Materials Science · Magnetism and coupled material responses

Shape memory and other responsive materials

Useful background: Atoms, bonding, structure and defects; Energy, stability and environmental context; Measuring and checking material claims. Each worked case explains the quantities it uses.

Back to the chapter

After reading, you can

Distinguish recoverable transformation response from ordinary thermal expansion.
Explain how martensite variants and reverse transformation produce different recovery paths.
Compare lengths at matched temperature and distinguish immediate, heating-induced and unrecovered extension.
Calculate finite mechanical work on a stated pseudoelastic cycle without equating strain recovery with zero loss.
Identify the material mechanism, stimulus pathway and repeated-condition evidence needed for a responsive-material claim.

A change of structure can recover shape

A shape-memory alloy can recover a previously set shape when heating reverses a suitable transformation after deformation. Superelasticity is a related response in which stress induces a transformation and unloading reverses it in an appropriate temperature range. Ordinary thermal expansion is a different mechanism.

Austenite and martensite name the parent and product phases here, with different crystal structures. In a representative shape-memory alloy, martensite forms through coordinated atomic shifts rather than long-range redistribution of the alloying elements. Its differently oriented variants are related arrangements of the same phase. A self-accommodating mixture of variants can largely cancel their shape changes. Stress can favour some variants, changing the specimen’s shape while it remains martensitic. This is different from ordinary elastic stretching or irreversible dislocation slip.

On suitable heating, oriented martensite transforms back toward the parent austenite arrangement. The previously set shape can return if deformation and damage have not destroyed that recoverable relation. The word memory describes this structural/history dependence; the material does not identify an arbitrary shape to repair. Not every martensitic transformation is sufficiently reversible for useful shape memory. “Detwinned” is a common simplified label, but a real polycrystal need not become one completely untwinned variant.

In a one-way response, cooling the recovered unloaded object need not recreate the earlier deformed shape: martensite can form again in a self-accommodating arrangement. Repeating the motion may require a restoring load or another programming step. A two-way response, in which thermal cycling itself gives two different shapes, requires its own preparation and evidence; it does not follow from observing one-way recovery once.

Separate immediate unloading from recovery during heating

Use this original fictional length record. The same marked gauge begins at L₀ = 50.00 mm and 20 °C in a prepared low-temperature state. Pulling it gives 52.50 mm; unloading at 20 °C leaves 52.00 mm. The force is then negligible during heating to 80 °C and subsequent cooling to 20 °C. The temperatures are chosen record conditions, not a recipe or a transformation range for a named alloy. For the example, suitable independent structural observations support martensite reorientation followed by reverse transformation.

The imposed engineering strain is (52.50 − 50.00)/50.00 = 0.0500, or 5.00%. Immediate unloading recovers 0.50 mm, leaving 2.00 mm extension at the cold unloaded state. Calling that remaining extension permanent plastic strain immediately would be premature: part can still recover through the thermal path.

For the supplied comparison, the unstrained thermal reference is L_ref(T) = 50.00 mm + (0.00100 mm/°C)(T − 20 °C). This is an explicitly given baseline, equivalent to an initial-length expansion coefficient 2.00 × 10⁻⁵ K⁻¹ over this range. Actual transforming phases can have different expansion responses; this convenient common reference is not asserted for every alloy. At 80 °C, L_ref = 50.06 mm. The observed 50.10 mm therefore contains only 0.040 mm excess over that reference, rather than 0.10 mm of unexplained retained deformation.

After cooling, length is 50.04 mm at the original 20 °C and negligible force. Comparing matched endpoints gives unrecovered extension 0.040 mm, or 0.0800% of L₀. Of the 2.00 mm retained after cold unloading, 1.96 mm has recovered: the explicitly defined recovery fraction r = (L_unloaded,cold − L_final,cold)/(L_unloaded,cold − L₀) is 0.980, or 98.0%. Relative to the earlier maximum extension of 2.50 mm, total recovered fraction is instead 2.46/2.50 = 98.4%. The denominator belongs with the number.

