RU2687228C1 - Method for assessing fatigue damaging metal elements of aircraft structures during flight tests based on an extended modified fatigue curve - Google Patents

Abstract

FIELD: aviation.SUBSTANCE: invention relates to aircraft engineering, particularly to methods of estimating fatigue damage of structural elements. Method for assessing fatigue damaging metal elements of aircraft structure during flight tests involves measurement of values of voltages and temperatures in flight of strain gauges and temperature sensors located on different elements of structure, processing of results of these measurements by "complete cycles" method and Oding theory with reduction of flight cycles of voltages to zero-value ones σ, characterized by maximum values and number of their recurrence N. Further, processing results are compared with fatigue test data of structural elements or standard samples for calculation of accumulated during damageability conditions. Strain gages are located near critical points of the structure, but not closer than ten radii of curvature at critical points in the structure. For estimating measured voltages static component of voltages is additionally corrected by value of mounting voltages.EFFECT: possibility of evaluating damageability in the absence of complete fatigue characteristics.1 cl, 4 dwg, 5 tbl

Description

1 area of use.

This invention relates to methods for monitoring and measuring load parameters (overloads, stresses, forces, moments) acting on metal structural elements, and is intended to predict the life of structures during flight tests and studies.

2. The level of technology.

By the time of the start of flight tests there are no data on the actual loads on the structural elements, and information about the fatigue characteristics of the elements, as a rule, is not complete enough. Therefore, in the practice of flight tests there are cases of the appearance of fatigue cracks (or damage) in the structural elements, despite the relatively short time from the beginning of the flight tests to the appearance of these cracks.

At present, in the Russian Federation, attempts to predict fatigue strength during flight tests of airplanes, undertaken to increase their safety level, are performed using estimation calculations using schematization of the original flight data using the full cycle method (MPC, GOST 25.101-83). In this case, the so-called full cycles are distinguished from the registered processes of alternating voltages, and after their separation, the remainder or half cycles, which are then included in the calculation with half weight.

As a characteristic of material fatigue during flight tests, reference fatigue curves are used, which are σ - N dependencies, where σ is the largest alternating voltage corresponding to the number of cycles to N destruction (durability) or cracking of a structurally similar sample (strip with hole, cylindrical sample with ring groove, etc.) or - very rarely - elements of the real structure.

For the fatigue curve, it is customary to use the following power formula:

Nσ ^m = C = const,

where, as σ, the half-span of the stress of a cycle or its equivalent taking into account the asymmetry of the cycle is usually taken, the value m is called the exponent (or degree) of the fatigue curve.

A characteristic view of the fatigue curve in logarithmic coordinates is shown in FIG. 1. The ON ₁ area is a low-cycle fatigue area, the N ₁ -N _G section is usually called regular in aircraft manufacturing in the Russian Federation, and for N> N _{G it} is called a multi-cycle or high-frequency fatigue section. In these coordinates, the last two sections are represented by inclined straight lines corresponding to constant numbers m. The characteristic values of N ₁ = 10 ³ -10 ⁴ , N _G = 10 ⁵ -10 ⁷ . Point N _G is called the break point, if it exists.

As a rule, reference fatigue curves are determined on samples (materials from which structural elements are made) with a stress concentrator manufactured according to a certain standard, in the range of 10 ³ -10 ⁶ cycles for four loading levels. It is practically very difficult to obtain fully the parameters of the fatigue curve along the entire N axis, especially when N <N ₁ , therefore, such data in the reference literature are usually not available.

After the selection of complete cycles, they are reduced to equivalent neural (tensile) stress cycles at a constant m according to the modified Oding formulas adopted in the aircraft industry:

Where

σ _ai - the amplitude of the i-th cycle

σ _mi ^{_ the} average value of the i-th cycle

- параметр материала

- material parameter

In general, the traditional methodology for conducting flight strength tests is most fully described in the book of MD. Klyachko and E.V. Arnautova ("Flight strength tests of aircraft. Static loads". M., Mashinostroenie, 1985). It contains a description of the schematization of the stress process, measured in flight using strain gauges, for estimating equivalent to the damage levels of loading on the basis of the Oding formulas. A more modern exposition of the theory of schematization and its application for assessing fatigue damage during the operation of aircraft is given in the book V.L. Reichera (“Fatigue damage”. M., MATI, 2006).

After obtaining equivalent stresses, assuming C = 1, the conditional damageability is found

Where

p _i = 1 for full cycles and p _i = 1/2 for half cycles.

тогда модифицированные формулы Одинга превращаются в немодифицированный вариант.The value of the UE is calculated for m = 1, 2, 3, 4, 5, 6, 7, 8. Often take

then Oding's modified formulas turn into an unmodified version.

In conclusion, the calculated value of the total equivalent (damage) voltage

The positive side of calculating UE is that, based on it, the influence of different m on damage parameters, including σ _equiv , can be estimated without being tied to a specific place of construction and not taking into account C value. Similarly, you can calculate UE and equivalent values for forces or aircraft overload n _y by processing the records of these parameters, assuming a linear relationship between forces or overloads with stresses.

Significant disadvantages of the described methodology are the following:

- to determine the degree of damage, it is necessary to know the calculated or laboratory and bench estimates of UE and σ _eq , which are either not available at the beginning of flight tests or are not sufficiently accurate;

- calculation of the UE and σ _eq are carried out with constant m, which in the section of low-cycle fatigue leads to overestimated values of resource consumption, and in the zone N> NG - to underestimated values.

Along with the MPC, in the course of flight tests, it is used in the analysis of fatigue damage during long stationary loading sections of the flight by the spectral summation method (MLS), in which, at a constant m, the frequency is equivalent to damage. Calculations of the UE for the analyzed mode are reduced to summing the products of the duration of this section calculated on each designated section of the specified mode for the equivalent frequency and the value of the standard deviation of the voltage on the section elevated to the power of m. The effect of the average load on the damage value can be taken into account in the MCC using fairly time-consuming iterative calculations of local fatigue constants (C and m). In addition, the MSS has the same drawbacks as when evaluating UE on the basis of the MOC. Thus, to use the Oding formulas (based on the MPC) and the MSS, it is necessary to have data on the values of stresses (loads and overloads) during the flight and on the values of the parameters m, and for the MCC and the C constants of the fatigue curve, different for different structural elements and depending from the material of the elements and the stress level.

