JP2007198838A - Breakage probability calculation method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a breakage probability calculation method for analyzing stochastically a process from the generation of a plurality of cracks up to breakage, using a Monte Carlo simulation method. <P>SOLUTION: This breakage probability calculation method is provided with a crack number determination process 21, a trial frequency assigning process 22, a determination array process 23, a progress/coalescence analytical process 24 for receiving a result in the determination array process 23, and for analyzing a progress process and a coalescence process as to the plurality of cracks, using a theory of probability, and a breakage analytical process 25 for analyzing a breakage process of failing equipment or a member of a measuring object, using the theory of probability. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a failure probability calculation method for calculating a highly reliable failure probability using a Monte Carlo simulation method.

  In recent periodic inspections of nuclear power plants and the like, the risk of destruction of nuclear plant equipment or components has become an indicator for maintaining nuclear plant equipment or components safely and efficiently. The risk of failure is that if a crack due to stress corrosion cracking (SCC) is found in the equipment, the plant will operate and an excessive load such as an earthquake will be applied to the place where the crack has developed, causing damage. It is expressed as the product of the probability of destruction and damage caused by damage including the cost of restoration.

  However, since the maintenance of nuclear equipment has conventionally been in accordance with design and construction standards, even if cracks are detected in the inspection, the distribution of cracks, inspection capability, load conditions, Statistical data on material properties etc. has been deleted and is hardly accumulated. In addition, the cost required for evaluating the risk of destruction varies greatly between individual plants, and it is difficult to obtain information. For this reason, it was difficult to evaluate both the probability of destruction and the risk of destruction.

  For this reason, there are documents (for example, Non-Patent Document 1, Patent Documents 1 to 5 etc.) that show the concept of nuclear equipment or member destruction risk, but they are actively used for maintenance of actual plants. The stage has not been reached. Risks are also used for safety evaluation and safety design of nuclear power plants (for example, Patent Documents 6 and 7), but they are different from the risk of destruction phenomena caused by actual cracks. Emphasis is placed only on harsh events that affect sex.

On the other hand, maintenance based on risk has been studied in thermal power plants, and patent applications relating to maintenance based on the risk have been filed. However, it is not maintenance under systematic laws and standards such as maintenance standards in nuclear power plants, but the discretion of the operator is large and the maintenance management system is different. In addition, the crack progressability evaluation and the fracture probability evaluation are not predictions based on fracture mechanics, but are prediction methods based on a plurality of crack growth trends based on a lot of plant data. For this reason, in a nuclear power plant, since there is not much crack data like a thermal power plant, application to a nuclear power plant apparatus is practically difficult.
ASME Code Sec. XI, Code Case N-560, 577, 578. JP2005-3730 JP 2005-26250 A JP 2003-303243 A JP2003-4599 JP2004-191359 Japanese Patent Application No. 6-250348 JP 2002-73155 A

  The present invention has been made in consideration of such points, and probabilistically analyzes the process from the generation of multiple cracks to fracture using the Monte Carlo simulation method based on laboratory data. It is an object of the present invention to provide a destruction probability calculation method capable of calculating a destruction probability with high reliability.

The present invention relates to a fracture probability calculation method for calculating the probability that a device or member used in various plants such as a power plant such as a nuclear reactor or a chemical plant will be destroyed, and a crack generated on the surface in advance using a Monte Carlo simulation method. Crack number determination step for determining the number N, trial number specification step for specifying the total number of trials M for evaluating whether the device or member to be measured is destroyed by the crack, and occurrence of each crack determined for each trial A determining and arranging step of determining and arranging a position (x ⁱ , y ⁱ , z ⁱ ), a size / shape (a ₀ ⁱ , c ₀ ⁱ ) and a direction d ₀ ⁱ (i = 1, 2,..., N); In response to the results of the decision sequence process, in one trial, the progress and coalescence analysis process for analyzing the progress and coalescence process for any number of cracks using probability theory and the results of the progress and coalescence analysis process are received. A failure analysis process that uses probability theory to analyze the destruction process in which the device or member to be measured is destroyed, and the determination sequence process, the progress / merge analysis process, and the failure analysis process are repeated M times for all trials. In the failure probability calculation step, the failure probability P _f is calculated by dividing the number of trials m _F evaluated when the device or member to be measured is destroyed as a result of the evaluation in the failure analysis step by the total number of trials M. , The determination arrangement step includes the generation time t ₀ ⁱ , the generation position (x ⁱ , y ⁱ , z ⁱ ), the size / shape (a ₀ ⁱ , c ₀ ⁱ ) and the direction d ₀ ⁱ (i = 1, 1) for each crack. 2,..., N) are determined by the Monte Carlo simulation method, and the N cracks determined in the crack determination step are generated in the order of generation time t ₀ ⁱ (x ⁱ , y ⁱ , z ⁱ ). , Dimensions and shape (a ₀ ⁱ , c ₀ ⁱ ) And a crack arrangement step for rearranging the directions d ₀ ⁱ (i = 1, 2,..., N).

According to the present invention, in the determining and arranging step, the crack generation position (x ⁱ , y ⁱ , This is a fracture probability calculation method characterized by being used as z ⁱ ), dimension / shape (a ₀ ⁱ , c ₀ ⁱ ) and direction d ₀ ⁱ (i = 1, 2,..., N).

