JP4176777B2 - Method for predicting crack growth in gas turbine high-temperature parts and crack growth prediction apparatus using this method - Google Patents

Description

  The present invention relates to a method and an apparatus for predicting a probability distribution of a crack length of a fatigue crack generated in a high-temperature component of a gas turbine.

  Combustor inner cylinders, tail cylinders, turbine blades, stationary blades, and shrouds, which are high-temperature parts of gas turbines, are exposed to high-temperature and high-pressure combustion gas, and are subject to thermal stresses that fluctuate with starting and stopping. Susceptible to thermal fatigue and creep damage. In particular, turbine blades are severely damaged because they are also subjected to centrifugal force due to rotor rotation and gas bending force due to combustion gas, and strict maintenance management is required. Therefore, an inspection schedule is set at appropriate intervals, and parts are removed and inspected as necessary during inspection, and parts are replaced or repaired according to the degree of damage.

  On the other hand, since the inspection involves costs associated with the dismantling and inspection of the gas turbine device and power generation cannot be performed, it is desirable to increase the periodic inspection interval. For this reason, it is required to improve the durability of the gas turbine high-temperature components and to optimize the regular inspection interval. It is also desirable to reduce the cost and time required for repairing damaged high-temperature parts. For this purpose, a crack that is small enough not to expand to the extent that it loses its function by the next periodic inspection without repair. It is required to relax the repair standards to allow.

In order to meet the above-mentioned requirements, it is necessary to accurately predict the propagation behavior of a crack generated in a high-temperature part. Regarding the prediction of the crack length of high-temperature parts, for example, as disclosed in Patent Document 1 and Patent Document 2, the maximum crack length and oxide film thickness of the used parts (substantially synonymous with the high-temperature oxide layer of the present application) are set. A method of observing and predicting stress and temperature based on the result and predicting fatigue life based on the predicted value and a master curve obtained from a test piece is known. However, predicting the crack growth behavior based on the maximum crack length measurement result of the high-temperature parts used has the following problems.
JP-A-10-160646 Japanese Patent Laid-Open No. 9-19595

  The first problem is that in a high-temperature environment where a high-temperature oxidation layer (scale or altered layer generated by high-temperature oxidation) is generated, Although it is divided by the operation time and divided by the number of start / stop times, the latter means in the application of the present invention) although it is strongly dependent on the continuous operation time from start to stop The test data that reproduces this is not accumulated. That is, it is well known that the fatigue crack growth rate is affected by the holding time when the stress is held at the maximum or minimum load stress in the high-temperature fatigue test using a test piece (see Fig. 7). It is accumulating. However, the continuous operation time corresponding to the holding time in the actual operation of the gas turbine high-temperature parts may be several days, sometimes several months, and there is no test piece data on the effects of such long-time holding. It is difficult to statistically predict the fatigue crack growth behavior in the vicinity. This is because when a long-term holding fatigue test is performed using a test piece, it is necessary to perform a long-time holding load or strain waveform, which is a general-purpose hydraulic servo type fatigue used for fatigue testing. It is difficult to maintain the stress or strain at a constant value over a long period of time with the testing machine, the maintenance cost and labor cost of the testing machine for conducting the test are very high, and 1 for the cost. This is because only one test piece can be tested with one testing machine, and it takes time to collect data.

  The second problem is that the crack propagation behavior of high-temperature parts varies greatly as already disclosed in many known documents. This is probably because many influential factors have practically inevitable variations. Influential factors include high temperature combustion gas and cooling air temperature and heat transfer coefficient as environmental factors for high temperature components, thermal conductivity and thermal expansion coefficient as material characteristic factors, and fatigue crack initiation as a material strength characteristic factor in particular. There are dimensional tolerances such as wall thickness as a form factor, such as material parameters that define life (relationship between the number of repetitions and crack initiation life) and crack growth rate.

Therefore, the data on the maximum crack length or the maximum crack growth rate measured for a high-temperature part used in the operation of a gas turbine is based on the crack growth behavior when operating other high-temperature parts with different specifications or when operating conditions are changed. Cannot be used for prediction.

  In view of the above-mentioned problems, the first problem is to develop a reliable method for predicting fatigue crack propagation behavior in consideration of variations in various influencing factors. Specifically, based on reliable test results or analysis results, it is not a functional method that simply approximates the investigation results (inspection results) of actual parts with statistically processed regression curves. It is the development of a reliable prediction method that clarifies how the variation of various influencing factors is reflected in the variation of crack propagation behavior.

  The second issue is to reflect the influence of continuous operation time, which is considered to be the most uncertain factor among influence factors, in the prediction method based on the theory based on natural phenomena. It is. In other words, instead of using extrapolated values from the data on the effects of short-time holding obtained in fatigue tests of small test pieces, the effect of long-time holding (long continuous operation time) corresponding to actual operation is reflected. To develop a prediction method based on the collected data.

  The third problem is to develop a method for obtaining an appropriate repair criterion, that is, an allowable crack length at the time of inspection, using a crack growth curve obtained by a prediction method developed based on the above-mentioned problem. It is.

  The fourth problem is to develop a device that can predict a fatigue crack propagation behavior with high reliability that can solve the above-described problems.

  Means for solving the above-described problems will be described below.

  According to a first aspect of the present invention, a crack growth rate generated in a high-temperature part of a gas turbine is obtained, and a crack growth curve representing a crack length with respect to the number of start / stops is obtained from the growth rate. It is a crack growth prediction method that predicts changes in crack length. The crack growth rate is based on the start and stop of the gas turbine, the first growth rate increases the crack length, and the second growth rate increases the crack length based on the operation of the gas turbine. The second progress rate is calculated based on the maximum erosion depth due to high temperature oxidation in a time corresponding to the operation time of the gas turbine.

