WO2023185140A1

WO2023185140A1 - Method for measuring elastic constant of fiber reinforced plastic material

Info

Publication number: WO2023185140A1
Application number: PCT/CN2022/141763
Authority: WO
Inventors: 郭师峰; 曹欢庆; 何梓科; 谢银飞; 冯伟
Original assignee: 中国科学院深圳先进技术研究院
Priority date: 2022-04-02
Filing date: 2022-12-26
Publication date: 2023-10-05
Also published as: CN115166051A

Abstract

Disclosed in the present application is a method for measuring an elastic constant of a fiber reinforced plastic (FRP) material. The method comprises: providing a one-way slab prepared from an FRP material; making an ultrasonic wave incident on a first side of the one-way slab, and receiving, on the first side, the ultrasonic wave reflected by a second side, so as to obtain the actually measured propagation time of the ultrasonic wave in the one-way slab, wherein the first side and the second side are opposite sides of the one-way slab; calculating the theoretical propagation time of the ultrasonic wave in the one-way slab; and taking the sum of squared errors between the actually measured propagation time and the theoretical propagation time as an objective function, and performing back calculation by means of particle swarm optimization to obtain an elastic constant value until the objective function is minimized. In this way, in the present application, an elastic constant of an FRP material can be obtained by means of measurement, and there is no need to immerse an FRP one-way slab in water or rotate the FRP one-way slab, such that the in-situ nondestructive measurement of the elastic constant of the FRP material is realized.

Description

A method for measuring the elastic constant of fiber resin matrix composite materials

This application claims priority to the Chinese patent application submitted to the China Patent Office on April 2, 2022, with the application number 202210352062.3 and the invention title "A method for measuring the elastic constant of fiber resin matrix composite materials", the entire content of which is incorporated by reference. incorporated in this application.

Technical field

This application relates to the technical field of material performance testing, and in particular to a method for measuring the elastic constant of fiber resin matrix composite materials.

Background technique

Fiber Reinforced Plastic (hereinafter referred to as FRP material) has the characteristics of high specific strength and specific stiffness, and is increasingly used to replace traditional metal materials in many industrial fields, such as aerospace and wind turbine blades and civil engineering and other fields.

FRP materials are composed of a large number of fibers. The elastic properties of fiber-reinforced resin matrix composites show significant transverse isotropic characteristics, which is manifested in that the anisotropic symmetry axis is along the fiber direction. The elastic properties of FRP materials can be quantitatively characterized by a 6×6 stiffness matrix containing 5 independent elastic constants. Whether in the manufacturing or service stage of FRP materials, elastic constants are crucial parameters and can be used for structural strength calculations, material performance degradation assessment, and ultrasonic non-destructive testing of internal defects. Therefore, how to non-destructively measure the elastic constant of materials in situ has become an urgent and difficult problem that needs to be solved to improve the manufacturing quality and service safety of FRP structures.

In related technologies, mechanical tensile experiments are usually used to measure the elastic constant of FRP materials. However, using this method requires cutting samples along directions with different angles to the fiber direction of the FRP material. This testing method is a destructive measurement, and the sample preparation and experiment costs are high.

However, in the industrial field, the elastic constant of FRP materials cannot be measured destructively, and the method of in-situ non-destructive measurement of the elastic constant is an urgent need. The ultrasonic measurement method is a very promising method for non-destructive measurement of elastic constants. Commonly used ultrasonic measurement methods, such as the secondary penetration reflection method, place the sample under test with the upper and lower surfaces parallel to each other between the ultrasonic probe and the plane reflector. The axis of the ultrasonic probe is perpendicular to the surface of the plane reflector, and the ultrasonic probe faces the sample under test. Incident ultrasound. When the ultrasound passes through the sample under test for the first time, it will be vertically incident on the surface of the plane reflector behind the sample. After reflection, it can return along the original path and pass through the sample under test for the second time, and finally be received by the transmitting probe; at the same time, with the help of precision The goniometer rotates the measured sample and records the propagation time of the secondary penetrating reflected wave as a function of the incident angle. Based on this, the anisotropic phase velocity distribution of the sample can be calculated according to the ultrasonic propagation path, and the final inversion calculation is elastic constant value. However, the secondary penetration reflection method is usually carried out under water immersion conditions to ensure stable acoustic coupling effect, and the measurement process does not require a rotating mechanism. It is difficult for FRP material equipment in service in the industrial field to meet conditions such as water immersion and rotation.

technical problem

The main technical problem solved by this application is to provide a method for measuring the elastic constant of fiber resin matrix composite materials, which can meet the in-situ non-destructive measurement of the elastic constant of FRP materials in the industrial field.

Technical solutions

In order to solve the above technical problems, a technical solution adopted by this application is to provide a method for measuring the elastic constant of fiber resin matrix composite materials, including:

Provide one-way boards made of fiber resin matrix composite materials;

The ultrasonic wave is incident on the first side of the one-way plate, and the ultrasonic wave reflected by the second side is received on the first side to obtain the measured propagation time of the ultrasonic wave in the one-way plate. The first side The second side is the opposite two sides of the one-way plate;

Calculate the theoretical propagation time of the ultrasonic wave in the one-way plate;

The sum of square errors between the measured propagation time and the theoretical propagation time is used as an objective function, and the elastic constant value is calculated through particle swarm optimization inversion until the objective function is minimized.

beneficial effects

The beneficial effects of this application are: different from the existing technology, this application can measure ultrasonic waves on one side of the surface of a one-way plate made of FRP materials, and obtain the measured propagation time of ultrasonic waves in the FRP one-way plate. The sum of square errors between the measured propagation time and the calculated theoretical propagation time is used as the objective function. Finally, the elastic constant value of the FRP one-way plate is iteratively updated through particle swarm optimization technology until the objective function is minimized, and the elastic constant of the FRP one-way plate is obtained. There is no need to cut the material, and the requirements for the measurement environment are not high. There is no need for water immersion or rotation of the FRP one-way plate, and the in-situ non-destructive measurement of the elastic constant of the FRP material is achieved.

