A metal material torsional fatigue life prediction method based on M-integral

Abstract

The application discloses a metal material torsional fatigue life prediction method based on M-integral, and comprises the following steps: selecting a far-field closed integral path C surrounding a defect in a material, calculating three-dimensional M-integral and equivalent damage volume V of the defect D , judging damage degree of the material according to the size of V D ; defining a fatigue damage evolution rate as dV D / dN, defining a fatigue driving force as AM / A P , and establishing a metal material torsional fatigue model based on M-integral; a torsional fatigue experiment evaluation is conducted on a DD6 nickel-based alloy, and effectiveness of the fatigue model is verified. The torsional fatigue model provided in the application can uniformly describe damage processes under torsional fatigue load, including formation of a plastic zone, initiation of a micro crack and expansion of a macro crack, a standard for evaluating damage degree and predicting fatigue life of a metal material or structure under torsional fatigue load is provided, and the application has important significance for metal material damage and life prediction analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to a metal material life prediction method under the action of torsional fatigue load, and in particular to a metal material torsional fatigue life prediction method based on M-integral. BACKGROUND

[0002] Fatigue failure of major equipment is a key issue in solid fracture theory research. In complex and variable service environment, material damage caused by torsional fatigue becomes a key factor affecting the safety and reliability of major equipment structure. High-temperature alloy is widely used in aviation industry due to its excellent high-temperature mechanical properties, good fatigue resistance and high corrosion resistance. It is usually used to manufacture blades, turbine shafts and other components of aero-engines to withstand cyclic torsional load. However, under the action of cyclic torsional load, these components will have serious torsional fatigue problems. Therefore, accurately predicting the torsional fatigue life of high-temperature alloy and other metal materials is of great importance to ensure the safe and reliable operation of major equipment structures such as aero-engines.

[0003] At present, the research on torsional fatigue life prediction method of metal materials is generally based on the S-N curve of the material to analyze the life of the structure, which is greatly affected by factors such as processing technology, temperature and load, and needs to be distinguished for different defect types, resulting in that the damage of various defects to the metal material cannot be uniformly evaluated and calibrated. In addition, the traditional fatigue life prediction method, such as Paris formula, cannot consider the contribution of plastic dissipation at the crack tip to the driving force, so it is not suitable for elastic-plastic metal materials and can only deal with fatigue crack propagation in linear elastic materials, and cannot describe the damage evolution of complex defects (such as plastic zone, crack, hole, etc.) in the process of torsional fatigue.

[0004] Therefore, it is desirable to have an evaluation method that can improve at least one of the deficiencies of the prior art. SUMMARY

[0005] In view of the deficiencies in the prior art, the purpose of the present application is to propose a metal material torsional fatigue life prediction method based on M-integral. Based on the concept of M-integral in metal materials, the present application proposes an innovative torsional fatigue model. The new forms of fatigue damage evolution rate (dV D / dN) and fatigue driving force (ΔM / A P ) are introduced, where V D represents the equivalent damage volume of plastic zone and crack, N represents the number of cycles, ΔM represents the M-integral range of each load cycle, and A P represents the plastic zone area of the cross section. The torsional fatigue experiment of the metal material specimen is evaluated to verify the effectiveness of the fatigue model.

[0006] To achieve the above object, the technical scheme adopted by the present application is:

[0007] A metal material torsional fatigue life prediction method based on M-integral, comprising the following steps:

[0008] 1) selecting a far-field closed integral path C surrounding a defect in the material, calculating the three-dimensional M-integral of the defect along the far-field closed integral path C, and the result is denoted as M D ;

[0009] 2) M D is equal to the M-integral M Hole of a three-dimensional circular hole defect in an elastic material, that is,

[0010]

[0011] Wherein R is equal to the radius of a three-dimensional circular hole in an elastic material, sigma is the external load, and E is the elastic modulus of the material;

[0012] 3) the equivalent volume of the defect in the material is denoted as V D , then from step 2), we can get,

[0013]

[0014] According to the size of the equivalent volume V D of the defect in the material, the damage degree of the material is judged;

[0015] 4) define the fatigue damage evolution rate as dV D / dN, and define the fatigue driving force as Delta M / A P , wherein V D represents the equivalent damage volume of the defect in the material, N represents the number of cycles, Delta M represents the M-integral range of each load cycle, A P represents the plastic zone area of the cross section, and dV D / dN represents the material damage increment caused by each fatigue cycle; a metal material torsional fatigue life prediction model based on M-integral is established:

[0016] dV D / dN=c( Delta M / A P ) m

[0017] Wherein c and m are material parameters determined through experiments;

[0018] 5) the metal material test piece is subjected to a torsional fatigue experiment evaluation, and the effectiveness of the fatigue model is verified; the fatigue test shows that the fatigue model can uniformly describe the damage process under torsional fatigue load, from the initiation, aggregation of micro-cracks to the expansion of macro-cracks.

[0019] The further improvement of the present application is that in step 1), the three-dimensional M-integral is:

[0020]

[0021] Wherein, w = σ ij ε ij / 2 is the strain energy density; x i is the particle coordinate; σ kj , ε ij , u k and respectively are stress, strain, displacement; u k,i is the partial derivative of displacement to the relevant coordinate x i ; δ ij is the Kronecker symbol; n j is the outward normal vector around the defect closed integral path S; the subscript {} ,j indicates the partial derivative of the corresponding physical quantity to the coordinate x j .

