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Research Papers

The Concept of Physical Metric in the Thermomechanical Modeling of Phase Transformations With Emphasis on Shape Memory Alloy Materials

[+] Author and Article Information
Vassilis P. Panoskaltsis, Dimitris Soldatos

Department of Civil Engineering,
Demokritos University of Thrace,
12 Vassilissis Sofias Street,
Xanthi 67100, Greece

Lazaros C. Polymenakos

Autonomic & Grid Computing,
Athens Information Technology,
Peania 19002, Greece

Contributed by the Materials Division of ASME for publication in the Journal of Engineering Materials and Technology. Manuscript received July 14, 2012; final manuscript received February 1, 2013; published online April 2, 2013. Assoc. Editor: Xi Chen.

J. Eng. Mater. Technol 135(2), 021016 (Apr 02, 2013) (17 pages) Paper No: MATS-12-1167; doi: 10.1115/1.4023780 History: Received July 14, 2012; Revised February 11, 2013

In this work we derive a new version of generalized plasticity, suitable to describe phase transformations. In particular, we present a general multi surface formulation of the theory which is capable of describing the multiple and interacting loading mechanisms, which occur during phase transformations. The formulation relies crucially on the consideration of the intrinsic material (“physical”) metric as a primary internal variable and does not invoke any decomposition of the kinematical quantities into elastic and inelastic (transformation induced) parts. The new theory, besides its theoretical interest, is also important for application purposes such as the description and the prediction of the response of shape memory alloy materials. This is shown in the simplest possible setting by the introduction of a material model. The ability of the model in simulating several patterns of the experimentally observed behavior of these materials such as the pseudoelastic phenomenon and the shape memory effect is assessed by representative numerical examples.

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References

Figures

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Fig. 1

Finite shear. Shear stress τ12 versus shear strain γ.

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Fig. 2

Finite shear. Normal stress τ11 versus shear strain γ.

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Fig. 3

Plain strain (restrained tension): monotonic loading at various temperatures. Normal stress τ11 versus elongation λ.

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Fig. 4

Plain strain (restrained tension): monotonic loading at various temperatures. Normal stress τ33 versus elongation λ.

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Fig. 5

Plain strain (biaxial extension): monotonic loading at various temperatures. Normal stress τ11 versus elongation λ.

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Fig. 6

Plain strain (biaxial extension): monotonic loading at various temperatures. Normal stress τ33 versus elongation λ.

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Fig. 7

Cycle 1: normal stress τ11 versus angle of rotation φ

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Fig. 8

Cycle 1: shear stress τ12 versus angle of rotation φ

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Fig. 9

Cycle 1: normal stress τ22 versus angle of rotation φ

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Fig. 10

Cycle 1: martensite fraction ξ versus angle of rotation φ

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Fig. 11

Cycle 2: normal stress τ11 versus angle of rotation φ

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Fig. 12

Cycle 2: shear stress τ12 versus angle of rotation φ

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Fig. 13

Cycle 2: normal stress τ22 versus angle of rotation φ

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Fig. 14

Cycle 2: martensite fraction ξ versus angle of rotation φ

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