CN111881564B - Method for predicting amplitude-variable fatigue life of mechanical structure - Google Patents
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Abstract
The invention discloses a method for predicting the amplitude-variable fatigue life of a mechanical structure, which is based on the traditional fatigue accumulation damage theory, introduces a correlation function to carry out equivalent transformation on the damage of the structure in the amplitude-variable loading process, and carries out fatigue life prediction on the basis. The method considers the influence of the loading sequence and the material microstructure on the fatigue life, improves the prediction precision of the fatigue life and reduces the test cost.
Description
Technical Field
The invention relates to a mechanical structure fatigue life prediction method, in particular to a mechanical structure amplitude-variable fatigue life prediction method.
Background
The failure of the mechanical structure in the service process can cause economic loss and even personal injury, and the fatigue failure is the most important one of a plurality of failure modes. Therefore, the fatigue performance of the mechanical structure is determined, the fatigue life of the mechanical structure is accurately predicted, and the method is particularly important in the mechanical design process.
The most common fatigue life prediction model is a nominal stress-life (S-N) model, and later, an accumulated damage theory is proposed in order to solve the fatigue life prediction problem when a mechanical structure is subjected to variable amplitude loading, and through decades of development, various different life prediction models are proposed, but the models have some problems: (1) extensive experimentation is required to determine specific material parameters; (2) the effect of the internal microstructure of the material on fatigue life is not considered.
Therefore, how to provide a prediction method for the amplitude-variation fatigue life of a mechanical structure can overcome the problems. Is a problem that needs to be solved by those skilled in the art.
Disclosure of Invention
In view of the above, the present invention provides a method for predicting the amplitude-variable fatigue life of a mechanical structure.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for predicting the amplitude-variable fatigue life of a mechanical structure comprises the following specific test steps:
step 1: determination of fatigue S-N curve of material under banner loading condition
Based on a material standard fatigue test method, a conventional fatigue S-N curve of a material used for a mechanical structure under a banner loading condition is measured through tests, test data points are drawn in a log sigma-logN coordinate plane and are subjected to linear fitting, and an S-N curve equation under the material banner loading condition is obtained as follows:
logσ a ＝mlogN f +n (1)
in the formula, σ a For the magnitude of the loading stress in the fatigue test, N f M and n are fitting parameters for corresponding fatigue life,
step 2: determination of microstructure size of fatigue fracture in banner test
Measuring the area of the fatigue fracture crack source region and recording as area inc Taking the arithmetic square root of the area
As a result of its characteristic dimensions, it is possible,
measuring the area of the fish eye region of the fatigue fracture and recording as area fe Taking the arithmetic square root of the area
As a result of its characteristic dimensions, it is possible,
and 3, step 3: calculating fatigue damage using residual life factor
The traditional cumulative damage theory considers fatigue failure to be a process of continuous accumulation of damage, and generally considers that fatigue damage D is related to loading stress sigma, loading cycle number n, cycle number increment dn and intrinsic parameters p of certain materials, therefore, the damage increment dD can be regarded as a function of the parameters:
dD＝f(D,σ,n,dn；p) (2)
if the relative damage increment dD/D is linearly related to the relative loading cycle number increment dn/n, then:
where f (σ; p) is a function related to the fatigue loading process and material properties,
in practical applications, the remaining life of the material is of more concern than the amount of damage to the material, and for this purpose, a remaining life coefficient α is defined:
α＝N R /N f (4)
in the formula, N R Indicates the remaining fatigue life of the material, N f The fatigue damage after introducing the residual life coefficient α can be expressed as follows, determined by the S-N curve of the material:
D＝1-α f(σ；p) (5)
and 4, step 4: determining remaining life in a multi-level loading process
Applying a multistage cyclic load to the material, wherein the material is subjected to multistage loading to generate fatigue fracture, for convenience of description, the loading stage is represented by a subscript i, the loading stage is represented by a subscript j, the residual life coefficient alpha of the brand-new material is 1, and the loading stress is sigma 1 Number of loading cycles n 1 The residual life coefficient after the loading of the first stage is as follows:
α 11 ＝(N f1 -n 1 )/N f1 (6)
in the formula, alpha 11 For the residual life factor, n, under the first stage loading stress after the first stage loading 1 Number of loading cycles applied under first order loading stress, N f1 Considering the influence of the first stage loading, the damage equivalence is carried out before the second stage loading for the banner loading fatigue life corresponding to the first stage loading stress, and the loading stress is sigma 2 Number of loading cycles n 2 Introducing the number of equivalent loading cycles n 12 Denotes that the material has a loading stress of σ 2 Loading n under the condition 12 Sub-cycle and stress at σ 1 Loading n under the condition 1 The damage caused by the secondary circulation is equal, and the second-stage stress sigma corresponding to the first-stage loaded stress can be obtained 2 The equivalent remaining life coefficient of (a) is:
α 12 ＝1-n 12 /N f2 (7)
in the formula, alpha 12 A residual life factor, N, corresponding to a second level of loading stress after the first level of loading f2 Loading fatigue life for the banner corresponding to the second level loading stress,
the united type (5) and the formula (7) can obtain:
in the formula, f (σ) 1 (ii) a p) and f (σ) 2 (ii) a p) are respectively the stress level σ 1 And stress level σ 2 And the corresponding correlation function, and further, the residual life coefficient after the second stage loading can be determined:
α 22 ＝α 12 -n 2 /N f2 (9)
similarly, the stress sigma of the material at the j-th level is obtained through loading in i stages j The following corresponding remaining life coefficients are:
the corresponding remaining life is:
N Rij ＝α ij N fj (11)
and 5: determining equivalent impairment transform correlation function f (sigma; p)
Before determining the correlation function f (sigma; p), the concept of a damage map needs to be introduced, and the definition is as follows: the region enclosed by the S-N curve and two coordinate axes is a damage graph, in the damage graph, any point (N, sigma) corresponds to a determined damage value D, points with the same damage are connected into a line, called an equal damage line, and the equal damage line meets two conditions: (1) any equal damage lines are not intersected; (2) all the iso-damage lines do not intersect the coordinate axes (σ ═ σ - s Except when such is the case),
assuming the isodamage line is a straight line, the isodamage line can represent a straight line system:
logσ＝Alogn+B (12)
in the formula, A and B are respectively a slope and an intercept, and for the stress fatigue problem, only the elastic deformation of the material is considered, so that all the isodamage lines are generally considered to pass through the point (1, sigma) s ) From this, it is possible to obtain:
B＝logσ s (13)
the value of B can be substituted for formula (12):
logσ＝Alogn+logσ s (14)
two points (sigma) are taken on an equal damage line 1 ,n 1 ) And (σ) 2 ,n 12 ) The equal damage line passing through the two points needs to satisfy the following conditions:
logσ 1 ＝Alogn 1 +logσ s (15)
logσ 2 ＝Alogn 2 +logσ s (16)
the combination of the two types (8), (15) and (16) and the replacement of n by alpha can obtain:
generally speaking, under the high-low stress loading condition, the residual life factor is reduced, and under the low-high stress loading condition, the residual life factor is increased, and considering the influence of the loading sequence in the actual loading process, a "loading factor" is introduced here, and is defined as:
in the formula, mu j+1 Is the "loading factor" between the j-th order stress and the (j +1) -th order stress,
in summary, for a multi-level loading process, the correlation function between any two levels is:
step 6: construction of S-N curves containing microstructure dimensions
Defining a coefficient delta for characterizing the microstructure size of the material, which is used for characterizing the expansion of the material from the microcracks to the fish eye size, wherein the coefficient delta is:
in the formula (I), the compound is shown in the specification,
and
the characteristic sizes of the fish eye and the crack origin measured in step 2,
under the same loading stress, the fatigue life of the material is increased along with the increase of delta, and the fatigue life N of the material under the same stress f A linear fit to δ in logarithmic coordinates can give its relationship:
lnN f ＝alnδ+b (21)
wherein a and b are fitting parameters, and for the same material, the fitting parameter a under different stresses is a constant value, and b can be regarded as a stress related to loadingForce amplitude sigma a Equation (21) can be written as:
f(lnσ a )＝lnN f -alnδ (22)
if the S-N curve is considered to be a linear straight line under a log-log coordinate system, the S-N curve under the internal failure mode of the material can be expressed as:
σ a ＝exp[A+Bln(N f δ -a )] (23)
wherein A, B is a material-dependent fitting parameter, and based on equation (23), for any stress level σ under multi-step amplitude loading conditions j Corresponding fatigue life N fj Comprises the following steps:
N fj ＝exp((lnσ j -A)/B+alnδ) (24)
and 7: establishing a life prediction model
The combined vertical type (11), (19) and (24) can obtain the corresponding residual life of the mechanical structure at any stage and any stress level in the variable amplitude loading process as follows:
if the loading history of the mechanical structure is known, a total fatigue life prediction model of the mechanical structure under the condition of variable amplitude loading can be obtained:
the fatigue life of the mechanical structure under the condition of variable amplitude loading can be predicted through the fatigue life prediction model.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and it is also possible for those skilled in the art to obtain other drawings based on the provided drawings without creative efforts.
FIG. 1 is a flow chart of a microstructure-fatigue life prediction method of an embodiment of the present invention;
FIG. 2 is a conventional S-N plot of an embodiment of the present invention;
FIG. 3 is a drawing showing an example of the present invention ln (N) f .δ -3.36 ) And ln σ a Fitting a relational graph;
FIG. 4 is a graph of predicted life versus experimental life for an example of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
Fig. 1 is a flowchart of a microstructure-fatigue life prediction method according to an embodiment of the present invention, and as shown in fig. 1, the microstructure-fatigue life prediction method includes:
s101: measuring a conventional S-N curve under the loading of the material banner through a fatigue test, and determining an S-N curve equation of the conventional S-N curve;
s102, measuring the microstructure size of the fatigue fracture based on the fatigue test of S101;
s103, introducing a residual life coefficient, and calculating damage by using the residual life coefficient based on the traditional accumulated damage theory;
s104, deducing the change of the residual service life in the multi-stage loading process based on S103;
s105, determining a commutation correlation function f (sigma; p) in the equivalent damage conversion process;
s106, constructing an S-N curve containing the size of the microstructure based on the S101 and the S102;
and S107, establishing a fatigue life prediction model based on S101-S106, and predicting the life.
In S101, an example is made of a materialYield strength sigma s The conventional fatigue S-N curve of the material is obtained through a fatigue characteristic test and is shown in figure 2, and the S-N curve equation is as follows:
σ max ＝1980-129.4×log(N f ) (a)
s102, in the concrete implementation, the characteristic size of each test fracture needs to be measured. First, the area of the fatigue fracture crack origin (inclusion or defect) needs to be determined and is marked as area inc Taking the arithmetic square root of the area
As its characteristic dimension. Then measuring the area of the fatigue fracture fisheye area and recording as area fe Taking the arithmetic square root of the area
As its feature size, it is subsequently used for reconstruction of the S-N curve in S106.
When the S103, S104 and S105 are implemented, they need not be deduced again, and the conclusion in the specification is used directly, that is:
D＝1-α f(σ；p) (b)
in the specific implementation of S106, first, a coefficient δ of the microstructure size needs to be calculated, and the calculation of the coefficient needs to use the fracture characteristic size measured in S102
And
the calculation formula is as follows:
under the same loading stress, the stress of the steel is increased,as delta increases, the fatigue life exhibited by the material increases, and N is the fatigue life of the material under the same stress f A linear fit to δ in logarithmic coordinates can give its relationship:
lnN f ＝alnδ+b (e)
in the formula, a and b are fitting parameters. For the same material, the fitting parameters a under different stresses are constant, and b can be considered as the magnitude of the loading stress σ a Equation (20) can be written as:
f(lnσ a )＝lnN f -alnδ (f)
for this example, the fit yields a — 3.36, i.e.:
f(lnσ a )＝lnN f -3.36lnδ＝ln(N f .δ -3.36 ) (g)
ln(N f .δ -3.36 ) And ln σ a The relationship between the two is one-to-one, as shown in fig. 3, the two are plotted in the same coordinate axis, and linear fitting can be performed to obtain the relationship:
lnσ max ＝7.18-0.07ln(N f .δ -3.36 ) (h)
the formula (h) is the S-N curve equation of the material containing the microstructure size. For any stress level sigma under the condition of multistage amplitude-variable loading j Corresponding fatigue life N fj Comprises the following steps:
N fj ＝exp((lnσ j -7.18)/(-0.07)+3.36lnδ) (i)
in the specific implementation of S107, a life prediction formula is first required:
in the formula, sigma n j For the number of cycles that have been applied to the material, N fj Calculated by the formula (i), f (σ) j (ii) a p) is obtained by the formula (c), whereby the fatigue life of the material can be predicted. The materials of this example were subjected to variable amplitude loading tests, the test data of which are shown in the table belowThe fatigue life of the luffing test is predicted using this model and compared to test data, as shown in fig. 4. The coincidence degree of the fatigue life predicted by the model and the test life is higher, the deviation is basically controlled within 3 times, and the microstructure-fatigue life prediction model is higher in accuracy.
TABLE 1 example materials luffing loading test data
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (1)
1. A prediction method for amplitude-variable fatigue life of a mechanical structure is characterized by comprising the following specific test steps:
step 1: determination of fatigue under Material Banner Loading conditionsS-NCurve
Based on a material standard fatigue test method, the conventional fatigue of the material used for the mechanical structure under the condition of banner loading is measured through testsS-NCurves plotting test data points at
In a coordinate plane, linear fitting is carried out to obtain the material under the condition of banner loadingS-NEquation of the curveComprises the following steps:
in the formula (I), the compound is shown in the specification,
for the magnitude of the loading stress in the fatigue test,N f in order to have a corresponding fatigue life,m、nare all fitting parameters;
step 2: determination of microstructure size of fatigue fracture in banner test
Measuring the area of the crack source region of the fatigue fracture, and recording the area as
Taking the arithmetic square root of the area
As a result of its characteristic dimensions, it is possible,
the area of the fisheye region of the fatigue fracture is determined and recorded as
Taking the arithmetic square root of the area
As its characteristic dimension;
and step 3: calculating fatigue damage using residual life factor
The traditional accumulated damage theory considers that fatigue damage is a process that damage is accumulated continuously, and considers that fatigue damageDAnd the loading stressσNumber of loading cyclesnIncrement of the number of cyclesdnAnd intrinsic parameters of certain materialspCorrelation, therefore, increase in damagedDCan be viewed as a function of these several parameters:
if the relative damage is increaseddD/DAnd increment of relative loading cycle numberdn/nLinear correlation, then:
in the formula
As a function of fatigue loading process and material properties,
in practical application, the residual life of the material is more concerned than the damage amount of the material, and for this reason, a residual life coefficient is defined
：
In the formula (I), the compound is shown in the specification,N R which represents the remaining fatigue life of the material,N f indicating that the material is under a loading stress of
The corresponding fatigue life of the steel wire is short,N f by passing materialS-NCurve determination with introduction of residual life factor
After, fatigue damage can be expressed as:
and 4, step 4: determining remaining life in a multi-level loading process
Applying a multi-stage cyclic load to the material, the material undergoing a multi-stage loadingFatigue fracture, subscript for ease of description, loading stageiIndicating, subscripts for loading orderjShows the coefficient of residual life of a completely new material
Loaded with a stress ofσ 1 The number of loading cycles isn 1， The residual life factor after loading in the first stage is:
in the formula (I), the compound is shown in the specification,
for the residual life factor under the first stage loading stress after the first stage loading,n 1 for the number of loading cycles applied under the first stage loading stress,N f1 considering the influence of the first stage loading, the method carries out damage equivalence before the second stage loading for the banner loading fatigue life corresponding to the first stage loading stress, and the loading stress isσ 2 The number of loading cycles isn 2 Introducing the equivalent number of loading cyclesn 12 Denotes that the material is under a loading stress ofσ 2 Loaded under conditionsn 12 The sub-cycle and the stress ofσ 1 Loaded under conditionsn 1 The damage caused by the secondary circulation is equal, and the stress corresponding to the second stage after the first stage loading can be obtainedσ 2 The equivalent remaining life coefficient of (a) is:
in the formula (I), the compound is shown in the specification,
for the remaining life factor after the first stage loading corresponding to the second stage loading stress, N f2 loading fatigue life of the banner corresponding to the second stage loading stress;
the united type (5) and the formula (7) can obtain:
in the formula (I), the compound is shown in the specification,
and with
