CN113408048A - Method for predicting hole edge multi-crack propagation - Google Patents
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Abstract
The invention provides a method for predicting hole edge multi-crack propagation, which comprises the following steps: s1, setting a plurality of holes, and taking two points from the horizontal positions of two sides of each hole to form the following test points: A. b, C, D, E, F, ·, N; s2, performing a simulation experiment on the initial crack propagation life of the test points by using a Monte Carlo simulation method to generate the initial crack propagation life of each test point: n is a radical of00,N01,N02,N03,N04,N06…Nn. The invention has the beneficial effects that: the distribution of the variables does not need to be approximate, and the variable simulation distribution can be completed through a sampling means; correlations and dependencies between individual variables can be modeled; accuracy can be ensured by increasing the number of cycles; the model can be changed rapidly to carry out variable parameter analysis.
Description
Technical Field
The invention belongs to the field of safety verification, and particularly relates to a method for predicting hole edge multi-crack propagation.
Background
The aircraft is used as a bearing main body for civil aviation transportation, plays a vital role in a transportation system, and not only causes huge economic loss to enterprises such as airlines when an accident occurs in the operation process of the aircraft, but also threatens the life safety of the public and damages the public interests. In order to improve the safety level of civil aviation transportation and keep the inherent airworthiness of the whole life cycle of the aircraft, continuous and effective safety evaluation on the civil aviation aircraft is a necessary work. The Safety evaluation of the civil aircraft runs through the whole life cycle of the aircraft, System Safety Analysis (SSA) needs to be carried out in the design stage, and the inherent Safety level of the aircraft is determined; in the operation stage, civil aircrafts are subjected to risk events such as corrosion, fatigue damage, heavy landing, lightning stroke and the like, and the risk level of the aircraft structure shows an ascending trend along with the increase of service time. Once structural damage caused by various risk events occurs, structural failure may be caused, and a catastrophic accident may be caused.
The civil aviation manufacturing industry of China starts late, at present, ARJ-21 airplanes enter a continuous passenger carrying operation stage, C919 airplanes enter a trial flight evidence obtaining stage, and domestic wide-body airplane projects start to be orderly promoted, but the research and development and the manufacturing of domestic civil airplanes are still in a starting stage, and a systematic operation risk assessment method and a systematic operation risk assessment flow are not established. At present, the research on the continuous security analysis and evaluation of the civil aircraft in the operation stage is not developed at home, and the gap is urgently needed to be filled along with the increasing investment of the domestic civil aircraft in operation.
Disclosure of Invention
In view of the above, the present invention is directed to a method for predicting multi-crack propagation at a hole edge, so as to solve the above-mentioned disadvantages.
In order to achieve the purpose, the technical scheme of the invention is realized as follows:
a method of predicting hole-edge multi-crack propagation, comprising the steps of:
s1, setting a plurality of holes, and taking two points from the horizontal positions of two sides of each hole to form the following test points:
A、B、C、D、E、F、···、N；
s2, performing a simulation experiment on the initial crack propagation life of the test points by using a Monte Carlo simulation method to generate the initial crack propagation life of each test point:
N00,N01,N02,N03,N04,N06…Nn；
s3, defining the initial crack life as the cycle number of the crack when the crack develops from 0 to Xmm, and determining that the logarithmic life of the initial crack satisfies N based on the experiment0A log normal distribution of N (μ, σ);
s4, setting the appointed circulation times Nd，NdAlso referred to as a specified lifetime, the number of cycles per test point reaches NdThe simulation cycle is ended no matter how the crack is expanded;
s5, judging that the number reaches NdThe condition of crack generation of the test point is used for extending the crack of the test point to the initial life and NdMaking comparison, if less than NdIt is considered that cracks occur at this position, and if it exceeds NdWhen the specified service life is determined, no crack is generated at the position;
s6, sequencing the initial life of the cracks of the test points from small to large, and setting the initial life of the crack expansion as the minimum value N of the initial life in the initial life of the crack expansion of the test pointsminSetting the length of the position at the beginning to be Xmm, if the service lives of other positions are the same, simultaneously setting the length to be Xmm, and setting the service lives of other positions to be more than NminThe position of (a) indicates that the crack size is 0;
s7, sequencing the initial life of crack propagation of the test points from small to large, and comparing the rest test points in the step S6 by taking the initial life of crack propagation of each test point as a reference in sequence;
s8, crack propagation calculation is carried out on the position, larger than 0, of each crack obtained in the steps S6 and S7, the crack growth length da of each test point needs to be calculated for increasing Z of the set cycle number, and the following formula is utilized:
wherein C is 2.34 × 10-8M is 3.427, dN is Z;
s9, when the length of each crack is obtained by each inner layer circulation, adding judgment:
g305 ═ 305 (97.74-15 — total crack length per test point)/97.74;
s10, setting a G judgment rule based on the G value aiming at the G value obtained in the step S9, and marking the marking result as safe/unsafe according to the G judgment rule;
s11, counting the times of safety and insecurity, displaying the times of each insecurity reason, and calculating the failure probability of the test piece, wherein the failure probability is the final result of the program, and the calculation formula of the failure probability is as follows:
where N is the total number of external cycles.
