CN110632161B - Experimental measurement device and decoupling method for shear direction flexoelectric coefficient - Google Patents

Experimental measurement device and decoupling method for shear direction flexoelectric coefficient Download PDF

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CN110632161B
CN110632161B CN201910880205.6A CN201910880205A CN110632161B CN 110632161 B CN110632161 B CN 110632161B CN 201910880205 A CN201910880205 A CN 201910880205A CN 110632161 B CN110632161 B CN 110632161B
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test piece
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嵇辉
徐明龙
刘开园
张舒文
武彤晖
申胜平
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Xian Jiaotong University
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Abstract

An experimental measurement device for shear direction flexoelectric coefficients and a decoupling method are provided, the experimental measurement device comprises a semi-cylindrical test piece or a semi-circular truncated cone-shaped test piece processed by a flexoelectric material, clamping ends fixedly connected to two ends of the test piece, electrodes symmetrically distributed on the side surface of the test piece, a charge amplifier connected with the electrodes, a signal processing module connected with the charge amplifier, and loading equipment for applying torque to the test piece; the loading equipment outputs torque to the test piece, and the test piece is subjected to torsional deformation; the semicircular column generates a shear strain gradient along the radial direction to generate electric polarization, and the semicircular table respectively generates a shear strain gradient along the radial direction and the axial direction to generate electric polarization; the polarized charges are sent to a charge amplifier through an electrode, converted into voltage signals and transmitted to a signal processing module, and then a force-electricity coupling equation of the test pieces with two different shapes in a pure torsion state is established after the load parameters, the flexural electric material parameters and the test piece structure parameters of loading equipment are combined, so that radial and axial flexural electric coefficients can be decoupled respectively.