According to the present invention, in the determining and arranging step, the projection generation position, the projection size, and the projection direction of a plurality of cracks obtained by projecting from a plurality of principal stress directions orthogonal to the actual crack surface are respectively expressed as the crack generation position (x ⁱ , y ⁱ , z ⁱ ), dimensions / shape (a ₀ ⁱ , c ₀ ⁱ ) and direction d ₀ ⁱ (i = 1, 2,..., N), and a plurality of principal stresses in the fracture probability calculation step. The destruction probability corresponding to each projection occurrence position, projection size, and projection direction obtained for each projection from the direction is calculated, and the largest destruction probability is calculated as the destruction probability P in the destruction probability calculation step. _It is a destruction probability calculation method characterized by being used as _f .

The present invention is characterized in that, in the determining and arranging step, an actual crack generation position is calculated using projection generation positions of a plurality of cracks, and is used as a crack generation position (x ⁱ , y ⁱ , z ⁱ ). This is a destruction probability calculation method.

  The present invention calculates a fracture probability characterized by analyzing a progress process and a coalescence process in a progress / coalescence analysis process and analyzing a fracture process in a fracture analysis process for all cracks in one trial. Is the method.

  In the present invention, in the n-th trial, for a crack generated between 0 and a predetermined time interval ΔT × n, the progress process and the coalescence process are analyzed in the progress and coalescence analysis process, and the fracture process is performed in the fracture analysis process. Is a failure probability calculation method characterized in that is analyzed.

  According to the present invention, in the progress / merging analysis step, the crack progressing process and the coalescence process are analyzed using the first material characteristics and the first loading condition, and the first material characteristics and the first loading condition are analyzed by the progress / merging analysis. This is a fracture probability calculation method characterized in that it is the same for all cracks at any time of the progressing process and coalescence process analyzed in the process.

  According to the present invention, in the progress and coalescence analysis step, the crack progressing process and the coalescence process are analyzed using the first material characteristics and the first load condition, and the first load condition is performed once every time interval ΔT. Although it is the same in all the trial steps, the first material characteristic is a fracture probability calculation method characterized by being determined for each crack by the Monte Carlo simulation method even in the same trial.

  According to the present invention, in the progress / merging analysis step, the crack progressing process and the coalescence process are analyzed using the first material characteristic and the first load condition, and the first material characteristic is obtained once per time interval ΔT. Although it is the same in all the trial steps, the first load condition is a fracture probability calculation method characterized by being determined for each crack by the Monte Carlo simulation method even in the same trial.

  According to the present invention, in the progress / merging analysis step, the crack progressing process and the coalescence process are analyzed using the first material characteristic and the first load condition, and the first material characteristic and the first load condition are analyzed every time interval ΔT. This is a fracture probability calculation method characterized by being determined by the Monte Carlo simulation method for each crack even in one trial performed.

  According to the present invention, it is possible to provide a failure probability calculation method for calculating a highly reliable failure probability by probabilistically analyzing a process from occurrence of a plurality of cracks to failure using a Monte Carlo simulation method. it can.

First Embodiment Hereinafter, a first embodiment of a fracture probability calculating method according to the present invention will be described with reference to the drawings. Here, FIG. 1 to FIG. 4 are diagrams showing a first embodiment of the present invention.

  First, a calculation system 40 in which the destruction probability calculation method of the present invention is executed will be described with reference to FIG. The destruction probability calculation method of the present invention is used to calculate the probability that a reactor device or member will be destroyed.

As shown in FIG. 3, the calculation system 40 determines a crack to be generated using probability theory and arranges the determination sequence function 9, and the progress / cracking process is analyzed using probability theory. Combined analysis function 10, destruction analysis function 11 for analyzing the destruction process in which the device or member to be measured is destroyed using the establishment theory, and the number of trials evaluated that the device or member to be measured is destroyed the m _F and a fracture probability calculation function 12 for calculating the failure probability P _f by dividing the total number of trials.

  As shown in FIG. 3, the calculation system 40 has an SCC generation database (DB) 5 in which data related to crack generation time, dimensions / shape, generation position and direction are input, and data related to materials. A material database (DB) 6 and a load database (DB) 7 into which data relating to loads are input are provided. Among these, the material database 6 includes a first material property database 51 containing data related to crack propagation characteristics (first material properties) 41 and a second material containing data related to strength properties and fracture toughness (second material properties) 42. And a material property database 52. The load database 7 includes a first load condition database 53 relating to residual stress and operating load (first load condition) 43 and a second load condition database 54 relating to operating load and seismic load (second load condition) 44. ing.

  In FIG. 3, the determination array function 9 of the calculation system 40 determines a crack to be generated using the SCC generation database 5 containing data on the crack generation time, dimensions / shape, generation position, and direction.

  In FIG. 3, the progress / combination analysis function 10 of the calculation system 40 includes a first material property database 51 containing data on the crack propagation property (first material property) 41, residual stress and operating load (first load). Condition) Using the first load condition database 53 containing data on 43, the crack growth process and coalescence process are analyzed.