Description of drawings

Figure 1 is a schematic flow chart of an embodiment of the method for measuring the elastic constant of the fiber resin matrix composite material of the present application;

Figure 2 is a schematic structural diagram of a one-way plate made of FRP material in the Cartesian coordinate system;

Figure 3 is a schematic diagram of the group velocity distribution of three modes of ultrasonic waves in a plane perpendicular to the fiber direction and in a plane parallel to the fiber direction;

Figure 4 is a schematic diagram of the arrangement of a linear array phased array ultrasonic probe in one embodiment of the method for measuring the elastic constant of fiber resin matrix composite materials of the present application;

Figure 5 is a schematic diagram of the propagation path of ultrasonic waves in the cross section of the FRP one-way plate perpendicular to the fiber direction in one embodiment of the method for measuring the elastic constant of the fiber resin matrix composite material of the present application;

Figure 6 is a schematic diagram of the propagation path of ultrasonic waves in the cross-section parallel to the fiber direction of the FRP one-way plate in one embodiment of the method for measuring the elastic constant of the fiber resin matrix composite material of the present application;

Figure 7 is a scanning image of a linear array probe according to an embodiment of the method for measuring the elastic constant of fiber resin matrix composite materials according to the present application;

Figure 8 is a comparison chart of the theoretical propagation time and the measured propagation time in the experimental data of Example 1 of the measurement method of the elastic constant of the fiber resin matrix composite material of the present application;

Figure 9 is the change of the objective function value with the number of iterations in the experimental data of the first embodiment of the method for measuring the elastic constant of the fiber resin matrix composite material of the present application;

Figure 10 is a table of measurement results according to one embodiment of the method for measuring the elastic constant of the fiber-resin matrix composite material of the present application.

Embodiments of the invention

The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of this application.

In the description of this application, reference to the description of the terms "one embodiment," "some embodiments," "an example," "a specific example," or "some examples" or the like means that specific features are described in connection with the embodiment or example. , mechanisms, materials or features are included in at least one embodiment or example of this application. In this specification, the schematic expressions of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the specific features, mechanisms, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, those skilled in the art may combine and combine different embodiments or examples and features of different embodiments or examples described in this specification unless they are inconsistent with each other.

Please refer to Figure 1. Figure 1 is a schematic flow chart of one embodiment of the method for measuring the elastic constant of the fiber resin matrix composite material of the present application. This embodiment includes the following steps:

S11: Provide one-way boards made of fiber resin matrix composite materials.

Please also refer to Figure 2, which is a schematic structural diagram of a one-way plate made of FRP material in the Cartesian coordinate system.

A one-way board made of FRP material is provided. In the FRP one-way board, the fibers have a unique and same direction, and the shape of the FRP one-way board can be a cuboid.

Define the Cartesian coordinate system with the z-axis along the fiber direction of the FRP one-way board, the y-axis along the thickness direction of the FRP one-way board, and the x-axis along the surface extension direction of one side of the FRP one-way board, and the surface is consistent with the y and z axes. vertical.

Generally, the elastic properties of FRP unidirectional plates are transversely isotropic and can be quantitatively characterized by a 6×6 elastic stiffness matrix C.

The matrix contains a total of 5 independent elastic constants: the first elastic constant C ₁₁ , the second elastic constant C ₆₆ , the third elastic constant C ₁₃ , the fourth elastic constant C ₄₄ , and the fifth elastic constant C ₃₃ .

This matrix can be expressed as follows:

There are three different modes of ultrasonic waves propagating inside the FRP one-way plate, namely Quasi Longitudinal (QL), vertically polarized Quasi Shear Vertical (QSV) and horizontally polarized Quasi Shear Horizontal (QSH) . The changes in the group velocity of the three modes of ultrasonic waves with respect to the propagation direction angle can be calculated by solving the Christoffel equation.

As shown in Figure 3, Figure 3 is a schematic diagram of the group velocity distribution of three modes of ultrasonic waves in a plane perpendicular to the fiber direction and in a plane parallel to the fiber direction. (a) is a schematic diagram of the group velocity distribution of three modes of ultrasonic waves in a plane perpendicular to the fiber direction, and (b) is a schematic diagram of the group velocity distribution of three modes of ultrasonic waves in a plane parallel to the fiber direction.

It can be seen from (a) in Figure 3 that in the plane perpendicular to the fiber direction, the QL, QSV, and QSH wave group velocities are constant, do not change with the propagation direction angle, and are isotropically distributed, and the QL wave group velocity > QSV wave group velocity > QSH wave group velocity.

At this time, the first elastic constant C ₁₁ and the second elastic constant C ₁₁ can be expressed as follows:

in,

and

represent the QL and QSV wave group velocities in the plane perpendicular to the fiber direction respectively, ρ is the density of the FRP unidirectional plate, and ρ can be measured by the Archimedean drainage method.

It can be seen from Figure 3 (b) that in the plane parallel to the fiber direction, the QL, QSV, and QSH wave group velocities all change with the propagation direction angle and present anisotropic distribution, and QL wave group velocity > QSV wave group velocity > QSH Wave group velocity.

At this time, the fifth elastic constant C ₃₃ can be expressed as follows:

in,

represents the group velocity of the QL wave along the fiber direction in the plane parallel to the fiber direction (propagation in the plane parallel to the fiber direction and the angle is 0), ρ is the density of the FRP unidirectional plate.

