阅读说明：本技术 一种基于超声背反射的横观各向同性材料损伤评价方法 (Transverse isotropic material damage evaluation method based on ultrasonic back reflection ) 是由 罗忠兵 林莉 钱恒奎 金士杰 于 2020-11-25 设计创作，主要内容包括：一种基于超声背反射的横观各向同性材料损伤评价方法,属于高端装备制造领域。利用超声背反射法采集横观各向同性材料等厚板状试样在不同损伤阶段的背反射信号；通过互相关处理计算试样不同方向上的超声波延时及速度,利用模拟退火优化算法反演得到垂直板面方向弹性刚度矩阵,并对其进行Bond变换得到弹性各向同性对称轴方向弹性刚度矩阵；计算弹性模量及各向异性因子,并建立其与试样损伤参数之间的关系。该方法可得到横观各向同性材料不同损伤状态下弹性特征并进行损伤评价,与传统方法相比具有测试精度高、无损、成本低等优势,对力、热、湿、辐照等多种因素导致的损伤都具有良好的应用前景。(A transverse isotropic material damage evaluation method based on ultrasonic back reflection belongs to the field of high-end equipment manufacturing. Collecting back reflection signals of a transverse isotropic material equal-thickness plate-shaped sample at different damage stages by using an ultrasonic back reflection method; ultrasonic time delay and speed of the sample in different directions are calculated through cross-correlation processing, a simulated annealing optimization algorithm is used for inversion to obtain an elastic stiffness matrix in the direction perpendicular to the plate surface, and Bond transformation is carried out on the elastic stiffness matrix to obtain an elastic isotropic symmetry axis direction elastic stiffness matrix; and calculating the elastic modulus and the anisotropy factor, and establishing a relation between the elastic modulus and the anisotropy factor and the damage parameter of the sample. The method can obtain the elastic characteristics of the transverse isotropic material in different damage states and perform damage evaluation, has the advantages of high test precision, no damage, low cost and the like compared with the traditional method, and has good application prospect on damage caused by various factors such as force, heat, humidity, irradiation and the like.)

1. A transverse isotropic material damage evaluation method based on ultrasonic back reflection is characterized by comprising the following specific calculation steps:

(1) acquisition of ultrasonic back-reflected signals

Processing a transverse isotropic material into an equal-thickness plate-shaped sample along a direction parallel to an elastic isotropic symmetry axis; respectively collecting back reflection signals of the elastic isotropic surface and the elastic anisotropic surface of the sample at different damage stages by using an ultrasonic back reflection method, wherein the back reflection signals in the direction perpendicular to the plate surface are used as reference signals, and the rest are used as working signals;

(2) ultrasonic time delay measurement and ultrasonic velocity calculation

Calculating the time delay between the working signal and the reference signal by cross-correlation processingFurther calculating the ultrasonic velocity v (theta) in the plate-shaped sample under different incidence angles_r) The calculation method is shown as formula (1);

wherein, theta_iIs the ultrasonic incident angle, θ_rIs the angle of refraction, v, of the ultrasonic waves into the sample_wIs the ultrasonic velocity, v, in water_nIs the ultrasonic velocity, Δ t, in the sample measured from the reference signal₀The ultrasonic wave delay is realized when the sample is vertically incident or when the sample is not present,is the time delay between the working signal and the reference signal, and h is the thickness of the plate-shaped sample;

(3) elastic constant calculation

C₁₁Is the elastic constant, C, associated with the longitudinal wave velocity of the ultrasonic wave in the isotropic plane₆₆Is the elastic constant related to the ultrasonic transverse wave velocity in the isotropic plane; c₁₁And C₆₆Calculating by ultrasonic velocity in the elastic isotropic surface, wherein the calculation formula is shown as a formula (2) and a formula (3);

where ρ is the sample density and v is_LThe ultrasonic longitudinal wave velocity in the elastic isotropic plane;

wherein v is_TThe ultrasonic transverse wave speed in the elastic isotropic plane;

solving a global optimal solution of the complex nonlinear problem by using a simulated annealing optimization algorithm, and inverting an elastic constant; defining an objective function F as the square of the difference between the theoretically calculated ultrasonic velocity and the experimentally measured ultrasonic velocity, as shown in formula (4);

