CN104090033A - Establishment method of simulation model for FDTD ultrasonic testing of coarse-grained materials based on EBSD spectrum - Google Patents

Abstract

A coarse grain material FDTD ultrasonic detection simulation model establishment method based on an EBSD map belongs to the technical field of ultrasonic nondestructive detection. The method comprises the following steps: directly obtaining a crystal orientation map of a coarse crystal material by using an EBSD (electron back scattering) technology, selecting a threshold angle to define crystal grains in the map according to an actual crystal grain structure in a macroscopic metallograph, filling the crystal grains with colors corresponding to main orientations, and obtaining an image consisting of square pixel points through gray processing. Euler angle of crystal grain orientation corresponding to gray valueΦ、Showing the elastic anisotropic stiffness matrix used to quantitatively calculate the grains. Compared with the former model, the model has the advantages of accurate description of the crystal grain structure and the crystal grain orientation, high operation efficiency and the like, and is used for solving the problems of defect quantification, positioning and qualification in ultrasonic detection of coarse-grained materialsThe problem provides the basis of the model. The invention can also be expanded to the establishment of ultrasonic simulation models of austenitic welding seams, dual-phase titanium alloys and other elastic anisotropic polycrystalline materials, and has good popularization and application prospects.

Description

Establishment method of simulation model for FDTD ultrasonic testing of coarse-grained materials based on EBSD spectrum

technical field

The invention relates to a method for establishing an FDTD ultrasonic detection simulation model of a coarse-grained material based on an EBSD spectrum, in particular to the technical field of ultrasonic nondestructive testing.

Background technique

Coarse-grained materials such as austenitic stainless steel are widely used in nuclear power and chemical industries, and their safety has attracted much attention. Due to the complex coarse grain structure and grain orientation, this kind of material has strong elastic anisotropy, which leads to serious beam deflection, structural noise, signal distortion and other phenomena in the process of ultrasonic nondestructive testing, making it difficult to accurately locate defects , quantitative and qualitative.

In order to solve the above problems, researchers in this field try to establish corresponding ultrasonic testing simulation models, and describe the interaction between ultrasonic waves and elastic anisotropic structures by means of simulation. The early model was developed on the basis of the weld simulation model. The modeling idea was mainly to divide the model into multiple anisotropic units with reference to the macroscopic metallographic photos of the material. At the same time, according to the growth characteristics of columnar grains and combined with material science knowledge, the crystal orientation of the unit is artificially set. Since this semi-empirical method does not provide accurate measurements of the orientation and distribution of the grains, the ultrasonic calculations of the model differ greatly from the experimental results. Although XRD (X-Ray Diffraction, X-ray diffraction) was introduced later to measure the local crystal orientation of the material, and the orientation setting of the model was corrected to a certain extent, the distribution characteristics of the grain orientation could not be accurately measured, making the model development has been constrained.

In 2009, the French Atomic Energy Commission developed a simulation model based on the Thiessen polygonal graphics method in CIVA commercial software. The model uses the convex closed area surrounded by Thiessen polygons as the simulated grain, and assumes that the grain is an elastic isotropic medium. Although this model can describe the grain structure more accurately, the method of equivalent elastic anisotropy by setting the sound velocity fluctuation between elastic isotropic grains through a random function does not consider the change characteristics of sound velocity with the direction of ultrasonic propagation , leading to a large discrepancy between the calculated results of the model and the experimental results.

In recent years, electron backscattered diffraction (EBSD) has been accepted by more and more material research scholars at home and abroad. This technique can not only characterize the grain morphology of materials but also quantitatively describe the grain orientation of materials, which is considered as the combination of SEM and XRD. In 2009, researchers at the University of Birmingham used EBSD technology to scan the cross-section of an austenitic weld and obtain a crystal orientation map. Referring to the map features, a model consisting of 157 elastic anisotropic elements was drawn using the CAD function in CIVA software. Finally, according to the crystal orientation of the element, the corresponding stiffness matrix is assigned to complete the establishment of the model. Compared with previous models, this model obtained from experimental data can describe the grain structure and grain orientation more accurately.

However, since the number of elastic anisotropic units affects the calculation efficiency of the model, in order to shorten the calculation time, the model has to be simplified by reducing the number of units. Even so, for a model with 157 units, it still takes nearly 100 Hour. In addition, this simplification has less influence on the calculation results for the coarse orientation ordered columnar crystals. Different from welds, coarse-grained materials not only contain columnar grains with ordered orientation, but also equiaxed grains with random orientation, and the grain size is relatively small. If the above simplified method is adopted, the grain structure and orientation will be seriously distorted, which will affect the calculation accuracy of the model. Therefore, the process of dividing the elastic anisotropic units of coarse-grained materials requires restoring the grain structure as much as possible to ensure the calculation accuracy. At the same time, it is necessary to adopt corresponding methods to improve the computational efficiency of this high-precision model.