  In FIG. 3, the fracture analysis function 11 includes a second material characteristic database 52 containing data on strength characteristics and fracture toughness (second material characteristics) 42, and data on operating loads and seismic loads (second load conditions) 44. The failure process in which the device or member to be measured is destroyed is analyzed using the second load condition database 54 including

As shown in FIG. 3, the calculation system 40 has an analysis condition setting function 8 for inputting an analysis target and an analysis condition, and specifying database reference. Further, the calculation system 40 is configured to input data, numerical data with respect to temporal changes in individual crack dimensions, failure probability P _f at a certain time interval (see FIG. 4A), and states of a plurality of cracks 14 at a specified time (see FIG. 4 (b ₁ )-(b ₃ )) and a crack size change with respect to the time axis (see FIG. 4C).

4 (b ₁ )-(b ₃ ), the operation time t is t ₀ <t ₁ <t _2, and FIG. 4 (b ₁ ) shows a state in which the crack 14 has occurred, (B ₂ ) shows a state in which the generated crack 14 has progressed, and FIG. 4 (b ₃ ) shows a state in which the plurality of cracks 14 that have progressed are combined.

  Next, the destruction probability calculation method according to the present invention will be described.

  Since the number of cracks is also considered as a random variable, first, the number N of cracks generated on the surface is determined in advance using the Monte Carlo simulation method (crack number determination step 21) (see FIG. 1).

  Next, as shown in FIG. 1, the total number of trials M for evaluating whether the device or member to be measured is destroyed by the crack is designated (trial number designation step 22).

Next, as shown in FIG. 1 and FIG. 3, in the decision array function 9, the occurrence position (x ⁱ , y ⁱ , z ⁱ ), size / shape (a ₀ ⁱ , c ₀ ) determined for each trial. ⁱ ) and directions d ₀ ⁱ (i = 1, 2,..., N) are determined and arranged using probability theory (decision arrangement step 23). The determined arrangement step 23 will be described later.

  Next, as shown in FIG. 1 and FIG. 3, the progress / merging analysis function 10 receives the result of the determination sequence step 23 and uses the probability process for the progressing process and the coalescence process for a plurality of cracks in one trial. (Advance and merge analysis step 24).

  Next, as shown in FIGS. 1 and 3, the failure analysis function 11 analyzes the failure process in which the device or member to be measured is destroyed using the establishment theory in response to the result of the progress / merging analysis step 24. (Destruction analysis step 25).

  Next, as shown in FIG. 1, in response to the result of the breakdown analysis step 25, it is evaluated whether or not the device or member that is the measurement target has been destroyed (destruction evaluation step 26).

  As shown in FIG. 1, the above-described determination sequence step 23, progress / merging analysis step 24, fracture analysis step 25, and fracture evaluation step 26 are repeated for a predetermined number of trials M.

Finally, as shown in FIGS. 1 and 3, the failure probability calculation function 12 receives the result of the evaluation in the failure analysis step 25 and evaluates the number of trials m _F evaluated that the measurement target device or member is destroyed. the calculating the failure probability P _f by dividing the total number of attempts M (fracture probability calculating step 27). That is, the destruction probability P _f is defined as m _F / M. Note that if the number of trials evaluated that the device or member to be measured is not destroyed is m _NF , M = m _F + m _NF .

  Next, the above-described determination sequence step 23 will be described with reference to FIG.

In the decision arranging step 23, first, as shown in FIG. 2, the occurrence time t ₀ ⁱ , the occurrence position (x ⁱ , y ⁱ , z ⁱ ), size / shape (a ₀ ⁱ , c ₀ ⁱ ) and The direction d ₀ ⁱ (i = 1, 2,..., N) is determined by the Monte Carlo simulation method (crack determination step 31).

Next, as shown in FIG. 2, N cracks determined in the crack determination step 31 are generated in the order of generation time t ₀ ⁱ , the generation position (x ⁱ , y ⁱ , z ⁱ ), size / shape (a ₀ ⁱ , C ₀ ⁱ ) and the direction d ₀ ⁱ (i = 1, 2,..., N) are rearranged (crack arranging step 32).

Thus, in the order of occurrence time t ₀ ⁱ , the crack generation position (x ⁱ , y ⁱ , z ⁱ ), dimension / shape (a ₀ ⁱ , c ₀ ⁱ ) and direction d ₀ ⁱ (i = 1, 2, .., N) can be sorted to distinguish between cracks that have occurred and propagated by a predetermined time and cracks that have not occurred. For this reason, it is possible to analyze in detail a process in which a plurality of cracks are generated, propagated and merged with time.

Second Embodiment Next, a second embodiment of the present invention will be described with reference to FIG. The second embodiment shown in FIG. 5 is a projection of the projected crack 18 obtained by projecting from the principal stress σ ₁ direction orthogonal to the surface of the actual crack 17 in the decision arranging step 23 performed by the decision arranging function 9. The generation position, projection size, and projection direction are set as the crack generation position (x ⁱ , y ⁱ , z ⁱ ), size / shape (a ₀ ⁱ , c ₀ ⁱ ) and direction d ₀ ⁱ (i = 1, 2,... , N), and the others are substantially the same as those of the first embodiment shown in FIGS.