in the formula, N is the number of measured sound velocity data points,the ultrasonic velocity V is obtained by trying to solve an elastic constant and substituting the elastic constant into a Christoffel equation_i ^expMeasuring ultrasonic velocity for the experiment; theta_iIs the ultrasonic incident angle; taking the annealing temperature difference as 10^-5DEG C, and the function tolerance error is 10^-9(m/s)⁴(ii) a By calculated C₁₁And C₆₆Iterative inversion calculation with C₁₁、C₆₆、C₁₃、C₃₃And C₄₄The nonsingular solution of the Christoffel equation of (A) to obtain the elastic constant C₁₃、C₃₃And C₄₄Obtaining a vertical plate surface direction elastic rigidity matrix C_ij(90 degree), as shown in formula (5), C₁₁、C₆₆、C₁₃、C₃₃And C₄₄Is its 5 independent elastic constants;

wherein the elastic constant C₁₂＝C₁₁-2C₆₆；

(4) Elastic stiffness matrix transformation

Bond transformation is carried out on the formula (5), and an elastic stiffness matrix C in the elastic isotropic symmetry axis direction is obtained by changing the rotation angle alpha in the vertical plate surface direction to 90 DEG_ij(0°)，M₁(. alpha.) is the Bond transformation matrix, C_ij(90 °) is the elastic stiffness matrix in the vertical plate direction, and α is the rotation angle in the vertical plate direction; the calculation method is shown as formula (6), wherein the elastic constant C₂₃＝C₂₂-2C₄₄，C₁₁、C₁₂、C₂₂、C₄₄And C₅₅Is C_ij(0 °) of 5 independent elastic constants;

where alpha is 90 deg. the angle of rotation,

(5) calculation of modulus of elasticity

Inverting the formula (6) to obtain an elastic isotropic symmetry axis direction flexibility matrix S shown as a formula (7);

elastic modulus E in the direction of the elastic isotropic symmetry axis₁And modulus of elasticity E in the direction perpendicular to the plane of the plate₂Through the coefficient of compliance S₁₁、S₂₂Calculating the calculation method shown in the formula (8) and the formula (9);

(6) anisotropy factor calculation

According to C in (6)_ijElastic constant C of (0 DEG)₁₁、C₁₂、C₄₄Calculating the anisotropy factor A_rThe calculation method is shown as formula (10);

(7) damage correlation establishment

Repeating the steps (1) to (6) to obtain the C of the transverse isotropic material under different sample damage parameters_ij(0 °) elastic constant, elastic modulus and anisotropy factor; in the vertical type (6) C_ijElastic constant C of (0 DEG)₁₁、C₁₂、C₂₂、C₄₄And C₅₅Correlation with sample damage parameters; elastic modulus E in the vertical type (8), (9)₁、E₂Correlation with sample damage parameters; anisotropy factor A in the vertical form (10)_rAnd the correlation between the parameters of the sample damage.

2. The transverse isotropic material damage evaluation method based on ultrasonic back reflection as claimed in claim 1, wherein: the sample damage comprises damp heat, thermal oxygen, irradiation and mechanical damage.

Technical Field

The invention relates to a transverse isotropic material damage evaluation method based on ultrasonic back reflection, and belongs to the field of high-end equipment manufacturing.

Background

Transverse isotropic materials are equipped with important applications at many high ends. For example, directionally solidified nickel-based superalloys are widely used in aircraft engines, and Carbon Fiber Reinforced resin-based Composites (CFRP) are widely used in key components in the fields of aviation, aerospace, automobiles, and the like. In the service process of the corresponding component, the corresponding component is inevitably influenced by factors such as temperature, humidity, ultraviolet radiation, external force and the like, and the material is damaged in different forms such as aging, fatigue and the like, so that the performance is reduced, and therefore, the evaluation of the damage of the transverse isotropic material which is in service for a long time in a severe environment is particularly important.

The traditional mechanical testing methods such as stretching or bending are simple in principle, and the experimental testing device is mature, but the method is destructive to materials, high in testing cost, difficult to measure partial parameters (such as non-axial elastic modulus), and large in data fluctuation, so that a nondestructive and accurate testing method must be developed. The nondestructive testing evaluation technology can avoid damaging the component body, can also find hidden defects under the condition of keeping the performance characteristics of the component, wherein ultrasonic testing is widely applied to defect testing and performance evaluation of materials by virtue of the characteristics of high testing sensitivity, accurate positioning and the like of the ultrasonic testing, and the elastic constant can be calculated based on sound velocities of media in different directions by utilizing the ultrasonic technology, so that the evaluation of the elastic performance is realized, the cost is low, the sample is not damaged, and the general attention of researchers is paid.

