CN113406146A - Infrared phase-locking thermal imaging defect identification method for honeycomb sandwich structure - Google Patents

Infrared phase-locking thermal imaging defect identification method for honeycomb sandwich structure Download PDF

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CN113406146A
CN113406146A CN202110835808.1A CN202110835808A CN113406146A CN 113406146 A CN113406146 A CN 113406146A CN 202110835808 A CN202110835808 A CN 202110835808A CN 113406146 A CN113406146 A CN 113406146A
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temperature
heat flow
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CN113406146B (en
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李慧娟
石亮
王俊涛
张方洲
张祥春
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China Aero Polytechnology Establishment
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Abstract

The invention provides an infrared phase-locking thermal imaging defect identification method for a honeycomb sandwich structure, which comprises the following steps: s1, constructing an analytic model of temperature change and distribution of the test piece by adopting an infrared phase-locked thermal imaging detection method; s2, extracting amplitude and phase information of a steady-state or quasi-steady-state process in the temperature signal by adopting a digital phase locking method, and obtaining defect characteristics by utilizing the influence of defects on the phase information; s3, constructing a finite difference model of the heat conduction process, and deducing the heating surface temperature of the test piece considering the radiation and convection; and S4, establishing a heat and electricity equivalent model of the heat conduction process, and confirming the existence of the defects. The invention fully considers the constant heat flow and the alternating heat flow and the influence of transverse heat diffusion in the honeycomb sandwich structure, and is effective for the detection process range of defects of different types and different depths and the detection of different defects.

Description

Infrared phase-locking thermal imaging defect identification method for honeycomb sandwich structure
Technical Field
The invention belongs to the technical field of nondestructive testing, and particularly relates to an infrared phase-locking thermal imaging defect identification method for a honeycomb sandwich structure.
Background
Honeycomb sandwich structures are emerging and rapidly used in a wide variety of fields, are much lighter and more rigid than conventional materials and structures, and have a significant weight reduction effect on products. Because various process parameters are difficult to accurately control in the manufacturing process, the honeycomb sandwich structure is easy to cause unstable quality and large discreteness, and various defect types such as debonding, layering, poor bonding, air holes, inclusion, honeycomb core deformation and the like appear, and the detection effect and efficiency of the traditional detection methods such as ray, ultrasonic and the like are not good and need to be improved urgently. Under the background, the infrared thermal imaging detection method is popularized and applied, wherein the infrared phase-locked thermal imaging defect identification method adopts an external excitation source with energy changing according to a sine rule to excite and load a component or a material, combines the infrared thermal imaging technology with the digital phase-locked signal processing technology, and separates a useful signal from a noise signal. The method actively loads a thermal excitation signal with a specific modulation frequency on a test piece, so that different periodic responses are generated between the damaged part inside the test piece and a matrix, the response can influence the temperature field distribution on the surface of the test piece, and the signal with the specific phase-locked frequency is extracted by utilizing software and hardware, so that whether damage exists inside the test piece and the damage characteristics can be obtained through analysis.
During infrared phase-locked thermal imaging detection, sine-law heat flow is adopted for excitation, the temperature process oscillates along with time according to sine-law change, along the heat flow transmission direction, along with the increase of the transmission depth, the temperature gradually attenuates, namely the energy is attenuated continuously, if the depth of the defect in the test piece is deep and the energy cannot be transmitted to the defect depth, the temperature signal cannot contain the influence information of the defect on the temperature change, and at the moment, the defect detection cannot be carried out. The point temperature history and distribution of the test piece in the heat flow excitation process are very complex, but the temperature signals contain a large amount of information, the amplitude and phase information of the steady-state or quasi-steady-state process in the temperature signals can be extracted by adopting a phase-locking method, and the defect characteristics can be accurately determined by utilizing the influence of defects on the information, so that nondestructive detection is realized. According to the analysis of the infrared phase-locked thermal imaging detection principle, process parameters in the detection process comprise a plurality of influence factors such as a wave band range, integral time, thermal sensitivity, loading amplitude, loading frequency, loading period, phase-locked frequency, a phase value, environmental influence, loading distance and the like, and the detection process of products with different structures, thicknesses and sizes is difficult to effectively determine by adopting a traditional process test method.
As mentioned above, the honeycomb sandwich structure has many defect types, and the process influencing factors of the infrared phase-locking thermal imaging defect identification method are also many. The process influence factor is a multi-factor set, and a certain coupling relation exists among all factors; the weights of all process factors are different during different defect detection, so that infrared phase-locking thermal imaging detection of defects in the honeycomb sandwich structure is a complex nonlinear relation. Therefore, it is very urgent and necessary to find an infrared phase-locking thermal imaging defect identification method for honeycomb sandwich structure aiming at the detection process range of defects with different types and depths and the detection effectiveness of different defects.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides an infrared phase-locking thermal imaging defect identification method for a honeycomb sandwich structure. The method comprises the steps of constructing an analytic model of temperature change and distribution of a test piece based on Fourier one-dimensional heat conduction model analysis by adopting an infrared phase-locked thermal imaging detection technology; extracting amplitude and phase information of a steady-state or quasi-steady-state process in the temperature signal by adopting a digital phase locking method to obtain defect characteristics; constructing a finite difference model of the heat conduction process, and deducing the temperature of the heating surface of the test piece considering the radiation and convection; establishing a heat conduction heat and electricity equivalent model; and carrying out finite element analysis on the infrared phase-locking thermal imaging detection of the honeycomb sandwich structure, determining whether defect detection can be carried out according to an amplitude diagram and a phase diagram of the infrared phase-locking thermal imaging detection technology, and determining a reasonable detection parameter range. The invention fully considers the constant heat flow and the alternating heat flow and the influence of transverse heat diffusion in the honeycomb sandwich structure, and is very effective for the detection process range of defects of different types and different depths and the detection of different defects.