The remaining 0.040 mm is unrecovered after this defined observation path, not proof of one damage mechanism or of irreversibility under every later treatment. Plastic slip, retained transformation, altered reference shape, mounting or measurement effects require discriminating evidence. The diagram follows record order, not a measured strain-versus-temperature law. Heating/cooling rates and waiting times would be needed to interpret intermediate behaviour.

Original gauge observations, not a material specification. Small recovery forces are neglected in this teaching record. Compare the initial and final cold unloaded states for the final residual; the hot length needs its thermal reference.
Stage	Gauge T (°C)	Load state	L (mm)	L_ref (mm)
1 · prepared	20	Unloaded	50.00	50.00
2 · pulled	20	Loaded	52.50	50.00
3 · unloaded	20	Unloaded	52.00	50.00
4 · heated	80	Unloaded	50.10	50.06
5 · cooled	20	Unloaded	50.04	50.00

Original five-stage gauge record, not measured alloy data. Each horizontal line extends from the common zero to L minus the supplied temperature-dependent reference length. Scale is 140 pixels per millimetre of excess; no physical strip or atomic structure is drawn. Prepared at 20 degrees Celsius unloaded: L and reference both 50.00 millimetres, zero excess. Pulled at 20 degrees Celsius: L 52.50, reference 50.00, excess 2.50 millimetres. Unloaded at 20 degrees Celsius: L 52.00, reference 50.00, excess 2.00 millimetres. Heated unloaded to 80 degrees Celsius: L 50.10, reference 50.06, excess 0.040 millimetre. Cooled unloaded to 20 degrees Celsius: L 50.04, reference 50.00, excess 0.040 millimetre. The hot point is a square and the other points circles; stage labels explicitly identify load and temperature. Vertical positions show record order, not equal elapsed time or intermediate transformation kinetics. The final cold residual is 0.0800 percent of the initial 50.00-millimetre gauge. Recovering 1.96 of the 2.00 millimetres retained after unloading gives the defined 98.0 percent recovery. Source transformation data, phase fractions and a material processing recipe are not encoded.

Recover during unloading by reversing a stress-induced transformation

Begin a separate experiment at a fixed temperature where austenite is stable without load and a reversible stress-induced transformation is available. Sufficient stress can form favourably oriented martensite. Unloading can reverse that transformation while the temperature is maintained, giving superelasticity, also called pseudoelasticity. It is not merely a very low ordinary elastic modulus. At a different temperature, slip or other irreversible processes can intervene before useful transformation recovery.

Use the original piecewise-straight loop in the next table and figure. The specimen is stipulated to repeat this idealised cycle at a uniform controlled temperature, with matched specimen/history and negligible unrecorded motion. Engineering stress is σ = F/A₀ and strain ε = ΔL/L₀, using original area A₀ and original gauge length L₀. Stress is in megapascals, MPa; the table writes strain in percent, while calculations use the fraction. No phase fraction, elastic modulus, transformation stress or safe limit of a real alloy is inferred from these chosen lines.

Load through (0%,0 MPa), (1%,200 MPa), (5%,240 MPa), (6%,400 MPa); unload through (5%,160 MPa), (1%,120 MPa) and back to (0%,0 MPa). At ε = 3%, the loading stress is 220 MPa but unloading stress is 140 MPa. The difference at the same strain is hysteresis: response depends on the path and internal state. A single function of current strain alone cannot represent both branches.

The model returns to its initial strain, yet mechanical input and output differ. For each straight segment, work per original gauge volume is average σ times change in ε. This follows because force times gauge-extension change, divided by A₀L₀, is engineering stress times fractional-strain change in this axial account. Use ε as a fraction: 1% is 0.01. Loading gives 13.0 MJ/m³; mechanical work returned during unloading is 9.00 MJ/m³. Their difference is 4.00 MJ/m³ per complete repeatable cycle. In the stipulated maintained-temperature cycle with no net stored-energy change, that net work leaves as heat. Fully recovered strain therefore does not mean a loss-free cycle.