  In the second embodiment shown in FIG. 5, the same parts as those in the first embodiment shown in FIGS.

In the decision arrangement step 23 performed by the decision arrangement function 9, the projection generation position and projection of the projected crack 18 obtained from the principal stress σ ₁ plane 19 by projecting from the direction of the principal stress σ ₁ orthogonal to the surface of the actual crack 17. The dimension and the projection direction (see FIG. 5) are changed to the crack generation position (x ⁱ , y ⁱ , z ⁱ ), dimension / shape (a ₀ ⁱ , c ₀ ⁱ ) and direction d ₀ ⁱ (i = 1, 2, ..., N).

  For this reason, when analyzing the crack generation process, progress process, coalescence process, and fracture process, the variables used in the Monte Carlo simulation method can be reduced, and the analysis can be performed easily and quickly.

Third Embodiment Next, a third embodiment of the present invention will be described with reference to FIG. The third embodiment shown in FIG. 6 is obtained by projecting from the principal stress σ ₁ direction and the principal stress σ ₂ direction orthogonal to the actual surface of the crack 17 in the decision arrangement step 23 performed by the decision arrangement function 9. The projection generation position, projection size, and projection direction of the two types of projected cracks 18 and 20 are shown as crack generation position (x ⁱ , y ⁱ , z ⁱ ), size / shape (a ₀ ⁱ , c ₀ ⁱ ) and It is used as the direction d ₀ ⁱ (i = 1, 2,..., N). In the failure probability calculation step 27 performed by the failure probability calculation function 12, the failure probability corresponding to each projection generation position, projection size, and projection direction obtained for each projection from the main stress σ ₁ direction and the main stress σ ₂ direction. Are calculated, and the maximum destruction probability among the calculated destruction probabilities is used as the destruction probability P _f in the destruction probability calculation step 27. Other configurations are substantially the same as those of the second embodiment shown in FIG.

  In the third embodiment shown in FIG. 6, the same parts as those of the second embodiment shown in FIG.

In the failure probability calculation step 27 performed by the failure probability calculation function 12, each of the projection generation positions, the projection dimensions, and the projection directions determined for each projection from the main stress σ ₁ direction and the main stress σ ₂ direction is calculated. becomes maximum things out, it can be used as a failure probability P _f. For this reason, since it can be evaluated using the highest destruction probability P _f as to whether equipment or members used in the nuclear reactor are destroyed, it is possible to use these equipments and members while maintaining high safety. it can.

Fourth Embodiment Next, a fourth embodiment of the present invention will be described with reference to FIGS. In the fourth embodiment shown in FIG. 7, the generation of projection cracks 18 and 20 obtained by projecting from the principal stress σ ₁ direction and the principal stress σ ₂ direction in the decision arrangement step 23 performed by the decision arrangement function 9 is performed. The actual crack generation position is calculated using the position, and the actual crack generation position is used as the crack generation position (x ⁱ , y ⁱ , z ⁱ ). This is substantially the same as the second embodiment shown.

  In the fifth embodiment shown in FIGS. 7 to 9, the same parts as those in the second embodiment shown in FIG.

In the decision arrangement step 23 performed by the decision arrangement function 9, the actual occurrence position of the crack 17 is calculated, and the actual occurrence position of the crack 17 is used as the occurrence position (x ⁱ , y ⁱ , z ⁱ ) of the crack. Therefore, the failure probability P _f can be calculated with higher accuracy.

As a method of calculating the actual occurrence position of the crack 17 using the projection generation positions of a plurality of cracks, for example, the generation of the projected crack 18 obtained by projecting onto the principal stress σ ₁ surface 19 as shown in FIG. From the position (x ⁱ , y ⁱ , 0) and the generation position (0, y ⁱ , z ⁱ ) of the projected crack 20 obtained by projecting onto the principal stress σ2 surface 21 as shown in FIG. As shown, the actual occurrence position of the crack 17 can be calculated as (x ⁱ , y ⁱ , z ⁱ ).

7, a ₀ ⁱ indicates the depth of the i-th actual crack 17, a ₀ ^{i ′} indicates the depth of the i-th projected crack 18, and a ₀ ^{i ″} indicates the depth of the i-th projected crack 20. C ₀ ⁱ indicates the half length of the i-th actual crack 17, c ₀ ^{i ′} indicates the half length of the i-th projected crack 18, and c ₀ ^{i ″} indicates the i-th projected crack 20. The half length is shown.

Fifth Embodiment Next, a fifth embodiment of the present invention will be described. In the fifth embodiment, in one trial, all the cracks (N) are analyzed for the progress process and the coalescence process in the progress / coalescence analysis step 24 performed by the progress / coalescence analysis function 10. In the fracture analysis step 25, the fracture process is analyzed, and in the fracture evaluation step 26, it is evaluated whether or not the device or member to be measured is broken. The others are the first shown in FIGS. This is substantially the same as the embodiment.

When evaluating the soundness of equipment and members used in a nuclear reactor, it is generally evaluated by applying an excessive load such as an earthquake load at the end of the period when the crack is longest. For this reason, by performing the progress / merging analysis step 24, the fracture analysis step 25, and the fracture evaluation step 26 for all cracks (N) in one trial, a more accurate fracture probability P _f is obtained. Can be calculated.

