Hysteresis

Hysteresis

As was previously mentioned in this book, there are two forms of nitinol which are prized for very different properties, the first being superelasticity and the second being the shape memory effect.  It is possible to design a system that takes advantage of both of these mechanisms, but it is by far the rarity, rather than the norm.  Also, while there are a few principles that apply to both superelastic and shape memory nitinol, by and large, they rely on different mechanisms.  So, superelasticity and shape memory will be addressed as separate mechanisms in this book.

Superelasticity

One of the few mechanisms that apply to both superelastic and shape memory nitinol is the mechanism of hysteresis.  The Collins English Dictionary defines hysteresis as ‘a lag in a variable property of a system with respect to the effect producing it as this effect varies.’  With nitinol, the varying effect is temperature, so this means that there is a temperature gap that must be overcome to thermally induce the martensitic transformation.

What hysteresis means is that nitinol remains in its austenitic state even after the temperature has dropped well below the transition temperature. So, in a design using superelastic nitinol, the nitinol remains superelastic below the transition temperature. However, there is a danger.            When nitinol is put under a stress (force), the transition temperature rises. If this stress is large, then the transition temperature can rise quite substantially, causing a thermally induced martensitic transformation.  Then, when the stress is removed, the nitinol wire remains martensitic and does not return to its original shape until heated above its transformation temperature.

So, care must be taken to determine if this will be a problem in the design of a project.  If the superelastic nitinol will be undergoing generally small deformations, then it will not be a problem for the temperature to drop below the transition temperature.  However, if very large deformation is expected, then care must be taken to ensure that the nitinol is formulated so that the transition temperature is never reached.

As was previously discussed in Chapter 2, most materials are considered to be linear-elastic, meaning that they follow Hooke’s Law.  Materials that follow Hooke’s Law are called linear because the stress-strain curve looks like a straight line when it is drawn on a graph. Linear elastic materials are very simple to use in engineering projects because the mathematics required to model them are quite simple.  Nitinol, however, is far more complex.  In a stress-strain (force-deformation) graph, nitinol begins by following Hooke’s Law. However, after about 1.5% strain, the amount of force required levels off substantially.  This is referred to as the loading or upper plateau stress. As the nitinol continues to be deformed, the stress remains roughly the same until it reaches a second linear-elastic region.  When the force is released, the nitinol contracts linear-elastically until it reaches a second, lower plateau.  This is referred to as the lower or unloading plateau stress.  After the lower plateau is traversed, the nitinol then behaves as a linear-elastic material once again until the original shape is fully recovered.

When building a project with superelastic nitinol, care must be taken to design according to the upper and lower plateau stresses.  The existence of these two plateaus can be very detrimental to a project if they are not well understood first.

 

Shape Memory

 

Without a doubt, hysteresis is the most misunderstood aspect of working with nitinol as a shape memory material.  Even experienced scientists struggle with hysteresis.  Therefore, this section of this book must be taken very seriously before any project should be begun.

When looking at nitinol, most people–even scientists–only consider one temperature, the transition temperature.  Many articles published in research journals claim that nitinol transforms very rapidly or instantaneously at its transition temperature.  However, the term ‘transition temperature’ is a bit of a misnomer.  It makes it sound like the transition occurs at that temperature when, in reality, it finishes at that temperature.

Nitinol has eight critical temperatures that must be considered when building a system using nitinol.  These are usually referred in their shorthand form as Md, Af, As, Rf, Rs, M0, Ms, and Mfwith this list being in order from highest to lowest.  It must also be understood that this list applies to MOSTnitinol alloys, not all of them.  These can be in a substantially different order in certain alloys and some of the temperatures only exist in (or pertain to) certain alloys.

It’s pretty easy to figure out that ‘A’ refers to austenite and ‘M’ refers to martensite, but what do all of the subscripts mean?  The subscript ‘s’ refers to the temperature at which the transformation begins to occur.  The subscript ‘f’, as would make sense, refers to the temperature at which the transformation is finished.  The start and finish temperatures may be as little as 2°F (1°C) apart or they may be more than 40°F (20°C) apart.  Clearly, the closer the temperatures are, the faster the transition will occur. Hysteresis in nitinol alloys is measured as the difference between Afand Mf.

The M0temperature, also called the equilibrium temperature, is only important in alloys where Ms>As.  In these alloys, both phases are fighting to take over when the temperature is between Msand As.  However, nothing changes until the material temperature passes the equilibrium temperature–giving control to one phase or the other.

