CN112051146A - Fatigue life prediction method for fiber metal laminate under complex load - Google Patents

Fatigue life prediction method for fiber metal laminate under complex load Download PDF

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CN112051146A
CN112051146A CN202010893886.2A CN202010893886A CN112051146A CN 112051146 A CN112051146 A CN 112051146A CN 202010893886 A CN202010893886 A CN 202010893886A CN 112051146 A CN112051146 A CN 112051146A
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stress
fatigue life
metal laminate
value
fiber metal
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孟维迎
李宇鹏
张啸尘
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Shenyang Jianzhu University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0001—Type of application of the stress
    • G01N2203/0003—Steady
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0014—Type of force applied
    • G01N2203/0016—Tensile or compressive
    • G01N2203/0017—Tensile
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0014—Type of force applied
    • G01N2203/0016—Tensile or compressive
    • G01N2203/0019—Compressive
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058—Kind of property studied
    • G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
    • G01N2203/0073—Fatigue
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058—Kind of property studied
    • G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
    • G01N2203/0075—Strain-stress relations or elastic constants
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02—Details not specific for a particular testing method
    • G01N2203/06—Indicating or recording means; Sensing means
    • G01N2203/067—Parameter measured for estimating the property
    • G01N2203/0676—Force, weight, load, energy, speed or acceleration
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02—Details not specific for a particular testing method
    • G01N2203/06—Indicating or recording means; Sensing means
    • G01N2203/067—Parameter measured for estimating the property
    • G01N2203/0682—Spatial dimension, e.g. length, area, angle

Abstract

The invention provides a method for predicting fatigue life of a fiber metal laminate under complex load. Firstly, applying a fatigue life test with a stress ratio of 0.06, -1 and 10 to the fiber metal laminate, performing a static tension test and a static compression test on the fiber metal laminate, calculating a constant amplitude fatigue life value under each cyclic stress in a complex load spectrum based on a piecewise linear difference method, and finally calculating the accumulated damage rate of the complex load spectrum to the fiber metal laminate to obtain the fatigue life of the fiber metal laminate under any complex load; the invention provides an average stress correction model suitable for a fiber metal laminate, which can accurately solve the fatigue life value under any stress ratio, and corrects the damage accumulation model considering the residual strength based on Hashin hypothesis and combined with Miner damage accumulation theory by considering the characteristics of irregular load spectrum, so that the predicted fatigue life is more effective and the implementation process is simpler and more convenient.

Description

Fatigue life prediction method for fiber metal laminate under complex load
Technical Field
The invention relates to the technical field of fatigue performance research of aviation structural materials, in particular to a fatigue life prediction method of a fiber metal laminate under complex load.
Background
Since the middle of the 20 th century, it has become a great trend to continuously improve various properties of structural materials in order to meet the rapid development requirements of the aerospace industry. Many countries are increasingly pressing to research and apply new materials, and research and application of materials are put at the head of scientific research. To date, the new materials that have received increasing attention are composites, with various advanced composites occupying a significant proportion of the new materials. The composite materials can meet the weight reduction requirement of structural design, and have some unique advantages compared with metal materials, such as specific strength, specific rigidity, excellent fatigue resistance and excellent corrosion resistance. Composite structures have been widely used in the aerospace field due to their excellent overall properties.
Fiber Reinforced Metal Laminates (Fiber Reinforced Metal Laminates, FRMLs for short, also known as Fiber Metal Laminates, FMLs for short) are used as a novel composite material, have high impact resistance of a Metal layer and high fracture toughness of a composite Fiber layer, and are the best choice of aerospace materials. The fatigue performance is particularly important as an important aerofatigue structural component. At present, a great deal of work is made on fatigue crack propagation machines of fiber metal laminates by a plurality of scholars and respective models are provided, but no model can perfectly express the fatigue crack propagation process of the laminates; some scholars carry out relevant research on the fatigue crack initiation life of the fiber metal laminate under constant amplitude and provide corresponding models, but no general model can accurately predict the crack initiation life of the laminate under different stress ratios; the research on the total fatigue life of the laminate (including the crack initiation life and the crack propagation life) is mainly based on the test and is still in the initial stage at present.
For fiber metal laminate materials, the conventional fatigue life research method mainly aims at the research of fatigue crack initiation life and fatigue crack propagation life respectively, and finds a critical crack initiation and crack propagation length specified according to experience, and sums the fatigue crack initiation life and the fatigue crack propagation life according to the critical crack length. The method based on the damage mechanism relates to the properties of fiber and matrix materials, the interface properties of a laminated structure and the like, and due to the complexity of the material structure of a fiber metal layer and the complexity of the phenomenon in the variable amplitude load fatigue process, the critical crack length of crack initiation and crack propagation can not be accurately determined while the fatigue crack initiation life and the fatigue crack propagation life precision can not be ensured, so that the method not only has a complex analysis and calculation process, but also brings lower prediction precision. The current research on the prediction of the fatigue life of the composite material based on the damage mechanism is limited. Therefore, the phenomenological method is more necessary for predicting the fatigue life of the fiber metal layer plate material under variable amplitude load, and the semi-empirical phenomenological method based on the macroscopic mechanical property of the composite material avoids the construction of an independent hypothesis unit and obtains the parameters of the model through data curve fitting. At present, a phenomenological method suitable for predicting the fatigue life of a fiber metal laminate under variable amplitude load is not reported.
