CN113029880B - Phased array ultrasonic evaluation method of grain size - Google Patents

Phased array ultrasonic evaluation method of grain size Download PDF

Info

Publication number
CN113029880B
CN113029880B CN202110330345.3A CN202110330345A CN113029880B CN 113029880 B CN113029880 B CN 113029880B CN 202110330345 A CN202110330345 A CN 202110330345A CN 113029880 B CN113029880 B CN 113029880B
Authority
CN
China
Prior art keywords
grain size
representing
longitudinal wave
phased array
attenuation coefficient
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202110330345.3A
Other languages
Chinese (zh)
Other versions
CN113029880A (en
Inventor
关雪飞
刘雨
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Graduate School Of Chinese Academy Of Engineering Physics
Original Assignee
Graduate School Of Chinese Academy Of Engineering Physics
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Graduate School Of Chinese Academy Of Engineering Physics filed Critical Graduate School Of Chinese Academy Of Engineering Physics
Priority to CN202110330345.3A priority Critical patent/CN113029880B/en
Publication of CN113029880A publication Critical patent/CN113029880A/en
Application granted granted Critical
Publication of CN113029880B publication Critical patent/CN113029880B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume, or surface-area of porous materials
    • G01N15/02—Investigating particle size or size distribution
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/04—Analysing solids
    • G01N29/11—Analysing solids by measuring attenuation of acoustic waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
    • G01N29/44—Processing the detected response signal, e.g. electronic circuits specially adapted therefor
    • G01N29/4409—Processing the detected response signal, e.g. electronic circuits specially adapted therefor by comparison
    • G01N29/4418—Processing the detected response signal, e.g. electronic circuits specially adapted therefor by comparison with a model, e.g. best-fit, regression analysis
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
    • G16C60/00—Computational materials science, i.e. ICT specially adapted for investigating the physical or chemical properties of materials or phenomena associated with their design, synthesis, processing, characterisation or utilisation

Abstract

The invention provides a phased array ultrasonic evaluation method of a grain size, which comprises the following steps: obtaining an experimental longitudinal wave scattering attenuation coefficient by using the primary bottom echo and the secondary bottom echo; deducing a radiation sound field of the linear phased array probe by a Huygens principle, receiving average sound pressure through the probe, defining a diffraction correction coefficient of the linear phased array probe and calculating a final diffraction correction coefficient; obtaining a theoretical relation between the grain size and the longitudinal wave scattering attenuation coefficient according to a Weaver ultrasonic scattering model, and obtaining a proxy model of the grain size and the theoretical longitudinal wave scattering attenuation coefficient by utilizing polynomial fitting based on a nonlinear least square method; and substituting the experimental longitudinal wave scattering attenuation after the diffraction loss is eliminated into a proxy model, and inverting the grain size value. The method eliminates diffraction loss interference, fuses multi-angle sound beam information, greatly reduces relative errors compared with the traditional method, and provides a feasible and reliable means for grain size estimation of polycrystalline materials.