Contents of the invention

The purpose of the present invention is to provide a method for establishing a simulation model of FDTD ultrasonic detection of coarse-grained materials based on EBSD spectrum. Compared with previous models, this model should have the advantages of accurate description of grain structure and grain orientation, and higher efficiency of model calculation. It can also simulate the structural noise in ultrasonic testing of coarse-grained materials, which is helpful for in-depth understanding of the interaction between ultrasonic waves and anisotropic grains, and provides a model basis for solving the quantitative, localization, and qualitative problems of defects in coarse-grained materials. At the same time, the invention can also be extended to the establishment of ultrasonic simulation models of other elastic anisotropic polycrystalline materials such as austenitic weld seams and duplex titanium alloys, and has good promotion and application prospects.

The technical solution adopted in the present invention is: a method for establishing a simulation model for FDTD ultrasonic detection of coarse-grained materials based on EBSD atlas, comprising the following steps:

(1) According to the national standard "GB/T19501-2004 General Principles of Electron Backscatter Diffraction Analysis Method", the samples were pretreated by cutting, grinding, mechanical polishing, and stress-relieving electrolytic polishing. Select 40μm scan step to perform EBSD analysis on the sample to be tested;

(2) Use the EBSD device to scan the entire cross-section of the sample, each time about 6mm ² , and then splicing the obtained small-area maps in order, and finally obtain a complete crystal orientation map composed of multiple maps;

(3) According to the grain structure of the actual material, use the channel5 analysis software to adjust the threshold angle in the crystal orientation map, determine the grain outline of the model, and use it as the elastic anisotropy unit of the model;

(4) Use channel5 analysis software to count the color scale value with the largest number of pixels in each unit, and then unify the colors of all pixels in the grain into this color scale value, and record the corresponding Euler value of this color scale value horn;

(5) Export the EBSD spectrum as a picture in JPG format, then open it in Photoshop software, convert it into a grayscale image, set the color scale value of the grain to the corresponding grayscale value, export and save the grayscale in PCX picture format picture;

(6) Using the Euler angle corresponding to the grain Φ, Obtain the direction cosine matrix R representing the crystal orientation,

The rotation matrix R _D is derived from the 9 array elements R ₁₁ to R ₃₃ in R,

${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>\left(\begin{array}{cccccc}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& \mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}& \mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}\\ {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 32</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}& \mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}& \mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}\\ {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 32</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}& \mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 32</span>}}& \mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}& \mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 32</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}\\ {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}\\ {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 32</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 32</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}\\ {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 32</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 32</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}& {\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}\end{array}\right)<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Use _RD to rotate the constitutive stiffness matrix C to obtain the elastic stiffness matrix C' under the grain orientation,

${\mathrm{<span\; class="notranslate">\; C</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}\mathrm{<span\; class="notranslate">\; C</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Among them, C is a 6×6 matrix consisting of 3 independent elastic constants,

$\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; =</span>\left(\begin{array}{cccccc}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 44</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 44</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; 0</span>}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 44</span>}}\end{array}\right)<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

(7) Input the model into the FDTD ultrasonic numerical simulation program, set the lower boundary of the model as a solid-vacuum interface, and set the other three boundaries as infinite boundaries, choose Gaussian pulse fitting waveform as the sound source, and place it in different positions of the model, Numerical calculations are carried out, and finally the simulation results are compared with the experimental results.

The effects and benefits of the present invention are: the FDTD ultrasonic detection simulation model constructed using EBSD experimental data solves the problem that the previous model is difficult to accurately describe the grain structure and elastic anisotropy, and also improves the calculation efficiency problem, and can calculate the same The actual detection of similar ultrasonic time-domain waveforms is helpful for in-depth understanding of the propagation characteristics of ultrasonic waves in coarse-grained materials, and provides a reliable model basis for quantitative, localization, and qualitative analysis of defects.

Description of drawings

Figure 1 is the EBSD crystal orientation map of Z3CN20-09M axial-radial section.

Figure 2 shows the influence of different threshold angles on the grain profile (a) 0 degrees, (b) 5 degrees, (c) 10 degrees, (d) 15 degrees, (e) 20 degrees, (f) 30 degrees.

Figure 3 is a macroscopic metallographic photo of Z3CN20-09M.

Figure 4 is the grain profile determined with a threshold angle of 20 degrees.

Figure 5 is a grayscale image after grayscale processing.

Figure 6 is the location of the analog probe.

Fig. 7 is the ultrasonic time-domain waveform and FFT spectrum curve of the analog probe.

Figure 8 is a comparison of simulation and experimental results of ultrasonic time-domain signals.