с помощью расчетов на основе МПЦ и модифицированных формул Одинга по совокупности результатов выполненных полетов и прямого применения широко известной гипотезы линейного суммирования повреждаемости Палмгрена-Майнера:To obtain specific estimates of resource consumption instead of UE it seems more appropriate to use absolute damage during flight tests.

using calculations based on the MPC and modified Oding formulas for the totality of the results of the flights performed and the direct application of the well-known hypothesis of linear summation of the Palmgren-Meiner damage:

- число циклов с уровнем

до разрушения. При исчерпании ресурса полагают П=1. Именно этот подход применен в настоящей заявке.where N _i - the number of selected cycles with a voltage level σ _oi ,

- number of cycles with level

before the destruction. When the resource is exhausted, P = 1 is assumed. This approach is applied in the present application.

As analogues of this application can be considered the following developments for monitoring fatigue damage during aircraft operation:

1) patents for the invention: “Devices for calculating the consumption of the life of an airframe of an aircraft” No. RU 2068198 of 06/17/1992 and “Method for monitoring loads and fatigue damage in the conditions of aircraft operation” No. RU 2599108 of 07.07.2015;

2) the methodology for monitoring the state of the structure (SHM) described in the article "2018 by the Innovative Structural Fatigue Monitoring Solution for General Aviation Aircraft" by Keryk C, Sabatini R., Kourousis K., Gardi A., Silva JM, J.Aerosp . Technol. Manag.V.10, 2018.

The first analogue used the approach of calculating equivalent (according to Odung or equivalent to the “rain” method) cycles of bending moments (stresses) at the fatigue-critical points assigned by the project documentation based on dependencies (referred to as correlations in the first patent), measured moments (stresses) for various flight modes from the objective control of the vertical overload in the center of gravity defined in the system, as well as built during ground-based life tests of the aircraft’s structures (and not samples material) fatigue curves. The use of this approach in flight tests is significantly limited, since it requires preliminary information about the dependence of bending moments on overload and on the characteristics of the structure according to the bench life test data. In addition, this approach is not suitable for assessing the fatigue of structural elements whose loading is largely independent of the vertical overload at the center of gravity. Corresponding to the first analogue development was used in the operation of a number of Russian civil aircraft.

In the second version, a solution is proposed for the fatigue monitoring of aging Australian aircraft. In this case, the approach described in the first analogue is expanded, which is natural for later development, due to:

- adding to the list of correlations of effects on equivalent (by the method of “rain”) cycles of moments (stresses) measured in the newest flight-navigation complex, horizontal overloads in the center of gravity and angular velocities along the three axes of the aircraft, as a solid;

- indications of the possibility of using data on fatigue laboratory testing of samples of materials from which the upgraded element is made to be used in upgrading individual structural elements.

In both developments-analogues, when comparing equivalent load cycles with the data of laboratory fatigue tests, the possibility of achieving load levels corresponding to low-cycle fatigue is not considered. The latter circumstance is a significant drawback, even when monitored during operation, as during rough landings or when maneuvers forced to ensure flight safety with exceeding restrictions, but not leading to an immediate accident, the indicated levels can be reached. In such cases, leveling is required, but the effect of these cases on the consumption of the resource remains unclear.

Important in the case of using fatigue curves of material samples for assessing damage during flight tests, or when specified possible upgrading of individual structural elements, is the question of the dependence of fatigue characteristics not only on the material of structural elements, loading type (tension-compression, bending, torsion), its conditions (environment, temperature), but also on the parameters of stress concentrators, near which fatigue cracks usually occur, but stresses are not measured (due to their significant change the length of the strain gauge). Prediction of damage during flight tests, without taking into account the effect of stress concentrators, is possible only if preliminary laboratory fatigue tests of real aircraft structural elements made using serial technology and prepared by sensors are obtained in the same way and at the same points as in flight tests. To some extent, the severity of this problem is somewhat reduced due to the features of aviation reference books, in which the fatigue characteristics for samples of materials are given for the most common concentration factors in aircraft construction, mainly for the case of a strip with a hole with dimensions close to those recommended for riveted seams. Less commonly, data are given for samples without stress concentrators, the so-called “smooth” samples.

The above problems of damage with increased loads and insufficient information on fatigue characteristics are relevant not only for flight tests, but also for the design of aircraft with regard to fatigue. The last question is set out in detail in the work of R. Haywood. (Design taking into account fatigue. M., Mashinostroenie, 1969). The formulas in it allow to give fairly reliable approximate estimates of the estimates in the following parts:

- fatigue characteristics in the area of N <N1 for aluminum alloys and low-strength steels with tensile strengths (temporary tensile strength) σв≤1100 MPa;

- Effects of stress concentration on fatigue strength, including cases of asymmetrical loading.

Similar methods have been developed by a number of domestic authors, including M.N. Stepnov for the field of elastic deformations, S.V. Serensen and V.P. Kogaev for the area of elastic-plastic deformations. But they require the use of additional assumptions and constants in the calculations, as well as they are characterized by increased complexity, especially during asymmetrical loading cycles and stress concentration, which is typical for aircraft construction.

For an adequate assessment of equivalent voltages, the possible presence of mounting (residual) voltages should be taken into account, to which special attention is given in this application.

Problematic is also the case of damage to the elements of aircraft structures with local, so-called "acoustic" vibrations. The experience of flight tests showed that such damage usually occurs with significant uniaxial static (low-frequency) loading, accompanied by mid-frequency and high-frequency (200 ÷ 2000 Hz) bending deformations. A typical sample for fatigue assessments of similar elements of an aircraft design could be considered a strip with a hole. But in the recommended methods of fatigue testing of samples of materials there are no tensile tests with bending, respectively, there are no reference data for this case.

Along with the listed computational methods for estimating the consumption of aircraft structures by many authors in the Russian Federation and abroad, the use of resource consumption sensors is proposed. However, assessments with their use in flight strength studies are associated with a number of shortcomings, the main of which are the following:

- the impossibility for the most part of the installation of these sensors in the immediate vicinity of the area where fatigue damage occurs;

- a noticeable signal about the beginning of fatigue damage occurs when the resource margin is already small for the safe continuation of tests, including taking into account the possible appearance of critical loading levels in the course of performing further test modes.

