Displacive phase transformations in solids. (English) Zbl 0585.73198
Summary: We study diffusionless transformations in solids which involve a sudden change of shape at a certain temperature. We assume the existence of a free energy which depends on the local change of shape and the temperature. Properties of this function reflect the underlying symmetry of the parent and product phases and an exchange of stability from parent to product phase as the body is cooled through the transformation temperature \(\theta_ 0\). We concentrate on two questions: (i) How can loads be applied to cause the body to transform to a particular variant of the product phase at or above \(\theta_ 0?\) (ii) Can the parent phase be recovered by applying some system of loads at or below \(\theta_ 0?\)
Theory and experiment are compared for thermoelastic martensitic transformations in shape-memory materials and for the \(\alpha\)-\(\beta\) transformation in quartz.
Theory and experiment are compared for thermoelastic martensitic transformations in shape-memory materials and for the \(\alpha\)-\(\beta\) transformation in quartz.
MSC:
| 74A15 | Thermodynamics in solid mechanics |
| 82D25 | Statistical mechanics of crystals |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74B20 | Nonlinear elasticity |
Keywords:
alpha-beta transformation in quartz; necessary and sufficient; conditions for stability of piecewise homogeneous deformations; dead loading; piecewise linear deformations; transformation surface; uniquely determined by symmetry of parent phase and transformation; strain; point of convexity of free energy; hydrostatic pressure; martensitic phase; effects of load and loading device on; transformation temperature; on stability and arrangement of phases; diffusionless transformations; sudden change of shape; existence of a free energy; thermoelastic martensitic transformations; shape-memory materialsReferences:
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