CN108693055B - Method for acquiring material fatigue performance of thin sheet sample - Google Patents

Abstract

The invention discloses a method for obtaining material fatigue properties of a thin-film sample, comprising the following steps: Step 1: complete a tension-compression symmetrical cyclic loading test of a multi-level strain amplitude of the thin-film sample under strain control, and obtain a cyclically stable load- Displacement curve; Step 2: Connect the hysteresis loop cusps of the load-displacement curve as the cyclic load-displacement curve, and use the cyclic load-displacement relationship to predict the cyclic stress-strain relationship conforming to the Ramberg-Osgood constitutive model; Step 3: Use the cyclic stress-displacement relationship The strain relationship is a material parameter, and the relationship between the real strain amplitude ε _r of the fatigue source RVE, the stress amplitude σ _r and the measured and controlled strain amplitude ε _eq is established; Step 4: Establish a fatigue life estimation model according to ε _r and σ _r to obtain the material fatigue performance; The invention overcomes the material size limitation of the traditional fatigue performance test detection method, and does not need to rely on empirical formulas, and is suitable for different materials and sample configurations.

Description

Method for obtaining material fatigue properties of thin specimens

technical field

The invention relates to the field of fatigue performance testing, and specifically introduces a method for obtaining material fatigue performance of thin-film samples.

Background technique

As the basic content of structural stability and system safety evaluation, the fatigue mechanical properties of materials are of great significance to engineering safety analysis. The low-cycle fatigue properties of a material mainly include the low-cycle stress-strain relationship and the fatigue life curve of the material: the former describes the intrinsic physical relationship of the mechanical behavior of the material under elastoplastic fatigue loading, and is the strength analysis of the service structure under cyclic loading. Importance; the latter describes the service state of materials under cyclic loading, and is the basic curve for life assessment and safety assessment of materials or structures.

A large number of mechanisms or components are subjected to cyclic loads such as temperature and pressure for a long time, and the material fatigue performance of key structures is necessary for system safety evaluation and failure analysis. However, on the one hand, due to the wide application of small devices or thin-walled pipes in life and production, such as microelectromechanical systems, biomedical engineering, and new energy systems, due to the limitation of material size, it is difficult to meet the sampling requirements of traditional testing methods; On the one hand, in order to meet the residual life detection requirements of micro-damage sampling of active structures, such as aircraft engine blades and reactors, boilers, pipes, etc., it is difficult to complete this task by using existing fatigue test methods.

Fatigue performance testing of thin-film specimens is a method used for material fatigue performance testing in the past 30 years. .E,Cyclic Stress-Strain and Fatigue Properties of Sheet Steel as Affected by Load Spectra[J].Testing and Evaluation.1983.66-74.) and Wisner (Wisner SB, Reynolds MB, Adamson RB. Fatigue Behavior of Irradiated and UnirradiatedZircaloy and Zirconium [J]. American Society for Testing and Materials, 1994.499-520) and others designed funnel-arc plate-shaped specimens to carry out symmetrical cyclic tests, using the average strains in the thickness direction and width direction to carry out cyclic control tests, in order to study the thin plate Fatigue research provides sample configuration design and test technical support; Jia Qi, Cai Lixun (Jia Qi. Research and application of fatigue and fracture performance testing methods for special-shaped samples [D]. Southwest Jiaotong University, Master, 2011.; Jia Qi, Cai Lixun , Bao Chen. Low-cycle fatigue test method for thin sheet materials considering cyclic plasticity correction [J]. Engineering Mechanics, 2014, 1:030.) The low-cycle fatigue test was also completed with funnel plate specimens. The material proposes the stress-strain hysteresis loop rising segment in the stable stage of the strain amplitude as the cyclic stress-strain relationship of the material, and completes the prediction of the fatigue life of special materials; Yin Tao, Cai Lixun, etc. (Yin Tao, Cai Lixun, Chen Hui, Yao Di .Research on the testing method of material elastic-plastic cyclic constitutive relation based on micro-slice funnel specimen[J].Engineering Mechanics, 2017; The test method of [J]. Chinese Journal of Mechanical Engineering, 2017, 1:030.) Low-cycle fatigue testing of finished materials using millimeter-thick funnel-sheet specimens. Since the external force work is equal to the variable energy, the strain energy is divided into energy separation functions related to the material, geometry and deformation, and the deformation energy is used as the bridge to establish the relationship between load, displacement and material, geometry, etc. The energy separation function is as follows:

