Modeling of Dislocation Mobility in Metals: Effect of Obstacles and Thermal Processes
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MODELING OF DISLOCATION MOBILITY IN METALS: EFFECT OF OBSTACLES AND THERMAL PROCESSES Masato Hiratani, Hussein M. Zbib, School of Mechanical and Materials Engineering, Washington State University Pullman, WA 99164-2920 ABSTRACT Thermally activated dislocation glide velocity through weak point obstacle arrays is studied analytically and computationally. Thermal activation rate is estimated using the modified Friedel relations under the weak obstacle approximation. The average flight velocity after an activation event as a function of stress and temperature is obtained by the discrete dislocation dynamics (DD). This numerical calculation includes the effect of self-stress, interaction with electrons and phonons, and the inertial effect. These results are implemented into a phenomenological model to study the dislocation velocity under various conditions. The model can reproduce both obstacle control and drag control motion in low and high velocity regions, and a flow stress anomaly at transient regions. INTRODUCTION Understanding of percolation of dislocations through obstacles is important for modeling the mechanical stability of crystalline materials. In the initial stage of deformation of the well purified materials, limited numbers of dislocations interacts with localized obstacles such as stacking fault tetrahedra (SFTs), vacancy loops, or impurity dilatation centers, which have short range stress fields. The dislocation glide in those cases is essentially jerky and consists of successive small burst of dislocation segments from one local obstacle to the next, as observed in in-situ electron microscopy of material deformation [1]. As a generalization of many experimental data [2], the behavior of velocity v of individual dislocation at various temperature T and the resolved shear stress σ shows two distinctive features in low and high velocity regions around v~1m/s. In the low velocity region, the stress and temperature dependence obeys a power law (non– linear σ dependence) and Arrhenius-type law, respectively. This indicates that the dislocation motion is thermally activated, and local obstacles of various types and the Peierls lattice barrier control the glide resistance. On the other hand, the stress dependence becomes linear and the temperature dependence is reversed in the high velocity region. The motion is controlled by various drag mechanisms resulting from interaction between moving dislocation and quasi-particles such as phonons and electrons. Each controlling mechanism has been studied for long time, however, a few attempts have been made to couple these mechanisms in a unified model, that can describe complex problems such as softening of superconducting materials at low velocity/thermal activation regions, which cannot be described by single mechanism. Suggested combined models ([3][4][5][6]) show that dislocations can overcome local obstacles dynamically by inertial effect at low temperatures where phonon drag practically freezes out. Among them, Landau [6] suggested a consistent approach including
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