CN109614678A - The method for scratching defect bottom stress coefficient of concentration for calculating alloy surface - Google Patents
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Abstract
The method that the invention discloses a kind of to scratch defect bottom stress coefficient of concentration for calculating alloy surface, initially sets up the elastic mechanics model of gap problem, obtains the corresponding stress concentration function of different depth notch；Then alloy surface is established using finite element software ABAQUS to scratch and subsequent load Simulation Calculation, scratch destruction and elimination that model is drawn unit using breaking strain control workpiece, subsequent load calculates on the basis of scratching model, considers the influence that the local residual stress at scuffing concentrates stress with local plastic strain naturally；The local stress that is finally obtained according to finite element numerical analysis obtains factor of stress concentration correction formula as a result, be modified to factor of stress concentration expression formula.The present invention provides the method and formula of the factor of stress concentration that assessment alloy material surface scratches, the analysis of Fatigue-life for this kind of material structure of the defect containing surface scratching provides foundation.
Description
Technical field
The present invention relates to metal structures and fatigue of materials fault analysis field, more particularly to one kind is for calculating alloy surface
The method for scratching defect bottom stress coefficient of concentration.
Background technique
The fatigue life of metal (alloy) structure and its existing defect are closely related, and the design of aeronautic structure is just from tradition
Safe life method change to damage tolerance and defect tolerance method.Defect torlerable limit analysis dependent on fault location local stress,
The analysis of strain regime.
Surface scratching is one of the defect that metal structure is most commonly encountered, and may be occurred in the manufacture and use stage, can be right
Its fatigue life makes a big impact.Surface scratching can not only generate stress concentration, but also also cause office during scuffing
The residual stress and plastic deformation in portion, these can all concentrate stress and have an impact.Stress collection caused by the defects of scratching at present
Middle analysis portion is perfect, and existing a few thing is based entirely on analysis on elasticity, does not account for above-mentioned local remnants and answers
Power and plastic deformation influence, therefore are actually unable in and accurately reflect true situation.
Summary of the invention
The technical problem to be solved by the present invention is to provide one kind based on for defect involved in background technique
Calculate the method that alloy surface scratches defect bottom stress coefficient of concentration.
The present invention uses following technical scheme to solve above-mentioned technical problem:
The method for scratching defect bottom stress coefficient of concentration for calculating alloy surface comprising the steps of:
Step 1) according to the elastic stress field function near notch, and then releases the equation of the components of stress, by introducing side
Boundary's condition acquires the general solution of the stress field under midplane extrusion load near notch, obtains the expression of the indentations bottom factor of stress concentration
Formula obtains the corresponding stress concentration function of notch of different bottom radius and depth；
Step 2) creates cutter and part model using ABAQUS software, and setting cutter is rigid body, and workpiece is elastoplasticity
The destruction and elimination of breaking strain control unit are arranged by vumate subprogram, face face is defined between cutter and workpiece and is connect for body
The size of touching, scratch is characterized by bottom radius R and depth D；After nonlinear kinetics calculates generation scratch, analyzed using restarting
Method imports the model after scratching, this model contains the residual stress and plastic strain information of scuffing process, then applies and hangs down
Directly in the tensile load in scratch direction, destruction and elimination that model is drawn unit using breaking strain control workpiece are scratched,
Subsequent load calculates on the basis of scratching model, it is contemplated that the local residual stress and local plastic strain at scuffing are to stress collection
In influence, the subsequent load bottom stress of scuffing for obtaining the multiple groups difference bottom radius R, depth D of finite element modelling concentrates system
Several numerical results；
Step 3) is modified Elasticity indentations bottom tabulated SCFs up to formula, introduces corrected parameter；According to
The numerical result of the subsequent load bottom stress coefficient of concentration of scuffing of the multiple groups difference bottom radius R, depth D of finite element modelling,
Corrected parameter is fitted with the variation function of R, D, the local stress obtained according to finite element numerical analysis is as a result, in step 1)
Tabulated SCFs be modified up to formula, the factor of stress concentration after being corrected.
