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The Theory of Critical Distances Applied to the Prediction of Brittle Fracture in Metallic Materials


1 Mechanical Engineering Dept., Trinity College Dublin, Ireland

Structural Durability & Health Monitoring 2005, 1(2), 145-154.


The Theory of Critical Distances (TCD) is a general term for any of those methods of analysis which use continuum mechanics in conjunction with a characteristic material length constant, L. This paper discusses the use of two simple versions of the TCD: a point-stress approach which we call the Point Method (PM) and a line-average approach: the Line Method (LM). It is shown that they are able to predict the onset of unstable, brittle fracture in specimens of metallic materials containing notches of varying root radii. The approach was successful whatever the micromechanism of crack growth (cleavage or ductile tearing); values of L determined from experimental data were found to be broadly similar to microstructural quantities (e.g. grain size) but an understanding of the micromechanism of failure is not necessary since the TCD is a continuum-mechanics approach. The TCD, in this form, can be thought of as an extension of linear elastic fracture mechanics (LEFM). Whereas LEFM requires one characteristic parameter (Kc), the TCD requires two parameters: Kc and L. The TCD is subject to many of the same limitations as LEFM: in particular it is shown here that the value of L varies with the level of constraint at the notch. However the use of the TCD greatly extends the applications of LEFM, allowing predictions to be made for notches and stress concentration features of any geometry for which an elastic stress analysis can be obtained.


Cite This Article

, D. (2005). The Theory of Critical Distances Applied to the Prediction of Brittle Fracture in Metallic Materials. Structural Durability & Health Monitoring, 1(2), 145–154.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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