As a novel composite material, the fiber metal laminated plate structure is more complex, and the fatigue damage mechanism is more complex. Therefore, the technical method suitable for the traditional composite material life prediction is not suitable for the fiber metal laminate any more. Recent research shows that for an average stress correction model and a damage failure criterion, different models have great influence on the accuracy of the fatigue life prediction of the composite material laminate under spectral load. Aiming at the defects of the service life prediction method of the fiber metal laminate in the prior art, a phenomenological method is needed to be adopted to research an average stress correction model suitable for the material of the fiber metal laminate, and the prediction of the fatigue life of the fiber metal laminate is realized by combining the irregular load spectrum characteristic and the fatigue damage failure rule of the laminate.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for predicting the fatigue life of a fiber metal laminate under complex load, which comprises the following steps:
step 1: respectively carrying out fatigue life tests on the fiber metal laminate under the conditions that the constant amplitude circulating stress ratio is 0.06, -1 and 10, and obtaining fatigue life S-N curves with the stress ratios of 0.06, -1 and 10;
step 2: calculating a constant amplitude fatigue life value of the fiber metal laminate under the ith cyclic stress based on a piecewise linear difference method;
and step 3: repeating the step 2 by changing i to 1,2, …, n, and calculating the constant amplitude fatigue life value under each cyclic stress in the complex load spectrum;
and 4, step 4: calculating the accumulated damage rate D of the complex load spectrum to the fiber metal laminate through a formula (1), when the D is equal to 1, considering that the fiber metal laminate is damaged, and when the fiber metal laminate is damaged, the frequency of corresponding cyclic stress in the complex load spectrum is the fatigue life of the fiber metal laminate;
Figure BDA0002657793280000021
in the formula (I), the compound is shown in the specification,
Figure BDA0002657793280000022
represents the constant amplitude fatigue life value of the fiber metal laminate under the ith cyclic stress, niThe number of times of the i-th cyclic stress is shown, and alpha and beta are material parameters of the fiber metal laminate.
The step 2 comprises the following steps:
step 2.1: calculating the stress ratio of each cyclic stress in the complex load spectrum by using the formula (2),
Figure BDA0002657793280000023
in the formula, RiStress ratio, σ, representing the i-th cyclic stressmin,iThe trough value, σ, representing the i-th cyclic stressmax,iThe wave crest value of the ith cyclic stress is shown, and n represents the number of cyclic stresses in the complex load spectrum;
step 2.2: determining the stress ratio R of the ith cyclic stress in the load spectrum according to the formula (2)iThen, the stress ratio R is calculated by the formula (3)iAverage stress of
Figure BDA0002657793280000031
Figure BDA0002657793280000032
Step 2.3: taking any two stress ratios of 0.06, -1 and 10 as known stress ratio Ru、RvI.e. satisfy at σm-σaR on the coordinate planeiAt RuAnd RvTo (c) to (d);
step 2.4: setting an initial value N of fatigue life according to a known stress ratio RuCalculating the average stress corresponding to the fatigue life initial value N by using the S-N curve dual logarithmic equation
Figure BDA0002657793280000033
Stress amplitude
Figure BDA0002657793280000034
When R isu< 1.0, and the known stress ratio R was calculated by the formulas (4) to (5)uAverage stress corresponding to lower fatigue life initial value N
Figure BDA0002657793280000035
Stress amplitude
Figure BDA0002657793280000036
Figure BDA0002657793280000037
Figure BDA0002657793280000038
Wherein N represents an initial value of fatigue life,
Figure BDA0002657793280000039
represents the stress ratio RuThe cyclic stress wave peak value a corresponding to the lower initial value NuRepresents the stress ratio RuSlope of the lower S-N curve in a log-log coordinate system, buRepresents the stress ratio RuThe intercept of the lower S-N curve in a double logarithmic coordinate system;
when R isu＞1.0，The known stress ratio R is calculated by the equations (6) to (7)uAverage stress corresponding to lower fatigue life initial value N
Figure BDA00026577932800000310
Stress amplitude
Figure BDA00026577932800000311
Figure BDA00026577932800000312
Figure BDA00026577932800000313
Step 2.5: according to a known stress ratio RvCalculating the average stress corresponding to the fatigue life initial value N by using the S-N curve dual logarithmic equationStress amplitude
Figure BDA00026577932800000315
When R isv< 1.0, and the known stress ratio R was calculated by the formulas (8) to (9)vAverage stress corresponding to lower fatigue life initial value N
Figure BDA0002657793280000041
Stress amplitude
Figure BDA0002657793280000042
Figure BDA0002657793280000043
Figure BDA0002657793280000044
Wherein N represents fatigueThe initial value of the service life of the plant,
Figure BDA0002657793280000045