As for the third elastic constant C ₁₃ and the fourth elastic constant C ₄₄ related to the QL and QSV wave anisotropic group velocity distribution in the plane parallel to the fiber direction, please continue to refer to the following description of this embodiment.

S12: The ultrasonic wave is incident on the first side of the one-way plate, and the ultrasonic wave reflected by the second side is received on the first side.

Ultrasonic waves are incident on the first side of the FRP one-way plate, causing the ultrasonic waves to propagate in different directions in the FRP one-way plate. Part of the ultrasonic wave propagates through the FRP one-way plate to the second side of the FRP one-way plate, is reflected by the second side, and then propagates back to the first side. Among them, the first side and the second side are opposite two sides of the FRP one-way plate. In the cuboid FRP one-way plate, the first side and the second side are parallel to each other.

After the ultrasonic wave is incident on the first side of the FRP one-way plate, the ultrasonic wave reflected from the second side is then received on the first side, and the time of transmitting the ultrasonic wave and the time of reflection are recorded, and the time interval is used as the measured propagation time.

The ultrasonic waves received by the first side include the ultrasonic waves reflected once by the second side, and may also receive the ultrasonic waves reflected once by the second side, reflected by the first side, and reflected twice by the second side. In other more embodiments, it is possible to receive three or more reflected ultrasonic waves, which are not exhaustive here.

In some embodiments, the ultrasonic waves received by the first side may also include ultrasonic waves directly emitted by the first side without being reflected by the second side, which will be described in detail in the following embodiments.

Furthermore, to obtain the elastic constant of the FRP one-way plate, it is necessary to know the propagation time of the ultrasonic wave propagating in the plane perpendicular to the fiber direction of the FRP one-way plate and the ultrasonic wave propagating in the plane parallel to the fiber direction of the FRP one-way plate.

Alternatively, a linear array phased array ultrasonic probe can be used to obtain the actual propagation time of ultrasonic waves propagating in a plane perpendicular to the fiber direction of the FRP unidirectional plate and ultrasonic waves propagating in a plane parallel to the fiber direction of the FRP unidirectional plate.

Please refer to Figure 4. Figure 4 is a schematic diagram of the arrangement of a linear array phased array ultrasonic probe in one embodiment of the method for measuring the elastic constant of fiber resin matrix composite materials of the present application.

As shown in (a) of Figure 4, the steps of measuring the actual propagation time of ultrasonic waves propagating in a plane perpendicular to the fiber direction of the FRP unidirectional plate may include:

① Define the Cartesian coordinate system with the z-axis along the fiber direction of the FRP one-way board, the y-axis along the thickness direction of the FRP one-way board (direction from the first side to the second side), and the x-axis extending along the first side surface of the FRP one-way board. direction, and the surface is perpendicular to the y and z axes, where the xz plane coincides with the first side of the FRP one-way plate.

② Set up a linear array phased array ultrasonic probe on the first side of the FRP one-way plate, and the ultrasonic probe is in direct contact with the first side. The ultrasonic probes are arranged at equidistant intervals along the fiber direction perpendicular to the FRP unidirectional plate, that is, towards the x-axis direction.

③Use an ultrasonic probe to simultaneously transmit QL waves or QSV waves on the first side of the FRP one-way plate, and use different ultrasonic probes to receive the QL waves or QSV waves reflected on the second side of the FRP one-way plate.

④ The time when the ultrasonic probe receives the peak signal strength is regarded as the receiving time, and the time interval between the receiving time and the transmitting time is set as the measured propagation time.

It can be seen from the description in step S11 of the above embodiment and FIG. 3(a) that the ultrasonic wave received by the first side includes the ultrasonic wave reflected once by the second side and the ultrasonic wave reflected twice by the second side, and in the direction perpendicular to the fiber In the plane, QL wave group velocity > QSV wave group velocity. Therefore, when QL waves and QSV waves are emitted at the same time, the same ultrasonic probe will receive reflected ultrasonic waves at different time points.

At the same time, QL waves and QSV waves may also be converted into QSV waves or QL waves after being reflected by the second side of the FRP one-way plate, which increases the mode of ultrasonic waves received by the ultrasonic probe (with different modes in the FRP one-way plate). Propagation path classification).

The following describes the modes of ultrasonic waves received by several ultrasonic probes in chronological order.

①QL→QL wave: The QL wave emitted by the ultrasonic probe on the first side of the FRP one-way plate does not undergo waveform conversion after being reflected once by the second side, and is received by the ultrasonic probe.

②QL→QSV wave or QSV→QL: The QL wave emitted by the ultrasonic probe on the first side of the FRP one-way plate is converted into a QSV wave after one reflection on the second side and is received by the ultrasonic probe; or, the ultrasonic probe is on the FRP one-way plate. The QSV wave emitted by the first side of the plate is converted into QL wave after one reflection by the second side, and is received by the ultrasonic probe.

③QL→QL→QL→QL wave: The QL wave emitted by the ultrasonic probe on the first side of the FRP one-way plate is received by the ultrasonic probe after being reflected once by the second side, reflected by the first side, and twice reflected by the second side. And no waveform conversion occurs for each reflection.

④QL→QL→QL→QSV wave, QL→QL→QSV→QL, QL→QSV→QL→QL wave: The QL wave emitted by the ultrasonic probe on the first side of the FRP one-way plate is reflected once on the second side and then on the second side. The reflection on one side and the secondary reflection on the second side are received by the ultrasonic probe, and the waveform conversion occurs on the second reflection on the second side, the first reflection on the first side, or the primary reflection on the second side; and

QSV→QL→QL→QL wave: The QSV wave emitted by the ultrasonic probe on the first side of the FRP one-way plate is received by the ultrasonic probe through primary reflection on the second side, reflection on the first side, and secondary reflection on the second side. And the waveform conversion occurs during the first reflection on the second side.

