Method for obtaining elastic-plastic fatigue crack growth rate based on low-cycle fatigue test

Abstract

This invention discloses a method for obtaining the elastoplastic fatigue crack propagation rate based on low-cycle fatigue testing, comprising obtaining the crack depth α in the field of fatigue crack propagation rate acquisition technology. i The ratio of the diameter of the sample to the diameter D, a i / D and modulus ratio E ui / E u0 First calibration relationship; obtain crack propagation rate da / dN; obtain stress intensity factor ΔK i With crack depth a i The third calibration formula; obtain the elastic-plastic fracture toughness value ΔJ i Calculate the relationship; obtain the crack propagation rate da / dN and the elastoplastic fracture toughness value ΔJ. i The fitting formula is provided. This invention can obtain the fatigue crack propagation rate of metallic materials in the elastoplastic state through low-cycle fatigue testing, breaking the limitation of existing fatigue crack propagation tests that are only applicable to linear elastic stress state and normal stress ratio. It solves the problem that the fatigue crack propagation rate in the elastoplastic state cannot be tested, and can be applied to the life assessment and damage tolerance evaluation of tough materials under high loads.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fatigue crack growth rate acquisition, in particular to a method for acquiring elastic-plastic fatigue crack growth rate based on low-cycle fatigue test. BACKGROUND

[0002] Defects such as holes, scratches or damages will inevitably exist or be produced in the production, processing and long-term operation of engineering component materials, and the fatigue crack growth rate of the material is a key indicator for judging whether the component containing defects can be safely operated. At present, the fatigue crack growth rate test of metal materials is based on the standard "GBT 6398-2017 Metal Material Fatigue Crack Growth Rate Test Method", and the recommended sample is a rectangular cross-section sample with an initial crack prepared. A lower alternating load is applied to the sample, and the crack depth is calculated by measuring the notch opening displacement of the sample using a COD rule to obtain the relationship between the fatigue crack growth rate and the linear elastic stress intensity factor ΔK. The relationship between the crack depth and the notch opening displacement in the standard is obtained based on the linear elastic strain state calibration, and is suitable for the plane strain crack propagation state under a lower load. However, for ductile materials, the plastic zone at the crack tip increases under a higher load exceeding the yield strength, which does not meet the requirement of small-scale yielding in linear elastic fracture mechanics, and the plane strain stress intensity factor ΔK is not suitable for description. At present, there is no perfect test method for the fatigue crack growth rate under the elastic-plastic state.

[0003] Since the sample is subjected to alternating load-induced crack propagation during the low-cycle fatigue and crack propagation rate test of metal materials, scholars at home and abroad have conducted many studies on the relationship between low-cycle fatigue behavior and crack propagation rate. The main focus is on establishing a prediction formula for linear elastic fatigue crack growth rate based on several fitting parameters of low-cycle fatigue. The construction of existing prediction formulas usually ignores the difference in stress ratio of alternating load, resulting in low reliability of the calculation results. Moreover, low-cycle fatigue usually uses high load higher than the yield strength, and the crack tip is in a large-scale yielding state. Whether it can be equivalent to the fatigue crack propagation failure criterion based on small-scale yielding stress-strain field is still controversial. Therefore, at present, there is no method for accurately acquiring the fatigue crack growth rate of metal materials under the elastic-plastic state. SUMMARY

[0004] Therefore, the purpose of the present application is to provide a method for acquiring elastic-plastic fatigue crack growth rate based on low-cycle fatigue test, so as to solve the technical problem that the fatigue crack growth rate of metal materials under the elastic-plastic state cannot be acquired.