represents the stress ratio RvThe cyclic stress wave peak value a corresponding to the lower initial value NvRepresents the stress ratio RvSlope of the lower S-N curve in a log-log coordinate system, bvRepresents the stress ratio RvThe intercept of the lower S-N curve in a double logarithmic coordinate system;
when R isvIs greater than 1.0, and the known stress ratio R is calculated by the formulas (10) to (11)vAverage stress corresponding to lower fatigue life initial value N
Figure BDA0002657793280000046
Stress amplitude
Figure BDA0002657793280000047
Figure BDA0002657793280000048
Figure BDA0002657793280000049
Step 2.6: according to
Figure BDA00026577932800000410
At σm-σaDetermining stress ratio R on coordinate planeuNon-zero coordinate point corresponding to lower fatigue life initial value N
Figure BDA00026577932800000411
At σm-σaDetermining stress ratio R on coordinate planevNon-zero coordinate point corresponding to lower fatigue life initial value N
Figure BDA00026577932800000412
Step 2.7: solving for σ by equation (12)m-σaPassing point on coordinate plane
Figure BDA00026577932800000413
The expression of the linear equation l, l is shown in equation (12):
Figure BDA00026577932800000414
step 2.8: solving for stress ratio R by equation (13)iAt σm-σaCorresponding linear equation l on the coordinate planei，liIs shown in equation (13):
Figure BDA00026577932800000415
step 2.9: simultaneous linear equations l, liSolving the intersection O of two straight linesiWherein point of intersection OiThe abscissa of (a) is expressed as:
Figure BDA0002657793280000051
in formula (II), sigma'm,iRepresents the stress ratio RiAverage stress value corresponding to the initial value N of the lower fatigue life;
step 2.10: average stress value sigma 'corresponding to initial value N of fatigue life'm,iSubstituting into formulas (15) and (16), and continuously adjusting fatigue life value to average stress value
Figure BDA0002657793280000052
Satisfies the inequality (15), the average stress value satisfying the inequality (15)
Figure BDA0002657793280000053
And average stress value
Figure BDA0002657793280000054
Substituting the corresponding fatigue life value into a formula (16) to obtain the response of the fiber metal laminate in the ith cycleConstant amplitude fatigue life value under force
Figure BDA0002657793280000055
Figure BDA0002657793280000056
Figure BDA0002657793280000057
Further, when the known stress ratios with the values of 0.06, -1 and 10 are obtained, two stress ratios can not be found, so that the stress ratio R to be solved is not obtainediAt σm-σaSatisfies R on the coordinate planeiAt RuAnd RvIn between, the fiber metal laminate needs to be subjected to static tensile test to obtain ultimate tensile strength sigmauts(ii) a Carrying out static compression test on the fiber metal laminate to obtain ultimate compression strength sigmaucs；
When the stress ratio R is to be solvediIs less than 1.0, and from known stress ratios with values of 0.06, -1, 10, two stress ratios can not be found so that the stress ratio R to be solvediAt σm-σaSatisfies R on the coordinate planeiAt RuAnd RvIn the meantime, the stress ratio R is calculated by using the formula (17)iAverage stress value sigma 'corresponding to lower fatigue life initial value N'm,i：
Figure BDA0002657793280000058
When the stress ratio R is to be solvediIs more than 1.0, and from known stress ratios with values of 0.06, -1, 10, two stress ratios can not be found so that the stress ratio R to be solvediAt σm-σaSatisfies R on the coordinate planeiAt RuAnd RvIn between, the stress ratio R is calculated by the formula (18)iAverage stress value sigma 'corresponding to lower fatigue life initial value N'm,i：
Figure BDA0002657793280000059
The invention has the beneficial effects that: the invention provides a fatigue life prediction method of a fiber metal laminate under a complex load, which further improves the accuracy of fatigue life prediction of the fiber metal laminate under the complex load and provides a theoretical basis and practical value for further research and development and application of the fiber metal laminate; in view of the obvious weight reduction effect brought by replacing the traditional aviation aluminum alloy with the fiber metal laminate, the fiber metal laminate has the advantages of prolonging the service life, prolonging the detection period, reducing the maintenance cost and the like, the deep understanding of the fatigue performance of the fiber metal laminate is very important, and an important research basis is provided for the fiber metal laminate to be more and more applied to important aerospace equipment. The invention can enrich and perfect the damage tolerance design evaluation technology and reliability evaluation theory of the fiber metal laminated plate material, and provide important test basis and theoretical basis for further research and development and application of the structural material, thereby further promoting the high-speed development of the aerospace field. In addition, the research and development of the aerospace materials can improve the performance of the aerospace equipment and simultaneously can greatly reduce the cost of the aerospace equipment, thereby bringing great social and economic benefits.