3. Disclosure of the invention.

A. Technical result.

The proposed method for assessing the damage to the metal structures of aircraft during flight tests allows, based on reference data on the fatigue of samples of metallic materials:

- assess damageability (rather than conditional damageability) in the absence of sufficiently complete fatigue characteristics, in particular at a low-cycle site, based on the proposed approaches for determining fatigue characteristics for aluminum alloys, and in cases of steels and titanium alloys - for obtaining certain, although less accurate ( but with an additional margin of damage rating;

- determine and also take into account the magnitude of installation voltages to improve the accuracy of estimates of damage;

- to evaluate the damageability of thin-walled structural elements with the simultaneous action of bending and axial stresses.

B. Essential features.

To achieve this technical result in the proposed method of assessing the fatigue damage of metal elements of aircraft structure during flight tests, including the measurement of flight values of stress and temperature by strain gauges and thermal sensors placed on various structural elements, processing the results of these measurements using the "full cycle method" and theory Oding with reduction of flight stress cycles to a neutral σ _0i characterized by maximum values and numbers of their repeatability and N _i , comparing the results of processing with the data of fatigue tests of structural elements or type samples for calculating the damage accumulated during the mode (flight, flight totality), strain gauges are located near the critical points of the structure, but no closer than ten radii of curvature at critical points of the structure, for evaluation the voltages measured in flight, the static component of the voltages is additionally corrected by the magnitude of the mounting voltages obtained when comparing the resistance measurements sensors before and after installation of structural elements on the plane.

в к-ых дискретных точках числа циклов N_к, дополненную (с учетом возможности возникновения при летных испытаниях нагрузок, превышающих расчетные значения) областью малоцикловой усталости (10²≤N_к≤10⁴), определяемую в зависимости от материалов конструкции, в случае алюминиевых сплавов для гладкого образца путем расчета по преобразованной формуле Хэйвуда при отнулевом нагружении - To calculate the damage in the absence or incompleteness of fatigue test data for the analyzed structural element build the estimated modified fatigue curve

at the k-th discrete points of the number of cycles N _c , supplemented (taking into account the possibility of occurrence during flight tests of loads exceeding the calculated values) with a low-cycle fatigue region (10 ² ≤N _to ≤ 10 ⁴ ), determined depending on the construction materials, in the case of aluminum alloys for a smooth specimen by calculating the converted Haywood formula under load conditions

Where

a ₂ = 0,00653 MPa ^-1

n _to = lgN _to ,

σ _0k ^{is the} zero voltage of the calculated fatigue curve for a smooth sample at the k-th point,

σ _in - temporary resistance of the material of the analyzed element;

образца с концентраторами напряжений отнулевые циклы корректируются в отношении эффективных коэффициентов концентрации напряжений с раздельным учетом (с помощью модифицированной формулы Одинга с параметром материала

) динамической и статической составляющих напряжений:to go to the calculated fatigue curve

specimen with stress concentrators, the zero cycles are adjusted for effective stress concentration factors with separate accounting (using the modified Oding formula with the material parameter

) dynamic and static components of voltage:

using the effective concentration ratio of the dynamic component of stresses calculated using the Haywood formulas

Where

(in a number of sources the values of 1 / K _{S are given} , it is often assumed that K _S ≈ 1);

a is the stress concentration attenuation coefficient;

ρ - radius of curvature at the base of the notch or fillet (or radius of the hole), mm;

b - material constant;

n _to - the decimal logarithm of the destructive number of cycles N _i ;

(для алюминиевых сплавов);

(for aluminum alloys);

(для сталей при: к_осл=17,7 на поперечном отверстии;

(for steels with: to _donkey = 17.7 at the transverse hole;

_donkey = 14.1 per fillet, _donkey = 10.6 at the groove);

σ _{max n} = (σ _mn ⁺ σ _an ) is the maximum fatigue rated voltage at the base n = IgN = 5.

In principle, it is possible to use different versions of Haywood or other authors, including formulas that do not contain q _a , but they give results more distant from reference data, since they do not sufficiently take into account the geometry of the samples and the increase in their sensitivity to concentration with increasing frequency.

in the regular segment (10 ⁴ ≤N≤10 ⁶ ), the last point of the low-cycle segment is taken as the first point and a power dependence is used according to the data for the sample with a concentrator corresponding to the actual design;

- in the case of steels in the regular section, reference data is used if the reference concentration coefficient corresponds to the design, and the low-cycle section is replaced on a logarithmic scale with a straight line connected to the point of temporal resistance σv on the stress axis; if the reference concentration coefficient does not match the design, the reference data on the regular section is first reduced to the case of a smooth sample and corrected for the actual concentration ratio, and the low-cycle section is replaced by a straight line;

- in the case of thin-walled elements of aircraft structures that are simultaneously subjected to re-static stretching, as well as mid-frequency and high-frequency bending vibrations, different values of theoretical concentration coefficients are used in building the fatigue curve: recalculation of average values of stress cycles;

then find the number of cycles on the fatigue curve corresponding to the levels of equivalent flight cycles,

where m ^p _{к, к + 1} is a local indicator of the fatigue curve between adjacent points of the low-cycle region, defined as

разрушающих эквивалентных циклов в интервалах между двумя N_к, определенные по модифицированной кривой усталости в точках σ_0i, и вычисляется оценка повреждаемости Пin conclusion, the quotients are found of dividing the repeatability N _{i of} complete cycles (with the addition of half numbers of repetition remainder, half cycles) by the numbers

destructive equivalent cycles in the intervals between two N _k , determined by the modified fatigue curve at the points σ _0i , and the damage estimate is calculated П

the safety factor η is finally introduced

P (η) = ηP;

if the resource consumption per flight P is less than 0.01, it is recommended to take measures - mitigate further testing modes or monitor the possible development of cracks on the analyzed aircraft structural element.