[0005] The technical scheme adopted by the present application is: a method for acquiring elastic-plastic fatigue crack growth rate based on low-cycle fatigue test, which is used for acquiring the fatigue crack growth rate of metal materials under the elastic-plastic state, and the method comprises the following steps:

[0006] Obtaining the crack initiation unloading elastic modulus E of low cycle fatigue test u0 and the tensile unloading elastic modulus E after crack initiation ui ;

[0007] Obtaining the ratio a / D of the crack depth a i and the specimen diameter D i Obtaining the first calibration relation of the modulus ratio E ui / E u0 ;

[0008] Obtaining the crack propagation rate da / dN

[0009] Obtaining the ratio S / S0 of the crack surface area S ci and the specimen cross section area S0 ci Obtaining the second calibration relation of the modulus ratio E ui / E u0 ;

[0010] Obtaining the third calibration relation of the stress intensity factor AK i and the crack depth a i ;

[0011] Obtaining the calculation relation of the elastic-plastic fracture toughness value ΔJ i and the stress intensity factor AK i , the crack surface area S ci , the specimen cross section area S0 and the plastic zone area U pi ;

[0012] Obtaining the fitting formula of the crack propagation rate da / dN and the elastic-plastic fracture toughness value ΔJ i .

[0013] Preferably, the first calibration relation is:

[0014]

[0015] wherein p0~p n are calibration coefficients of the first calibration relation, and D is the specimen diameter.

[0016] Preferably, the second calibration relation is:

[0017]

[0018] wherein q0~q n are calibration coefficients of the second calibration relation, and S0 is the original cross section area of the specimen.

[0019] Preferably, the third calibration relation is:

[0020]

[0021] wherein, △F is the fatigue load range value, △F=F max -F min ; S0 is the original cross-sectional area of the sample, and D is the sample diameter, k0~k n is the calibration coefficient of the third calibration formula.

[0022] Preferably, 4≤n≤6.

[0023] Preferably, the calculation formula is:

[0024]

[0025] wherein, △J ei is the elastic component, and △J pi is the plastic component.

[0026] Preferably, the fitting formula is:

[0027]

[0028] wherein, C is the fitting coefficient, and m is the fitting index.

[0029] Preferably, the sample is a round bar sample; wherein the calculation formula of the crack surface area S ci is:

[0030]

[0031] wherein, S c is the crack surface area, θ is the angle value of the crack chord length corresponding to the central angle, a is the length of the deepest part of the crack, 2c is the chord length of the intersection of the crack and the sample surface, and D is the sample diameter,

[0032] Preferably, the sample of the low-cycle fatigue test is a round bar sample; after the low-cycle fatigue test is completed, the heating coloring method is used to mark the crack front edge.

[0033] Preferably, the obtaining of the crack propagation rate da / dN specifically comprises: calculating the crack depth a i corresponding to the unloading elastic modulus of each cycle of the low-cycle fatigue, i drawing the a-N curve of the crack depth a i and the cycle number N, and using the secant method or the polynomial method to obtain the crack propagation rate da / dN.

[0034] The beneficial effects of the present application are:

[0035] The method of the present application can obtain the fatigue crack propagation rate of the metal material in the elastic-plastic state through the low-cycle fatigue test, which not only simplifies the test process, but also reduces the test cost; the method of the present application is suitable for any strain ratio and high-temperature test environment, breaks the limitation that the existing fatigue crack propagation test is only suitable for linear elastic stress state and positive stress ratio, solves the problem that the fatigue crack propagation rate in the elastic-plastic state cannot be tested, and can be applied to the life evaluation and damage tolerance evaluation of ductile materials under the action of a higher load, and is especially suitable for the fatigue crack propagation life evaluation of circular cross-section components. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 A schematic diagram of a semi-elliptical crack of a circular cross-section sample of the present application;

[0037] Figure 2 A relationship curve between the tensile unloading elastic modulus and the cycle number of the present application;

[0038] Figure 3 A relationship curve between the crack depth and the cycle number of the present application;

[0039] Figure 4 A crack propagation rate curve in the elastic-plastic state of the present application. DETAILED DESCRIPTION

[0040] The specific embodiments of the present application will be further described in detail below with reference to the accompanying drawings. These embodiments are only used to illustrate the present application, and are not limiting to the present application.

