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On the fractal nature of crack branching in MgF2

Published online by Cambridge University Press:  31 January 2011

J. J. Mecholsky Jr ,
Richard Linhart ,
Brian D. Kwitkin  and
Roy W. Rice
J. J. Mecholsky Jr
Affiliation:
University of Florida, Gainesville, Florida 32611
Richard Linhart
Affiliation:
University of Florida, Gainesville, Florida 32611
Brian D. Kwitkin
Affiliation:
University of Florida, Gainesville, Florida 32611
Roy W. Rice
Affiliation:
5411 Hopark Drive, Alexandria, Virginia 22310–1109
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Abstract

Nineteen disks of IR window grade, hot pressed magnesium fluoride (˜0% porosity, grain size ˜1 μm) previously loaded in ring-on-ring flexure tests were used to analyze the crack branching patterns. Fractal geometry was used to determine the crack branching fractal dimension which was named the crack branching coefficient or CBC. The failure stress was proportional to the CBC and the number of pieces generated during the fracture. Thus, the number of pieces was proportional to the crack branching coefficient. The crack branching coefficient is distinct from the fractal dimension obtained from the onset of mist and hackle on the fracture surface. The fractal dimension of the fracture surface is, in most cases for brittle materials, a constant and related to the crack tip stress field. The crack branching fractal dimension is a function of the stress at fracture and the far-field stress distribution, or in other words, related to both the type and magnitude of loading. The findings in this work have strong implications for many commercial processes such as comminution, attrition, grinding, and basic studies in crack branching.

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Articles
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Journal of Materials Research , Volume 13 , Issue 11 , November 1998 , pp. 3153 - 3159
Copyright
Copyright © Materials Research Society 1998

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