Further optimize as the present invention for calculating the method that alloy surface scratches defect bottom stress coefficient of concentration
The detailed step of scheme, step 1) is as follows:
Enable notch elastic stress field nearby are as follows:
ψ (z)=bzλ+czμ
In formula, a, b, c, d are plural forms, and λ and μ are real number, λ > 0 and λ > μ；
The expression formula for releasing the components of stress is as follows:
σθ=λ rλ-1[a1(1+λ)cos(1-λ)θ+b1cos(1+λ)θ+a2(1+λ)sin(1-λ)θ-b2sin(1+λ)θ]
+μrμ-1[d1(1+μ)cos(1-μ)θ+c1cos(1+μ)θ+d2(1+μ)sin(1-μ)θ-c2sin(1+μ)θ]
σr=λ rλ-1[a1(3-λ)cos(1-λ)θ-b1cos(1+λ)θ+a2(3-λ)sin(1-λ)θ+b2sin(1+λ)θ]
+μrμ-1[d1(3-μ)cos(1-μ)θ-c1cos(1+μ)θ+d2(3-μ)sin(1-μ)θ+c2sin(1+μ)θ]
τrθ=λ rλ-1[a1(1-λ)sin(1-λ)θ+b1sin(1+λ)θ-a2(1-λ)cos(1-λ)θ+b2cos(1+λ)θ]
+μrμ-1[d1(1-μ)sin(1-μ)θ+c1sin(1+μ)θ-d2(1-μ)cos(1-μ)θ+c2cos(1+μ)θ]
In formula, (r, θ) indicates the polar coordinates of alloy surface any point, σθ、σrAnd τrθIt indicates point θ, the r and tangential answers
Force component, a1、a2It is real part, the imaginary part of a, b respectively1、b2It is real part, the imaginary part of b, c respectively1、c2It is real part, the imaginary part of c respectively,
d1、d2It is real part, the imaginary part of d respectively；
It introduces with downstream condition:
In formula, (u, v) indicates that coordinate of the alloy surface any point in auxiliary coordinates, q are the real number from 1 to 2；r0、
u0、v0The respectively coordinate of notch arc section depth and notch free boundary；
The general solution for obtaining notch stress field near notch under the effect of midplane extrusion load, in indentations bottom point r=r0, θ
Expression formula at=0 are as follows:
In formula, R indication notch bottom arc radius；χb、χc、χdExpression formula is as follows:
In formula,
Then indentations bottom point tabulated SCFs reach formula are as follows:
In formula, Kθ、Kr、KrθRespectively indicate any point θ, r and the tangential factor of stress concentration.
Further optimize as the present invention for calculating the method that alloy surface scratches defect bottom stress coefficient of concentration
The detailed step of scheme, step 3) is as follows:
Step 3.1) is modified indentations bottom tabulated SCFs up to formula, introduces corrected parameter a1、a2:
Step 3.2) is answered according to the subsequent load bottom of scuffing of the multiple groups difference bottom radius R of finite element modelling, depth D
The numerical result of power coefficient of concentration, fits λ, μ, χ respectivelyb、χc、χdFunction between 2 α of subtended angle of Elasticity notch closes
It is formula；
Step 3.3), the scuffing for multiple groups difference the bottom radius R, depth D of finite element modelling, extracts its model bottom
Residual stress and subsequent load scratch bottom stress component products, acquire stress concentration factor Kθ、Kr, and then obtain multiple groups not
The corresponding corrected parameter a with the scuffing of bottom radius R, depth D1、a2Value；
Step 3.4), according to the corresponding corrected parameter of scuffing of the multiple groups difference bottom radius R of finite element modelling, depth D
a1、a2Value, using polynomial form respectively to a1、a2It is fitted, obtains a1、a2Fitting function, and then corrected
The factor of stress concentration afterwards.
The invention adopts the above technical scheme compared with prior art, has following technical effect that
1. the notional result of stress field near v-notch to be applied to the calculating of stress field near alloy surface scratch, have
Targetedly；
2. combining finite element modelling, it is contemplated that the plasticity of scratch more tallies with the actual situation.
Detailed description of the invention
Fig. 1 is the model schematic of notch elasticity analysis；
Fig. 2 is implementation flow chart of the invention；
Fig. 3 (a) is the finite element model of integral grid in surface scratching of the present invention simulation；
Fig. 3 (b) is the finite element model of Local grid in surface scratching of the present invention simulation；
Fig. 4 is the matched curve of coefficient lambda；
Fig. 5 is the matched curve of coefficient μ；
Fig. 6 is coefficient χbMatched curve；
Fig. 7 is coefficient χcMatched curve；
Fig. 8 is coefficient χdMatched curve；
Fig. 9 is coefficient a1With the variation surface chart of scratch depth D, bottom radius R；
Figure 10 is coefficient a2With the variation surface chart of scratch depth D, bottom radius R.