[0041] In the description of the present application, it should be noted that the orientations or positional relationships indicated by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like are based on the orientations or positional relationships shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and therefore cannot be understood as indicating or implying that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application. In addition, the terms "first", "second" are only for description purposes, and cannot be understood as indicating or implying relative importance.

[0042] In the description of the present application, it should be noted that, unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connection" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium, or it can be the communication inside two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0043] Furthermore, in the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0044] Examples, such as Figures 1-4 As shown, a method for obtaining the elastoplastic fatigue crack propagation rate based on low-cycle fatigue testing is used to obtain the fatigue crack propagation rate of metallic materials in an elastoplastic state. The method includes the following steps:

[0045] Obtain the crack initiation unloading elastic modulus E from low-cycle fatigue tests. u0 And the tensile unloading elastic modulus E after crack initiation ui .

[0046] Obtain the crack depth a i The ratio of the diameter of the sample to the diameter D, a i / D and modulus ratio E ui / E u0 The first calibration relation is: First, calculate the crack depth 'a' corresponding to each cycle in the low-cycle fatigue test using the first calibration formula. i Then, by plotting the crack depth a i With the number of loops N i The aN curve was used to obtain the crack propagation rate da / dN.

[0047] Obtain the crack surface area S ci The ratio S to the cross-sectional area S0 of the sample ci / S0 and modulus ratio E ui / E u0 The second calibration relation is: The crack surface area S corresponding to each cycle in the low-cycle fatigue test is calculated using the second calibration formula. ci .

[0048] Obtain the stress intensity factor ΔK i With crack depth a i The third calibration relation is: The crack depth a in the low-cycle fatigue test was calculated using the third calibration formula. i The corresponding stress intensity factor ΔK i .

[0049] Obtain the elastic-plastic fracture toughness value ΔJ i With stress intensity factor ΔK i Crack area S ci The cross-sectional area S0 and the area of ​​the plastic region U of the sample pi The calculation formula is as follows: And the corresponding elastic-plastic fracture toughness value of each cycle in the low cycle fatigue test is calculated by calculating the relationship i .

[0050] The power function fitting formula of the crack propagation rate da / dN and the elastic-plastic fracture toughness value ΔJ i is obtained, and the power function fitting formula is:

[0051] The fatigue crack propagation rate obtaining method of the application can obtain the fatigue crack propagation rate of the metal material in the elastic-plastic state through the low cycle fatigue test, which not only simplifies the test process, but also reduces the test cost; the fatigue crack propagation rate obtaining method of the application is suitable for any strain ratio and high temperature test environment, breaks the limitation that the existing fatigue crack propagation test is only suitable for linear elastic stress state and positive stress ratio, solves the problem that the fatigue crack propagation rate in the elastic-plastic state cannot be tested, and can be applied to the life evaluation and damage tolerance evaluation of ductile materials under the action of a higher load, and is especially suitable for the fatigue crack propagation life evaluation of circular cross-section components.

[0052] In embodiment 1, as shown in Figures 1-4 , a method for obtaining an elastic-plastic fatigue crack propagation rate based on a low cycle fatigue test is used to obtain the fatigue crack propagation rate of a metal material in an elastic-plastic state, and the method comprises the following steps:

[0053] S1: According to the low cycle fatigue test standard "GBT 15248-2008 Metal Material Axial Constant Amplitude Low Cycle Fatigue Test Method", the extensometer is clamped on the round bar sample, and the two ends of the sample are clamped on the fatigue testing machine, the strain amplitude is controlled to perform fatigue test, and the test is stopped until the predetermined load decreases by a predetermined percentage or the sample is broken. During the entire test process, the corresponding maximum load F max , minimum load F min , tensile unloading elastic modulus E u and hysteresis loop of each cycle are recorded by software.