A thermal-recovery actuator is a different energy boundary: it also receives heat and may exchange work with a restoring load or constraint. Its thermal efficiency cannot be obtained from this separate isothermal mechanical loop. If shape change is prevented, recovery can instead generate stress; free-recovery length does not determine blocked force without the constrained response and geometry.

Original ideal repeatable isothermal mechanical cycle. Follow the displayed order. Values are engineering quantities; use fractional strain for work.
Path	ε (%)	σ (MPa)
Start/load	0	0
Load	1	200
Load	5	240
Load/turn	6	400
Unload	5	160
Unload	1	120
Return	0	0

Separate original ideal repeatable isothermal mechanical loop, not the thermal length record or a real alloy measurement. Horizontal engineering strain is zero to 6 percent, at 80 pixels per percentage point. Vertical engineering stress is zero to 450 megapascals, at 1.05 pixels per megapascal. Solid blue loading with circles follows 0 percent at 0 megapascals, 1 percent at 200, 5 percent at 240 and 6 percent at 400. Dashed orange unloading with square markers follows 6 percent at 400, 5 percent at 160, 1 percent at 120 and returns to 0 percent at zero. Shared endpoints have nested markers. A diagonal hatch fills the closed area between the complete paths. Work input is 13.0 megajoules per cubic metre of original gauge volume; returned mechanical work magnitude is 9.00 and net work is 4.00 in the same units. Strain must be converted from percent to fraction when integrating stress times strain. At 3 percent strain, loading and unloading stresses differ, 220 and 140 megapascals. The prescribed temperature and state permit transformation reversal; the graph itself does not identify phase fractions or certify transformation physics, thermal efficiency, fatigue life or operating limits.

Training and range matter

Transformation temperatures, stress, shape-setting or training history and microstructure influence response. Repeated use can change hysteresis or accumulate damage. Report recoverable strain and operating conditions rather than describing a material as having unrestricted memory.

Heating and cooling usually do not transform at one identical temperature. A_s and A_f denote the start and finish of forming austenite during the specified heating path; M_s and M_f denote martensite start and finish during cooling. These are path/condition-dependent characterisations, not four universal constants or a claim of four distinct phases. Intermediate phases may occur. A temperature between reported limits can correspond to different states depending on prior heating, cooling and stress.

Transformation exchanges latent heat as the structure changes. A specimen can therefore warm or cool locally during mechanical transformation even when the room temperature is steady. Heat transfer to the surroundings, geometry and loading rate can change the measured loop. A machine or chamber setting alone does not prove the isothermal condition used in the illustrative model.

Shape setting establishes a reference geometry through a suitable material/process history. Training changes response through chosen repeated thermomechanical histories; these terms are not interchangeable guarantees. Functional fatigue means a change in the intended response, such as reduced recovery, shifted transformation conditions or changed hysteresis. Structural fatigue concerns damage and cracks. They can interact, but neither a stable-looking loop nor a lower loop area alone establishes long life. Compare residual strain, useful travel or force and full loop/temperature records under matched conditions.

Name both the trigger and the mechanism

Responsive describes a change caused by an input, while shape memory additionally concerns a prepared reference and recovery history. Ordinary thermal expansion follows changing interatomic spacing; it does not by itself restore a programmed deformation. Reversible elastic strain on unloading is another response without a martensitic memory cycle. The comparison therefore needs more than the observation “it moved when stimulated”.

Some shape-memory polymers fix a temporary deformation through restricted segment motion and recover when an appropriate switching process restores mobility while the supporting network remains effective. Physical or chemical network constraints can matter. That is a different structural route from the alloy’s reversible crystal transformation. The polymer architecture and thermal/mechanical response lessons supply the chain-level preparation; there is no universal switching temperature or all-polymer memory claim.