Drawings
FIG. 1 shows a graph of σ in the present inventionm-σaAn equal life chart corresponding to different S-N curves on a coordinate plane;
FIG. 2 is a schematic diagram of the linear interpolation principle of the piecewise linear CLD model of the present invention;
FIG. 3 is a schematic structural view of a glass fiber reinforced aluminum lithium alloy laminate according to the present invention; wherein FIG. (a) is a schematic view of a 2/1 laminate structure, and FIG. (b) is a schematic view of a 3/2 laminate structure;
FIG. 4 is a front view of a glass fiber reinforced aluminum lithium alloy fatigue test piece according to the present invention;
FIG. 5 is a drawing of a glass fiber reinforced aluminum lithium alloy 2/1 laminate fatigue test piece of the present invention, wherein (a) is a front view of a 2/1 laminate fatigue test piece, and (b) is a top view of a 2/1 laminate fatigue test piece;
FIG. 6 is a drawing of a glass fiber reinforced aluminum lithium alloy 3/2 laminate fatigue test piece of the present invention, wherein (a) is a front view of a 3/2 laminate fatigue test piece, and (b) is a top view of a 3/2 laminate fatigue test piece;
FIG. 7 is a plot of Mini-Twist spectral loadings in an example of the present invention;
FIG. 8 is a P-S-N graph corresponding to a fatigue loading test in the present invention, in which (a) shows a P-S-N graph of a 2/1 laminate at a constant amplitude stress ratio of 0.06, (b) shows a P-S-N graph of a 3/2 laminate at a constant amplitude stress ratio of 0.06, (c) shows a P-S-N graph of an 2/1 laminate at a constant amplitude stress ratio of-1, (d) shows a P-S-N graph of a 3/2 laminate at a constant amplitude stress ratio of-1, (e) shows a P-S-N graph of a 2/1 laminate at a constant amplitude stress ratio of 10, (f) shows a P-S-N graph of a 3/2 laminate at a constant amplitude stress ratio of 10, and (g) shows a P-S-N graph of a 2/1 laminate at a Mini-Twist spectrum, FIG. (h) shows the S-N plot of 3/2 plies under Mini-Twist spectral loading;
FIG. 9 is a plot of the lifetime of a glass fiber reinforced aluminum lithium alloy 2/1 laminate of the present invention for three stages, where plot (a) shows a plot of the lifetime obtained by the Goodman model and plot (b) shows a plot of the lifetime obtained by the method of the present invention;
FIG. 10 is a plot of the lifetime of a glass fiber reinforced aluminum lithium alloy 3/2 laminate of the present invention on a three-stage scale, wherein (a) shows a plot of the lifetime obtained by the Goodman model and (b) shows a plot of the lifetime obtained by the method of the present invention;
FIG. 11 is a graph comparing the fatigue life prediction curve of the glass fiber reinforced aluminum lithium alloy laminate under Mini-Twist spectrum load with the prediction curve of the conventional method in the prediction method of the present invention, wherein (a) shows the prediction curve of the glass fiber reinforced aluminum lithium alloy 2/1 laminate, and (b) shows the prediction curve of the glass fiber reinforced aluminum lithium alloy 3/2 laminate.
Detailed Description
The invention is further described with reference to the following figures and specific examples. An average stress correction model, namely a Constant Life graphs (CLD for short), is a prediction tool for evaluating the fatigue Life of a material under Constant amplitude loading, and can reflect the comprehensive influence of material characteristics and average stress on the fatigue Life performance. Among the main parameters used to construct a CLD model are: stress amplitude, average stress and stress ratio, wherein the stress ratio is the ratio of the wave valley value to the wave peak value of the cyclic stress.
The piecewise linear difference method (also called piecewise linear CLD model) is based on sigmam-σaThe model is constructed by ultimate compression strength, ultimate tensile strength and a plurality of known S-N curves, the stress ratio corresponding to the known S-N curves is usually 10, -1 and 0.06, the fatigue S-N curves under any stress ratio can be obtained by performing linear interpolation between static and fatigue data determined by experiments, and the schematic diagram of the linear interpolation principle is shown in FIG. 2.
A fatigue life prediction method under a fiber metal laminate complex load comprises the following steps of firstly applying a fatigue life test with a stress ratio of cyclic stress of 0.06, -1 and 10 to the fiber metal laminate, carrying out a static tension test and a static compression test on the fiber metal laminate, then calculating a constant amplitude fatigue life value under each cyclic stress in a complex load spectrum based on a piecewise linear difference method, and finally calculating the accumulated damage rate of the complex load spectrum to the fiber metal laminate to obtain the fatigue life of the fiber metal laminate under any complex load, wherein the method specifically comprises the following steps:
step 1: respectively carrying out fatigue life tests on the fiber metal laminate under the conditions that the constant amplitude circulating stress ratio is 0.06, -1 and 10, and obtaining fatigue life S-N curves with the stress ratios of 0.06, -1 and 10;
step 2: calculating the constant amplitude fatigue life value of the fiber metal laminate under the ith cyclic stress based on a piecewise linear difference method, wherein the constant amplitude fatigue life value comprises the following steps:
step 2.1: calculating the stress ratio of each cyclic stress in the complex load spectrum by using the formula (2),
Figure BDA0002657793280000071
in the formula, RiStress ratio, σ, representing the i-th cyclic stressmin,iThe trough value, σ, representing the i-th cyclic stressmax,iThe wave crest value of the ith cyclic stress is shown, and n represents the number of cyclic stresses in the complex load spectrum;
step 2.2: determining the stress ratio R of the ith cyclic stress in the load spectrum according to the formula (2)iThen, the stress ratio R is calculated by the formula (3)iAverage stress of
Figure BDA0002657793280000081
Figure BDA0002657793280000082
Step 2.3: taking any two stress ratios of 0.06, -1 and 10 as known stress ratio Ru、RvI.e. satisfy at σm-σaR on the coordinate planeiAt RuAnd RvAs shown in fig. 1;
step 2.4: setting an initial value N of fatigue life according to a known stress ratio RuCalculating the average stress corresponding to the fatigue life initial value N by using the S-N curve dual logarithmic equation
Figure BDA0002657793280000083
Stress amplitude
Figure BDA0002657793280000084
When R isu< 1.0, and the known stress ratio R was calculated by the formulas (4) to (5)uAverage stress corresponding to lower fatigue life initial value N
Figure BDA0002657793280000085
Stress amplitude
Figure BDA0002657793280000086
Figure BDA0002657793280000087
Figure BDA0002657793280000088
Wherein N represents an initial value of fatigue life,
Figure BDA0002657793280000089
represents the stress ratio RuThe cyclic stress wave peak value a corresponding to the lower initial value NuRepresents the stress ratio RuSlope of the lower S-N curve in a log-log coordinate system, buRepresents the stress ratio RuThe intercept of the lower S-N curve in a double logarithmic coordinate system;