Further, the method of calculating Δ K in step S8 is:
when reaching the cycle number NdWhen the crack length is 0, the delta K is 0;
when reaching the cycle number NdWhen the crack length is greater than 0:
ΔK＝β*108*(π*(2.5+a))0.5 (2)
wherein a is the cycle number reaching the cycle number N of the test point of the hole edgedThe beta factor of the crack length is B1, B2, B3 and B4 in a form of continuous multiplication, and pairs of B1, B2, B3 and B4Different forms of cracks, differing in their coefficients.
Further, the calculation method of B1:
where x is (a +2.5)/2.5, a is the current crack length, 2.5 denotes the hole radius, Fh2Coefficient B1 used for hole edge single crack;
calculation method of B2:
where x is (a +2.5)/2.5, a is the current crack length, 2.5 denotes the hole radius, Fh1Coefficient B2 used for hole-edge double cracking;
calculation method of B3:
wherein x is 5/(15-1.5a), FohAIs the impact factor B3 for adjacent wells;
calculation method of B4:
wherein x is 2 × a1/(12-a1-a2), a1 is the crack length at the position to be determined, and a2 is the crack length of the hole edge adjacent to the crack development direction; fOCAIs the adjacent crack influencing factor B4.
Further, when B3 is calculated, B3 judgment method is introduced: when a exceeds the specified length, the internal cycle is ended in advance before the specified cycle times are reached, the result is marked as unsafe, and the reason is marked as the length of the single crack exceeds the limit;
when B4 is calculated, a B4 judgment method is introduced: when the length of 12-a1-a2 is less than the specified length, the internal cycle is ended in advance before the specified number of cycles is reached, and the result is marked as unsafe, and the reason is marked as the single crack length is exceeded.
Compared with the prior art, the method for predicting the hole edge multi-crack propagation has the following beneficial effects:
the distribution of the variables does not need to be approximate, and the variable simulation distribution can be completed through a sampling means; correlations and dependencies between individual variables can be modeled; accuracy can be ensured by increasing the number of cycles; the model can be changed rapidly to carry out variable parameter analysis. In the field of security evaluation, the Monte-Carlo method has an advantage over analysis methods such as fault tree and markov, in that more complex system behaviors such as random propagation of multiple cracks and structural failure behaviors can be simulated, and accurate evaluation is difficult using a general probabilistic method. Therefore, when the Monte-Carlo method is adopted to predict the crack propagation failure of the multi-crack at the hole edge, the operation process of the simulation experiment needs to be optimized, the operation amount is reduced and the operation efficiency is improved under the condition of ensuring the precision.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate an embodiment of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a schematic diagram of three wells and a test point ABCDEF of the three wells used in the example;
FIG. 2 is a schematic diagram of a linear fitting process of scatter data during B1 calculation;
FIGS. 3 and 4 are schematic diagrams illustrating the relationship between the boundary correction factor and the geometric parameter in the calculation process of B2;
FIG. 5 is a flow chart of a method of predicting hole-edge multi-crack propagation.