Description

Phased array ultrasonic evaluation method of grain size
Technical Field
The invention belongs to the technical field of grain size evaluation, and particularly relates to a phased array ultrasonic evaluation method for grain size.
Background
The grain size is an important factor influencing the mechanical properties of the polycrystalline material, such as yield strength, creep strength, corrosion resistance and the like. For example, the Hall-Petch effect indicates that the hardness and yield stress of a material generally increase as the grain size decreases. However, during heat treatment, melting or machining, the actual grain size may deviate from the design value. Therefore, the effective evaluation of the grain size has important significance for ensuring the safe service of the key components.
The evaluation of the grain size can be classified into a destructive method and a non-destructive method. The destructive method mainly uses a metallographic method and an electron back scattering diffraction method, but only can detect local information, and requires a precise instrument and a complex analysis program, resulting in low detection efficiency. Non-destructive methods such as ultrasonic inspection provide an effective and efficient option for determining grain size, where ultrasonic velocity, attenuation and back reflection characteristics have been reported for assessing grain size. In recent years, with the great development of the ultrasonic scattering theory, the attenuation method has become a powerful tool for evaluating the grain size. When an elastic wave propagates in a polycrystalline material composed of random anisotropic grains, scattering occurs at grain boundary interfaces, resulting in energy dissipation. Thus, reflection echo attenuation provides a reliable method for indirectly measuring grain size. However, most studies adopt a single crystal probe, and only one attenuation information can be obtained at one detection position, which greatly limits the grain size evaluation efficiency of large-size parts. Phased array supersound can realize sound beam deflection and focus through control delay, and then can acquire multi-angle data and realize single-point dynamic focusing to realize quick, low-cost detection. However, in the grain size evaluation using phased array ultrasound, diffraction loss due to sound beam diffusion exists, and the scattering attenuation cannot be directly measured from the experiment. For a phased array probe, the acoustic beam has not only focusing properties but also deflection properties. This requirement requires not only consideration of the transmit delay for achieving deflection or focusing, but also of the receive delay for superimposing all the received signals, which makes the diffraction correction of a phased array probe more complicated than the conventional single-probe diffraction correction, and no correction method has been available for a phased array probe. Therefore, it is very urgent and necessary to find a method for evaluating the grain size using phased array ultrasound based on the attenuation method.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a phased array ultrasonic evaluation method for grain size. The method comprises the steps of obtaining an experimental longitudinal wave scattering attenuation coefficient by utilizing primary bottom surface echoes and secondary bottom surface echoes, deducing a radiation sound field of a linear phased array probe by a Wheatstone principle, receiving average sound pressure by the probe, defining a diffraction correction coefficient of the linear phased array probe and calculating a final diffraction correction coefficient, obtaining a theoretical relation between a grain size and the longitudinal wave scattering attenuation coefficient according to a Weaver ultrasonic scattering model, obtaining a proxy model of the grain size and the theoretical longitudinal wave scattering attenuation coefficient by utilizing polynomial fitting based on a nonlinear least square method, and substituting the experimental longitudinal wave scattering attenuation after diffraction loss is eliminated into the proxy model to obtain a grain size value. The method eliminates diffraction loss interference, fuses multi-angle sound beam information, greatly reduces relative errors compared with the traditional method, and provides a feasible and reliable means for determining the grain size of the polycrystalline material.
The invention provides a phased array ultrasonic evaluation method of a grain size, which comprises the following steps:
s1, deriving an expression of the experimental longitudinal wave scattering attenuation coefficient: deriving an experimental measured experimental longitudinal wave scattering attenuation coefficient expression by using the amplitudes of the primary bottom surface echo and the secondary bottom surface echo in the frequency domain, wherein the step S1 specifically comprises the following steps;
s11, in the contact pulse reflection method, ignoring energy loss at the interface, amplitude V of the primary bottom surface echo BW1 and the secondary bottom surface echo BW2 in the frequency domainBW1(f)、VBW2(f) Respectively as follows:
VBW1(f)＝V0(f)DBW1exp[-2αL(f)H/cosθ] (1)
VBW2(f)＝V0(f)DBW2exp[-4αL(f)H/cosθ] (2)
wherein: v0(f) Representing an initial amplitude from the probe surface; h represents the thickness of the material; θ represents the acoustic beam steering angle in PA; dBW1And DBW2Diffraction coefficients respectively representing the primary bottom surface echo BW1 and the secondary bottom surface echo BW 2; alpha is alphaLRepresenting the attenuation coefficient of longitudinal wave scattering; f represents a frequency;
s12, dividing the formula (1) by the formula (2) to obtain the experimental longitudinal wave scattering attenuation coefficient alphaLComprises the following steps:
Figure BDA0002974548060000021
