CN114021357A - Structure random fatigue life estimation method based on stress probability density method - Google Patents

Abstract

The invention discloses a structure random fatigue life estimation method based on a stress probability density method, which comprises the steps of firstly, respectively extracting positive stress and shear stress of a thin-wall structure in three directions of x, y and z in a space coordinate system under the action of random load; then acquiring the Von Mises stress of the thin-wall structure which obeys Weibull distribution, and solving the Von Mises stress component square process to obtain Weibull parameters m and eta; then, stress of non-Gauss process is obtained based on the condition of narrow-band random processPeak probability density function P_p(s); finally, based on Miner linear accumulated damage theory, combining with stress peak probability density function P of non-Gauss process_p(s) establishing a stochastic fatigue life estimation model to determine the fatigue life of the thin-walled structure. The invention is not only suitable for the narrow-band stress process, but also suitable for the broadband random stress process after broadband correction.

Description

Stochastic Fatigue Life Estimation Method for Structure Based on Stress Probability Density Method

technical field

The invention relates to the technical field of aircraft life assessment, in particular to a method for estimating random fatigue life of a structure based on a stress probability density method.

Background technique

Thin-walled shell structures such as aero-engine combustion chamber flame tubes, afterburner thermal insulation and anti-vibration screens, and space shuttle skins are subject to complex mechanical, aerodynamic, thermal and high-sound-intensity noise loads during operation. These loads are often multi-axial fatigue loads, and these loads are random, and under the action of these loads, complex internal stresses will be generated, resulting in fatigue failure of thin-walled shell structures.

In the traditional random fatigue life estimation method, the stress time history of the structure is sampled and cycle counted, and then the damage summation calculation is performed according to Miner's theory. In this way, the designer can only estimate the fatigue life of the component if he fully knows the load time history experienced by the component. However, in the design stage of the product and component, it is difficult to obtain the detailed load time history of the dangerous point. In addition, when the load time history cannot be measured in the dangerous position of some structures, the fatigue life of the components cannot be estimated by this traditional method.

SUMMARY OF THE INVENTION

In view of the above-mentioned deficiencies of the prior art, the present invention provides a method for estimating the random fatigue life of a structure based on the stress probability density method.

In order to solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for estimating random fatigue life of structures based on the stress probability density method, including the following steps:

Step 1: Under the action of random loads, extract the normal stress and shear stress of the thin-walled structure in the three directions of x, y, and z in the spatial coordinate system;

Step 2: Under the action of random load, obtain the Von Mises stress of the thin-walled structure obeying the Weibull distribution, solve the square process of the Von Mises stress component, and obtain the Weibull parameters m and η;

The Von Mines stress is defined in three-dimensional space as:

Among them, s _v represents the Von Mines stress, s _x , s _y , and s _z represent the normal stress in the x, y, and z directions, respectively, and s _xy , s _yz , and s _xz represent the shear stress in the x, y, and z directions, respectively;

Step 3: Based on the conditions of the narrow-band stochastic process, the stress peak probability density function P _p (s) of the non-Gauss process is obtained. The process is as follows:

Step 3.1: The response of the weakly damped system is identified as a narrow-band random process, and the approximate expression of the stress peak probability density function P _p (s) of the non-Gauss process is derived:

where Γ() is the gamma function; s is the stress amplitude. For the Von Mises stress process, the amplitude is the combination of the effective peak value and the process standard deviation, namely:

s= _seffective +σ( _sv )= _sv -E( _sv )+σ( _sv )

where s _v is the Von Mises stress, s is the _effective peak value of the Von Mises stress, E(s _v ) and σ(s _v ) are the mean and standard deviation of the Von Mises stress, respectively;

Step 3.2: Integrate the formula in Step 3.1 to obtain the peak probability density function P _p (s) of the Von Mises stress process as:

Step 4: Based on Miner's linear cumulative damage theory, combined with the stress peak probability density function P _p (s) of the non-Gauss process, a random fatigue life estimation model is established to determine the fatigue life of thin-walled structures. The process is as follows:

Step 4.1: For the narrow-band stochastic process, the Basquin equation is used as the failure model for fatigue life estimation. According to the Miner linear cumulative damage theory, combined with the stress peak probability density function, the fatigue life T under the narrow-band stochastic process is determined. The process is as follows:

Step 4.1.1: According to Miner's linear cumulative damage theory, under the constant amplitude stress load, the damage caused by n working cycles is:

为线性累计损伤率，当循环比总和等于1时发生破坏；n_i表示薄壁结构在等幅应力载荷下的工作循环次数；N_i表示在同样的应力幅值载荷下的薄壁结构的疲劳寿命值；in,

is the linear cumulative damage rate, failure occurs when the sum of the cycle ratios is equal to 1; _ni represents the number of working cycles of the thin-walled structure under the constant stress load; _Ni represents the fatigue of the thin-walled structure under the same stress amplitude load life value;

Step 4.1.2: Use the peak probability density function P _p (s) of the stress process to represent the number of working cycles of the thin-walled structure within the stress amplitude s and the fatigue life T, the formula is:

n _i =n(s)=E[M _T ]·T·P _p (s)

Step 4.1.3: The curve of the relationship between the applied stress amplitude level s and the fatigue life N of the standard specimen is the S-N curve equation:

s ^b N=K

In the formula, b and K are the material constants determined in the material S-N curve;

Step 4.1.4: Combine the formulas from Step 4.1.2 and Step 4.1.3 with Step 4.1.1 to obtain an integral expression:

After derivation, the fatigue life T under the narrow-band random process is obtained:

Among them, E[M _T ] is the average occurrence rate of stress cycles; P _p (s) is the peak probability density function of the stress process; K and b are the material constants determined in the SN curve of the material;

Step 4.1.5: For a narrow-band stochastic process, E[M _T ] is equal to the zero crossing rate E[0], and the total number of cycles to calculate the failure of the thin-walled structure is:

N _T =TE[0]

Among them, _NT is the total number of cycles when the thin-walled structure fails.

Step 4.2: For the broadband stochastic process, combined with the influence of the local peak value on the fatigue life of the thin-walled structure, the fatigue life T is corrected according to the Wirsching model, and the fatigue life T ₁ suitable for the broadband stochastic process is obtained. The process is as follows:

Step 4.2.1: The Wirsching model corrects the fatigue life according to the different power spectral density shapes of the stress response, and obtains the life estimation formula suitable for broadband random vibration:

Among them, λ is the correction factor, E[D] is the damage crossing rate;

Step 4.2.2: For a broadband stochastic process, E[M _T ] is equal to the stress peak occurrence rate E[P], and the corrected total number of cycles N _T1 is:

m为材料S-N曲线的负倒数斜率，α为不规则因子。where the correction factor

m is the negative reciprocal slope of the SN curve of the material, and α is the irregularity factor.

The beneficial effects produced by the above technical solutions are:

1. The method for estimating the random fatigue life of a structure based on the stress probability density method provided by the present invention only involves the statistical parameter of the power spectral density of the load history, which is only related to the frequency structure of the system input and response, and does not involve the random amplitude of the load history. sequence. Therefore, in the design stage of the structure, even if the designer cannot obtain the detailed information of the load history in advance, as long as the statistical parameters of the random stress process that the structure will experience is estimated in advance based on past experience or statistical simulation, combined with the existing fatigue design theory, the Stochastic fatigue life prediction for structures.

2. The method provided by the present invention not only performs fatigue life estimation, but also performs broadband correction on the calculation results, so that the method of the present invention is not only suitable for narrow-band stress processes, but also for broadband random stress processes after wide-band correction.