The above are the possible modes of ultrasonic waves received by the ultrasonic probe. The actual test may also include more modes, which is not exhaustive here.

As shown in (b) of Figure 4, the steps of measuring the actual propagation time of ultrasonic waves propagating in a plane parallel to the fiber direction of the FRP unidirectional plate may include:

② Set up a linear array phased array ultrasonic probe on the first side of the FRP one-way plate, and the ultrasonic probe is in direct contact with the first side. The ultrasonic probes are set at equidistant intervals along the fiber direction of the FRP unidirectional plate, that is, set in the z-axis direction.

③Use an ultrasonic probe to simultaneously transmit QL waves or QSV waves on the first side of the FRP one-way plate, and use different ultrasonic probes to receive QL waves and QSV waves propagating along different paths on the first side of the FRP one-way plate.

It can be seen from the description in step S11 of the above embodiment and FIG. 3(b) that the ultrasonic wave received by the first side ultrasonic probe includes the ultrasonic wave that propagates along the fiber direction on the first side plane, does not undergo reflection, and is only reflected once on the second side. Ultrasonic waves, as well as ultrasonic waves reflected twice on the second side, and in the plane parallel to the fiber direction, QL wave group velocity > QSV wave group velocity. Therefore, when QL waves and QSV waves are emitted at the same time, the ultrasonic probe will receive ultrasonic waves at different time points.

At the same time, QL waves and QSV waves may also be converted into QSV waves or QL waves after being reflected by the second side of the FRP one-way plate, which increases the mode of ultrasonic waves received by the ultrasonic probe (classified by propagation path).

①QL wave (0°): The QL wave emitted by the ultrasonic probe on the first side of the FRP one-way plate propagates along the fiber direction on the first side plane and is then received by other ultrasonic probes.

②QL → QL wave: The QL wave emitted by the ultrasonic probe on the first side of the FRP one-way plate does not undergo waveform conversion after one reflection on the second side, and is received by the ultrasonic probe.

③QSV → QSV wave: The QSV wave emitted by the ultrasonic probe on the first side of the FRP one-way plate does not undergo waveform conversion after being reflected once by the second side, and is received by the ultrasonic probe.

④QL→QL→QL→QL wave: The QL wave emitted by the ultrasonic probe on the first side of the FRP one-way plate is received by the ultrasonic probe after being reflected once by the second side, reflected by the first side, and twice reflected by the second side. And no waveform conversion occurs for each reflection.

⑤QSV→QSV→QSV→QSV wave: The QSV wave emitted by the ultrasonic probe on the first side of the FRP one-way plate is received by the ultrasonic probe after being reflected once by the second side, reflected by the first side, and twice reflected by the second side. And no waveform conversion occurs for each reflection.

Therefore, through the above method, based on the ultrasonic time received by the same ultrasonic probe, the receiving time of different propagation modes can be distinguished, and finally the ultrasonic wave propagating perpendicular to the fiber direction of the FRP unidirectional plate or plane propagating parallel to the fiber direction of the FRP unidirectional plate can be obtained The actual propagation time of ultrasonic waves.

Continuing to refer to Figure 1, step S12 includes:

S13: Calculate the theoretical propagation time of ultrasonic waves in the one-way plate.

After the above steps, the measured time of ultrasonic wave propagation in the FRP one-way plate has been obtained. However, the actual measured time does not necessarily accurately reflect the actual propagation time of the corresponding ultrasonic wave. Therefore, it is necessary to calculate the theoretical propagation time corresponding to each measured ultrasonic wave in the FRP one-way plate.

In this embodiment, there are different calculation methods for ultrasonic waves corresponding to different propagation paths. The following takes the ultrasonic wave modes of several propagation paths as examples.

Please refer to Figures 4 and 5. Figure 5 is a schematic diagram of the propagation path of ultrasonic waves in the cross section of the FRP one-way plate perpendicular to the fiber direction in one embodiment of the method for measuring the elastic constant of the fiber resin matrix composite material of the present application.

A rectangular coordinate system is established on this section, with the y-axis along the thickness direction of the FRP one-way plate and the x-axis along the direction of the ultrasonic probe arrangement. where d is the thickness of the one-way plate, p ₀ is the distance between the ultrasonic probes, and i and j are the numbers of the ultrasonic probes.

Among them, the i-th ultrasonic probe transmits an ultrasonic probe, and the j-th ultrasonic probe receives an ultrasonic probe. The coordinates of the transmitting-end ultrasonic probe are ( _xi , 0), and the coordinates of the receiving-end ultrasonic probe are (x _j , 0).

The ultrasonic propagation direction angle is defined as the angle formed by the clockwise rotation of the x-axis to the corresponding direction.

In the ultrasonic waves propagating perpendicular to the fiber direction of the FRP unidirectional plate shown in Figure 5, the following modes of ultrasonic waves are included:

In this case, the coordinates of the second side reflection point

Located at ((x _i +x _j )/2,d), the corresponding outgoing ultrasonic propagation direction angle can be expressed as:

The theoretical propagation time of QL→QL wave is:

Among them, d is the distance between the first side and the second side, x _i -x _j is the distance difference between the transmitting end ultrasonic probe and the receiving end ultrasonic probe,

is the velocity function of the QL wave propagating in the plane perpendicular to the fiber direction of the FRP unidirectional plate.

②QL→QL→QL→QL wave: The QL wave emitted by the ultrasonic probe on the first side of the FRP one-way plate is received by the ultrasonic probe after being reflected once by the second side, reflected by the first side, and twice reflected by the second side. And no waveform conversion occurs for each reflection.

