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We demonstrate reversible movement of 1/2[11[over ]0](110) dislocation loops generated from nanodisturbances in a beta-titanium alloy. High resolution transmission electron microscope observations during an in situ tensile test found three reversible deformation mechanisms, nanodisturbances, dislocation loops and martensitic transformation, that are triggered in turn with increasing applied stress. All three mechanisms contribute to the nonlinear elasticity of the alloy. The experiments also revealed the evolution of the dislocation loops to disclination dipoles that cause severe local lattice rotations.

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In this paper a second-order two-scale (SOTS) analysis method is developed for a static heat conductive problem in a periodical porous domain with radiation boundary condition on the surfaces of cavities. By using asymptotic expansion for the temperature field and a proper regularity assumption on the macroscopic scale, the cell problem, effective material coefficients, homogenization problem, first-order correctors and second-order correctors are obtained successively. The characteristics of the asymptotic model is the coupling of the cell problems with the homogenization temperature field due to the nonlinearity and nonlocality of the radiation boundary condition. The error estimation is also obtained for the original solution and the SOTS’s approximation solution. Finally the corresponding finite element algorithms are developed and a simple numerical example is presented.

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