  The second invention is a method for predicting the probability distribution of the fatigue crack length occurring in a high-temperature component of a gas turbine by applying the Monte Carlo method, and includes the following steps. The first step is a step of obtaining a probability distribution of each parameter by statistically processing the actually measured value or the calculated value of the parameter for predicting the temperature and stress of the target part. In the second step, among the parameters for predicting the fatigue characteristics of the target part, the probability distribution of each parameter is obtained by statistically processing actual measurement values or calculated values of parameters other than the parameters statistically processed in the first step. This is a step for obtaining. In the third step, based on the probability distribution of each parameter obtained in the first and second steps, the value of each parameter is determined by a random number according to the probability distribution, and the determined parameters are combined, This is a step of creating a sufficient number of parameter combinations to calculate the probability distribution of fatigue crack length described later. In the fourth step, for each combination of parameters created in the third step, the numerical values of the respective parameters are input to perform heat and stress analysis, the temperature and stress of the target component are calculated, and the target In this step, the fatigue characteristics of each combination of parameters are calculated using the temperature and stress of the component and the operating conditions of the gas turbine, and a fatigue crack growth curve is obtained. The fifth step is a step of obtaining a fatigue crack length probability distribution by statistically processing the fatigue crack growth curve for each combination of parameters obtained in the fourth step.

In the fourth step, the crack growth rate used to calculate the fatigue crack growth curve is
Obtaining by combining the first growth rate at which the crack length increases based on the start and stop of the gas turbine and the second growth rate at which the crack length increases based on the operation of the gas turbine It is characterized by.

  In the present invention, the second progress rate may be calculated based on a maximum erosion depth due to high-temperature oxidation in a time corresponding to an operation time of the gas turbine.

  In the present invention, the second progress rate may be calculated as being proportional to a maximum erosion depth due to high-temperature oxidation in a time corresponding to an operation time from start to stop of the gas turbine.

  In the present invention, the second growth rate may be calculated based on high-temperature creep crack growth test data of a material constituting the part.

  In the present invention, the second growth rate is calculated based on the maximum erosion depth due to high-temperature oxidation in a time corresponding to the operation time of the gas turbine and high-temperature creep crack growth test data of the material constituting the part. You may do that.

  The third invention is a method of determining the allowable crack length at the time of inspection using the fracture limit crack length of the high-temperature component and the fatigue crack growth curve in the combination of each parameter obtained by the above-described method. . (1) In each of the fatigue crack growth curves, the crack length at the number of times of starting and stopping retroactive by the number of times of starting and stopping between inspections from the number of times of starting and stopping when the crack length becomes the failure limit crack length. Determining a probability distribution of the crack length, and (2) calculating a cost caused by the damage of the part and a cost required for repairing or replacing the part assuming a certain allowable crack length. (3) changing the assumed allowable crack length a plurality of times to calculate the cost caused by the breakage of the part and the cost required for repairing or replacing the part; and (4) calculated in the above step. In addition, based on the relationship between the allowable crack length and the cost caused by breakage of the component, and the relationship between the allowable crack length and the cost required for repair or replacement of the component, an appropriate allowable Determining a length, a method for determining an acceptable crack length at the time of tests, including.

  4th invention is an apparatus which estimates the probability distribution of the fatigue crack length which generate | occur | produces in the gas turbine high temperature components by applying the Monte Carlo method. This includes (1) an input unit for measured values or calculated values of parameters for predicting the temperature and stress of the target component and fatigue characteristics of the target components, and (2) a storage unit for storing the measured values or calculated values. (3) first calculation means for statistically processing the actual measurement value or calculation value stored in the storage means to obtain a probability distribution of each parameter; and (4) each of the calculation values obtained by the first calculation means. Based on the probability distribution of the parameters, the value of each parameter is determined by a random number according to the probability distribution, and a sufficient number of the above-described parameters are combined to calculate the probability distribution of the fatigue crack length described later. A second calculation means for creating a determined combination of parameters; and (5) a numerical value of each parameter is input for each combination of parameters created by the second calculation means, A third calculation means for performing temperature and stress analysis and calculating the temperature and stress of the target part in each parameter combination; and (6) in the combination of each parameter calculated by the operating condition of the gas turbine and the third calculation means. A fourth calculation means for calculating a fatigue characteristic in each parameter combination using the temperature and stress of the target part and obtaining a fatigue crack growth curve from the calculated value of the fatigue characteristic; and (7) a fourth calculation means. And fifth calculation means for obtaining a probability distribution of the fatigue crack length by statistically processing the obtained fatigue crack growth curve. Here, the fourth calculation means includes (a) the progress speed caused by the number of times the gas turbine is started and stopped, and (b) the operation time from the start to the stop of the gas turbine. High-temperature creep crack growth test data of the material that constitutes the part due to the growth rate calculated from the maximum erosion depth due to high-temperature oxidation at the corresponding time and (c) the operation time from start to stop of the gas turbine It is characterized by having a function to calculate by dividing into the progress rate calculated from.

  Further, in the present invention, based on the survey result data of the high-temperature parts actually used for operation, it is calculated from the relational expression between the operation time of the gas turbine and the maximum erosion depth or the maximum erosion depth due to the high-temperature oxidation. At least one of the progressed speeds may be corrected.

