Failure Analysis

   Failure as a Design      Criterion

   Fracture Mechanics


Tutorial Questions


Griffith Equation


Stress Intensity Factor and Fracture Toughness Testing


Characterising Sub-Critical Growth
 -  Fatigue Life Prediction
 -  Stress Corrosion Cracking


Theory Resource

Professor M Neil James - New tutorial homepage:

This tutorial has been developed by Professor M Neil James at the University of Plymouth, and is based on a number of years experience with the problems that arise in teaching applied fracture mechanics to engineering undergraduates. The author would welcome feedback and comments and can be contacted at: Copyright of original material is retained by the author.

His home page is:

He has also developed web-based resources dealing with 'Design as a Generic Tool' that cover issues around the philosophy of design, ethics in engineering, sustainability and failure as a design criterion. This latter document contains extensive analysis of some classic failures, drawing out the implications for design and technological advance. The latest activity is the development of an extensive set of of interactive failure analysis case studies, which includes a comprehensive fractography resource.


Fracture mechanics is the field of solid mechanics that deals with the behaviour of cracked bodies subjected to stresses and strains. These can arise from primary applied loads or secondary self-equilibrating stress fields (e.g. residual stresses). The power of fracture mechanics really lies in the fact that local crack tip phenomena can, to a first order, be characterised by relatively easily measured global parameters, e.g. crack length and nominal global stress (calculated in the absence of the crack), together with finite geometry correction factors Use of fracture mechanics in engineering critical assessment of defects has been codified in documents like British Standards PD 6493 : 1991 (Guidance on Methods for Assessing the Acceptability of Flaws in Fusion Welded Structures - currently under revision as BS 7910 - Guide on Methods of Assessing the Acceptability of Flaws in Structures) and the CEGB R6 procedure (Assessment of the Integrity of Structures Containing Defects).   These procedures involve two-parameter assessment through a Failure Assessment Diagram (FAD) which considers the independent possibility of plastic collapse and fast fracture, and are available in software packages, e.g. Crackwise from TWI (PD 6493) and R6-Code from British Energy.

A number of parameters which characterise the propensity for fast fracture have been defined; the decision as to which one is applicable to a particular case is determined by the level of crack tip plasticity (see Fig. 6.1 from Fracture Mechanics by HL Ewalds and RJH Wanhill, Edward Arnold 1989). Epfm.gif (103477 bytes)
In the regime where the global stress-strain response of the body is linear and elastic (LEFM), the stress intensity factor K is used. In the plastic collapse region, design can be done on the basis of ensuring that net section yield does not occur, whilst in the elastic-plastic region EPFM, nowadays called yielding fracture mechanics YFM, is applicable. The fracture characterising parameters in YFM are the J-integral and the crack opening displacement, COD. All these fracture characterising parameters meet both the Griffith energy criterion for fast crack growth, and the critical stress/strain criterion. For simple cases, fracture problems can be approached via the Griffith equation, which is particularly suitable for sharp cracks/defects in brittle materials.

Some additional information on the history of fracture mechanics, particularly the three modes (ways) of loading a crack and on the stress concentrations associated with a crack, can be found in the concrete dam section of the simscience web site which provides a number of examples of simulations of engineering phenomena.

For this introductory course in fracture mechanics, tutorial questions are based on the Griffith equation or use of the stress intensity factor, with account taken of local crack tip plasticity through Irwin's plastic zone correction to crack length. Decisions as to whether LEFM is valid or not are based on assessing the extent of crack tip plasticity, relative to the crack and specimen dimensions.

Note that elementary knowledge of solid mechanics is required to apply elementary fracture mechanics successfully. Several detailed stress analysis websites are available that cover solid mechanics in much greater detail than this tutorial requires, and they form an excellent resource for students. 

Other fracture mechanics tutorials are available on the internet, e.g. at the site developed by Douglas Wright at the University of Western Australia, which deals fracture problems as a subset of Design and Analysis of Machine Elements.


Failure Analysis  -  Fracture Mechanics  -  Failure As A Design Criterion