A magnetic trigger can also be indirect. In reported polymer composites, magnetic nanoparticles heated under an alternating field and triggered thermal shape recovery. The field label did not mean that the polymer underwent the alloy’s martensitic transformation or that direct magnetic force alone caused the return. Distinguish input → energy transfer → structural response → measured output. A matched heating-only comparison, actual specimen temperature and appropriate unfilled or field-free controls can test a heating account; one moving specimen cannot uniquely identify the mechanism.

For any proposed use, specify the initial/reference state, stimulus history, actual temperature, stress/constraint, geometry, measured displacement or force, time, cycles and uncertainty. Compare the intended output over that domain. Neither a demonstration, a material name nor a large one-cycle recovery establishes useful power, safety, compatibility or component lifetime.

Worked examples

Work through the case

An actuator recovers shape only within a specified thermal cycle. Does failure to recover outside that cycle disprove the reported response?

Check the transformation regime.
Compare stress and training history.
Assess the response within its stated conditions.

Not necessarily. Shape-memory behaviour has a restricted operating range.

Two recovery percentages answer different questions

Use the five-stage thermal record. Find the unrecovered cold strain, the fraction recovered from the cold unloaded extension and the fraction recovered from maximum extension. Why not use hot length directly?

At matched 20 °C and negligible force, excess length is 50.04 − 50.00 = 0.040 mm. Divide by 50.00 mm to get strain 0.000800 = 0.0800%.
Cold unloaded extension was 52.00 − 50.00 = 2.00 mm; the thermal path recovers 52.00 − 50.04 = 1.96 mm. The defined r is 1.96/2.00 = 0.980.
Maximum extension was 2.50 mm. Total return from 52.50 to 50.04 recovers 2.46 mm, giving 2.46/2.50 = 0.984. These definitions include different portions of the path.
The hot gauge length includes the supplied thermal baseline 50.06 mm. Its excess is 50.10 − 50.06 = 0.040 mm; using 50.10 − 50.00 mixes temperatures.

Unrecovered cold strain is 0.0800%; recovery is 98.0% of the cold unloaded extension or 98.4% of maximum extension. Report the path and denominator.

Recovery with positive net mechanical work

For the supplied isothermal loop, calculate work in, work out and net work per original volume. Find net work for a 25.0 mm³ gauge.

Loading: (0+200)/2 × 0.01 + (200+240)/2 × 0.04 + (240+400)/2 × 0.01 = 1.00 + 8.80 + 3.20 = 13.0 MPa.
Returned work magnitude: (400+160)/2 × 0.01 + (160+120)/2 × 0.04 + (120+0)/2 × 0.01 = 2.80 + 5.60 + 0.600 = 9.00 MPa.
The closed-cycle difference is 4.00 MPa = 4.00 × 10⁶ J/m³. Stress times fractional strain is an energy density, since 1 Pa = 1 J/m³.
25.0 mm³ = 25.0 × 10⁻⁹ m³. Multiply to obtain 0.100 J net input per cycle under this model.

13.0 MJ/m³ enters mechanically, 9.00 MJ/m³ is returned, and 4.00 MJ/m³ remains as net input: 0.100 J for the stated volume. Zero final strain does not imply zero hysteretic loss.

Changed dimensions need a fresh matched comparison

A different gauge starts at 40.00 mm and 20 °C, retains 41.20 mm after unloading, and ends at 40.12 mm after the supplied complete heating/cooling observation at the original temperature and load. Find the same defined recovery fraction and final residual strain. Is the material intrinsically inferior to the first?

Retained extension is 1.20 mm and unrecovered extension is 0.12 mm. Recovery is (1.20 − 0.12)/1.20 = 0.900.
Final strain relative to its own reference is 0.12/40.00 = 0.00300 = 0.300%.
The two supplied ratios differ, but no common alloy, processing, imposed strain, heating path, constraint or cycle history was established. Those conditions are needed for an intrinsic-material comparison.

The defined recovery is 90.0%, with 0.300% unrecovered cold strain. These records alone do not rank intrinsic material quality.