s2, deriving a final diffraction correction coefficient expression of the linear phased array sensor: deducing a radiation sound field of the linear phased array probe by using a Huygens principle, receiving average sound pressure by using the probe, and defining a diffraction correction coefficient of the linear phased array sensor;
s3, calculating a final diffraction correction coefficient of the linear phased array sensor: calculating the sound field of a single array element of the primary bottom wave and the secondary bottom wave by adopting a multi-Gaussian sound beam model, and substituting the result into a final diffraction correction coefficient expression of the linear phased array sensor for solving;
s4, deducing a theoretical relation between the grain size and the longitudinal wave scattering attenuation coefficient: obtaining a theoretical relation between the grain size and the longitudinal wave scattering attenuation coefficient according to a Weaver ultrasonic scattering model;
s5, calculating the grain size: substituting the final diffraction correction coefficient of the linear phased array sensor into the step S1 to obtain an experimental longitudinal wave scattering attenuation coefficient with the diffraction loss removed, and fitting by using a nonlinear least square method to obtain a proxy model of the grain size and the theoretical longitudinal wave scattering attenuation coefficient based on the theoretical relationship between the grain size and the longitudinal wave scattering attenuation coefficient and by combining the data of the grain size and the experimental longitudinal wave scattering attenuation coefficient:
Figure BDA0002974548060000031
wherein: g (a, alpha)L) A proxy function representing a grain size estimate; a represents a fitting parameter;
Figure BDA0002974548060000032
the average grain size is indicated.
Further, the step S2 specifically includes the following steps:
s21, defining the diffraction correction coefficient alphadiff(f) Comprises the following steps:
Figure BDA0002974548060000033
wherein:
Figure BDA0002974548060000034
and
Figure BDA0002974548060000035
the received signal amplitudes respectively representing the primary bottom surface echo BW1 and the secondary bottom surface echo BW2 in the frequency domain are considered only with respect to the beam diffraction characteristics;
s22, for the conventional linear phased array ultrasonic probe, the amplitude of the received signal is Vtheory(f)：
Figure BDA0002974548060000036
Wherein: n represents the number of array elements; sn(f) Representing a system function; t is tn(f) Representing an acoustic/elastic transfer function; Δ tn(receive)Represents a reception time delay; ω 2 pi f denotes an angular frequency;
s23 transfer function tnIs defined as:
Figure BDA0002974548060000037
wherein: fBAnd FTRespectively representing the blocking force and the compression force applied to the surfaces of the receiving array element and the transmitting array element; p is a radical of0Represents the initial sound pressure and p0＝ρcLv0ρ is the density of the test block, v0Representing the initial speed of the surface vibration of the array element;
Figure BDA0002974548060000038
is the average sound pressure received by the surface of the nth array element, and is expressed as:
Figure BDA0002974548060000039
wherein: p (x)nAnd f) represents a certain point x on the surface of the nth array elementnThe sound pressure of (2);
Figure BDA00029745480600000310
is the surface area of the nth receiving array element;
s24 Wheatstone theory shows that the sound field p (x) is completenAnd f) is:
Figure BDA00029745480600000311
wherein: p is a radical ofn(xnAnd f) denotes that the nth array element is in xnPosition radiation sound pressure; Δ tn(transmit)Representing a transmission time delay;
s25, substituting the formulas (5) to (8) into the formula (4) to obtain the final diffraction correction coefficient alpha of the linear PA sensordiff(f)：
Figure BDA0002974548060000041
Wherein: m, N indicates the total number of array elements;
Figure BDA0002974548060000042
is the surface area of the mth receiving array element;
Figure BDA0002974548060000043
a sound field of a single array element representing a primary bottom wave;
Figure BDA0002974548060000044
representing the sound field of a single array element of the quadratic bottom wave.
Preferably, the step S4 specifically includes the following steps:
s41, obtaining the scattering attenuation coefficient alpha of the polycrystal based on the Weaver modelL(f)：
Figure BDA0002974548060000045
Wherein: LL represents scattering from longitudinal wave to longitudinal wave; LT denotes scattering from longitudinal waves to transverse waves; c. CLAnd cTRespectively representing the velocities of longitudinal waves and transverse waves; thetapsRepresenting incident waves
Figure BDA0002974548060000046
And scattered waves
Figure BDA0002974548060000047
The scattering angle between; l (theta)ps) And M (theta)ps) Represents the inner product between the elastic modulus of the single crystal and the wave vector;
Figure BDA0002974548060000048
and
Figure BDA0002974548060000049
representing two-point spatial correlation function
Figure BDA00029745480600000410
The spatial fourier transform of (a), the spatial correlation function describes the probability that two random points at a distance r are located on the same grain;
s42 inner product L (theta) between single crystal elastic modulus and wave vector for cubic symmetric crystalps) And M (theta)ps) Comprises the following steps:
Figure BDA00029745480600000411
wherein: v ═ c11-c12-2c44Denotes the elastic constant c of a single crystal11、c12、c44The calculated anisotropy coefficient;
s43, assuming the crystal grains are equiaxed crystal grains etaLL(θps) And ηLT(θps) Respectively as follows:
Figure BDA00029745480600000412
wherein: k is a radical ofL、kTRespectively representing longitudinal wave number and transverse wave number;
s44, substituting the formulas (15) to (16) into the formula (14), the theoretical longitudinal wave scattering attenuation coefficient alphaL(f) Comprises the following steps:
Figure BDA0002974548060000051
preferably, the transmission delay Δ t in the step S2n(transmit)Is calculated as follows:
assuming that the deflection angle of the acoustic beam is theta and the depth of focus is F, the nth array elementIs delayed by Δ tn(transmit)Comprises the following steps:
Figure BDA0002974548060000052
wherein:
Figure BDA0002974548060000053
d represents the distance between array elements;
the receiving time delay delta t of the nth array elementn(receive)Comprises the following steps:
Figure BDA0002974548060000054
wherein:
Figure BDA0002974548060000055
representing the maximum transmission delay among all array elements.
Preferably, the sound field of the single array element of the primary bottom wave in step S25 is represented as:
Figure BDA0002974548060000056
wherein: m1Representing a first complex symmetric matrix; m2Representing a second complex symmetric matrix; p is a radical of0(f) Represents the initial sound pressure; the sound field of the single array element of the secondary bottom wave is represented as:
Figure BDA0002974548060000057
wherein: m3Representing a third complex symmetric matrix; m4A fourth complex symmetric matrix is represented.
Preferably, the experimental longitudinal wave scattering attenuation coefficient includes diffraction loss caused by scattering attenuation caused by crystal grains and sound beam diffusion.
Preferably, the final diffraction attenuation coefficient expression in step S2 is not only suitable for contact measurement, but also suitable for water immersion detection, and in the case of water immersion, it is only necessary to perform corresponding correction on the emission delay through a ray tracing algorithm.
Compared with the prior art, the invention has the technical effects that:
1. the invention designs a grain-size phased array ultrasonic evaluation method, which considers that diffraction loss is taken as a non-negligible part in total attenuation, deduces a diffraction correction coefficient expression of a linear phased array transducer based on a Wheatstone principle, and provides a correction coefficient solving method.
2. The phased array ultrasonic evaluation method for the grain size, which is designed by the invention, integrates the multi-angle sound beam evaluation results, greatly reduces the relative error compared with the traditional method, and provides a feasible and reliable means for grain size estimation of polycrystalline materials.
Drawings
Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings.
FIG. 1 is a flow chart of a grain-sized phased array ultrasonic evaluation method of the present invention;
FIG. 2a is a schematic diagram of a phased array ultrasound experimental setup of the present invention;
FIG. 2b is an example A-wave diagram of a phased array ultrasound experiment zero degree beam of the present invention;
FIG. 3 is a graph showing the relationship between the diffraction correction factor and the steering angle and the focal length at f-5 MHz according to the present invention;
FIG. 4 is a graph of the average experimental attenuation coefficient for diffraction-corrected and no diffraction-corrected versions of the present invention;
FIG. 5 is a graph of the fit of the grain size to the scattering attenuation coefficient of the present invention;
FIG. 6 is a graph of grain size results from a phased array experimental evaluation of the present invention;
FIG. 7a is a gold phase diagram of the XY plane of the coupon of the present invention;
FIG. 7b is a gold phase diagram of the XZ plane of the coupon of the present invention;
FIG. 7c is a metallographic image of the YZ plane of the test piece of the present invention.
The main reference numbers:
a phased array probe 1.
Detailed Description
The present application will be described in further detail with reference to the following drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. It should be noted that, for convenience of description, only the portions related to the related invention are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
Fig. 1 shows a grain-sized phased array ultrasonic evaluation method of the present invention, i.e., a grain-sized phased array ultrasonic acquisition method, which includes the steps of:
s1, deriving an expression of the experimental longitudinal wave scattering attenuation coefficient: and deriving an experimental longitudinal wave scattering attenuation coefficient expression of experimental measurement by using the amplitudes of the primary bottom surface echo and the secondary bottom surface echo in a frequency domain, wherein the experimental longitudinal wave scattering attenuation coefficient comprises the scattering attenuation caused by crystal grains and the diffraction loss caused by sound beam diffusion.
S11, in the contact pulse reflection method, ignoring energy loss at the interface, amplitude V of the primary bottom surface echo BW1 and the secondary bottom surface echo BW2 in the frequency domainBW1(f)、VBW2(f) Respectively as follows:
VBW1(f)＝V0(f)DBW1exp[-2αL(f)H/cosθ] (1)
VBW2(f)＝V0(f)DBW2exp[-4αL(f)H/cosθ] (2)
wherein: v0(f) Representing an initial amplitude from the probe surface; h represents the thickness of the material; θ represents the acoustic beam steering angle in PA; dBW1And DBW2Diffraction coefficients respectively representing the primary bottom surface echo BW1 and the secondary bottom surface echo BW 2; alpha is alphaLRepresenting the attenuation coefficient of longitudinal wave scattering; f represents a frequency;
s12, dividing the formula (1) by the formula (2) to obtain the experimental longitudinal wave scattering attenuation coefficient alphaLComprises the following steps:
Figure BDA0002974548060000071
s2, deriving a final diffraction correction coefficient expression of the linear phased array sensor: a radiation sound field of the linear phased array probe 1 is deduced according to the Wheatstone principle, and the average sound pressure is received through the probe to define a diffraction correction coefficient of the linear phased array sensor.