[0054] S2: As shown in Figure 2 , the E u -N i curve of the tensile unloading elastic modulus E u and the cycle number N i is drawn; in the E u -N i curve, the tensile unloading elastic modulus E u decreases in the middle and late stages of the low cycle fatigue test, the cycle number at the beginning of the decrease is selected as the crack initiation cycle number, which is denoted as N u0 , and the tensile unloading elastic modulus corresponding to the crack initiation cycle number N u0 is taken as the crack initiation elastic modulus, which is denoted as E u0Crack initiation cycle number N u0 The tensile unloading modulus corresponding to the previous number of cycles is the tensile unloading modulus before crack initiation, and the number of cycles for crack initiation N is... u0 The tensile unloading modulus corresponding to the subsequent number of cycles is the tensile unloading modulus after crack initiation, denoted as E. ui .

[0055] S3: Calculate the tensile unloading elastic modulus E after crack initiation. ui With crack initiation elastic modulus E u0 The ratio E ui / E u0 .

[0056] S4: After low-cycle fatigue testing, the specimens are imprinted using a heat-dyeing method, and the crack depth is measured after fracture; among other things, such as... Figure 1 As shown, the crack surface shape of low-stress fatigue is generally semi-elliptical. The length of the deepest part of the crack is denoted as a, and the chord length where the crack intersects the sample surface is denoted as 2c.

[0057] S5: Obtain crack depth a i The ratio a to the sample diameter D i / D and modulus ratio E ui / E u0 The first calibration relation is: Used to calculate the crack depth 'a' corresponding to each cycle in a low-cycle fatigue test. i For round bar specimens of the same material and radial dimensions that have already been calibrated, the calibration coefficients (p0~p1) in the first calibration formula are... n The value is constant and the known calibration coefficient can be used directly. For the first calibration of a round bar sample, the specific calibration process is as follows:

[0058] The first calibration method: Take n=5, refer to S1-S3 to conduct low-cycle fatigue tests on multiple round bar specimens of the same specifications, and obtain the crack depth 'a' corresponding to the last cycle of the 5 round bar specimens. i And the tensile unloading elastic modulus E after crack initiation ui Then, the calibration coefficients p0 to p5 in the first calibration formula are obtained through calculation.

[0059] The second calibration method: Taking n=5, perform low-cycle fatigue tests on the round bar specimens according to S1-S3, and obtain the crack depth 'a' corresponding to 5 cycles for the same round bar specimen through finite element analysis. i and the tensile unloading elastic modulus E after crack initiation ui Then, the calibration coefficients p0 to p5 in the first calibration formula are obtained through calculation.

[0060] S6: Calculate the crack depth a corresponding to each cycle of low cycle fatigue test according to the first calibration relationship i ; as shown in Figure 3 , the crack depth a i and the cycle number N i are plotted, and the crack propagation rate da / dN is obtained by using secant method or polynomial method.

[0061] S7: Obtain the ratio S ci / S0 of the crack surface area S ci and the specimen cross-sectional area S0, and the modulus ratio E ui / E u0 of the second calibration relationship, and the second calibration relationship is: for calculating the crack surface area S ci corresponding to each cycle of low cycle fatigue test.

[0062] wherein, for the same material and the same radial size of round bar specimen, the calibration coefficients (q0-q n , 4≤n≤6) in the second calibration relationship are constant values, and the known calibration coefficients can be directly used.

[0063] wherein, the calibration method of the calibration coefficients q0-q n refers to the calibration method of the calibration coefficients p0-p n in the first calibration relationship.

[0064] In determining the calibration coefficients in the second relationship, the calculation formula of the crack surface area S ci is: and the calculation formula of the specimen cross-sectional area S0 is:

[0065] wherein, S c is the crack surface area, θ is the central angle angle corresponding to the crack chord length, D is the specimen diameter,

[0066] S8: Obtain the third calibration relationship of the stress intensity factor △K i and the crack depth a i , and the third relationship is: for calculating the stress intensity factor △K i corresponding to the crack depth a i in the low cycle fatigue test.

[0067] wherein, △F is the fatigue load range value, △F=F max -F min ; S0 is the original cross-sectional area of the specimen, D is the specimen diameter, k0-k nThese are the calibration coefficients for the third calibration relation.