when R isu> 1.0, the known stress ratio R is calculated by the formulae (6) to (7)uAverage stress corresponding to lower fatigue life initial value N
Figure BDA00026577932800000810
Stress amplitude
Figure BDA00026577932800000811
Figure BDA00026577932800000812
Figure BDA00026577932800000813
Step 2.5: according to a known stress ratio RvCalculating the average stress corresponding to the fatigue life initial value N by using the S-N curve dual logarithmic equation
Figure BDA00026577932800000814
Stress amplitude
Figure BDA00026577932800000815
When R isv< 1.0, and the known stress ratio R was calculated by the formulas (8) to (9)vAverage stress corresponding to lower fatigue life initial value N
Figure BDA00026577932800000816
Stress amplitude
Figure BDA00026577932800000817
Figure BDA0002657793280000091
Figure BDA0002657793280000092
Wherein N represents an initial value of fatigue life,
Figure BDA0002657793280000093
represents the stress ratio RvThe cyclic stress wave peak value a corresponding to the lower initial value NvRepresents the stress ratio RvSlope of the lower S-N curve in a log-log coordinate system, bvRepresents the stress ratio RvThe intercept of the lower S-N curve in a double logarithmic coordinate system;
when R isvIs greater than 1.0, and the known stress ratio R is calculated by the formulas (10) to (11)vAverage stress corresponding to lower fatigue life initial value N
Figure BDA0002657793280000094
Stress amplitude
Figure BDA0002657793280000095
Figure BDA0002657793280000096
Figure BDA0002657793280000097
Step 2.6: according to
Figure BDA0002657793280000098
At σm-σaDetermining stress ratio R on coordinate planeuNon-zero coordinate point corresponding to lower fatigue life initial value N
Figure BDA0002657793280000099
At σm-σaDetermining stress ratio R on coordinate planevNon-zero coordinate point corresponding to lower fatigue life initial value N
Figure BDA00026577932800000910
Step 2.7: solving for σ by equation (12)m-σaPassing point on coordinate plane
Figure BDA00026577932800000911
The expression of the linear equation l, l is shown in equation (12):
Figure BDA00026577932800000912
step 2.8: solving for stress ratio R by equation (13)iAt σm-σaCorresponding linear equation l on the coordinate planei，liIs shown in equation (13):
Figure BDA00026577932800000913
step 2.9: simultaneous linear equations l, liSolving the intersection O of two straight linesiWherein point of intersection OiThe abscissa of (a) is expressed as:
Figure BDA00026577932800000914
in formula (II), sigma'm,iRepresents the stress ratio RiAverage stress value corresponding to the initial value N of the lower fatigue life;
further, when the known stress ratios with the values of 0.06, -1 and 10 are obtained, two stress ratios can not be found, so that the stress ratio R to be solved is not obtainediAt σm-σaSatisfies R on the coordinate planeiAt RuAnd RvIn between, the fiber metal laminate needs to be subjected to static tensile test to obtain ultimate tensile strength sigmauts(ii) a Carrying out static compression test on the fiber metal laminate to obtain ultimate compression strength sigmaucs；
When the stress ratio R is to be solvediIs less than 1.0, and from known stress ratios with values of 0.06, -1, 10, two stress ratios can not be found so that the stress ratio R to be solvediAt σm-σaSatisfies R on the coordinate planeiAt RuAnd RvIn the meantime, the stress ratio R is calculated by using the formula (17)iAverage stress value sigma 'corresponding to lower fatigue life initial value N'm,i：
Figure BDA0002657793280000101
When the stress ratio R is to be solvediIs more than 1.0, and from known stress ratios with values of 0.06, -1, 10, two stress ratios can not be found so that the stress ratio R to be solvediAt σm-σaSatisfies R on the coordinate planeiAt RuAnd RvIn between, the stress ratio R is calculated by the formula (18)iAverage stress value sigma 'corresponding to lower fatigue life initial value N'm,i：
Figure BDA0002657793280000102
Step 2.10: average stress value sigma 'corresponding to initial value N of fatigue life'm,iSubstituting into formulas (15) and (16), and continuously adjusting fatigue life value to average stress value
Figure BDA0002657793280000103
Satisfies the inequality (15), the average stress value satisfying the inequality (15)
Figure BDA0002657793280000104
And average stress value
Figure BDA0002657793280000105
Substituting the corresponding fatigue life value into a formula (16) to obtain a constant amplitude fatigue life value of the fiber metal laminate under the ith cyclic stress
Figure BDA0002657793280000106
Figure BDA0002657793280000107
Figure BDA0002657793280000108
And step 3: repeating the step 2 by changing i to 1,2, …, n, and calculating the constant amplitude fatigue life value under each cyclic stress in the complex load spectrum;
assuming that the accumulated damage value is not changed when the stress condition under variable amplitude loading is changed in the fatigue process, and fatigue failure occurs when the residual strength is equivalent to the maximum loading stress, the accumulated damage rate D under each cyclic stress in the complex load spectrum is calculated through a residual strength-damage accumulated coupling model proposed by Yao and Himmel as shown in a formula (19)i'；
Figure BDA0002657793280000111
In the formula (I), the compound is shown in the specification,
Figure BDA0002657793280000112
represents the constant amplitude fatigue life value of the fiber metal laminate under the ith cyclic stress, niTo representThe action times of the ith circulating stress, wherein alpha and beta represent the material parameters of the fiber metal laminate;
according to Hashin's assumption, it is considered that the damage path will not change no matter whether the applied stress condition changes during the fatigue process, and in formula (19), the damage D is accumulatedi' is determined by the parameters α, β, that is, if the parameters α, β are constant regardless of whether the applied stress condition changes, the cumulative damage path will not change. Therefore, based on Hashin assumption, the parameters alpha and beta in the formula (19) are defined as constants, and the characteristics of irregular load spectrum are considered, based on Miner damage accumulation theory, the formula (19) is substituted into
Figure BDA0002657793280000113
Deriving formula (2) in the following step 4;
and 4, step 4: calculating the accumulated damage rate D of the complex load spectrum to the fiber metal laminate through a formula (1), when the D is equal to 1, considering that the fiber metal laminate is damaged, and when the fiber metal laminate is damaged, the frequency of corresponding cyclic stress in the complex load spectrum is the fatigue life of the fiber metal laminate;
Figure BDA0002657793280000114
in the formula (I), the compound is shown in the specification,
Figure BDA0002657793280000115
represents the constant amplitude fatigue life value of the fiber metal laminate under the ith cyclic stress, niThe number of the i-th cyclic stress is shown, alpha and beta show material parameters of the fiber metal laminate, the values of the alpha and the beta are determined according to residual strength test data, and for the fiber metal laminate material, the parameter alpha is usually 0.35 beta and the parameter beta is 2 pi/3 according to experience.