Sixth Embodiment Next, a sixth embodiment of the present invention will be described with reference to FIG. The sixth embodiment shown in FIG. 10 is a progress / combination analysis step performed by the progress / combination analysis function 10 for a crack that occurs between 0 and a predetermined time interval ΔT × n in the n-th trial. 24. Analyzing the progress process and coalescence process in 24, then analyzing the fracture process in the fracture analysis step 25 performed by the fracture analysis function 11, and then whether the device or member to be measured is destroyed in the fracture evaluation step 26 The others are substantially the same as those of the first embodiment shown in FIGS.

  In the sixth embodiment shown in FIG. 10, the same parts as those in the first embodiment shown in FIGS. 1 to 4 are denoted by the same reference numerals, and detailed description thereof is omitted.

According to the present embodiment, as shown in FIG. 10, in the first trial, for the crack occurring between 0 and ΔT, first, the progress process and the coalescence process are analyzed in the progress and coalescence analysis process 24, and then In the fracture analysis step 25, the fracture process is analyzed, and then in the fracture evaluation step 26, it is evaluated whether or not the device or member to be measured is broken. Next, in the fracture probability calculation step 27, the fracture probability from 0 to ΔT P _f is calculated. In the second trial, as described above, for the crack occurring between 0 and ΔT × 2, the progress / merging analysis step 24, the fracture analysis step 25, the fracture evaluation step 26, and the fracture probability calculation step 27 are sequentially repeated. It is. In the n-th trial, for a crack occurring between 0 and a predetermined time interval ΔT × n, a progress / merging analysis step 24, a fracture analysis step 25, a fracture evaluation step 26, and a fracture probability calculation step 27 are sequentially performed. performed, it is repeatedly performed until it reaches the final time t _F predetermined.

Thus, since the change with respect to the driving _| operation time of the probability that the apparatus or member which is a measuring object will be destroyed can be calculated _| required according to time passage, the change of the destruction probability Pf according to time passage can be obtained. For this reason, it is possible to obtain a fracture probability P _f that is closer to the actual situation, and it is possible to reliably maintain the equipment and members.

Seventh embodiment

  Next, a seventh embodiment of the present invention will be described with reference to FIG. In the seventh embodiment, in the progress / merging analysis step 24 performed by the progress / merging analysis function 10, the same progress characteristic (first Material characteristics) 41 and residual stress and operating load (first load condition) 43 are used, and the others are substantially the same as those in the fifth embodiment.

In the progress / merging analysis step 24 performed by the progress / merging analysis function 10, the same progress characteristic (first material characteristic) 41, residual stress, and In order to calculate the fracture probability P _f using the operating load (first load condition) 43, the progress characteristic (first material characteristic) 41 and the residual stress and the operating load (first load condition) 43 are determined for each trial. it is not necessary to have eliminated, it is possible to easily and quickly calculate the failure probability P _f.

  Next, the flow of each process in the present embodiment will be described with reference to FIG.

  First, as shown in FIG. 11, a progress characteristic (first material characteristic) 41, a residual stress, and an operating load (first load condition) 43 are determined by a Monte Carlo simulation method.

  Next, as shown in FIG. 11, it is evaluated whether a crack has occurred by time t.

  If cracks do not occur, as shown in FIG. 11, the process of coalescence of the cracks that have occurred is analyzed, whether or not the cracks coalesce is determined, and then the number and size of the cracks are updated. .

  On the other hand, if a crack has occurred, as shown in FIG. 11, the crack growth process is analyzed using the Monte Carlo simulation method, and then the size of the crack is updated.

  Here, when the number of cracks Ni increased every trial reaches the total number of cracks N, as shown in FIG. 11, the cracks are generated as in the case where no cracks are generated. Analyze the coalescence process of cracks, determine if the cracks coalesce, then update the number and size of the cracks.

  On the other hand, when the number of cracks Ni has not reached the total number of cracks N, as shown in FIG. 11, it is evaluated whether a new crack has occurred due to the progressed crack. The above-described steps are repeated until no new cracks are generated or the number of cracks Ni reaches the total number of cracks N.

Also, as shown in FIG. 11, after the process of coalescence of the cracks that have occurred is analyzed, it is determined whether or not the cracks are coalesced, and the number and dimensions of the cracks are updated. Determine whether _F has been reached. Here, if not reached, the above-described process is repeated again from the time obtained by adding a predetermined time interval ΔT to the time t. On the other hand, if the time t has reached the final time t _F is specified in advance, and ends the progress-coalescence analysis step 24 at which point, the process proceeds to fracture analysis step 25.

Modification 7-1
Next, Modification 7-1 will be described with reference to FIG. In the modified example 7-1, the same residual stress and operating load (first load) are applied in the entire process of one trial performed at every time interval ΔT in the progress / joining analysis step 24 performed by the progress / joining analysis function 10. Condition) 43, and even in the same trial, the growth characteristics (first material characteristics) 41 determined by the Monte Carlo simulation method are used for each crack, and the others are the same as in the fifth embodiment. It is almost the same.