  According to the first invention, the fatigue crack growth curve is obtained using a crack growth rate equation obtained by synthesizing two types of growth rates, thereby predicting the influence of continuous operation time from start to stop. Therefore, the fatigue crack growth behavior corresponding to each plant and each operating condition can be estimated with high reliability.

  According to the second invention, the measured value or the calculated value of the parameter necessary for the calculation of the fatigue crack length is statistically processed, the parameter combination for performing the Monte Carlo method is created, the thermal and stress analysis is performed, and 2 Fatigue crack growth curves corresponding to each plant and each operating condition are obtained by obtaining a fatigue crack growth curve using the crack growth rate equation obtained by synthesizing different types of growth rates and obtaining a probability distribution of fatigue crack length. The probability distribution of the evolution behavior of can be estimated with high reliability.

  According to the third aspect of the present invention, the damage limit crack length of the high-temperature part and the fatigue crack growth curve obtained in the second aspect are used, and the cost caused by the part breakage and the repair or replacement of the part are required. By calculating the relationship between the cost and the allowable crack length and determining the allowable crack length at the time of inspection based on this, an appropriate repair standard can be set economically.

  According to the fourth aspect of the present invention, the input means for the measured or calculated values of the parameters necessary for predicting the temperature and stress of the target part and the fatigue characteristics of the target part, and the first calculation for obtaining the probability distribution of each parameter Means, a second calculation means for creating a combination of parameters for performing the calculation by the Monte Carlo method, a third calculation means for calculating temperature and stress by performing thermal and stress analysis, and obtaining a fatigue crack growth curve Crack growth rate, which includes fourth calculation means and fifth calculation means for obtaining a probability distribution of fatigue crack length, and is used for calculating a fatigue crack growth curve in the fourth calculation means. Is a time corresponding to the operation time of the gas turbine, which is caused by (a) the progress speed resulting from the number of times the gas turbine starts and stops, and (b) the operation time from the start to the stop of the gas turbine. The progress calculated from the maximum erosion depth due to high temperature oxidation and (c) the operation calculated from the high temperature creep crack growth test data of the material constituting the part due to the operation time from start to stop of the gas turbine By having a structure characterized by having a function to calculate according to speed, a large amount of data can be statistically and analyzed at high speed, and fatigue cracks corresponding to each plant and each operating condition can be processed. It is possible to obtain an apparatus capable of estimating the progress behavior with high reliability.

  Here, a method and apparatus for predicting the probability distribution of the crack length of a fatigue crack generated at the tip (top) of a turbine turbine stage rotor blade exposed to a very high temperature environment as a gas turbine high-temperature component is taken. However, it is basically the same as that relating to other high-temperature parts, except for those specifically mentioned.

  The turbine first stage blade is made of a Ni-base superalloy. As shown in FIG. 2, a crack is generated in the tip portion due to repeated thermal stress generated with the start and stop of the gas turbine, and the crack propagates in the rotor radial direction (the height direction of the moving blade). Here, the crack length means the amount of crack propagation that can be confirmed on the blade surface as shown in FIG. For parts and parts where crack growth in the thickness direction is a problem, the amount of progress in the depth direction may be defined. If the crack penetrates into the internal cooling passage as the crack progresses, the cooling function is lowered and the turbine efficiency is lowered. Therefore, it is considered that the function necessary for the moving blade is impaired. As described above, a state in which a necessary function is impaired or a state in which the operation of the gas turbine is hindered is regarded as a failure, and the crack length at this time is defined as a failure limit crack length.

  A flow for obtaining a probability distribution of fatigue crack length is shown in FIG. The procedure for estimating the crack length of the tip portion of the turbine first stage blade will be described with reference to this figure.

(First step)
Statistical processing of parameters necessary for predicting the temperature and stress of the chip portion and its vicinity is performed. Necessary parameters include material characteristic factors, boundary condition factors, and shape factors. Thermal conductivity, thermal expansion coefficient, elastic modulus, etc. as material characteristic factors, and gas pressure, gas temperature, heat transfer coefficient between combustion gas and component surface, gas pressure of cooling air, gas temperature as boundary condition factors The heat transfer coefficient between the cooling air and the component surface, and the shape factor includes the wall thickness of the target part. These data may include not only experimental or analytical data obtained only for carrying out the method of the present invention, but also data accumulated from the past and those obtained from known literature. It is better that the number of data is large for the statistical processing described later. The data for each of these parameters is a collection of raw data values that have not been statistically processed. These data are stored in each database system (data storage device) shown in FIG. 8, and parameters necessary for calculation can be read or displayed. Although common to the second step described later, if statistical analysis has already been performed and a probability distribution function parameter has been obtained, the step of statistical processing may be skipped.

  Next, statistical processing is performed on the raw data values, which are parameters necessary for the calculation and stored in the database, using a calculation means (computer). Here, statistical processing is to obtain statistical values such as the average value and standard deviation of each parameter so that it can be used for Monte Carlo simulation described later, or to apply a probability distribution of each parameter to an appropriate distribution function such as a normal distribution, This includes processing such as obtaining a parameter that defines the distribution function. The result of the statistical processing is stored in the database system and displayed on the display means as necessary.

(Second step)
Processing is performed on parameters for predicting the fatigue characteristics of the target part. Fatigue properties consist of properties related to crack initiation and properties related to crack propagation. In order to predict these characteristics, it is necessary to determine the fatigue crack initiation life and fatigue crack growth life. Thus, the relational expression between the stress intensity factor range (or the repeated J integral range) and the crack growth rate is applied. These equations are determined based on fatigue test data obtained from a small test piece taken from an actual part or a material material having a metal structure equivalent to that of the actual part.