The invention provides an infrared phase-locking thermal imaging defect identification method for a honeycomb sandwich structure, which comprises the following steps:
s1, constructing an analytic model of temperature change and distribution of the honeycomb sandwich structure defect test piece based on Fourier one-dimensional heat conduction model analysis by adopting an infrared phase-locked thermal imaging detection method;
s2, extracting amplitude and phase information of a steady state or quasi-steady state process in the temperature signal by adopting a digital phase locking method, and obtaining defect characteristics by utilizing the influence of defects on the phase information, wherein the method specifically comprises the following substeps:
s21, when there is a defect in the honeycomb sandwich structure material or the member, the material-defect structure or the composite material is regarded as a multilayer structure in which the temperature change of each layer satisfies:
Figure BDA0003176936160000021
wherein: t isiRepresents the temperature of the ith interlayer medium; rhoiRepresents the density of the ith interlayer medium; c. CiRepresents the specific heat of the ith sandwiched medium; k is a radical ofiRepresents the thermal conductivity of the ith interlayer medium; z represents the coordinate of the heat conduction direction; t represents time; the heating surface boundary conditions were:
Figure BDA0003176936160000022
the boundary conditions of heat conduction between the two layers of media are as follows:
Figure BDA0003176936160000023
Figure BDA0003176936160000024
wherein: ri,i+1Representing the contact thermal resistance between two layers of media; p represents the constant heat flow hfpRepresenting the heat transfer coefficient of the front of the plate; f. ofeRepresents a modulated excitation loading frequency; t isfpRepresents the plate front surface temperature;
lower surface boundary conditions:
Figure BDA0003176936160000031
s22, under the steady state condition, obtaining a temperature distribution expression of each layer of medium;
Ti(Z,t)＝Tdi(Z)+Tai(Z)·exp(j2πfet) (6)
wherein: t isdi(Z) represents the temperature generated by the constant heat flow in the ith layer of medium; t isai(Z)exp(j2πfet) represents the temperature generated by the modulated heat flow in the ith layer medium;
s23, wherein formula (6) is substituted by formulae (1) to (5):
Figure BDA0003176936160000032
-k1ddTZ1＝P2-hfpTfp Z＝0 (8)
Figure BDA0003176936160000033
Figure BDA0003176936160000034
Figure BDA0003176936160000035
Figure BDA0003176936160000036
wherein: a. thei、BiIs a constant, the value of which is determined by the boundary condition; alpha is alphaiRepresents the thermal diffusion coefficient of the i-th layer medium and has the unit of m2/s；
When S24 and Z is 0, the temperature generated by modulating the heat flow on the heating surface is:
Ta1(0)＝A1+B1 (13)
then the general formula (14)
Figure BDA0003176936160000037
Obtaining:
Am＝Abs(Ta1(0))＝Abs(A1+B1) (15)
Figure BDA0003176936160000038
wherein the content of the first and second substances,
Figure BDA0003176936160000039
a phase representing a surface temperature; obtaining the amplitude and the phase of a surface temperature signal of the test piece through the formula (15) and the formula (16), obtaining the difference between a defect position and a non-defect position, and effectively inhibiting noise through amplitude and phase information extraction to obtain defect information;
s3, constructing a finite difference model of the heat conduction process, and deducing the heating surface temperature of the test piece considering the radiation and convection;
s4, establishing a heat and electricity equivalent model of the heat conduction process, and confirming the existence of the defects, wherein the method specifically comprises the following substeps:
s41, establishing a heat conduction heat and electricity equivalent model for phase-locked method heat wave detection;
s42, establishing a heat and electricity equivalent model of the heat conduction process;
when periodic heat flow is transmitted in a material with defects, reflected heat waves are generated on the surface of a test piece due to the defects, and the amplitude and the phase of the reflected heat waves are determined by the following formulas (59) to (60):
Figure BDA0003176936160000041
Figure BDA0003176936160000042
wherein: a. therIs the amplitude of the reflected thermal wave, PhaserIndicating the phase of the reflected thermal wave.
Preferably, step S1 specifically includes the following sub-steps:
s11, adopting an infrared phase-locking thermal imaging detection method, wherein the heat flow of external excitation changes according to a sine rule:
Figure BDA0003176936160000043
wherein: i (t) represents the intensity of external excitation loading heat flow, and the unit is W; p represents the power loaded by external excitation, and the unit is W; f. ofeRepresents the modulation excitation loading frequency in Hz;
s12, when the heat flow is transferred in the flat plate with limited thickness, the transfer process is described by a Fourier one-dimensional heat conduction model:
Figure BDA0003176936160000044
wherein: c represents the specific heat of the test piece material; ρ represents the density of the specimen material; k represents the thermal conductivity of the test piece material;
s13, assuming that the material is isotropic, and considering the heat accumulation caused by the constant heat flow part, the equation (18) is solved analytically to obtain the temperature change along with the time and the thickness under the stable or quasi-stable state:
Figure BDA0003176936160000045
wherein:
Figure BDA0003176936160000046
represents the thermal diffusion length; am represents an amplitude gain factor of the temperature signal;
s14, the temperature is increased instantaneously due to the heat accumulation of the test piece caused by the constant heat flow part, and the temperature change of the whole test piece caused by the constant heat flow satisfies the following differential equation:
Figure BDA0003176936160000047
wherein: rthIndicating the thermal resistance of the test piece material; t isamRepresents the ambient temperature;
when the initial boundary condition is satisfied, i.e. T (0, ∞) ═ T is satisfiedamUnder the conditions, the formula (20) is solved:
T(0,t)＝Tam+ΔT(1-e-t/τ) (21)
wherein: τ denotes a time constant, τ ═ ρ cRth；
Figure BDA0003176936160000057
S15, combining the formula (19) and the formula (21) to obtain the temperature change history and distribution of the test piece under the excitation condition of the heat flow changing in a sine rule:
Figure BDA0003176936160000051
preferably, in step S23, formula (14) results from the following steps:
s231, heating the front surface of the flat plate, wherein convection and radiation heat exchange will occur on the front surface and the rear surface of the flat plate due to the fact that the temperature of the surface of the flat plate is higher than the ambient temperature, and the heat exchange boundary conditions on the surface of the flat plate are as follows:
Figure 1
Figure BDA0003176936160000053
wherein: t isfpRepresents the temperature of the front surface of the plate in units of ℃; h isfpRepresents the heat transfer coefficient of the front surface of the flat plate in units ofkJ/m2·℃； TrpRepresents the temperature of the back surface of the plate in units of ℃; h isrpRepresenting the heat transfer coefficient of the back surface of the flat plate;
s232, when the steady state is reached, the Fourier one-dimensional heat conduction model formula (18) is used for solving
T(Z,t)＝Td(Z)+Ta(Z)exp(j2πfet) (25)
Wherein: t isd(Z) represents the temperature at which the constant heat flow occurs; t isa(Z)exp(j2πfet) represents the temperature at which the modulated heat flow is generated;
s233, assuming that the heat exchange coefficient is a constant value, and the temperature generated by the constant heat flow does not change along with the time, the following results are obtained:
Figure BDA0003176936160000054
the boundary conditions are as follows:
Figure BDA0003176936160000055
Figure BDA0003176936160000056
wherein: t isdfRepresenting the temperature generated by the front surface of the constant heat flow flat plate; t isdrConstant heat flow generates temperature on the back surface of the plate;
s234, substituting the formula (25) and the formula (26) into the formula (18) to obtain:
Figure BDA0003176936160000061
the boundary conditions are as follows:
Figure BDA0003176936160000062
Figure BDA0003176936160000063
wherein: t isafRepresenting the temperature at which the modulated heat flow is generated at the front surface of the plate; t isarRepresenting the temperature at which the modulated heat flow is generated at the back surface of the plate;
s235, obtained by solving the formula (29):
Ta(Z)＝Bexp(-γZ)+Cexp(γZ) (32)
wherein:
Figure BDA0003176936160000064
B. c is a constant, the value of which is determined by the boundary conditions; alpha represents the unit of thermal diffusivity m2/s；
S236 is represented by formula (30) to (32):
Figure BDA0003176936160000065
s237, when Z is 0, the substitution formula (33) gives:
Figure BDA0003176936160000066
so that
Figure BDA0003176936160000067
Wherein:
Figure BDA0003176936160000068
a phase representing a surface temperature;
preferably, the expression of the temperature distribution of each layer of the medium in step S22 is obtained from equation (25).
