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The structure of shock and interphase layers for a heat conducting Maxwellian rate-type approach to solid-solid phase transitions: Part I: thermodynamics and admissibility

Abstract : One continues the qualitative analysis started in Part I (Fciu and Molinari in Acta Mech) concerning the thermomechanical characteristics of a steady, structured moving phase boundary in a shape memory alloy (SMA) by a quantitative investigation. The internal structure of these interphase layers is governed by a Maxwellian rate-type constitutive equation coupled or not with the Fourier heat conduction law. We consider as equilibrium stress-strain-temperature response function for the Maxwellian model an explicit piecewise linear thermoelastic relation for an SMA bar which can exist in the austenite phase A and in two variants of martensite M (+/-). Its thermal properties are built in agreement with experimental results on NiTi. This equilibrium relation has the atypical property that not only the derivative of the stress response function with respect to the strain changes its sign, but also the derivative with respect to the temperature. Considerable temperature variation is generated by impact-induced phase transformations due to the large amount of latent heat released (absorbed) inside the transition layer. One gets strong heating (cooling) across a compressive A -> M (-) (expansive M (-) -> A) propagating interphase layer. A significant lower (larger) temperature than that at the front and Hugoniot back state is obtained inside an impact-induced M (+)-> M (-) (M (-)-> M (+)) interphase layer. The experimental finding of this phenomenon of temperature undershoot (overshoot) could be a valuable indication for the existence of an interphase layer.
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https://hal.univ-lorraine.fr/hal-01502127
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Submitted on : Wednesday, April 5, 2017 - 10:04:15 AM
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Cristian Faciu, Alain Molinari. The structure of shock and interphase layers for a heat conducting Maxwellian rate-type approach to solid-solid phase transitions: Part I: thermodynamics and admissibility. Acta Mechanica, Springer Verlag, 2013, 224 (9), pp.1917-1941. ⟨10.1007/s00707-013-0847-9⟩. ⟨hal-01502127⟩

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