As an example of the relational expression between the strain range and the fatigue crack initiation life, the Manson-Coffin equation is known,
Δεp × Nf ^ α = Ci (Δεp: plastic strain range, Nf: fracture life of small specimen)
It is expressed. Here, α and Ci are temperature-dependent material constants and are parameters for predicting the fatigue crack initiation life. α and Ci may be formulated as a function of temperature, and the constant of this equation may be used as a parameter for predicting the fatigue crack initiation life. Note that the fracture life Nf of a small test piece is generally considered to correspond to the crack generation life of an actual part. (For example, Non-Patent Document 1) A relational expression using stress instead of strain is also known.

Japan Society of Materials Science, “Basics of High Temperature Strength” p. 61, issued October 20, 1999

As an example of the relationship between the stress intensity factor and the crack growth rate, the following equation:
da / dN = Cp × ΔK ^ m (da / dN: crack growth rate, ΔK: stress intensity factor range)
Is known as the Paris rule. Here, Cp and m are material constants and depend not only on temperature but also on stress (or strain) waveforms. The stress (strain) waveform is a change in stress (strain) with time in one iteration shown in FIG. 7, and the stress change rate (Δσ / t1 and Δσ / t3) and the holding time t2 affect the crack growth rate. Effect. In the operation of the gas turbine, it means that the continuous operation time from the start to the stop corresponds to the holding time, and the crack growth speed varies depending on the continuous operation time. For example, Non-Patent Document 2 describes that the crack growth rate depends on temperature, and that the retention time dependency is very small at 800 ° C., but strongly depends on the retention time at 900 ° C. As a result of detailed investigation and investigation on the mechanism of crack propagation in the present invention, it has become clear that a plurality of mechanisms (phenomena) are involved. Details are as described below.
Proceedings of the Annual Meeting of the Japan Society of Mechanical Engineers 2002 (Vol. 2), p. 237-238

  In the present invention, a crack propagation mechanism shown in FIG. 3 is proposed based on the results of investigating cracks generated in a small test piece and a high-temperature part used for gas turbine operation. That is, in a state where a crack is generated, combustion gas enters from a crack opening in a high temperature environment, and oxygen is supplied from the crack initiation surface to the vicinity of the crack tip, thereby generating a high temperature oxide layer. Here, the high-temperature oxide layer (or simply an oxide layer) is a scale and an altered layer produced by high-temperature oxidation of a metal, and these are defined in JIS standards described later. The generated oxide layer is fragile, so it cracks due to stress fluctuation caused by temperature change, gas pressure change or centrifugal force change at stop or next start, and as a result, the crack grows by the thickness of the oxide layer To do. Then, the behavior that the crack propagates again in the base metal due to the stress fluctuation at the start / stop is repeated. Since the crack of the oxide layer is caused by a microstructural mechanism (for example, brittle slip surface separation) different from the crack growth of the base metal (for example, a slip mechanism peculiar to the metal) due to stress fluctuation, It is difficult to express by the known crack growth rate formula (Paris's law) that formulates the crack growth of metal due to stress fluctuation. In other words, it is judged that it is not appropriate to express the rate of progress by different mechanisms in a single expression.

  In addition, in the JIS standard (for example, JIS Z 2274) relating to fatigue tests, it is stipulated that extrapolation is not allowed in the prediction of fatigue characteristics based on discussions based on a large number of experimental data. If the basic idea of this rule is applied mutatis mutandis, the material constants Cp and m in long-time stress holding are predicted by extrapolation based on the material constants Cp and m obtained in the crack growth rate test with short-time stress holding. The conventional method of performing (for example, approximating with a regression curve) is considered to be unreliable.

  Therefore, in the present invention, first, the amount of crack growth in one cycle from start to stop through continuous operation is defined as (1) the amount of crack growth mainly in the base metal part due to the fluctuation of thermal stress due to start or stop of the gas turbine. And (2) the amount of crack propagation due to cracking of the brittle high-temperature oxide layer generated from the start to the stop. (1) depends on the number of times of starting and stopping the gas turbine and does not depend on the operation time between starting and stopping, and (2) indicates starting of the gas turbine. It can be expressed as a second growth rate (second crack growth rate) that does not depend on the number of stops but depends on the operation time between start and stop. Further, the second growth rate is characterized in that it is not data predicted by extrapolation based on data obtained in a short-time stress (strain) retention test. Details will be described later. By incorporating the formula obtained by faithfully modeling these physical phenomena into the prediction method, the crack growth behavior due to gas turbine operation is not approximated by a regression curve based on mere influence factors, but physically. It is possible to describe according to a meaningful expression, and it is possible to improve reliability.

  The second crack growth rate can be obtained from the result of the high temperature oxidation test. The high-temperature oxidation test is defined in JIS-Z-2281 and JIS-Z-2282, etc., but referring to this, the test equipment and test conditions are changed to reproduce the environment in the high-temperature combustion gas in the gas turbine. It is possible to do. A test piece taken from an actual part or a material having the same metal structure as that of the part is placed in a heating furnace and exposed to a high-temperature combustion gas maintained at a constant temperature. Thereafter, the test piece is taken out, cut and processed, and the cross section is observed to measure the maximum erosion depth. The high-temperature oxidation test does not change the test conditions depending on the external conditions (fluctuation in hydraulic pressure due to changes in atmospheric temperature or changes in the dimensions of the tester body) even when exposed for a long time over several days. In addition, there is no problem of deterioration of servo valves and hydraulic oil due to prolonged testing, and therefore the burden on the tester and test manager is extremely small. Since it can be put in a high temperature furnace, a lot of data can be obtained at once.

