RU2518413C1 - Method for evaluating gamma-percentile life of product by nondestructive check results - Google Patents

Abstract

FIELD: instrumentation.

SUBSTANCE: gamma-percentile life of a product is defined basing on the results of ultrasound, eddy current, radiographic and other methods of nondestructive check of material defects of a product or of group of products. The method is based on the evaluation of residual defectiveness.

EFFECT: possibility to evaluate the actual defectiveness of a product after check and repair of the revealed defects and definition of the actual level of gamma-percentile life of a product before it is destructed or damaged in operation.

2 cl, 5 dwg

Description

The invention relates to test methods, in particular for evaluating the durability of the product, more precisely, the gamma-percent resource of the product. The invention can be applied in transport, nuclear and traditional energy, aviation, shipbuilding, petrochemicals, oil, gas and product pipelines, agricultural machinery and other fields of technology and engineering.

A gamma-percent resource is a resource during which the product does not reach the limit state with probability γ, expressed as a percentage (GOST53480-2009 Reliability in technology. Terms and definitions).

As a prototype, a method for determining the quality of products disclosed in patent RU 2243586 C1 (published on December 27, 2004) was selected. This method allows you to determine residual defects. However, this method does not allow to determine the reliability parameters of the product, in particular gamma-percent resource, and their change during operation of the product.

The limiting conditions of products (mechanical products) are usually associated with defects in the metal (or other structural material) from which the product is made. In accordance with existing rules and regulations, the technique establishes the permissible sizes of discontinuities, the exceeding of which is prohibited. Such discontinuities are called defects. Defects, if detected by non-destructive testing methods, are repaired by repair. During operation, discontinuities and defects in the material of the product can develop and increase in size, leading to final breakdown or destruction of the product. For the timely detection of dangerous discontinuities, non-destructive testing is used.

The gamma-percent resource of the product by the present invention is proposed to be determined by the results of non-destructive testing (hereinafter referred to as NC) of discontinuities, inhomogeneities and other defects of the product material or group of products (parts, structural elements, etc.), including ultrasonic, eddy current, radiographic and others NK methods.

It is believed that after non-destructive testing and repair according to its results of all identified defects in the product, there are no defects. Moreover, it is believed that the reliability and safety of the product in operation is ensured (see, for example, regulatory documents in the field of nuclear energy: “Rules for the design and safe operation of equipment and pipelines of nuclear power plants” PNAEG-7-008-89, “Equipment and pipelines nuclear power plants. Welded joints and surfacing. Control rules "PNAEG-7-010-89, Gosatomnadzor of Russia, Energoatomizdat, 1991).

In fact, at present, there are practically no methods and means of non-destructive testing in technology that are guaranteed to detect all defects with 100% certainty. Therefore, there is always a certain probability of missing a defect, including a defect that is dangerous (that is, the development of which during operation will lead to damage to the product or its destruction). It is known (for example, Arkadov G.V., Getman A.F., Rodionov A.N. Reliability of equipment and pipelines of nuclear power plants and optimization of their life cycle, M., Energoatomizdat, 2010 .; Gurvich A.K. Reliability of flaw detection control as reliability of the Flaw Detector - Operator - Medium complex, Flaw Detection, 1992, No. 3, pp. 5-13), which in almost all cases of ND there is a significant probability of missing a large defect significantly exceeding the permissible sizes. In practice, it turns out that almost always after defects and elimination of identified defects in the product, defects still remain. It is these remaining defects that ultimately determine the reliability and durability of the product.

Existing methods for assessing the gamma percent resource of a product are based on formal mathematical approaches that do not take into account the real defects remaining in the product. For example, within the framework of existing theories of reliability, the actual level of the gamma-percent resource of a product is determined by the results of mathematical processing of the so-called failure flow of the same type of products in operation (Ostreykovsky V.A. Operation of nuclear power plants, Moscow, Energoatomizdat, 1999, section 3.5: Methods of analysis of discontinuities in nuclear power plant equipment). The disadvantage of such approaches is that the products in use must be damaged or destroyed before their actual level of reliability and safety can be assessed.

The technical result to which this invention is directed is that it allows you to evaluate the actual defectiveness of the product after checking and repairing the detected defects and determine the actual level of the gamma-percent resource of the product before it is destroyed or damaged in operation.

