Magnetostriction is a property ofmagnetic materials that causes them to change their shape or dimensions during the process ofmagnetization. The variation of materials' magnetization due to the appliedmagnetic field changes the magnetostrictive strain until reaching its saturation value, λ. The effect was first identified in 1842 byJames Joule when observing a sample ofiron.[1]
Magnetostriction applies to magnetic fields, whileelectrostriction applies to electric fields.
Magnetostriction causes energy loss due to frictional heating in susceptible ferromagnetic cores, and is also responsible for the low-pitched humming sound that can be heard coming from transformers, where alternating currents produce a changing magnetic field.[2]
Internally, ferromagnetic materials have a structure that is divided intodomains, each of which is a region of uniform magnetization. When a magnetic field is applied, the boundaries between the domains shift and the domains rotate; both of these effects cause a change in the material's dimensions. The reason that a change in the magnetic domains of a material results in a change in the material's dimensions is a consequence ofmagnetocrystalline anisotropy; it takes more energy to magnetize a crystalline material in one direction than in another. If a magnetic field is applied to the material at an angle to an easy axis of magnetization, the material will tend to rearrange its structure so that an easy axis is aligned with the field to minimize thefree energy of the system. Since different crystal directions are associated with different lengths, this effect induces astrain in the material.[3]
The reciprocal effect, the change of the magnetic susceptibility (response to an applied field) of a material when subjected to a mechanical stress, is called theVillari effect. Two other effects are related to magnetostriction: theMatteucci effect is the creation of a helical anisotropy of the susceptibility of a magnetostrictive material when subjected to atorque and theWiedemann effect is the twisting of these materials when a helical magnetic field is applied to them.
The Villari reversal is the change in sign of the magnetostriction ofiron from positive to negative when exposed to magnetic fields of approximately 40 kA/m.
On magnetization, a magnetic material undergoes changes in volume which are small: of the order 10−6.
Likeflux density, the magnetostriction also exhibitshysteresis versus the strength of the magnetizing field. The shape of this hysteresis loop (called "dragonfly loop") can be reproduced using theJiles-Atherton model.[4]
Magnetostrictive materials can convert magnetic energy intokinetic energy, or the reverse, and are used to buildactuators andsensors. The property can be quantified by the magnetostrictive coefficient, λ, which may be positive or negative and is defined as the fractional change in length as the magnetization of the material increases from zero to thesaturation value. The effect is responsible for the familiar "electric hum" (Listenⓘ) which can be heard neartransformers and high power electrical devices.
Cobalt exhibits the largest room-temperature magnetostriction of a pure element at 60microstrains. Among alloys, the highest known magnetostriction is exhibited byTerfenol-D, (Ter forterbium, Fe foriron, NOL forNaval Ordnance Laboratory, and D fordysprosium). Terfenol-D,TbxDy1−xFe2, exhibits about 2,000 microstrains in a field of 160 kA/m (2 kOe) at room temperature and is the most commonly used engineering magnetostrictive material.[5]Galfenol,FexGa1−x, andAlfer,FexAl1−x, are newer alloys that exhibit 200-400 microstrains at lower applied fields (~200 Oe) and have enhanced mechanical properties from the brittle Terfenol-D. Both of these alloys have <100> easy axes for magnetostriction and demonstrate sufficient ductility for sensor and actuator applications.[6]
Another very common magnetostrictive composite is the amorphous alloyFe81Si3.5B13.5C2 with its trade nameMetglas 2605SC. Favourable properties of this material are its high saturation-magnetostriction constant, λ, of about 20microstrains and more, coupled with a lowmagnetic-anisotropy field strength, HA, of less than 1 kA/m (to reachmagnetic saturation).Metglas 2605SC also exhibits a very strong ΔE-effect with reductions in the effectiveYoung's modulus up to about 80% in bulk. This helps build energy-efficient magneticMEMS.[citation needed]
Cobaltferrite,CoFe2O4 (CoO·Fe2O3), is also mainly used for its magnetostrictive applications like sensors and actuators, thanks to its high saturation magnetostriction (~200 parts per million).[7] In the absence ofrare-earth elements, it is a good substitute forTerfenol-D.[8] Moreover, its magnetostrictive properties can be tuned by inducing a magnetic uniaxial anisotropy.[9] This can be done by magnetic annealing,[10] magnetic field assisted compaction,[11] or reaction under uniaxial pressure.[12] This last solution has the advantage of being ultrafast (20 min), thanks to the use ofspark plasma sintering.
In earlysonar transducers during World War II,nickel was used as a magnetostrictive material. To alleviate the shortage of nickel, the Japanese navy used aniron-aluminium alloy from theAlperm family.
Single-crystal alloys exhibit superior microstrain, but are vulnerable to yielding due to the anisotropic mechanical properties of most metals. It has been observed that forpolycrystalline alloys with a high area coverage of preferential grains for microstrain, the mechanical properties (ductility) of magnetostrictive alloys can be significantly improved. Targeted metallurgical processing steps promoteabnormal grain growth of {011} grains ingalfenol andalfenol thin sheets, which contain two easy axes for magnetic domain alignment during magnetostriction. This can be accomplished by adding particles such asboride species[13] andniobium carbide (NbC)[14] during initial chill casting of theingot.
For a polycrystalline alloy, an established formula for the magnetostriction, λ, from known directional microstrain measurements is:[15]
λs = 1/5(2λ100+3λ111)
During subsequenthot rolling andrecrystallization steps, particle strengthening occurs in which the particles introduce a "pinning" force atgrain boundaries that hinders normal (stochastic) grain growth in an annealing step assisted by aH2S atmosphere. Thus, single-crystal-like texture (~90% {011} grain coverage) is attainable, reducing the interference withmagnetic domain alignment and increasing microstrain attainable for polycrystalline alloys as measured by semiconductingstrain gauges.[16] These surface textures can be visualized usingelectron backscatter diffraction (EBSD) or related diffraction techniques.
For actuator applications, maximum rotation of magnetic moments leads to the highest possible magnetostriction output. This can be achieved by processing techniques such as stress annealing and field annealing. However, mechanical pre-stresses can also be applied to thin sheets to induce alignment perpendicular to actuation as long as the stress is below the buckling limit. For example, it has been demonstrated that applied compressive pre-stress of up to ~50 MPa can result in an increase of magnetostriction by ~90%. This is hypothesized to be due to a "jump" in initial alignment of domains perpendicular to applied stress and improved final alignment parallel to applied stress.[17]
These materials generally show non-linear behavior with a change in applied magnetic field or stress. For small magnetic fields, linear piezomagnetic constitutive[18] behavior is enough. Non-linear magnetic behavior is captured using a classical macroscopic model such as thePreisach model[19] and Jiles-Atherton model.[20] For capturing magneto-mechanical behavior, Armstrong[21] proposed an "energy average" approach. More recently, Wahiet al.[22] have proposed a computationally efficientconstitutive model wherein constitutive behavior is captured using a "locally linearizing" scheme.
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