Try the reasoning

Is every thermally expanding material a shape-memory material?
Show the answer and reasoning
No.
The mechanisms differ.
Why measure repeated cycles?
Show the answer and reasoning
Functional response and damage can evolve.
One cycle does not establish durability.
A new supplied reference expands from 30.000 mm at 20 °C according to α = 2.00 × 10⁻⁵ K⁻¹. At 70 °C, measured length after recovery is 30.060 mm. Find the reference length and excess over it. Does comparison with 30.000 mm alone isolate unrecovered deformation?
Show the answer and reasoning
L_ref = 30.030 mm and excess is 0.030 mm. The raw 0.060 mm includes 0.030 mm of the supplied thermal baseline.
Use ΔT = 50 K: αL₀ΔT = 0.030 mm. A matched final cold observation is still preferable for the defined cold recovery fraction; a baseline assumption is not independent evidence of every transformation or plastic contribution.
An unloaded shape-memory element recovers on heating. After cooling without a restoring load it remains near the recovered shape. Has its one-way behaviour failed?
Show the answer and reasoning
No. One-way recovery does not require spontaneous recreation of the earlier deformed shape on cooling.
Self-accommodating martensite can reform without that large macroscopic deformation. A two-way motion or externally reset actuator needs its own preparation, loading and cycle evidence.
Interpolate the original loop at 2.00% strain on loading and on unloading. Can one measured strain select a unique stress here?
Show the answer and reasoning
Loading gives 210 MPa; unloading gives 130 MPa. Strain alone does not select the branch.
Both middle segments change by 40 MPa over four percentage points. The state/history differs despite equal current strain. The loop is a supplied response, not a phase-fraction measurement.
A 10.0 mm³ gauge is stipulated to repeat the original loop twice per second at maintained uniform temperature, with no additional loss. Find mean net mechanical input power. Does it give thermal actuator efficiency?
Show the answer and reasoning
0.0800 W. It is not the thermal efficiency of a heated actuator.
Multiply 4.00 × 10⁶ J/m³ by 10.0 × 10⁻⁹ m³ and 2 s⁻¹. That accounts for this repeated mechanical loop only; heating input, thermal storage/losses and the actuator’s useful output were not supplied.
A free specimen shortens 2 mm during thermal recovery. A report multiplies that distance by an arbitrary spring stiffness to declare the force of a fully blocked actuator. Is that force established?
Show the answer and reasoning
No. The free-recovery record does not supply the blocked-force response.
Constraint changes stress and can change the transformation path. A stated coupled constitutive/fixture model or actual constrained measurement, geometry and temperature history is needed.
A programmed nanoparticle/polymer strip recovers in an alternating magnetic field and also in a field-free bath with the same measured temperature history. What mechanism is consistent, and what remains to test?
Show the answer and reasoning
Thermally triggered recovery is consistent; the magnetic field may deliver heat through the particles. This does not by itself establish a unique pathway or an alloy-like martensitic mechanism.
Compare actual internal temperature, constraint, particle-free controls and relevant structure/response. Similar output does not identify identical energy-transfer or molecular mechanisms.
After cycling, loop area is lower but residual strain is larger and recovered travel smaller. May lower area alone be called improved durability?
Show the answer and reasoning
No. Lower dissipated work can accompany loss of the desired function.
Retain the complete matched response record and investigate evolving transformation, slip or damage. Functional stability and crack resistance are distinct questions; a finite trend is not a lifetime guarantee.

What to carry forward

Identify the transformation or response mechanism.
Specify training, cycling and operating range.
Compare matched temperature/load endpoints and name the recovery denominator.
One-way heating recovery and isothermal pseudoelastic unloading follow different histories.
Recovered strain can coexist with a positive closed-cycle mechanical loss.
A trigger name does not uniquely identify the energy-transfer or structural mechanism.
Transformation, constraint, preparation and repeated history belong in a useful responsive-material claim.

References

Teaching resources and research supporting this lesson’s explanations and examples.