In addition, to build a curve in the low-cycle fatigue zone, a computational model [σ ^p _R (N)] is constructed in the section from N = 0.25 to N ₁ = 10 ⁴ (R is the loading asymmetry coefficient). At site 10 ⁴ ≤N≤10 ⁶ reference data are used, which are adjusted if necessary. For example, if the reference values of stresses σ ^p _R relate to the case of the loading asymmetry coefficient R = 0.1 (σ ^p _R = σ ^p _0.1 ), the stress values are reduced by the modified Oding formula to the values σ ^p ₀ corresponding to neutral load:

To construct the calculated models of aluminum alloys, the case of a smooth sample is considered. The original version of the considered Haywood formula for smooth samples of aluminum alloys has the following form:

where n = lgN; σ _in - tensile strength (temporary resistance).

According to Haywood, the calculation of equivalent cycles is not supposed, and then the solving equation assumes the calculation of the number of destructive cycles for σ _a and σ _m given by the aircraft design; such a solving equation has a high degree, and can only be solved numerically.

Due to the fact that the calculated fatigue curve does not have an explicit analytical expression, for further calculations on the N axis, a sequence of values of N _k is assigned, which are referred to as reference, in the range of N = 0.25-10 ⁶ , on a logarithmic scale as uniform as possible frequent to provide acceptable piecewise linear approximation

At station N = 10 ² -10 ⁴ calculates the equivalent stress σ at otnulevom loading ₀ (for which _ai σ = σ = σ _{0 mi} / 2). The case of zero loading leads to a simplification of the solving equations for the Haywood formula and, consequently, to an increase in its accuracy. The original Haywood formula is converted to the function σ ₀ from σ _in and n:

(МПа),

(Mpa)

where a ₂ = 0.00653 MPa ^-1 , n _к is the logarithm of the number of cycles at the k-th point of the simulated section of the fatigue curve.

при N=10². Для участка N=10⁴-10⁶ значения σ₀ вычисляются на основе степенной формулыPlot N = 0-10 ^{2 is} modeled on a logarithmic straight line between points σ _in with N = 0.25 and the calculated

with N = 10 ² . For the plot N = 10 ⁴ -10 ^{6, the} values of σ ₀ are calculated on the basis of the power formula

lgσ ₂ = lgσ ₁ - (lgN ₂ -lgN ₁ ) / m

using reference values of the indicators of the fatigue curve for samples that have the same values as the analyzed element of the aircraft, the values of theoretical coefficients K _t stress concentration. In this case, as σ ₀ (for N = 10 ⁴ ), the calculated value of the last point of the segment N≤10 ^{4 is} taken. Achievement of values N> 10 ⁶ will be considered irrelevant for the case of flight tests.

To take into account the effect of stress concentrators on fatigue strength, the calculated section of the fatigue curve is corrected according to reference data for 10 ² ≤N≤10 ⁴ and the entire curve is corrected if there are experimental data for a smooth sample, using, in particular, the formulas given by Haywood for effective concentration factors in the case of a non-zero mean stress value. The correction begins with an estimate or selection based on the reference data of the value of the theoretical coefficient of concentration K _t at the allegedly fatigue-critical points of the analyzed structural element, as well as the assessment or selection (based on Haywood's recommendations) of a number of material parameters and geometry of this structural element. Further, the formulas below Haywood values calculated sensitivity coefficient to the stress concentration q _a (N) and the concentration ratio K _and for semispan equivalent stress, as well as the concentration ratio K _m values for average equivalent stress.

From the graphical dependencies mentioned in the mentioned work of Haywood, one can obtain approximate linear expressions for the constants b:

1) for steels with σ _in = 1300 ... 2000 MPa

b = 237,9-1,06⋅σ _in,

2) for aluminum alloys with σ _в = 500 ... 600 MPa (the experience of comparative calculations for a number of aluminum alloys listed in reference books on aviation materials showed the admissibility of a certain extension of this range)

b = 363,3-5,83⋅σ _in.

In principle, it is possible to use different versions of Haywood or other authors, including formulas that do not contain q _a , but they give results more distant from reference data, since they do not sufficiently take into account the geometry of the samples and the increase in their sensitivity to concentration with increasing frequency.

. Для случая отнулевого нагружения для которого σ_ак=σ_mк=σ₀/2, используя формулу Одинга, получаем:When calculating K _m, in contrast to Haywood, who uses the value of the ratio of the maximum stress of the fatigue curve on the basis of N = 10 ⁷ cycles to σ _в , this ratio is taken on the basis of 10 ⁵ cycles, which is used by A.Z. Vorobyev et al. (Resistance to fatigue of structural elements, M., Mashinostroenie, 1990). An even more significant difference consists in combining the obtained concentration factors K _ak and K _m with a modified Oding formula. The result is the following working formula for the calculated values

. For the case of loading otnulevogo for which _ak σ = σ ₀ = σ _MK / 2 using the formula Oding, we obtain:

For steels that are not covered by the Haywood formulas, reference data is used in the regular section if the reference concentration coefficient K _t corresponds to the design, and the low-cycle section is replaced by a straight line connected to point σ _in on the stress axis. If the reference concentration coefficient does not match the design, the data on the regular section of steel (but not titanium alloys) are first reduced to the case of a smooth sample and corrected for the real concentration ratio, and the low-cycle section is constructed similarly.

For the case of acoustic vibrations of thin-walled elements of aircraft structures that are simultaneously subjected to re-static stretching, as well as mid-frequency and high-frequency bending vibrations, different values of theoretical concentration coefficients — bending for effective coefficient of concentration for recalculating amplitudes of cycles and axial for effective concentration factor for recalculation of average values of cycles. In this case, to obtain estimates of P, the aforementioned estimates of K _a (N) and K _m are used, using different values of K _t for the sample in the form of a strip with holes. In particular, for the case of a strip with a hole at b / d = 10, the value of K _t = 2.73 for stretching and K _t = 2.08 for bending (Troshchenko VT and others. Fatigue resistance of metals and alloys. Reference book, h I, Kiev, Naukova Dumka, 1987). Next, using the Heywood formulas, the parameters of the fatigue curve are estimated and the prediction of damage for the given case is calculated.

Таким образом, получаются значения усталостной кривой анализируемого элемента конструкции с учетом концентрации напряжений.Then σ _ai = σ _0/2 values are divided into K _ac, and the values of σ _mi = σ _0/2 are divided into K _m. On the basis of these calculations, using the modified Oding's formulas, the calculated equivalent values are calculated (due to the stress concentration)

Thus, we obtain the values of the fatigue curve of the analyzed structural element, taking into account the stress concentration.

