Mechanical behavior and damage kinetics in nodular cast iron: Part I. Damage mechanisms
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. INTRODUCTION
IN some ductile materials, fracture arises by nucleation, growth, and coalescence of voids. Several experimental and theoretical laws have been proposed to account for these different parts of the ductile fracture process. To predict void nucleation in the case of large particles (.1 mm), a continuum plasticity approach is generally used.[3–6] The inclusion is usually assumed to be hard, elastic, and isolated in an infinite matrix. It is shown that the local stress in the inclusion or at the interface can be written as a sum of the imposed macroscopic stress and an internal stress resulting from the inhomogeneity in deformation between the matrix and the inclusion. The latter one can be calculated from Eshelby’s theory applied to a plastically deforming matrix.[5,7] For the sake of simplicity, the incompatibility stress can be expressed as lEp«peq, where l is the inclusion shape factor, Ep a tangent plastic modulus, and «peq the equivalent plastic strain. A cavity nucleates at a critical local stress s c, which is dependent on critical macroscopic mechanical parameters. However, in most materials, factors such as shape, orientation[8,9,10] or spacing between particles,[11] are randomly distributed. Since such factors modify the incompatibility stress, nucleation becomes a continuous process and more complicated to predict. To describe such a phenomenon, some authors[11,12] have discussed the statistics of the particles. In this theoretical way, Chu and Needleman have adopted the simple idealization that there is a mean critical stress (or a critical strain for small particles) for nucleation and that the nucleation stress is distributed in a normal way about that mean. Concerning the second part of the damage process, numerous studies have provided analytical laws to describe growth of a single void. Various void geometries (cylindrical, spherical) and matrix behaviors (rigid-plastic, linearly, or powerlaw viscous) have been used.[13,14,15] All these approaches C. GUILLEMER-NEEL, Research Scientist, X. FEAUGAS, Assistant Professor, and M. CLAVEL, Professor, are with the Laboratoire Roberval UMR UTC-CNRS, Equipe Me´canique, De´partement de Ge´nie Me´canique, Universite´ de Technologie de Campie`gne, 60205 Campie`gne Cedex, France. E-mail corresponding author at: [email protected] Manuscript submitted July 6, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A
agree with the following classical growth law: dR/R 5 f(x)d«peq, where R is the mean actual void radius, x the stress triaxiality, and «peq the plastic strain. Among these analyses, the coupled Gurson–Tvergaard’s model[16,17] will be favored in the following. The void growth is then derived from the macroscopic behavior of the porous material by means of the mass balance equation. The last stage of ductile fracture is certainly the least understood since void coalescence is an instability process. Different modes of coalescence have been reported: necking of the intervoid matrix, plastic shear localization, nucleation of small voids betw
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