Description of drawings

1 is a flowchart of a method for estimating random fatigue life of a structure based on a stress probability density method in an embodiment of the present invention;

FIG. 2 is a schematic diagram of each functional module during software development of the method for estimating random fatigue life of a structure based on the stress probability density method according to an embodiment of the present invention.

Detailed ways

The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and embodiments. The following examples are intended to illustrate the present invention, but not to limit the scope of the present invention.

As shown in FIG. 1 , the method for estimating the random fatigue life of a structure based on the stress probability density method in this embodiment is as follows.

Step 1: Under the action of random loads, extract the normal stress and shear stress of the thin-walled structure in the three directions of x, y, and z in the spatial coordinate system;

Step 2: Under the action of random load, obtain the Von Mises stress of the thin-walled structure obeying the Weibull distribution, solve the square process of the Von Mises stress component, and obtain the Weibull parameters m and η;

The Von Mines stress is defined in three-dimensional space as:

Among them, s _v represents the Von Mines stress, s _x , s _y , and s _z represent the normal stress in the x, y, and z directions, respectively, and s _xy , s _yz , and s _xz represent the shear stress in the x, y, and z directions, respectively;

According to the digital characteristic theorem of random variables and the above formula, we can get:

为Von Mines应力平方过程

的均值，

为VonMines应力分量平方过程的的均值，E(s_x)、E(s_y)为Von Mines应力分量的均值，

为VonMines应力平方过程

的方差，

为Von Mines应力分量平方过程的的方差，σ²(s_x)Von Mines应力分量的方差。in,

is the Von Mines stress squared process

the mean of ,

is the mean value of the square process of the VonMines stress component, E(s _x ), E(s _y ) are the mean value of the Von Mines stress component,

is the VonMines stress squared process

Variance,

is the variance of the Von Mines stress component squared process, σ ² (s _x ) the variance of the Von Mines stress component.

For the zero-mean Guass process, the random variable X obeys a normal distribution with a mean of 0 and a variance of σ ² , that is, X～N(0,σ ² ), there are:

In the formula, E(X ^k ) is the k-th power mean of the random variable X, (k-1)! ! =(k-1)(k-3)...×3×1

σ ² (X ² )=E(X ⁴ )-[E(X ² )] ² =2σ ⁴

Among them, σ ² (X ² ) is the quadratic variance of the random variable X, and E(X ² ) is the quadratic mean of the random variable X;

的方差

为：For the Von Mines stress process obeying the Weibull distribution, the Von Mines stress squared process can be derived

Variance

for:

In the formula, Γ() is the gamma function.

By solving the formulas simultaneously, the Weibull parameters m and sum can be obtained.

Step 3: Based on the conditions of the narrow-band stochastic process, the stress peak probability density function P _p (s) of the non-Gauss process is obtained. The process is as follows:

Step 3.1: The response of the weakly damped system is identified as a narrow-band random process, and the approximate expression of the stress peak probability density function P _p (s) of the non-Gauss process is derived:

where Γ() is the gamma function; s is the stress amplitude. For the Von Mises stress process, the amplitude is the combination of the effective peak value and the process standard deviation, namely:

s= _seffective +σ( _sv )= _sv -E( _sv )+σ( _sv )

where s _v is the Von Mises stress, s is the _effective peak value of the Von Mises stress, E(s _v ) and σ(s _v ) are the mean and standard deviation of the Von Mises stress, respectively;

Step 3.2: Integrate the formula in Step 3.1 to obtain the peak probability density function P _p (s) of the Von Mises stress process as:

Step 4: Based on Miner's linear cumulative damage theory, combined with the stress peak probability density function P _p (s) of the non-Gauss process, a random fatigue life estimation model is established to determine the fatigue life of thin-walled structures. The process is as follows:

Step 4.1: For the narrow-band stochastic process, the Basquin equation is used as the failure model for fatigue life estimation. According to the Miner linear cumulative damage theory, combined with the stress peak probability density function, the fatigue life T under the narrow-band stochastic process is determined. The process is as follows:

Step 4.1.1: According to Miner's linear cumulative damage theory, under the constant amplitude stress load, the damage caused by n working cycles is:

为线性累计损伤率，当循环比总和等于1时发生破坏；n_i表示薄壁结构在等幅应力载荷下的工作循环次数；N_i表示在同样的应力幅值载荷下的薄壁结构的疲劳寿命值；in,

is the linear cumulative damage rate, failure occurs when the sum of the cycle ratios is equal to 1; _ni represents the number of working cycles of the thin-walled structure under the constant stress load; _Ni represents the fatigue of the thin-walled structure under the same stress amplitude load life value;

Step 4.1.2: Use the peak probability density function P _p (s) of the stress process to represent the number of working cycles of the thin-walled structure within the stress amplitude s and the fatigue life T, the formula is:

n _i =n(s)=E[M _T ]·T·P _p (s)

Step 4.1.3: The curve of the relationship between the applied stress amplitude level s and the fatigue life N of the standard specimen is the S-N curve equation:

s ^b N=K

In the formula, b and K are the material constants determined in the material S-N curve;

Step 4.1.4: Combine the formulas from Step 4.1.2 and Step 4.1.3 with Step 4.1.1 to obtain an integral expression:

After derivation, the fatigue life T under the narrow-band random process is obtained:

Among them, E[M _T ] is the average occurrence rate of stress cycles; P _p (s) is the peak probability density function of the stress process; K and b are the material constants determined in the SN curve of the material;

Step 4.1.5: For a narrow-band stochastic process, E[M _T ] is equal to the zero crossing rate E[0], and the total number of cycles to calculate the failure of the thin-walled structure is:

N _T =TE[0]

Among them, _NT is the total number of cycles when the thin-walled structure fails.

Step 4.2: For the broadband stochastic process, combined with the influence of the local peak value on the fatigue life of the thin-walled structure, the fatigue life T is corrected according to the Wirsching model, and the fatigue life T ₁ suitable for the broadband stochastic process is obtained. The process is as follows:

Step 4.2.1: The Wirsching model corrects the fatigue life according to the different power spectral density shapes of the stress response, and obtains the life estimation formula suitable for broadband random vibration:

Among them, λ is the correction factor, E[D] is the damage crossing rate;

Step 4.2.2: For a broadband stochastic process, E[M _T ] is equal to the stress peak occurrence rate E[P], and the corrected total number of cycles N _T1 is:

m为材料S-N曲线的负倒数斜率，α为不规则因子。where the correction factor

m is the negative reciprocal slope of the SN curve of the material, and α is the irregularity factor.

In this embodiment, the software development of the random fatigue life estimation method of the structure based on the stress probability density method is also carried out. The schematic diagram of the structure of each functional module is shown in Figure 2, wherein the functional module 1 is used for stress data acquisition and VonMines stress calculation; function Module two is used for process parameter calculation; function module three is used for fatigue life estimation.

Claims (5)

1. a structural random fatigue life estimation method based on stress probability density method, is characterized in that, comprises the steps: Step 1: Under the action of random loads, extract the normal stress and shear stress of the thin-walled structure in the three directions of x, y, and z in the spatial coordinate system; Step 2: Under the action of random load, obtain the Von Mises stress of the thin-walled structure obeying the Weibull distribution, solve the square process of the Von Mises stress component, and obtain the Weibull parameters m and η; The Von Mines stress is defined in three-dimensional space as:

