Abstract
Ductile fracture of structural metals occurs mainly by the nucleation, growth and coalescence of voids. Here an overview of continuum models for this type of failure is given. The most widely used current framework is described and its limitations discussed. Much work has focused on extending void growth models to account for non-spherical initial void shapes and for shape changes during growth. This includes cases of very low stress triaxiality, where the voids can close up to micro-cracks during the failure process. The void growth models have also been extended to consider the effect of plastic anisotropy, or the influence of nonlocal effects that bring a material size scale into the models. Often the voids are not present in the material from the beginning, and realistic nucleation models are important. The final failure process by coalescence of neighboring voids is an issue that has been given much attention recently. At ductile fracture, localization of plastic flow is often important, leading to failure by a void-sheet mechanism. Various applications are presented to illustrate the models, including welded specimens, shear tests on butterfly specimens, and analyses of crack growth.
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Notes
An alternative limit-analysis based on velocity fields orthogonal to these spheroids was proposed by Garajeu et al. (2000).
There is a slight gap between numerical and theoretical results for the orientation angle \(\theta \); but this gap is present from the very start of the loading (and not compensated afterwards), which indicates that it may be due to the difficulty, when examining the numerical results, of defining an orientation angle for an almost spherical, but not strictly ellipsoidal cavity.
That softening models have their roots in homogenization is very often only implicit, but in the case of Gurson-type models quite clear and explicit.
This means that the homogenization procedure based on such boundary conditions intrinsically remains a model, in contrast with other procedures using rigorous, for instance periodic, boundary conditions.
The price to pay is, unfortunately, a larger bandwidth of the stiffness matrix than for a first-gradient model, because this matrix does not only “connect” first-neighbor nodes (contained in the same element), but also “third-neighbor” ones (having first neighbors lying in the same element).
The emphasis is ours.
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Acknowledgments
AAB acknowledges the support of the National Science Foundation under Grant Number CMMI-1405226. AN is grateful for the support provided by the National Science Foundation under Grant Number CMMI-1200203.
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An erratum to this article can be found at http://dx.doi.org/10.1007/s10704-016-0159-x.
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Benzerga, A.A., Leblond, JB., Needleman, A. et al. Ductile failure modeling. Int J Fract 201, 29–80 (2016). https://doi.org/10.1007/s10704-016-0142-6
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DOI: https://doi.org/10.1007/s10704-016-0142-6