A Continuum Model for Single Crystal Cyclic Plasticity
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A Continuum Model for Single Crystal Cyclic Plasticity Biqiang Xu and Yanyao Jiang Department of Mechanical Engineering (312), University of Nevada Reno, NV 89557, U.S.A. ABSTRACT A constitutive model was developed to bridge the cyclic plasticity behavior of single crystals and the corresponding characteristic dislocation structures. Yield and flow were built on the individual slip systems. The Armstrong-Frederick kinematic hardening rule was invoked to capture the Bauschinger effect. A material memory parameter was introduced to consider the amplitude dependence of cyclic hardening. Latent hardening considering the interactions among the slip systems was used to describe the anisotropic cyclic behavior. The experimental results of copper single crystals were used to validate the model developed. It was found that the model was able to adequately describe the well-known three distinctive regions in the cyclic stressstrain curve of the FCC single crystal oriented for single slip and the associated dislocation substructures. The model was capable of capturing the enhanced hardening observed in copper single crystals in multi-slip orientations. For a given loading history, the model can predict not only the saturated stress-strain response but also the detailed evolution of the transient cyclic behavior. The characteristic dislocation structures can be featured with the slip evolution. INTRODUCTION Cyclic plasticity is a reflection of the evolution of microstructures. Copper single crystals oriented for single slip display three distinct regions in the cyclic stress-strain (CSS) curve characterized with a plateau corresponding to the formation of the persistent slip bands (PSBs) [1]. Single crystals oriented for multi-slip were studied with an effort to correlate the behavior of the polycrystalline materials [2]. No plateau exists in the CSS curve of the multi-slip oriented copper single crystals. The cyclic hardening and saturated resolved stresses are critically dependent on the crystal orientation. Most of the crystal plasticity models were developed for monotonic loading or saturated responses under cyclic loading. Little work has been conducted to verify the suitability of the existing models for the predictions of the CSS responses and the corresponding dislocation substructures of single crystals oriented in different directions and subjected to a range of loading magnitudes. In crystal plasticity, an important issue is the consideration of the latent hardening. The current work focuses on a cyclic plasticity model that can capture most of the experimental observations made on copper single crystals. CRYSTAL PLASTICITY MODEL The yield condition is defined in the individual slip system,
(
y α = τ α − xα
)
2
− kα ≤ 0
(1)
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where τ α and x α re
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