Failure Modes and Grain-Boundary Effects in Polycrystalline Materials
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FAILURE MODES AND GRAIN-BOUNDARY EFFECTS IN POLYCRYSTALLINE MATERIALS M. A. ZIKRY AND W. M. ASHMAWI Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7910 ABSTRACT Dislocation-density based multiple-slip constitutive formulations and specialized computational schemes are introduced to account for large-strain ductile failure modes in polycrystalline aggregates. Furthermore, new kinematically based interfacial grain-boundary regions and formulations are introduced to account for dislocation-density transmission, absorption, and pile-ups that may occur due to grain-boundary misorientations and void interactions. INTRODUCTION Physically based descriptions are needed that can account for dominant physical mechanisms that may occur at different physical scales. Grain-boundary (GB) structure, orientation, and distribution are essential microstructural features that characterize the initiation and evolution of failure modes in crystalline metals, alloys, and intermetallics. The primary purpose of this study is the introduction of an inelastic dislocation density-based multiple-slip crystalline constitutive formulation that can be used to obtain a detailed understanding and accurate prediction of interrelated local material mechanisms that control and affect global deformation and ductile failure modes in f.c.c. polycrystalline aggregates with random GB orientations and distributions. In this formulation, the length scale between multiple-slip crystalline formulations and dislocation densities is bridged by coupling evolutionary equations for the mobile and immobile dislocation densities, through the temperature dependent flow stress and slip-rates on each slip system, to a multiple-slip rate-dependent crystal plasticity formulation. The derivation of these evolutionary equations are based on accepted physical relations, and generally account for thermally activated dislocation activities such as generation, interaction, and annihilation that are generally representative of the dislocation structures in cubic crystalline metals (see for example [1]). Most polycrystalline formulations generally do not account for GB effects such as dislocation-density and slip transmission, blockage, and absorption. These effects could result due to GB orientation, structure, or interfacial stress mismatches (see, for example, Zikry and Kao [2], Ashmawi and Zikry [3], Randle [4], and Nes [5]). In this study, GB effects are accounted for by the introduction of interfacial regions that are used to track slip and dislocation density transmissions and intersections. These accurate representations of overall polycrystalline aggregate behavior are needed for the prediction of failure initiation and evolution due to GB interactions with void clusters.
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MULTIPLE-SLIP CRYSTAL PLASTICITY FORMULATION The crystal plasticity constitutive framework used in this study is based on the formulation developed in Kameda and Zikry [6]. In that formulation, it has been assumed that the deformat
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