Preferably, the step S3 specifically includes the following steps:
s31, establishing a finite difference model of the heat conduction process in a polar coordinate system, wherein the temperature change of all nodes follows the Fourier heat conduction and heat exchange law:
Figure BDA0003176936160000069
wherein: delta EIRepresenting input system energy; delta EORepresenting the output system energy; delta EAIndicating that the system is increasing energy; Δ t represents a time increment;
s32, acquiring node energy exchange, and calculating the temperature of a given unit and the unit volume of the given node to obtain the areas of axial heat flow and radial heat flow;
s33, the radial and axial heat flows at the minor element nodes (r, Z) are obtained from the fourier heat conduction model:
Figure BDA0003176936160000071
wherein: k is a radical ofrRepresents the radial thermal conductivity of the material; t isprRepresents the temperature at the node radial direction r at a given time; t isp(r+Δr)Represents the temperature at the node radial direction r + Δ r at a given time;
Figure BDA0003176936160000072
wherein: k is a radical ofzRepresents the axial thermal conductivity of the material; t ispZRepresents the temperature at the node axis Z at a given time; t isp(Z+ΔZ)Represents the temperature at the node axis Z + Δ Z at a given time;
s34, considering the action of the external excitation heat source, when the heat flow is diffused inward along the upper surface of the test piece, the temperature change at the upper surface (Z is 0) of the test piece is:
Figure BDA0003176936160000073
wherein: delta TpRepresenting the surface temperature change of the test piece;
s35, diffusing heat flow inside the test piece under the action of an external excitation heat source, and simultaneously carrying out heat exchange between the surface of the test piece and the outside through radiation and convection so as to obtain the boundary conditions of the heat transfer process of the test piece under the action of the external excitation heat source:
initial conditions:
T(r,Z,0)＝Tam (39)；
heat flow by radiation and convection at the specimen surface (surface Z ═ 0 and surface Z ═ L):
Figure BDA0003176936160000074
Figure BDA0003176936160000075
wherein: Δ q ofradRepresenting radiant heat flow; Δ q ofconRepresenting convective heat flow; hradRepresents the radiant heat transfer coefficient; hconRepresents the convective heat transfer coefficient; t issIndicating the surface temperature of the test piece;
s36, the temperature of the heating surface of the test piece considering the radiation and convection is as follows:
Figure BDA0003176936160000076
wherein: t isfsRepresenting the thermally excited surface temperature of the test piece; t issaThe thermally excited surface temperature of the test piece under adiabatic conditions is shown.
Preferably, the step S32 specifically includes the following steps:
s321, heat transfer of heat flow along radial and axial directions, respectively, so that energy exchange at the node (r, Z) is:
Figure BDA0003176936160000081
wherein: Δ q ofrMeans radial directionHeat flow; Δ q ofzRepresenting axial heat flow (depth direction heat flow); Δ V represents the unit volume;
s322, thereby obtaining the temperature of the given cell:
Figure BDA0003176936160000082
wherein: t isfA temperature representing a given time increment; t ispA temperature representing a current time;
s323, unit volume at a given node (r, Z) is:
ΔV＝ΔZ·ACrossed,z (45)
wherein: a. theCrossed,zRepresents the area of axial heat flow transfer;
s324, the area of the axial heat flow transfer is the area of the heat flow transfer in the micro segment from Z to Z + Δ Z along the axial direction, the area of the radial heat flow is the area of the heat flow transfer in the micro segment from r to r + Δ r along the radial direction, and then the areas of the heat flow transfer in the two directions are:
ACrossed,z＝π(r2-(r-Δr)2) (46)
ACrossed,r＝2πrΔZ (47)
wherein: a. theCrossed,rThe area of radial heat flow transfer is indicated.
Preferably, the step S41 specifically includes the following steps:
s411, the transfer process of the heat flow in the semi-infinite flat plate can be described by adopting a simple one-dimensional heat conduction model, and the heat flow is obtained by a Fourier heat transfer model:
Figure BDA0003176936160000083
wherein: q represents heat flow density (J/m)2s)；
Figure BDA0003176936160000084
Represents a temperature gradient (K/m);
s412, for a given cross-sectional area and thickness of the heat change region, the relationship between the temperature difference and the amount of absorbed or released heat is obtained by equation (48):
Figure BDA0003176936160000085
wherein: q represents the absorption or release of heat; Δ T represents a temperature difference; rtDenotes the thermal resistance, Rt＝Lk·AS；ASRepresents a cross-sectional area; l represents a thickness;
s413, when the system is heated, the internal energy of the system is increased, and then:
Figure BDA0003176936160000086
Ct＝ρ·c·AS·L (51)
wherein: ctRepresents the heat capacity;
s414, obtaining a one-dimensional heat conduction-circuit equivalent model from equations (48) and (51):
Figure BDA0003176936160000091
Ce＝ρ·c·L·AS (53)
wherein: reRepresents an equivalent resistance; ceRepresents an equivalent capacitance;
therefore, the conduction of heat flow (heat wave) in the test piece can be equivalent to an RC low-pass filter circuit, and the transmission process of the heat flow in the test piece is analyzed by using the RC low-pass filter circuit model.
Preferably, the step S42 specifically includes the following steps:
s421, setting the amplitudes of the incident thermal wave and the reflected thermal wave to be A respectivelyiAnd ArThen, the superposed thermal wave amplitude of the two thermal waves on the surface should satisfy:
Figure BDA0003176936160000092
wherein: a. thecRepresenting the superimposed thermal wave amplitude; a. theiRepresenting the amplitude of the incident thermal wave; a. therRepresenting the reflected thermal wave amplitude;
Figure BDA0003176936160000097
representing the phase difference between the incident thermal wave and the reflected thermal wave;
s422, in a cycle, sampling at a phase difference of 90 ° to obtain:
Figure BDA0003176936160000093
Figure BDA0003176936160000094
Figure BDA0003176936160000095
Figure BDA0003176936160000096
and S423, for the defects contained in the material, adopting a thermal and electrical equivalent model for establishing the transmission process of the periodic heat flow in the material, and calculating the amplitude and the phase of the reflected heat wave generated on the surface of the test piece by the periodic heat flow and simulating the reflected heat wave by using the model so as to confirm the existence of the defects.
Compared with the prior art, the invention has the technical effects that:
1. the invention designs an infrared phase-locking thermal imaging defect identification method for a honeycomb sandwich structure, which is different from a conventional infrared phase-locking thermal imaging detection simulation method in that a one-dimensional conduction model is adopted.
2. The invention designs an infrared phase-locking thermal imaging defect identification method for a honeycomb sandwich structure, which is characterized in that a display integration method is adopted to solve a model in a transient process, load loading and signal processing are carried out, the amplitude and the phase of a temperature signal are solved, and the amplitude range and the phase range of a defective part and a non-defective part are determined.
3. The invention designs an infrared phase-locking thermal imaging defect identification method for a honeycomb sandwich structure, which defines that the temperature of a test piece is gradually attenuated along the heat flow transmission direction along with the increase of the transmission depth under the heat flow excitation condition of a sine rule, and has a heat diffusion length, wherein the size of the heat diffusion length is related to the heat conductivity coefficient, specific heat, density and heat flow excitation loading frequency of a material; it is clear that for air defects, reasonable heat flow excitation loading frequency and sampling analysis period number are needed to accurately determine defect characteristics so that the amplitude and phase difference are large.