In order to verify the accuracy of the fatigue life prediction, specific tests are performed below, the glass fiber reinforced aluminum lithium alloy laminate for the tests is 2/1 and 3/2 layer structure, 2/1 and 3/2 layer structure is shown in figures (a) and (b) in fig. 3, fig. 4 is a front view of a glass fiber reinforced aluminum lithium alloy laminate test piece, and the 2/1 structure layer laminate is formed by laying two layers of aluminum lithium alloy plates and one layer of fiber prepreg layer, and is shown in fig. 5; 3/2 the laminate is made of three layers of aluminum lithium alloy plates and two layers of fiber prepreg layers, and is shown in FIG. 6; wherein, the aluminum lithium alloy adopts 2060-T8 aluminum lithium alloy (2060 aluminum lithium alloy for short), and the thickness of the aluminum lithium alloy is the same as that of the alloy plate; the fiber prepreg layer is composed of SY-24/S4C9-1200 materials, wherein the fiber prepreg layer comprises high-strength S4 fibers and SY-24 adhesive, for the high-strength S4 fibers, the mean value of the tensile breaking strength of yarns is more than or equal to 780MPa, the mean value of the strength of dipped yarns is more than or equal to 3000MPa, the content of combustible substances is 0.65-1.25%, the water content is less than or equal to 0.2%, and the volume fraction of the fibers is 74.7%; for the SY-24 adhesive, the mean value of the tensile shear strength is more than or equal to 30MPa, and the mean value of the peel strength is more than or equal to 6 kN/m; the sampling direction of the aluminum lithium alloy layer is the longitudinal direction of the material, and the layering direction of the fiber prepreg is 0 degree.
A flat plate open-hole test piece is adopted in the S-N curve test of the fatigue of the 2060 aluminum lithium alloy and glass fiber reinforced 2060 aluminum lithium alloy laminate. The length of the sample is 230mm, the width is 25mm, the diameter of the round hole is 4mm, the hollow distance between the two round holes is 25mm, and the sample form is shown in FIG. 4. Wherein the net section stress concentration coefficients of the aluminum lithium alloy plate, the 2/1 laminate and the 3/2 laminate are respectively 2.60, 2.57 and 2.56.
The test equipment used in this example is a SHIMADZU (SHIMADZU) low-frequency fatigue testing machine employing an electro-hydraulic servo control system. The tester can realize constant amplitude loading and conventional amplitude loading. The equipment is qualified by the national legal metrological department and is in the valid period. The laboratory regularly maintains and examines test equipment, guarantees equipment normal operating. The equipment parameters are shown in the table 1,
TABLE 1 SHOMDZU Low-frequency fatigue testing machine equipment parameters
Figure BDA0002657793280000121
The test was carried out according to the standard "fatigue test method for axial loading of metallic materials" (HB 5287-1996). The criterion for failure of the fiber metal laminate is complete fracture of the metal layer in the laminate. The test was conducted in a room temperature air environment with a sine wave loading. The test adopts 4 loading modes, which are respectively as follows: constant Amplitude (CA) stress ratio R is 0.06, Constant Amplitude (CA) stress ratio R is-1, Constant Amplitude (CA) stress ratio R is 10, Mini-Twist spectrum carrier. The schematic diagram of the Mini-Twist spectrum amplitude-loading is shown in fig. 7, and an S-N curve test adopts three levels of stress levels, wherein 3-5 samples are used in each level. To ensure a minimum amount of valid data at each level of stress, a confidence level of no less than 95% should be guaranteed.
For constant amplitude fatigue load loading, a SHIMADZU fatigue testing machine is adopted for testing, and the testing frequency is 10 Hz. For the Mini-Twist spectrum load, a SHIMADZU fatigue testing machine is adopted for testing, and the load application frequency is 5Hz and 10 Hz. Namely respectively applying Mini-Twist spectrums with high, medium and low 3-level stress levels, and when applying spectrum loads with high and medium-level stress levels, the load application frequency is 5 Hz; when a spectral load of low stress level is applied, the load application frequency is 10 Hz.