Specific embodiment
Technical solution of the present invention is described in further detail with reference to the accompanying drawing:
The present invention can be embodied in many different forms, and should not be assumed that be limited to the embodiments described herein.On the contrary,
It is thorough and complete to these embodiments are provided so that the disclosure, and model of the invention will be given full expression to those skilled in the art
It encloses.In the accompanying drawings, for the sake of clarity it is exaggerated component.
As shown in Figure 1 and Figure 2, the invention discloses one kind for calculating alloy surface and scratching defect bottom stress and concentrate is
Several methods, by taking TB6 titanium alloy as an example, the components of stress expression formula of v-notch base point first under derivation midplane extrusion load,
Detailed process are as follows:
Elastic stress field near notch
ψ (z)=bzλ+czμ
The expression formula that the components of stress can be released is as follows
σθ=λ rλ-1[a1(1+λ)cos(1-λ)θ+b1cos(1+λ)θ+a2(1+λ)sin(1-λ)θ-b2sin(1+λ)θ]
+μrμ-1[d1(1+μ)cos(1-μ)θ+c1cos(1+μ)θ+d2(1+μ)sin(1-μ)θ-c2sin(1+μ)θ]
σr=λ rλ-1[a1(3-λ)cos(1-λ)θ-b1cos(1+λ)θ+a2(3-λ)sin(1-λ)θ+b2sin(1+λ)θ]
+μrμ-1[d1(3-μ)cos(1-μ)θ-c1cos(1+μ)θ+d2(3-μ)sin(1-μ)θ+c2sin(1+μ)θ]
τrθ=λ rλ-1[a1(1-λ)sin(1-λ)θ+b1sin(1+λ)θ-a2(1-λ)cos(1-λ)θ+b2cos(1+λ)θ]
+μrμ-1[d1(1-μ)sin(1-μ)θ+c1sin(1+μ)θ-d2(1-μ)cos(1-μ)θ+c2cos(1+μ)θ]
To solve above-mentioned equation, need to introduce with downstream condition
The general solution that can be obtained v-notch stress field near notch under the effect of midplane extrusion load, in indentations bottom point
(r=r0, θ=0) expression formula be
Due to the form under the tangible specific loading of above formula, the expression formula of the indentations bottom point factor of stress concentration is
Then the finite element model of titanium alloy sheet surface scratching is established using ABAQUS.The size of scratch is by bottom radius R
It is characterized with depth D, establishes the finite element model of multiple groups scratch size.Model meshes are as shown in figure 3, using ABAQUS/
Explicit shows that Nonlinear Dynamics are analyzed.Cutter is set as rigid body, and titanium alloy sheet is elasticoplastic body, associated materials
Parameter is shown in Table 1.By v-umate subprogram, the destruction and deletion of failure strain judging unit are defined, simulation obtains near scratch
Residual stresses and strains field.
1 TB6 titanium alloy correlation mechanical property parameters of table
Since subsequent load tensile load needs to consider the residual stress and plastic strain of scratch, using restarting point
Analysis method imports and scrapes TB6 titanium alloy sheet geometry and ess-strain field data after wound model calculates, and then applies and stretch
Load.
V-notch bottom stress formula is finally modified to following form
Modified theoretical formula shares seven coefficients and needs to demarcate, wherein λ, μ, χb、χcAnd χdFive coefficients can be by first
The coefficient of beginning model carries out interpolation solution.When table 2 gives 2 α difference of v-notch opening angle, the value of above-mentioned five coefficients.