между двумя последовательными значениями n_к=lgN_к, что в свою очередь позволяет воспользоваться степенной формулой для вычисления

на участках между назначенными N_к.On the basis of piecewise linear approximation (at 10 ² ≤N _to ≤10 ⁴ in the calculated part of the curve and at 10 ⁴ ≤N _to ≤ 10 ⁶ for the curve based on experimental data corrected taking into account the stress concentration) the constant values of local indicators are found

between two successive values _for n = lgN _k, which in turn allows us to use the formula for calculating power

in the areas between the designated N _to .

After the application of the MPC, the equivalent nebulous values of the stresses σ _{0i of} full cycles and half cycles are calculated, based on σ _ai and σ _mi .

To take into account the effect of mounting stresses on the fatigue strength of aircraft structures, it is proposed to assemble these elements with strain gauges at the points where the load on the structure is measured during flight tests before mounting these elements. Measuring the resistance of strain gauges with high accuracy (with an ohmmeter not lower than 0.02 class) before installation and after installation of the element determines the magnitude of the installation voltage, which is added to the static component σ _mi before calculating the equivalent level σ _0i .

разрушающих эквивалентных циклов в интервалах между двумя N_к, найденные по модифицированной кривой усталости в точках σ_0i. В результате суммирования полученных отношений получаются значения накопленной (на режиме, в полете или совокупности полетов) усталостной повреждаемости П, или П(%)=П⋅100. В случае если расход ресурса за один полет П≥1%, следует принять меры - смягчить режимы дальнейших испытаний или следить за возможным развитием трещин на анализируемом элементе конструкции самолета.In conclusion, the quotients are found of dividing the repeatability N _{i of the} complete cycles (with the addition of half numbers of the repeatability residue, half cycles) by the numbers

destructive equivalent cycles in the intervals between two N _c , found from the modified fatigue curve at σ _0i . As a result of summing the obtained relations, the values of the accumulated (on-flight, in-flight or flight totals) fatigue damage value are obtained, or П (%) = П⋅100. If the resource consumption per flight is ≥1%, measures should be taken - to soften the modes of further testing or to monitor the possible development of cracks on the analyzed structural element of the aircraft.

The proposed method is illustrated by drawings and tables:

in fig. 1 shows a characteristic view of the fatigue curve;

in fig. 2 shows a flowchart of the process of obtaining an estimate of stresses in analyzing a mode (flight);

in fig. 3 shows a flowchart of the organization of the process of obtaining estimates of damage accumulated during the course (flight);

in fig. 4 shows a comparison of the fatigue curve values for a smooth specimen of material B93 obtained during laboratory tests and using the proposed method;

для диапазона 2≤n_к≤4;Table 1 shows the calculation of the reference values.

for the range of 2≤n _to ≤4;

для диапазона 4<n_к≤6;Table 2 shows the calculation of the reference values.

for the range 4 <n _to ≤6;

table 3 shows the parameters and results of the calculation of damage P;

Table 4 shows the data of laboratory fatigue testing of material B93 p. h. T2;

Table 5 shows the values of the successive designated fiducials destructive cycles (n = lgN _{to k)} in the calculation of the claimed method.

FIG. 2-3 denote the following blocks and sub-blocks:

1. Memory of the onboard voltage recorder.

2. Memory of the flight recorder of flight parameters.

3. Computer number 1, designed to assess the voltage.

4. Electronic copy 1.

5. Electronic copy 2.

6. Stresses (in machine codes).

7. Temperatures at points close to measurement points 6.

8. A block of constants designed for stress estimation.

) и испытательных режимов.9. Lists: analyzed design elements (with their

) and test modes.

10. Cross-point voltage measurement.

11. Marking of voltage measurement channels.

12. Calibration coefficients of stress.

13. Electric voltage zeros.

14. Cross measurement of temperature measurements 7.

15. Marking of temperature channels 7.

16. Calibration coefficients of temperatures 7.

17. Electric temperature zeros 7.

18. Calculation of the initial physical values of stress.

19. Calculation of initial physical values of temperatures 7.

20. Data for the calculation of temperature corrections to stresses.

21. Temperature corrections to voltages.

22. The selection of a sequence of extrema from the process of stress for the schematization of this sequence.

23. Selection in the sequence of extrema of complete cycles and half cycles.

24. Calculation in each cycle (half cycle) of the half-span values σ _ai , the formation of a common array of half-squares for the entire analyzed mode (flight).

25. Calculation in each cycle (half-cycle) of average values σ _mi , their correction by the value of mounting voltage 26, formation of a common array of corrected average values for the whole analyzed mode (flight).

26. Data on installation voltages.

27. Calculation of equivalent neutral voltage σ _{0i the} formation of a common array (σ _0i , N _i ) for the entire analyzed mode (flight).

28. Electronic copy of the results of stress estimates.

29. Computer number 2, designed to assess the accumulated during the mode (flight, flight) damage P.

30. Block of constants: reference values of the indices m and σ _in fatigue curves at regular sites, reference values of parameters for calculating equivalent values of σ _0i , reference values of theoretical coefficients K _t of stress concentration, attenuation coefficients "a" of stress concentration, constants b for the estimated estimate q _a coefficient of sensitivity to stress concentration, fatigue maximum rated σ (5) of the voltage based on the 10 ⁵ intended for assessment of damage to the resource consumption and P n (%), and s ENTOV margin considering the influence on a resource differences of structural elements of the test samples.

31. Block of calculation formulas for:

- Heywood calculations of the values of σ ₀ (σ _in ) for the range N = 10 ² -10 ⁴ ;

- calculating σ ₀ (m) by the power formula of the fatigue curve for N> 10 ⁴ ;

- calculation of local indices m _{к, к + 1} degrees of fatigue curves;

- calculations using the power formula of the values of σ _0i at points other than the reference;

- calculations by a specialized formula of parameters by a modified Oding formula.

32. A block of a given sequence of reference values N _to .

33. Calculation of the reference values σ ₀ (k) using the converted Haywood formulas (for 10 ² ≤N≤10 ⁴ ) and the power formula (with the reference exponent m) for N> 10 ⁴ .

