Constitutive model of quasicrystal plasticity: Strain-rate and temperature dependence
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Constitutive model of quasicrystal plasticity: Strain-rate and temperature dependence Marc Heggen and Michael Feuerbacher Institut für Festkörperforschung, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany ABSTRACT A constitutive model describing the plasticity of icosahedral quasicrystals [1] was applied to icosahedral Al-Pd-Mn over a wide range of experimental deformation conditions. The model incorporates the evolution of two microstructural parameters: The first, as in crystals, is the dislocation density; the second is a quasicrystal-specific order parameter that accounts for deformation-induced disordering and thermally activated reordering of the quasicrystal structure. Significant strain-rate dependence was found which can be understood by the interactive evolution of these two microstructural parameters. The present work shows that the constitutive model comprehensively describes the features of quasicrystal plasticity over a wide range of experimental conditions. INTRODUCTION The most significant feature of quasicrystal plasticity is the lack of work hardening at high strains. For crystalline materials work hardening is observed, i.e. the flow stress increases at high strains due to the occurrence of subsequent stages of dislocation interaction processes [2, 3]. In quasicrystals an oppositional behavior is found. The flow stress decreases continuously at high strains, i.e. work softening occurs. Work softening has been observed in various quasicrystalline materials like i-Al-Cu-Fe [4], i-Al-Pd-Mn [5, 6], and i-Zn-Mg-Dy quasicrystals [7]. Work softening in i-Al-Pd-Mn quasicrystals was shown to be accompanied by a decrease of the dislocation density at high strains [8]. Recently, the same behavior was observed in i-Zn-MgDy quasicrystals [9]. The basic assumption of the cluster-friction model, which was the first qualitative description of quasicrystal plasticity, is that Mackay-type clusters act as rate-controlling obstacles for dislocation motion [6]. The ordered structure of the quasicrystal, and hence the density of clusters, is destroyed locally during dislocation motion, which leads to the decrease of the density of clusters in the course of plastic deformation. The decrease of obstacles, which limit the dislocation velocity, weakens the structure and leads to work softening in a constantstrain-rate experiment. The first constitutive description of quasicrystal plasticity was published in a pioneering paper by Guyot and Canova [10]. In 2001 a quantitative model formulation of the plastic deformation behavior was presented by Feuerbacher and coworkers [1]. In this work, the degree of order in the quasicrystal structure was expressed introducing an order parameter λ in a heuristic way. Different contributions like topological or chemical order are not distinguished. The evolution of the order parameter λ and the dislocation density ρ in a constant-strain-rate experiment is described in terms of constitutive equations. Stress-strain curves and dislocationdensity evolutions calculated correspo
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