JP2024045955A - Limit load evaluation method and limit load evaluation device - Google Patents

Abstract

To provide a limit load evaluation method capable of swiftly providing a maintenance plan by quickly performing a soundness assessment on cracks detected during inspection.SOLUTION: The limit load evaluation method is a limit load evaluation method of the ductile failure limit in a structure with n adjacent multiple cracks. The strain distribution of a structure with n adjacent multiple cracks is predicted by correcting the distortion εpre at any position based on an equation (1) that is expressed as the product of the strain distribution εi resulting from elastic-plastic analysis for a single crack condition and the ratio εi/ε0 of the strain ε0 in a sound state. The critical load (plastic collapse load) is estimated and evaluated from the obtained strain distribution. Here, 2≤n.SELECTED DRAWING: Figure 1

Description

TECHNICAL FIELD The present invention relates to a limit load evaluation method and a limit load evaluation device for evaluating the soundness of piping used, for example, in a power plant, particularly at a portion where deterioration over time or fatigue damage is expected.

For example, in power generation plants that are aging, improving the accuracy of health evaluation technology for aging equipment is important for improving safety and extending the life of the plant.

In conventional health evaluation technology, if a crack is detected through non-destructive testing during a periodic inspection, crack growth evaluation and critical crack size evaluation are performed, taking into account aging deterioration events expected from the operating conditions of the equipment. It is confirmed that soundness can be maintained by the next inspection.

Further, in general, the critical crack size in soundness evaluation is derived using a simple evaluation formula or the finite element method. In soundness evaluation using a simple evaluation formula, as shown in Patent Document 1, in the case of small cracks with a predetermined size or less, the nonlinear fracture mechanics evaluation method is used, and in the case of large cracks, the ultimate load is used. It is evaluated using a simple evaluation formula based on the evaluation method. Therefore, in cases where there are multiple cracks in close proximity, it is assumed that the evaluation will be excessively on the safe side, such as by projecting the cracks onto the same surface for evaluation.

As shown in Patent Document 2, limit evaluation using the finite element method requires a process of creating an analytical model that matches the geometric shape of the stress concentration area and the crack shape detected during inspection, and performing calculations, which can require extremely high calculation costs depending on the conditions.

JP 2009-14683 A JP 2014-149246 A

As a result, limit load assessments that reflected the crack shapes obtained through non-destructive testing could not be carried out promptly, and the time required to develop maintenance plans often led to extended shutdown periods for power plants.

In addition, since there is no way to quickly and efficiently reflect the crack shape obtained through non-destructive testing into an analytical model and provide crack growth evaluation results in a short period of time, conservative life expectancy with a large safety factor is not available.・Remaining life evaluation is being conducted. As a result, the remaining life of the power plant equipment is estimated to be short, leading to a decrease in the efficiency of the power plant as a whole.

The present invention is an invention for solving the above problems, and aims to provide a limit load evaluation method and limit load evaluation device that can provide a rapid maintenance plan by quickly performing a soundness evaluation of cracks detected during inspection.

ここで、２≦ｎである。 In order to solve the above-mentioned problems, the critical load evaluation method of the present invention is a critical load evaluation method for the ductile failure limit of a structure having n adjacent multiple cracks. By correcting the strain ε _pre at an arbitrary position based on equation (1), which is expressed as the product of the ratio ε _i /ε ₀ of the strain distribution ε _i as a result of plastic analysis and the strain ε ₀ in a healthy state, n It is characterized by predicting the strain distribution of a structure with multiple cracks in close proximity, and estimating and evaluating the critical load (plastic collapse load) from the obtained strain distribution.

Here, 2≦n.

Further, the critical load evaluation device of the present invention is a critical load evaluation device for a structure having a plurality of adjacent cracks, and includes a storage section that stores elastic-plastic analysis results for a single crack under a plurality of shape conditions; Based on the information obtained in , and the crack conditions to be evaluated obtained by the inspection equipment, _the ratio ε _{i /} The strain distribution of a structure with n adjacent multiple cracks is predicted by correcting the strain ε _pre at an arbitrary position based on the equation (1) expressed as the product of ε ₀ , and the fracture A calculation unit that estimates and evaluates a limit (plastic collapse load).
Other aspects of the present invention will be explained in the embodiments described below.

According to the present invention, it is possible to quickly perform limit load assessments for structures with multiple closely spaced cracks detected during inspection, making it possible to provide rapid maintenance plans.

FIG. 2 is a flow diagram showing an evaluation procedure in the limit load evaluation system according to the embodiment. FIG. 3 is a diagram showing an example of crack size ratio conditions used in analysis for creating a DB of strain distribution for a structure having a single penetrating crack. FIG. 13 is a diagram showing an example of crack size ratio conditions used in analysis for DB generation of strain distribution for a structure having a single semi-elliptical surface crack. FIG. 2 is a diagram schematically showing a structure having a plurality of adjacent penetrating cracks. FIG. 2 is a diagram schematically showing a structure having a single through crack. FIG. 13 is a diagram showing strain distribution in the results of an elastic-plastic analysis of a flat plate having multiple adjacent through cracks. FIG. 13 is a diagram showing the results of predicting the strain distribution of a flat plate having multiple closely spaced through cracks based on an embodiment. FIG. 8 is a diagram showing the results of comparing the strain distribution in the horizontal direction from the end of the through crack of the flat plate having a plurality of adjacent through cracks shown in FIGS. 6 and 7. FIG. FIG. 1 is a block diagram showing the configuration of an evaluation device according to an embodiment. FIG. 1 shows a schematic of a structure having multiple closely spaced surface semi-elliptical cracks.

Embodiments for implementing the present invention will be described in detail with reference to the drawings as appropriate.
FIG. 1 is a flow diagram showing an evaluation procedure in a limit load evaluation system 1 according to an embodiment. The limit load evaluation system 1 shown in FIG. 1 evaluates, for example, the limit load (plastic collapse load) of equipment in power plant equipment. An overview of the processing process in Critical Load Evaluation System 1 is that an elastic-plastic analysis is performed in advance on the elastic-plastic analysis results of the evaluation target part in a healthy state and on a single crack model assuming multiple crack shapes. Preparation process 11 of creating a database, on-site measurement process 12 of performing non-destructive inspection during periodic inspections and measuring the crack shape of the evaluation target part, and correcting and estimating the strain distribution according to the measured crack shape and arrangement. The process also includes an evaluation step 13 in which the limit load is calculated based on the strain distribution and the soundness is evaluated.

In this embodiment, it is assumed that the advance preparation process 11 and the on-site measurement process 12 are performed mainly manually in advance, and the evaluation process 13 is performed by a computer or the like. Note that the evaluation of a flat plate having multiple adjacent through cracks will be described here.

<Preparation step 11>
First, in the advance preparation process 11 (first stage), specifically in the process step S10, an elastic-plastic analysis is performed using a single crack model for multiple crack shapes assumed in the evaluation target. Next, in the process step S11, the crack shape and position and strain distribution data of the obtained elastic-plastic analysis results are stored in a database. Here, it is recommended to use the constitutive equations defined by Ramberg-Ossgood and power-law plasticity described in formulas (2) and (3) for the elastic-plastic analysis.

ここで、εは全ひずみ、σは応力、Ｅはヤング率である。また、ａ、ｂ、ｍは塑性特性項に対する任意の材料定数である。

Here, ε is the total strain, σ is the stress, and E is the Young's modulus. Further, a, b, and m are arbitrary material constants for the plastic property term.

A plurality of DBs are prepared in advance based on the crack dimensions (surface crack width L _i , depth a _i ) and plate thickness t.

FIG. 2 is a diagram showing an example of crack size ratio conditions used for analysis for creating a DB of strain distribution for a structure having a single through crack. FIG. 3 is a diagram illustrating an example of crack size ratio conditions used in an analysis for creating a DB of strain distribution for a structure having a single surface semi-elliptic crack.

For example, Figure 2 shows the case of evaluating a single through crack, where the ratio L/t of plate thickness t to crack width L is calculated under four conditions. When modeling a surface semi-elliptical crack, the crack depth a must also be considered as a parameter, so the number of conditions for the desired strain distribution εi increases, such as calculating four conditions for each of the crack width L and depth _a (total of 16 conditions) as shown in Figure 3.

Here, an example was shown in which DB conversion was considered with four conditions for each condition, but it goes without saying that the strain distribution ε _i can be estimated with higher accuracy if the number of conditions is larger and the conditions are set more precisely and the DB conversion is performed. Furthermore, if the measured crack size does not match the calculated result, the strain distribution ε _i can be approximately determined by interpolating and extrapolating the crack size as a reference.

<On-site measurement process 12>
Next, in an on-site measurement step 12 (second stage) in which a non-destructive inspection is performed during a periodic inspection to measure the shape of cracks in the evaluation target part, specifically, in processing step S12, a method generally used to detect cracks is performed. The shape and arrangement of cracks are measured by UT inspection (ultrasonic flaw detection).

<Evaluation process 13>
Evaluation process 13 (third stage) evaluates the critical load of the structure based on the obtained crack shape and position information, using the crack distribution data of the evaluation target evaluated in the second stage inspection. The strain distribution is estimated using the DB-based elastic-plastic analysis results, the limit load is calculated, and the soundness evaluation results are provided. Specifically, in processing step S13, equation (1) is expressed as the product of the strain distribution ε _i as a result of elastic-plastic analysis of a single crack and the ratio ε _i /ε ₀ of the strain ε ₀ in a healthy state. The strain ε _pre at an arbitrary position is estimated based on . In the case of a structure having a plurality of adjacent cracks, the strain distribution is finally estimated by multiplying the cyclic strain ratio according to the number n of cracks.

ここで、２≦ｎである。

Here, 2≦n.

The limit load is calculated in processing step S14 based on the obtained strain distribution, and the limit load result is provided by comparing it with the load applied in the actual machine in processing step S15.

FIG. 4 is a diagram schematically showing a structure having a plurality of adjacent through cracks. FIG. 5 is a diagram schematically showing a structure having a single through crack. FIG. 4 is a schematic diagram showing a situation where a tensile load or displacement 23 is applied to a flat plate 20 having two through cracks 21 (surface crack width L ₁ ) and two through cracks 22 (surface crack width L ₂ ). In this embodiment, multiple cracks as shown in FIG. 4 are prepared by using the strain distribution obtained by analyzing the single crack condition of the through crack 28 (surface crack width L ₃ ) shown in FIG. 5 in advance. Estimate the critical load in a structure with

Here, when estimating the critical load on the flat plate with two through cracks in Fig. 4, first, for the through crack 21, the strain distribution obtained in the analysis for a single crack with an arbitrary surface crack width L ₃ is calculated. The coordinates are corrected and mapped using the surface crack length ratio L ₃ /L ₁ . The strain distribution obtained at this time is assumed to be ε ₁ . Next, for the other through crack 22, the coordinates of the strain distribution obtained in the analysis for a single crack with a surface crack width L ₃ are corrected and mapped using the surface crack length ratio L ₃ /L _2. . The strain distribution obtained at this time is assumed to be _ε2 .

The strain distribution in the plate with two through cracks shown in Figure 4 can be obtained by correcting the strain distribution at any position according to formula ( ₁ ) using the obtained strain distribution ε _pre and the strain distribution around the cracks as the standard _, thereby estimating the limit load.

Figure 6 shows the strain distribution in the elastic-plastic analysis results of a flat plate with multiple adjacent through cracks. Figure 7 shows the results of predicting the strain distribution of a flat plate with multiple adjacent through cracks based on an embodiment.

That is, FIG. 6 is a diagram showing the strain distribution around the cracks in the elastic-plastic analysis result for the flat plate having two adjacent cracks as described above, and FIG. 7 shows the strain distribution ε _pre obtained as a result of evaluation under the same crack conditions as FIG. 6 based on the embodiment.

Fig. 8 is a diagram showing the results of comparing the strain distribution in the horizontal direction from the end of the through crack 21 of a flat plate having multiple adjacent through cracks shown in Fig. 6 and Fig. 7. Reference numeral 44 in Fig. 8 indicates the distance x from the crack end, and reference numeral 43 indicates the strain distribution output position. From the comparison results, it can be seen that the strain distribution (ε _pre ) obtained by this embodiment can accurately reproduce the strain distribution (ε _FEA ) obtained by the elastic-plastic analysis, and that this method is effective.

Figure 9 is a block diagram showing the configuration of the evaluation device 31 according to this embodiment. The evaluation device 31 according to this embodiment is configured to include a communication unit 33, a calculation unit 34, a memory unit 35, an output unit 41, and an input unit 42. The memory unit 35 is configured with a database unit 39 that stores the results of the elastic-plastic analysis, and a crack information unit 40 that complements the crack shape and position information obtained by the inspection. Data can be stored directly in the database unit 39 and the crack information unit 40, or it can be downloaded via the communication unit 33 and the network NW.

The calculation unit 34 is composed of a crack position evaluation unit 36 that evaluates the relative coordinates of the crack, a strain distribution estimation unit 37 that estimates the strain distribution according to the crack position, and a limit load evaluation unit 38 that calculates the limit load based on the estimated strain distribution. Here, the physical positional relationship of the evaluation device 31 with the inspection device 30 is not particularly limited, and the evaluation device 31 may be located in a different place. The strain distribution estimation unit 37 estimates the strain distribution and limit load based on the formula (1) shown in the above-mentioned processing step S13.

The input unit 42 is a device for inputting instructions to a computer, such as a keyboard or mouse, and inputs instructions such as starting a program. The output unit 41 is a display or the like, and displays the execution status and results of processing by the evaluation device 31. The communication unit 33 exchanges various data and commands with other devices.

The calculation unit 34 is a central processing unit (CPU) that executes various programs stored in the memory. The storage unit 35 is an external storage device that stores various data for the evaluation device 31 to execute processing.

<Modification>
FIG. 4 illustrates the flat plate 20 having two through cracks 21 (surface crack width L ₁ ) and 22 (surface crack width L ₂ ), but is not limited thereto.

FIG. 10 is a schematic diagram showing a situation where a tensile load or displacement 23 is applied to a flat plate having two semi-elliptic cracks on its surface. In the case of surface semi-elliptic cracks, crack depths a ₁ and a ₂ are added as parameters to the conditions for through cracks, but the evaluation procedure is the same.

If the surface crack width L _j in the case of non-penetrating cracks of surface elliptical cracks is the standard, and the surface crack width L _i to be evaluated is the aspect ratio a _j /L between the crack depth a _j and the plate thickness t _{j j} and L _j / _Li are the same, and the coordinates in the strain distribution are corrected by the ratio of L _j / _Li for the surface crack width L _i to be evaluated.

ここで、２≦ｎである。 The limit load evaluation method and limit load evaluation device of the present embodiment described above have the following features.
(1) A method for evaluating the limit load of the ductile fracture limit of a structure having n adjacent cracks, characterized in that the strain distribution of a structure having n adjacent cracks is predicted by correcting the strain ε _pre at an arbitrary position based on equation (1) expressed as the _product of the ratio ε _i /ε ₀ of the strain distribution ε i resulting from an elastic-plastic analysis of a single crack condition and the strain ε ₀ in a healthy state, and the limit load (plastic collapse load) is evaluated from the obtained strain distribution.

Here, 2≦n.

(2) (1) is characterized in that the surface crack width _Lj in an elastic-plastic analysis having a single crack is used as a reference, and the position (coordinate) in the strain distribution for the surface crack width _Li to be evaluated is corrected by the surface crack width ratio _Lj / _Li .

(3) In (1), the aspect ratio a _j /L _j of the crack depth a _j and the plate thickness t _j , based on the surface crack width L _j when a non-penetrating crack of a surface elliptical crack is targeted, It is characterized in that the position (coordinate) in the strain distribution is corrected by the ratio of L _j /L _i with respect to the surface crack width L _i to be evaluated using an analysis result in which L _j /L _i is the same (Fig. 10).

(4) The limit load evaluation method has a database that stores coordinates normalized by strain distribution, stress distribution, and load and surface crack length ratio _lj /l _i based on each crack shape including aspect ratios _aj / _Lj and _Lj /L _i based on elastic-plastic analysis for multiple crack conditions such as surface elliptical cracks and through cracks, and includes a process of measuring cracks in a piping by non-destructive testing and obtaining the dimensions and arrangement of the cracks, and a process of estimating the fracture limit under multiple crack conditions from a single crack based on the limit load evaluation method described in any of (1) to (3).

ここで、εは全ひずみ、σは応力、Ｅはヤング率であり、ａ、ｂ、ｍは塑性特性項に対する任意の材料定数である。 (5) In (1), the elastic-plastic analysis is characterized in that the characteristics defined by Ramberg-Ossgood and power-law plasticity described in equations (2) and (3) are used.

where ε is the total strain, σ is the stress, E is Young's modulus, and a, b, and m are arbitrary material constants for the plastic characteristic terms.

