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

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 charac- teristic 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 un- stable, 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 deter- mined from experimental data were found to be broadly similar to microstructural quantities (e.g. grain size) but an understandingof themicromechanism offailureis not necessary since the TCD is a continuum-mechanics ap- proach. 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 issubjectto many ofthesame limitationsas 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 theTCD greatly extends theapplicationsofLEFM, al- lowingpredictionsto be made fornotches and stresscon- centration features of any geometry for which an elastic stress analysis can be obtained. keyword: Theory of critical distances, brittle fracture, metals, constraint.