As an example, if we have a sample of nitinol at Mfand begin heating it.  The first critical temperature that we reach is As.  However, nothing changes until we reach M0.  If we continue warming until we reach Ms, the nitinol is partly martensite and partly austenite.  If we begin cooling it, that ratio of martensite to austenite remains the same until the equilibrium temperature is crossed. Then, the austenite begins transforming back into martensite.  In alloys like this, where Ms>As, it is possible to take advantage of a partial transition for the shape memory effect with a very small temperature change.

The Mdtemperature doesn’t apply to most designs.  Mdis the martensite difficult temperature. Above this temperature, it is very difficult to form stress induced martensite.  One of the earliest applications of nitinol made use of the Md temperature.  The hydraulic fittings on the F-15 fighter were held together using nitinol rings. These rings had an Afof around 90°F (30°C) but the hysteresis was very wide so that they had to be cooled in liquid nitrogen to get them below Mf.  Then they were stretched so that they would clear the hydraulic hose.  Upon heating above Af, they would shrink down with incredible force.  These rings were sold under the trade name Cryofitâ.

The last two temperatures in the list are Rsand Rf. These are the start and finish temperatures of the R-phase.  It is important to understand the R-phase when working with nitinol.  The R-phase behaves very differently from the normal martensitic transformation.

It is important to note that not all nitinol alloys exhibit the R-phase.  The R-phase is called that because of the rhombohedral shape of the crystal structure.  The R-phase can recover roughly a 1% deformation thermo-elastically.  The biggest difference between the R-phase transformation and the martensitic transformation is that R-phase is hysteresis free.  This means that if motion is needed at a very specific temperature, the R-phase is the mechanism to use.  On the other hand, since the recovery is just 1%, it’s possible that the R-phase transition can be ignored altogether.  In either case, a knowledge of the R-phase is necessary to make an educated decision.

Enough beating around the bush, the real question is: ‘how big is the hysteresis?’ Well, regular binary (just 50/50 nickel and titanium) has a hysteresis of roughly 70°F (40°C). With third element alloying, the hysteresis can be reduced to just 20°F (11°C) or expanded to more than 250°F (140°C). Great care must be taken when determining if or how much the hysteresis of an alloy will affect design parameters.

Now, how can you determine what all of these temperatures are? Unfortunately, the only recognized test to measure all eight of these temperatures is the use of differential scanning calorimetry in accordance with ASTM F2004.  However, if just the austenite start and finish temperatures are needed, ASTM F2082, Bend and Free Recovery (BFR) works quite well.

In a BFR test, ASTM dictates that the sample of nitinol must be wrapped around a mandrel (or round object) with a radius 20 times the thickness of the sample. This bend results in an average deformation of 2.5%.  Now, slowly warm the sample of nitinol.  The range of acceptable rates of temperature change is 1-3°F per minute (1-2°C/min).  When the nitinol sample begins to move, this temperature is As.  When the nitinol has finished moving, this temperature is Af.

The BFR test is one that can be conducted with very few materials other than what can be found in the home.  So, what materials are needed for this test?

  • Something round (a broomstick usually works well)
  • A thermometer
  • Something with a large thermal inertia (a pot of water works well)

The thermometer is the wild card in the home version of this test.  A typical digital thermocouple based thermometer has an accuracy of roughly 2°F (1°C).  A mercury or alcohol thermometer has an accuracy of roughly 5°F (2°C), so this is something to keep in mind.  Digital thermometers are generally much cheaper online and the quality of manufacture is generally quite comparable.

Hysteresis is an important aspect of working with nitinol.  Understanding what hysteresis is and how it can either benefit or inhibit a system is crucial to success with nitinol, whether you’re a researcher or a hobbyist.  Since the question of what hysteresis is and how to measure it has been covered, it is time to discuss how to control it and what the benefits and drawbacks of controlling the hysteresis might be.

The most popular nitinol shape memory alloy, after binary nitinol is the ternary alloy NiTiCu.  In this alloy, some of the nickel has been replaced with copper–dropping the hysteresis substantially.  With a 10% copper content, the hysteresis drops to just 20°F (11°C). On the other hand, adding hafnium widens the hysteresis dramatically.

Let’s take a look at some applications where having a wide or narrow hysteresis is good.  A wide hysteresis is good when you want something to work just once without intentional re-setting.  For example, a magic trick that is designed to respond to skin temperature.  In this case, the magician wants to trigger the trick, changing the shape of the object (perhaps to make a fork bend), and then the audience members cannot unbend it.  A wide hysteresis would ensure that the reverse transformation does not begin until the magician is ready to reset his trick.

A narrow hysteresis is good when you want something to activate frequently. For example, if you were building a robot that needs to make frequent movements, one of the ways is to reduce the hysteresis so that it doesn’t need to cool as much to return to the martensitic state.

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