34. The calculation of the coefficients q _a sensitivity to stress concentration and the effective coefficients of stress concentration K _ak (for the half-sizes σ _ai ) and K _m (for average values σ _mi ).

.35. Calculation based on the values of σ ₀ (k), K _ak and K _{m the} corrected stresses

.

степени модифицированной (с учетом концентрации напряжений) кривой усталости на участках, где требуется оценка промежуточных (между реперными) значений уровней.36. The calculation of the values of local indicators

the degree of modified (taking into account stress concentration) fatigue curve in areas where it is necessary to estimate intermediate (between reference) values of levels.

,

, σ_0i и n_к) значений

.37. Calculation using a power formula (using

,

, σ _0i and n _to ) values

.

38. The calculation of the values of P _i . Linear summation of the values of P _i to obtain the accumulated damage P and the corresponding resource consumption P (%), the creation of a memory block of these results. The introduction of the safety factor.

39. Electronic copy of the memory results.

FIG. 2-3. A block diagram of the computing complex for the implementation of the proposed approach is presented.

Flight measurement processing is performed in block 3 (computer No. 1), in which data from the specified measurements are received from blocks 1 (onboard voltage recorder memory) and 2 (onboard flight parameters recorder memory). From the indicated blocks (1 and 2) the information enters the blocks 4 and 5 of the electronic memory of the computer (4 for block 1 and 5 for block 2). Analysis and processing of this information is performed separately for each channel for measuring stresses, corresponding to a strain gauge on the element analyzed during flight strength testing of the structure in each flight mode due to control from unit 9, which selects the analyzed channel and the analyzed flight mode in accordance with the processing task. Subunit 9 is contained in block 8 - a block of constants set by the operator before starting processing. Based on the control signal from 9, block 6 selects from the memory block 4 electrical signals of the analyzed voltages and, converting their machine codes, transmits the coded values of the voltage signals to block 18 to calculate the initial physical values of the voltages. The indicated physical values are marked in accordance with the channel number given in 9 using subblock 10 (cross-connects) and subblock 11 (markings). To calculate the initial physical values of the voltages, in block 18, the values of the calibration coefficients are supplied from subblock 12, and from subblock 13, the values of electrical zeros for voltages. Another operation performed in block 18 is the introduction of temperature corrections. The values of temperature corrections to voltages are determined in block 21 on the basis of corrected temperatures near the strain gauges and temperature corrections derived from the subblock 20. The specified temperatures are determined in block 19 after:

- selection of sub-block 7 (temperatures) included in block 5 on the basis of control from 9 temperature signals corresponding to the analyzed voltage channel;

- taking into account the crossover and marking of measured temperatures through subblocks 14 and 15;

- taking into account the corresponding values of the calibration coefficients and electrical zeros through subblocks 16 and 17.

(присущей анализируемому элементу конструкции и передаваемой из 9) вычисляются по модифицированным формулам Одинга маркированные в соответствии с принадлежностью к циклам или полуциклам значения эквивалентных отнулевых напряжений σ_0i. Полученные значения σ_0i и числа N_i одинаковых значений σ_0i передаются на электронную копию 28 результатов оценок напряжений для последующей передачи в блок 29 (компьютер №2), с помощью которого выполняется оценка накопленной за режим (полет) повреждаемости исследуемых элементов конструкции.For damage assessments, the variable voltage process defined in block 18 is converted in block 22 to a sequence of extremes, from which the sequence of full cycles and half-cycles of stress are distinguished by the algorithm of the full cycle method in block 23. Then, in block 24, the values of half-sizes of stresses σ _ai in cycles (half cycles) are calculated, and in block 25, the average values of stresses σ _mi in cycles (half cycles), and the corresponding arrays are formed. In the same blocks, the values of σ _ai and σ _mi are marked with special labels that indicate to which array the specified values belong - to the array for cycles or to the array for half-cycles. The values of average stresses, estimated during installation of the aircraft and contained in block 26, are added to the mean stress values in block 25 and the values of σ _ai and σ _mi from blocks 24 and 25 are then transferred to block 27, where using these variables and constants

(inherent to the analyzed structural element and transmitted from 9) are calculated by the modified Oding's formulas marked in accordance with the belonging to the cycles or half-cycles the values of the equivalent neurovoltage σ _0i . The obtained values of σ _0i and the number N _{i of the} same values of σ _0i are transmitted to the electronic copy 28 of the results of stress estimates for subsequent transfer to block 29 (computer No. 2), which is used to estimate the damage accumulated for the mode (flight) of the structural elements under study.

In block 29, two computational processes are performed in parallel:

в назначенных (к) реперных точках и локальных показателей степени mpк,к+1 с помощью блоков 30-36;- calculation of fatigue curve values

in the assigned (k) reference points and local exponents mpk, k + 1 using blocks 30-36;

- calculation using local power dependencies of fatigue-destroying numbers of Npi cycles using block 37 and damageability P accumulated in the analyzed structural element during the mode (flight) and estimated in block 38.

These calculations are performed in the following sequence.

In block 33, the reference values of the fatigue curve under zero load σ ₀ (k) are calculated using the sections of curves in the low-cycle zone transferred from block 30 for the corresponding measurement channel σ _in (for calculating using the modified Haywood formulas) curves in the "regular" zone) and taken from a block of 32 logarithms (n _to ) the reference values of the numbers of cycles N _to .

Accounting for the effect of stress concentrators is done by dividing the reference values by the stress concentration factors. We consider σ _a = σ _m = σ ₀ (k) / 2, which are separately divided into concentration factors for the amplitude (K _a ) and for the average value (K _m ), calculated using the Haywood formulas. In the calculations of the indicated coefficients performed in block 34, the following are used:

- Constants (a, b) inherent in the material of the analyzed structural element contained in block 30 and the value of the minimum radius in the concentrator;

- the values of nk contained in block 32, used in the calculations of the values of the sensitivity sensitivity coefficients qa.