S21, defining the diffraction correction coefficient alphadiff(f) Comprises the following steps:
Figure BDA0002974548060000072
wherein:
Figure BDA0002974548060000073
and
Figure BDA0002974548060000074
the primary bottom echo BW1 and the secondary bottom echo BW2 are shown separately in the frequency domain with only the received signal amplitude of the beam diffraction characteristic taken into account.
S22, for the conventional linear phased array ultrasonic probe, the amplitude of the received signal is Vtheory(f)：
Figure BDA0002974548060000075
Wherein: n represents the number of array elements; sn(f) Representing a system function; t is tn(f) Representing an acoustic/elastic transfer function; ω 2 pi f denotes an angular frequency; Δ tn(receive)Represents the receive time delay and is:
Figure BDA0002974548060000081
wherein:
Figure BDA0002974548060000082
representing the maximum transmission delay among all array elements.
S23 transfer function tnIs defined as:
Figure BDA0002974548060000083
wherein: fBAnd FTRespectively representing the blocking force and the compression force applied to the surfaces of the receiving array element and the transmitting array element; p is a radical of0Represents the initial sound pressure and p0＝ρcLv0ρ is the density of the test block, v0Representing the initial speed of the surface vibration of the array element;
Figure BDA0002974548060000084
is the average sound pressure received by the surface of the nth array element, and is expressed as:
Figure BDA0002974548060000085
wherein: p (x)nω) represents a certain point x on the surface of the nth array elementnThe sound pressure of (2).
Figure BDA0002974548060000086
Is the surface area of the nth receiving array element;
s24 Wheatstone theory shows that the sound field p (x) is completenAnd f) is:
Figure BDA0002974548060000087
wherein: p is a radical ofn(xnAnd f) denotes that the nth array element is in xnPosition radiation sound pressure; Δ tn(transmit)Representing the transmission time delay.
Assuming that the deflection angle of the acoustic beam is theta and the depth of focus is F, the emission delay delta t of the nth array elementn(transmit)Comprises the following steps:
Figure BDA0002974548060000088
wherein:
Figure BDA0002974548060000089
d represents the distance between array elements.
S25, substituting the formulas (5) to (8) into the formula (4) to obtain the final diffraction correction coefficient alpha of the linear PA sensordiff(f)：
Figure BDA00029745480600000810
Wherein: m, N indicates the total number of array elements;
Figure BDA00029745480600000811
is the surface area of the mth receiving array element;
Figure BDA00029745480600000812
representing the acoustic field of a single array element of a primary bottom wave,
Figure BDA0002974548060000091
the sound field of a single array element representing the secondary bottom wave is respectively represented as:
Figure BDA0002974548060000092
Figure BDA0002974548060000093
wherein: m1Representing a first complex symmetric matrix; m2Representing a second complex symmetric matrix; m3Representing a third complex symmetric matrix; m4Represents a fourth doubletWeighing a matrix; p is a radical of0(f) Representing the initial sound pressure.
The final diffraction attenuation coefficient expression is not only suitable for contact measurement, but also suitable for water immersion detection, and under the condition of the water immersion, the emission delay is corrected correspondingly only through a ray tracing algorithm.
S3, calculating a final diffraction correction coefficient of the linear phased array sensor: and calculating the sound field of a single array element of the primary bottom wave and the secondary bottom wave by adopting a multi-Gaussian sound beam model, and substituting the result into a final diffraction correction coefficient expression of the linear phased array sensor for solving.
S4, deducing a theoretical relation between the grain size and the longitudinal wave scattering attenuation coefficient: and obtaining the theoretical relation between the grain size and the longitudinal wave scattering attenuation coefficient according to a Weaver ultrasonic scattering model.
S41, obtaining the scattering attenuation coefficient alpha of the polycrystal based on the Weaver modelL(f)：
Figure BDA0002974548060000094
Wherein: LL represents scattering from longitudinal wave to longitudinal wave; LT denotes scattering from longitudinal waves to transverse waves; c. CLAnd cTRespectively representing the velocities of longitudinal waves and transverse waves; thetapsRepresenting incident waves
Figure BDA0002974548060000095
And scattered waves
Figure BDA0002974548060000096
The scattering angle between; l (theta)ps) And M (theta)ps) Represents the inner product between the elastic modulus of the single crystal and the wave vector;
Figure BDA0002974548060000097
and
Figure BDA0002974548060000098
representing two-point spatial correlation function
Figure BDA0002974548060000099
The spatial fourier transform of (a), the spatial correlation function describes the probability that two random points at a distance r are located on the same grain.
S42 inner product L (theta) between single crystal elastic modulus and wave vector for cubic symmetric crystalps) And M (theta)ps) Comprises the following steps:
Figure BDA0002974548060000101
wherein: v ═ c11-c12-2c44Denotes the elastic constant c of a single crystal11、c12、c44The calculated anisotropy coefficient.
S43, assuming the crystal grains are equiaxed crystal grains etaLL(θps) And ηLT(θps) Respectively as follows:
Figure BDA0002974548060000102
wherein: k is a radical ofL、kTRepresenting the longitudinal and transverse wave wavenumbers, respectively.
S44, substituting the formulas (15) to (16) into the formula (14), the theoretical longitudinal wave scattering attenuation coefficient alphaL(ω) is:
Figure BDA0002974548060000103
s5, calculating the grain size: substituting the final diffraction correction coefficient of the linear phased array sensor into the step S1 to obtain an experimental longitudinal wave scattering attenuation coefficient with the diffraction loss removed, and fitting by using a nonlinear least square method to obtain a proxy model of the grain size and the theoretical longitudinal wave scattering attenuation coefficient based on the theoretical relationship between the grain size and the longitudinal wave scattering attenuation coefficient and by combining the data of the grain size and the experimental longitudinal wave scattering attenuation coefficient:
Figure BDA0002974548060000104
wherein: g (a, alpha)L) A proxy function representing a grain size estimate; a represents a fitting parameter;
Figure BDA0002974548060000105
the average grain size is indicated.
The present invention will be described in further detail with reference to specific examples.
Grain size evaluation experiments were performed on specimens of AISI 304 stainless steel (06Cr19Ni10) with dimensions as shown in fig. 2 a. The density of the stainless steel is 7930kg/m3The elastic constant of the single crystal is c11＝204.6GPa、c12＝137.7GPa、c44126.2 GPa. The thickness of the test piece was 49.5 mm. As shown in fig. 2a, the ultrasonic phased array probe 1 is vertically incident to the surface of the test block by using a contact pulse reflection method. In order to avoid the influence of surface roughness, the test block is polished smooth and a liquid coupling agent is adopted to form stable direct contact. In this case, the thickness of the coupling layer is negligible. In the experiment, a phased array longitudinal wave probe consisting of 16 array elements is adopted, and the center frequency is 5 MHz. The maximum sampling frequency of the data acquisition system is 100 MHz. The specific parameters of the probe are shown in table 1. The longitudinal wave sound velocity of the test piece was measured to be 5727 m/s.
Figure BDA0002974548060000111
TABLE 1
According to the numerical analysis result as shown in fig. 3, the energy of the acoustic beam is more concentrated, and the focal length is set to 10 mm. The scanning angle of the PA transducer is set to-10 degrees, and the interval is 1 degree. And collecting signals of different positions on the test block. By selecting the time window, the BW1 and BW2 signals in the time domain are extracted, and the peak values are obtained. The peak values of the two echoes are used for calculating the longitudinal wave attenuation coefficient of the experiment. For example, the full wave signal shown in FIG. 2b represents a zero degree beam signal, with a corresponding attenuation calculated to be 10.7 Np/m. The average experimental attenuation for the detection zone (about 1/5 for the test block) is shown in fig. 4. The diffraction attenuation is calculated by the formula (11), and the longitudinal wave attenuation corrected by the diffraction attenuation is obtained. The resulting attenuation is considered to be the grain-induced scattering attenuation. As shown in fig. 4, the diffraction attenuation components have a large ratio in the total attenuation. Experimental and diffractive attenuation coefficients have similar trends. After correction, the attenuation appears more stable and consistent under different beam angles.
The forward results and fitted curves are shown in FIG. 5, where the frequency is 5MHz, the proxy function G (a, α)L) The determination is as follows:
Figure BDA0002974548060000112
the maximum relative error of the fit is 0.0218%, which is sufficient for general applications. It should be noted that the proxy model is not necessary, and is used here only for computational convenience.
The experimental attenuation coefficient after the diffraction correction shown in fig. 4 was substituted into equation (19), and the crystal grain size was obtained. The final evaluation results are shown in fig. 6. Each scatter mark represents an estimate of the average grain size. The dotted line is the average of all angle acoustic beam measurements and is the evaluation result of the fused multi-angle measurement. The grain size finally evaluated in this example was 46.11. mu.m.
In order to verify the effectiveness and accuracy of the proposed phased array method, the grain size measured by an optical microscope is used as a reference value. Three orthogonal planes of the test piece were sampled to obtain the desired metallographic image. The resulting micrograph is shown in FIG. 7. It can be seen that the sampled grains exhibit equiaxed grains, satisfying the scattering model hypothesis. The average grain size was measured to be 44.9. + -. 2.3 μm according to ASTM E112. The relative error of the multi-angle estimation result compared to the gold phase value is 2.71%. By comparison, when no diffraction correction was used, the relative error increased to 49.32%.
The invention designs a grain-size phased array ultrasonic evaluation method, which considers that diffraction loss is taken as a non-negligible part in total attenuation, deduces a diffraction correction coefficient expression of a linear phased array transducer based on a Wheatstone principle, and provides a correction coefficient solving method. The designed method integrates the multi-angle sound beam evaluation results, compared with the traditional method, the method has the advantages that the relative error is greatly reduced, and a feasible and reliable means is provided for grain size estimation of the polycrystalline material.
Finally, it should be noted that: although the present invention has been described in detail with reference to the above embodiments, it should be understood by those skilled in the art that: modifications and equivalents may be made thereto without departing from the spirit and scope of the invention and it is intended to cover in the claims the invention as defined in the appended claims.