Detailed ways

The establishment method of FDTD ultrasonic testing simulation model for coarse-grained materials based on EBSD maps, taking the Z3CN20-09M main pipeline material of a pressurized water reactor nuclear power plant with a thickness of 96mm as an example, includes the following steps:

(1) Taking Z3CN20-09M with a thickness of 96mm as the research object, cut a sample of 96mm×12mm×2mm along the pipeline axis-radial direction, and then cut the sample into four pieces of 24mm×12mm×2mm for EBSD analysis, and the rest with Time-domain waveforms for ultrasonic testing. According to the national standard "GB/T19501-2004 General Principles of Electron Backscatter Diffraction Analysis Method", the samples were pretreated by grinding, mechanical polishing, and stress-relieving electrolytic polishing. Select 40μm scan step to perform EBSD analysis on the sample to be tested;

(2) As a microscopic measurement tool, EBSD can only scan a 6mm ² area at a time, and needs to be scanned sequentially. A total of 271 small-area EBSD maps were obtained on the surface of the four samples, which were stitched using channel5 analysis software, and finally the EBSD orientation map was obtained by stitching 271 pictures, as shown in Figure 1.

(3) Use the channel5 analysis software to determine the grain outline in the original orientation map, and then obtain the grains of the simulation model as the elastic anisotropy unit. According to the national standard "GB/T19501-2004 General Principles of Electron Backscatter Diffraction Analysis Method" and the international standard "ISO24173 General Principles of Electron Backscatter Diffraction Orientation Determination Method", the grains in the EBSD map are defined as adjacent regions whose misorientation is lower than a threshold angle collection. For example, the threshold angle is 10 degrees, that is, adjacent orientations whose crystal orientation angles differ within 10 degrees are counted as one crystal grain. As an important parameter to determine the grain boundary and grain position, the selection of the threshold angle is very critical. It can be seen from Figure 2 that when the threshold angle is less than 10 degrees, the white frame is full of small-sized grains. As the threshold angle increases, the small-sized grains become less and less. When the threshold angle reaches 30 degrees, the white The largest grain in the box has merged with adjacent grains into the same grain. Therefore, the smaller the threshold angle, the larger the number of grains in the model and the smaller the average grain diameter. On the contrary, when the threshold angle is too large, grains that are not originally oriented in one direction will merge together, resulting in the number of grains in the model being smaller than the actual number of grains in the material. By comparing the macroscopic metallographic photos in Figure 3, it is found that when the threshold angle is 20 degrees, the morphology of the model is consistent with the macroscopic structure of the material, as shown in Figure 4.

(4) After determining the grain outline of the model, unify the orientations within the grain outline so that each grain has only a unique crystal orientation. Use the channel5 analysis software to count the set of Euler angles with the largest number of pixels in each grain outline. Correspondingly, modify the color of the grains to the color corresponding to the main Euler angles, and finally obtain 10 orientations or colors Composed EBSD map;

(5) Export the atlas as a picture composed of 2400×300 pixels, open it in Photoshop software, set the 10 colors in the original picture to the corresponding grayscale values, export and save the grayscale picture in PCX image format, as Figure 5 shows. The Euler angles corresponding to each gray level are shown in Table 1. The model consists of 2400 × 300 square grid pixels of different gray levels, and the grid size is 40 μm, which corresponds to the scanning step. Each pixel is composed of a gray value, and each gray value corresponds to a set of Euler angles representing the grain orientation Φ,

Table 1 Corresponding colors, gray values and Euler angles of different orientation regions

(6) Using the Euler angle corresponding to the grain Φ, The direction cosine matrix R representing the crystal orientation is obtained, and the rotation matrix R _D can be deduced from the nine array elements R ₁₁ to R ₃₃ in R, and the constitutive stiffness matrix C is rotated by R _D to obtain the The elastic stiffness matrix C', where C is a 6×6 matrix consisting of three independent elastic constants.

(7) Input the model into the finite-difference time-domain ultrasonic numerical simulation program, the upper, left, and right are infinite boundaries, and the lower end is the solid-vacuum boundary. The grid width is selected as 25pixel/mm, which corresponds to the resolution of the EBSD map, and the entire model consists of 2400×300 pixels. A 2mm aperture single-array element is selected for ultrasonic loading, and the analog probe is placed in the center of the model, 2mm to the right of the center, 4mm to the right of the center, 2mm to the left of the center, and 4mm to the left of the center, as shown in Figure 6. The 1MHz Gaussian pulse fitting waveform is selected as the sound source, and the waveform and the actual sound source are fitted into a waveform composed of 201 points. The 1MHz fitting waveform is shown in (a) in Figure 7 below, and its spectrum characteristics after fast Fourier transform (FFT) are shown in Figure 7 (b) with a main frequency of 1.04MHz. Finally, the wave equation is solved by using the finite difference in time domain to accurately calculate the transmission, reflection, and refraction behaviors between the ultrasonic wave and the anisotropic grain at each propagation position, and the time domain waveform shown in Figure 8 is obtained. At the same time, a 1MHz probe was used to collect the time-domain waveform of the Z3CN20-09M sample with a thickness of 96mm, and then the measured waveform was compared with the simulated waveform. It can be seen from Figure 8 that the two waveforms are basically consistent. And compared with CIVA software, the calculation time of the FDTD simulation program does not depend on the number of anisotropic units in the model, and it only takes a few minutes to run once.

Claims (1)

1. the coarse grain material FDTD Ultrasonic Detection Building of Simulation Model method based on EBSD collection of illustrative plates, is characterized in that, comprises the steps:

(1) according to " GB/T19501-2004 Electron Back-Scattered Diffraction analytical approach general rule " national standard, to sample cut, the pre-service such as polishing, mechanical buffing, destressing electropolishing, select 40 μ m scanning steps to carry out EBSD analysis to sample to be tested;

(2) utilize EBSD device to scan the whole cross section of sample, each about 6mm ², then in order the zonule collection of illustrative plates obtaining is spliced to the final perfect crystal orientation collection of illustrative plates being spliced into by multiple collection of illustrative plates that obtains;

(3) according to the crystalline granular texture of real material, utilize channel5 analysis software to adjust the threshold angle in crystal orientation collection of illustrative plates, determine the grain contours of model, set it as the elastic anisotropy unit of model;

(4) utilize channel5 analysis software to count the color range value that in each unit, pixel quantity is maximum, be then this color range value by the color unification of all pixels in crystal grain, and write down Eulerian angle corresponding to this color range value;

(5) EBSD collection of illustrative plates is exported as to the picture of JPG form, then in Photoshop software, open, be converted into gray level image, the color range value of crystal grain is arranged to corresponding gray-scale value, derive and preserve gray-scale map with PCX picture format;

(6) utilize the Eulerian angle that crystal grain is corresponding Φ, try to achieve the direction cosine matrix R that represents crystal orientation,

By 9 array element R in R ₁₁to R ₃₃derive rotation matrix R _d,

$R_D=\left(\begin{array}{cccccc}{R}_{11}^2& R_{12}^2& R_{13}^2& 2R_{11}{R}_{12}& 2R_{11}{R}_{13}& 2R_{12}{R}_{13}\\ R_{21}^2& R_{22}^2& R_{32}^2& 2R_{21}{R}_{22}& 2R_{21}{R}_{23}& 2R_{22}{R}_{23}\\ R_{31}^2& R_{32}^2& R_{33}^2& 2R_{31}{R}_{32}& 2R_{31}{R}_{33}& 2R_{32}{R}_{33}\\ R_{11}{R}_{21}& R_{12}{R}_{22}& R_{13}{R}_{23}& R_{11}{R}_{22}+R_{12}{R}_{21}& R_{11}{R}_{23}+R_{13}{R}_{21}& R_{12}{R}_{23}+R_{13}{R}_{21}\\ R_{11}{R}_{31}& R_{12}{R}_{32}& R_{13}{R}_{33}& R_{11}{R}_{32}+R_{11}{R}_{31}& R_{11}{R}_{33}+R_{13}{R}_{31}& R_{11}{R}_{33}+R_{13}{R}_{31}\\ R_{21}{R}_{31}& R_{22}{R}_{32}& R_{23}{R}_{33}& R_{21}{R}_{32}+R_{22}{R}_{31}& R_{21}{R}_{33}+R_{23}{R}_{31}& R_{22}{R}_{23}+R_{23}{R}_{31}\end{array}\right)---\left(2\right)$

Utilize R _dto this structure stiffness matrix, C is rotated, obtain elastic stiffness Matrix C under this grain orientation ',

$C^{\&prime;}=R_{D}C{R}_D^{-1}---\left(3\right)$

Wherein, C is 6 × 6 matrixes, by 3 independently elastic constant form,

$C=\left(\begin{array}{cccccc}{C}_{11}& C_{12}& C_{12}& 0& 0& 0\\ C_{12}& C_{11}& C_{12}& 0& 0& 0\\ C_{12}& C_{12}& C_{11}& 0& 0& 0\\ 0& 0& 0& C_{44}& 0& 0\\ 0& 0& 0& 0& C_{44}& 0\\ 0& 0& 0& 0& 0& C_{44}\end{array}\right)---\left(4\right)$

(7) mode input is arrived to the ultrasonic numerical simulation program of FDTD, the lower boundary of model is set to solid-vacuum interface, its excess-three border is set to infinite boundary, select Gauss pulse matching waveform as sound source, be placed on the diverse location of model, carry out numerical evaluation, finally analog result and experimental result are contrasted.