Coefficient value under 2 v-notch difference subtended angle of table
| 2α | λ | μ | χb | χc | χd |
| 0° | 0.5 | -0.5 | 1 | 4 | 0 |
| 30° | 0.5014 | -0.4561 | 1.0707 | 3.7907 | 0.0632 |
| 45° | 0.5050 | -0.4319 | 1.1656 | 3.5721 | 0.0828 |
| 60° | 0.5122 | -0.4057 | 1.3123 | 3.2832 | 0.0960 |
| 90° | 0.5448 | -0.3449 | 1.8414 | 2.5057 | 0.1046 |
| 120° | 0.6157 | -0.2678 | 3.0027 | 1.5150 | 0.0871 |
| 135° | 0.6736 | -0.2198 | 4.1530 | 0.9933 | 0.0673 |
| 150° | 0.7520 | -0.1624 | 6.3617 | 0.5137 | 0.0413 |
It can be seen that λ, μ, χb、χcAnd χdFive coefficients are related with 2 α, intended using multinomial the data in table 2
It closes, by checking computations, good fitting effect can achieve using quartic polynomial.The matched curve of five coefficients is respectively such as
Shown in Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8.
The functional form for being fitted five obtained coefficients is as follows
λ=0.50004-7.57728e-5(2α)+3.60152e-7(2α)2-5.03161e-9(2α)3+3.93471e-10(2α
)4
μ=- 0.49997+0.00133 (2 α)+4.71162e-6(2α)2-2.47154e-8(2α)3+2.27488e-10(2α)4
χb=1.00965-0.01534 (2 α)+7.71715e-4(2α)2-9.65263e-6(2α)3+4.51083e-8(2α)4
χc=4.00092-0.00338 (2 α) -1.02814e-4(2α)2-9.48405e-7(2α)3+4.99967e-9(2α)4
χd=6.82524e-5+0.00265(2α)-1.98575e-5(2α)2+5.20311e-8(2α)3-1.67154e-10(2
α)4
It can be taken by above-mentioned interpolation formula (12)-(16) in the hope of the related coefficient of size scratches different in finite element model
Value, is shown in Table 3.
The different size scratch stress field relevant parameter interpolation results of table 3
At this point, there was only a in correction formula (12)1、a2Two undetermined parameters extract finite element scuffing model bottom remnants and answer
Power and subsequent load scratch bottom stress component products, acquire stress concentration factor Kθ、Kr, and then calculate different sizes and draw
The corresponding undetermined parameter a of trace1、a2Value, is shown in Table 4.
Table 4 solves undetermined parameter a using finite element result1、a2
| R | D | r0 | Kθ | Kr | a1 | a2 |
| 0.15 | 0.15 | 0.15 | 2.405 | 0.279 | 0.6210 | 0.2161 |
| 0.15 | 0.25 | 0.15 | 2.795 | 0.356 | 1.0750 | 0.2543 |
| 0.15 | 0.3 | 0.15 | 3.024 | 0.342 | 1.3251 | 0.2498 |
| 0.2 | 0.15 | 0.15 | 2.169 | 0.206 | 0.5119 | 0.1994 |
| 0.2 | 0.25 | 0.2 | 2.599 | 0.241 | 0.9282 | 0.2008 |
| 0.2 | 0.3 | 0.2 | 2.804 | 0.281 | 1.1519 | 0.2309 |
| 0.3 | 0.15 | 0.15 | 2.070 | 0.137 | 0.4159 | 0.3104 |
| 0.3 | 0.25 | 0.25 | 2.402 | 0.177 | 0.7642 | 0.1946 |
| 0.3 | 0.3 | 0.3 | 2.640 | 0.222 | 0.9640 | 0.2432 |
| 0.4 | 0.15 | 0.15 | 1.926 | 0.095 | 0.3521 | 1.5536 |
| 0.4 | 0.25 | 0.25 | 2.272 | 0.137 | 0.6396 | 0.2318 |
| 0.4 | 0.3 | 0.3 | 2.394 | 0.160 | 0.7985 | 0.2189 |
Obviously, a1、a2It is related with scratch bottom radius R and depth D, using polynomial form respectively to a1、a2Intended
It closes, the degree of polynomial takes secondary, makees a1、a2Variation curved surface with scratch bottom radius R and depth D is as shown in Figure 9, Figure 10, intends
It is as follows to close functional form:
a1=0.2625-2.0730R+4.4715D+3.7296R2+2.6483D2-6.7259RD
a2=0.2357-0.9434R+0.6909D+1.872R2-1.285RD-0.04571D2。
Those skilled in the art can understand that unless otherwise defined, all terms used herein (including skill
Art term and scientific term) there is meaning identical with the general understanding of those of ordinary skill in fields of the present invention.Also
It should be understood that those terms such as defined in the general dictionary should be understood that have in the context of the prior art
The consistent meaning of meaning will not be explained in an idealized or overly formal meaning and unless defined as here.
