Editing Shape-memory alloy (section)

== Pseudoelasticity ==
SMAs display a phenomenon sometimes called superelasticity, but is more accurately described as [[pseudoelasticity]]. “Superelasticity” implies that the atomic bonds between atoms stretch to an extreme length without incurring plastic deformation. Pseudoelasticity still achieves large, recoverable strains with little to no permanent deformation, but it relies on more complex mechanisms.
 
[[File:Pseudoelasticity_Animation.ogg|thumb|left|An animation of pseudoelasticity]]
SMAs exhibit at least 3 kinds of pseudoelasticty. The two less-studied kinds of pseudoelasticity are pseudo-twin formation and rubber-like behavior due to short range order.<ref>{{Cite journal |last1=Kazuhiro Otsuka |last2=Ren |first2=Xiaobing |date=1997 |title=Origin of rubber-like behaviour in metal alloys |journal=Nature |language=en |volume=389 |issue=6651 |pages=579–582 |doi=10.1038/39277 |issn=1476-4687|bibcode=1997Natur.389..579R |s2cid=4395776 }}</ref>

[[File:Superelastic behavior of the austenitic to martensitic phase transformation.png|thumb|upright=1.5|At stresses above the martensitic stress (A), austenite will transform to martensite and induce large macroscopic strains until no austenite remains (C). Upon unloading, martensite will revert to austenite phase beneath the austenitic stress (D), at which point strain will be recovered until the material is fully austenitic and little to no deformation remains.<ref>{{Cite journal|last1=Qian|first1=Hui|last2=Li|first2=Hongnan|last3=Song|first3=Gangbing|last4=Guo|first4=Wei|date=2013|title=Recentering Shape Memory Alloy Passive Damper for Structural Vibration Control|journal=Mathematical Problems in Engineering|volume=2013|pages=1–13|doi=10.1155/2013/963530|issn=1024-123X|doi-access=free}}</ref>]]
The main pseudoelastic effect comes from a stress-induced phase transformation. The figure on the right exhibits how this process occurs.

Here a load is isothermally applied to a SMA above the austenite finish temperature, A<sub>f</sub>, but below the martensite deformation temperature, M<sub>d</sub>. The figure above illustrates how this is possible, by relating the pseudoelastic stress-induced phase transformation to the shape memory effect temperature induced phase transformation. For a particular point on A<sub>f,</sub> it is possible to choose a point on the M<sub>s</sub> &nbsp;line with a ''higher'' temperature, as long as that point M<sub>d</sub> also has a higher ''stress''. The material initially exhibits typical elastic-plastic behavior for metals. However, once the material reaches the martensitic stress, the austenite will transform to martensite and detwin. As previously discussed, this detwinning is reversible when transforming back from martensite to austenite. If large stresses are applied, plastic behavior such as detwinning and slip of the martensite will initiate at sites such as grain boundaries or inclusions.<ref name="Shaw">{{Cite journal|last1=Shaw|first1=J.|last2=Kyriakides|first2=S.|year=1995|title=Thermomechanical aspects of NiTi |journal=Journal of the Mechanics and Physics of Solids|volume=43|issue=8|pages=1243–1281|bibcode=1995JMPSo..43.1243S|doi=10.1016/0022-5096(95)00024-D}}</ref><ref>{{Cite journal |last1=Chowdhury |first1=Piyas |last2=Sehitoglu |first2=Huseyin |date=2017|title=A revisit to atomistic rationale for slip in shape memory alloys|journal=Progress in Materials Science |volume=85 |pages=1–42 |doi=10.1016/j.pmatsci.2016.10.002|issn=0079-6425|doi-access=free }}</ref> If the material is unloaded before plastic deformation occurs, it will revert to austenite once a critical stress for austenite is reached (σ<sub>as</sub>). The material will recover nearly all strain that was induced from the structural change, and for some SMAs this can be strains greater than 10 percent.<ref name="Ma">{{Cite journal |last1=Ma |first1=J. |last2=Karaman |first2=I. |last3=Noebe |first3=R. D.|year=2010|title=High temperature shape memory alloys|journal=International Materials Reviews |volume=55|issue=5|pages=257|doi=10.1179/095066010x12646898728363|bibcode=2010IMRv...55..257M |s2cid=218662109 }}</ref><ref>{{Cite journal |last1=Tanaka |first1=Y. |last2=Himuro|first2=Y.|last3=Kainuma|first3=R.|last4=Sutou|first4=Y.|last5=Omori|first5=T.|last6=Ishida|first6=K.|date=2010-03-18|title=Ferrous Polycrystalline Shape-Memory Alloy Showing Huge Superelasticity |journal=Science|volume=327|issue=5972|pages=1488–1490|doi=10.1126/science.1183169|pmid=20299589 |issn=0036-8075|bibcode=2010Sci...327.1488T |s2cid=9536512 }}</ref> This hysteresis loop shows the work done for each cycle of the material between states of small and large deformations, which is important for many applications.

[[File:Shape memory effect vs pseudoelasticity.png|alt=|left|thumb|Stress-Temperature graph of martensite and austenite lines in a shape memory alloy.]]
In a plot of strain versus temperature, the austenite and martensite start and finish lines run parallel. The SME and pseudoelasticity are actually different parts of the same phenomenon, as shown on the left.

The key to the large strain deformations is the difference in crystal structure between the two phases. Austenite generally has a cubic structure while martensite can be monoclinic or another structure different from the parent phase, typically with lower symmetry. For a monoclinic martensitic material such as Nitinol, the monoclinic phase has lower symmetry which is important as certain crystallographic orientations will accommodate higher strains compared to other orientations when under an applied stress. Thus it follows that the material will tend to form orientations that maximize the overall strain prior to any increase in applied stress.<ref>{{Cite journal|last1=Frankel|first1=Dana J.|last2=Olson|first2=Gregory B.|date=2015|title=Design of Heusler Precipitation Strengthened NiTi- and PdTi-Base SMAs for Cyclic Performance|journal=Shape Memory and Superelasticity|volume=1|issue=2|pages=162–179|doi=10.1007/s40830-015-0017-0|issn=2199-384X|bibcode=2015ShMeS...1...17F|doi-access=free}}</ref> One mechanism that aids in this process is the twinning of the martensite phase. In crystallography, a twin boundary is a two-dimensional defect in which the stacking of atomic planes of the lattice are mirrored across the plane of the boundary. Depending on stress and temperature, these deformation processes will compete with permanent deformation such as slip.

σ<sub>ms</sub> is dependent on parameters such as temperature and the number of nucleation sites for phase nucleation. Interfaces and inclusions will provide general sites for the transformation to begin, and if these are great in number, it will increase the driving force for nucleation.<ref>{{Cite journal|last1=San Juan|first1=J.|last2=Nó|first2=M.L.|date=2013|title=Superelasticity and shape memory at nano-scale: Size effects on the martensitic transformation|journal=Journal of Alloys and Compounds|language=en|volume=577|pages=S25–S29|doi=10.1016/j.jallcom.2011.10.110}}</ref> A smaller σ<sub>ms</sub> will be needed than for homogeneous nucleation. Likewise, increasing temperature will reduce the driving force for the phase transformation, so a larger σ<sub>ms</sub> will be necessary. One can see that as you increase the operational temperature of the SMA, σ<sub>ms</sub> will be greater than the yield strength, σ<sub>y</sub>, and superelasticity will no longer be observable.