Abstract

Shape memory alloys (SMAs) demonstrate the ability to return to some previously defined shape or size, after plastic deformation, when subjected to appropriate thermal procedure. Such properties of shape memory alloys were studied by making use of computer simulations. The simulations were developed using molecular dynamic techniques based on the embedded atom model. These simulations show austenitic / martensitic transitions leading to shape memory effects in NiAl alloys. Temperature induced transitions were observed at different concentrations of NiAl. Plots between temperature and strain, show hysteresis during the cycle of heating and cooling over a range of temperature. From these curves, different values of transition temperatures were calculated with different compositions of NiAl alloys. Isotherms of NiAl alloy (Al 40%) were also obtained during loading and unloading at different temperatures. These isotherms were found in good agreement with Falk’s model based on Landau’s phenomenology.

Introduction

There exists an important class of alloys that exhibit a remarkable quality of shape memory and trainability [1]. These alloys are commonly called as intelligent materials or shape memory alloys. If such alloys are plastically deformed at one temperature, they will completely recover their original shape on being raised to a higher temperature. This behaviour is shown in Figure 1. In recovering to their shape these alloys can produce a displacement or a force, or a combination of both as a function of temperature. Because of these remarkable properties, shape memory alloys can be used in variety of industrial and medical applications [2].

Figure 1.  A typical one-way shape-memory spring deformed to several times its original length will spontaneously return to its original shape in hot water.

Molecular Dynamics (MD) computer simulation methods have become very important tools for the study of equilibrium and transport properties of model condensed matter systems. In the present work we have used the MD techniques to study bulk properties and phase transitions occurring in the NiAl shape memory alloys.
In molecular dynamics method, one investigates the time evolution of positions and velocities of particles of the system. This is done by construction a suitable intermolecular potential model, and solving the Newtonian equations of motion of these particles with a suitable numerical algorithm. The algorithm gives a detailed information about velocities and positions of the particles after regular intervals of time. This information then used to calculate thermodynamical averages of different physical quantities [3],[4],[5].
So using these technique, austenitic / martensitic transitions leading to shape memory effects in NiAl alloys were successfully explored.

After initialising the system, equations of motion were solved by the Nordsieck algorithm [11] with a time step of 10-15 s. This algorithm provided detailed information of velocities and positions of particles after each time step of 10-15 s. During this process, periodic boundary conditions were also imposed [4].

Then this data of positions and velocities was used to calculate the time averages of various thermodynamic quantities such as total internal energy, temperature, pressure, pressure, volume, stress tensor etc.

Two types of computer experiments were performed with different compositions of Ni-Al shape memory alloy. To explore temperature induced phase transitions, first run of constant energy for 25 ps was performed and during this run the system was allowed to be relaxed. After this run a series of constant temperature and constant pressure (NPT) runs were performed over a wide range of temperature (100 K - 1000 K). Each (NPT) run was performed at zero applied load with dynamic periodic lengths for 10 ps. Thermodynamic averages of different quantities were calculated after 7 ps (equilibration time for the system). Similarly above procedure was carried out to study the stress induced phase transitions. But these isotherms were obtained keeping temperature constant during the series of (NPT) runs over a wide range of externally applied stresses (5000 bar - 120000 bar). This series of runs were also performed with dynamic periodic lengths. Output files of each run of computer program containing the data of positions and velocities were used as input data of next run.

To keep the temperature constant velocities were rescaled at each time step, through the use of equipartition theorem as

 

where k is the Boltzman constant and N is the number of atoms. If the required temperature is T, then the velocities are rescaled by a factor of (T/To) [4],[5].

Results and discussions

Temperature induced transitions leading to shape memory effects

Hysteresis shown in figures 2 to 7 are clear evidence of shape memory effects in Ni-Al alloys. These plots shows austenitic / martensitic phase transitions during cooling and heating the alloy sample. During cooling process austenitic phase (low strain and high energy) is transformed into martensite phase which has high strain and low energy. Similarly, on heating the martensitic phase is converted into austenitic phase. These hysteresis show one way shape memory effect because on heating, the system goes into austenitic phase where heating and cooling curves ideally overlaps. But in martensitic region these curves does not overlap exactly, so the alloy showed only one way shape memory effect. The alloy can exhibit two way shape memory effect after undergoing proper thermomechanical cycling process (training).
Transition temperatures, given in table 1, were calculated for different compositions of Ni-Al alloy.

 

 

 

 

 

 Table 1:  Austenitic / martensitic transition temperature data against different alloy compositions. Temperature is in K. Ms martensite start temperature, Mf martensite finish temperature, As austenite start temperature, Af austenite finish temperature.
 

Isothermal loading at different temperatures

Figures 8 to 11 illustrate isotherms on loading at different temperatures. These stress vs strain curves were taken for the alloy with 40% Al. Loading leads the material from austenitic to martensitic phase. At lower temperatures (below As) sharp transitions can be observed as shown in Figures 8 and 9. But at higher temperatures (above Af) these transitions begin to vanish, as shown in Figures 9 and 10. In Figure 11 there is no austenitic to martensitic phase transition at all. This behaviour is exactly according to Falk’s model.  So unloading above Af leads the system to complete shape recovery because at high temperature the system does not undergo plastic deformation due to austenitic - martensitic transition. Figure 12 shows plastic deformation at 400 K, which has not disappeared even on unloading, but on heating above Af, plastically deformed material returns back to its original shape.

 

 

 

Conclusion

NiAl alloys exhibit phase transitions leading to shape memory effects during thermomechanical process, which were successfully observed. We have explored one way shape memory effect in NiAl at different alloy concentrations. Isothermal behaviour of the alloy was found in good agreement with Falk’s model of shape memory alloys based on simple Landau’s theory. These alloys can be trained to exhibit two way shape memory effects imposing continues cycling process of loading and unloading or cooling and heating. MD computer simulations based on EAM alloy model were found successful in studying shape memory behaviour and structural transitions. The area of study can be extended to the more well known copper-based shape memory alloys constructing suitable EAM potentials for these alloys.
 

References

1. G. J. Monkman Journal of Intelligent Material Systems and Structure, 5, (1994).
2. J. D. Harrison and D. E. Hodgson, Shape Memory Effects in Alloys, J. Perkins, Ed., Plenum Press, p 517, (1975).
3. R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles, McGraw Hill, New York, (1981).
4. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press Oxford.
5. H. C. Andersen, M. P. Allen, A. Bellemans, J. Board, J. H. R. Clarke, M. Ferrario, and J. P. Ryckaert, (1984), New Molecular Dynamics Methods for Various Ensembles, Rapport d’ activite scientifique du CECAM, pp 82-115.
6. F. Falk, Acta Metallurgica, 28, 1773, (1980).
7. M. S. Daw and M. I. Baskes Phys. Rev. B 50, 1285 (1983).
8. S. M. Foiles, M. I. Baskes, and M. S. Daw, Phys. Rev. B 33, 7983 (1986).
9. R. A. Johnson, Phys. Rev. B 37, 3924 (1988).
10.  R. A. Johnson, Phys. Rev. B 37, 6121 (1988).
11. C. W. Gear, Numerical Initial value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, N J, (1971).