Above-described specific embodiment has carried out further the purpose of the present invention, technical scheme and beneficial effects
It is described in detail, it should be understood that being not limited to this hair the foregoing is merely a specific embodiment of the invention
Bright, all within the spirits and principles of the present invention, any modification, equivalent substitution, improvement and etc. done should be included in the present invention
Protection scope within.
Claims (3)
1. the method for scratching defect bottom stress coefficient of concentration for calculating alloy surface, which is characterized in that comprise the steps of:
Step 1) according to the elastic stress field function near notch, and then releases the equation of the components of stress, by introducing perimeter strip
Part acquires the general solution of the stress field under midplane extrusion load near notch, obtains the expression formula of the indentations bottom factor of stress concentration,
Obtain the corresponding stress concentration function of notch of different bottom radius and depth；
Step 2) creates cutter and part model using ABAQUS software, and setting cutter is rigid body, and workpiece is elasticoplastic body, is led to
The destruction and elimination for crossing vumate subprogram setting breaking strain control unit, define plane-plane contact between cutter and workpiece, draw
The size of trace is characterized by bottom radius R and depth D；Nonlinear kinetics calculates generate scratch after, using restarting analysis method
Import the model after scratching, this model contains the residual stress and plastic strain information of scuffing process, then apply perpendicular to
The tensile load in scratch direction scratches destruction and elimination that model is drawn unit using breaking strain control workpiece, subsequent
Load calculates on the basis of scratching model, it is contemplated that local residual stress and local plastic strain at scuffing concentrated stress
It influences, obtains the subsequent load bottom stress coefficient of concentration of scuffing of the multiple groups difference bottom radius R, depth D of finite element modelling
Numerical result；
Step 3) is modified Elasticity indentations bottom tabulated SCFs up to formula, introduces corrected parameter；According to limited
The numerical result of the subsequent load bottom stress coefficient of concentration of scuffing of the multiple groups difference bottom radius R, depth D of member simulation, fitting
Corrected parameter is with the variation function of R, D out, and the local stress obtained according to finite element numerical analysis is as a result, to answering in step 1)
Power coefficient of concentration expression formula is modified, the factor of stress concentration after being corrected.
2. the method according to claim 1 for scratching defect bottom stress coefficient of concentration for calculating alloy surface, special
Sign is that the detailed step of step 1) is as follows:
Enable notch elastic stress field nearby are as follows:
ψ (z)=bzλ+czμ
In formula, a, b, c, d are plural forms, and λ and μ are real number, λ > 0 and λ > μ；
The expression formula for releasing the components of stress is as follows:
σθ=λ rλ-1[a1(1+λ)cos(1-λ)θ+b1cos(1+λ)θ+a2(1+λ)sin(1-λ)θ-b2sin(1+λ)θ]
+μrμ-1[d1(1+μ)cos(1-μ)θ+c1cos(1+μ)θ+d2(1+μ)sin(1-μ)θ-c2sin(1+μ)θ]
σr=λ rλ-1[a1(3-λ)cos(1-λ)θ-b1cos(1+λ)θ+a2(3-λ)sin(1-λ)θ+b2sin(1+λ)θ]
+μrμ-1[d1(3-μ)cos(1-μ)θ-c1cos(1+μ)θ+d2(3-μ)sin(1-μ)θ+c2sin(1+μ)θ]
τrθ=λ rλ-1[a1(1-λ)sin(1-λ)θ+b1sin(1+λ)θ-a2(1-λ)cos(1-λ)θ+b2cos(1+λ)θ]
+μrμ-1[d1(1-μ)sin(1-μ)θ+c1sin(1+μ)θ-d2(1-μ)cos(1-μ)θ+c2cos(1+μ)θ]
In formula, (r, θ) indicates the polar coordinates of alloy surface any point, σθ、σrAnd τrθIt respectively indicates point θ, the r and tangential answers
Force component, a1、a2It is real part, the imaginary part of a, b respectively1、b2It is real part, the imaginary part of b, c respectively1、c2It is real part, the imaginary part of c respectively,
d1、d2It is real part, the imaginary part of d respectively；
It introduces with downstream condition:
In formula, (u, v) indicates that coordinate of the alloy surface any point in auxiliary coordinates, q are the real number from 1 to 2；r0、u0、v0
The respectively coordinate of notch arc section depth and notch free boundary；
The general solution for obtaining notch stress field near notch under the effect of midplane extrusion load, in indentations bottom point r=r0, at θ=0
Expression formula are as follows:
In formula, R indication notch bottom arc radius；χb、χc、χdExpression formula is as follows:
In formula,
Then indentations bottom point tabulated SCFs reach formula are as follows:
In formula, Kθ、Kr、KrθRespectively indicate any point θ, r and the tangential factor of stress concentration.