[0068] Among them, the calibration coefficients k0~k n The calibration method refers to the calibration coefficients p0 to p in the first calibration formula. n The calibration method.

[0069] S9: Obtain the area U of the plastic region enclosed by the hysteresis loop for each iteration. pi .

[0070] S10: Obtain the elastic-plastic fracture toughness value ΔJ for each cycle. i The calculation formula is:

[0071] Used to calculate the elastoplastic fracture toughness value ΔJ corresponding to each cycle in the low-cycle fatigue test. i .

[0072] Among them, △J ei For the elastic component, ΔJ pi This is the plastic component.

[0073] S11: As Figure 4 As shown, the crack depth propagation rate da i / dN and elasto-plastic fracture toughness value △J i Power function fitting was performed to obtain the fitting parameters between crack propagation rate and elastoplastic fracture toughness value:

[0074]

[0075] Where C is the fitting coefficient and m is the fitting exponent.

[0076] Specific embodiments, such as Figures 1-4 As shown, a method for obtaining the elastoplastic fatigue crack propagation rate based on low-cycle fatigue testing is described. The method includes the following steps:

[0077] S1: The test material is processed into a round bar specimen with a diameter D = 8 mm. An extensometer is clamped onto the round bar specimen to control and measure the strain. The round bar specimen with the extensometer is mounted on a fatigue testing machine, and a triangular wave fatigue test is performed on the specimen using strain control. The strain ratio is -1, and the strain amplitude is ±0.4%. The fatigue test is run until failure and fracture. In this embodiment, the number of failures N f =6424 cycles, the sample material was 30Cr2Ni4MoV alloy, the elastic modulus E = 202 GPa and the yield strength R at room temperature. p0.2 =810MPa, tensile strength R m =910 MPa.

[0078] S2: During the low-cycle fatigue test, software is used to record the maximum load F corresponding to each cycle. max Minimum load F min , tensile unloading elastic modulus E u And hysteresis loop.

[0079] S3: As Figure 2 As shown, plot the tensile unloading elastic modulus E. u and the number of iterations N i E u -N i Curve. In E u -N i On the curve, the elastic modulus E under tensile unloading in the middle and late stages of the fatigue test u The number of cycles at the point where the descent begins is selected as the crack initiation cycle number, denoted as N. u0 In this embodiment, N u0 = 4860 times; crack initiation cycle number N u0 The corresponding tensile unloading elastic modulus is the crack initiation elastic modulus, denoted as E. u0 In this embodiment, E u0 =186900MPa.

[0080] S4: Calculate the number of crack initiation cycles N u0 The tensile unloading elastic modulus E after crack initiation ui With crack initiation elastic modulus E u0 The ratio E ui / E u0 .

[0081] S5: Based on crack depth a i The ratio a to the sample diameter D i / D and modulus ratio E ui / E u0 First calibration relation Calculate the crack depth 'a' corresponding to each cycle in the low-cycle fatigue test. i .

[0082] S6: As Figure 3 As shown, plot the crack depth a. i With the number of loops N i The aN relationship curve was obtained, and the crack propagation rate da / dN was obtained using the secant method or the polynomial method.

[0083] S7: Based on the crack surface area S ci The ratio S to the cross-sectional area S0 of the sample ci / S0 and modulus ratio E ui / E u0 The second calibration relation Calculate the crack surface area S corresponding to each cycle in the low-cycle fatigue test. ci .

[0084] S8: Based on the stress intensity factor ΔK i With crack depth a i The third calibration relation Calculation of crack depth a in low-cycle fatigue tests i The corresponding stress intensity factor ΔK i .

[0085] S9: Calculate the area U of the plastic region using experimental software. pi And obtain it directly from the test data list.

[0086] S10: Based on the elastic-plastic fracture toughness value ΔJ i Calculation formula Calculate the elastic-plastic fracture toughness value ΔJ for each cycle. i .

