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Prof C M F Rae

This course examines the use of Fracture Mechanics in the prediction of mechanical failure. We explore the range of macroscopic static failure modes and extend these principles to fatigue failure.

The first part of the course (Fracture) focusses on fast fracture in brittle and ductile materials, principally metals. This includes the characteristics of fracture surfaces, inter-granular and intra-granular failure, cleavage and micro-ductility. The quantitative application of Elastic Fracture Mechanics is explained, together with the modifications necessary to include ductile cleavage behaviour.

In the second part of the course (Fatigue) we describe the range of fatigue failure including high and low cycle fatigue and thermo-mechanical fatigue. The effects of variables in testing regimes and the environment and microstructure are included. The various strategies used to predict the service lives of components are critically discussed. The potential origins of crack formation are considered and the quantitative application of the Paris law and fracture mechanics to predict the growth of fatigue cracks is described.

This lecture course will cover:


  • Revision of concept of energy release rate, G, and fracture energy, R. Obreimoff's experiment. Brittle and ductile failure. Timeline for developments.
  • Linear Elastic Fracture Mechanics, (LEFM). We look at the three loading modes and hence the state of stress ahead of the crack tip. This leads to the definition of the stress concentration factor, stress intensity factor and the material parameter the critical stress intensity factor.
  • Superposition principle. Mixed mode loading and the prediction of crack growth direction.
  • Plasticity at the crack tip and the principles behind the approximate derivation of plastic zone shape and size. Limits on the applicability of LEFM. The effect of constraint, definition of plane stress and plane strain and the effect of component thickness.
  • Concept of G - R curves: measuring G and K.
  • Elastic-Plastic Fracture Mechanics; (EPFM). The definition of alternative failure prediction parameters, Crack Tip Opening Displacement, and the J integral. Measurement of parameters and examples of use.
  • Reading fracture surfaces: The effect of microstructure on fracture mechanism and path, ductile and cleavage failure, factors improving toughness.


  • Definition of terms used to describe fatigue cycles, High Cycle Fatigue, Low Cycle Fatigue, mean stress R ratio, strain and load control.
  • Total life and damage tolerant approaches to life prediction: Paris law and S-N curves.
  • Adapting test data to real conditions: Goodman's rule and Miner's rule. Micro-mechanisms of fatigue damage, fatigue limits and initiation and propagation control, leading to a consideration of factors enhancing fatigue resistance.
  • Factors affecting crack growth rates: Creep, oxidation and corrosion. Dissipation energy criterion for crack growth.