And (3) test results: the fatigue life data of the fiber reinforced aluminum lithium alloy 2/1 laminate and 3/2 laminate materials under different loading modes are mainly concentrated on 5 multiplied by 104～5×105And (4) performing secondary circulation, wherein the secondary circulation comprises eight pieces of fatigue stress-life curve (S-N curve for short) data, and performing linear fitting on the sorted data to obtain eight pieces of median S-N curves. In the field of aerospace, the requirement on the performance of materials is high, and a probability stress-life curve (P-S-N curve for short) of the materials is often used. Due to the few data points tested, the sample information aggregation principle and method is applied herein to fit P-S-N curves with confidence of 0.95 and reliability of 0.90 and 0.99, respectively, as shown in fig. 8 (a) to (h), where P-50% represents the S-N curve with a survival rate of 50%, P-90% represents the S-N curve with a survival rate of 90%, and P-99% represents the S-N curve with a survival rate of 99%.
According to the test data of the glass fiber reinforced aluminum-lithium alloy 2/1 laminate, a Goodman model and the method of the invention are respectively adopted to construct an equal lifetime line graph of the 2/1 laminate under three-level lifetime levels 37722, 76560 and 555904, as shown in FIG. 9; from the test data for the glass fiber reinforced aluminum lithium alloy 3/2 laminates, iso-life line plots of 3/2 laminates at tertiary life levels 47643, 110154, 307610 were constructed using the Goodman model and the method of the present invention, respectively, as shown in fig. 10. The basic data in fig. 9-10 are static strength data and fatigue life data, and three S-N curves with known stress ratios can be obtained by fitting according to the fatigue life data, wherein the stress ratios are respectively 0.06, -1 and 10. Wherein the Goodman model may construct an equal lifetime map using only static strength data and one S-N curve with a stress ratio of-1. The method provided by the invention can be used for directly solving the equal-life curve by applying a linear interpolation theory.
Respectively adopting a traditional method Goodman model combined with a Miner criterion, carrying out an S-N curve for predicting the fatigue life of a fiber reinforced aluminum lithium alloy laminate (2/1 laminate and 3/2 laminate) under the load of a Mini-Twist spectrum by the method provided by the invention, and a comparison graph of the S-N curve and a test S-N curve is shown in FIG. 11, wherein scattered points in the graph represent data points obtained by a fatigue test, and as can be seen from FIG. 11, for two materials of a 2/1 laminate and a 3/2 laminate, the traditional method Goodman model combined with the Miner criterion highly estimates the fatigue performance of the tested materials, which results in optimistic evaluation on the fatigue life; the invention provides a conservative prediction result, in the aspect of prediction accuracy, the prediction result of the invention is closer to a test data curve than a Goodman model combined with Miner criterion, the prediction result is better, and the invention is not based on any hypothesis, and is constructed by a linear interpolation method among fatigue test data, so that the fatigue behavior of the researched material can be accurately described.

Claims (3)

1. A fatigue life prediction method for a fiber metal laminate under complex load is characterized by comprising the following steps:
step 1: respectively carrying out fatigue life tests on the fiber metal laminate under the conditions that the constant amplitude circulating stress ratio is 0.06, -1 and 10, and obtaining fatigue life S-N curves with the stress ratios of 0.06, -1 and 10;
step 2: calculating a constant amplitude fatigue life value of the fiber metal laminate under the ith cyclic stress based on a piecewise linear difference method;
and step 3: repeating the step 2 by changing i to 1,2, …, n, and calculating the constant amplitude fatigue life value under each cyclic stress in the complex load spectrum;
and 4, step 4: calculating the accumulated damage rate D of the complex load spectrum to the fiber metal laminate through a formula (1), when the D is equal to 1, considering that the fiber metal laminate is damaged, and when the fiber metal laminate is damaged, the frequency of corresponding cyclic stress in the complex load spectrum is the fatigue life of the fiber metal laminate;
Figure FDA0002657793270000011
in the formula (I), the compound is shown in the specification,
Figure FDA0002657793270000012
represents the constant amplitude fatigue life value of the fiber metal laminate under the ith cyclic stress, niThe number of times of the i-th cyclic stress is shown, and alpha and beta are material parameters of the fiber metal laminate.
