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The in-situ continuous cooling ␤-to-␣ transformation kinetics of extra-pure (EP) Ti and of grade-4 commercially pure (CP) Ti were investigated using a fully computer-controlled resistivity-temperature realtime measurement apparatus and transmission electron microscopy. The ␤-to-␣Ј martensitic transformation occurs under near pure shear condition, and the habit plane of lath-type martensite was determined to be parallel to , which is in good agreement with the prediction of the crystallographic theory. The M s temperature of EP-Ti was measured as 800 °C and can be raised by up to about 40 °C due to the generation of thermal stress and local deformation during rapid cooling. The massive transformation was, for the first time, observed to occur over a wide range of cooling rates in an EP-Ti. The massive start temperature and its occurrence were, unlike the martensitic transformation, hardly affected by the generation of thermal stress and local deformation during rapid cooling. The stable regime of massive transformation in a grade-4 CP-Ti was considerably shifted toward a slower cooling rate side and was significantly contracted at the same time. This is because the presence of iron impurity not only largely suppresses the massive transformation but also significantly delays a long-range diffusional transformation. 54336b(4150)a¿

The elastic behavior of Ti–40 wt % Nb single crystal near martensite start (Ms) temperature was studied using a resonant ultrasound spectroscopy measurements and the first principle calculation. The experimental results showed that both c′ and cs shear moduli tended to soften as the temperature decreased from room temperature down to and across the Ms temperature of 267 K, suggesting that both the {112}⟨111⟩ and {110}⟨110⟩ shears were operating during martensitic transformations of disordered bcc to orthorhombic structure. The consideration of detailed atomic mechanisms involved in the shear sequences and the calculation of the energy of intermediate state suggested that the {110}⟨110⟩ shear was operating as primary shear and the {112}⟨111⟩ shear operating as a secondary shear to complete the transformation. The measurement further showed that the anisotropy constant, A, was rather increasing at the transition temperature approaching Ms, similarly to the transformation of ordered bcc (B2) to orthorhombic (B19) martensite.

A three-dimensional contact problem with the orthotropic Coulomb friction is formulated in the form of a system of nonlinear equations. The nonlinear complementarity formulation derived naturally from the three-dimensional frictional contact phenomenon is used in the numerical analysis without such linearization as previously introduced. The probability-one homotopy method known as a globally convergent zero-finding algorithm is implemented as an exact method and applied to each incremental step. The method is illustrated by two three-dimensional problems and the results are compared with those of commercial package and other approximations.

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