Time dependent stress-strain curves of nonlinear anelastic solids
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Time Dependent Stress-Strain Curves of Nonlinear Anelastic Solids
intentional when automodulation is studied. Another observation peculiar to a large deformation in the vicinity of the martensitic transformation is the stressstrain curve, recent examples of which can be found in the work of Otsuka, Shimizu, W a y m a n and Coil) These stress-strain curves are strongly nonlinear at large strains where martensite is induced. In addition, they display a pronounced hysteresis at large strains. In this letter, it will be shown that b o t h of these characteristics also constitute essential features of a nonlinear anelastic solid. It is thus possible to interpret the stress-strain curve when martensite is strain induced in terms of the properties of this solid. The fact that martensite can be strain induced means that the austenitic phase possesses a metastable state. The free energy of this metastable state can be lowered by the application of an external stress. If this stress is sufficiently high, the martensitic phase becomes stable. The free energy, F, of austenite may thus be described by the polynomial F(?Q =
1 / 2 C 2 h 2 + l/4C4~k4 + 1/6C6 ~6.
[1]
The quantity ~ is a deformation parameter suitable to describe a tensile test, 2~ = (1 - lo)/lo. Here, l o is the original sample length and l - l o denotes the travel of the crosshead. The constants C, are macroscopic mechanical constants characteristic of the material under test. It is noted that F(~) has a secondary minimum, i.e., a metastable state if ( C 4 / 2 C 6 ) 2 ~ C : / C 6. The formation of martensite takes time. This aspect is not reflected in Eq. [1]. It m a y be introduced by treating the free energy as a time-dependent quantity. Such an approach, if carried out rigorously, renders the problem very complex. A simple way of introducing the element of time consists of defining two free energies--an unrealaxed free energy, F , , and a relaxed free energy, Fr. The former refers to very fast deformations and introduces the non
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