In the formula: f ₁ (K) is the material function, f ₂ (ξ) is the geometric deformation domain function, f ₃ (h) is the deformation function, α is the plastic equivalent deformation volume coefficient, β is the equivalent strain coefficient; according to the cycle Load-displacement relationship, reverse prediction to obtain material elastic modulus E, strength coefficient K and hardening exponent n conforming to the Ramberg-Osgood constitutive model;

Among them, η, β, γ are coefficients related to materials and geometry. Taking the cyclic stress-strain relationship as the material property, the stress and strain of the root RVE of the material under any strain amplitude are obtained by finite element calculation, and the fatigue life prediction of the material is completed.

Hui Chen,Cai Lixun(Hui Chen,Cai Lixun.Theoretical model for predicting uniaxial stress-strain relation by dual conical indentation based on equivalent energy principle[J].Acta Materialia,2016,121:181-189.Hui Chen,CaiLixun.Unified elastoplastic model based on a strain energy equivalence principle[J].Applied Mathematical Modelling,2017,52:664–671;Hui Chen,CaiLixun.Unified ring-compression model for determining tensile properties of tubular materials[J].2017,13:210-220. Peng Y Q, Cai L X, Chen H, et al. A new method based on energy principle to predict uniaxial stress-strain relations of ductile materials by small punch testing[J]. International Journal of Mechanical Sciences, 2018.) proposed Chen-Cai energy et al. According to the effective method, the total deformation energy of the deformation domain is equivalent to the product of the average deformation energy and the volume of the domain through the integral median value of the deformation domain; according to the momentum theorem, the work of the external force is equal to the variable of the internal energy, and the relationship between the load displacement and the strain is established. :

Thereby, the theoretical connection between the load-displacement relationship and the stress-strain relationship is established.

In the prior art, the low-cycle symmetric fatigue test has been completed for the thin-film funnel sample, which provides the support of test conditions and test techniques; and the specific geometric relationship of the thin-film funnel sample (the thin-film width W/funnel radius R=3) is given. Load-displacement semi-analytical model; it is used to predict the cyclic stress-strain relationship of materials and complete the prediction of fatigue life; however, this model is only for the sample configuration with geometric similarity, and it is not common to other sample configurations. In the Chen-Cai energy equivalent method, the theoretical guidance of the energy equivalent method is given, and there are calculation examples for the uniaxial constitutive relationship of different sample configurations, which provides guidance for the acquisition of the cyclic stress-strain relationship effect.

SUMMARY OF THE INVENTION

The invention provides a method for obtaining the material fatigue properties of thin slice samples, which overcomes the material size limitation of the traditional fatigue performance test detection method, and can obtain the material cyclic stress-strain relationship and predict the material fatigue life without relying on empirical formulas.

The technical scheme adopted in the present invention is: a method for obtaining material fatigue properties of thin-film samples, comprising the following steps:

Step 1: Obtain a cyclically stable load-displacement curve through the symmetric cyclic loading test of the multi-level strain amplitude of the thin sheet under strain control;

Step 2: Connect the hysteresis loop cusps of the load-displacement curve as the cyclic load-displacement curve, and use the cyclic load-displacement relationship to predict the cyclic stress-strain relationship conforming to the Ramberg-Osgood constitutive model;

Step 3: Using the cyclic stress-strain relationship as the material parameter, establish the relationship between the fatigue source RVE real strain amplitude ε _r , the stress amplitude σ _r and the measurement and control strain amplitude ε _eq ;

Step 4: Establish a fatigue life estimation model according to ε _r and σ _r to obtain material fatigue properties.