[0087] S11: As Figure 4 As shown, the crack depth propagation rate da i / dN and elasto-plastic fracture toughness value △J i Power function fitting was performed to obtain the fitting parameters between crack propagation rate and elastoplastic fracture toughness value:

[0088]

[0089] Where, C = 9.178 × 10 -20 KJ / m 2 m = 8.091, effective range da / dN ∈ (5 × 10 -4 ~5×10 -3 ).

[0090] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and substitutions can be made without departing from the technical principles of the present invention, and these improvements and substitutions should also be considered within the scope of protection of the present invention.

Claims

1. A method for obtaining an elastic-plastic fatigue crack growth rate of a metal material in an elastic-plastic state based on a low-cycle fatigue test, characterized by, The method comprises the following steps: Obtaining the crack initiation unloading elastic modulus E of low cycle fatigue test u0 and the tensile unloading elastic modulus E after crack initiation ui ; The ratio of the crack depth a corresponding to each cycle in the low cycle fatigue test to the specimen diameter D i The ratio of the crack depth a to the modulus ratio E i The ratio of the crack depth a to the modulus ratio E ui The ratio of the crack depth a to the modulus ratio E u0 The first calibration relationship of a and a first calibration relationship of a i The first calibration relationship of a and a first calibration relationship of a i The a-N curve of the crack depth a and the cycle number N i The crack propagation rate da / dN acquiring a ratio S of a crack surface area S corresponding to each cycle in the low cycle fatigue test and a specimen cross section area So ci ci a ratio E of a modulus ratio E ui / E u0 a second calibration formula of the ratio S ci ;​ acquired in the low cycle fatigue test i corresponding stress intensity factor ΔK i and the crack depth a i a third calibration equation, and calculating the stress intensity factor ΔK i by the third calibration equation; Obtaining the value of the elastic-plastic fracture toughness △J corresponding to each cycle in the low-cycle fatigue test i and the stress intensity factor △K i , the crack surface area S ci , the specimen cross-sectional area S0 and the plastic zone area U pi , and calculating the value of the elastic-plastic fracture toughness △J i through the calculation formula; Power function fitting is performed on the crack propagation rate da / dN and the elastic-plastic fracture toughness value ΔJ to obtain a fitting formula of the crack propagation rate da / dN and the elastic-plastic fracture toughness value ΔJ. The first calibration relationship is: p0~p n is a calibration coefficient of the first calibration relationship; The second calibration relationship is: q0~q n is a calibration coefficient of the second calibration relationship; The third calibration relationship is: ΔF is the fatigue load range value, ΔF = F max - F min ; k0~k n is the calibration coefficient of the third calibration relationship; The calculation relationship is: wherein, ΔJ ei is the elastic component, ΔJ pi is the plastic component; The fitting formula is: Wherein, C is a fitting coefficient, and m is a fitting index.

2. The method of obtaining the elastic-plastic fatigue crack growth rate based on low cycle fatigue test according to claim 1, characterized in that, 4≤n≤6。 3. The method of obtaining the elastic-plastic fatigue crack growth rate based on low cycle fatigue test according to claim 1, characterized in that, The sample is a round bar sample; wherein the crack surface area S ci The calculation formula is: where S c is the crack surface area, θ is the angle value of the crack chord length corresponding to the central angle, a is the length of the deepest part of the crack, 2c is the chord length of the intersection of the crack and the sample surface, D is the sample diameter, 4. The method of obtaining the elastic-plastic fatigue crack growth rate based on low cycle fatigue test according to claim 1, characterized in that, The sample of the low-cycle fatigue test is a round bar sample; after the low-cycle fatigue test is completed, a heating coloring method is used to mark the crack front.

5. The method of obtaining the elastic-plastic fatigue crack growth rate based on low cycle fatigue test according to claim 1, characterized in that, The method for calculating the crack propagation rate da / dN includes: calculating the crack depth a corresponding to the unloading elastic modulus of each cycle of the low-cycle fatigue test i , drawing an a-N curve of the crack depth a i and the cycle number N i , and obtaining the crack propagation rate da / dN using a secant method or a polynomial method.

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