Abstract
Damage diffusion, concentration and localization are investigated by introducing a small non-uniform initial damage in the material. Several parameters characterizing the local and global damage non-uniformities are defined mathematically, and relations are established between these parameters and the constitutive laws for damaged materials through a simple one-dimensional calculation. The influence of damage non-uniformity on the material failure is illustrated by a quantity termed rupture toughness, defined as the specific plastic work the material can absorb prior to failure. Six continuum damage models are examined for their damage distribution characteristics by means of this methodology. For rate independent processes under stress controlled loading, the damage models based solely on the effective stress, such as the models advanced by Broberg ( J. appi. Mech. 41, 809, 1974) and by Roussiler (contribution to the research of fracture of metals in the elastic-plastic fields. Thesis of Ecole Polytech., Univ. Paris, 1979), show damage localization at a relatively low damage level, and a global concentration on both damage and plastic deformation fields. The same features are incorporated in Gurson's model ( J. Engng Mater. Tech. 99, 2, 1977) provided void nucleation is ignored. As to the creep damage processes, the phenomenological theory of Kachanov ( Ivz. Akad. Nauk., S.S.R., Otd. Tech. Nauk., No. 8, 1958) shows a range of damage distribution behaviour according to the ranges of its parameters and initial damage distribution. Damage diffusion prevails for creep damage growth controlled by grain boundary diffusion ( Cocks and Ashby, Prog. Mater. Sci. 27, 189, 1982). For the creep damage processes controlled by surface diffusion ( Cocks and Ashby, 1982), however, damage localization occurs at an early stage of damage evolution.
Published Version
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