2. The method for predicting the fatigue life of the fiber metal laminate under the complex load according to claim 1, wherein the step 2 comprises the following steps:
step 2.1: calculating the stress ratio of each cyclic stress in the complex load spectrum by using the formula (2),
Figure FDA0002657793270000013
in the formula, RiStress ratio, σ, representing the i-th cyclic stressmin,iThe trough value, σ, representing the i-th cyclic stressmax,iThe wave crest value of the ith cyclic stress is shown, and n represents the number of cyclic stresses in the complex load spectrum;
step 2.2: determining the stress ratio R of the ith cyclic stress in the load spectrum according to the formula (2)iThen, the stress ratio R is calculated by the formula (3)iAverage stress of
Figure FDA0002657793270000014
Figure FDA0002657793270000015
Step 2.3: taking any two stress ratios of 0.06, -1 and 10 as known stress ratio Ru、RvI.e. satisfy at σm-σaR on the coordinate planeiAt RuAnd RvTo (c) to (d);
step 2.4: setting an initial value N of fatigue life according to a known stress ratio RuCalculating the average stress corresponding to the fatigue life initial value N by using the S-N curve dual logarithmic equation
Figure FDA0002657793270000021
Stress amplitude
Figure FDA0002657793270000022
When R isu< 1.0, and the known stress ratio R was calculated by the formulas (4) to (5)uAverage stress corresponding to lower fatigue life initial value N
Figure FDA0002657793270000023
Stress amplitude
Figure FDA0002657793270000024
Figure FDA0002657793270000025
Figure FDA0002657793270000026
Wherein N represents an initial value of fatigue life,
Figure FDA0002657793270000027
represents the stress ratio RuThe cyclic stress wave peak value a corresponding to the lower initial value NuRepresents the stress ratio RuSlope of the lower S-N curve in a log-log coordinate system, buRepresents the stress ratio RuThe intercept of the lower S-N curve in a double logarithmic coordinate system;
when R isu> 1.0, the known stress ratio R is calculated by the formulae (6) to (7)uAverage stress corresponding to lower fatigue life initial value N
Figure FDA0002657793270000028
Stress amplitude
Figure FDA0002657793270000029
Figure FDA00026577932700000210
Figure FDA00026577932700000211
Step 2.5: according to a known stress ratio RvCalculating the average stress corresponding to the fatigue life initial value N by using the S-N curve dual logarithmic equation
Figure FDA00026577932700000212
Stress amplitude
Figure FDA00026577932700000213
When R isv< 1.0, and the known stress ratio R was calculated by the formulas (8) to (9)vAverage stress corresponding to lower fatigue life initial value N
Figure FDA00026577932700000214
Stress amplitude
Figure FDA00026577932700000215
Figure FDA00026577932700000216
Figure FDA00026577932700000217
Wherein N represents an initial value of fatigue life,
Figure FDA00026577932700000218
represents the stress ratio RvThe cyclic stress wave peak value a corresponding to the lower initial value NvRepresents the stress ratio RvSlope of the lower S-N curve in a log-log coordinate system, bvRepresents the stress ratio RvThe intercept of the lower S-N curve in a double logarithmic coordinate system;
when R isvIs greater than 1.0, and the known stress ratio R is calculated by the formulas (10) to (11)vAverage stress corresponding to lower fatigue life initial value N
Figure FDA0002657793270000031
Stress amplitude
Figure FDA0002657793270000032
Figure FDA0002657793270000033
Figure FDA0002657793270000034
Step 2.6: according to
Figure FDA0002657793270000035
At σm-σaDetermining stress ratio R on coordinate planeuNon-zero coordinate point corresponding to lower fatigue life initial value N
Figure FDA0002657793270000036
At σm-σaDetermining stress ratio R on coordinate planevNon-zero coordinate point corresponding to lower fatigue life initial value N
Figure FDA0002657793270000037
Step 2.7: solving for σ by equation (12)m-σaPassing point on coordinate plane
Figure FDA0002657793270000038
The expression of the linear equation l, l is shown in equation (12):
Figure FDA00026577932700000315
step 2.8: solving for stress ratio R by equation (13)iAt σm-σaCorresponding linear equation l on the coordinate planei，liIs shown in equation (13):
Figure FDA0002657793270000039
step 2.9: simultaneous linear equations l, liSolving the intersection O of two straight linesiWherein point of intersection OiThe abscissa of (a) is expressed as:
Figure FDA00026577932700000310
in formula (II), sigma'm,iRepresents the stress ratio RiAverage stress value corresponding to the initial value N of the lower fatigue life;
step 2.10: average stress value sigma 'corresponding to initial value N of fatigue life'm,iSubstituting into formulas (15) and (16), and continuously adjusting fatigue life value to average stress value
Figure FDA00026577932700000311
Satisfies the inequality (15), the average stress value satisfying the inequality (15)
Figure FDA00026577932700000312
And average stress value
Figure FDA00026577932700000313
Substituting the corresponding fatigue life value into a formula (16) to obtain a constant amplitude fatigue life value of the fiber metal laminate under the ith cyclic stress
Figure FDA00026577932700000314
Figure FDA0002657793270000041
Figure FDA0002657793270000042
3. The method for predicting the fatigue life of the fiber metal laminate under the complex load according to claim 2, wherein when the known stress ratio is 0.06, -1, 10, two stress ratios can not be found, so that the stress ratio R to be solved isiAt σm-σaSatisfies R on the coordinate planeiAt RuAnd RvIn between, the fiber metal laminate needs to be subjected to static tensile test to obtain ultimate tensile strength sigmauts(ii) a Carrying out static compression test on the fiber metal laminate to obtain ultimate compression strength sigmaucs；
When the stress ratio R is to be solvedi< 1.0 and from the known stress ratios taken at values 0.06, -1, 10, two could not be foundThe stress ratio is such that the stress ratio R to be solvediAt σm-σaSatisfies R on the coordinate planeiAt RuAnd RvIn the meantime, the stress ratio R is calculated by using the formula (17)iAverage stress value sigma 'corresponding to lower fatigue life initial value N'm,i：
Figure FDA0002657793270000043
When the stress ratio R is to be solvediIs more than 1.0, and from known stress ratios with values of 0.06, -1, 10, two stress ratios can not be found so that the stress ratio R to be solvediAt σm-σaSatisfies R on the coordinate planeiAt RuAnd RvIn between, the stress ratio R is calculated by the formula (18)iAverage stress value sigma 'corresponding to lower fatigue life initial value N'm,i：
Figure FDA0002657793270000044
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