с использованием модифицированной формулы Одинга, содержащейся в блоке 31. B блоке 37 вычисляются значения разрушающих чисел N^p _i циклов, соответствующие уровням эквивалентных напряжений σ_0i полученным в блоке 27 компьютера №1. При указанных вычислениях используются

, σ_0i, n_к и значения вычисленных в блоке 36 локальных степенных показателей m^p _к,к+1. After that, in block 35, the reference values adjusted by the concentration coefficients are calculated

using the modified Oding formula contained in block 31. In block 37, the values of destructive numbers N ^p _i cycles are calculated, corresponding to the equivalent stress levels σ _0i obtained in block 27 of computer No. 1. When specified calculations are used

, σ _0i , n _к and the values of local power exponents m ^p _{к, к + 1} calculated in block 36 _.

Finally, in block 38, the desired values of damage accumulated during the mode (flight) of P are calculated, which are transmitted to block 39 of the external electronic memory.

4. Examples of the use of the proposed method.

Were independently successfully tested two procedures of the proposed method:

- linear summation of damage for the prediction of the consumption of the resource and the investigated part from a new material, tested in 24 typical pilot flights of a transport aircraft;

- Assessment of mounting stresses to predict pipeline service lives.

4.1. Use linear summation to estimate damage in average typical experimental flight and compare calculated (using converted Haywood formulas) fatigue curve with laboratory fatigue test materials.

a) Constants used.

Material grade - aluminum alloy В93 p. H. T2. The tensile strength of B93 in p. H. T2 σ _in = 450 MPa.

The reference value of the exponent of the “regular” part of the fatigue curve of a smooth specimen B93 n. H. T2 m _spr = 4.77.

The type of the fatigue curve is a neutral equivalent load σ ₀ (N).

The value of the theoretical concentration coefficient K _t = 2.6.

Material constant for calculation by the modified Oding formula of equivalent loading values

Assigned values of N _to and n _to :

- N _to = 100; 316.2278; 1000; 3162,278; 10,000; 31622.78; 100,000; 316227.8; 10,000,000; 3162278; 100,000;

- n _to = lgN _to = 2; 2.5; 3; 3.5; four; 4.5; five; 5.5; 6; 6.5; 7

The stress concentration attenuation coefficient in the aluminum alloy under consideration is a = (a ₁ / σ _в ) ⁶ = 0.0606 mm, a ₁ = 282 MPa⋅mm ^1/6 ; (a / ρ) ^0.5 = 0.142. The radius of curvature in the assumed fatigue critical place is ρ = 3 mm.

The material parameter for calculating the sensitivity coefficient q _a to stress concentration is b = 100.

The characteristic ratio for a given material limit fatigue strength based on the 10 ⁵ to the limit of its tensile strength σ (n _k = 5) / σ _a = 0.496.

b) Data for calculation: the values obtained from the results of flight materials processing on computer No. 1 (correspond to paragraph 27 of the flowchart in Fig. 2) are the values of equivalent neutral voltages σ _0i in the analyzed flight mode.

c) Computational procedures.

“Reference” voltage levels are calculated using the converted Haywood formula (1) at 2≤n _to ≤4 (corresponds to paragraph 33 of the flowchart in Fig. 3).

“Reference” stress levels are found (paragraph 33 of the flowchart) using power formulas at 4 <n _to ≤6:

The sensitivity coefficient values are calculated (paragraph 34 of the block diagram) using the formula (4).

The values of the effective coefficients K _{ak of the} concentration of half-ranges of stress (paragraph 34 of the flowchart) are calculated by formula (2) with K _s = 1.

The effective coefficient K _{m of} concentration of average stress values (paragraph 34 of the flowchart) is calculated by the formula (3): K _m = 1.308 with K _s = 1.

(пункт 35 блок-схемы) по формуле (5).Calculate the equivalent (nezuli) calculated values (taking into account the concentration)

(paragraph 35 of the block diagram) according to the formula (5).

The values of the local exponents of the calculated design fatigue curve are calculated (paragraph 36 of the flowchart):

циклов для каждого получаемого в полете эквивалентного значения σ_0i (пункт 37 блок-схемы):Calculated from the use of local power dependences destructive by fatigue numbers

cycles for each equivalent σ _0i value obtained in flight (paragraph 37 of the flowchart):

, которые суммируются для получения оценок П и П(%) (пункт 38 блок-схемы):Calculated for the analyzed mode (flight) damageability P, i.e. the ratio of the numbers N _i recorded in flight cycles (with the addition of half numbers of half cycles) calculated on computer No. 1 to the numbers of the corresponding

, which are summarized to obtain estimates of P and P (%) (paragraph 38 of the flowchart):

At the final stage, the safety factor η is entered: P (η) = Pη, and an electronic copy of the results is created.

d) The results of calculations using the specified formulas.

The results of the calculations are given in Tables 1-3. The obtained damage value P = 0.003149, achieved in a typical type flight, corresponds to the average resource exhaustion within 1 / P = 633 flights without taking into account the required reserve, and taking into account the minimum safety factor η, say η = 3, will allow 211 flights. However, it is obvious that the material В93 p. H. T2 for the investigated part with marked loads cannot be used due to the mismatch of the calculated resource with the required one for long-term operation.

e) Comparison of the calculated fatigue curve with laboratory fatigue test materials.

In preparation for the study of damageability of a part from material B93, part t. T2 was obtained in the laboratory of one of the design bureau in a wide range of numbers of destructive cycles fatigue curve N _i (σ _0i ) for a smooth sample of the specified material, including a low-cycle portion. The data from these tests are shown in FIG. 3 and in table 4.

From the data in Table 4 can be compared to the data in Table 5, comprising successive designated fiducials values n = lgN _{to a} destructive cycles and the corresponding computed values of the claimed method σ _0k otnulevyh maximum stress (extracts from Tables 1 and 2).

The results of this comparison are clearly illustrated in FIG. 4. These tables confirm good agreement between experimental and calculated data.

4.2. Assessment of mounting stresses to predict pipeline life.

a) General recommendations based on experience with the method.

The strain gauge method of measuring strain during installation can be used if the strain gages can be applied to the studied structural elements (for example, to the pipelines of systems) before they are mounted on the flight test object and to conduct flight tests with glued load cells.