In this case, the coordinates of the point where the QL wave is reflected once on the second side and twice on the second side

Located at ((x _i +x _j )/4,d) and (3(x _i +x _j )/4,d).

The corresponding outgoing ultrasonic propagation direction angle can be expressed as:

The theoretical propagation time of QL→QL→QL→QL wave is:

③QL→QSV wave or QL→QL→QL→QSV wave: The QL wave is converted into a QSV wave after being reflected once by the second side and is received by the ultrasonic probe; or the QL wave is reflected once by the second side, then the first The side reflection and the second side reflection are converted into QSV waves after the second side reflection and are received by the ultrasonic probe.

In this case, to calculate the theoretical propagation time, the second side can be discretized into grid points first, and based on the velocity function of the QL wave group or QSV wave group propagating in the plane perpendicular to the fiber direction of the FRP unidirectional plate, QL→ The time required for a QSV wave or a QL→QL→QL→QSV wave to propagate through all possible grid points, and the calculated shortest time is set as the theoretical propagation time.

Please refer to Figures 4 and 6. Figure 6 is a schematic diagram of the propagation path of ultrasonic waves in the cross-section of the FRP one-way plate parallel to the fiber direction in one embodiment of the method for measuring the elastic constant of the fiber-resin matrix composite material of the present application.

A rectangular coordinate system is established on this section, with the y-axis along the thickness direction of the FRP one-way plate and the z-axis along the direction of the ultrasonic probe arrangement. where d is the thickness of the one-way plate, p ₀ is the distance between the ultrasonic probes, and i and j are the numbers of the ultrasonic probes.

Among them, the i-th ultrasonic probe transmits an ultrasonic probe, and the j-th ultrasonic probe receives an ultrasonic probe. The coordinates of the transmitting-end ultrasonic probe are (z _i ,0), and the coordinates of the receiving-end ultrasonic probe are (z _j ,0).

The ultrasonic propagation direction angle is defined as the angle formed by the clockwise rotation of the z-axis to the corresponding direction.

Among the ultrasonic waves propagating in a plane parallel to the fiber direction of the FRP unidirectional plate shown in Figure 6, the following modes of ultrasonic waves are included:

In this case, the QL wave mode and sound speed are constant, and the corresponding theoretical propagation time is:

Among them, |ij|p ₀ is the distance between the transmitting end ultrasonic probe and the receiving end ultrasonic probe,

is the propagation speed of the QL wave in the direction parallel to the fiber of the unidirectional plate and the angle is 0 (along the fiber direction on the first side plane).

In this case, the coordinates of the reflection point of the QL wave on the second side

Located at ((z _i +z _j )/2,d).

The propagation direction angle of QL wave emission is:

The theoretical propagation time of QL→QL wave is:

Where, z _i -z _j is the distance difference between the transmitting end ultrasonic probe and the receiving end ultrasonic probe, d is the distance between the first side and the second side,

is the velocity function of the QL group propagating in a plane parallel to the fiber direction of the FRP unidirectional plate.

In this case, the QSV wave is reflected at the second side point

Located at ((z _i +z _j )/2,d)

The propagation direction angle of the QSV wave emission is:

The theoretical propagation time of QSV→QSV wave is:

Among them, z _i -z _j is the distance difference between the transmitting end ultrasonic probe and the receiving end ultrasonic probe, d is the distance between the first side and the second side,

is the velocity function of the QSV wave propagating in a plane parallel to the fiber direction of the FRP unidirectional plate.

In this case, the two reflection points on the second side

They are located at ((z _i +z _j )/4,d) and (3(z _i +z _j )/4,d) respectively.

The propagation direction angle of QL wave emission is:

The theoretical propagation time of QL→QL→QL→QL wave is:

is the velocity function of the QL wave propagating in a plane parallel to the fiber direction of the unidirectional plate.

Two reflection points on the second side

They are located at ((z _i +z _j )/4,d) and (3(z _i +z _j )/4,d) respectively.

The propagation direction angle of the QSV wave emission is:

The theoretical propagation time of QSV→QSV→QSV→QSV wave is:

is the velocity function of the QSV wave propagating in a plane parallel to the fiber direction of the unidirectional plate.

The above lists the calculation of the theoretical time of ultrasonic waves in FRP one-way plates under different circumstances. Those skilled in the art can also obtain the theoretical time of more propagation modes based on this.

Through the above steps, the measured propagation time and theoretical propagation time of ultrasonic waves with multiple propagation paths in the FRP one-way plate have been obtained. Please refer to Figure 1, Figure 5 and Figure 6. After step S13, it also includes:

S14: Use the sum of squared errors between the measured propagation time and the theoretical propagation time as the objective function, and calculate the elastic constant value through particle swarm optimization inversion until the objective function is minimized.

It can be seen from formula (17) that the elastic constants of the FRP one-way plate can include: the first elastic constant C ₁₁ , the second elastic constant C ₆₆ , the third elastic constant C ₁₃ , the fourth elastic constant C ₄₄ , and the fifth elastic constant C ₃₃ .

Among them, the fifth elastic constant C ₃₃ is only related to the QL wave propagating along the fiber direction.

is the propagation speed of the QL wave in the direction parallel to the fiber of the one-way plate and the angle is 0, and ρ is the density of the one-way plate.

The fifth elastic constant C ₃₃ of the FRP one-way plate can be obtained by combining equation (7) and equation (8).

The first elastic constant C ₁₁ , the second elastic constant C ₆₆ , the third elastic constant C ₁₃ and the fourth elastic constant C ₄₄ can be calculated through particle swarm optimization.