The high temperature oxidation test results are processed in the following procedure. The measured maximum erosion depth (the sum of the scale due to oxidation defined by JIS and the thickness of the altered layer) is obtained as a function of time and temperature, and the material constant is determined. Because high temperature oxidation is due to diffusion of oxygen atoms,
d = β × t ^ h (d: maximum erosion depth, t: time)
It can be expressed as. Here, β and h are material constants and depend on temperature. If the time t is a time corresponding to the continuous operation time between one start and stop determined by the operating conditions of the gas turbine, the maximum erosion depth generated at the time t is proportional to the second crack growth rate. Will be or will be equal. There are two reasons why it is “proportional” here. One is because the generation rate of the deteriorated layer in the vicinity of the crack tip as shown in FIG. 3 may be slower than the generation rate in the flat plate due to the shape of the crack, etc. The other reason is that This is because, depending on the environment, the maximum erosion depth may not be accurately measured depending on the state of scale adhesion. In such a case, an experientially reasonable proportional constant may be obtained and multiplied by the measured value. Empirically, it can be practically set to 1.

  Here, based on the data actually obtained, the method of the present invention, that is, the crack growth rate is obtained by synthesizing the first crack growth rate and the second crack growth rate, and this is shown in FIG. It is shown as “Calculation formula of crack growth rate considering high temperature oxidation”. Here, the former is the crack growth rate obtained based on the result of the crack growth test without stress holding, and the latter is the maximum erosion depth due to high temperature oxidation in the time corresponding to the continuous operation time from start to stop. It is the crack growth rate determined as equal (proportional constant is 1). In the figure, for comparison, the conventional method, that is, the crack growth rate is described according to the above-mentioned Paris law, and the fatigue crack growth test is performed by changing the stress holding time in the range of 0 to 1 hour. Crack growth predicted and calculated by applying material constants Cp and m obtained by extrapolation corresponding to the retention time in gas turbine operation (continuous operation time from start to stop) based on the obtained material constants The rate is shown as “Calculation formula of crack growth rate without considering high temperature oxidation”. The numerical values of the various parameters applied to the crack growth rate calculation are average values, and thus the calculated crack growth rate is the average value (50% probability) of variation. The plot in the figure is the crack growth rate obtained from the crack length measured during the periodic inspection, which is obtained by dividing the crack propagation amount during the periodic inspection by the number of start and stop during that period. From the figure, the crack growth rate according to the present invention faithfully reproduces the crack propagation behavior generated in actual operation, which proves that the idea of the present invention is valid.

  The second crack growth rate can be obtained by the high-temperature oxidation test using the test piece as described above. However, the investigation results of the scale and altered layer formation status in the actual parts that were operated (gas turbine operating time and high-temperature oxide layer) If the amount of formation (relationship with the maximum erosion depth) is sufficient, and the conditions of the high-temperature environment (temperature, etc.) are correctly grasped, it is possible to estimate only from the survey results of these actual parts. is there. What is necessary is just to correct | amend a proportionality constant as needed based on the investigation result of the high temperature oxidation layer (maximum erosion depth) produced | generated in the actual component. Actual parts have a history of long-term high-temperature retention that cannot be obtained by testing small test pieces, and can be obtained by long-term data interpolation rather than short-time extrapolation. It is convenient and reliable to collect.

  As described above, the crack propagation behavior strongly depends on the temperature and stress (or strain) waveforms (holding time, etc.), so fatigue caused by small test pieces corresponding to the temperature and stress (strain) waveforms of the actual parts. Although test data is required, if there is no corresponding data, it is possible to interpolate data corresponding to temperature and waveform from data of other conditions. Regarding the stress (strain) waveform, the operation condition, specifically, the operation time from the start to the stop is regarded as a constant stress (or strain) time (t2 in FIG. 7) and applied. Although there is an influence at the time of stress fluctuation (t1 and t3 in FIG. 7), in actual gas turbine operation, t1 and t3 are negligibly short as compared with t2, and thus ignoring is not a problem.

  Material parameters at specific temperatures related to these fatigue properties, α, Ci, Cp, m, β, h (Ci, m are constants not including the effect of holding time) or these parameters as a function of temperature The material constants are stored in the database system (storage means), like the parameters for predicting the temperature and stress in the first step, statistical processing is performed using the calculation means (computer), and the probability distribution Statistical parameters that can represent the function are determined and stored in the database system. Further, the apparatus is configured so that the above-described material parameters or correction coefficients are corrected as necessary every time inspection results and investigation results of parts used for operation are obtained. In particular, since the data on the maximum erosion depth has a great influence on the fatigue life, there is not always much data (especially data on actual parts) at present, so such a device is useful.

  The above is a description of crack growth in a very high temperature environment such as a turbine one-stage rotor blade. On the other hand, for the moving and stationary blades at the rear stage of the turbine exposed to a temperature range where high temperature oxidation is not dominant, the creep crack growth of the base metal part is dominant during continuous operation between start and stop, This must be taken into account as the second crack growth rate. The creep crack growth described here is constant during continuous operation even in a high temperature region where a high-temperature oxide layer does not occur in a Ni-based or Co-based superalloy having excellent high-temperature strength. It is a phenomenon that develops under tensile stress. Such a phenomenon is known as a normal creep phenomenon, but a specific alloy exhibits a rapid crack growth rate that deviates significantly from the extrapolated value from the low temperature side based on the Larson mirror parameter in a temperature range of about 700 ° C. This was found in the invention of the present prediction method. The parameter that defines the crack growth rate due to creep crack growth can be obtained by a creep crack growth test in which a small test piece is applied with a constant load for a long time. The creep crack growth test can be performed with a static load compared to the high-temperature fatigue crack growth test, which is an alternating load, so it is less expensive in terms of maintenance, operation, and maintenance of the testing machine, and the test jig is devised. By doing so, it is possible to test several specimens at the same time. It should be noted that this creep crack growth is likely to occur even at a high temperature where the formation of a high-temperature oxide layer is significant under the action of tensile stress. If it is small compared to, it can be ignored. Since the tip portion (the side exposed to the high-temperature combustion gas) of the first stage blade taken up in this embodiment is in a compressed state due to thermal stress, there is no need to consider creep cracks.