Respectively of stress orderσ 1 Stress levelσ 2 And the corresponding correlation function, and further, the residual life coefficient after the second stage loading can be determined:
in the same way, can obtainiLoading in stages with material injStage stressσ j The following corresponding remaining life coefficients are:
the corresponding remaining life is:
and 5: determining equivalent impairment transform correlation functions
Determining a correlation function
Before, firstly, the concept of a damage map is introduced, and the following definitions are defined:S-Nthe region enclosed by the curve and two coordinate axes is a damage map, and any point in the damage map
All correspond to a determined damage valueDPoints with the same damage are connected into a line, called as an equal damage line, and the equal damage line meets two conditions: (1) any equal damage lines are not intersected; (2) all the isodamage lines do not intersect the coordinate axes,σ=σ s except when the water is used for the treatment,
assuming that the isodamage line is a straight line, the isodamage line can represent a straight line system:
in the formulaAAndBthe slope and intercept, respectively, for the stress fatigue problem, only the elastic deformation of the material is considered, and therefore, all isodamage lines are considered to pass through the point (1,σ s ) Thereby, it is possible to obtain:
will be provided withBCan be obtained by substituting the value of (2):
two points are taken on one damage line (σ 1 , n 1 ) And (a)σ 2 , n 12 ) The equal damage line passing through the two points needs to satisfy the following conditions:
combined vertical type (8), (15) and (16) andnby usingαThe replacement may be:
under the condition of high-low stress loading, the residual life coefficient is reduced, under the condition of low-high stress loading, the residual life coefficient is increased, and in consideration of the influence of a loading sequence in the actual loading process, a loading coefficient is introduced, and the loading coefficient is defined as follows:
in the formula (I), the compound is shown in the specification,μ j+1 is as followsjStage stress and (1)j+1) stress level;
for a multi-level loading process, the correlation function between any two levels is:
step 6: building up dimensions containing microstructuresS-NCurve
Defining a coefficient characterizing the microstructure dimensions of a materialδThe expansion factor and coefficient for characterizing the expansion of the material from microcracks to fish eye sizesδComprises the following steps:
in the formula (I), the compound is shown in the specification,
and
the characteristic sizes of the fish eye and the crack origin measured in step 2,
under the same loading stress, withδThe fatigue life of the material is increased, and the fatigue life of the material under the same stress is prolongedN f Andδthe relationship can be obtained by linear fitting in logarithmic coordinates:
in the formula (I), the compound is shown in the specification,a、ball are fitting parameters, for the same material, fitting parameters under different stressesaIn order to be a constant value,bcan be regarded as relating to the magnitude of the loading stressσ a Equation (21) can be written as:
if it is considered thatS-NThe curve is a linear straight line under a double logarithmic coordinate system and under the material internal failure modeS-NThe curve can be expressed as:
wherein A, B is a material-dependent fitting parameter, and is based on equation (23) for any stress level under the condition of multi-level amplitude loadingσ j Corresponding fatigue lifeN fj Comprises the following steps:
and 7: establishing a life prediction model
The combined type (11), (19) and (24) can obtain the corresponding residual life of the mechanical structure at any stage and any stress level in the variable amplitude loading process as follows:
if the loading history of the mechanical structure is known, a total fatigue life prediction model of the mechanical structure under the condition of variable amplitude loading can be obtained:
the fatigue life of the mechanical structure under the variable amplitude loading condition can be predicted through the fatigue life prediction model.
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| 基于疲劳驱动力能量损伤参数修正的非线性疲劳寿命预测;薛齐文等;《中国铁道科学》;20200315(第02期);全文 * |
| 多级等幅疲劳加载下RPC的损伤累积及剩余寿命预测;余自若等;《北京工业大学学报》;20100715(第07期);全文 * |
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