Detailed Description
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
The method has an inner layer of circulation and an outer layer of circulation, wherein the outer layer of circulation is a Monte Carlo simulation experiment and is mainly used for generating an initial crack propagation life, the number of circulation times of the outer layer of circulation is set to be 10 ten thousand times in the simulation experiment (the number can be adjusted according to simulation conditions and simulation precision), and the specific process is as follows:
as shown in figure 1, 3 holes are set, cracks can be generated at six positions A, B, C, D, E and F (horizontal positions at two sides of each hole), in order to simulate a multi-crack sample, a Monte Carlo simulation method is adopted, and each outer layer circulation generates 6 initial lives (N) of cracks00,N01,N02,N03,N04,N06). The initial crack life is the number of cycles for the crack to develop from 0 to 1mm, and the logarithmic life of the initial crack is determined to satisfy N based on experiments0N (μ, σ) (experimentally measured μ -4.969, σ -0.326) is lognormal. The method can be used for researching the expansion and residual strength conditions of multiple cracks under the given cycle number, the service life of the test piece is from the initial crack service life to the test piece failure, the service life interval is approximately 7 ten thousand to 12 ten thousand, and the given cycle N isdThe range may be approximately in this interval (the given cycle parameter may be adjusted).
Setting a specified number of cycles NdWhen this number is reached, the inner layer cycle ends regardless of crack propagation.
Judging the specified service life NdAnd comparing the 6 initial lives extracted by the first step MC method with 86000 times, if the initial lives are less than 86000 times, determining that the position has cracks, if the initial lives are more than 86000 times, determining that the position has no cracks when the specified life is reached, and always setting the crack length of each position to be 0. For example, four positions, i.e., a 110000, B80000, C90000, D110000, E85000, F92000, and A, C, D, F, are considered as no crack generation, marked, and then not calculated (the crack growth length da is not calculated).
Sorting six service lives of ABCDEF from small to large, setting the initial life of crack propagation as the minimum value 80000 of the initial life of the 6 cracks, wherein the length of the position at the beginning is 1mm, if the service lives of the rest positions are the same, simultaneously setting the position to be 1mm, and recording the size of the crack of the position with the rest life being larger than 80000 as 0.
The number of subsequent cycles increases, each time a determination is required, and if the number of cycles is equal to or greater than the initial life of the location, the crack size at the location is changed to 1.
Entering a crack propagation link, setting the growth length da of the crack at each position every time the cycle number is increased by 1000 for the position (judgment) where the crack is greater than 0, and utilizing the following formula:
wherein C is 2.34 × 10-8M is 3.427, dN is 1000 since the crack growth length da needs to be calculated every 1000 increments of the number of cycles of the above setting;
the calculation of Δ K is complicated and requires a large amount of judgment. The specific calculation process is as follows:
(1) when the crack length is 0, Δ K is 0;
(2) when the crack length is greater than 0:
ΔK＝β*108*(π*(2.5+a))0.5 (2)
wherein a is the total length of the cracks from the hole edge to the set cycle number, the beta factor is in a form of B1, B2, B3 and B4 multiplication, and the coefficients of B1, B2, B3 and B4 are different for different types of cracks. The specific calculation is as follows:
1) calculation of B1:
f is obtained by performing nonlinear fitting on the scatter data in FIG. 2h2(x) Function (3) for a/R:
where x is (a +2.5)/2.5, a is the current crack length, 2.5 denotes the hole radius, Fh2The coefficient B1 used for single crack at the edge of the hole.
2) Calculation of B2:
as can be seen from FIG. 3, the boundary correction factor Fh1Has a specific curve function relation with the geometric parameter a/R. Nonlinear fitting of the data in FIG. 3 using MATLAB yields a correlation for Fh1The expression of the curve function is shown in formula (4):
where x is (a +2.5)/2.5, a is the current crack length, and 2.5 represents the hole radius. Fh1Coefficient B2 used for hole-edge double cracking;
3) calculation of B3:
wherein x is 5/(15-1.5a), FohAThe influence factor B3 (adjacent hole in crack propagation direction) of the adjacent hole is added, judgment is carried out here, when a exceeds 7mm, the internal circulation is ended in advance before the specified circulation frequency (86000) in the embodiment is reached, the result is marked as unsafe, and the reason is marked as single crack length overrun;
4) calculation of B4:
where x is 2 × a1/(12-a1-a2), a1 is the crack length at the position to be determined, and a2 is the crack length at the edge of the hole adjacent to the crack growth direction (since points a and B are two test points at the edge of the same hole, for example, point a1 in the figure is the crack length at point a, and a2 is the crack length at point B). FOCAIs the adjacent crack influencing factor B4 (hole edge crack in crack propagation direction).
When the judgment is added here, when the length of 12-a1-a2 is less than 2mm, the inner circulation is ended in advance before the specified number of circulation times (86000) in the embodiment is reached, and the result is marked as unsafe, and the reason is marked as the single crack length is out of limit.