  As described above, creep crack growth is caused by a mechanism different from cracking of the high-temperature oxide layer, but the point that it depends on the operation time from start to stop is the same. Handled as a speed of progress.

(Third step)
Based on the statistical processing result of each parameter obtained in the first and second steps, data for obtaining a crack growth curve is created by applying the Monte Carlo method. The Monte Carlo method is a numerical calculation method that solves a problem by trial and error using random random variables such as random numbers, and as a means of predicting statistical data including variations as in the present invention. Sometimes it is used. (For example, Patent Document 3)

JP 2005-26250 A

  First, a number N of data combinations sufficient to perform statistical processing are created. FIG. 5 shows an example in which N combinations are created. (However, the numerical values in the table shown in FIG. 5 are standardized based on the average value and standard deviation in each parameter, and it is necessary to input and convert the average value and standard deviation when calculating.) The high-temperature gas pressure, thermal conductivity, etc. are randomly assigned based on the probability distribution of each parameter created in the first and second steps. The probability distribution almost coincides with the probability distribution (normal distribution as an example here) of each parameter created in the first and second steps. The reason for “substantially” is that the values that can actually be taken are discretized numerical values, and therefore do not exactly match. As a result, for parameters that have a small effect on fatigue properties, it is possible to reduce the number that can be taken in consideration of the time required for calculation. In addition, two parameters in the same combination that have no correlation, for example, high-temperature gas pressure, elastic modulus, and wall thickness change independently of each other. The parameter having a strong correlation is, for example, the relationship between Cp and m in the fatigue crack growth test described above. It is known that if Cp and m are obtained for various materials and plotted, Cp and m have a strong correlation. However, when Cp varies in the same material, m also has a strong correlation with Cp. This has been found in the present invention.

  The material characteristic value depends on the temperature, and the temperature of the target part varies depending on the variation of environmental factors in each combination. Therefore, it is preferable from the viewpoint of reliability that the material characteristic parameter is displayed as a function having the temperature as a variable. However, in the case of a parameter whose temperature dependence is small or, as a result, when the variation in temperature of the target part is small, the parameter may be independent of temperature for the purpose of shortening the calculation time. FIG. 5 illustrated is a value calculated on the assumption that the variation in temperature of the target part is small. The created N sets of data combinations are temporarily stored in the storage means.

(Fourth step)
The N sets of data created in the third step are input to obtain N crack growth curves. Specifically, the material characteristic factor, boundary condition factor, and shape factor data in the first set of combinations are input or read, thermal / stress analysis is performed, and the temperature distribution and stress distribution in the target part of the part are obtained. Using the obtained temperature distribution and stress distribution, parameters for predicting fatigue characteristics are input or read, and first, the number of start / stops at which a crack is generated is obtained from, for example, the aforementioned Manson-Coffin equation. Next, the obtained temperature distribution and stress distribution and the continuous operation time between one start and stop input as the operating conditions of the gas turbine are input, and the stress, temperature and material constant obtained in the second step are input. When the number of start and stop times after crack initiation is determined by the differential method, for example, by substituting these parameters into the first crack growth rate and second crack growth rate equations Find the relationship of crack length. The calculation is advanced, and when the crack length reaches the fracture limit crack length stored separately in the memory means, the calculation is terminated assuming that the crack growth curve of the first set combination is obtained, and the crack propagation is completed. The curve is displayed on the display means and simultaneously stored in the database system. Subsequently, the crack growth curve of the second set of combinations is obtained by the same procedure as described above using the data of the second set of combinations. In this way, the calculation is repeated to obtain N crack growth curves. The obtained curve is displayed by display means such as a display as shown in FIG. 6 (a), for example, and once stored in the storage means.

  The failure limit crack length that is the end point of the crack growth curve is the limit length that does not lose the function as a part if it is less than that length, and is determined based on the design unless there is a risk of scattering etc. Therefore, it is good also as a definite value without a dispersion | variation. However, if it is defined by the idea that the fracture limit crack length is determined by the low stress high cycle fatigue crack growth start limit due to resonance, for example, vibration stress due to resonance and critical stress intensity factor under crack growth (ΔKth) May be used as a parameter of a random variable, and the fracture limit crack length may be obtained as a parameter based on these parameters.

(Fifth step)
Statistical processing is performed using the N crack growth curves obtained in the fourth step, and a probability distribution of fatigue crack length is obtained. The probability distribution mentioned here is the probability distribution of the number of start / stop times at which the crack reaches a specific length or the probability distribution of the crack length at a specific number of start / stop times, and the specific crack length and the specific number of start / stop times. May be determined according to the application.