Disclosure of Invention

The invention aims to provide a transverse isotropic material damage evaluation method based on ultrasonic back reflection, which establishes a correlation between an elastic constant, an elastic modulus and an anisotropy factor and transverse isotropic material damage parameters by measuring and calculating an elastic stiffness matrix of the transverse isotropic material in different damage states. Compared with the traditional evaluation method, the method has the advantages of improving the test precision, achieving the purposes of nondestructive and low-cost test, and having good application to various damage forms of metal and nonmetal materials, such as damp heat, thermal oxidation, irradiation, mechanics and the like.

The technical scheme adopted by the invention is as follows: a transverse isotropic material damage evaluation method based on ultrasonic back reflection is characterized in that a transverse isotropic material is processed into an equal-thickness plate-shaped sample along a direction parallel to an elastic isotropic symmetry axis, and back reflection signals of the sample at different damage stages are respectively collected by an ultrasonic back reflection method; calculating ultrasonic time delays of the sample in different directions through cross-correlation processing, and calculating ultrasonic speed; then, inverting through a simulated annealing optimization algorithm to obtain elastic stiffness matrixes in the vertical plate surface direction in different damage states, and performing Bond transformation on the elastic stiffness matrixes to obtain elastic stiffness matrixes in the elastic isotropic symmetry axis direction; and respectively calculating the elastic modulus in the direction vertical to the plate surface, the elastic modulus in the direction of the elastic isotropic symmetry axis and the anisotropy factor, and establishing a relation between the elastic modulus in the direction vertical to the plate surface, the elastic modulus in the direction of the elastic isotropic symmetry axis and the anisotropy factor and the damage parameter of the sample. The specific calculation steps are as follows:

(1) acquisition of ultrasonic back-reflected signals

Processing a transverse isotropic material into an equal-thickness plate-shaped sample along a direction parallel to an elastic isotropic symmetry axis; respectively collecting back reflection signals of the elastic isotropic surface and the elastic anisotropic surface of the sample at different damage stages by using an ultrasonic back reflection method, wherein the back reflection signals in the direction perpendicular to the plate surface are used as reference signals, and the rest are used as working signals;

(2) ultrasonic time delay measurement and ultrasonic velocity calculation

Calculating the time delay between the working signal and the reference signal by cross-correlation processingFurther calculating the ultrasonic velocity v (theta) in the plate-shaped sample under different incidence angles_r) The calculation method is shown as formula (1);

wherein, theta_iIs the ultrasonic incident angle, θ_rIs the angle of refraction, v, of the ultrasonic waves into the sample_wIs the ultrasonic velocity, v, in water_nIs the ultrasonic velocity, Δ t, in the sample measured from the reference signal₀The ultrasonic wave delay is realized when the sample is vertically incident or when the sample is not present,is the time delay between the working signal and the reference signal, and h is the plate specimen thickness.

(3) Elastic constant calculation

C₁₁Is the elastic constant, C, associated with the longitudinal wave velocity of the ultrasonic wave in the isotropic plane₆₆Is the elastic constant related to the ultrasonic transverse wave velocity in the isotropic plane; c₁₁And C₆₆Calculating by ultrasonic velocity in the elastic isotropic surface, wherein the calculation formula is shown as a formula (2) and a formula (3);

where ρ is the sample density and v is_LThe ultrasonic longitudinal wave velocity in the elastic isotropic plane;

wherein v is_TThe ultrasonic transverse wave speed in the elastic isotropic plane;

solving a global optimal solution of the complex nonlinear problem by using a simulated annealing optimization algorithm, and inverting an elastic constant; defining an objective function F as the square of the difference between the theoretically calculated ultrasonic velocity and the experimentally measured ultrasonic velocity, as shown in formula (4);

wherein N is the number of measured sound velocity data points，The ultrasonic velocity is obtained by trying to solve an elastic constant and substituting the elastic constant into a Christoffel equation,measuring ultrasonic velocity for the experiment; theta_iIs the ultrasonic incident angle; taking the annealing temperature difference as 10^-5DEG C, and the function tolerance error is 10^-9(m/s)⁴By calculated C₁₁And C₆₆Iterative inversion calculation with C₁₁、C₆₆、C₁₃、C₃₃And C₄₄The nonsingular solution of the Christoffel equation of (A) to obtain the elastic constant C₁₃、C₃₃And C₄₄Obtaining a vertical plate surface direction elastic rigidity matrix C_ij(90 degree), as shown in formula (5), C₁₁、C₆₆、C₁₃、C₃₃And C₄₄Is its 5 independent elastic constants;