Due to the non-uniformity of the material at the microscopic level, the non-uniform distribution of chemical components, the non-uniform distribution of non-metallic inclusions, etc., the development characteristic (first material characteristic) 41 is in a random state. It has become. Here, as described above, by using the same residual stress and the operating load (first load condition) 43 in the whole process of one trial performed at every time interval ΔT, random progress characteristics (first material characteristics) ) 41 can be appropriately taken into account, and the failure probability P _f can be calculated with higher accuracy. On the other hand, even in the same trial, by using the progress characteristics (first material characteristics) 41 determined by the Monte Carlo simulation method for each crack, it is possible to maintain ease and speed.

  Next, the flow of each step in this embodiment will be described with reference to FIG.

  First, as shown in FIG. 12, the residual stress and the operating load (first load condition) 43 are determined by the Monte Carlo simulation method.

  Next, as shown in FIG. 12, it is evaluated whether a crack has occurred by time t.

  If cracks do not occur, as shown in FIG. 12, the process of coalescence of the cracks that have occurred is analyzed, whether or not the cracks coalesce is determined, and then the number and size of the cracks are updated. .

  On the other hand, when the crack has occurred, as shown in FIG. 12, the progress characteristic (first material characteristic) 41 is determined by the Monte Carlo simulation method.

  Next, as shown in FIG. 12, the crack growth process is analyzed using the Monte Carlo simulation method, and then the size of the crack is updated.

  Here, when the number of cracks Ni increased for each trial has reached the total number of cracks N, as shown in FIG. 12, it has occurred as in the case where the cracks described above have not occurred. Analyze the coalescence process of cracks, determine if the cracks coalesce, then update the number and size of the cracks.

  On the other hand, when the number of cracks Ni has not reached the total number of cracks N, as shown in FIG. 12, it is evaluated whether a new crack has occurred due to the progressed crack. The above-described steps are repeated until no new cracks are generated or the number of cracks Ni reaches the total number of cracks N.

Also, as shown in FIG. 12, after analyzing the coalescence process of the cracks that have occurred, determining whether or not the cracks coalesce, and updating the number and dimensions of the cracks, the time t is a predetermined final time t Determine whether _F has been reached. If not reached here, the above-described process is repeated again from the time obtained by adding a predetermined time interval ΔT to time t. On the other hand, if the time t has reached the final time t _F is specified in advance, and ends the progress-coalescence analysis step 24 at which point, the process proceeds to fracture analysis step 25.

Modification 7-2
Next, Modification 7-2 will be described with reference to FIG. In the modified example 7-2, the same progress characteristics (first material characteristics) 41 in all processes of one trial performed at each time interval ΔT in the progress / merging analysis process 24 performed by the progress / merging analysis function 10. Even in the same trial, the residual stress and the operating load (first load condition) 43 determined by the Monte Carlo simulation method are used for each crack, and the others are the same as in the fifth embodiment. It is almost the same.

In general, the residual stress and the operating load change depending on the progress of cracks, that is, the time (note that the magnitude of the load generated depends on the time when the earthquake motion is expected to occur). Here, as described above, by using the same progress characteristic (first material characteristic) 41 in all the processes of one trial performed every time interval ΔT, the residual stress and the operating load (first Load condition) 43 can be appropriately taken into consideration, and a more accurate failure probability P _f can be calculated. On the other hand, even in the same trial, by using the residual stress and operating load (first load condition) 43 determined by the Monte Carlo simulation method for each crack, it is possible to maintain ease and speed.

  Next, the flow of each step in the present embodiment will be described with reference to FIG.

  First, as shown in FIG. 13, a progress characteristic (first material characteristic) 41 is determined by a Monte Carlo simulation method.

  Next, as shown in FIG. 13, it is evaluated whether a crack has occurred by time t.

  If no crack has occurred, as shown in FIG. 13, the process of coalescence of the cracks that have occurred is analyzed, whether or not the cracks are coalesced, and then the number and size of the cracks are updated. .

  On the other hand, when the crack has occurred, as shown in FIG. 13, the residual stress and the operating load (first load condition) 43 are determined by the Monte Carlo simulation method.

  Next, as shown in FIG. 13, the crack growth process is analyzed using the Monte Carlo simulation method, and then the crack dimensions are updated.

  Here, when the number of cracks Ni increased every trial reaches the total number of cracks N, as shown in FIG. 13, the cracks are generated as in the case where the cracks are not generated. Analyze the coalescence process of cracks, determine if the cracks coalesce, then update the number and size of the cracks.

  On the other hand, when the number of cracks Ni has not reached the total number of cracks N, as shown in FIG. 13, it is evaluated whether a new crack has occurred due to the progressed crack. The above-described steps are repeated until no new cracks are generated or the number of cracks Ni reaches the total number of cracks N.

Also, as shown in FIG. 13, after the coalescence process of the cracks that have occurred is analyzed, it is determined whether or not the cracks are coalesced, and the number and dimensions of the cracks are updated. Determine whether _F has been reached. If not reached here, the above-described process is repeated again from the time obtained by adding a predetermined time interval ΔT to time t. On the other hand, if the time t has reached the final time t _F is specified in advance, and ends the progress-coalescence analysis step 24 at which point, the process proceeds to fracture analysis step 25.