The specific calculation mode of the beta factor is as follows:
if the crack at a certain position of the hole edge is 0, not calculating, or making k equal to 0;
1) for two positions of A, F on both sides with cracks, i.e. cracks on both sides (where the crack length is greater than 0), if the crack length is equal to 0 on the other side of the hole, i.e. the BE side corresponding to AF has no cracks, the following formula is used:
β＝B1 (7)
if the crack length is greater than 0 (i.e. there is a crack in AF and also in BE as in FIG. 2) on the other side of the hole, i.e. there is already a crack initiated:
β＝B2 (8)
2) for initial cracks at the inner side positions of B, E two side holes, firstly judging whether the corresponding A, F position has no cracks, and then using B1; b2 was used with cracks, in any case B3 must be present at this time, if there is no crack at the corresponding C or D, then not multiply B4: that is, β -B1-B3 or β -B2-B3, and if there is a crack at the corresponding position C, D, it needs to be multiplied by B4, that is, β -B1-B3-B4 or β -B2-B3-B4.
3) For the crack at C, D, as in B, E, β -B1 × B3 or β -B2 × B3 or β -B1 × B3 × B4 or β -B2 × B3 × B4, considering the case of the crack corresponding to position C, D.
Substituting the calculated parameter β into the following formula:
ΔK＝β*108*(π*(2.5+a))0.5 (9)
Δ K was obtained and recorded at each position and finally substituted into crack propagation equation (1).
Increasing the number of times of each cycle by 1000, namely calculating da corresponding to each crack by dN-1000, adding the da to the existing crack length to obtain a of each crack after each cyclej＝aj+daj。
And (3) adding judgment after the length of each crack is obtained by each inner layer circulation:
g305 ═ (97.74-15 — sum of lengths of all cracks (from a to F positions))/97.74 (10)
If G is greater than 150, marking the result as safe;
if G is still larger than 150 after the specified cycle number of 86000 is reached, the result of the inner cycle is safe;
if the value G is lower than 150 before reaching the specified number of cycles (86000), the inner-cycle calculation is ended and the mark result is unsafe.
If the result is unsafe when the specified cycle number is reached, recording as one-time failure n i1 is ═ 1; if the marking result is safe, recording ni＝0。
Description of G: if any judgment condition is not met, the result is marked as unsafe, and the reason is marked as low residual strength; when the three conditions are met, the result of the internal circulation is safe after the specified circulation times of 86000 is reached.
And G, when the judgment is finished, when the outer-layer circulation times are reached, counting the results of each inner-layer circulation, counting the times of safety and unsafe, displaying the times of each unsafe reason, and calculating the failure probability of the test piece to serve as the final result of the program.
The failure probability is calculated by the formula:
where N is the total number of external cycles.
Those of ordinary skill in the art will appreciate that the elements and method steps of the examples described in connection with the embodiments disclosed herein may be embodied in electronic hardware, computer software, or combinations of both, and that the components and steps of the examples have been described in a functional general in the foregoing description for the purpose of clearly illustrating the interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
In the several embodiments provided in the present application, it should be understood that the disclosed method and system may be implemented in other ways. For example, the above described division of elements is merely a logical division, and other divisions may be realized, for example, multiple elements or components may be combined or integrated into another system, or some features may be omitted, or not executed. The units may or may not be physically separate, and components displayed as units may or may not be physical units, that is, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment of the present invention.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit and scope of the present invention, and they should be construed as being included in the following claims and description.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (8)
1. A method of predicting hole-edge multi-crack propagation, comprising the steps of:
s1, setting a plurality of holes on the sample, and taking two points from the horizontal positions of two sides of each hole to form the following test points: A. b, C, D, E, F, ·, N;
s2, using Monte cardAnd performing a simulation experiment on the initial crack propagation life of the test points by using a Luo simulation method to generate the initial crack propagation life of each test point: n is a radical of00,N01,N02,N03,N04,N06…Nn；
S3, defining cycle times of the initial crack life generated by using the Monte Carlo simulation method when the crack develops from 0 to Xmm, and determining that the logarithmic life of the initial crack satisfies N based on the experiment0A log normal distribution of N (μ, σ);
s4, setting the appointed circulation times Nd，NdAlso referred to as a specified lifetime, the number of cycles per test point reaches NdThe simulation cycle is ended no matter how the crack is expanded;
s5, judging that the number reaches NdThe condition of crack generation of the test point is used for extending the crack of the test point to the initial life and NdMaking comparison, if less than NdIt is considered that cracks occur at this position, and if it exceeds NdWhen the specified service life is determined, no crack is generated at the position;
s6, calculating the crack length of each test point;
and S7, after the length of each crack is obtained, G judgment is carried out, and the failure probability is calculated according to the G judgment result.
