Applications of the Theory of Critical Distances in Failure Analysis

Abstract

The Theory of Critical Distances (TCD) is the name which I use to describe a group of methods employed for the prediction of failure in cases where stress concentrations are present and where the failure mode involves cracking, such as fatigue and brittle fracture. Some of these methods are more than fifty years old, some very recent. Precise predictions are possible in cases where accurate stress field information is available, for example using finite element analysis (FEA). In the present paper, however, I concentrate on the use of the TCD for approximate, order-of-magnitude predictions, because these can be very useful during failure analysis. Two material constants are required: the critical distance L and (depending on which method is used) either a critical stress ?o or a critical stress intensity KC. Values of L in engineering materials can vary from microns to centimetres. The critical stress may be equal to the plain specimen strength (static or cyclic) but is often significantly higher. In what follows I show through a series of examples and case studies how knowledge of the approximate values of L and ?o can be very useful when conducting a failure analysis, in assessing the significance of defects and design features. I propose, for the first time in this article, a series of dimensionless numbers, composed of material constants and design variables, which I believe could usefully be adopted in fracture mechanics in the same spirit as they have been in other branches of engineering, such as fluid mechanics.