Modification 7-3
Next, Modification 7-3 will be described with reference to FIG. Modification 7-3 is determined by the Monte Carlo simulation method for each crack even in one trial performed at each time interval ΔT in the progress / coalescence analysis step 24 performed by the progress / coalescence analysis function 10. The progress characteristics (first material characteristics) 41 and the residual stress and operating load (first load condition) 43 are used, and the others are substantially the same as in the fifth embodiment.

Due to the non-uniformity of the material at the microscopic level, the non-uniform distribution of chemical components, the non-uniform distribution of non-metallic inclusions, etc., the development characteristic (first material characteristic) 41 is in a random state. It has become. Further, the residual stress and the operating load change with the progress of cracks, that is, with time. Here, as described above, even in one trial performed at each time interval ΔT, the propagation characteristic (first material characteristic) 41 determined by the Monte Carlo simulation method for each crack, the residual stress, and the operating load ( By using the first load condition (43), it is possible to appropriately take into account the random development characteristics (first material characteristics) 41 and the residual stresses and operating loads (first load conditions) 43 that change with time. Therefore, it is possible to calculate the fracture probability P _f with higher accuracy.

  Next, the flow of each process in the present embodiment will be described with reference to FIG.

  First, as shown in FIG. 14, it is evaluated whether a crack has occurred by time t.

  If cracks do not occur, as shown in FIG. 14, analyze the coalescence process of the cracks that occur, determine whether the cracks coalesce, and then update the number and size of the cracks .

  On the other hand, when the crack has occurred, as shown in FIG. 14, the progress characteristic (first material characteristic) 41 and the residual stress and the operating load (first load condition) 43 are determined by the Monte Carlo simulation method. .

  Next, as shown in FIG. 14, the crack growth process is analyzed using the Monte Carlo simulation method, and then the size of the crack is updated.

  Here, when the number of cracks Ni increased for each trial reaches the total number of cracks N, as shown in FIG. 14, the cracks are generated as in the case where the cracks are not generated. Analyze the coalescence process of cracks, determine if the cracks coalesce, then update the number and size of the cracks.

  On the other hand, when the number of cracks Ni has not reached the total number of cracks N, as shown in FIG. 14, it is evaluated whether a new crack has occurred due to the progressed crack, and thereafter, the crack progresses. The above-described process is repeated until no new cracks are generated or the number of cracks Ni reaches the total number of cracks N.

Further, as shown in FIG. 14, after the coalescence process of the cracks that have occurred is analyzed, it is determined whether or not the cracks are coalesced, the number and dimensions of the cracks are updated, and then the time t is a predetermined final time t Determine whether _F has been reached. If not reached here, the above-described process is repeated again from the time obtained by adding a predetermined time interval ΔT to time t. On the other hand, if the time t has reached the final time t _F is specified in advance, and ends the progress-coalescence analysis step 24 at which point, the process proceeds to fracture analysis step 25.

Note In the embodiment described above, after determining the sequence step 23, in the development-coalescence analysis step 24, after analyzing the end time t _F at a single attempt, performs destructive analysis step 25 and fracture evaluation step 26, destruction showed manner for obtaining the probability P _f, not limited thereto, sequenced step 23, the progress-coalescence analysis step 24 performs a destructive analysis step 25 and failure assessment step 26, after obtained the failure probability P _f, It may be a flow in which the process is repeated from the decision arranging step 23 again by changing the time interval ΔT.

The flowchart which shows 1st and 5th embodiment of the destruction probability calculation method by this invention. The flowchart which shows the determination arrangement | sequence process in the destruction probability calculation method of 1st Embodiment of a destruction probability calculation method. Schematic which shows the calculation system which performs the destruction probability calculation method by this invention. (A) to (c) is a schematic diagram for explaining one function of a calculation system for executing a fracture probability calculation method according to the present invention. Schematic for demonstrating 2nd Embodiment of the destruction probability calculation method by this invention. Schematic for demonstrating 3rd Embodiment of the destruction probability calculation method by this invention. Schematic for demonstrating 4th Embodiment of the destruction probability calculation method by this invention. Schematic which shows the state which projected the crack from principal stress (sigma) ₁ direction in 4th Embodiment of the fracture probability calculation method by this invention. Schematic which shows the state which projected the crack from main stress (sigma) ₁ direction and main stress (sigma) ₂ direction in 4th Embodiment of the fracture probability calculation method by this invention. The flowchart which shows 6th Embodiment of the destruction probability calculation method by this invention. The flowchart which showed the progress and uniting analysis process in 7th Embodiment of the fracture probability calculation method by this invention. The flowchart which showed the progress and coalescence analysis process in the modification 7-1 of the destruction probability calculation method by this invention. The flowchart which showed the progress and coalescence analysis process in the modification 7-2 of the destruction probability calculation method by this invention. The flowchart which showed the progress and coalescence analysis process in the modification 7-3 of the destruction probability calculation method by this invention.