wherein the elastic constant C₁₂＝C₁₁-2C₆₆；

(4) Elastic stiffness matrix transformation

Bond transformation is carried out on the formula (5), and an elastic stiffness matrix C in the elastic isotropic symmetry axis direction is obtained by changing the rotation angle alpha in the vertical plate surface direction to 90 DEG_ij(0°)，M₁(. alpha.) is the Bond transformation matrix, C_ij(90 °) is the elastic stiffness matrix in the vertical plate direction, and α is the rotation angle in the vertical plate direction; the calculation method is shown as formula (6), wherein the elastic constant C₂₃＝C₂₂-2C₄₄，C₁₁、C₁₂、C₂₂、C₄₄And C₅₅Is its 5 independent elastic constants.

Where alpha is 90 deg. the angle of rotation,

(5) calculation of modulus of elasticity

Inverting the formula (6) to obtain an elastic isotropic symmetry axis direction flexibility matrix S shown as a formula (7);

elastic modulus E in the direction of the elastic isotropic symmetry axis₁And modulus of elasticity E in the direction perpendicular to the plane of the plate₂Through the coefficient of compliance S₁₁、S₂₂Calculating the calculation method shown in the formula (8) and the formula (9);

(6) anisotropy factor calculation

According to C in (6)_ijElastic constant C of (0 DEG)₁₁、C₁₂、C₄₄Calculating the anisotropy factor A_rThe calculation method is shown as formula (10);

(7) damage correlation establishment

Repeating the steps (1) to (6) to obtain the C of the transverse isotropic material under different sample damage parameters_ij(0 °) elastic constant, elastic modulus and anisotropy factor; in the vertical type (6) C_ijElastic constant C of (0 DEG)₁₁、C₁₂、C₂₂、C₄₄、C₅₅Correlation with sample damage parameters; elastic modulus E in the vertical type (8), (9)₁、E₂Correlation with sample damage parameters; anisotropy factor A in the vertical form (10)_rAnd the correlation between the parameters of the sample damage.

The invention has the beneficial effects that: through the ultrasonic back reflection-based damage evaluation method for the transverse isotropic material, elastic stiffness matrixes of the transverse isotropic material in different damage states can be obtained, and the correlation among elastic constants, elastic moduli and anisotropic factors and damage parameters of the transverse isotropic material is established. Compared with the traditional damage evaluation method, the method has the advantages of high test precision, no damage, low cost and the like, is wide in application range, and has good application prospects in various damage evaluations of metal and nonmetal materials, such as damp heat, thermal oxidation, irradiation, mechanics and the like.

Drawings

Fig. 1 is a schematic diagram of an ultrasound back reflection signal acquisition system.

In fig. 2, (a) is a time domain waveform of a truncated CFRP unidirectional board 0 ° reference signal and a 0.9 ° working signal, and (b) is a correlation coefficient curve of signal cross-correlation processing.

In fig. 3, (a) is a sound velocity change diagram of the elastic isotropic surface of the CFRP unidirectional plate under different thermo-oxidative aging times and different incidence angles, and (b) is a sound velocity change diagram of the elastic anisotropic surface.

FIG. 4 is a graph of the change of elastic constant of CFRP unidirectional plates under different thermo-oxidative aging time.

FIG. 5 shows the elastic modulus E of the CFRP unidirectional sheet in the direction of the elastic isotropic symmetry axis under different thermal-oxidative aging times₁And modulus of elasticity E in the direction perpendicular to the plane of the plate₂And (5) a variation graph.

FIG. 6 is a graph of anisotropy factor changes for CFRP unidirectional sheets at different thermo-oxidative aging times.