An example embodiment of the invention is illustrated by the following graphic materials:

Figure 1 presents the curves of residual defects before the start of operation and at the end of operation. Figure 2 shows a schematic diagram of a defect in a pipeline with an ellipse with half shafts a and c. Figure 3 shows a set of defects of critical and permissible sizes. Figure 4 shows a histogram of defects detected in the product, the curves of the original and residual defects. Figure 5 shows a graph for determining the probability of detection of defects.

The technical result is achieved in that the method for determining the gamma-percent product life of the product includes determining the product defectiveness by non-destructive testing, and for this particular product or group m of the same type of product, the critical dimensions χ _{cr of} defects in the operation mode and the dimensions [χ] _d allowable in operation are determined _{. e.} defects, the results of the control are presented in the form of a histogram in coordinates (N _obn , χ), where N _obn is the number of defects detected during the control, χ is the characteristic defect size, and when controlling m of the same type of products, the control results are summarized and presented as a single histogram, determined the probability of detecting defects P _water , determine the initial defect N _ref = f (χ), determine the residual defect N _rem = φ (χ) as the difference N _ref and N _obn , residual defect is divided into a reliable part χ≤χ _d and the probabilistic part χ> χ _d where χ is the characteristic size of the defect, χ _d is the size of the defects on the border between the reliable and probabilistic parts, determined from:

$${\displaystyle \underset{{\chi }_d}{\overset{{\chi }_{m\mathrm{but}\mathrm{to}\mathrm{from}}}{\int }}\varphi \left(\chi \right)d\chi =\mathrm{one}}$$

where χ _max - the maximum possible defect sizes in this product;

the obtained probabilistic part of the residual defectiveness is taken as the initial curve of the residual defectiveness, which shifts to the right on the graph in the coordinates (logP _p ; χ), where P _p is the probability of failure due to the development of defects in operation, while the development value is determined by calculation, depending on mechanism and operating conditions; the resulting new curve is taken as the final curve of residual defectiveness and the values of the gamma-percent resource are determined from it according to the criteria of either the occurrence of an unacceptable defect in operation or the destruction criterion, in this case, in the first case, use the equation:

γ _t ([χ] _cu ) = [1-P _p (χ _cu )] × 100%,

and in the second case, the equation:

γ _t (χ _cr ) = [1-P _p (χ _cr )] × 100%.

The probability part of the gamma-percent resource of the product γ _t is determined from the probabilistic part of the final residual defectiveness as the probability of the absence of an unacceptable size in the product by the formula:

$${\gamma }_t\left({\left[\chi \right]}_{d.\mathrm{uh}.}\right)=\left[\mathrm{one}-\frac{\mathrm{one}}{m}{\displaystyle \underset{{\left[\chi \right]}_{d.\mathrm{uh}.}}{\overset{{\chi }_{m\mathrm{but}\mathrm{to}\mathrm{from}}}{\int }}\varphi \left(\chi \right)d\chi }\right]$$

and the gamma-percent resource of the product according to the criterion of destruction can be determined as the probability of the absence of discontinuity in the product, equal to or greater than χ _cr by the formula:

$${\gamma }_t\left({\chi }_{\mathrm{to}R}\right)=\left[\mathrm{one}-\frac{\mathrm{one}}{m}{\displaystyle \underset{{\chi }_{\mathrm{to}R}}{\overset{{\chi }_{m\mathrm{but}\mathrm{to}\mathrm{from}}}{\int }}\varphi \left(\chi \right)d\chi }\right]$$

In order for the gamma-percent resource to be expressed as a percentage, it is necessary to multiply the value by γ _t ([χ] _doe ) or γ _t (χ _cr ) multiply by 100%.

As a rule, the linear dimension a of the defect, or a combination of the linear dimensions of the defect, or the area of the defect, or the volume of the defect, is chosen as the characteristic size χ of the defect.