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 an infrared phase-locked thermal imaging defect identification method for honeycomb sandwich structures of the present invention;
FIG. 2 is a schematic diagram of the transfer process of the modulated sinusoidally varying heat flow of the present invention in a plate;
FIG. 3 is a schematic diagram showing the temperature history of the surface of the test piece and the influence of different time constants on the temperature history;
FIG. 4 is a schematic diagram of the temperature time history and the distribution along the thickness direction of the test piece in a steady state or a quasi-steady state of the invention;
FIG. 5 is a schematic diagram of the temperature history and the distribution along the thickness direction of the test piece under the excitation of heat flow changing in a sine rule;
FIG. 6 is a schematic view of a multilayer structure of a material or component of the present invention;
FIG. 7 is a schematic view of a thermal conduction model in a polar coordinate system according to the present invention;
FIG. 8a is a schematic view of an axial heat flow transfer surface of the present invention;
FIG. 8b is a schematic view of a radial heat flow transfer surface of the present invention;
FIG. 9a is one of the two-dimensional finite difference thermal conductivity computational interfaces of the present invention;
FIG. 9b is a schematic view of one of the two-dimensional finite difference thermal conductivity computational interfaces of the present invention;
FIG. 10 is an equivalent circuit schematic diagram of a one-dimensional heat conduction model of the present invention.
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 an infrared phase-locked thermal imaging defect identification method for honeycomb sandwich structure of the present invention, which comprises the following steps:
s1, constructing an analytic model of temperature change and distribution of the test piece based on Fourier one-dimensional heat conduction model analysis by adopting an infrared phase-locked thermal imaging detection technology;
the main principle of the infrared phase-locking thermal imaging detection technology is that thermal waves are transmitted and reflected inside a test piece under the action of an external excitation source with the intensity changing according to a sine rule, when defects exist inside the test piece, the reflected thermal waves or the penetrated thermal waves can change, and the characteristics of the defects inside the test piece can be determined by measuring the amplitude and the phase of a thermal wave signal. Therefore, the conduction process of the heat flow with regular sinusoidal change in the test piece is deeply researched, and a theoretical basis is laid for the application of the infrared phase-locking method heat wave detection technology.
S11, an infrared phase-locking thermal imaging detection technology is an active infrared thermal wave detection technology, the infrared phase-locking thermal imaging detection technology is adopted, and the heat flow of external excitation changes according to a sine rule:
Figure BDA0003176936160000111
wherein: i (t) represents the intensity of external excitation loading heat flow, and the unit is W; p represents the power loaded by external excitation, and the unit is W; f. ofeRepresents the modulation excitation loading frequency in Hz;
the heat flow with sine regular change is injected into a flat plate with limited thickness, when the area is much larger than the thickness, the transverse diffusion of the heat flow can be ignored, and only the transmission in the thickness direction is considered, so that the problem of one-dimensional heat conduction can be converted, as shown in figure 1.
S12, when the heat flow is transferred in the flat plate with limited thickness, the transfer process is described by a Fourier one-dimensional heat conduction model:
Figure BDA0003176936160000112
wherein: c represents the specific heat of the test piece material; ρ represents the density of the specimen material; k represents the thermal conductivity of the test piece material;
the given heat flow conditions described in equation (2) include two components, one is a constant heat flow component which causes heat to build up in the test piece and increase the temperature; the second is the alternating heat flow portion, which will cause temperature oscillation with a frequency consistent with the heat flow excitation loading frequency.
S13, assuming that the material is isotropic, and considering the heat accumulation caused by the constant heat flow part, the equation (2) is solved analytically to obtain the temperature change along with the time and the thickness under the stable or quasi-stable state:
Figure BDA0003176936160000113
wherein:
Figure BDA0003176936160000114
represents the thermal diffusion length; am represents an amplitude gain factor of the temperature signal;
formula (3) describes the change condition of the test piece under the heat flow loading condition of sine regular change and under the stable or quasi-stable state of the temperature of the test piece, so that the length of heat flow which can be transmitted to the interior of the test piece is related to the thermal characteristics of the material and the heat flow excitation loading frequency, and the frequency of the temperature change of the test piece is consistent with the heat flow excitation modulation frequency in the stable or quasi-stable state; when the thermal characteristics of the test piece material change or defects exist in the test piece material, the amplitude of the test piece material changes due to the surface temperature of the test piece under the condition of a stable or quasi-stable state, phase difference can also be generated, whether defects exist in the test piece material or not can be judged through the information, and defect characteristics can be determined, so that a theoretical basis is laid for nondestructive testing by adopting an infrared phase-locking thermal imaging detection technology.
S14, the temperature is increased instantaneously due to the heat accumulation of the test piece caused by the constant heat flow part, and the temperature change of the whole test piece caused by the constant heat flow satisfies the following differential equation:
Figure BDA0003176936160000121
wherein: rthIndicating the thermal resistance of the test piece material; t isamRepresents the ambient temperature;
when the initial boundary condition is satisfied, i.e. T (0, ∞) ═ T is satisfiedamUnder the condition, the formula (4) is solved:
T(0,t)＝Tam+ΔT(1-e-t/τ) (5)
wherein: τ denotes a time constant, τ ═ ρ cRth；
Figure BDA0003176936160000122
Equation (5) describes the process by which the test piece causes a momentary temperature rise under thermal flow excitation, resulting in: the time for the temperature change of the test piece to reach a stable or quasi-stable state is related to the specific heat, density and thermal resistance of the material, namely the thermal characteristics of the material.
S15, combining the formula (3) and the formula (5) to obtain the temperature change history and distribution of the test piece under the excitation condition of sine-law change heat flow:
Figure BDA0003176936160000123
the formula (6) gives out an analytic model of the temperature change and distribution of the test piece based on Fourier one-dimensional heat conduction model analysis under the excitation of sine regular change heat flow, and the temperature history of the test piece and the temperature distribution condition along the heat flow transmission direction are analyzed through the model.
S2, extracting amplitude and phase information of a steady-state or quasi-steady-state process in the temperature signal by adopting a digital phase locking method, and obtaining defect characteristics by utilizing the influence of defects on the information;
as shown in fig. 2, for a given time constant, the temperature history is changed into two processes, namely a transient history process and a steady state history process, the transient process is mainly determined by the time constant, the smaller the time constant is, the shorter the time for reaching the steady state process is, the faster the speed is, the time constant is determined by the thermal characteristics of the material, the different thermal characteristics of the material have different time constants of heat transfer, and whether defects exist in the test piece or not and the characteristics are determined by analyzing the speed of the signal reaching the steady state process.
As shown in fig. 3, in the steady state or quasi-steady state process, the temperature history oscillates with time according to the sine law, along the heat flow transmission direction, the temperature gradually attenuates with the increase of the transmission depth, that is, the energy is continuously attenuated, if the depth of the defect inside the test piece is deep, if the energy is not transmitted to the depth of the defect, the temperature signal will not contain the information about the influence of the defect on the temperature change, and at this time, the defect detection cannot be performed. As shown in fig. 4, for sinusoidal heat flow excitation, the point temperature history and distribution of the test piece in the heat flow excitation process are very complex, but the temperature signals contain a large amount of information, amplitude and phase information in a steady-state or quasi-steady-state process in the temperature signals can be extracted by using a digital phase-locking method, and the defect characteristics can be accurately obtained by using the influence of defects on the information, so that nondestructive detection is realized.
S21, heating the front surface of the flat plate, wherein the surface temperature of the flat plate is higher than the ambient temperature, convection and radiation heat exchange will occur on the front surface and the rear surface of the flat plate, and the heat exchange boundary conditions on the surface of the flat plate are as follows:
Figure 2
Figure BDA0003176936160000132
wherein: t isfpRepresents the temperature of the front surface of the plate in units of ℃; h isfpRepresents the heat transfer coefficient of the front surface of the flat plate in kJ/m2·℃； TrpRepresents the temperature of the back surface of the plate in units of ℃; h isrpRepresenting the heat transfer coefficient of the back surface of the flat plate;
the heat flow is divided into two parts, one part is constant heat flow P/2, and the other part is modulated heat flow (P/2) exp (j2 pi f)et), the constant heat flow steadily increases the plate surface temperature, while another part will produce a modulated oscillation of the plate surface temperature.