3. the method according to claim 1 for scratching defect bottom stress coefficient of concentration for calculating alloy surface, special
Sign is that the detailed step of step 3) is as follows:
Step 3.1) is modified indentations bottom tabulated SCFs up to formula, introduces corrected parameter a1、a2:
Step 3.2), according to the subsequent load bottom stress collection of scuffing of the multiple groups difference bottom radius R of finite element modelling, depth D
The numerical result of middle coefficient, fits λ, μ, χ respectivelyb、χc、χdFunctional relation between 2 α of subtended angle of Elasticity notch；
Its model bottom remnants are extracted in step 3.3), the scuffing for multiple groups difference the bottom radius R, depth D of finite element modelling
Stress and subsequent load scratch bottom stress component products, acquire stress concentration factor Kθ、Kr, and then obtain multiple groups difference bottom
The corresponding corrected parameter a of scuffing of portion radius R, depth D1、a2Value；
Step 3.4), according to the corresponding corrected parameter a of scuffing of the multiple groups difference bottom radius R of finite element modelling, depth D1、a2
Value, using polynomial form respectively to a1、a2It is fitted, obtains a1、a2Fitting function, and then after being corrected
The factor of stress concentration.
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| CN110849753B (en) * | 2019-12-09 | 2020-09-29 | 大连理工大学 | Metal material fatigue strength prediction method based on micro scratches |
| CN110849753A (en) * | 2019-12-09 | 2020-02-28 | 大连理工大学 | Metal material fatigue strength prediction method based on micro scratches |
| CN111175157A (en) * | 2020-01-15 | 2020-05-19 | 西安交通大学 | Low-cycle fatigue performance evaluation method for welding joint |
| CN111175157B (en) * | 2020-01-15 | 2021-01-19 | 西安交通大学 | Low-cycle fatigue performance evaluation method for welding joint |
| CN111625985B (en) * | 2020-06-01 | 2023-05-23 | 恒创联拓(青岛)航空科技有限公司 | Fatigue notch coefficient data processing method, storage medium and information processing terminal |
| CN111625985A (en) * | 2020-06-01 | 2020-09-04 | 中国人民解放军海军航空大学青岛校区 | Fatigue notch coefficient data processing method considering corrosion and residual stress |
| CN111881601A (en) * | 2020-07-01 | 2020-11-03 | 中国电建集团昆明勘测设计研究院有限公司 | Earth and rockfill dam material constitutive model construction method based on deep learning and finite element unit method |
| CN111881601B (en) * | 2020-07-01 | 2023-08-15 | 中国电建集团昆明勘测设计研究院有限公司 | Soil and rock dam material constitutive model construction method based on deep learning |
| CN113109188A (en) * | 2021-03-26 | 2021-07-13 | 北京工业大学 | Airplane key structural member fatigue crack propagation online monitoring device |
| CN113505513B (en) * | 2021-07-21 | 2022-06-07 | 广西交科集团有限公司 | Calculation method for stress concentration coefficient of rusted suspender |
| CN113505513A (en) * | 2021-07-21 | 2021-10-15 | 广西交科集团有限公司 | Calculation method for stress concentration coefficient of rusted suspender |
| CN113505427B (en) * | 2021-07-30 | 2022-05-03 | 广西交科集团有限公司 | Method for calculating stress concentration coefficient of suspender with upper and lower rusted ball pits |
| CN113505427A (en) * | 2021-07-30 | 2021-10-15 | 广西交科集团有限公司 | Method for calculating stress concentration coefficient of suspender with upper and lower rusted ball pits |
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