In one of the options approximate the histogram (N _obn , χ) by the equation:

N _obn (χ) = A ₁ χ ^-n1 {1- (1-η) exp [-α (χ-χ ₀ )] - η} or

N _obn (χ) = A ₂ exp (-n ₂ χ) {1- (1-η) exp [-α (χ-χ ₀ )] - η},

where A ₁ , A ₂ , n ₁ , n ₂ , α, η are constants that are determined from the condition that the equation N _obn (χ) is as close as possible to the control results presented in the form of a histogram,

χ ₀ is the minimum defect size available for detection,

the initial defectiveness N _ref is determined by the formula:

N _ref = Aχ ^-n _,

and the probability of detecting a _water defect P by the formula:

P _water = 1- (1-η) exp [-α (χ-χ ₀ )] - η.

In the particular case, as the characteristic size%, we take the semi-minor axis a of the ellipse, which schematizes the defect, and the ratio a / c is taken constant for all a , determined from the condition of the maximum rate of development of the defect under operating conditions.

At the same time, the minimum defect size χ _{0 that} is available for detection is determined when setting up the flaw detector used to control the product, or as the minimum defect size that was detected during inspection.

To simplify the calculations, the constant η can be taken equal to 0.

, или $$N_{исх}=A_a{a}^{-n_a}$$

, или $$N_{исх}=A_{a,c}{(a^2/c)}^{-n_{a,c}}$$

, или $$N_{исх}=A_F{F}^{-n_F}$$

,The dependence (N _ref , χ) is approximated by an equation of the type N _ref = A _χ exp (-n _χ χ), or N _ref = A _a exp (-n _a a ), or N _ref = A _{a, c} exp [-n _{a , c} ( a ² / c)], or N _ref = A _F exp (-nF), or $$N_{\mathrm{and}\mathrm{from}x}=A_{\chi }{\chi }^{-n_{\chi }}$$

, or $$N_{\mathrm{and}\mathrm{from}x}=A_a{a}^{-n_a}$$

, or $$N_{\mathrm{and}\mathrm{from}x}=A_{a,c}{(a^2/c)}^{-n_{a,c}}$$

, or $$N_{\mathrm{and}\mathrm{from}x}=A_F{F}^{-n_F}$$

,

where a , c are the linear dimensions of the defect, F is the area of the defect,

n, A are the coefficients selected from the condition of maximum approximation of the analytical curve to the experimental data.

The method can be used for a specific product or group of similar products, the gamma-percent resource of which must be determined using the well-known NK method when monitoring by an operator of known skill, followed by repair of identified defects.

Using the methods of fracture mechanics, critical sizes of defects in the operating mode for a given product χ _cr and maximum permissible defects in operation [χ] _{doe are determined.} (norms of product defects), determined according to the applicable regulatory documents and / or technical specifications for manufacturing (for example, for nuclear technology - according to the regulatory method M-02-91. χ - characteristic defect size, for example, the linear size of the defect, or a combination of linear dimensions defect, or defect area, or defect volume.

Figure 1 illustrates the fact that the residual defect curve defined by the above method is taken as the initial (i.e., at the time of assessment, for example, before the start of operation) residual defect (curve 1 in figure 1), which during the operation t _e (for due to the fact that the defects grow) will shift to the right (figure 1, curve 2). The new residual defectiveness curve is taken as the final residual defectiveness curve.

The set of defects of critical dimensions (curve 3), allowable for operation dimensions (curve 2), as well as the allowable sizes of discontinuities in the manufacture (curve 1) are shown in Fig.3.

Non-destructive testing of the product (ND) is carried out by the selected method (ultrasonic, eddy current, radiographic and other ND methods), technical means of control and operators of a certain qualification and then eliminate the discovered defects in it (by repair).

The results of the control are presented in the form of a histogram in the coordinates "characteristic defect size χ is the number of detected defects of a given size N _ed ."

Next, determine the probability of detecting a defect P_watersinitial defect N_out= f (χ) and residual defectiveness N_ost= φ (χ) as the difference N_out and N_update .

These dependencies can be determined in the following way.

NK results are presented in the form of analytical expressions.

The structure of the equation that can describe the results of the NC presented on the histogram, figure 4, is as follows:

N _obn (χ) = N _ref (χ) P _water (χ),

where N _obn is the number of defects detected during inspection per unit of characteristic size. If the semimajor axis of the ellipse with which the defect is schematized is selected as the characteristic size, then the dimension N _obn - mm ^-1 ;

N _ref is the function of the initial (before repair and repair) defectiveness with the same dimension as N _obn ;

P _water - the probability of detecting a defect of a given size χ.