S22, when reaching the steady state, the formula (2) is solved
T(Z,t)＝Td(Z)+Ta(Z)exp(j2πfet) (9)
Wherein: t isd(Z) represents the temperature at which the constant heat flow occurs; t isa(Z)exp(j2πfet) represents the temperature at which the modulated heat flow is generated;
s23, assuming that the heat exchange coefficient is a constant value, the temperature generated by the constant heat flow does not change along with the time, and then the following results are obtained:
Figure BDA0003176936160000133
the boundary conditions are as follows:
Figure BDA0003176936160000134
Figure BDA0003176936160000135
wherein: t isdfRepresenting the temperature generated by the front surface of the constant heat flow flat plate; t isdrConstant heat flow generates temperature on the back surface of the plate;
s24, substituting the formula (9) and the formula (10) into the formula (2) to obtain:
Figure BDA0003176936160000136
the boundary conditions are as follows:
Figure BDA0003176936160000137
Figure BDA0003176936160000138
wherein: t isafRepresenting the temperature at which the modulated heat flow is generated at the front surface of the plate; t isarRepresenting the temperature at which the modulated heat flow is generated at the back surface of the plate;
s25, solved by formula (13):
Ta(Z)＝B exp(-γZ)+C exp(γZ) (16)
wherein:
Figure BDA0003176936160000141
B. c is a constant, the value of which is determined by the boundary conditions; alpha represents the unit of thermal diffusivity m2/s；
S26, represented by formula (14) to (16):
Figure BDA0003176936160000142
s27, when the component or material is nondestructively detected by adopting an infrared phase-locking thermal imaging detection technology, the periodic change rule of the surface temperature of the component or material is mainly analyzed, and when Z is 0, the formula (17) is replaced by the formula (17):
Figure BDA0003176936160000143
so that
Figure BDA0003176936160000144
Wherein:
Figure BDA0003176936160000145
a phase representing a surface temperature;
s28, a defect exists in the material or member, and the material-defect structure or the composite material, etc. may be regarded as a multi-layer structure, as shown in fig. 5. In the multilayer structure, the temperature change of each layer satisfies the formula (2), and then:
Figure BDA0003176936160000146
wherein: t isiIndicating the temperature of the ith layer of medium; rhoiRepresenting the density of the ith layer of media; c. CiRepresents the specific heat of the ith layer of media; k is a radical ofiRepresents the thermal conductivity of the ith layer medium;
the heating surface boundary conditions were:
Figure BDA0003176936160000147
the boundary conditions of heat conduction between the two layers of media are as follows:
Figure BDA0003176936160000148
Figure BDA0003176936160000149
wherein: ri,i+1Representing the contact thermal resistance between two layers of media;
lower surface boundary conditions:
Figure BDA0003176936160000151
s29, obtaining an expression of the temperature distribution of each layer of the medium from the formula (9) under the steady state condition:
Ti(Z,t)＝Tdi(Z)+Tai(Z)·exp(j2πfet) (25)
wherein: t isdi(Z) represents the temperature generated by the constant heat flow in the ith layer of medium; t isai(Z)exp(j2πfet) represents the temperature generated by the modulated heat flow in the ith layer medium;
s210, substituting formula (25) for formulae (20) to (24):
Figure BDA0003176936160000152
Figure BDA0003176936160000153
Figure BDA0003176936160000154
Figure BDA0003176936160000155
Figure BDA0003176936160000158
Tai(Z)＝Aiexp(-γiZ)+Biexp(γiZ)
Figure BDA0003176936160000156
wherein: a. thei、BiIs a constant, the value of which is determined by the boundary condition; alpha is alphaiRepresents the thermal diffusion coefficient of the i-th layer medium and has the unit of m2/s；
When S211 and Z are 0, the temperature generated by modulating the heat flow on the heating surface is:
Ta1(0)＝A1+B1 (32)；
then, as can be seen from equation (19):
Am＝Abs(Ta1(0))＝Abs(A1+B1) (33)
Figure BDA0003176936160000157
the amplitude and the phase of the surface temperature signal of the test piece are calculated through the formula (33) and the formula (34), the difference between the defect position and the non-defect position can be obtained, the noise can be effectively inhibited through the extraction of the amplitude and the phase information, and the defect information is obtained.
S3, constructing a finite difference model of the heat conduction process, and deducing the heating surface temperature of the test piece considering the radiation and convection;
s31, because the theoretical model is complex to solve, the finite difference method can carry out relatively accurate numerical solution on the geometric shapes of different defects. In order to analyze the conduction of the sine-law-change heat flow in a test piece with a relatively complex structure, a finite difference method is adopted to calculate the surface temperature change of the test piece caused by the conduction of the sine-law-change heat flow in the test piece with defects, a finite difference model of a heat conduction process is established under a polar coordinate system, and the temperature change of all nodes follows a second law of thermodynamics (namely an energy conservation law) and a Fourier heat conduction and exchange law:
Figure BDA0003176936160000161
wherein: delta EIRepresenting input system energy; delta EORepresenting the output system energy; delta EAIndicating that the system is increasing energy; Δ t represents a time increment;
s32, acquiring node energy exchange, and calculating the temperature of a given unit and the unit volume of the given node to obtain the areas of axial heat flow and radial heat flow;
s321, as shown in fig. 6, the heat flow is transferred along the radial and axial directions, respectively, so that the energy at the node (r, Z) is exchanged as:
Figure BDA0003176936160000162
wherein: Δ q ofrRepresents radial heat flow; Δ q ofzRepresenting axial heat flow (depth direction heat flow); Δ V represents the unit volume.
S322, thereby obtaining the temperature of the given cell:
Figure BDA0003176936160000163
wherein: t isfA temperature representing a given time increment; t ispIndicating the temperature at the current time.
The axial and radial heat flows are calculated as shown in fig. 8a and 8b for the surfaces where the heat flows are transferred in the axial and radial directions, respectively.
S323, unit volume at a given node (r, Z) is:
ΔV＝ΔZ·ACrossed,z (38)
wherein: a. theCrossed,zThe area of axial heat flow transfer is indicated.
S324, the area of the axial heat flow transfer is the area of the heat flow transfer in the micro segment from Z to Z + Δ Z along the axial direction, the area of the radial heat flow is the area of the heat flow transfer in the micro segment from r to r + Δ r along the radial direction, and then the areas of the heat flow transfer in the two directions are:
ACrossed,z＝π(r2-(r-Δr)2) (39)
ACrossed,r＝2πrΔZ (40)
wherein: a. theCrossed,rThe area of radial heat flow transfer is indicated.