Claims (7)

1. A method for phased array ultrasonic evaluation of grain size, the method comprising the steps of:
s1, deriving an expression of the experimental longitudinal wave scattering attenuation coefficient: deriving an experimental measured experimental longitudinal wave scattering attenuation coefficient expression by using the amplitudes of the primary bottom surface echo and the secondary bottom surface echo in the frequency domain, wherein the step S1 specifically comprises the following steps;
s11, in the contact pulse reflection method, ignoring energy loss at the interface, amplitude V of the primary bottom surface echo BW1 and the secondary bottom surface echo BW2 in the frequency domainBW1(f)、VBW2(f) Respectively as follows:
VBW1(f)＝V0(f)DBW1exp[-2αLH/cosθ] (1)
VBW2(f)＝V0(f)DBW2exp[-4αLH/cosθ] (2)
wherein: v0(f) Representing an initial amplitude from the probe surface; h represents the thickness of the material; θ represents the acoustic beam steering angle in PA; dBW1And DBW2Diffraction coefficients respectively representing the primary bottom surface echo BW1 and the secondary bottom surface echo BW 2; alpha is alphaLRepresenting the scattering attenuation coefficient of the experimental longitudinal wave; f represents a frequency;
s12, dividing the formula (1) by the formula (2) to obtain the experimental longitudinal wave scattering attenuation coefficient alphaLComprises the following steps:
Figure FDA0003482507350000011
s2, deriving a final diffraction correction coefficient expression of the linear phased array sensor: deducing a radiation sound field of the linear phased array probe by using a Huygens principle, receiving average sound pressure by using the probe, and defining a diffraction correction coefficient of the linear phased array sensor;
s3, calculating a final diffraction correction coefficient of the linear phased array sensor: calculating the sound field of a single array element of the primary bottom wave and the secondary bottom wave by adopting a multi-Gaussian sound beam model, and substituting the result into a final diffraction correction coefficient expression of the linear phased array sensor for solving;
s4, deducing a theoretical relation between the grain size and the longitudinal wave scattering attenuation coefficient: obtaining a theoretical relation between the grain size and the longitudinal wave scattering attenuation coefficient according to a Weaver ultrasonic scattering model;
s5, calculating the grain size: substituting the final diffraction correction coefficient of the linear phased array sensor into the step S1 to obtain an experimental longitudinal wave scattering attenuation coefficient with the diffraction loss removed, and fitting by using a nonlinear least square method to obtain a proxy model of the grain size and the theoretical longitudinal wave scattering attenuation coefficient based on the theoretical relationship between the grain size and the longitudinal wave scattering attenuation coefficient and by combining the data of the grain size and the experimental longitudinal wave scattering attenuation coefficient:
Figure FDA0003482507350000012
wherein: g (a, alpha)L) A proxy function representing a grain size estimate; a represents a fitting parameter;
Figure FDA0003482507350000013
the average grain size is indicated.
2. The method for phased array ultrasonic evaluation of grain size according to claim 1, wherein the step S2 specifically comprises the steps of:
s21, defining the diffraction correction coefficient alphadiff(f) Comprises the following steps:
Figure FDA0003482507350000021
wherein:
Figure FDA0003482507350000022
and
Figure FDA0003482507350000023
the received signal amplitudes respectively representing the primary bottom surface echo BW1 and the secondary bottom surface echo BW2 in the frequency domain are considered only with respect to the beam diffraction characteristics;
s22, for the conventional linear phased array ultrasonic probe, the amplitude of the received signal is Vtheory(f)：
Figure FDA0003482507350000024
Wherein: n represents the total number of array elements; sn(f) Representing a system function; t is tn(f) Representing an acoustic/elastic transfer function; Δ tn(receive)Represents a reception time delay; ω 2 pi f denotes an angular frequency;
s23 Acoustic/elastic transfer function tn(f) Is defined as:
Figure FDA0003482507350000025
wherein: fBAnd FTRespectively representing the blocking force and the compression force applied to the surfaces of the receiving array element and the transmitting array element; p is a radical of0Represents the initial sound pressure and p0＝ρcLv0ρ is the density of the test block, v0Representing the initial speed of the surface vibration of the array element;
Figure FDA0003482507350000026
is the average sound pressure received by the surface of the nth array element, and is expressed as:
Figure FDA0003482507350000027
wherein: p (x)nAnd f) represents a certain point x on the surface of the nth array elementnThe sound pressure of (2);
Figure FDA0003482507350000028
is the surface area of the nth receiving array element;
s24 Wheatstone theory shows that the sound field p (x) is completenAnd f) is:
Figure FDA0003482507350000029
wherein: p is a radical ofn(xnAnd f) denotes that the nth array element is in xnPosition radiation sound pressure; Δ tn(transmit)Representing a transmission time delay;
s25, substituting the formulas (5) to (8) into the formula (4) to obtain the final diffraction correction coefficient alpha of the linear PA sensordiff(f)：
Figure FDA00034825073500000210
Wherein: m, N indicates the total number of array elements;
Figure FDA0003482507350000031
is the surface area of the mth receiving array element;
Figure FDA0003482507350000032
a sound field of a single array element representing a primary bottom wave;
Figure FDA0003482507350000033
represents twoThe sound field of a single array element of the sub-bottom wave.
3. The method for phased array ultrasonic evaluation of grain size according to claim 2, wherein the step S4 specifically comprises the steps of:
s41, obtaining theoretical longitudinal wave scattering attenuation coefficient alpha of polycrystal based on Weaver modelL(f)：
Figure FDA0003482507350000034
Wherein: LL represents scattering from longitudinal wave to longitudinal wave; LT denotes scattering from longitudinal waves to transverse waves; c. CLAnd cTRespectively representing the velocities of longitudinal waves and transverse waves; thetapsRepresenting incident waves
Figure FDA0003482507350000035
And scattered waves
Figure FDA0003482507350000036
The scattering angle between; l (theta)ps) And M (theta)ps) Represents the inner product between the elastic modulus of the single crystal and the wave vector;
Figure FDA0003482507350000037
and
Figure FDA0003482507350000038
representing two-point spatial correlation function
Figure FDA0003482507350000039
The spatial fourier transform of (a), the spatial correlation function describes the probability that two random points at a distance r are located on the same grain;
s42 inner product L (theta) between single crystal elastic modulus and wave vector for cubic symmetric crystalps) And M (theta)ps) Comprises the following steps:
Figure FDA00034825073500000310
wherein: v ═ c11-c12-2c44Denotes the elastic constant c of a single crystal11、c12、c44The calculated anisotropy coefficient;
s43, assuming the crystal grains are equiaxed crystal grains etaLL(θps) And ηLT(θps) Respectively as follows:
Figure FDA00034825073500000311
wherein: k is a radical ofL、kTRespectively representing longitudinal wave number and transverse wave number;
s44, substituting the formulas (15) to (16) into the formula (14), the theoretical longitudinal wave scattering attenuation coefficient alphaL(f) Comprises the following steps:
Figure FDA0003482507350000041
4. the method for phased array ultrasonic evaluation of grain size according to claim 3, wherein the emission time delay Δ t in step S2n(transmit)Is calculated as follows:
assuming that the deflection angle of the sound beam is theta and the depth of focus is F, the emission time delay of the nth array element is delta tn(transmit)Comprises the following steps:
Figure FDA0003482507350000042
wherein:
Figure FDA0003482507350000043
d represents the distance between array elements;
the receiving time delay delta t of the nth array elementn(receive)Comprises the following steps:
Figure FDA0003482507350000044
wherein:
Figure FDA0003482507350000045
representing the maximum value of the transmission time delay in all array elements.
5. The method for phased array ultrasonic evaluation of crystal grain size according to claim 2, wherein the sound field of a single array element of the primary bottom wave in the step S25 is represented as:
Figure FDA0003482507350000046
wherein:
Figure FDA0003482507350000047
a sound field of a single array element representing a primary bottom wave; c. CLRepresents the velocity of the longitudinal wave; x is the number ofnA point representing the surface of the nth array element; m1Representing a first complex symmetric matrix; m2Representing a second complex symmetric matrix; p is a radical of0(f) Represents the initial sound pressure;
the sound field of the single array element of the secondary bottom wave is represented as:
Figure FDA0003482507350000051
wherein: m3Representing a third complex symmetric matrix; m4A fourth complex symmetric matrix is represented.
6. The method for phased array ultrasonic evaluation of grain size according to claim 1, wherein the experimental longitudinal wave scattering attenuation coefficient includes diffraction loss due to grain-induced scattering attenuation and acoustic beam diffusion.
7. The phased array ultrasonic evaluation method of the grain size according to claim 1, characterized in that the final diffraction attenuation coefficient expression in the step S2 can be used for contact measurement or for water immersion detection, in which case, only the emission delay needs to be modified correspondingly by ray tracing algorithm.
CN202110330345.3A 2021-03-12 2021-03-12 Phased array ultrasonic evaluation method of grain size Active CN113029880B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110330345.3A CN113029880B (en) 2021-03-12 2021-03-12 Phased array ultrasonic evaluation method of grain size

