CN110988136B - Solid material single-crack nonlinear ultrasonic coefficient characterization method - Google Patents
Solid material single-crack nonlinear ultrasonic coefficient characterization method Download PDFInfo
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- CN110988136B CN110988136B CN201911354595.XA CN201911354595A CN110988136B CN 110988136 B CN110988136 B CN 110988136B CN 201911354595 A CN201911354595 A CN 201911354595A CN 110988136 B CN110988136 B CN 110988136B
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Abstract
A solid material single-crack nonlinear ultrasonic coefficient characterization method is characterized by comprising the following steps: carrying out nonlinear ultrasonic testing on the solid material; and performing fast Fourier transform on the obtained signals to calculate a coefficient nonlinear coefficient beta ', and evaluating a single crack in the material through the nonlinear coefficient beta'. The invention has the following advantages: (1) the nonlinear ultrasonic coefficient beta' derived from the model of the interaction of the crack and the ultrasonic wave can be used for representing and developing microcracks in the material more accurately; (2) compared with the traditional nonlinear coefficient, the nonlinear coefficient beta 'provided by the invention is more convenient to combine with geometrical relevant information such as crack length, width and angle, and the like, so that the nonlinear coefficient beta' has important significance in later detection result analysis.
Description
Technical Field
The invention relates to the field of nondestructive testing, in particular to a solid material single-crack nonlinear ultrasonic coefficient characterization method.
Background
Nonlinear ultrasonic testing is an emerging nondestructive testing technique. Nonlinear ultrasonic techniques are classified into a higher harmonic method, a coaxial mixing method, a resonance offset method, and the like according to the difference of nonlinear acoustic phenomena to be studied. The main content of the research of the invention belongs to the field of a higher harmonic method.
The high-order harmonic technology is mainly used for evaluating the damage of a material according to a high-order frequency doubling amplitude generated in a frequency spectrum by ultrasonic waves. The technology has the characteristics of relatively simple and convenient operation and relatively easy data processing. Meanwhile, the technology is sensitive to the structural microscopic characteristics, and errors cannot be avoided in the detection process, so that the accuracy of the test is influenced to a great extent. Classical nonlinear acoustics to which the nonlinearity generated by the crystal structure change belongs, depending on the source of the nonlinear ultrasound; the non-linearity resulting from the interaction of the flaw with the ultrasonic wave falls into the category of non-classical non-linear acoustics.
As mentioned above, the theory of classical nonlinearity appears early and has been studied more extensively. However, the study of nonlinear nonlinearity is less, and the theory is based on more reference on the relevant study of classical nonlinearity. Therefore, the method starts from a related model of the sound-interface, derives the index of the damage characterization aiming at the type of the unbonded interface in the solid material, and can more conveniently reflect the geometrical characteristics of the crack according to the index, wherein the characteristics are incompetent to the traditional nonlinear ultrasonic index.
Disclosure of Invention
The invention aims to provide a nonlinear ultrasonic coefficient for characterizing a single crack interface in a material, wherein the nonlinear ultrasonic coefficient is based on the characteristics of higher harmonics after ultrasonic waves pass through a crack-containing body.
The invention provides a solid material single-crack nonlinear ultrasonic coefficient characterization method, which comprises the following steps:
carrying out nonlinear ultrasonic testing on the solid material;
performing fast Fourier transform on the obtained signal;
the nonlinear coefficient of the coefficient beta' is calculated,
the nonlinear coefficient β' is defined as:
in the formula (I), the compound is shown in the specification,
ξ - θ cos θ denotes the ultrasound efficiency of the second harmonic,
indicating a phase threshold causing contact-acoustic nonlinear effects, E0As the linear elastic modulus, γ represents the difference between the linear elastic modulus and the elastic modulus at the crack interface, ε0Critical strain value for the CAN Effect, A1Is the fundamental wave amplitude, omega is the main frequency of the test signal, CLIs the velocity of longitudinal wave;
characterizing individual cracks within a material by a nonlinear coefficient β ', the characterizing individual cracks within a material by a nonlinear coefficient β' comprising:
the crack length n is characterized using the following formula,
β′∝n.；
the crack width was characterized using the following formula:
β′∝sinθ-θcosθ,
the crack angle is characterized using the following formula:
β′∝cos2α。
and alpha is the crack inclination angle.
Compared with the existing detection method, the invention has the following advantages: (1) the nonlinear ultrasonic coefficient beta' derived from the model of the interaction of the crack and the ultrasonic wave can be used for representing and developing microcracks in the material more accurately; (2) compared with the traditional nonlinear coefficient, the nonlinear coefficient beta' provided by the invention is more convenient to combine with geometrical relevant information such as crack length, width and angle, and the like, and has important significance in later-stage detection result analysis.
Drawings
FIG. 1 is a flow chart of a nonlinear coefficient β' characterizing a single crack in a material.
FIG. 2 is a graph comparing time domain curves of solid materials with complete and single cracks.
FIG. 3 is a graph comparing frequency domain curves of solid materials with complete and single cracks.