S33, radial and axial heat flows at the minor element nodes (r, Z) are calculated from the fourier heat conduction model:
Figure BDA0003176936160000171
wherein: k is a radical ofrRepresents the radial thermal conductivity of the material; t isprRepresents the temperature at the node radial direction r at a given time; t isp(r+Δr)Represents the temperature at the node radial direction r + Δ r at a given time;
Figure BDA0003176936160000172
wherein: k is a radical ofzRepresents the axial thermal conductivity of the material; t ispZRepresents the temperature at the node axis Z at a given time; t isp(Z+ΔZ)Represents the temperature at the node axis Z + Δ Z at a given time;
s34, considering the action of the external excitation heat source, when the heat flow is diffused inward along the upper surface of the test piece, the temperature change at the upper surface (Z is 0) of the test piece is:
Figure BDA0003176936160000173
wherein: delta TpRepresenting the surface temperature change of the test piece;
s35, diffusing heat flow inside the test piece under the action of an external excitation heat source, and simultaneously carrying out heat exchange between the surface of the test piece and the outside through radiation and convection so as to obtain the boundary conditions of the heat transfer process of the test piece under the action of the external excitation heat source:
initial conditions:
T(r,Z,0)＝Tam (44)；
heat flow by radiation and convection at the specimen surface (surface Z ═ 0 and surface Z ═ L):
Figure BDA0003176936160000174
Figure BDA0003176936160000175
wherein: Δ q ofradRepresenting radiant heat flow; Δ q ofconRepresenting convective heat flow; hradRepresents the radiant heat transfer coefficient; hconRepresents the convective heat transfer coefficient; t issIndicating the surface temperature of the test piece;
s36, the temperature of the heating surface of the test piece considering the radiation and convection is as follows:
Figure BDA0003176936160000176
wherein: t isfsRepresenting the thermally excited surface temperature of the test piece; t issaRepresents the thermally excited surface temperature of the test piece under adiabatic conditions;
the finite difference calculation program of temperature change caused by heat flow conduction in the test piece is compiled by using the formulas (36) to (40) and VC + +, the program is adopted to calculate the temperature distribution and the temperature change course of the test piece by using the pulse heating method and the modulation heating method, and a finite difference calculation interface is shown in FIG. 8.
S4, establishing a heat and electricity equivalent model of the heat conduction process:
in order to further research the influence of the defects in the material or the component on the heat flow in the material or the component in the transfer process, a thermal and electric equivalent model method is adopted to analyze an unstable one-dimensional transient heat transfer model. Matlab \ Simulink is adopted to establish a thermal and electrical equivalent model for modulating heat flow to transfer in a material or a component, and the model can be adopted to calculate the phase of a reflected heat wave of the modulated heat flow at the defect and non-defect positions of a given material and structure.
S41, establishing a heat conduction heat and electricity equivalent model of phase-locked method heat wave detection:
s411, the transfer process of the heat flow in the semi-infinite flat plate can be described by adopting a simple one-dimensional heat conduction model, and the heat flow is obtained by a Fourier heat transfer model:
Figure BDA0003176936160000181
wherein: q represents heat flow density (J/m)2s)；
Figure BDA0003176936160000182
Represents a temperature gradient (K/m);
s412, for a given cross-sectional area and thickness of the heat change region, the relationship between the temperature difference and the amount of absorbed or released heat is obtained by equation (48):
Figure BDA0003176936160000183
wherein: q represents the absorption or release of heat; Δ T represents a temperature difference; rtDenotes the thermal resistance, Rt＝L/k·AS；ASRepresents a cross-sectional area; l represents a thickness;
s413, when the system is heated, the internal energy of the system is increased, and then:
Figure BDA0003176936160000184
Ct＝ρ·c·AS·L (51)
wherein: ctRepresents the heat capacity;
s414, obtaining a one-dimensional heat conduction-circuit equivalent model shown in fig. 9 from equations (48) and (51):
Figure BDA0003176936160000185
Ce＝ρ·c·L·AS (53)
wherein: reRepresents an equivalent resistance; ceRepresents an equivalent capacitance;
therefore, the conduction of heat flow (heat wave) in the test piece can be equivalent to an RC low-pass filter circuit, and the transmission process of the heat flow in the test piece is analyzed by using the RC low-pass filter circuit model.
S42, establishing a heat conduction and electricity equivalent model based on Matlab/Simulink:
the infrared phase-locking thermal imaging detection technology adopts heat flow modulated according to a sine rule to heat the surface of a test piece, the heat flow is transferred to the inside of the test piece to form thermal waves, when the thermal physical characteristics inside the material are changed, namely, defects exist inside the material, the thermal waves are reflected, and the amplitude and the phase of the reflected thermal waves can be extracted by adopting a phase-shifting method.
S421, setting the amplitudes of the incident thermal wave and the reflected thermal wave to be A respectivelyiAnd ArThen, the superposed thermal wave amplitude of the two thermal waves on the surface should satisfy:
Figure BDA0003176936160000191
wherein: a. thecRepresenting the superimposed thermal wave amplitude; a. theiRepresenting the amplitude of the incident thermal wave; a. therRepresenting the reflected thermal wave amplitude;
Figure BDA0003176936160000198
representing the phase difference between the incident thermal wave and the reflected thermal wave;
s422, in a cycle, sampling at a phase difference of 90 ° to obtain:
Figure BDA0003176936160000192
Figure BDA0003176936160000193
Figure BDA0003176936160000194
Figure BDA0003176936160000195
the amplitude and phase of the reflected thermal wave are calculated by equations (55) to (58):
Figure BDA0003176936160000196
Figure BDA0003176936160000197
wherein: phaserRepresenting the phase of the reflected thermal wave;
the periodic heat flow is transmitted in the material with the defects, the surface of the test piece generates reflected heat waves due to the defects, and the amplitude and the phase of the reflected heat waves can be calculated by a one-dimensional heat conduction-circuit equivalent RC low-pass filter circuit and equations (59) to (60).
And S423, establishing a heat and electricity equivalent model of the periodic heat flow in the material containing a type of defect, as shown in FIG. 10. The model is used for calculating the amplitude and the phase of the reflected thermal wave generated on the surface of the test piece by the periodic heat flow and simulating the reflected thermal wave.
The invention fully considers the constant heat flow and the alternating heat flow and the influence of transverse heat diffusion in the honeycomb sandwich structure, and is effective for the detection process range of defects of different types and different depths and the detection of different defects. In the construction process of heat conduction, a finite difference model is utilized to deduce and consider the temperature of the heating surface of the test piece under the action of radiation and convection; establishing a heat conduction heat and electricity equivalent model; and carrying out finite element analysis on the infrared phase-locking thermal imaging detection of the honeycomb sandwich structure, determining whether defect detection can be carried out according to an amplitude diagram and a phase diagram of the infrared phase-locking thermal imaging detection technology, and determining a reasonable detection parameter range.