Specifically, the sum of squared errors between the measured propagation time and the theoretical propagation time can be used as the objective function, and the elastic constants are inverted through particle swarm optimization until the objective function converges to the global minimum. At this time, the variable value is the final value obtained by this fiber. The final material elastic constant measurement value obtained under the embodiment of the measurement method of the elastic constant of the resin matrix composite material.

Further, the calculation of the first elastic constant C ₁₁ and the second elastic constant C ₆₆ is related to the ultrasonic wave propagating in the plane perpendicular to the fiber direction.

Define the objective function:

Among them, d is the distance between the first side and the second side, that is, the thickness of the FRP one-way plate,

is the measured propagation time of ultrasonic waves propagating in a plane perpendicular to the fiber direction of the one-way plate,

is the theoretical propagation time of ultrasonic waves propagating in a plane perpendicular to the fiber direction of the one-way plate. in,

and

After going through the above steps, it is known that

Obtained through measurement,

It can be calculated from formula (4) or (6).

Using particle swarm optimization technology, the first elastic constant C ₁₁ , the second elastic constant C ₆₆ and the d value of the FRP one-way plate are iteratively updated until the objective function converges to the global minimum, at which time the variable value is the final measured value.

In this embodiment, not only the values of the first elastic constant C ₁₁ and the second elastic constant C ₆₆ can be measured, but also the thickness of the FRP one-way plate can be obtained, which provides an option for thickness measurement of the FRP one-way plate.

Further, the calculation of the third elastic constant C ₁₃ and the fourth elastic constant C ₄₄ is related to the ultrasonic wave propagating in a plane parallel to the fiber direction.

Define the objective function:

is the measured propagation time of ultrasonic waves propagating in a plane parallel to the fiber direction of the one-way plate,

is the theoretical propagation time of ultrasonic waves propagating in a plane parallel to the fiber direction of the one-way plate. in

and

After the above steps it is known that

can be calculated,

It can be calculated from formula (10), (12), (14) or (16).

The above measured propagation times correspond to the corresponding theoretical propagation times.

Alternatively, the calculation can be performed by using waves with different propagation paths, such as QL→QL waves propagating in the vertical fiber plane, or QL→QL→QL→QL waves, or QL→QL waves propagating in parallel fiber planes. , QSV→QSV wave, QSV→QSV→QSV→QSV wave or QL→QL→QL→QL wave. The calculation method of the theoretical propagation time of various mode waves has been provided above. Those skilled in the art can choose the mode arbitrarily. Calculation.

Using particle swarm optimization technology, the third elastic constant C ₁₁ and the fourth elastic constant C ₆₆ of the FRP one-way plate are iteratively updated until the objective function converges to the global minimum, at which time the variable value is the final measured value.

Through the above steps, the elastic constant of the FRP one-way plate is finally obtained.

The beneficial effects included in this embodiment include but are not limited to:

The phased array ultrasonic bottom reflection method is used to measure and collect ultrasonic signals propagating in different directions. During the entire measurement process, there is no need to rotate the sample to change the direction of ultrasonic propagation, and the operation process is simple;

And by utilizing the wave type conversion caused by the reflection of the upper and lower surfaces of the FRP material under test, multiple modes of ultrasonic signals propagating in different directions can be generated at the same time. Using only a single linear array phased array ultrasonic probe, different modes of ultrasonic sound velocity distribution can be achieved. Simultaneous measurement without the need for complex other devices to assist measurement;

And when measuring the actual propagation speed of ultrasonic waves in FRP materials, you only need to set the linear array phased array ultrasonic probe on one side of the FRP material. The entire operation can be completed manually without the need for other rotating mechanisms;

Moreover, the measurement process can be performed on one side of the surface of the material being tested, without the need for sample cutting and water immersion. It can be used for in-situ non-destructive measurement of actual structures, which is beneficial to the in-situ non-destructive measurement of FRP material equipment in service in the industrial field and also saves money. Measure losses;

And it can realize the complete measurement of five elastic constants and obtain the thickness of FRP material at the same time, providing a variety of choices and inspiration for the thickness measurement of FRP materials.

The following is to measure the elastic constant of the carbon fiber reinforced resin-based (Carbon Fiber Reinforced Plastic, CFRP) composite one-way plate using the elastic constant measurement method of the fiber resin matrix composite material of this application, and conduct experiments to verify the reliability of the method of this application:

The CFRP one-way plate (Zhongfu Shenying Carbon Fiber Co., Ltd., Lianyungang, China) used in this experiment is made of T700 carbon fiber/3419 epoxy resin prepreg, containing a total of 32 layers, with a total thickness of 4.45mm, using The density of the material measured by Archimedes' method is 1.5587g/cm3.

The measurement is performed using a 5K0.8×10N-32CH linear array phased array ultrasonic probe (Nippon Probe Co., Ltd., Yokohama, Japan). The probe center frequency is 5MHz and contains a total of 32 array elements. The center distance between adjacent array elements is p0= 1.0mm.

The probe is placed on the surface of the CFRP one-way plate in direct contact.

Use a small amount of water to fill the air gap between the probe and the material surface, and place a steel block on the probe to provide stable pressure and keep the acoustic coupling effect stable. Use the Vantage 64LE high-frequency multi-channel research ultrasound platform system (Verasonics Co., Ltd. , Kirkland, USA) controls the excitation and reception of the linear array phased array ultrasonic probe. The No. 1 array element emits ultrasonic waves, and at the same time, all 32 array elements independently receive the bottom surface reflection echo signal. The sampling frequency is 62.5MHz, and a total of 32 Column ultrasound time domain waveform data.