Among them, s _v represents the Von Mines stress, s _x , s _y , and s _z represent the normal stress in the x, y, and z directions, respectively, and s _xy , s _yz , and s _xz represent the shear stress in the x, y, and z directions, respectively; Step 3: Based on the condition of the narrow-band stochastic process, the stress peak probability density function P _p (s) of the non-Gauss process is obtained; Step 4: Based on Miner's linear cumulative damage theory, combined with the stress peak probability density function P _p (s) of the non-Gauss process, a random fatigue life estimation model is established to determine the fatigue life of thin-walled structures. 2. The method for estimating the random fatigue life of a structure based on the stress probability density method according to claim 1, wherein the process of the step 3 is as follows: Step 3.1: The response of the weakly damped system is identified as a narrow-band random process, and the approximate expression of the stress peak probability density function P _p (s) of the non-Gauss process is derived:

where Γ() is the gamma function; s is the stress amplitude. For the Von Mises stress process, the amplitude is the combination of the effective peak value and the process standard deviation, namely: s= _seffective +σ( _sv )= _sv -E( _sv )+σ( _sv ) where s _v is the Von Mises stress, s is the _effective peak value of the Von Mises stress, E(s _v ) and σ(s _v ) are the mean and standard deviation of the Von Mises stress, respectively; Step 3.2: Integrate the formula in Step 3.1 to obtain the peak probability density function P _p (s) of the Von Mises stress process as:

3. The method for estimating the random fatigue life of a structure based on the stress probability density method according to claim 1, wherein the process of the step 4 is as follows: Step 4.1: For the narrow-band stochastic process, the Basquin equation is used as the failure model for fatigue life estimation, and the fatigue life T under the narrow-band stochastic process is determined according to the Miner linear cumulative damage theory combined with the stress peak probability density function; Step 4.2: For the broadband stochastic process, combined with the influence of the local peak value on the fatigue life of the thin-walled structure, the fatigue life T is corrected according to the Wirsching model, and the fatigue life T ₁ suitable for the broadband stochastic process is obtained. 4. The method for estimating random fatigue life of structures based on the stress probability density method according to claim 3, wherein the process of step 4.1 is as follows: Step 4.1.1: According to Miner's linear cumulative damage theory, under the constant amplitude stress load, the damage caused by n working cycles is:

in,

is the linear cumulative damage rate, failure occurs when the sum of the cycle ratios is equal to 1; _ni represents the number of working cycles of the thin-walled structure under the constant stress load; _Ni represents the fatigue of the thin-walled structure under the same stress amplitude load life value; Step 4.1.2: Use the peak probability density function P _p (s) of the stress process to represent the number of working cycles of the thin-walled structure within the stress amplitude s and the fatigue life T, the formula is: n _i =n(s)=E[M _T ]·T·P _p (s) Step 4.1.3: The curve of the relationship between the applied stress amplitude level s and the fatigue life N of the standard specimen is the S-N curve equation: s ^b N=K In the formula, b and K are the material constants determined in the material S-N curve; Step 4.1.4: Combine the formulas from Step 4.1.2 and Step 4.1.3 with Step 4.1.1 to obtain an integral expression:

After derivation, the fatigue life T under the narrow-band random process is obtained:

Among them, E[M _T ] is the average occurrence rate of stress cycles; P _p (s) is the peak probability density function of the stress process; K and b are the material constants determined in the SN curve of the material; Step 4.1.5: For a narrow-band stochastic process, E[M _T ] is equal to the zero crossing rate E[0], and the total number of cycles to calculate the failure of the thin-walled structure is: N _T =TE[0] Among them, _NT is the total number of cycles when the thin-walled structure fails. 5. The method for estimating random fatigue life of structures based on the stress probability density method according to claim 4, wherein the process of step 4.2 is as follows: Step 4.2.1: The Wirsching model corrects the fatigue life according to the different power spectral density shapes of the stress response, and obtains the life estimation formula suitable for broadband random vibration:

Among them, λ is the correction factor, E[D] is the damage crossing rate; Step 4.2.2: For a broadband stochastic process, E[M _T ] is equal to the stress peak occurrence rate E[P], and the corrected total number of cycles N _T1 is:

where the correction factor

m is the negative reciprocal slope of the SN curve of the material, and α is the irregularity factor.

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