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 (8)

1. An infrared phase-locking thermal imaging defect identification method for a honeycomb sandwich structure is characterized by comprising the following steps:
s1, constructing an analytic model of temperature change and distribution of the honeycomb sandwich structure defect test piece based on Fourier one-dimensional heat conduction model analysis by adopting an infrared phase-locked thermal imaging detection method;
s2, extracting amplitude and phase information of a steady state or quasi-steady state process in the temperature signal by adopting a digital phase locking method, and obtaining defect characteristics by utilizing the influence of defects on the phase information, wherein the method specifically comprises the following substeps:
s21, when there is a defect in the honeycomb sandwich structure material or the member, the material-defect structure or the composite material is regarded as a multilayer structure in which the temperature change of each layer satisfies:
Figure RE-FDA0003204243140000011
wherein: t isiRepresents the temperature of the ith interlayer medium; rhoiRepresents the density of the ith interlayer medium; c. CiRepresents the specific heat of the ith sandwiched medium; k is a radical ofiRepresents the thermal conductivity of the ith interlayer medium; z represents the coordinate of the heat conduction direction; t represents time;
the heating surface boundary conditions were:
Figure RE-FDA0003204243140000012
the boundary conditions of heat conduction between the two layers of media are as follows:
Figure RE-FDA0003204243140000013
Figure RE-FDA0003204243140000014
wherein: ri,i+1Representing the contact thermal resistance between two layers of media; p represents the constant heat flow hfpRepresenting the heat transfer coefficient of the front of the plate; f. ofeRepresents a modulated excitation loading frequency; t isfpRepresents the plate front surface temperature;
lower surface boundary conditions:
Figure RE-FDA0003204243140000015
s22, under the steady state condition, obtaining a temperature distribution expression of each layer of medium;
Ti(Z,t)＝Tdi(Z)+Tai(Z)·exp(j2πfet) (6)
wherein: t isdi(Z) represents the temperature generated by the constant heat flow in the ith layer of medium; t isai(Z)exp(j2πfet) represents the temperature generated by the modulated heat flow in the ith layer medium;
s23, wherein formula (6) is substituted by formulae (1) to (5):
Figure RE-FDA0003204243140000021
Figure RE-FDA0003204243140000022
Figure RE-FDA0003204243140000023
Figure RE-FDA0003204243140000024
Figure RE-FDA0003204243140000025
Figure RE-FDA0003204243140000026
wherein: a. thei、BiIs a constant, the value of which is determined by the boundary condition; alpha is alphaiRepresents the thermal diffusion coefficient of the i-th layer medium and has the unit of m2/s；
When S24 and Z is 0, the temperature generated by modulating the heat flow on the heating surface is:
Ta1(0)＝A1+B1 (13)
then the general formula (14)
Figure RE-FDA0003204243140000027
Obtaining:
Am＝Abs(Ta1(0))＝Abs(A1+B1) (15)
Figure RE-FDA0003204243140000028
wherein the content of the first and second substances,
Figure RE-FDA0003204243140000029
a phase representing a surface temperature; by the formulae (15) and (16) Obtaining the amplitude and the phase of a surface temperature signal of the test piece, obtaining the difference between a defective part and a non-defective part, and effectively inhibiting noise through amplitude and phase information extraction to obtain defect information;
s3, constructing a finite difference model of the heat conduction process, and deducing the heating surface temperature of the test piece considering the radiation and convection;
s4, establishing a heat and electricity equivalent model of the heat conduction process, and confirming the existence of the defects, wherein the method specifically comprises the following substeps:
s41, establishing a heat conduction heat and electricity equivalent model for phase-locked method heat wave detection;
s42, establishing a heat and electricity equivalent model of the heat conduction process;
when periodic heat flow is transmitted in a material with defects, reflected heat waves are generated on the surface of a test piece due to the defects, and the amplitude and the phase of the reflected heat waves are determined by the following formulas (59) to (60):
Figure RE-FDA00032042431400000210
Figure RE-FDA0003204243140000031
wherein: a. therIs the amplitude of the reflected thermal wave, PhaserIndicating the phase of the reflected thermal wave.
2. The infrared phase-locked thermal imaging defect identification method for the honeycomb sandwich structure as claimed in claim 1, wherein the step S1 specifically comprises the following sub-steps:
s11, adopting an infrared phase-locking thermal imaging detection method, wherein the heat flow of external excitation changes according to a sine rule:
Figure RE-FDA0003204243140000032
wherein: i (t) represents the intensity of external excitation loading heat flow, and the unit is W; p represents the power loaded by external excitation, and the unit is W; f. ofeRepresents the modulation excitation loading frequency in Hz;
s12, when the heat flow is transferred in the flat plate with limited thickness, the transfer process is described by a Fourier one-dimensional heat conduction model:
Figure RE-FDA0003204243140000033
wherein: c represents the specific heat of the test piece material; ρ represents the density of the specimen material; k represents the thermal conductivity of the test piece material;
s13, assuming that the material is isotropic, and considering the heat accumulation caused by the constant heat flow part, the equation (18) is solved analytically to obtain the temperature change along with the time and the thickness under the stable or quasi-stable state:
Figure RE-FDA0003204243140000034
wherein:
Figure RE-FDA0003204243140000035
represents the thermal diffusion length; am represents an amplitude gain factor of the temperature signal;
s14, the temperature is increased instantaneously due to the heat accumulation of the test piece caused by the constant heat flow part, and the temperature change of the whole test piece caused by the constant heat flow satisfies the following differential equation:
Figure RE-FDA0003204243140000036
wherein: rthIndicating the thermal resistance of the test piece material; t isamRepresents the ambient temperature;
when the initial boundary condition is satisfied, i.e. T (0, ∞) ═ T is satisfiedamUnder the conditions, the formula (20) is solved:
T(0,t)＝Tam+ΔT(1-e-t/τ) (21)
wherein: τ denotes a time constant, τ ═ ρ cRth；
Figure RE-FDA0003204243140000037
S15, combining the formula (19) and the formula (21) to obtain the temperature change history and distribution of the test piece under the excitation condition of the heat flow changing in a sine rule:
Figure RE-FDA0003204243140000041
3. the infrared phase-locked thermographic defect identification method for honeycomb sandwich structure of claim 1, wherein formula (14) in step S23 is obtained by the steps of:
s231, heating the front surface of the flat plate, wherein convection and radiation heat exchange will occur on the front surface and the rear surface of the flat plate due to the fact that the temperature of the surface of the flat plate is higher than the ambient temperature, and the heat exchange boundary conditions on the surface of the flat plate are as follows:
Figure RE-FDA0003204243140000042
Figure RE-FDA0003204243140000043
wherein: t isfpRepresents the temperature of the front surface of the plate in units of ℃; h isfpRepresents the heat transfer coefficient of the front surface of the flat plate in kJ/m2·℃；TrpRepresents the temperature of the back surface of the plate in units of ℃; h isrpRepresenting the heat transfer coefficient of the back surface of the flat plate;
s232, when the steady state is reached, the Fourier one-dimensional heat conduction model formula (18) is used for solving
T(Z,t)＝Td(Z)+Ta(Z)exp(j2πfet) (25)
Wherein: t isd(Z) represents the temperature at which the constant heat flow occurs; t isa(Z)exp(j2πfet) represents the temperature at which the modulated heat flow is generated;
s233, assuming that the heat exchange coefficient is a constant value, and the temperature generated by the constant heat flow does not change along with the time, the following results are obtained:
Figure RE-FDA0003204243140000044
the boundary conditions are as follows:
Figure RE-FDA0003204243140000045
Figure RE-FDA0003204243140000046
wherein: t isdfRepresenting the temperature generated by the front surface of the constant heat flow flat plate; t isdrConstant heat flow generates temperature on the back surface of the plate;
s234, substituting the formula (25) and the formula (26) into the formula (18) to obtain:
Figure RE-FDA0003204243140000047
the boundary conditions are as follows:
Figure RE-FDA0003204243140000048
Figure RE-FDA0003204243140000049
wherein: t isafIndicating modulated heat flowThe temperature generated at the front surface of the plate; t isarRepresenting the temperature at which the modulated heat flow is generated at the back surface of the plate;
s235, obtained by solving the formula (29):
Ta(Z)＝Bexp(-γZ)+Cexp(γZ) (32)
wherein:
Figure RE-FDA0003204243140000051
B. c is a constant, the value of which is determined by the boundary conditions; alpha represents the unit of thermal diffusivity m2/s；
S236 is represented by formula (30) to (32):
Figure RE-FDA0003204243140000052
s237, when Z is 0, the substitution formula (33) gives:
Figure RE-FDA0003204243140000053
so that
Figure RE-FDA0003204243140000054
Wherein:
Figure RE-FDA0003204243140000055
indicating the phase of the surface temperature.