Further, the fatigue source strain amplitude and stress amplitude are based on the cyclic stress-strain relationship. The specific process of step 2 is as follows:

S1: Linearly fit the elastic segment of the cyclic load-displacement curve, and fit the plastic segment through a power law to obtain the slope S, the loading curvature C and the exponent m, respectively;

where: h _e is the elastic displacement, h is the elastic-plastic displacement, and P is the external load;

S2: Bring the S and C obtained from the above formula into the following formula:

where E is the elastic modulus of the material, K is the stress intensity coefficient, n is the strain hardening exponent, k ₀ , k ₁ and k ₂ are constants, R is the characteristic length in the sample, and A* represents the characteristic area;

S3: Substitute the E, K, and n obtained in step S2 into the Ramberg-Osgood model to obtain the cyclic stress-strain relationship of the material;

where ε is the total strain, ε _e is the elastic strain, and ε _p is the plastic strain.

Further, the k ₀ , k ₁ and k ₂ are obtained by finite element calibration, and the relationship is as follows:

In the formula, a ₁ , a ₂ and a ₃ are k ₀ coefficients, b ₁ , b ₂ and b ₃ are k ₁ coefficients, c ₁ , c ₂ and c ₃ are k ₂ coefficients, and λ is a geometric factor.

Further, in the step 4, the Manson-Coffin model fatigue life prediction is adopted.

Further, the samples include funnel-shaped samples and annular samples.

Further, in the funnel-shaped sample, the conversion formulas of the measured and controlled strain amplitude _εm across both sides of the funnel, the true strain amplitude _εr at the root of the funnel, and the average stress amplitude _σa and the true stress amplitude _σr are established by finite element. The strain ranges for low fatigue are as follows:

Wherein the average stress amplitude σ _a =P/A, A is the cross-sectional area of the funnel root, c ₁ ～c ₂ , d ₁ ～d ₂ are the coefficients related to the material geometry and material properties.

The beneficial effects of the present invention are:

(1) The method of the present invention overcomes the material size limitation of the traditional fatigue performance test detection method, and does not need to rely on empirical formulas, and can accurately obtain the cyclic stress-strain relationship of the material according to the unified and simple calibration of the finite element, and complete the material fatigue life prediction, Applicable to different materials and sample configurations;

(2) The present invention solves the key problems of the fatigue state of small structural parts, thin-walled pipes, welding materials and residual life detection of micro-damage sampling of active structures;

(3) The present invention is of great significance to the acquisition of material fatigue mechanical properties of thin-walled structures and tiny components that widely exist in key engineering fields such as microelectromechanical systems, aviation, energy systems, and biomedicine.

Description of drawings

FIG. 1 is a schematic diagram of a sample working section adopted in the embodiment of the present invention.

FIG. 2 is the finite element analysis model of the annular sample in the embodiment of the present invention.

FIG. 3 is a Ramberg-Osgood power law constitutive curve in the present invention.

Fig. 4 is the cyclic load-displacement curve of the GH4169 circular ring sheet sample in the embodiment of the present invention.

FIG. 5 is the predicted result of the cyclic stress-strain curve of the GH4169 annular thin slice sample in the embodiment of the present invention.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

A method for acquiring fatigue properties of thin-film sample materials, comprising the following steps:

Step 1: Perform an axial tension-compression symmetrical cyclic test on the sample to obtain a load-displacement curve;

As shown in Figure 1, the sample is of funnel shape and annular shape, and its working section configuration diagram is shown in Figure 1; the finite element analysis model of the annular sample is shown in Figure 2; the micro-force test loading device is used Load the funnel and ring sheet specimens symmetrically in tension and compression cycles to obtain the number of cycles under each load and the peak and valley values of load and displacement for each cycle, and obtain the load-displacement (P-h) curve; The fatigue test is an important part of the technical solution of the present invention; the sample is completed under the strain control of the fatigue sample; in order to obtain sufficient low-cycle fatigue information of the material, the minimum life of the material is about 1000 times, and the maximum life is about 10,000 times. The strain amplitude is divided into 7 grades, and each grade is not less than two samples.

