The shape memory effect is a very close to superelasticity phenomena (named also "pseudoelasticity").  Really, superelasticity assume as an reversible response to stress, caused by a phase transformation in some materials, so-called SMA materials.  The difference of these definitions is interpreted in the following way: superelasticity (or pseudoelasticity, which  is seemed better in terminological sense) show us the type of deformational behaviour, traditionally relating to elastic one. On another hand, shape memory denote the possibility of body made of SMA materials, return to the old configuration. And, unlike SMA, superelastic materials may realize the reverse deformations without temperature application, only due to instability of their structure.  In this sense, SMA materials are controlled  superelastic materials!

So, one can use  superelastic wire as SMA element (see, please, the paper Kamita T., Matsuzaki Y. One-dimensional pseudoelastic theory of shape memory alloys // Smart Mater and Struct. 7 (1998), P. 489–495); Smart Materials Taxonomy / CRC Press, Taylor & Francis Group, 2015. – 277 p.

Best regards, Serge

Superelastic and Shape memory effect are the names given at two particular trajectories followed by the Shape Memery Alloys in the stress-strain-Temperature space. This alloys exhibit a complex behavior due the existence of a solid-solid transition between two phases (technically austenite and martensite). This phase transition can be induced in both directions by applying temperature changes or by mechanical loading.  When the material is mechanically loaded at a temperature bellow Mf (Martensite finish temperature) for which the material is in fully martensite state, it remains strained upon unloading (likewise plastically deformed). But original dimensions can be recovered upon heating above a temperature Af (austenite finish). This is the trajectory associated with Shape Memory Effect. 

Superelastic effect has place when the material in a fully austenite state is mechanically loaded up to a critical stress SA-M, for which the transition to martensite is induced. In this case, the loading direction selects the cristallographic variants of the appearing martensite, and the sample can develop strains up to 10 % in the case of NiTi SMA. Now, when the load is relaxed, the reverse transformation from martensite to austenite has place when the stress drops below a critical vale SM-A. During reverse transformation, the material can recover practically the original dimensions. In this superelastic trajectory, a dissipative hysteresis is described, being possible to utilize this kind of materials as damping devices.  

What if I have NiTi archwire which has martensite structure at the start? I have a big problem to understant superelastcicity then....

I checked the structure of archwires at the initial stage. The had 100% martensite phase. Then these were used during the orthodontic treatment. After that I chcked structures again and turned out martensite again. What about austenite in that case?

Dear João Pedro Oliveira

thank you so much for your reply! Yes, I said about the room temp stage. But I'm still curious about one thing:

When you take an archwire, NiTi at room temp. and you bend it. All the time we have room temp. What about these situation? When we get austenite if do not change the temperature?

I mean this situation:

https://www.youtube.com/watch?v=rzJDlN2o36M&t=60s

In this case, have we got martensite transformation too?

Dear João Pedro Oliveira

I think I understand it now and the most helpful answer was your first one! :)

I carried out some tests on superelastic NiTi archwires. I checked the structure of them and I saw martensite (at room temperature). Then I got stuck, because I couldn't find out why everybody writting about austenite at the start, when I all the time had martensite (at the start ;) ). But now I understand, that at room temperature archwires have martensite and the characteristic plot stress-strain is started when it is in oral enviroment and got oral temperature. Am I right?

I also uderstand that my superelastic archwires (2nd generation, without heat-activation) are austenitic. Yes?

Hmm actually my archwires (they I are in the initial state, took straight from the producer's package and they are called "superelastic wires") at the room temperature have martensite phase (after light microscope observation ). And when I deform it (simple bending) and then unload they come back to the original position...

Superelasticity is an isotherm process and the phase transformation from austenite to martensite phase occurred under an external load. Since, martensite is unstable phase, after external load diapered it will transformed again to austenite phase. In the other hand, any SMA that shows superelasticity can also exhibits shape memory effect (SME) as well, which is due to heating and cooling process. Meanwhile, the available SMAs in markets, that their superelasticity supposed to be used, having low phase transformation temperatures. So you have to find out their SME in temperatures less than room temperature.

they are called "superelastic wires":

The term "superelastic wire" of the producer is amateurish even if it means the state at the room temperature, because this state can due to the hysteresis be both: martensitic (shape memory) after cooling under Mf and heating to T Ms when Ms

Superelasticity

It is the ability of SMA to recover to its original state with associated stress–strain hysteresis due to mechanical loading–unloading under isothermal conditions. Also It is an elastic (reversible) response to an applied stress, caused by a phase transformation between the austenitic and martensitic phases of a crystal. SE takes place at temperatures above Af.

But

Shape Memory Effect

It is the effect of restoring the original shape of plastically deformed material by heating it. This involves the transformation of detwinned (deformed) martensite to Austenite. The Phase transformation is mainly due to Heating. SME takes place between Mf and Af

Pls, look at the attached pic from the reference below for the complete answer.

https://link.springer.com/content/pdf/10.1007/978-0-387-47685-8.pdf

In my opinion the best way to start is the following article:

Otsuka, K., and C. M. Wayman. "Mechanism of shape memory effect and superelasticity." Shape memory materials (1998): 27-48.