By Michael Innes
Writer of detective novels, Priscilla Pringle, is happy to discover that she is sharing a railway compartment with a gentleman who occurs to be interpreting one in every of her books—Murder within the Cathedral. he's army officer, Captain Bulkington, who acknowledges leave out Pringle and provides her £500 to collaborate on a detective novel. To everyone's shock, pass over Pringle is quite inquisitive about Captain Bulkington, yet is she out of her intensity?
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The great success of fracture mechanics has been to show that, under certain well-defined conditions, the propagation of the crack can be predicted using some very simple linear elastic analysis. When these conditions prevail, we are in the realm of Linear Elastic Fracture Mechanics (LEFM). We will first describe the basic theory of LEFM, leaving discussion of its limitations and assumptions for later. , 2002; Knott, 1973). We can predict the conditions necessary for brittle fracture, and also for slow crack growth by fatigue and stress-corrosion cracking, assuming that a crack already exists.
The justification for using LEFM is generally explained as follows: provided the non-linear zone is small compared to the dimensions of the body – that is provided the surrounding linear-elastic zone is much larger than the process zone – then conditions of stress and strain inside the non-linear zone, though they may be poorly known, are nevertheless uniquely characterised by conditions within the linear zone. This statement is much easier to make than it is to prove – for the interested reader I feel that Broberg, in his recent book, probably comes closest to a theoretical proof (Broberg, 1999).
We have not discussed here many of the more advanced techniques, which will be described in subsequent chapters; however, these techniques are, for the most part, used only in academic research and not in engineering practice. The current position is unsatisfactory, containing limitations which ultimately affect our ability to design load-bearing structures with confidence. We can predict material failure with precision only in two rather special cases. The first is simple tension, as described by the stress–strain curve, and the second is the propagation of pre-existing cracks as described by LEFM.