Fig. 4 is a graph showing the effect of the excitation amplitude on the nonlinear coefficient β'.
Fig. 5 shows the effect of crack length on the non-linearity factor β'.
Fig. 6 shows the effect of crack width on the non-linear coefficient β'.
Fig. 7 is a graph showing the effect of crack angle on the nonlinear coefficient β'.
Detailed Description
The invention aims to provide a nonlinear ultrasonic coefficient for characterizing a single crack interface in a material, and particularly the coefficient is based on the characteristics of higher harmonics after ultrasonic waves pass through a crack-containing body. According to the method, the characterization of cracks existing in the solid material is realized on the basis of the nonlinear ultrasonic characteristics through the analysis and derivation of a Contact Acoustic Nonlinear (CAN) model.
According to the CAN model, the tensile-compressive cycles induced by the ultrasonic waves passing through the crack interface will result in a change in the elastic modulus of the crack interface. For an isotropic elastic medium, its modulus of elasticity CAN be expressed in the CAN model as
In the formula, E0As the linear elastic modulus, γ represents the difference between the linear elastic modulus and the elastic modulus at the crack interface, ε0Critical strain values for the CAN effect.
The stress-strain relationship at the crack interface based on the CAN model CAN be written as
The solution of formula (2) is
In the formula (I), the compound is shown in the specification,
denotes the phase threshold causing the CAN effect and gamma denotes the difference between the linear elastic modulus and the crack interface elastic modulus.
The complete second harmonic can be written as
In the formula, ξ ═ sin θ — θ cos θ represents the ultrasonic efficiency of the second harmonic.
The nonlinear coefficient β' can be defined as
The relationship between the nonlinear characteristic parameter beta 'and the geometrical characteristics of the crack obtained on the basis of the nonlinear characteristic parameter beta' can be expressed as follows:
(1) length of crack
Assuming that the second harmonic derived above is generated by a unit length crack, the second harmonic of the n cracks is
Therefore, the nonlinear coefficient β' is linearly related to the crack length n
β′∝n. (7)
(2) Width of crack
As shown in fig. 1, the strain corresponding to the hatched portion causes the CAN effect, which is also the root cause of the generation of higher harmonics. The influence of the crack width on the nonlinear ultrasonic coefficient β' is expressed by ζ ═ sin θ - θ cos θ in the formula (5). The relation between the crack width and the nonlinear ultrasonic coefficient beta' is
(3) Crack angle
The crack angle is defined as the angle between the incident wave direction and the normal direction of the crack interface. The relationship between the crack angle β 'and the nonlinear ultrasonic coefficient β' can be written as
β′∝cos2α. (9)
The traditional nonlinear ultrasonic parameters are derived by expanding a stress-strain equation of a material to a high-order term, and the principle and the expression of the traditional nonlinear ultrasonic parameters are essentially different from the nonlinear ultrasonic coefficient obtained by the invention. The nonlinear ultrasonic parameter beta' provided by the invention has a remarkable effect on detecting a single crack in a material. In combination of formulas (5) and (6), the nonlinear coefficient depends on the excitation amplitude of the ultrasonic wave to some extent, which has important guiding significance in practical tests, and the excitation amplitude of the ultrasonic wave is not suitable to be changed in the nonlinear ultrasonic test of the same group of materials. The method provides a basis for generating higher harmonics due to the interaction of ultrasonic waves in the material and cracks with different lengths, widths and angles, and provides a theoretical basis for the evaluation of detection results.
The method for characterizing the nonlinear ultrasonic coefficient beta' of the single crack in the solid material provided by the invention has the following key steps (a flow chart is shown in figure 1): (1) according to the second harmonic generation condition mentioned in the invention, selecting a signal amplifier with high power, and increasing the excitation amplitude of the test signal; (2) fixing the transmitting end and the receiving end, and keeping the testing distance unchanged due to more microcracks existing in the solid material; (3) performing FFT (fast Fourier transform) on the obtained ultrasonic signal to obtain a corresponding frequency spectrum curve; (4) by
The nonlinear coefficient was determined and the cracks in the material were evaluated in combination with equations (7), (8) and (9).
Compared with the existing detection method, the invention has the following advantages: (1) the nonlinear ultrasonic coefficient beta' derived from the model of the interaction of the crack and the ultrasonic wave can be used for representing and developing microcracks in the material more accurately; (2) compared with the traditional nonlinear coefficient, the nonlinear coefficient beta' provided by the invention is more convenient to combine with geometrical relevant information such as crack length, width and angle, and the like, and has important significance in later-stage detection result analysis.
The following uses finite element software Abaqus, in conjunction with specific examples, to demonstrate that the nonlinear coefficient β' proposed by the present invention is capable of characterizing a single crack in a solid material:
a solid test block size of 10mm by 10mm is defined in two dimensions. In order to obtain the characterization results of the nonlinear coefficient beta' on the length, width, angle and ultrasonic excitation amplitude of the crack, a finite element model of 4 groups of solid test blocks needs to be established. The excitation frequency of the ultrasonic wave is 100KHz, and the excitation amplitude range of the ultrasonic wave is 0 to 50 Pa. For comparison, the time domain and frequency domain curves of the complete test block and the test block containing cracks are shown in fig. 2 and 3.