When developing this technology, a digital Ohm-34 ohmmeter was used to measure the resistance of strain gauges carried out before and after installation. With a break in the measurements before and after installation on the object, not exceeding 2 days, and the presence of screw terminals for connecting the sensors to the device (in order to reduce and ensure the stability of the contact resistance) measurement errors of the mounting voltages were: ± 20 MPa on steel; ± 10 MPa on titanium; ± 7 MPa on the duralumin.

b) Recommended sequence of operations.

1. Selection of strain gauges for resistance (R ₀ = 200 ± 0.1 Ohm). For stability of strain gages S strain sensors must belong to the same batch. Soldering to them output ends.

2. Preparation of places of the load cell sticker (sanding, degreasing, etc.).

3. Sticker strain gauges according to the adopted technology.

4. Preparation of the element for installation at the facility.

5. Measurement of resistance R _{CB of} strain gauges pasted on the element before the element is mounted on the object at the temperature at which the resistance will be measured and after installation.

6. Installation of the element on the object and exposure of the object with the mounted element at a constant temperature of at least 4 hours.

7. Measurement of the resistance of strain gauges designed to assess mounting voltages.

8. Calculation of mounting stresses σ _m

σ _m = (R _M -R _SV ) ⋅E / (R _SV ⋅S),

Where

R _CB and R _M - respectively, the resistance of the strain gauges, measured before installation and after installation on the object,

S is the coefficient of strain sensors of strain gauges specified in the passport of the lot of strain gauges,

E is the modulus of elasticity.

c) Review of the experience of using strain gauge method for estimating mounting stresses.

The strain gauge method of estimating the mounting stresses was successfully applied during flight strength studies of the aircraft’s pipelines: Yak-42, Il-76, An-74, etc. It was found that installation voltages in pipelines can reach significant values (up to 200 MPa in the case of steel pipelines) and noticeably (up to 70 MPa) change from installation to installation for the same point, which can occur, for example, during repairs , replacement engines and other units.

This shows that the consideration of assembly stresses plays an important role in the assessment of the life of aircraft structural elements at the stage of flight strength tests.

Claims (37)

Method for assessing the fatigue damage of metal elements of aircraft structures during flight tests based on an extended modified fatigue curve, which includes in-flight measurement of stress values and temperatures by strain gauges and thermal sensors placed on various structural elements, processing the results of these measurements using the “full cycle method” and the Oding theory reduction of flight stress cycles to a neutral σ _0i characterized by maximum values and numbers of their repeatability N _i , comparing the res processing data with fatigue data of structural elements or type samples for calculating damage accumulated during the mode (flight, flight totality), characterized in that the strain gauges are located near critical points of the structure, but not closer than ten radii of curvature at critical points of the structure, for assessments of in flight voltages, the static component of the voltages is additionally corrected for the magnitude of the mounting voltages obtained by comparing the tensile resistance measurements Odatchikov before and after installation of structural elements on the aircraft, to calculate the damage in the absence or incompleteness of fatigue test data for the analyzed structural element build the calculated modified fatigue curve

at the k-th discrete points of the number of cycles N _c , supplemented (taking into account the possibility of the occurrence during flight tests of loads exceeding the calculated values) with a low-cycle fatigue region (10 ² ≤N _to ≤ 10 ⁴ ), determined depending on the materials of construction: - in the case of aluminum alloys for a smooth sample, by calculating using the transformed Haywood formula for a neural loading

Where a ₂ = 0,00653 MPa ^-1 n _to = lgN _to , σ _0k is the zero voltage of the calculated fatigue curve for a smooth sample at the k-th point, σ _in - temporary resistance of the material of the analyzed element; to go to the calculated fatigue curve

The sample with stress concentrators is neutralized in terms of effective stress concentration coefficients with separate consideration (using the modified Oding formula with material parameter æ) of the dynamic and static stress components:

using the effective concentration ratio of the dynamic component of stresses calculated using the Haywood formulas

and the effective concentration ratio of the static component of the voltage

based on the sensitivity coefficient q _a and the theoretical stress concentration coefficient K _t , Where

(in a number of sources the values of 1 / K _{S are given} , it is often believed that K _S ≈1); a is the stress concentration attenuation coefficient; ρ is the radius of rounding at the base of the notch or fillet (or the hole radius), mm; b - material constant; n _to - the decimal logarithm of the destructive number of cycles N _i ;

= (28.8 / σ _in ) ³ (for aluminum alloys);

= to _donkey / σ _in (for steels with: to _donkey = 17.7 at the transverse bore; to _donkey = 14.1 for fillets, to _donkey = 10.6 at the groove); σ _{max n} = (σ _mn + σ _an ) maximum fatigue rated voltage at the base n = lgN = 5; in the regular segment (10 ⁴ ≤N≤10 ⁶ ), the last point of the low-cycle segment is taken as the first point and a power dependence is used according to the data for the sample with a concentrator corresponding to the actual design; - in the case of steels in the regular section, reference data is used if the reference concentration coefficient corresponds to the design, and the low-cycle section is replaced on a logarithmic scale with a straight line connected to the point of temporal resistance σ _in on the stress axis; if the reference concentration coefficient does not match the design, the reference data on the regular section is first reduced to the case of a smooth sample and corrected for the actual concentration ratio, and the low-cycle section is replaced by a straight line; - in the case of thin-walled elements of aircraft structures that are simultaneously subjected to re-static stretching, as well as medium-frequency and high-frequency bending vibrations, different values of theoretical concentration coefficients are used for building the fatigue curve - effective flexural coefficient for recalculating the amplitudes of the stress cycles and axial for effective flexural coefficient average values of stress cycles; then find the number of cycles on the fatigue curve corresponding to the levels of equivalent flight cycles,

where m ^p _{к, к + 1} is a local indicator of the fatigue curve between adjacent points of the low-cycle region, defined as

in conclusion, the quotients are found of dividing the repeatability N _{i of} complete cycles (with the addition of half numbers of repetition remainder, half cycles) by the numbers

destructive equivalent cycles in the intervals between two N _k , determined by the modified fatigue curve at the points σ _0i , and the damage estimate is calculated П

the safety factor η is finally introduced P (η) = ηP; if the resource consumption per single flight is ≥0.01, it is recommended to take measures - to soften the modes of further testing or to monitor the possible development of cracks on the analyzed structural element of the aircraft.

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