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110330345.3A CN113029880B (en) 2021-03-12 2021-03-12 Phased array ultrasonic evaluation method of grain size

Publications (2)

Publication Number Publication Date
CN113029880A CN113029880A (en) 2021-06-25
CN113029880B true CN113029880B (en) 2022-03-25

Family

ID=76472662

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110330345.3A Active CN113029880B (en) 2021-03-12 2021-03-12 Phased array ultrasonic evaluation method of grain size

Country Status (1)

Country Link
CN (1) CN113029880B (en)

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113671044A (en) * 2021-08-16 2021-11-19 西安航天动力机械有限公司 Method for digitally selecting phased array transducer detection parameters
CN113804591B (en) * 2021-09-03 2023-05-12 南昌航空大学 High-dimensional ultrasonic evaluation method for nickel-based alloy grain size
CN114544445B (en) * 2022-02-24 2022-09-16 北京领示科技有限公司 Elongated crystal grain size determination method based on phased array ultrasonic and back scattering method

Family Cites Families (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070000328A1 (en) * 2005-01-06 2007-01-04 Jonathan Buttram Ultrasonic method for the accurate measurement of crack height in dissimilar metal welds using phased array
CN1927765A (en) * 2006-09-22 2007-03-14 中国科学院上海硅酸盐研究所 Preparation method for non-homogeneous phase precipitation of strontium barium titanate-magnesium oxide composite material
CN102830049A (en) * 2012-09-03 2012-12-19 北京理工大学 Ultrasound array micronano detection method of particle sizes multiphase fluid particles
CN104297110B (en) * 2014-09-19 2017-05-10 中南大学 Crystal grain size ultrasonic non-destructive evaluation method without thickness measurement
US20180217104A1 (en) * 2015-07-22 2018-08-02 Fluor Technologies Corporation Nondestructive determination of toughness of metal, plastic, and composite materials
DE102015116376A1 (en) * 2015-09-28 2017-03-30 TIPCO Tudeshki Industrial Process Control GmbH Method for determining the particle size distribution of granules in a flow and measuring device
CN106680372B (en) * 2017-01-11 2020-03-31 江苏科技大学 Correction method for evaluating grain size of metal material by stress influence ultrasonic wave
CN209656636U (en) * 2019-01-08 2019-11-19 哈尔滨焊接研究院有限公司 Reference block is used in the detection of engine rotor assemblies inertia friction weld seam ultrasonic phase array
CN112129832B (en) * 2020-08-11 2024-02-13 天津大学 Sweep frequency ultrasonic attenuation measurement method for detecting content of disperse phase

Also Published As

Publication number Publication date
CN113029880A (en) 2021-06-25

Similar Documents

Publication Publication Date Title
CN113029880B (en) Phased array ultrasonic evaluation method of grain size
Thompson et al. Ultrasonics in nondestructive evaluation
CN106017372B (en) A kind of method of ultrasonic non-destructive measurement wear-resistant coating thickness and modulus of elasticity
Lee et al. Measuring Lamb wave dispersion curves of a bi-layered plate and its application on material characterization of coating
Osumi et al. Imaging slit in metal plate using aerial ultrasound source scanning and nonlinear harmonic method
JP2003004710A (en) Method for inspecting padded pipe
Kupperman et al. Ultrasonic NDE of cast stainless steel
Lobkis et al. Three-dimensional transducer voltage in anisotropic materials characterization
JP2003130851A (en) Elastic parameter measuring device for material surface and coating layer
Moss et al. Investigation of ultrasonic transducers using optical techniques
Margetan et al. The practical application of grain noise models in titanium billets and forgings
Hesse et al. A single probe spatial averaging technique for guided waves and its application to surface wave rail inspection
Titov et al. Measurements of velocity and attenuation of leaky waves using an ultrasonic array
Bottiglieri et al. Corrective Techniques for the Ultrasonic Nondestructive Evaluation of Ceramic Materials
Kauppinen The evaluation of integrity and elasticity of thermally sprayed ceramic coatings by ultrasonics
Nageswaran et al. Evaluation of the phased array transmit-receive longitudinal and time-of-flight diffraction techniques for inspection of a dissimilar weld
Zhitlukhina et al. Analysis of the space-time dynamics of acoustic fields on the surface of a solid
Seldis Longitudinal and transverse wave attenuation estimations
Leo-Shin et al. Nondestructive determination of elastic constants of thin plates based on PVDF focusing ultrasound transducers and Lamb wave measurements
Xu et al. Wave velocity measurement in the through-thickness direction of the anisotropic material plate with ultrasonic polar scan
Peterson et al. Assessment of Corrosion Damage in Steel Samples Using Electro-Magnetic Acoustic Measurements
Fu et al. Roughness correction method for the measurement of attenuation coefficient using contact transducers
Karpelson Ultrasonic evaluation of hydrogen concentration and hydride properties in zirconium alloys
Hebaz et al. Longitudinal critically refracted wave for residual stress assessment on a welded plate using 3D laser vibrometry
Lin et al. Ultrasonic testing of the diffusion bonding of titanium alloys

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant