RU2783064C1 - Method for automated determination of the periodicity of the relief of fractures of destroyed materials - Google Patents

Abstract

FIELD: material engineering.

SUBSTANCE: invention is intended for automated determination of the periodicity of the relief of fractures of destroyed materials. The essence of the invention lies in the fact that by means of a scanning electron microscope, a fracture of a destroyed sample is examined and an image of its section with fatigue grooves formed in the structure of the destroyed sample under study is obtained, after which the image is analyzed on a computer using a one-dimensional Fourier transform. Sections are carried out according to the obtained fracture photograph, directed along the growth of the fatigue crack and intersecting the fatigue grooves, and one-dimensional brightness functions D_n(r) are obtained depending on the length of the section r. Using the software, the coefficients of the discrete Fourier series F_n(r_k) are automatically obtained, where k is the number of the discrete Fourier series, r_k is the period corresponding to the number of the discrete Fourier series. The step of the fatigue groove characterizing the fatigue crack growth rate is determined by the value of the argument r_i of the function of local maxima P(r_i) corresponding to the maximum value of this function P (r_i).

EFFECT: providing the possibility of increasing the reliability of determining the periodicity of the relief of fractures of destroyed materials, including at the initial stage of the formation of fatigue grooves, which makes it possible to more accurately determine the service life of a part made of the material under study during its operation.

2 cl, 15 dwg

Description

The invention relates to measuring technology and can be used to determine the periodicity in the structure of the surface of the destroyed material under the influence of periodic repetition of the applied load (fatigue failure).

On the surface of fatigue fractures, one can find specific banded formations - fatigue grooves, which is one of the main signs of the fatigue nature of fracture. The fracture surface with fatigue grooves is a periodic structure with an approximately triangular shape of the profile obtained along the development of the fracture. In almost all proposed models, fatigue grooves reflect the consistent position of the fatigue crack front at different stages of development. The experiments on fatigue crack growth with marking of individual blocks of fatigue cycles have shown that for polycrystalline materials the formation of one fatigue groove corresponds to one loading cycle.

With this type of fracture, a typical characteristic of the relief is a periodic structure of fatigue grooves or macro- and microlines. The size of these objects (width) reflects the distance of crack propagation in one cycle of material loading (crack growth rate). Knowing the crack growth rate makes it possible to determine the survivability of the part, i.e. the duration of maintaining the integrity of the part during the development of a fatigue crack in it. Such data form the basis of a number of criteria by which the resource of safe operation of equipment (primarily aerospace) is determined.

In this context, the question arises of determining the pitch of fatigue grooves with high accuracy. To eliminate the subjective factor of the operator and at the same time improve the accuracy of measurements, it is preferable to carry out measurements in automatic mode. However, up to now, the measurement of UB parameters has been carried out in the "manual" mode. At the same time, the researcher (fractographer) measured the parameters of the fatigue grooves directly from the image obtained in the electron microscope, taking measurements from point to point. Measurements for relatively large fatigue grooves (about 1 µm) are not difficult. Problems arise when studying fatigue grooves formed at the initial stage of formation (with a step size of about 0.01 μm). This task requires a highly qualified researcher. In some cases, measuring the parameters of fatigue grooves is complicated by the conditions of fatigue crack growth, namely, oxidation and/or secondary damage to the relief. All this introduces significant difficulties in the correct measurement of the pitch of fatigue grooves.

Most modern electron microscopes are equipped with software with the ability to apply a two-dimensional Fourier transform or a Fourier transform of a profile. The Fourier transform gives a good result when transforming the profiles of fatigue grooves with a constant pitch and relatively large fatigue grooves that form at the final stage of crack growth.

When reading from a scanning electron microscope in an electronic computer, the image line is fixed perpendicular to the comb structure of the fracture, the profile of the signal having the appropriate periodicity. To accurately determine the periods of this structure, it is most convenient to use the spectral method of image analysis using one-dimensional and two-dimensional Fourier transforms. Fourier analysis makes it possible to carry out an integral metrological study of periodic structures without measuring each individual step of fatigue grooves. In this case, first of all, the subjective influence of the gauge on obtaining the final size of the surface relief parameter, which in the quantitative fatigue fracture fractography is the step of fatigue grooves, is excluded.

The closest in technical essence and achieved technical result is the method described in the book of Shanyavsky A.A. “Safe Fatigue Failure of Aircraft Structures. Synergetics in engineering applications”, publishing house “Monograph”, 2003, section “Fourier fractography”, p. With. 206-214. A well-known method for determining the periodicity of the relief of fractures of destroyed materials is characterized by the fact that a fracture of a destroyed sample is examined by means of a scanning electron microscope, an image of the area of the indicated fracture with fatigue grooves formed in the structure of the investigated destroyed sample is obtained, the image is analyzed on an electronic computer using a one-dimensional Fourier transform.

However, this method does not make it possible to determine the periodicity under conditions of a low crack growth rate at the initial stages of destruction, and especially under adverse conditions (surface oxidation, secondary damage to the relief, etc.)

The technical result achieved by using the claimed method is to increase the reliability of determining the periodicity of the relief of fractures of destroyed materials, including at the initial stage of the formation of fatigue grooves, which makes it possible to more accurately determine the service life of a part made from the material under study during its operation. The reliability of determining the pitch of fatigue grooves in the proposed method is also maintained under critical conditions, for example, during surface oxidation, fracture damage due to mutual contact of the crack edges in such processes.

The technical result of the invention is achieved by the fact that in the proposed method for automated determination of the periodicity of the relief of fractures of fractured materials using a scanning electron microscope, the fracture of the fractured sample is examined, an image of the section of the specified fracture with fatigue grooves formed in the structure of the investigated fractured sample is obtained, the image is analyzed on an electronic computer with using a one-dimensional Fourier transform, according to the proposal, a fracture area is selected from which the fatigue crack growth rate will be determined, the brightness, contrast and magnification of the scanning electron microscope are adjusted, which are optimal for viewing fatigue grooves on it, sections are made according to the obtained photograph of the fracture, directed along the growth of the fatigue crack and crossing fatigue grooves and obtain one-dimensional brightness functions Dn(r) depending on the length of the drawn section r, where n is the number of the section along which Fourier transform, the software automatically obtains the coefficients of the discrete Fourier series F _n (r _k ), brightness functions D _n (r),

where F _n (r _k ) are the coefficients of the discrete Fourier series,

k is the number of the diskette Fourier series,

r _k - period corresponding to the number of the discrete Fourier series,

from the Fourier series, the cumulative function of the local Fourier maxima Ф (r _min ,r _i ) is obtained by the transformation:

where F(ri) are the averaged Fourier coefficients of the discrete transform over the set of section profiles,

, где

, where

r _min - the minimum possible period, depending on the resolution of the photo,

r _i - varies from the minimum - r _min to the maximum possible value of the period - r _max , and the maximum value is determined by the length of the section,

get the derivative of the cumulative function Ф (r _min ,r _i ) - the function of local maxima Р(r _i ):

determine the step of the fatigue groove, which characterizes the growth rate of a fatigue crack, by the value of the argument r _i of the function of local maxima Р(r _i ), corresponding to the maximum value of this function P(r _i ):

The magnification range of the microscope at which fatigue grooves are observed is from 1000 to 30000 times.

The essence of the invention is illustrated by graphic materials, where:

figure 1 is an enlarged photo taken under a microscope, the surface of fatigue failure, which is selected section n, perpendicular to the fatigue grooves;

figure 2 is a plot of the brightness level D(n) from the distance for the section n;

figure 3 is a plot of the coefficients of the Fourier series F _n from the distance r;

figure 4 is a graph of the cumulative function f(n) from the distance r;

figure 5 is a graph of the function P(n) from the distance r;

figure 6 is a graph of the function P(n) from the distance r in the range from 0 to 0.3 μm;

figure 7 - General view of the sample, where the crosses show the places where the measurement of the step of the fatigue grooves was carried out;

figure 8 - area located at a distance of 410 μm from the focus, which was determined step fatigue grooves;

figure 9 - Fourier transform F(n) of the area located at a distance of 410 μm from the source;

figure 10 - function of local maxima P(n) area, located at a distance of 410 μm from the source;

figure 11 - area located at a distance of 940 μm from the focus, which was determined step fatigue grooves;

Fig.12 - Fourier transform F(n) of the area located at a distance of 940 μm from the focus;

figure 13 - function of local maxima P(n) area located at a distance of 940 μm from the focus;

Fig.14 - dynamics of growth of a fatigue crack for a sample tested at a temperature of 750°C;

Fig.15 - increment cycles from the distance to the source for the sample tested at a temperature of 750°C.

The claimed method is carried out as follows.

Using a scanning electron microscope, the fracture of the sample destroyed during testing is examined. Choose a fracture site, which is observed periodic structure - fatigue grooves (figure 1). Adjust the brightness, contrast and magnification of the scanning electron microscope, optimal for viewing fatigue grooves on it. Empirically, a magnification is selected that is sufficient to consider fatigue grooves on it, characterizing the growth of a fatigue crack. At the same time, brightness and contrast are selected in such a way that there are no highlights and darkening.

Sections are made according to the obtained photograph of the fracture, directed along the growth of the fatigue crack and crossing the fatigue grooves and one-dimensional brightness functions D _n (r) are obtained depending on the length of the section drawn (r), where n is the number of the section along which the Fourier transform is performed,

using software, the coefficients of the discrete Fourier series F _n (r _k ), brightness functions D _n (r) are automatically obtained:

where F _n (r _k ) are the coefficients of the discrete Fourier series,

k is the number of the diskette Fourier series,

r _k - period corresponding to the number of the discrete Fourier series,

n is the number of the section along which the Fourier transform is carried out,

From the Fourier series, the cumulative function of the local Fourier maxima Ф (r _min ,r _i ) is obtained by the transformation:

where F(r _i ) are the averaged Fourier coefficients of the discrete transform over the set of section profiles,

where r _min is the minimum possible period, depending on the resolution of the photo,

r _i - varies from the minimum - r _min to the maximum possible value of the period - r _max , and the maximum value is determined by the length of the section,

get the derivative of the cumulative function Ф (r _min ,r _i ) - the function of local maxima P(r _i ):

determine the step of the fatigue groove, which characterizes the growth rate of a fatigue crack, by the value of the argument r _i of the function of local maxima P(r _i ), corresponding to the maximum value of this function P(r _i )

To improve the accuracy of determining the period, the choice of magnification is important. It is necessary that the period of the object does not fall into the range corresponding to low frequencies due to the large distance between the periods r _i (the period of the object will shift to these dimensions at high magnifications), and does not fall into the range corresponding to high frequencies (too low magnification) due to reducing the resolution, which reveals the periodicity of the structure. To determine the desired magnification, you can shoot an object at different magnifications and use this method for each magnification. This will allow us to determine at what increase the maximum of the function is in the optimal range of periods. Optimum for this method is the magnification range of the microscope from 1000 to 30000 times.

Having obtained the crack growth rate, we can determine the duration of crack development using the following formula

where M is the number of measurements,

r _n and d _n are the distance to the source and the crack growth rate, respectively

Example. This method was used to study the fracture of a destroyed cylindrical sample tested for low-cycle fatigue at a temperature of 750°C (surface oxidation is observed at this temperature). Sample material - nickel granulated alloy EP741NP. The grain size of the alloy from which the samples were made does not exceed 140 μm. Cylindrical specimens were cut from the high pressure turbine hub of a turbojet engine in the axial direction of the disk. The microstructure of the alloy after heat treatment is a solid solution of γ-Ni with an average grain size of ~40 μm, along the grain boundaries there are large particles of the strengthening intermetallic γ'-phase up to 3 μm in size.

Loading parameters when testing specimens: cycle shape - sinusoidal; loading frequency - 1 Hz; the controlled parameter during loading is the range of deformation in the cycle Δε = 0.6; cycle asymmetry coefficient R _ε = (ε _min / ε _max ) = 0.

The coordinates of the focus were fixed. A search was made for areas where the formation of fatigue grooves can be observed. For each local section of the fracture, the coordinates were fixed, which made it possible to calculate the distance to the focus, and the step of the fatigue grooves was measured using the program (the size of which characterizes the growth rate of a fatigue crack in one loading cycle), Fig.7.

In Fig.8. shows a section of the fracture surface located at a distance of 410 μm from the focus, on which a section of the sections for which the period was measured was marked with a rectangle. Figure 9 shows the resulting function Fn(r). Using the formulas described above, the function of local maxima P(r _i ) shown in Fig.10 was obtained, in which the maximum value of P(r _i ) corresponds to r _i = 0.37 μm. Therefore, the pitch of the fatigue grooves is 0.37 µm.

In Fig.11. shows a section of the fracture surface located at a distance of 940 μm from the source, on which a section of the sections for which the period was measured was marked with a rectangle. Figure 12 shows the resulting function Fn(r), figure 13 is the function of local maxima P(r _i ) in which the maximum value of P(r _i ) corresponds to r _i = 1.39 μm. Therefore, the pitch of the fatigue grooves is 1.39 µm.

Measuring the pitch of fatigue grooves in local fracture sections made it possible to obtain the dynamics of fatigue crack growth, where the fatigue groove pitch is equal to the crack growth rate (crack advancement in one loading cycle). Figure 14 shows the resulting crack growth dynamics.

Using the resulting crack growth graph, it is possible to calculate the number of crack development cycles using the following formula

where M is the number of measurements,

r _n and d _n - respectively, the distance to the source and the rate of crack growth. The dynamics of crack growth made it possible to estimate the duration of the development of destruction and, therefore, calculate the survivability, which is equal to 1300 cycles (Fig.15).

Claims (18)

1. A method for automatically determining the periodicity of the relief of fractures of destroyed materials, characterized in that the fracture of the destroyed sample is examined by means of a scanning electron microscope, an image of the section of the indicated fracture with fatigue grooves formed in the structure of the investigated destroyed sample is obtained, the image is analyzed on an electronic computer using a one-dimensional Fourier transforms, characterized in that they select the section of the fracture, which will be used to determine the growth rate of a fatigue crack, adjust the brightness, contrast and magnification of the scanning electron microscope, optimal for examining fatigue grooves on it, cross-sections are made according to the obtained photograph of the fracture, directed along the growth of the fatigue crack and crossing the fatigue grooves, and one-dimensional brightness functions D _n (r) are obtained depending on the length of the drawn section r, where n is the number of the section along which the Fourier transform is performed, using the software, the coefficients of the discrete Fourier series F _n (r _k ) of the brightness function D _n (r) are automatically obtained, where F _n (r _k ) are the coefficients of the discrete Fourier series, k is the number of the diskette Fourier series, r _k - period corresponding to the number of the discrete Fourier series, from the Fourier series, the cumulative function of the local Fourier maxima Ф(r _min ,r _i ) is obtained by the transformation:

where F(r _i ) are the averaged Fourier coefficients of the discrete transform over the set of section profiles,

, where r _min - the minimum possible period, depending on the resolution of the photo, r _i - varies from the minimum - r _min to the maximum possible value of the period - r _max , and the maximum value is determined by the length of the section, get the derivative of the cumulative function Ф(r _min ,r _i ) - the function of local maxima Р(r _i ):

determine the step of the fatigue groove, which characterizes the growth rate of a fatigue crack, by the value of the argument r _i of the function of local maxima P(r _i ), corresponding to the maximum value of this function P(r _i ):

. 2. The method for determining the periodicity of the relief of fractures of destroyed materials according to claim 1, characterized in that the magnification range of the microscope, in which fatigue grooves are observed, is from 1000 to 30000 times.

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