ここで、２≦ｎである。 (6) A critical load evaluation device (for example, evaluation device 31) for a structure having a plurality of adjacent cracks, which includes a storage section 35 that stores elastic-plastic analysis results for a single crack under a plurality of shape conditions; Based on the information obtained from the information and the crack conditions to be evaluated obtained by the inspection device 30, the ratio ε i of the strain distribution ε _i as a result of elastic-plastic analysis for a single crack condition to the strain ε ₀ in a healthy state _. The strain distribution of a structure with n adjacent multiple cracks is predicted by correcting the strain ε _pre at an arbitrary position based on the equation (1) expressed as the product of /ε ₀ , and from the obtained strain distribution It is characterized by having a calculation unit 34 that estimates and evaluates the limit load (plastic collapse load).

Here, 2≦n.

1 Limit load evaluation system 11 Advance preparation process 12 On-site measurement process 13 Evaluation process 20 Flat plate 21, 22, 28 Penetrating crack 23 Displacement 30 Inspection device 31 Evaluation device (limit load evaluation device)
33 Communication section 34 Calculation section 35 Storage section 36 Crack position evaluation section 37 Strain distribution estimation section 38 Limit load evaluation section 39 Database section 40 Crack information section 41 Output section 42 Input section 43 Sign (strain distribution output position)
44 Sign (distance x from the crack edge)
a ₁ , a ₂ crack depth L ₁ , L ₂ , L ₃ surface crack width t plate thickness

Claims (6)

A method for evaluating the critical load of the ductile failure limit of a structure having n adjacent multiple cracks, the method comprising:
The strain ε at any position is expressed as the product of the ratio ε _i /ε ₀ of the strain distribution ε _i resulting from the elastic-plastic analysis for a single crack condition and the strain ε ₀ in a healthy state. A critical load evaluation method characterized by predicting the strain distribution of a structure having n adjacent multiple cracks by correcting _pre , and evaluating the critical load from the obtained strain distribution.

Here, 2≦n. It is characterized by correcting the position in the strain distribution with respect to the surface crack width L _i to be evaluated using the surface crack width ratio L _j /L _i based on the surface crack width L _j in elastic-plastic analysis having a single crack. The limit load evaluation method according to claim 1. The limit load evaluation method described in claim 1, characterized in that the surface crack width _Lj in the case of a non-penetrating surface elliptical crack is used as a reference, and analysis results in which the aspect ratios _aj / _Lj and _Lj / _Li with the crack depth _aj and plate thickness _tj are the same are used, and the coordinates in the strain distribution for the surface crack width _Li to be evaluated are corrected by the ratio _Lj / _Li . a database for storing coordinates normalized by strain distribution, stress distribution, load, and surface crack length ratio lj/lj based on each crack shape including aspect ratios _aj / _Lj and _Lj / _Lj , the coordinates being normalized by surface crack length ratio _lj / _lj and the surface ...
measuring cracks in the pipe by non-destructive testing to obtain dimensions and locations of the cracks;
A limit load evaluation method, comprising: a step of estimating a fracture limit under a multiple crack condition from a single crack based on the limit load evaluation method according to any one of claims 1 to 3. 2. The limit load evaluation method according to claim 1, wherein the elastic-plastic analysis uses characteristics defined by Rambelg-Ossgood and power law plasticity as shown in equations (2) and (3).

where ε is the total strain, σ is the stress, E is Young's modulus, and a, b, and m are arbitrary material constants for the plastic characteristic terms. 1. An apparatus for assessing limit loads of a structure having multiple closely spaced cracks, comprising:
A storage unit that stores elastic-plastic analysis results for a single crack under a plurality of geometric conditions;
Based on the information acquired from the memory unit and the crack conditions of the evaluation target obtained by the inspection device,
a calculation unit that predicts the strain distribution of a structure having n adjacent cracks by correcting the strain ε _pre at an arbitrary position based on equation (1) expressed as the product of the ratio ε _i /ε ₀ of the strain distribution ε _i resulting from an elastic-plastic analysis of a single crack condition and the strain ε ₀ in a healthy state, and estimates the limit load (plastic collapse load) from the obtained strain distribution.

Here, 2≦n.

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