bond. In contrast, unbonded interfaces that can decohere without difficulty to initiate a crack are expected to be present as defects resulting from most current production processes, including mainly melting and casting, as well as powder metallurgy and metal spraying. Because most engineering metals are made via a melting and casting route, cast metals and their wrought derivatives are discussed mainly here. This short note examines the evidence that the tensile failure of metals occurs probably exclusively from unbonded interfaces entrained during manufacture.
II.
THE PROBLEM
A fascinating question arises as to how failure can occur if the preexisting Griffith crack or the preexisting population of pores did not exist. This is not a trivial question because even a cursory overview of solidification (and of other bulk forming processes such as condensation from a vapor) gives strong pointers that such defects are not to be expected. A. Classic Continuum Theory Using a classic approach, it is easy and quick to demonstrate that solidification cannot produce defects such as a pore: The well-known equation fo
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