Influence of crystalline orientation on the thermal-energy convertion efficiency in shape memory alloys

A theoretical study about the influence of crystalline orientation on the energy conversion efficiency of two shape memory alloys is present. The study consider single crystal samples in simple tension. The results showed higher properties for of the NiTi than Cu-Al-Be, especially in the temperature-increment ( T) necessary for get a conversion energy cycle. However, the study showed a crystalline orientation favorable for Cu-Al-Be.


Introduction
As it is well known an important application of shape memory materials is the designing of devices capable to transform thermal energy in to mechanical energy at low temperatures [1].Also as it is known, the above mention, cover a great range of cases as the recover energy in conventional thermal machines and the conversion of solar energy in very single way [2].Some authors has developed mathematical model for evaluate the energy conversion efficiency.Basically the models consider a fix and a removable loads, their strains associated and the work cycle in the stress-strain diagram [3].These models have been capable to determinate efficiency parameters for springs, wires and sheet made with shape memory alloys [1][2][3].Nevertheless nobody considers crystalline orientation and their possible influence in the energy conversion efficiency.In this work an analysis of the influence of the crystalline orientation in the energy conversion efficiency in two SMA; Cu-Al-Be and Ni-Ti is present.

Develop
For our analysis we consider single crystals samples in simple tension case which is easy represented in stress-strain diagrams as is shows in the   cycle with two curves that correspond to: a low and a high temperature cases.As is clear in Fig. 1 the parameters considered were: stress associate to fixed and work loads and low and high temperatures, both above to Af. Figure 2 shows a schematic diagram of the energy conversion cycle related to the states of the Fig. 1.Other parameters consider in the analysis are those properties of own alloys: Stress ratio, transformational system and transformation temperatures.
Our study consisted in the calculus of the specific energy obtained in a cycle for two shape memory alloys: Ni-Ti and Cu-Al-Be with several crystalline orientation around to main direction in

Results
For certain parameters proposed here, the Figs. 3 and 4 shows specific energy variation with the crystalline orientation variation for 3 paths along the main orientations of stereographic projection of austenitic phase structure.
As it was expected Ni-Ti SMA presented a higher energy by volume unit than the Cu-Al-Be SMA for any one crystalline orientation.In fact the energy by volume unit correspond to a cycle of energy conversion for Ni-Ti is twice than for Cu-Al-Be; 600 000 (J/m3) and 300 000 (J/m3) respectively.However it is not the principal advantage of NiTi SMA.
As is shows in the Figs. 5 and 6 the temperature-increment necessary to reach the work cycle for any one crystalline orientation is around 15 • C for Ti-Ni while for Cu-Al-Be for most crystalline-direction is around 60 • C except for crystalline direction near to [111] which the temperature increment for reach the work cycle is 20 • C.This result never have been reported before however it is well know that the SMA's are high anisotropic.Their importance is due to the energy conversion for a SMA with high temperatureincrement will be very difficult if his mass is great.The last is a hard restriction for designing of devices which convert thermal energy into mechanical energy employing SMA.

Conclusions
The results obtained here shows that NiTi is more efficient to convert energy in a simple tension cycle than Cu-Al-Be because: -The specific energy is twice.
-The temperature increase necessary for a energy conversion cycle is around 15 • C for any crystalline direction while for the second is about 60 • C for almost crystalline direction except to these near to [1 1 1].

Fig. 1 .
In this figure have been plotted a energy conversion a Corresponding author: jacop@unam.mxThis is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Article available at http://www.epj-conferences.orgor http://dx.doi.org/10.1051/epjconf/20137902005EPJ Web of Conferences

Figure 1 .
Figure 1.Energy conversion cycle in a stress-strain diagram.

Figure 2 .
Figure 2. Energy conversion cycle in a schematic diagram associate to Fig. 1.

Figure 3 .
Figure 3. Specific energy converted for Cu-Al-Be SMA.

Figure 6 .
Figure 6.Temperature increase necessary for a Energy conversion cycle for Cu-Al-Be SMA.