Description

Experimental measurement device and decoupling method for shear direction flexoelectric coefficient
Technical Field
The invention relates to the technical field of force-electricity coupling in design material science, in particular to an experimental measurement device and a decoupling method for a shear direction flexoelectric coefficient.
Background
The flexoelectric effect is a phenomenon that a material is deformed by strain gradient induced electric polarization or electric field gradient generated in the material by non-uniform deformation, and is a force-electricity coupling characteristic widely existing in dielectric materials. The flexoelectric effect is considered to be a promising alternative to the piezoelectric effect due to its presence in all dielectric materials. The research on the flexoelectric effect is still in a theoretical stage at present, but the research on the flexoelectric coefficient is always a research hotspot in the field. Since the flexoelectric coefficient is a fourth-order tensor, there are many flexoelectric coefficients in a material with low symmetry, and the electric charge measured in the experiment is often combined by a plurality of flexoelectric coefficients. Therefore, how to decouple the flexoelectric coefficients is a difficult point to study.
Disclosure of Invention
In order to fill the blank of the related experimental field, the invention aims to provide an experimental measurement device and a decoupling method for a shear direction flexoelectric coefficient, namely a semi-cylindrical or semi-circular truncated cone-shaped structure test piece is designed, a radial and axial shear strain gradient is constructed on the test piece through torsional deformation, so that electric polarization caused by the shear strain gradient is measured, and then the radial and axial flexoelectric coefficients are measured and decoupled respectively.
In order to achieve the above purpose, the invention adopts the following technical scheme.
The utility model provides an experimental measuring device of shear to flexoelectric coefficient which characterized in that: the device comprises a test piece 2 made of a flexoelectric material, a clamping end 1 fixedly connected with the upper end and the lower end of the test piece 2, electrodes 3 positioned on the side surface of the test piece 2 and symmetrically distributed along an axis, a charge amplifier 4 connected with the electrodes 3, a signal processing module 5 connected with the output end of the charge amplifier 4, and loading equipment 6 for outputting torque; the test piece 2 is a semi-cylindrical test piece or a semi-circular truncated cone shaped test piece loading device 6 which clamps the clamping ends 1 at two ends of the test piece 2 to apply torque, the semi-cylindrical test piece generates shear strain gradient along the radial direction to generate electric polarization, and the semi-circular truncated cone shaped test piece generates shear strain gradient along the radial direction and axial direction respectively to generate electric polarization.
The geometric center of the test piece 2 and the clamping end 1 are kept coincident so as to ensure that the test piece 2 is subjected to pure torsional load.
The electrodes 3 are at least 2 orders of magnitude less stiff than the flexoelectric material 2 and have good electrical conductivity.
The measurement accuracy of the charge amplifier 4 can meet the requirement of micro-charge measurement of the flexoelectric material 2.
The clamping end 1 is in a hexagonal prism shape, a quadrangular pyramid shape or a cylindrical shape which is matched with the shape of a chuck of the loading device 6.
The shear-direction flexoelectric coefficient test measurement device is used for decoupling the shear-direction flexoelectric coefficient, the clamping end 1 fixed on the test piece 2 is connected with the loading device 6, when the loading device 6 outputs torque, the torque is transmitted to the test piece 2 through the clamping end 1, and therefore the test piece 2 is subjected to torsional deformation and generates shear strain; when the test piece (2) is semi-cylindrical, the shear strain generates a strain gradient only in the radial direction and thus generates electric polarization of shear deflection electricity; when the test piece (2) is in a semicircular table shape, the shear strain generates a strain gradient in the radial direction and the axial direction, and thus two types of shear deflection electric polarization superposition are generated; the generated polarization charges are output to the input end of the charge amplifier 4 through the electrode 3, the charge amplifier converts charge signals into voltage signals and transmits the voltage signals to the signal processing module 5, and then the shear flexoelectric coefficients along the radial direction and the axial direction can be solved by combining the load parameters, the flexoelectric material parameters and the structural parameters of the test piece 2 of the loading equipment 6 and the simultaneous equations.
The method for solving the shear flexoelectric coefficients along the radial direction and the axial direction respectively comprises the following steps:
the charge generated by the test piece 2 under torsional deformation has a relation with the shear strain gradient of the material; the piezoelectric effect is not present in unpolarized flexoelectric materials, and the flexoelectric effect of a material can be simply expressed as:
Figure BDA0002205648530000031
wherein P isl、μijkl、ijAnd xkPolarization degree, flexoelectric coefficient, strain and gradient direction respectively; while the degree of polarization is described as the ratio of the charge to the charge distribution area, i.e. the degree of polarization
Figure BDA0002205648530000032
Wherein QlAnd a is the charge amount and the corresponding electrode area, respectively;
the shear strain of the semi-cylindrical test piece under pure torsion changes only along the radial direction, and the strain gradient is expressed as:
Figure BDA0002205648530000033
wherein gamma iszρIs the shear strain produced under the torsion state, M is the applied torque, ν and E are the Poisson's ratio and the elastic modulus of the material, R is the radius of the semi-cylinder, z and ρ are the axial and radial directions respectively under the cylindrical coordinate system, and n is the odd term in the calculation formula;
the shear strain of the semicircular truncated cone-shaped test piece under pure torsion changes along the radial direction and the axial direction respectively, and the strain gradient is expressed as follows:
Figure BDA0002205648530000034
