An Updated Lagrangian finite element formulation, valid for the analysis of large deformations in elastic and elasto-plastic materials, is derived and the structure of the associated computer program described. The formulation involves a Jaumann stress rate in the constitutive law. An eight-node isoparametric quadrilateral element is employed together with a procedure which repositions each mid-side node. Solutions to several structural examples are compared with analytical or experimental results. Both plane stress and plane strain conditions are assumed in a detailed study of a centre notch specimen under tensile loading. Comparison of results obtained using small and large strain programs show that the effect of crack tip blunting is greater in plane strain than in plane stress. Two fracture criteria are investigated. The effects of large scale plane strain yielding and crack tip blunting on the theoretical background to a criterion which requires a critical opening at a fixed distance behind the crack tip are assessed. The second criterion, based on the crack separation energy, had been employed previously to reproduce experimental results of stable crack growth despite differences between numerical and theoretical predictions. The present work confirms the theoretical predictions, in particular that the crack separation energy is zero for an infinitesimal crack advance. A mathematical analysis demonstrates that due to special circumstances in the previous numerical calculations, this criterion was in fact equivalent to a strain-related criterion.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:637972 |
| Date | January 1983 |
| Creators | Mackay, D. C. |
| Publisher | Swansea University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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