The inverse magnetostrictive effect, magnetoelastic effect or Villari effect, after its discoverer
Emilio Villari, is the change of the
magnetic susceptibility
In electromagnetism, the magnetic susceptibility (Latin: , "receptive"; denoted ) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization (magnetic moment per unit volume) to the ap ...
of a material when subjected to a mechanical stress.
Explanation
The
magnetostriction
Magnetostriction (cf. electrostriction) is a property of magnetic materials that causes them to change their shape or dimensions during the process of magnetization. The variation of materials' magnetization due to the applied magnetic field chan ...
characterizes the shape change of a ferromagnetic material during magnetization, whereas the inverse magnetostrictive effect characterizes the change of sample magnetization
(for given magnetizing field strength
) when mechanical stresses
are applied to the sample.
Qualitative explanation of magnetoelastic effect
Under a given uni-axial mechanical stress
, the flux density
for a given magnetizing field strength
may increase or decrease. The way in which a material responds to stresses depends on its saturation magnetostriction
. For this analysis, compressive stresses
are considered as negative, whereas tensile stresses are positive.
According to
Le Chatelier's principle
Le Chatelier's principle (pronounced or ), also called Chatelier's principle (or the Equilibrium Law), is a principle of chemistry used to predict the effect of a change in conditions on chemical equilibria. The principle is named after French c ...
:
This means, that when the product
is positive, the flux density
increases under stress. On the other hand, when the product
is negative, the flux density
decreases under stress. This effect was confirmed experimentally.
Quantitative explanation of magnetoelastic effect
In the case of a single stress
acting upon a single magnetic domain, the magnetic strain energy density
can be expressed as:
where
is the magnetostrictive expansion at saturation, and
is the angle between the saturation magnetization and the stress's direction.
When
and
are both positive (like in iron under tension), the energy is minimum for
= 0, i.e. when tension is aligned with the saturation magnetization. Consequently, the magnetization is increased by tension.
Magnetoelastic effect in a single crystal
In fact, magnetostriction is more complex and depends on the direction of the crystal axes. In
iron
Iron () is a chemical element with Symbol (chemistry), symbol Fe (from la, Wikt:ferrum, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 element, group 8 of the periodic table. It is, Abundanc ...
, the
00axes are the directions of easy magnetization, while there is little magnetization along the
11directions (unless the magnetization becomes close to the saturation magnetization, leading to the change of the domain orientation from
11to
00. This
magnetic anisotropy
In condensed matter physics, magnetic anisotropy describes how an object's magnetic properties can be different depending on direction. In the simplest case, there is no preferential direction for an object's magnetic moment. It will respond ...
pushed authors to define two independent longitudinal magnetostrictions
and
.
* In
cubic materials, the magnetostriction along any axis can be defined by a known linear combination of these two constants. For instance, the elongation along
10is a linear combination of
and
.
* Under assumptions of
isotropic magnetostriction (i.e.
domain
Domain may refer to:
Mathematics
*Domain of a function, the set of input values for which the (total) function is defined
**Domain of definition of a partial function
**Natural domain of a partial function
**Domain of holomorphy of a function
* Do ...
magnetization is the same in any crystallographic directions), then
and the linear dependence between the elastic energy and the stress is conserved,
. Here,
,
and
are the direction cosines of the domain magnetization, and
,
,
those of the bond directions, towards the crystallographic directions.
Method of testing the magnetoelastic properties of magnetic materials
Method suitable for effective testing of magnetoelastic effect in magnetic materials should fulfill the following requirements:
* magnetic circuit of the tested sample should be closed. Open magnetic circuit causes
demagnetization
In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Di ...
, which reduces magnetoelastic effect and complicates its analysis.
* distribution of stresses should be uniform. Value and direction of stresses should be known.
* there should be the possibility of making the magnetizing and sensing windings on the sample - necessary to measure
magnetic hysteresis
Magnetic hysteresis occurs when an external magnetic field is applied to a ferromagnet such as iron and the atomic dipoles align themselves with it. Even when the field is removed, part of the alignment will be retained: the material has become '' ...
loop under mechanical stresses.
Following testing methods were developed:
* tensile stresses applied to the strip of magnetic material in the shape of a ribbon.
Disadvantage: open magnetic circuit of the tested sample.
* tensile or compressive stresses applied to the frame-shaped sample. Disadvantage: only bulk materials may be tested. No stresses in the joints of sample columns.
* compressive stresses applied to the ring core in the sideways direction.
Disadvantage: non-uniform stresses distribution in the core .
* tensile or compressive stresses applied axially to the ring sample. Disadvantage: stresses are perpendicular to the magnetizing field.
Applications of magnetoelastic effect
Magnetoelastic effect can be used in development of
force sensors. This effect was used for sensors:
* in
civil engineering
Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewa ...
.
* for monitoring of large
diesel engine
The diesel engine, named after Rudolf Diesel, is an internal combustion engine in which ignition of the fuel is caused by the elevated temperature of the air in the cylinder due to mechanical compression; thus, the diesel engine is a so-ca ...
s in
locomotives.
* for monitoring of
ball valve
A ball valve is a flow control device which uses a hollow, perforated and pivoting ball to control fluid flowing through it. It is open when the ball's hole is in line with the flow inlet and closed when it is pivoted 90-degrees by the valve ...
s.
* for biomedical monitoring.
Inverse magnetoelastic effects have to be also considered as a side effect of accidental or intentional application of mechanical stresses to the magnetic core of inductive component, e.g.
fluxgates or generator/motor
stators when installed with interference fits.
References
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See also
*
Magnetostriction
Magnetostriction (cf. electrostriction) is a property of magnetic materials that causes them to change their shape or dimensions during the process of magnetization. The variation of materials' magnetization due to the applied magnetic field chan ...
*
Magnetocrystalline anisotropy
In physics, a ferromagnetic material is said to have magnetocrystalline anisotropy if it takes more energy to magnetize it in certain directions than in others. These directions are usually related to the principal axes of its crystal lattice. I ...
Magnetism
Magnetic ordering