Kinetics of biaxial dome formation by transformation superplasticity of titanium alloys and composites
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I. INTRODUCTION
TITANIUM alloys and titanium matrix composites are useful materials in aerospace applications due to their high strength and stiffness, good corrosion resistance, and low density.[1] Although, at elevated temperature, titanium matrix composites typically exhibit low tensile ductility, they can be made superplastic by repeatedly cycling through their ␣/ transformation temperature range while applying an external stress.[2] Polymorphic thermal cycling causes internal strains in these materials due to the volume change associated with the transformation, ⌬V /V, and the mismatch in the strengths and stiffnesses of each phase. Upon heating through the transformation range, the weaker polymorphic phase undergoes plastic flow (i.e., by creep at high homologous temperatures) to accommodate these transformation mismatch strains. In the absence of applied stress, the strain of transformation is generally reversible upon cooling through the transformation range. However, if a small external biasing stress is applied, deformation occurs preferentially in the direction of the applied stress during each transformation. The strain increment developed after a full thermal cycle (i.e., two transformations) has been found to be proportional to the applied stress,[3] indicating that the deformation is Newtonian (i.e., the stress exponent is unity). This type of deformation is known as transformation-mismatch plasticity, or when large strains are accumulated upon repeated cycling, transformation superplasticity. Greenwood and Johnson[3] developed a continuum-mechanics model of
MEGAN FRARY, previously Graduate Student, Department of Materials Science and Engineering, Northwestern University, is Research Engineer, Caterpillar, Inc., Technical Center, Peoria, IL 61656. CHRISTOPHER SCHUH, previously Graduate Student, Department of Materials Science and Engineering, Northwestern University, is Postdoctoral Fellow, Materials Science and Technology Division, Lawrence Livermore National Laboratory, Livermore, CA 94551. DAVID C. DUNAND, Associate Professor, is with the Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208. Manuscript submitted March 23, 2001. METALLURGICAL AND MATERIALS TRANSACTIONS A
transformation superplasticity that predicts this linear relationship between the strain increment, ⌬, after one thermal cycle and the external biasing stress, : ⌬ ⫽
4 ⌬V 5n 3 V 4n ⫹ 1 i
[1]
where i is the internal stress due to transformation, and n is the creep stress exponent of the weaker phase. The model of Greenwood and Johnson[3] assumes an isothermal transformation, which is not typically observed in two-phase alloys, such as Ti-6Al-4V. Schuh and Dunand[4] studied the temperature and time dependencies of transformation superplasticity in Ti-6Al-4V by varying the amplitude and frequency of the thermal cycles, and they examined how a partial-phase transformation affects the transformation-superplasticity strain rate. These authors developed a more complex model to describe
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