Elastic-plastic fracture analysis and design using the finite element method

The purpose of analysis in fracture mechanics is to determine characterising parameters which reflect the influence of loading and geometry on the crack tip environment of flawed bodies. Here practical methods are developed which permit the determination of such parameters in general situations. Extensive use of finite element methods has been made to provide relevant field values which are then manipulated to determine the required parameters. However the choice of method to determine field values is arbitrary and is dictated by the ease with which such field values may be found. It is in the manipulation of these values that the fracture mechanics philosophy is introduced.Contributions are made in three areas. First economic methods for the determination of the linear fracture mechanics parameter in general stiuations are developed which are of direct relevance to design procedures. Detailed discussion of the Dugdale model of fracture behaviour is then given and a general method for determining Dugdale model solutions is provided. This method is used to provide solutions for standard specimen geometries and it is suggested that such solutions will enable a rational evaluation of the general applicability of the model. However the method is such that, should sufficient confidence in the model be established, design calculations on its premises may be performed. Finally, it is demonstrated that materials which allow extensive plastic flow at a flaw tip prior to fracture may be analysed using the basic ideas of fracture mechanics. It is shown that a line integral provides a flaw tip environment parameter for materials deforming according to the physically appropriate Prandtl-Reuss laws of plasticity. It is hoped that these results will indicate a rational approach to correlating fracture behaviour in such situations.