Mechanical behavior and damage kinetics in nodular cast iron: Part II. Hardening and damage
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I. INTRODUCTION
THE partition of the hardening into an effective stress and a back (or internal) stress is widely encountered in the literature[1] dealing with fatigue testing,[2–7] the Bauschinger effect,[8,9,10] or creep,[11] but much less so when monotonic testing is considered.[12,13,14] In the latter case, the mechanical behavior of the material is generally described only by the true stress ((), and such a description is thought to be sufficient as long as no unloading is conducted. Such an approach is even more unusual when damage is considered.[13,15] Roughly summarized, the mechanical behavior is evaluated from the true stress and a damage parameter.[16–19] However, as far as the mechanical behavior—in terms of plasticity and damage—is concerned, the determination of the hardening mechanisms is very fruitful. The definition of effective and back stresses differs according to the authors, and methods are numerous to determine these components. The back stress (X ) induced by a two-phase structure is commonly evaluated by Brown and Stobb’s formula from Eshelby’s works.[10,12,20–25] In this formulation, the inclusion is supposed to be isolated in an infinite medium, so that interaction effects between closely spaced particles are not taken into account and the matrix grain scale is not considered (grain size and texture, for instance). Composite models[14,26] take into account also the differences in the mechanical behaviors of the two phases (dislocation walls and channels, for instance). To evaluate the effective and back stresses, the difference between the forward and reverse curves (D(), termed “permanent softening,” is often measured, especially in literature dealing with the Bauschinger effect. This difference is supposed to be equal to the back stress, such that D( 5 2X.[8,10,22–25] A “transient softening” is sometimes introduced as well, which is supposed to not influence the permanent softening level.[8,23,24,27] But it is observed that some twophase materials, in which important internal stresses are expected to arise, do not exhibit any permanent softening, 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 Compie`gne, 60205 Compie`gne, Cedex, France. E-mail corresponding author at: [email protected] Manuscript submitted July 6, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A
such as dual-phase steels, a/b titanium alloys,[28] NCI,[29,30] etc. In fact, the permanent softening approach assumes that the back stress is not relaxed during reverse loading. But, some works tend to establish that the internal stress is removed by reverse strain in an easier way than it is promoted by forward strain.[10,31,32] So, when the internal stress decays during reverse loading, such an approach does not apply anymore, and the previous relationship becomes D( 5 aX, with a P {0, 2}.[28,29] Much less information about the effect
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