(Sixth step)
Based on the probability distribution of the fatigue crack length obtained in the fifth step, the optimum allowable crack length is obtained from the viewpoint of cost. Here, the allowable crack length is the maximum crack length that will not be repaired and discarded even if a crack is detected during inspection. In order to reduce the number of parts that are damaged before the next periodic inspection and at the same time reduce the frequency of breakage, it is necessary to set the allowable crack length smaller. On the other hand, the smaller the allowable crack length, the more Costs such as material costs and labor costs required for replacement (hereinafter referred to as repair costs) will increase. Therefore, it is required to obtain an optimum allowable crack length that minimizes the overall cost. Here, the cost as a whole is the sum of the repair cost and the cost due to breakage. The cost caused by the damage is a repair cost due to a failure of other parts and devices caused by the damage and a damage due to the operation stop, and includes a cost related to the business damage of the business operator. In addition, the cost caused by breakage is the actual damage amount multiplied by the probability of breakage. Increasing the allowable crack length increases the probability of breakage. Cost increases.

  First, a procedure for obtaining an allowable crack length for repair standard creation using the N crack growth curves obtained in the fifth step will be described below. The procedure is shown in FIG. The obtained crack growth curves differ in the number of start and stop times reaching the fracture limit crack length (Fig. 6 (a)), but each crack growth curve is moved in the horizontal axis (start and stop number axis) direction, The points at which the fracture limit crack length acr is reached are matched (FIG. 6B). Next, a crack length distribution (probability distribution of crack length) at the number of start / stop times retroactive by a predetermined number of start / stop times between periodic inspections (ΔNss) is obtained. Here, the allowable crack length ato is provisionally determined. If the crack length is longer than the allowable crack length ato, which was provisionally determined at the time of inspection, repair the crack or discard the part without repairing it, and take action if the crack length is shorter than the allowable crack length ato. It is assumed that it will be used as it is after the inspection. At this time, the ratio of cracks having an allowable crack length at or less is assumed to be p (corresponding to the area of the black portion of the probability distribution in FIG. 6). This means that of the N crack growth curves, N × p crack growth curves are shorter than the allowable crack length. Next, each crack propagation curve is moved in the direction of the horizontal axis (the axis of the number of start / stop times) so that the same number of start / stop times is obtained when the crack length is the allowable crack length ato (FIG. 6C). As is apparent from this display, the crack length of N × p crack growth curves among the N crack growth curves reaches the fracture limit crack length acr by the next periodic inspection. That is, when a crack having a provisionally determined allowable crack length ato has occurred in the part, the result is that the probability that damage will occur before the next periodic inspection is equal to p in FIG. 6B. Therefore, it was shown that the relationship between the allowable crack length at and the probability of occurrence of breakage can be obtained by the method shown in FIG. 6 from the crack growth curve group obtained in the fifth step and the operating conditions.

  The probability p of occurrence of breakage is obtained by changing the allowable crack length ato by trial and error by the above-described method, and thereby the relationship between the allowable crack length and the cost caused by the breakage can be obtained. On the other hand, since the number of parts to be repaired or replaced beyond the allowable crack length can be predicted from the accumulated inspection data of the high-temperature parts, the relationship between the allowable crack length and the repair cost can be obtained. From this, as shown in FIG. 9, the relationship between the allowable crack length and the overall cost can be obtained. Find the allowable crack length that minimizes the overall cost, and make this the optimum value for the allowable crack length. The allowable crack length determined in this way is corrected in consideration of measurement errors at the time of crack measurement, and further, an appropriate allowable crack length is determined in consideration of various circumstances, and is reflected in the repair criteria. Applies during periodic inspections. In addition, in order to automatically determine the optimum allowable crack length, especially for business damage included in the cost due to breakage, an expression that can be converted into an amount or numerical parameter is set in advance and saved in the device, What is necessary is just to read into a calculation means at the time of calculation.

  The above steps can be executed manually using a computer such as a large computer terminal or a personal computer. However, it is necessary to input various costs or cost calculation formulas that must be relied on in advance by human judgment. If it is carried out, it is possible to finally obtain the allowable crack length automatically by batch processing or the like. In the present invention, as shown in FIG. 8, it is composed of data reading means, storage means, input means, calculation means, display means, etc., and is a large quantity for statistical processing corresponding to each step described in the above-mentioned embodiment. Including a device capable of data processing. Furthermore, it is efficient if the apparatus shown in FIG. 8 is connected to an in-house LAN or Internet line so that data can be obtained from various experimental databases and databases of other institutions.

  Although the embodiment of the invention has been described based on an example with reference to the drawings, this is merely an example of the embodiment, and the present invention is not limited to this embodiment.

The figure which shows the procedure which calculates | requires the probability distribution of the fatigue crack length in this invention, and allowable crack length Diagram showing cracks in blade tip The figure which shows the mechanism of the crack generation in the high temperature component disclosed by this invention Figure showing the comparison between crack growth rate predicted by the method of the present invention and that of the conventional method The figure which shows the combination of N sets of parameters for calculating the probability distribution of fatigue crack length The figure which shows the method of calculating | requiring the relationship between permissible crack length and the probability of failure | damage by the time of the next inspection based on the calculated N crack growth curve group. Diagram explaining the waveform of stress (strain) The figure which shows the structure of the apparatus which estimates the probability distribution of the fatigue crack length in this invention Diagram explaining how to find the optimum allowable crack length

Claims (6)

