A phase field model is presented to study dislocation formation (coherency loss) in two-phase binary alloys. In our model the elastic energy density is a periodic function of the shear and tetragonal strains, which allows multiple formation of dislocations. The composition is coupled to the elastic field twofold via lattice misfit and via composition-dependence of the elastic moduli. By numerically integrating the dynamic equations in two dimensions, we find that dislocations appear in pairs in the interface region and grow into slips. One end of each slip glides preferentially into the softer region, while the other end remains trapped at the interface. Under uniaxial stretching at deep quenching, slips appear in the softer region and do not penetrate into the harder domains, giving rise to a gradual increase of the stress with increasing applied strain in plastic flow.
We develop a nonlinear elasticity theory in which the elastic energy is a periodic function of five strain components in three dimensions. We then study dislocation formation under applied shear strain in one and two phase alloys. In two phase states loops of edge dislocations appear in the interface regions with increasing strain. They grow into the softer regions gliding along the Burgers vector. These results are crucial to understand mechanical properties of two phase solids.
Using a Ginzburg-Landau model, we study the phase transition behavior of
compressible Ising systems at constant volume by varying the temperature $T$
and the applied magnetic field $h$. We show that two phases can coexist
macroscopically in equilibrium within a closed region in the $T$-$h$ plane. It
occurence is favored near tricriticality. We find a field-induced critical
point, where the correlation length diverges, the difference of the coexisting
two phases and the surface tension vanish, but the isothermal magnetic
susceptibility does not diverge in the mean field theory. We also investigate
phase ordering numerically.Comment: 13 figure
We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure. With this new ingredient, solving the equations yields formation of dislocation dipoles or slips. In plastic flow high-density dislocations emerge at large strains to accumulate and grow into shear bands where the strains are localized. In addition to the elastic displacement, we also introduce the local free volume m. For very small m the defect structures are metastable and long-lived where the dislocations are pinned by the Peierls potential barrier. However, if the shear modulus decreases with increasing m, accumulation of m around dislocation cores eventually breaks the Peierls potential leading to slow relaxations in the stress and the free energy (aging). As another application of our scheme, we also study dislocation formation in two-phase alloys (coherency loss) under shear strains, where dislocations glide preferentially in the softer regions and are trapped at the interfaces.
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