Step 2: Connect the hysteresis loop cusps of the load-displacement curve as the cyclic load-displacement curve, and obtain the cyclic stress-strain relationship according to the Ramberg-Osgood model;

S1: Linearly fit the elastic segment of the cyclic load-displacement curve, and fit the plastic segment through a power law to obtain the slope S and the loading curvature C respectively;

where: h _e is the elastic displacement, h is the elastic-plastic displacement, and P is the external load;

S2: Bring the S and C obtained from the above formula into the following formula:

In the formula: E is the elastic modulus of the material, K is the stress intensity coefficient, n is the strain hardening index, k ₀ , k ₁ and k ₂ are constants, R is the characteristic length in the sample, and A* represents the characteristic area; The shape and structure of the sample used are shown in Figure 1. The A end of the loading line is the fixed end, and the B end is the displacement loading end; it is assumed that the characteristic length h ^* = R, and R represents the notch radius or ring of the arc funnel sample The outer diameter of the thin sample; the characteristic volume V ^* =h ^* A ^* , A ^* represents the characteristic area, for the funnel sample A ^* =(2w-πR)t, w is the width of the working section, t is the thickness of the sample; Ring sheet sample, A ^* =π(R ² -r ² ), r is the pore size of the sample.

Specimens with different geometric shapes are represented by the geometric factor λ, where for the funnel sheet specimen, λ=w/R, and λ∈[2.75,4]; and for the ring sheet specimen, λ=r/R, λ∈[0.48, 0.72]; in which the dimensionless constants k ₀ , k ₁ and k ₂ can be obtained through finite element analysis and calibration, and have a quadratic parabolic relationship with the geometric factor:

According to the measurement requirements, the loading line displacement of the funnel sheet sample, the displacement across the two sides of the funnel and the lateral displacement of the funnel root can be selected respectively, and the loading line displacement of the ring sample or the lateral displacement of the ring can be selected. Table 1 shows:

Table 1. List of parameters

For other geometries, just recalibrate k ₀ , k ₁ and k ₂ in the finite element and the model still works.

S3: Substitute the E, K, and n obtained in step S2 into the Ramberg-Osgood model to obtain the cyclic stress-strain relationship of the material;

where ε is the total strain, ε _e is the elastic strain, and ε _p is the plastic strain.

The present invention selects a Ramberg-Osgood (R-O) stress-strain relationship model that describes the yield zone better;

ε=ε _e +ε _p

Step 3: According to the cyclic stress-strain relationship, establish the relationship between the real strain amplitude ε _m of the fatigue source RVE, the stress amplitude σ _m and the average strain amplitude ε _eq ;

Step 4: Establish a fatigue life estimation model according to ε _m and σ _m to obtain material fatigue properties.

The strain amplitude-life curve is the basic curve for evaluating the fatigue life of materials or structures, and the existing standards have given the acquisition method; the key is to obtain the actual strain amplitude of the fatigue source RVE (Representative Volume Element, material representative volume element) and Stress amplitude: According to the material cyclic stress-strain relationship as material properties, simple finite element elastoplastic calculation is performed to establish the relationship between the fatigue source RVE real strain amplitude ε _m , stress amplitude σ _m and average strain amplitude ε _eq , according to ε _m and σ _m Establish the fatigue life Manson-Coffin estimation model, complete the life prediction, and obtain the material fatigue properties.

specific embodiment

The present invention takes the fatigue performance test of the funnel sheet sample and the ring sheet as an example. The sample is divided into a clamping section and a working section, and the working sections of the two kinds of samples are shown in Figure 1. A finite element simulation model is established. The mesh model of the working section is shown in Figure 2. One end is fixedly hinged, and the other end is loaded in one direction. The Ramberg-Osgood constitutive model is used to calculate the material properties. The model curve is shown in Figure 3, which includes elastic modulus, strengthening coefficient and hardening index. Different material parameters and geometric configuration parameters are changed to carry out finite element simulation of various working conditions. The corresponding load-displacement curve is obtained, and the elastic and plastic coefficients are calibrated.

The tension-compression symmetric fatigue test under strain control was completed by using the funnel sheet sample of GH4169 material, the thickness t=0.5mm, the arc radius R=1.2mm, and the working section width w=3.6mm; The displacement on both sides of the collection funnel is represented by h. Figure 4 shows the cyclically stable load-displacement hysteresis curve, and the cusp of the connecting hysteresis loop is the cyclic load-displacement characteristic curve.