The crack growth rate generated in the high-temperature part of the gas turbine is obtained, the crack growth curve representing the crack length with respect to the number of start / stops is obtained from the growth rate, and the crack length is calculated from the crack growth curve. In the crack growth prediction method that predicts changes,
Based on the start and stop of the gas turbine, the progress speed is combined with a first progress speed that increases the crack length and a second progress speed that increases the crack length based on the operation of the gas turbine. there is provided a method of Ru determined by,
The second evolution rate is
Performing a high-temperature oxidation test in a heating furnace using a test piece taken from the component or a material material having the same metal structure as the component; and
Obtaining a maximum erosion depth as a function of time and temperature based on the results of the high temperature oxidation test;
Calculating a maximum erosion depth due to high-temperature oxidation in a time corresponding to an operation time between one start and stop of the gas turbine based on the function ;
A crack growth prediction method characterized in that the second growth rate is obtained by a step of calculating as being proportional to or equal to the maximum erosion depth . A method for predicting a probability distribution of fatigue crack length generated in a high-temperature part of a gas turbine by applying a Monte Carlo method,
A first step of obtaining a probability distribution of each parameter by statistically processing an actual measurement value or a calculated value of a parameter for predicting the temperature and stress of the target part;
By statistically processing the measured values or the calculated values of the parameters for predicting the fatigue properties of the target component based on claim 1 can according crack growth prediction method, a second step of obtaining a probability distribution of each parameter,
Based on the probability distribution of each parameter obtained in the first and second steps, the value of each parameter is determined by a random number according to the probability distribution, and a combination of a plurality of parameters is created by combining the determined parameters. A third step,
For each combination of parameters created in the third step, the numerical value of each parameter is input to perform thermal and stress analysis, the temperature and stress of the target part are calculated, and the temperature and stress of the target part are calculated. A fourth step of calculating a fatigue characteristic in each parameter combination using a gas turbine operating condition and obtaining a fatigue crack growth curve;
A fifth step of obtaining a fatigue crack length probability distribution by statistically processing the fatigue crack growth curve for each combination of parameters obtained in the fourth step;
Including
The crack growth rate used to calculate the fatigue crack growth curve in the fourth step,
The first growth rate at which the crack length is increased based on the start and stop of the gas turbine and the second growth rate at which the crack length is increased based on the operation during one start / stop of the gas turbine A method for predicting the probability distribution of fatigue crack length, characterized by being obtained by combining Fatigue crack length according to the second expansion speed, to claim 2 and said maximum corrosion depth, and calculating on the basis of said high temperature component temperature creep crack propagation test of the material constituting the data To predict the probability distribution of The allowable crack length at the time of inspection is determined using the fracture limit crack length of the high-temperature component and the fatigue crack growth curve in each parameter combination obtained by the method according to claim 2 or 3. A method,
In each of the fatigue crack growth curves, the crack length at the number of start and stop times retroactive by the number of start and stop times between inspections from the number of start and stop times when the crack length becomes the failure limit crack length is determined. Obtaining a probability distribution of
Assuming a certain allowable crack length , using the probability distribution , determining the probability of failure after the number of start and stop between inspections;
Using the probability that the breakage will occur , calculating the cost caused by breakage of the high temperature component and the cost required to repair or replace the component;
Changing the assumed allowable crack length a plurality of times to calculate the cost caused by the breakage of the part and the cost required to repair or replace the part;
Determining calculated in the step, the costs incurred by the component failure, the allowable crack length the sum of the cost of repair or replacement of the component is minimized,
To determine the allowable crack length during inspection including A device that predicts the probability distribution of fatigue crack length generated in high-temperature components of a gas turbine by applying a Monte Carlo method,
An input means for measured or calculated values of parameters for predicting the temperature and stress of the target part and the fatigue characteristics of the target part;
Storage means for storing the actual measurement value or the calculated value;
First calculation means for statistically processing the actual measurement value or calculation value of the parameter stored in the storage means to obtain a probability distribution of each parameter;
In order to calculate the probability distribution of fatigue crack length by determining the value of each parameter with a random number according to the probability distribution based on the probability distribution of each parameter obtained by the calculation means, and combining the determined parameters Second calculating means for creating a combination of the determined parameters of:
For each combination of parameters created by the second calculation means, a numerical value of each parameter is input to perform heat and stress analysis, and a third temperature and stress of the target component in each parameter combination are calculated. Calculation means;
Fatigue characteristics in each parameter combination are calculated using the temperature and stress of the target part in each parameter combination calculated by the third calculation means and the operating conditions of the gas turbine, and the fatigue characteristics are calculated from the calculated fatigue characteristics. A fourth calculation means for obtaining a crack growth curve;
A fifth calculation means for obtaining a probability distribution of the fatigue crack length by statistically processing the fatigue crack growth curve obtained by the fourth calculation means;
The fourth calculation means includes a crack growth rate for calculating a fatigue crack growth curve,
The first rate of progress due to the number of start and stop times of the gas turbine;
A high temperature oxidation test is performed in a heating furnace using a test piece taken from the component or a material material having the same metal structure as the component, and the maximum erosion depth is determined based on the result of the high temperature oxidation test. A maximum erosion depth due to high-temperature oxidation in a time corresponding to an operation time between one start and stop of the gas turbine is calculated based on the function, and is proportional to or equal to the maximum erosion depth . The speed of development,
Due to the operating time of the gas turbine, the growth rate calculated from the high temperature creep crack growth test data of the material constituting the part,
Apparatus for predicting the probability distribution of the fatigue crack length, characterized that you have the ability to separately compute the. At least one of the relational expression between the operation time of the gas turbine and the maximum erosion depth or the growth rate calculated from the maximum erosion depth by the high temperature oxidation based on the survey result data of the high temperature parts actually used for operation The apparatus for predicting a probability distribution of fatigue crack length according to claim 5 , wherein:

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