Fig. 4 shows that the nonlinear coefficient β' rapidly increases when the ultrasonic wave amplitude is small, but tends to stabilize when the ultrasonic wave amplitude is sufficiently large. This is in agreement with the conclusions from the theoretical formulae (4) and (5).
The nonlinear ultrasonic coefficient β' of the solid test piece having cracks of 2mm, 2.5mm, 3mm, 3.5mm, 4mm, 4.5mm and 5mm lengths is shown in FIG. 5. The crack width was 0.01 mm. At a certain excitation voltage, the crack length is highly linearly related to the nonlinear ultrasonic coefficient β'. This is in agreement with the conclusion from the theoretical formula (7).
The nonlinear ultrasonic coefficient β' of the solid specimen containing cracks of 0.01mm, 0.014mm, 0.016mm, 0.018mm, 0.02mm and 0.022 width is shown in FIG. 6. The crack length was 4 mm. The crack width has a significant effect on the nonlinear ultrasonic coefficient β' over a certain ultrasonic excitation amplitude range. This is in agreement with the conclusion from the theoretical equation (8).
The nonlinear ultrasonic coefficient β' of the solid test piece containing 0 °, 15 °, 30 °, 45 °, 60 °, 75 °, 90 ° cracks is shown in fig. 7. The crack length was 4 mm. The crack width was 0.01 mm. Within a certain ultrasonic excitation amplitude range, the nonlinear ultrasonic coefficient beta' is reduced along with the increase of the crack angle. This is in agreement with the conclusion made by the theoretical formula (9).
All the 4 examples show that the nonlinear ultrasonic coefficient beta' derived from the CAN model has a good characterization effect on the geometric characteristics of a single crack in a solid, CAN reasonably reflect the nonlinear acoustic phenomenon generated by the crack and the ultrasonic action, and CAN be used for characterizing the length, the width and the angle of the crack in the solid material.
Claims (1)
1. Characterization method of single-crack nonlinear ultrasonic coefficient of solid material, A1Is the fundamental wave amplitude, omega is the main frequency of the test signal, CLIs the longitudinal wave velocity, and is characterized by comprising the following steps:
carrying out nonlinear ultrasonic testing on the solid material;
performing fast Fourier transform on the obtained signal;
the coefficient non-linear coefficient beta' is calculated,
the nonlinear coefficient β' is defined as:
in the formula (I), the compound is shown in the specification,
ξ - θ cos θ denotes the ultrasound efficiency of the second harmonic,
indicating a phase threshold causing contact acoustic nonlinear effects, E0As the linear elastic modulus, γ represents the difference between the linear elastic modulus and the elastic modulus at the crack interface, ε0Critical strain value for CAN Effect, A1Is the fundamental wave amplitude, omega is the main frequency of the test signal, CLIs the velocity of longitudinal wave;
characterizing individual cracks within a material by a nonlinear coefficient β ', the characterizing individual cracks within a material by a nonlinear coefficient β' comprising:
the crack length n is characterized using the following formula,
β′∝n.；
the crack width was characterized using the following formula:
β′∝sinθ-θcosθ,
the crack angle is characterized using the following formula:
β′∝cos2α；
and alpha is the crack inclination angle.
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| CN113237953B (en) * | 2021-05-19 | 2022-04-29 | 西南交通大学 | Method for measuring fatigue microcrack offset angle based on nonlinear ultrasound |
Citations (3)
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| US5457994A (en) * | 1992-11-06 | 1995-10-17 | Southwest Research Institute | Nondestructive evaluation of non-ferromagnetic materials using magnetostrictively induced acoustic/ultrasonic waves and magnetostrictively detected acoustic emissions |
| CN104807888A (en) * | 2015-04-13 | 2015-07-29 | 北京工业大学 | Non-collinear mixing ultrasonic testing method for microcrack length measurement |
| CN105372330A (en) * | 2015-11-09 | 2016-03-02 | 北京工业大学 | Non-linear Lamb wave frequency mixing method for detecting microcrack in plate |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5457994A (en) * | 1992-11-06 | 1995-10-17 | Southwest Research Institute | Nondestructive evaluation of non-ferromagnetic materials using magnetostrictively induced acoustic/ultrasonic waves and magnetostrictively detected acoustic emissions |
| CN104807888A (en) * | 2015-04-13 | 2015-07-29 | 北京工业大学 | Non-collinear mixing ultrasonic testing method for microcrack length measurement |
| CN105372330A (en) * | 2015-11-09 | 2016-03-02 | 北京工业大学 | Non-linear Lamb wave frequency mixing method for detecting microcrack in plate |
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| ***等.非线性振动声调制信号耦合特征分析.《机械工程学报》.2010,(第23期), * |
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