4. The infrared phase-locked thermal imaging defect identification method for the honeycomb sandwich structure according to claim 3, wherein the temperature distribution expression of each layer of the medium in the step S22 is obtained from the formula (25).
5. The infrared phase-locked thermal imaging defect identification method for the honeycomb sandwich structure according to claim 1, wherein the step S3 specifically comprises the following steps:
s31, establishing a finite difference model of the heat conduction process in a polar coordinate system, wherein the temperature change of all nodes follows the Fourier heat conduction and heat exchange law:
Figure RE-FDA0003204243140000056
wherein: delta EIRepresenting input system energy; delta EORepresenting the output system energy; delta EAIndicating that the system is increasing energy; Δ t represents a time increment;
s32, acquiring node energy exchange, and calculating the temperature of a given unit and the unit volume of the given node to obtain the areas of axial heat flow and radial heat flow;
s33, the radial and axial heat flows at the minor element nodes (r, Z) are obtained from the fourier heat conduction model:
Figure RE-FDA0003204243140000057
wherein: k is a radical ofrRepresents the radial thermal conductivity of the material; t isprRepresents the temperature at the node radial direction r at a given time; t isp(r+Δr)Represents the temperature at the node radial direction r + Δ r at a given time;
Figure RE-FDA0003204243140000061
wherein: k is a radical ofzRepresents the axial thermal conductivity of the material; t ispZRepresents the temperature at the node axis Z at a given time; t isp(Z+ΔZ)Represents the temperature at the node axis Z + Δ Z at a given time;
s34, considering the action of the external excitation heat source, when the heat flow is diffused inward along the upper surface of the test piece, the temperature change at the upper surface (Z is 0) of the test piece is:
Figure RE-FDA0003204243140000062
wherein: delta TpRepresenting the surface temperature change of the test piece;
s35, diffusing heat flow inside the test piece under the action of an external excitation heat source, and simultaneously carrying out heat exchange between the surface of the test piece and the outside through radiation and convection so as to obtain the boundary conditions of the heat transfer process of the test piece under the action of the external excitation heat source:
initial conditions:
T(r,Z,0)＝Tam (39)
heat flow by radiation and convection at the specimen surface (surface Z ═ 0 and surface Z ═ L):
Figure RE-FDA0003204243140000063
Δqcon＝Hcon(TS-Tam) (41)
wherein: Δ q ofradRepresenting radiant heat flow; Δ q ofconRepresenting convective heat flow; hradRepresents the radiant heat transfer coefficient; hconRepresents the convective heat transfer coefficient; t issIndicating the surface temperature of the test piece;
s36, the temperature of the heating surface of the test piece considering the radiation and convection is as follows:
Figure RE-FDA0003204243140000064
wherein: t isfsRepresenting the thermally excited surface temperature of the test piece; t issaThe thermally excited surface temperature of the test piece under adiabatic conditions is shown.
6. The infrared phase-locked thermal imaging defect identification method for the honeycomb sandwich structure according to claim 1, wherein the step S32 specifically comprises the following steps:
s321, heat transfer of heat flow along radial and axial directions, respectively, so that energy exchange at the node (r, Z) is:
Figure RE-FDA0003204243140000065
wherein: Δ q ofrRepresents radial heat flow; Δ q ofzRepresenting axial heat flow (depth direction heat flow); Δ V represents the unit volume;
s322, thereby obtaining the temperature of the given cell:
Figure RE-FDA0003204243140000071
wherein: t isfA temperature representing a given time increment; t ispA temperature representing a current time;
s323, unit volume at a given node (r, Z) is:
ΔV＝ΔZ·ACrossed,z (45)
wherein: a. theCrossed,zRepresents the area of axial heat flow transfer;
s324, the area of the axial heat flow transfer is the area of the heat flow transfer in the micro segment from Z to Z + Δ Z along the axial direction, the area of the radial heat flow is the area of the heat flow transfer in the micro segment from r to r + Δ r along the radial direction, and then the areas of the heat flow transfer in the two directions are:
ACrossed,z＝π(r2-(r-Δr)2) (46)
ACrossed,r＝2πrΔZ (47)
wherein: a. theCrossed,rThe area of radial heat flow transfer is indicated.
7. The infrared phase-locked thermal imaging defect identification method for the honeycomb sandwich structure according to claim 1, wherein the step S41 specifically comprises the following steps:
s411, the transfer process of the heat flow in the semi-infinite flat plate is described by adopting a one-dimensional heat conduction model, and the heat flow is obtained by a Fourier heat transfer model:
Figure RE-FDA0003204243140000072
wherein: q represents heat flow density (J/m)2s)；
Figure RE-FDA0003204243140000073
Represents a temperature gradient (K/m);
s412, for a given cross-sectional area and thickness of the heat change region, the relationship between the temperature difference and the amount of absorbed or released heat is obtained by equation (48):
Figure RE-FDA0003204243140000074
wherein: q represents the absorption or release of heat; Δ T represents a temperature difference; rtDenotes the thermal resistance, Rt＝L/k·AS；ASRepresents a cross-sectional area; l represents a thickness;
s413, when the system is heated, the internal energy of the system is increased, and then:
Figure RE-FDA0003204243140000075
Ct＝ρ·c·AS·L (51)
wherein: ctRepresents the heat capacity;
s414, obtaining a one-dimensional heat conduction-circuit equivalent model from equations (48) and (51):
Figure RE-FDA0003204243140000081
Ce＝ρ·c·L·AS (53)
wherein: reRepresents an equivalent resistance; ceRepresents an equivalent capacitance;
the conduction energy of the heat flow in the test piece is equivalent to an RC low-pass filter circuit, and the transfer process of the heat flow in the test piece is analyzed by utilizing the RC low-pass filter circuit model.
8. The infrared phase-locked thermal imaging defect identification method for the honeycomb sandwich structure according to claim 1, wherein the step S42 specifically comprises the following steps:
s421, setting the amplitudes of the incident thermal wave and the reflected thermal wave to be A respectivelyiAnd ArThen, the superposed thermal wave amplitude of the two thermal waves on the surface should satisfy:
Figure RE-FDA0003204243140000082
wherein: a. thecRepresenting the superimposed thermal wave amplitude; a. theiRepresenting the amplitude of the incident thermal wave; a. therRepresenting the reflected thermal wave amplitude;
Figure RE-FDA0003204243140000083
representing the phase difference between the incident thermal wave and the reflected thermal wave;
s422, in a cycle, sampling at a phase difference of 90 ° to obtain:
Figure RE-FDA0003204243140000084
Figure RE-FDA0003204243140000085
Figure RE-FDA0003204243140000086
Figure RE-FDA0003204243140000087
and S423, for the defects contained in the material, adopting a thermal and electrical equivalent model for establishing the transmission process of the periodic heat flow in the material, and calculating the amplitude and the phase of the reflected heat wave generated on the surface of the test piece by the periodic heat flow and simulating the reflected heat wave by using the model so as to confirm the existence of the defects.
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