Referring to the setting method in Figure 4, place the linear array probe along the plane perpendicular to the fiber direction and parallel to the fiber direction, and display the ultrasonic time domain waveform data collected by the bottom reflection method in the form of a B-scan image, as shown in Figure 7 The scan results shown are, Figure 7(a) is the ultrasonic B-scan image of the planar CFRP unidirectional plate when the ultrasonic wave propagates perpendicular to the fiber direction, and Figure 7(b) is the planar CFRP unidirectional plate when the ultrasonic wave propagates perpendicular to the fiber direction. Ultrasound B-scan image.

Based on the scanning results shown in Figure 7, based on the moment when the maximum amplitude of the target ultrasonic signal appears, the measured propagation time of the target ultrasonic signal received by different array elements is extracted.

The theoretical propagation time of the target ultrasonic signal is obtained through theoretical calculation.

The calculation results are shown in Figure 8. Figure 8 is a comparison chart between the theoretical propagation time and the measured propagation time, where exp represents the measured propagation time, cal represents the theoretical propagation time, and x and z in the coordinate system represent the receiving end ultrasonic probe and the transmitting end ultrasonic probe. Probe distance.

It can be seen from Figure 8 (a) that in a plane parallel to the fiber direction, the average time difference between the QL wave propagating along the fiber direction to two adjacent ultrasonic probe array elements is 0.10917 μs.

According to formula (8), the fifth elastic constant C ₃₃ is calculated:

C ₃₃ =1.5587×(1/0.10917) ² =130.78GPa.

Then using the ultrasonic propagation time in the plane perpendicular to the fiber direction shown in (a) of Figure 8, according to the objective function defined by equation (1), the particle swarm optimization technology is used to inversely calculate the first elastic constant C ₁₁ and the second elastic constant C ₆₆ and thickness d. The change of the objective function value with the number of iterations is shown in Figure 9(a), and the inversion calculation results are shown in Figure 10.

Then use the ultrasonic propagation time in the plane parallel to the fiber direction shown in (b) of Figure 8, and use the particle swarm optimization technology to inversely calculate the elastic constants C ₁₃ and C ₄₄ according to the objective function defined by Equation (1). The change of the objective function value with the number of iterations is shown in Figure 9(b), and the inversion calculation results are shown in Figure 10.

Verify the elastic constants measured by the above method through mechanical tensile experiments:

A 200 mm × 20 mm sample was cut from the tested CFRP unidirectional plate along the fiber direction, and the elastic modulus in the fiber direction E3 = 129.29 GPa was measured through mechanical tensile experiments.

Calculate Young’s modulus E3 from the elastic constant values listed in the table in Figure 10:

Compared with the measurement value of the mechanical tensile experiment, the measurement value obtained by the measurement method of this application has an error of only -4.58%, which confirms that the measurement method of the elastic constant of the fiber resin matrix composite material provided by this application has high reliability.

The above are only embodiments of the present application, and do not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the description and drawings of the present application, or directly or indirectly applied to other related technologies fields are equally included in the scope of patent protection of this application.

Claims

A method for measuring the elastic constant of fiber resin matrix composite materials, which is characterized by including:

Provide one-way boards made of fiber resin matrix composite materials;

The ultrasonic wave is incident on the first side of the one-way plate, and the ultrasonic wave reflected by the second side is received on the first side to obtain the measured propagation time of the ultrasonic wave in the one-way plate. The first side and The second side is the opposite two sides of the one-way plate;

Calculate the theoretical propagation time of the ultrasonic wave in the one-way plate;

The sum of square errors between the measured propagation time and the theoretical propagation time is used as an objective function, and the elastic constant value is calculated through particle swarm optimization inversion until the objective function is minimized.
The measuring method according to claim 1, characterized in that:

The first side receives ultrasonic waves propagating along different paths including: ultrasonic waves propagating in a plane perpendicular to the fiber direction of the one-way plate or ultrasonic waves propagating in a plane parallel to the fiber direction of the one-way plate.
The measurement method according to claim 2, characterized in that the objective function includes:

Where, d is the distance between the first side and the second side,
is the measured propagation time of the ultrasonic wave propagating in a plane perpendicular to the fiber direction of the one-way plate,
is the theoretical propagation time of the ultrasonic wave propagating in a plane perpendicular to the fiber direction of the one-way plate, C 11 is the first elastic constant of the one-way plate, and C 66 is the second elastic constant of the one-way plate.
The measurement method according to claim 3, characterized in that the calculation of the first elastic constant C 11 and the second elastic constant C 66 is related to the propagation of plane ultrasonic waves in the vertical fiber direction.
The measurement method according to claim 4, characterized in that the first elastic constant C 11 and the second elastic constant C 11 are:

in,
and
represent the QL and QSV wave group velocities in the plane perpendicular to the fiber direction respectively, and ρ is the density of the FRP unidirectional plate.
The measurement method according to claim 2, characterized in that the objective function includes:

in,
is the measured propagation time of the ultrasonic wave propagating in a plane parallel to the fiber direction of the one-way plate,
is the theoretical propagation time of the ultrasonic wave propagating in a plane parallel to the fiber direction of the one-way plate, C 13 is the third elastic constant of the one-way plate, and C 44 is the fourth elastic constant of the one-way plate .
The measurement method according to claim 6, characterized in that the calculation of the third elastic constant C13 and the fourth elastic constant C44 is related to ultrasonic waves propagating in a plane parallel to the fiber direction.
The measurement method according to claim 1, characterized in that the steps of injecting ultrasonic waves on the first side of the one-way plate and receiving the ultrasonic waves reflected by the second side on the first side include:

A linear array phased array ultrasonic probe is provided on the first side, and the ultrasonic probes are equidistantly spaced along a direction perpendicular to the fibers of the one-way plate;

Using the ultrasonic probe to transmit QL waves and QSV waves on the first side, and receiving QL waves and QSV waves reflected on the second side on the first side;

