A hybrid micromechanical-macroscopic model for the analysis of the tensile behavior of cavitating materials
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2/20/04
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A Hybrid Micromechanical-Macroscopic Model for the Analysis of the Tensile Behavior of Cavitating Materials P.D. NICOLAOU and S.L. SEMIATIN A new approach, which combines both micromechanical and macroscopic perspectives of deformation, was developed to simulate the uniaxial tensile deformation of cavitating materials. By this means, limitations and assumptions of previous models were avoided. These include the limitation to the analysis of a symmetric cavity array and a representative unit cell (microscopic models) and the assumption of a homogeneous cavity distribution and failure at a predefined critical cavity volume fraction (macroscopic models). The new model takes into account local variations in cavity density and the possible coalescence of discrete pairs of cavities not necessarily located on the same horizontal plane. The propensity for cavity coalescence via impingement or linkage (due to matrix rupture) was found to depend heavily on the initial cavity density. Simulations of the uniaxial tension test demonstrated that flow localization and thus failure occur earlier during the deformation and cavitation process when local cavity density variations are taken into account. However, the predicted cavity volume fraction at failure is the same for both the hybrid micro-macro and macroscopic models when the initial cavity density is high. In such cases, the predicted tensile ductility is therefore essentially identical.
I. INTRODUCTION
CAVITY formation occurs frequently during secondary (bulk) hot working and superplastic forming of metallic materials, and thus may severely limit the deformation that can be imposed. Nucleation sites for cavities include particles or inclusions, interphase boundaries in microduplex alloys, and matrix-reinforcement interfaces in composites. In severe cases, the nucleation, growth, and coalescence processes that characterize cavitation may lead to local or even gross failure. Because of its industrial significance, the problem of cavitation has therefore been investigated in detail from both experimental and theoretical standpoints. For example, a number of attempts have been made to develop predictive models. These models can be classified as being essentially micromechanical or continuum/macroscopic in nature.[1–8] Micromechanical models typically assume a symmetric array of pre-existing cavities within the material and treat the deformation behavior of a representative unit cell.[9,10,11] The unit cell consists of two regions, a cavity free (“uniform”) one and a cavitated one. The deformation of the unit cell is analogous to the behavior of a macroscopic tension sample with a geometric cross-sectional area defect. Thus, the deformation is higher in the cavity region of the microspecimen. Failure is predicted to occur when strain becomes highly localized in the cavitated region; such an event corresponds to cavity coalescence. The main limitations of micromechanical models are the assumptions that the cavity spacing is uniform and that cavitie
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