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Assessment of the shape of crack-tip plastic zones as a function of applied load

MacKenzie, P.M. and Walker, Colin (2003) Assessment of the shape of crack-tip plastic zones as a function of applied load. In: Handbook of Moiré Measurement. Institute of Physics, Bristol, UK, pp. 51-55. ISBN 0750305223

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Abstract

The plastic yield zones around the end of a crack have been the subject of intense investigation, particularly since the definition of the HRR stress and strain fields some 20 years ago. The whole treatment of the fracture process really depends on the extent of these zones, in relation to the crack length. and the size of the uncracked ligament but the detailed description of the zones has received only passing discussion, largely as a result of the experimental problems involved in obtaining data which will allow an accurate evaluation, particularly in view of the three-dimensional nature of the problem. In some test situations this need give little cause for anxiety. since experimental conditions may be controlled to give a defined yield zone. In general, however, such control cannot be exercised and knowledge of details of the yield locus may well become important. However, if we return to the general case in which, under a mixed loading regime, a crack-tip plastic field will develop, the definitive way of determining the yield locus would be through a knowledge of the strain fields and the use of a criterion which defines yield in terms of strain. For example. the von Mises criterion defines yield as σvM = (σ12 + σ22 - σ1σ2)1/2 (plane stress) such that when σvM &ges; σ0 (where σ0 is the uniaxial yield stress). then the state of the three-dimensional stress is such that the material is in a post-yield condition. In a situation of post-yield plane-stress, then it is possible to derive the stresses from the surface strain components. In this study. the surface strains have been measured using moire interferometry and the von Mises yield criterion assessed at a matrix of points around the crack-tip to detect values of σvM &ges; σ0. The yield locus then separates points where σvM &ges; σ0 from the region further from the crack-tip (in general), where σvM < σ0. This mechanistic definition is the one which is of interest in the calculation of energy-related fracture parameters: it may not produce the same result as would, for example, a surface polish-and-etch treatment to identify dislocation cores. In addition, it should be recalled that the plane-stress condition relates not to the specimen in general but to the region of the yield locus (7 refs.)