wherein k is the taper of the circular truncated cone;
for the shear direction flexoelectric coefficient measurement experimental device of the semi-cylindrical test piece and the semi-circular truncated cone test piece, the formula (2) is rewritten into the following mode:
Figure BDA0002205648530000041
wherein QaAnd QbPolarization charges, A, generated on the semi-cylindrical test piece and the semi-circular truncated test piece, respectivelyaAnd AbRespectively the corresponding electrode area;
Figure BDA0002205648530000045
is the circumferential direction under a cylindrical coordinate system;
Figure BDA0002205648530000043
and
Figure BDA0002205648530000044
shear flexoelectric coefficients in the radial and axial directions, respectively;
thus, the output signal of the signal processing module (5) and the load parameter, the flexoelectric material parameter and the structural parameter of the test piece (2) applied by the loading device (6) are calculated according to the formula (3) and the formula (4)The strain gradient is substituted into the formula (5), namely the shear flexural modulus in the radial direction is decoupled
Figure BDA0002205648530000047
And shear flexoelectric coefficient in the axial direction
Figure BDA0002205648530000046
Compared with the prior art, the invention has the following advantages:
1) the invention enriches the measurement means of the flexoelectric coefficient and obtains the unknown flexoelectric coefficient by a decoupling method.
2) Compared with other coefficient measurement modes, the method has the advantages that a plurality of shear flexoelectric coefficients are decoupled in one experiment by designing different experiment simultaneous equations, and the method is simple in structure and efficient in process.
In a word, the experimental measurement device for the shear direction flexoelectric coefficients and the decoupling method can obtain a plurality of shear flexoelectric coefficients, and make up for the blank and the deficiency of the prior art.
Drawings
Fig. 1 is a schematic structural diagram of an experimental measuring device for a semi-cylindrical test piece.
Fig. 2 is a schematic structural diagram of an experimental measurement device for a semicircular truncated cone-shaped test piece.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
As shown in fig. 1 and 2, a clamping end 1 fixed on a test piece 2 is connected with a loading device 6, when the loading device 6 outputs torque, the torque is transmitted to the test piece 2 through the clamping end 1, and thus the test piece 2 is subjected to torsional deformation and generates shear strain; when the test piece is semi-cylindrical, the shear strain generates a strain gradient only in the radial direction and thus generates electric polarization of shear deflection electricity; when the test piece is in a semicircular table shape, the shear strain generates a strain gradient in the radial direction and the axial direction, and two types of shear deflection electric polarization superposition are generated; the generated polarization charges are output to the input end of the charge amplifier 4 through the electrode 3, the charge amplifier converts charge signals into voltage signals and transmits the voltage signals to the signal processing module 5, and then the shear flexoelectric coefficients along the radial direction and the axial direction can be solved by combining the load parameters, the flexoelectric material parameters and the structural parameters of the test piece 2 of the loading equipment 6 and the simultaneous equations.
The method for solving the shear flexoelectric coefficients along the radial direction and the axial direction respectively comprises the following steps:
the charge generated by the test piece 2 under torsional deformation has a relation with the shear strain gradient of the material; the piezoelectric effect is not present in the unpolarized flexoelectric material, and the flexoelectric effect of the material is simply expressed as:
Figure BDA0002205648530000051
wherein P isl,μijkl,ijAnd xkPolarization degree, flexoelectric coefficient, strain and gradient direction respectively; while the degree of polarization is described as the ratio of the charge to the charge distribution area, i.e. the degree of polarization
Figure BDA0002205648530000052
Wherein QlAnd a is the charge amount and the corresponding electrode area, respectively;
the shear strain of the semicylinder (2-1) under pure torsion changes only along the radial direction, and the strain gradient is expressed as:
Figure BDA0002205648530000061
wherein gamma iszρIs the shear strain produced under the torsion state, M is the applied torque, ν and E are the Poisson's ratio and the elastic modulus of the material, R is the radius of the semi-cylinder, z and ρ are the axial and radial directions respectively under the cylindrical coordinate system, and n is the odd term in the calculation formula;
the shear strain of the semicircular truncated cone-shaped test piece under pure torsion changes along the radial direction and the axial direction respectively, and the strain gradient is expressed as follows:
Figure BDA0002205648530000062
wherein k is the taper of the circular truncated cone;
for the shear direction flexoelectric coefficient measurement experimental device of the semi-cylindrical test piece and the semi-circular truncated cone test piece, the formula (2) is rewritten into the following mode:
Figure BDA0002205648530000063
wherein QaAnd QbPolarization charges, A, generated on the semi-cylindrical test piece and the semi-circular truncated test piece, respectivelyaAnd AbRespectively the corresponding electrode area;
Figure BDA0002205648530000064
is the circumferential direction under a cylindrical coordinate system;
Figure BDA0002205648530000065
and
Figure BDA0002205648530000066
shear flexoelectric coefficients in the radial and axial directions, respectively;
the output signal of the signal processing module (5) and the corresponding strain gradients calculated from the load parameters, the flexoelectric material parameters and the structural parameters of the test piece (2) by the loading device (6) according to the equations (3) and (4) are thus introduced into the equation (5), i.e. the shear flexoelectric coefficients in the radial direction are decoupled
Figure BDA0002205648530000071
And shear flexoelectric coefficient in the axial direction
Figure BDA0002205648530000072
The flexoelectric material 2 shown, as a preferred embodiment of the present invention, has a high dielectric constant and a large elastic deformation range.
As a preferred embodiment of the present invention, the electrode 3 has good conductive properties and low attachment rigidity.