The time interval between the reception time and the transmission time is set as the measured propagation time.
The measurement method according to claim 8, characterized in that the ultrasonic waves received by the first side include QL waves and QSV waves that are reflected once and twice by the second side, and are in a plane perpendicular to the direction of the fiber. Within, QL wave group velocity > QSV wave group velocity.
The measurement method according to claim 8, wherein the QL wave is received by the ultrasonic probe after being reflected once by the second side, and the propagation direction angle of the QL wave is:

The theoretical propagation time is:

Where, d is the distance between the first side and the second side, xi - x j is the distance difference between the ultrasonic probe at the transmitting end and the ultrasonic probe at the receiving end,
is the velocity function of the QL wave propagating in a plane perpendicular to the fiber direction of the unidirectional plate.
The measurement method according to claim 8, wherein the QL wave is reflected by the ultrasonic probe after being reflected once by the second side, reflection by the first side, and secondary reflection by the second side in sequence. Receiving, the propagation direction angle of the QL wave is:

The theoretical propagation time is:

Where, d is the distance between the first side and the second side, xi - x j is the distance difference between the ultrasonic probe at the transmitting end and the ultrasonic probe at the receiving end,
is the velocity function of the QL wave propagating in a plane perpendicular to the fiber direction of the unidirectional plate.
The measurement method according to claim 8, characterized in that the QL wave is converted into a QSV wave after being reflected once by the second side and is received by the ultrasonic probe; or the QL wave passes through the second side in sequence. The primary reflection, the first side reflection, and the second side secondary reflection are converted into QSV waves after the second side reflection and are received by the ultrasonic probe;

The step of calculating the theoretical propagation time of the ultrasonic wave in the one-way plate includes:

discretizing the second side into grid points;

Based on the velocity function of the QL wave group or QSV wave group propagating in a plane perpendicular to the fiber direction of the one-way plate, the time required for the target ultrasonic wave to propagate through all possible grid points is calculated sequentially, and the calculated minimum time is set is the theoretical propagation time.
The measurement method according to claim 1, characterized in that the steps of injecting ultrasonic waves on the first side of the one-way plate and receiving the ultrasonic waves reflected by the second side on the first side include:

A linear array phased array ultrasonic probe is provided on the first side, and the ultrasonic probes are equidistantly spaced along the fiber direction of the one-way plate;

Using the ultrasonic probe to transmit QL waves and QSV waves on the first side, and receiving QL waves and QSV waves propagating along different paths on the first side;

The time interval between the reception time and the transmission time is set as the measured propagation time.
The measurement method according to claim 13, characterized in that the ultrasonic wave received by the first side ultrasonic probe includes propagation along the fiber direction on the first side plane without reflection and only once on the second side. Reflected and secondary reflected QL waves and QSV waves, and in the plane parallel to the fiber direction, the QL wave group velocity > QSV wave group velocity.
The measurement method according to claim 13, characterized in that the ultrasonic probe emits QL waves in a direction along the fiber of the one-way plate, and the QL wave propagates along the fiber direction of the one-way plate and is detected by the ultrasonic probe. take over;

The measured propagation time is:

The fifth elastic constant C 33 of the one-way plate is:

Among them, |ij|p 0 is the distance between the transmitting end ultrasonic probe and the receiving end ultrasonic probe,
is the propagation speed of the QL wave in the direction parallel to the fiber of the one-way plate and the angle is 0, and ρ is the density of the one-way plate.
The measurement method according to claim 13, wherein the QL wave is received by the ultrasonic probe after being reflected once by the second side, and the propagation direction angle of the QL wave is:

The theoretical propagation time is:

Where, z i -z j is the distance difference between the transmitting end ultrasonic probe and the receiving end ultrasonic probe, d is the distance between the first side and the second side,
is the velocity function of the QL wave propagating in a plane parallel to the fiber direction of the unidirectional plate.
The measurement method according to claim 13, wherein the QSV wave is received by the ultrasonic probe after being reflected once by the second side, and the propagation direction angle of the QSV wave is:

The theoretical propagation time is:

Where, z i -z j is the distance difference between the transmitting end ultrasonic probe and the receiving end ultrasonic probe, d is the distance between the first side and the second side,
is the velocity function of the QSV wave propagating in a plane parallel to the fiber direction of the unidirectional plate.
The measurement method according to claim 13, wherein the QL wave is reflected by the ultrasonic probe after being reflected once by the second side, reflection by the first side, and secondary reflection by the second side in sequence. Receiving, the propagation direction angle of the QL wave is:

The theoretical propagation time is:

Where, z i -z j is the distance difference between the transmitting end ultrasonic probe and the receiving end ultrasonic probe, d is the distance between the first side and the second side,
is the velocity function of the QL wave propagating in a plane parallel to the fiber direction of the unidirectional plate.
The measurement method according to claim 13, wherein the QSV wave is reflected by the ultrasonic probe after being reflected once by the second side, reflection by the first side, and secondary reflection by the second side in sequence. Receiving, the propagation direction angle of the QSV wave is:

The theoretical propagation time is:

Where, z i -z j is the distance difference between the transmitting end ultrasonic probe and the receiving end ultrasonic probe, d is the distance between the first side and the second side,
is the velocity function of the QSV wave propagating in a plane parallel to the fiber direction of the unidirectional plate.
The measurement method according to claim 1, characterized in that the ultrasonic wave is incident on the first side of the one-way plate, and the ultrasonic wave reflected by the second side is received on the first side to obtain the location of the ultrasonic wave at that location. The measured propagation times in one-way boards are described below, including:

using an ultrasonic probe to receive the ultrasonic waves;

Based on the ultrasonic wave time received by the same ultrasonic probe, the reception time of different propagation modes is distinguished to obtain the actual propagation time.