The form of the functions N _ref and P _water is determined on the basis of the condition of the greatest simplicity of expression, the minimum number of constants and the correspondence of the physically determined dependence of N _ref and P _water on χ. In a first approximation, the following equations can be used:

N _ref = Aχ ^-n ,

P _water = 1- (1-η) exp [-α (χ-χ ₀ )] - η,

N _obn (χ) = Aχ ^-n {1- (1-η) exp [-α (χ-χ ₀ )] - η},

where A, n, α, η, χ ₀ are constants.

The numerical values of the constants A, n, α, η are determined from the condition that the equation N _obn (χ) is as close as possible to the results of the NC presented as a histogram.

Moreover, χ ₀ - the minimum defect size that is available for detection - is determined when setting up the flaw detector used to control the product, or as the minimum defect size that was detected during the inspection; As a first approximation, η can be taken equal to 0. As a result, three unknowns remain, which greatly simplifies the task of determining them.

The constants A, n, α can be determined either by solving a system of three equations with respect to A, n and α, which are obtained if we take three points on the histogram, or they are determined using the least squares method.

Residual defectiveness N _ost is defined as the difference N _ref and N _obn :

N _ost (χ) = N _ref (χ) -N _obn (χ).

в области дефектов, важных для безопасности, определяют в виде числа дефектов в изделии, размеры которых равны или больше критических размеров χ_кр в режиме эксплуатации изделия:At the same time, the number of defects remaining in the product after repair and repair is determined in three ranges: residual defectiveness $$N_{\mathrm{about}\mathrm{from}t,\mathrm{to}R}^{\Sigma }$$

in the field of defects important to safety, it is determined as the number of defects in the product, the dimensions of which are equal to or greater than the critical dimensions χ _cr in the operation mode of the product:

; $$N_{\mathrm{about}\mathrm{from}t,\mathrm{to}R}^{\Sigma }=\frac{\mathrm{one}}{m}{\displaystyle \underset{{\chi }_{\mathrm{to}R}}{\overset{{\chi }_{PRed}}{\int }}{N}_{\mathrm{about}\mathrm{from}t}\left(\chi \right)d\chi }$$

;

имеется вероятность неразрушения изделия; at $$N_{\mathrm{about}\mathrm{from}t,\mathrm{to}R}^{\Sigma }<\mathrm{one}$$

there is a possibility of non-destruction of the product;

изделие не имеет запаса безопасности и не может быть допущено к эксплуатации;at $$N_{\mathrm{about}\mathrm{from}t,\mathrm{to}R}^{\Sigma }\ge \mathrm{one}$$

the product does not have a safety margin and cannot be approved for use;

в области дефектов, важных для надежности, определяют в виде числа дефектов, размеры которых превышают размеры дефектов [χ]_д.э., предельно допустимых в эксплуатации изделия:residual defectiveness $$N_{\mathrm{about}\mathrm{from}t,d.\mathrm{uh}.}^{\Sigma }$$

in the field of defects important for reliability, they are determined as the number of defects whose dimensions exceed the dimensions of the defects [χ] _doe maximum permissible in the operation of the product:

; при $$N_{ост,д.э.}^{\Sigma }\ge 1$$

изделие не имеет запаса надежности; $$N_{\mathrm{about}\mathrm{from}t,d.\mathrm{uh}.}^{\Sigma }=\frac{\mathrm{one}}{m}{\displaystyle \underset{{\chi }_{d.\mathrm{uh}.}}{\overset{{\chi }_{PRed}}{\int }}{N}_{\mathrm{about}\mathrm{from}t}\left(\chi \right)d\chi }$$

; at $$N_{\mathrm{about}\mathrm{from}t,d.\mathrm{uh}.}^{\Sigma }\ge \mathrm{one}$$

the product does not have a safety margin;

where m is the number of similar products.

When building a histogram, the horizontal axis χ must include the critical size of the defect, even if, as a result of the control, all detected defects did not reach critical sizes.

In the case of control of several products of the same type, all control results are summarized and presented in the form of a single histogram. The more products were monitored, the more reliable the final result.

The probability curve for the detection of defects from the dimensions of the defects a and c (any defect in the material can be conservatively described by an ellipse with the semiaxes a and c) can be approximated by the equation that most closely describes the experimental results of control, for example:

P _water = 1- (1-η) exp [-α _NK ( a - a ₀ ) (cc ₀ )] - η],

, or $$P_{\mathrm{at}\mathrm{about}d}=\mathrm{one}-\left(\mathrm{one}-\eta \right)\exp \left[-{\alpha }_{N\mathrm{TO}}\left(a-a_0\right)\frac{a}{c}\right]-\eta$$

,

or P _water = 1- (1-η) exp [-α _NK (χ-χ ₀ )] - η,

where α _NK - reliability coefficient of NK, characterizes the increase in the detection of defects depending on its size;

η is a constant characterizing the limiting detectability of the control by this method for an arbitrarily large defect size; if the dimensions of the part are small, then this value can be neglected by introducing an appropriate adjustment of the value of α _NC .

χ is the characteristic size of the defect, for example, its area;

χ ₀ is the minimum characteristic size of the defect;

a ₀ , c ₀ - minimum defect sizes available for detecting ND.

Next, the product is inspected, and the inspection results are presented in the form of a histogram in the coordinates "characteristic defect size χ - the number of detected defects of a given size N _{obn ed} ."

, или $$N_{исх}=A_a{a}^{-n_a}$$

, или $$N_{исх}=A_{a,c}{\left(a^2/c\right)}^{-n_{a,c}}$$

, или $$N_{исх}=A_F{F}^{-n_F}$$

, или $$N_{исх}=A_a{a}^{-n_a}\rho (c)$$

, или $$N_{исх}=A_{a,c}{a}^{-n}\frac{1}{\sqrt{2\pi D}}\exp \left[\raisebox{1ex}{${\left(c-\overline{c}\right)}^2$}\!\left/ \!\raisebox{-1ex}{$2D^2(c)$}\right.\right],$$

The initial defectiveness N _ref is defined as the ratio of N _{obd ed} / P _water (χ); the resulting histogram is approximated by an equation of the type N _ref = A _χ exp (-n _χ χ), or $$N_{\mathrm{and}\mathrm{from}x}=A_{\chi }{\chi }^{-n_{\chi }}$$

, or $$N_{\mathrm{and}\mathrm{from}x}=A_a{a}^{-n_a}$$

, or $$N_{\mathrm{and}\mathrm{from}x}=A_{a,c}{\left(a^2/c\right)}^{-n_{a,c}}$$

, or $$N_{\mathrm{and}\mathrm{from}x}=A_F{F}^{-n_F}$$

, or $$N_{\mathrm{and}\mathrm{from}x}=A_a{a}^{-n_a}\rho (c)$$

, or $$N_{\mathrm{and}\mathrm{from}x}=A_{a,c}{a}^{-n}\frac{\mathrm{one}}{\sqrt{2\pi D}}\exp \left[\raisebox{1ex}{${\left(c-\overline{c}\right)}^2$}\!\left/ \!\raisebox{-1ex}{$2D^2(c)$}\right.\right],$$

where a , c are the linear dimensions of the defect,

ρ _c is the distribution function of c, for example, the normal distribution law,

F is the area of the defect,

- коэффициенты, выбираемые из условия максимального приближения аналитической кривой к экспериментальным данным, при этом $$\overline{c}$$

- среднее значение c, а D - дисперсия.n, A, D, $$\overline{c}$$

- coefficients selected from the condition of maximum approximation of the analytical curve to the experimental data, while $$\overline{c}$$

is the average value of c, and D is the variance.

As the characteristic size, we can take the semi-minor axis a of the ellipse, which schematize the defect, while the ratio a / c is taken constant for all a, based on the condition for the maximum growth rate of the defect under operating conditions; wherein

$$N_{\mathrm{and}\mathrm{from}x}={\displaystyle \underset{0}{\overset{c_{m\mathrm{but}\mathrm{to}\mathrm{from}}}{\int }}\phi \left(a,c\right)dc=f\left(a\right)},$$

for example, in the case of a uniform stress field a / c = 2 and a normal law for a distribution with an average value of c = 2 a and a dispersion of D = a / 2, we get:

$$\begin{array}{l}{N}_{\mathrm{and}\mathrm{from}x}={\displaystyle \underset{0}{\overset{c_{m\mathrm{but}\mathrm{to}\mathrm{from}}}{\int }}A{a}^{-n}}\frac{\mathrm{one}}{\sqrt{2\pi D}}\exp \left[\raisebox{1ex}{$-{\left(c-\overline{c}\right)}^2$}\!\left/ \!\raisebox{-1ex}{$2D^2\left(c\right)$}\right.\right]dc=\\ =A{a}^{-n}{\displaystyle \underset{0}{\overset{c_{m\mathrm{but}\mathrm{to}\mathrm{from}}}{\int }}\frac{\sqrt{2}}{a\sqrt{\pi }}\exp [-{\left(c-2a\right)}^2/0.5a^2]dc=A{a}^{-n}}\end{array}$$

Residual defectiveness is obtained as the difference between N _ref and N _ed . Moreover, N _{obd ed} is determined from the analytical expression N _ex · P _waters (χ), i.e. residual defectiveness N _ost can be represented as the equation:

N _ost = N _ref (1-P _water ).

Further, residual defects are divided into a reliable part χ≤χ _d , in which defects with dimensions χ≤χ _d exist reliably, and the probabilistic part χ> χ _d , in which defects with sizes χ> χ _d may or may not exist.

The border between the reliable and probabilistic parts of the residual defect is determined from the condition:

$${\displaystyle \underset{{\chi }_d}{\overset{{\chi }_{m\mathrm{but}\mathrm{to}\mathrm{from}}}{\int }}\varphi \left(\chi \right)d\chi =\mathrm{one}}$$

where χ _max - the maximum possible defect sizes in this product.

The thus obtained probabilistic part of the residual defectiveness will be the initial curve of the residual defectiveness. During operation, curve 1 (due to the fact that the defects grow) will shift to the right (curve 2 in figure 1). The magnitude of the right shifts can be determined using well-known formulas depending on the initial size of the defect, for example, according to a regulatory document in nuclear energy RD EO-0330 or the above-mentioned monograph Arkadov G.V., Getman A.F. and Rodionova A.N. The resulting new residual defect curve will be the final residual defect.

The probability part of the gamma-percent resource of the product γ _t is determined from the probabilistic part of the final residual defectiveness as the probability of the absence of an unacceptable size in the product by the formula:

$${\gamma }_t\left({\left[\chi \right]}_{d.\mathrm{uh}.}\right)=\left[\mathrm{one}-\frac{\mathrm{one}}{m}{\displaystyle \underset{{\left[\chi \right]}_{d.\mathrm{uh}.}}{\overset{{\chi }_{m\mathrm{but}\mathrm{to}\mathrm{from}}}{\int }}\varphi \left(\chi \right)d\chi }\right]$$

and the gamma-percent resource of the product according to the criterion of destruction can be determined as the probability of the absence of discontinuity in the product, equal to or greater than χ _cr by the formula:

$${\gamma }_t\left({\chi }_{\mathrm{to}R}\right)=\left[\mathrm{one}-\frac{\mathrm{one}}{m}{\displaystyle \underset{{\chi }_{\mathrm{to}R}}{\overset{{\chi }_{m\mathrm{but}\mathrm{to}\mathrm{from}}}{\int }}\varphi \left(\chi \right)d\chi }\right]$$

In order for the gamma-percent resource to be expressed as a percentage, it is necessary to multiply the value of γ _t ([χ] _doe ) or γ _t (χ _cr ) multiplied by 100%.

The invention is illustrated by the following example.

It is necessary to determine the gamma percentage resource at the end of the design life of the pipeline with an internal diameter of D = 800 mm, wall thickness S = 34 mm of pearlite steel. The critical dimensions of the defects in the transverse welds are shown in figure 3 (curve 3). Permissible defects in operation were determined using the equations of fracture mechanics and safety factors (curve 2 in FIG. 3). The norms of defects in the manufacture are presented in figure 3 of curve 1.

As a result, the NK by a regular method and means before the start of operation (after installation) 71 discontinuities were discovered.

All identified discontinuities (defects) are presented in the form of a histogram in figure 4.

In this case, the defect width in the direction of the wall thickness, or rather, the semi-minor axis of the ellipse, with which all identified defects were schematized, was chosen as the characteristic size of the defect.

When the ratio a / s ≈ 0.5, the critical size of the defect corresponds to a _cr = 28 mm, [ a ] _doe = 11 mm, [ a ] _ex. = 1.15 mm (figure 2).

Despite the fact that the maximum size of a detected defect was a _max. = 13 mm, the abscissa axis contains a critical size a = 28 mm.

The equation describing the number of detected defects N _obn depending on the size a :

N _obn = A a ^-n [1-exp [-α ( a - a ₀ )].

According to the results of the control, the minimum detected defect had a = 0.6 mm, that is, a ₀ = 0.6 mm.

To determine the constants A, n, α solve a system of three equations with respect to these constants:

The 1st equation is obtained for a point with coordinates ( a = 1 mm, N _obn = 20) of FIG. 4:

20 = A · 1 ^-n [1-exp [-α (1-0.6)]];

The 2nd equation is obtained for a point with coordinates ( a = 5 mm, N _obn = 4) in FIG. 4:

4 = A · 5 ^-n [1-exp [-α (5-0.6)]];

The 3rd equation is obtained for a point with coordinates ( a = 13 mm, N _obn = 0.66) in FIG. 4:

0,66 = A · 13 ^-n [1-exp [-α (13-0,6)] ].

For the 3rd equation, N _obn = 0.66 was obtained as averaging the number of detected defects in the range from 11 to 13 mm, which was 2/3, where 2 is the number of detected defects, 3 is the number of intervals.

Finally, the system of equations has the form:

20 = A · [1-exp (-0.4α)];

4 = A · 5 ^-n [1-exp (-4,4α)];

0.66 = A · 13 ^-n [1-exp (-12,4α)].

The solution of the system of equations for A, n, α gave the following results:

A = 1000 mm, n = 2.56, α = 0.05 mm ^-1 _.

Substituting the constants A, n, α in the corresponding equations, we obtain: the equation of the initial defectiveness:

N _ref = 1000 a ^-2.56 ;

defect detection probability equation:

P _water = 1-exp [-0.05 ( a -0.6)];

residual defectiveness equation

N _ost (χ) = N _ref (χ) -N _obn (χ).

The resulting equations are presented in figure 4.

Solve the equations:

$${\gamma }_t\left({\left[\chi \right]}_{d.\mathrm{uh}.}\right)=\left[\mathrm{one}-\frac{\mathrm{one}}{m}{\displaystyle \underset{{\left[\chi \right]}_{d.\mathrm{uh}.}}{\overset{{\chi }_{m\mathrm{but}\mathrm{to}\mathrm{from}}}{\int }}\varphi \left(\chi \right)d\chi }\right]$$

$${\gamma }_t\left({\chi }_{\mathrm{to}R}\right)=\left[\mathrm{one}-\frac{\mathrm{one}}{m}{\displaystyle \underset{{\chi }_{\mathrm{to}R}}{\overset{{\chi }_{m\mathrm{but}\mathrm{to}\mathrm{from}}}{\int }}\varphi \left(\chi \right)d\chi }\right]$$

where φ (χ) = φ (χ) = N _ost ( a ) = N _ref ( a ) -N _obn ( a ), and m = 1

Moreover, a _max = S, where S is the thickness of the pipeline wall. Results solutions are presented in Figure 1 as curve 1. Possible exploitation in critical defects and marked, respectively [a] and a _CD.

Calculation results in coordinates {lg (l-χ); a } put on the graph (curve 1 in figure 1). The resulting curve 1 is the initial curve of the probabilistic part of the residual defectiveness.

During operation, defects will increase. The growth mechanism may vary depending on operating conditions. In our case, the growth of defects under the influence of cyclic loads prevails. In this case, we use an equation of the type:

$$\frac{da}{dN}=C\cdot {\left(\frac{\Delta K_{\mathrm{one}}}{\sqrt{\mathrm{one}-R}}\right)}^m$$

wherein:

C and m are constants depending on the material and operating conditions;

R is the asymmetry coefficient of the cycle, for a pressure cylinder is 0;

ΔK ₁ is the magnitude of the stress intensity factor.

The stress intensity factor for an inhomogeneous stress distribution in the crack region is determined by the equation:

, $$K_{\mathrm{one}}=Y*{\sigma }_{\mathrm{to}R}^{*}{\left(a/1000\right)}^{0.5}$$

,

Where

Y = (2-0.82 ( a / c)) / [1- (0.89-0.57 ( a / c) ^0.5 ) ³ ( a / c) ^{l, 5} ] ^3.25 ,

σ _cr = 0.61 σ ^A + 0.39σ ^B + [0.11 ( a / s) -0.28 ( a / s) (1- ( a / c) ^0.5 )] (σ ^A -σ ^B ), (5)

σ ^A is the stress at the crack tip;

σ ^B is the stress on the surface of the part at the root of the crack.

.For a special case $$Y=1.12\sqrt{\pi }$$

.

Integrating the above expression, it can be represented as:

$$N={\displaystyle \underset{a_0}{\overset{a_k}{\int }}\mathrm{one}/C\cdot {\left(\frac{\Delta K_{\mathrm{one}}}{\sqrt{\mathrm{one}-R}}\right)}^{m}da}$$

Substituting the previous expressions into the expression and solving it with respect to the final crack size a _k , we can determine the crack undergrowth Δ a _N under the influence of N loading cycles.

Determining the undergrowth of defects in this way for the upper, middle, and lower parts of the initial residual defect curve for the number of loading cycles at the end of the design life, we obtain the final residual defect curve (curve 2 in FIG. 1).

According to the final curve of residual defectiveness, we determine the gamma percentage resource of the pipeline according to the criteria for the detection of an unacceptable defect and the criterion of destruction (rupture), respectively:

γ _t ([χ] _c.u. ) = 1-P _p ( a _cu ) and γ _t (χ _cr ) = 1-P _p ( a _cr ),

or, to represent the probabilities as a percentage, the values of ji must be multiplied by 100%. Carrying out these calculations, we finally obtain:

- gamma percentage resource at the end of the design life by the criterion for the occurrence of an impermissible defect in operation

γ _t ([χ] _doe ) = 1-P _p ( a _doe ) = 1- (2 × 10Е-2) × 100% = 98%;

- gamma-percent resource at the end of the design life by the criterion of destruction of the pipeline

γ _t (χ _cr ) = 1-P _p ( a _cr ) = 1- (3 × 10E-6) × 100% = 99.9997%.

As follows from the above example, the method allows to determine the gamma percentage resource with a high degree of reliability.

Claims (2)

1. A method for determining the gamma percentage resource of a product, including determining the defectiveness of a product by non-destructive testing, characterized in that for a particular product or group m of the same type of product the critical dimensions χ _{cr of} defects in operation and the dimensions [χ] _{d.e .} defects, the results of the control are presented in the form of a histogram in coordinates (N _obn , χ), where N _obn is the number of defects detected during the control, χ is the characteristic defect size, and when controlling m of the same type of products, the control results are summarized and presented as a single histogram, determined the probability of detecting defects P _water , determine the initial defect N _ref = f (χ), determine the residual defect N _rem = φ (χ) as the difference N _ref and N _obn , residual defect is divided into a reliable part χ≤χ _d and the probabilistic part χ> χ _d , g de χ is the characteristic size of the defect, χ _d is the size of the defects on the border between the reliable and probabilistic parts, determined from:
$${\displaystyle \underset{{\chi }_{\mathrm{at}}}{\overset{{\chi }_{m\mathrm{but}\mathrm{to}\mathrm{from}}}{\int }}\phi \left(\chi \right)d\chi =\mathrm{one}},$$

where χ _max - the maximum possible defect sizes in this product;
the obtained probabilistic part of the residual defectiveness is taken as the initial curve of the residual defectiveness, which shifts to the right on the graph in the coordinates (logP _p ; χ), where P _p is the probability of failure due to the development of defects in operation, while the development value is determined by calculation, depending on mechanism and operating conditions; the resulting new curve is taken as the final curve of residual defectiveness and the values of the gamma-percent resource are determined from it according to the criteria of either the occurrence of an unacceptable defect in operation or the destruction criterion, in this case, in the first case, use the equation:
γ _t ([χ] _d.e. ) = [1-P _p (χ _d.e. )] × 100%,
and in the second case, the equation:
γ _t (χ _cr ) = [1-P _p (χ _cr )] × 100%. 2. The method according to claim 1, characterized in that the linear size of the defect, or a combination of the linear dimensions of the defect, or the area of the defect, or the volume of the defect, is selected as the characteristic size χ of the defect.

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