Claims (5)

1. A shear-direction flexoelectric coefficient decoupling method is carried out by an experimental measuring device of shear-direction flexoelectric coefficients, the experimental measuring device comprises a test piece (2) made of a flexoelectric material, a clamping end (1) fixedly connected with the upper end and the lower end of the test piece (2), electrodes (3) which are positioned on the side surface of the test piece (2) and symmetrically distributed along an axis, a charge amplifier (4) connected with the electrodes (3), a signal processing module (5) connected with the output end of the charge amplifier (4), and a loading device (6) for outputting torque; the test piece (2) is a semi-cylindrical test piece or a semi-circular truncated cone test piece; the loading device (6) clamps the clamping ends (1) at the two ends of the test piece (2) to apply torque, the semi-cylindrical test piece generates shear strain gradient along the radial direction to generate electric polarization, and the semi-circular table test piece generates shear strain gradient along the radial direction and the axial direction to generate electric polarization;
the method is characterized in that: the decoupling method comprises the following steps: connecting a clamping end (1) fixed on a test piece (2) with loading equipment (6), and when the loading equipment (6) outputs torque, transmitting the torque to the test piece (2) through the clamping end (1), so that the test piece (2) is subjected to torsional deformation and generates shear strain; when the test piece (2) is a semi-cylindrical test piece, the shearing strain only generates a strain gradient in the radial direction and thus generates electric polarization of shearing deflection electricity; when the test piece (2) is a semicircular frustum-shaped test piece, the shear strain generates a strain gradient in the radial direction and the axial direction, and two types of electric polarization superposition of shear deflection are generated; the generated polarization charges are output to the input end of a charge amplifier (4) through an electrode (3), charge signals are converted into voltage signals by the charge amplifier and transmitted into a signal processing module (5), and then the shear flexoelectric coefficients along the radial direction and the axial direction can be solved by simultaneous equations after the load parameters, the flexoelectric material parameters and the structural parameters of the test piece (2) of a loading device (6) are combined;
the method for solving the shear flexoelectric coefficients along the radial direction and the axial direction respectively comprises the following steps:
the charge generated by the test piece (2) under torsional deformation has a relation with the shear strain gradient of the material; the piezoelectric effect is absent in the unpolarized flexoelectric material, and the flexoelectric effect of the material is expressed as:
Figure FDA0002517093490000021
wherein P isl、μijkl、ijAnd xkPolarization degree, flexoelectric coefficient, strain and gradient direction respectively; while the degree of polarization is described as the ratio of the charge to the charge distribution area, i.e. the degree of polarization
Figure FDA0002517093490000022
Wherein: qlAnd a is the charge amount and the corresponding electrode area, respectively;
the shear strain of the semi-cylindrical test piece under pure torsion changes only along the radial direction, and the strain gradient is expressed as:
Figure FDA0002517093490000023
wherein: gamma rayzρIs the shear strain produced under the torsion state, M is the applied torque, ν and E are the Poisson's ratio and the elastic modulus of the material, R is the radius of the semi-cylinder, z and ρ are the axial and radial directions respectively under the cylindrical coordinate system, and n is the odd number term in the formula calculation;
the shear strain of the semicircular truncated cone-shaped test piece under pure torsion changes along the radial direction and the axial direction respectively, and the strain gradient is expressed as follows:
Figure FDA0002517093490000024
wherein k is the taper of the circular truncated cone;
for the shear direction flexoelectric coefficient measurement experimental device of the semi-cylindrical test piece and the semi-circular truncated cone test piece, the formula (2) is rewritten into the following mode:
Figure FDA0002517093490000031
wherein QaAnd QbPolarization charges, A, generated on the semi-cylindrical test piece and the semi-circular truncated test piece, respectivelyaAnd AbThe electrode areas are respectively corresponding to the semi-cylindrical test piece and the semi-circular truncated cone-shaped test piece;
Figure FDA0002517093490000032
is the circumferential direction under a cylindrical coordinate system;
Figure FDA0002517093490000033
and
Figure FDA0002517093490000034
shear flexoelectric coefficients in the radial and axial directions, respectively;
the output signal of the signal processing module (5) and the corresponding strain gradients calculated from the load parameters, the flexoelectric material parameters and the structural parameters of the test piece (2) by the loading device (6) according to the equations (3) and (4) are thus introduced into the equation (5), i.e. the shear flexoelectric coefficients in the radial direction are decoupled
Figure FDA0002517093490000035
And shear flexoelectric coefficient in the axial direction
Figure FDA0002517093490000036
2. The method for decoupling the shear-direction flexoelectric coefficient by the experimental measurement device of the shear-direction flexoelectric coefficient according to claim 1, characterized in that: the geometric center of the test piece (2) is kept coincident with the clamping end (1) so as to ensure that the test piece (2) is subjected to pure torsional load.
3. The method for decoupling the shear-direction flexoelectric coefficient by the experimental measurement device of the shear-direction flexoelectric coefficient according to claim 1, characterized in that: the rigidity of the electrode (3) is lower than that of the test piece (2) by at least 2 orders of magnitude and has good conductivity.
4. The method for decoupling the shear-direction flexoelectric coefficient by the experimental measurement device of the shear-direction flexoelectric coefficient according to claim 1, characterized in that: the measurement precision of the charge amplifier (4) can meet the micro-charge measurement requirement of a test piece (2) made of a deflection electric material.
5. The method for decoupling the shear-direction flexoelectric coefficient by the experimental measurement device of the shear-direction flexoelectric coefficient according to claim 1, characterized in that: the clamping end (1) is in a hexagonal prism shape, a quadrangular pyramid shape or a cylindrical shape matched with the shape of a chuck of the loading equipment (6).
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