Detailed Description

The schematic diagram of the ultrasonic back reflection signal acquisition system adopted by the invention is shown in figure 1. The used transverse isotropic material sample is a T300/AG-80 CFRP (carbon fiber reinforced plastics) unidirectional board, and the prepreg is prepared by autoclave molding, wherein the fiber direction of the prepreg is the elastic isotropic symmetry axis direction, the rotation angle change range of the sample is 0-45 degrees, and the angle stepping is 0.05 degrees; the mixture is aged by thermal oxidation at 150 ℃ for 0 day, 1 day, 2 days, 3 days and 15 days respectively. The specific calculation steps are as follows:

(1) acquisition of ultrasonic back-reflected signals

By means of an ultrasonic C scanning system, an angle rotation testing device and an oscilloscope, reference signals and working signals corresponding to 0-day aging of a T300/AG-80 CFRP unidirectional plate sample are collected, and a comparison between the reference signals at 0 degree and the working signals at 0.9 degree is shown in fig. 2 (a).

(2) Ultrasonic time delay measurement and ultrasonic velocity calculation

As shown in fig. 2(b), the 0 ° reference signal and the 0.9 ° working signal are processed by a cross-correlation processing technique, and the time τ corresponding to the maximum position of the correlation coefficient is-0.4 ns, which is the delay between the two signals. Ultrasonic velocity v (theta) at different incident angles of elastic isotropic surface and elastic anisotropic surface aged for 0 day and 3 days_r) The calculation results are shown in fig. 3(a) and (b), respectively.

(3) Elastic constant calculation

Elastic constant calculation and inversion are carried out according to the ultrasonic velocity of the elastic isotropic surface and the elastic anisotropic surface to obtain an elastic stiffness matrix C of the CFRP unidirectional plate in the direction vertical to the plate surface and with different thermal oxidation aging time_ij(90 °), for example, after aging for 0 day, ρ 1590.54kg/m³、v_L＝3035.15m/s、v_TCalculation yields C-1492.10 m/s₁₁＝14.65GPa、C₆₆＝3.54GPa，C₁₃、C₃₃And C₄₄The matrix C of the elastic rigidity along the direction of the vertical plate surface can be obtained by inversion of a simulated annealing optimization algorithm_ij(90°)。

(4) Elastic stiffness matrix transformation

Elastic rigidity matrix C for vertical plate surface direction_ij(90 °) Bond transformation was performed, and a fiber direction elastic stiffness matrix C was obtained by rotating the perpendicular plane direction by an angle α of 90 °_ij(0°)。

(5) Calculation of modulus of elasticity

Elastic rigidity matrix C to fiber direction_ijInverting the (0 degree) to obtain a fiber direction flexibility matrix S; coefficient of compliance S₁₁、S₂₂Calculating to obtain the fiber direction elastic modulus E of the CFRP unidirectional plate under different thermal oxidation aging times₁And modulus of elasticity E in the direction perpendicular to the plane of the plate₂。

(6) Anisotropy factor calculation

Elastic stiffness matrix C according to fiber direction_ijElastic constant C in (0 DEG)₁₁、C₁₂、C₄₄The anisotropy factor is calculated.

(7) Aging correlation establishment

Repeating the steps (1) to (6) to obtain the samples of the T300/AG-80 CFRP unidirectional board aged for different times C_ij(0 °) elastic constant, elastic modulus, and anisotropy factor. Different thermal oxidation ages with CFRP one-way plate are establishedThe correlation between the formation times is shown in fig. 4, 5, and 6, respectively.

As can be seen from FIG. 4, the fiber direction-dependent elastic constant C₁₁Other elastic constants do not change significantly as the aging time increases, first decreases, then increases, and then decreases. The reasons are that the volatilization of low molecular weight substances at the early stage of aging causes more pores to be generated inside the CFRP, namely, damage is generated, sound transmission is hindered, and the elastic constant is reduced; the increase in aging over time is due to the post-cure action of the resin and the enhancement of physical aging; in the later stage of aging, the number of cracks on the carbon fiber/resin interface is increased due to the weakening of post-curing action, and the elastic constant is reduced under the comprehensive action. E in FIG. 5₁The tendency of change is in accordance with the fibre-direction-dependent elastic constant, E₂Remains substantially unchanged, indicating that the damage caused by thermo-oxidative aging is mainly reflected in the fiber direction, i.e., E₁Is more sensitive to thermal-oxidative aging damage. Anisotropy factor A in FIG. 6_rThe trend of the change is consistent with the fiber direction-dependent elastic constant for the same reason as E in FIG. 5₁And (4) changing. Based on the parameters, multi-parameter representation of the thermal oxidation aging of the T300/AG-80 CFRP unidirectional board sample is realized.