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A set X ⊆ 2 ω with positive measure contains a perfect subset. We study such perfect subsets from the viewpoint of computability and prove that these sets can have weak computational strength. Then we connect the existence of perfect subsets of sets with positive measure with reverse mathematics.

Low-cost TiB whiskers reinforced titanium matrix composite (TMCs) was fabricated with enhanced mechanical performances using in situ technologies and hot working. Morphologies observation indicates that needle-like TiB whiskers with a hexagonal transverse section grow along the [010] direction due to B27 crystal structure and its growth mechanism. Mechanical properties tests show that the mechanical behavior of the TiB whiskers reinforced TMCs is dependent on the deformation amplitudes applied in hot-working. The improvement in yield strength by hot-working is attributed to the TiB whiskers realignment and the refinement of microstructure. Models are constructed to evaluate the realignment of TiB whisker during deformation and the increase in yield strength of the composite at elevated temperatures. These models clarify the alignment effect of TiB whiskers under various deformation amplitudes applied in hot-workings and reveals the yield strength dependence on TiB whiskers orientation.

Uniaxial compression experiments on open-cell copper foams are conducted at strain rates of 10 À2 s À1 , 10 À3 s À1 , and 10 À4 s À1 to obtain the true stress-strain curves. The effects of the strain rate, cell size, and porosity on the mechanical properties is studied. The deformation mechanism of the open-cell copper foams is investigated by experimental research and finite element analysis. The results showed that the compression strength, Young's modulus and yield strength increase with increasing strain rate and decreasing porosity and cell size. A lower strain rate results in higher strain sensitivity. Strainhardening behavior occurred in the process of high-strain-rate loading. The experimental and simulation results indicate that the failure mechanism of the open-cell copper foam is the layer-by-layer collapse failure mechanism and that stress concentrations form easily at the weak pore struts. The simulation results are consistent with the experimental data at the first and second stages. However, the value of true stress predicted by the simulation at the third stage is slightly higher than that of the experiments.

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