Explanation of symbols

14 crack 21 crack number determination process 22 trial number designation process 23 determination arrangement process 24 progress and coalescence analysis process 25 fracture analysis process 26 fracture evaluation process 27 fracture probability calculation process 31 crack determination process 32 crack arrangement process 41 first material property 42 first Two material characteristics 43 First load condition 44 Second load condition

Claims (10)

In the destruction probability calculation method for calculating the probability that the device or member is destroyed,
A crack number determination step for determining the number N of cracks generated on the surface in advance using a Monte Carlo simulation method;
A trial number designating step for designating the total number of trials M for evaluating whether the device or member to be measured is destroyed by the crack;
The crack generation position (x ⁱ , y ⁱ , z ⁱ ), dimension / shape (a ₀ ⁱ , c ₀ ⁱ ) and direction d ₀ ⁱ (i = 1, 2,..., N) determined for each trial are determined. A determining sequence step of determining and sequencing;
In response to the result of the determination sequence process, in one trial, the progress and coalescence analysis process for analyzing the progress process and coalescence process for any plurality of cracks using probability theory,
A failure analysis process that analyzes the failure process of the device or member being measured using probability theory in response to the results of the progress and coalescence analysis process,
The determination sequence process, the progress / coalescence analysis process, and the fracture analysis process are repeated for all trials M,
In the failure probability calculation step, as a result of the evaluation of the failure analysis step, the failure probability P _f is calculated by dividing the number of trials m _F evaluated that the measurement target device or member is destroyed by the total number of trials M,
The decision sequence step is
Generation time t ₀ ⁱ , generation position (x ⁱ , y ⁱ , z ⁱ ), size / shape (a ₀ ⁱ , c ₀ ⁱ ) and direction d ₀ ⁱ (i = 1, 2,..., N) for each crack A crack determination step for determining the thickness by a Monte Carlo simulation method;
The N cracks determined in the crack determination step are generated in the order of generation time t ₀ ⁱ , the generation position (x ⁱ , y ⁱ , z ⁱ ), size / shape (a ₀ ⁱ , c ₀ ⁱ ), and direction d ₀ ^i. A fracture probability calculation method comprising: a crack arrangement step for rearranging (i = 1, 2,..., N). In the determining and arranging step, the crack generation position (x ⁱ , y ⁱ , z ⁱ ) is determined from the crack generation position, projection size, and projection direction obtained by projecting from the principal stress direction orthogonal to the actual crack surface. 2. The fracture probability calculation method according to claim 1, wherein the fracture probability calculation method is used as dimensions, shapes (a ₀ ⁱ , c ₀ ⁱ ) and directions d ₀ ⁱ (i = 1, 2,..., N). In the determining and arranging step, the crack generation positions (x ⁱ , y) are respectively expressed as projection generation positions, projection dimensions, and projection directions of a plurality of cracks obtained by projecting from a plurality of principal stress directions orthogonal to the actual crack surface. ⁱ , z ⁱ ), dimension / shape (a ₀ ⁱ , c ₀ ⁱ ) and direction d ₀ ⁱ (i = 1, 2,..., N),
In the fracture probability calculation step, the fracture probability corresponding to each projection generation position, projection size, and projection direction obtained for each projection from a plurality of principal stress directions is calculated, and becomes the maximum among the calculated fracture probabilities. things, fracture probability calculation method according to claim 2, which comprises using as the failure probability P _f in failure probability calculating step. 4. In the determining and arranging step, an actual crack generation position is calculated using projection generation positions of a plurality of cracks, and is used as a crack generation position (x ⁱ , y ⁱ , z ⁱ ). Destruction probability calculation method described.   5. The progress process and coalescence process are analyzed in the progress / coalescence analysis step for all cracks in one trial, and the fracture process is analyzed in the fracture analysis process. The destruction probability calculation method according to any one of the above.   In the n-th trial, for the crack that occurs between 0 and a predetermined time interval ΔT × n, the progress process and coalescence process are analyzed in the progress / coalescence analysis process, and the fracture process is analyzed in the fracture analysis process. The destruction probability calculation method according to any one of claims 1 to 4, wherein the destruction probability is calculated. In the progress and coalescence analysis step, the crack growth process and coalescence process are analyzed using the first material characteristics and the first load condition,
The first material characteristic and the first load condition are the same for all cracks at any time of the progress process and the coalescence process analyzed in the progress / coalescence analysis process. The destruction probability calculation method according to any one of 5 and 6. In the progress and coalescence analysis step, the crack growth process and coalescence process are analyzed using the first material characteristics and the first load condition,
This first load condition is the same in all steps of one trial performed every time interval ΔT,
7. The fracture probability calculation method according to claim 5, wherein the first material property is determined by a Monte Carlo simulation method for each crack even in the same trial. 8. In the progress and coalescence analysis step, the crack growth process and coalescence process are analyzed using the first material characteristics and the first load condition,
This first material property is the same in all steps of one trial performed every time interval ΔT,
7. The fracture probability calculation method according to claim 5, wherein the first load condition is determined by a Monte Carlo simulation method for each crack even in the same trial. 8. In the progress and coalescence analysis step, the crack growth process and coalescence process are analyzed using the first material characteristics and the first load condition,
7. The method according to claim 5, wherein the first material property and the first load condition are determined by a Monte Carlo simulation method for each crack even in one trial performed every time interval ΔT. The destruction probability calculation method according to claim 1.

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