The linear segment of the curve is fitted with a straight line, and the pure plastic part is fitted with a power law to obtain the parameters of the Ramberg-Osgood constitutive model: elastic modulus E, strengthening coefficient K, and hardening exponent n, and substitute the obtained E, K, and n into the model The cyclic stress-strain relationship of the material is obtained; the cyclic stress-strain curves predicted according to different thin samples and the predicted results of the equivalent round bar fatigue test of the same material are shown in Figure 5. The cyclic stress-strain curves of different thin samples are basically Coinciding with the results of the equivalent round bars. In actual use, the sample size and geometric ratio can be adjusted according to the material size and test conditions, and the parameters of different geometric configurations of the working section can also be simply calculated by finite element. Using the cyclic stress-strain relationship to obtain the true stress and strain of the material, the fatigue life prediction method based on the stress and strain is more commonly used, and will not be repeated here.

In the present invention, the micro-force test loading device is used to load the funnel and the circular ring sheet sample in a tension-compression symmetrical cycle to obtain the number of cycles under each level of load and the load and displacement peak and valley values of each _cycle . /2) The cyclic stress-strain relationship of the material is predicted by the load-displacement hysteresis curve, and the relationship between ε _eq -ε _m and ε _eq -σ _m is established on this basis to complete the Manson-Coffin fatigue life prediction; the invention overcomes the The material size limitation of the traditional fatigue performance testing method does not need to rely on empirical formulas, and can obtain the cyclic stress-strain relationship of the material more accurately, and complete the fatigue life prediction of the material; The key technical issues in the residual life detection of micro-damage sampling of active structures; Predictive acquisition is important.

Claims (5)

1. A method for acquiring material fatigue performance of a sheet sample is characterized by comprising the following steps:

step 1: obtaining a load-displacement curve with stable circulation through a tension-compression symmetrical cyclic loading test of a sheet sample under the strain control in a multistage strain amplitude;

step 2: connecting the hysteresis loop sharp points of the load-displacement curve as a cyclic load-displacement curve, and predicting the cyclic stress-strain relation which accords with the Ramberg-Osgood constitutive model according to the cyclic load-displacement relation;

and step 3: the circulation stress-strain relation is taken as a material parameter to establish the RVE real strain amplitude of the fatigue source_rStress amplitude σ_rAnd measure and control strain amplitude_eqThe relationship of (1);

and 4, step 4: according to_rAnd σ_rEstablishing a fatigue life estimation model to obtain the fatigue performance of the material;

the specific process of the step 2 is as follows:

s1: performing linear fitting on the cyclic load-displacement curve elastic segment, and respectively obtaining a slope S, a loading curvature C and an index m through power law fitting on the plastic segment;

in the formula: h is_eElastic displacement, h elastic-plastic displacement and P external load;

s2: substituting S and C from the above formula into the following formula:

in the formula: e is the elastic modulus of the material, K is the stress intensity coefficient, n is the strain hardening index, K₀、k₁And k₂Is constant, R is the characteristic length of the sample, and A represents the characteristic area;

s3: substituting E, K, n obtained in the step S2 into a Ramberg-Osgood model to obtain a cyclic stress-strain relation of the material;

in the formula: in order to be the total strain,_ein order to be elastically strained,_pis a plastic strain.

2. The method for obtaining the material fatigue property of the thin slice sample according to claim 1, wherein the k is₀、k₁And k₂Obtained by finite element calibration and the relationship is as follows:

in the formula, a₁、a₂And a₃Is k₀Coefficient, b₁、b₂And b₃Is k₁Coefficient, c₁、c₂And c₃Is k₂The coefficient, λ, is the geometric factor.

3. The method for acquiring the material fatigue property of the flake sample according to claim 1, wherein a Manson-coffee model fatigue life prediction is adopted in the step 4.

4. The method for acquiring the material fatigue property of the thin slice sample as claimed in claim 1, wherein the sample comprises a funnel-shaped sample and a circular ring-shaped sample.

5. The method for obtaining material fatigue performance of thin slice sample according to claim 4, wherein in the funnel-shaped sample, the measurement and control strain amplitude across two sides of the funnel is established by finite elements_mAmplitude of true strain of funnel root_rAnd the mean stress amplitude σ_aWith the true stress amplitude sigma_rThe transformation formula of (c) in the low fatigue strain range is as follows:

wherein the mean stress amplitude σ_aP/A, A is the cross-sectional area of the root of the funnel, c₁～c₂、d₁～d₂Is a coefficient related to the material geometry and material properties.

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