2. The method of predicting hole-edge multi-crack propagation as set forth in claim 1, wherein:
sequencing the initial life of the cracks of the test points from small to large, and setting the initial life of the crack expansion as the minimum value N of the initial life in the initial life of the crack expansion of the test pointsminSetting the length of the position at the beginning to be Xmm, if the service lives of other positions are the same, simultaneously setting the length to be Xmm, and setting the service lives of other positions to be more than NminThe position of (a) indicates that the crack size is 0;
sequencing the initial life of the crack propagation of the test points from small to large, and comparing the rest test points in the step S6 by taking the initial life of the crack propagation of each test point as a reference in sequence;
and performing crack propagation calculation on the obtained position of each crack, wherein the crack growth length da of each test point needs to be calculated when the set cycle number increases by Z.
3. The method of predicting hole-edge multi-crack propagation according to claim 2, wherein: calculating the crack growth length da of each test point, wherein the calculation method comprises the following steps:
wherein C is 2.34 × 10-8M is 3.427, dN is Z.
4. The method for predicting hole-edge multi-crack propagation according to claim 2, wherein Δ K is calculated by:
when reaching the cycle number NdWhen the crack length is 0, the delta K is 0;
when reaching the cycle number NdWhen the crack length is greater than 0:
ΔK＝β*108*(π*(2.5+a))0.5 (2)
wherein a is the cycle number reaching the cycle number N of the test point of the hole edgedThe beta factors of the crack lengths are B1, B2, B3 and B4 in a form of continuous multiplication, and the coefficients of the B1, B2, B3 and B4 are different for different types of cracks.
5. The method of predicting hole-edge multi-crack propagation according to claim 4, wherein:
calculation method of B1:
where x is (a +2.5)/2.5, a is the current crack length, 2.5 denotes the hole radius, Fh2Coefficient B1 used for hole edge single crack;
calculation method of B2:
where x is (a +2.5)/2.5, a is the current crack length, 2.5 denotes the hole radius, Fh1Coefficient B2 used for hole-edge double cracking;
calculation method of B3:
wherein x is 5/(15-1.5a), FohAIs the impact factor B3 for adjacent wells;
calculation method of B4:
wherein x is 2 × a1/(12-a1-a2), a1 is the crack length at the position to be determined, and a2 is the crack length of the hole edge adjacent to the crack development direction; fOCAIs the adjacent crack influencing factor B4.
6. The method of predicting hole-edge multicracked propagation as claimed in claim 5, wherein:
when B3 is calculated, a B3 judgment method is introduced: when a exceeds the specified length, the internal cycle is ended in advance before the specified cycle times are reached, the result is marked as unsafe, and the reason is marked as the length of the single crack exceeds the limit;
when B4 is calculated, a B4 judgment method is introduced: when the length of 12-a1-a2 is less than the specified length, the internal cycle is ended in advance before the specified number of cycles is reached, and the result is marked as unsafe, and the reason is marked as the single crack length is exceeded.
7. The method for predicting hole-edge multi-crack propagation according to claim 6, wherein the G judgment is performed by:
g305 ═ 305 (97.74-15 — total crack length per test point)/97.74;
and setting a G judgment rule based on the G value aiming at the obtained G value, and marking the marking result as safe/unsafe according to the G judgment rule.
8. The method for predicting hole-edge multi-crack propagation according to claim 7, wherein the method for calculating the failure probability according to the G judgment result comprises the following steps: counting the times of safety and insecurity, displaying the times of each insecurity reason, and calculating the failure probability of the test piece, wherein the failure probability is used as the final result of the program, and the calculation formula of the failure probability is as follows:
where N is the total number of external cycles.
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Application publication date: 20210917 Assignee: TIANJIN HUALI ELECTRIC POWER EQUIPMENT Co.,Ltd. Assignor: CIVIL AVIATION University OF CHINA Contract record no.: X2024980001225 Denomination of invention: A method for predicting the propagation of multiple cracks at the edge of a hole Granted publication date: 20220923 License type: Common License Record date: 20240122 |