[0022] The further improvement of the present application is that in step 1), the defect in the material is one or more of a crack, a hole, a multi-crack or a multi-inclusion.

[0023] The further improvement of the present application is that in step 3), the different defect forms include plastic zone, crack, hole and inclusion.

[0024] The further improvement of the present application is that in step 3), the damage degree evaluation standard of different defect forms is calibrated by the value of equivalent volume V D .

[0025] The further improvement of the present application is that the greater the value of V D , the greater the damage degree, and vice versa.

[0026] The further improvement of the present application is that in step 5), in the experimental research, the change of the total potential energy change CTPE is introduced to measure the value of M-integral.

[0027] The further improvement of the present application is that the relationship between M-integral and the total potential energy change CTPE is expressed as:

[0028] M = 3CTPE.

[0029] The further improvement of the present application is that for the defective cylindrical sample, the change of the total potential energy is as follows:

[0030]

[0031] Wherein L is the length of the sample, σ θ is the circumferential stress on the elastic integral path, and u θis the circumferential displacement of the elastic integral path under internal load θ , σ r is the radial stress on the elastic integral path, u r is the radial displacement of the elastic integral path under internal load σ r .

[0032] Compared with the prior art, the present application has at least the following beneficial technical effects:

[0033] The M-integral-based metal material torsional fatigue life prediction method of the present application introduces a new parameter, equivalent damage volume (V D ), to represent the damage level of elastic-plastic materials, and the M-integral is calculated along the contour surrounding all defects instead of a single crack tip, which has special advantages in quantifying the damage degree of metal materials, and can uniformly describe the material damage caused by cracks, holes, dislocations, and plasticity in metal materials using M-integral; ΔM / A P is defined as the driving force of torsional fatigue damage evolution, which uniformly describes the torsional fatigue damage evolution of metal materials, including the initiation of micro-cracks and the growth of macro-cracks. The torsional fatigue model proposed in the present application can accurately describe the damage process under torsional fatigue load, including the formation of plastic zone, the initiation of micro-cracks, and the expansion of macro-cracks, and proposes a standard that can be used to evaluate the damage degree and predict the fatigue life of metal materials or structures under torsional fatigue load, which has great significance for material damage and life prediction analysis of metal material components.

[0034] In summary, the present application proposes a M-integral-based torsional fatigue life prediction method to evaluate the damage evolution of metal materials under fatigue load. For metal materials with defect damage, the damage degree of the material can be determined by calculating the corresponding M-integral value, and the damage level can be evaluated, and then the fatigue life can be predicted. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 is a schematic diagram of the torsional fatigue process of metal materials, wherein the gray part is the plastic zone.

[0036] Figure 2 is a schematic diagram of the principle of the material damage volume calibration method based on M-integral.

[0037] Figure 3 is a schematic diagram of the stress equivalent method for measuring M-integral under torsional load, wherein Figure 3 (a) is a three-dimensional schematic diagram, Figure 3 (b) is a two-dimensional cross-sectional schematic diagram, and the gray part is the plastic zone.

[0038] Figure 4Schematic diagram for the calculation of the total potential energy change CTPE.

[0039] Figure 5 Experimental flow chart for the measurement of torque-torsion angle curve of a non-defective specimen.

[0040] Figure 6 Experimental flow chart for the verification of the M-integral based metal material torsional fatigue life prediction model.

[0041] Figure 7 Schematic diagram of a specimen and a fatigue testing device, wherein Figure 7 (a) is a torsional fatigue testing device, Figure 7 (b) is a torsional fatigue specimen.

[0042] Figure 8 Schematic diagram of the relationship between the fatigue damage evolution rate dV D and the fatigue driving force AM, wherein Figure 8 (a) is the relationship between the fatigue damage rate and the fatigue driving force of specimen 1 when the fatigue torque ranges from 1.2 to 12 Nm, Figure 8 (b) is the relationship between the fatigue damage rate and the fatigue driving force of specimen 2 when the fatigue torque ranges from 1.2 to 12 Nm, Figure 8 (c) is the relationship between the fatigue damage rate and the fatigue driving force of specimen 1 when the fatigue torque ranges from 1.3 to 13 Nm, Figure 8 (d) is the relationship between the fatigue damage rate and the fatigue driving force of specimen 2 when the fatigue torque ranges from 1.3 to 13 Nm. DETAILED DESCRIPTION

[0043] Exemplary embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the drawings, it is understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that the present disclosure can be more thoroughly understood, and the scope of the present disclosure can be accurately conveyed to those skilled in the art. It should be noted that the embodiments in the present disclosure and the features in the embodiments can be combined with each other without conflict. The present disclosure will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0044] (1) The torsional fatigue process of a metal material is described:

[0045] The fatigue failure process of a metal material under torsional fatigue cyclic loading can be divided into three stages: the first stage, the plastic zone formation and growth stage; the second stage, the micro-crack initiation stage; and the third stage, the macro-crack propagation and final fracture stage, as shown in Figure 1 The torsional fatigue damage process of the three stages can be described by the following fatigue model:

[0046] dV D / dN=c(ΔM / A P ) m (1)

[0047] The first stage: under the constant torsional fatigue load, the maximum stress appears at the edge of the cross section of the specimen. With the increase of the number of fatigue cycles, the edge of the cross section of the specimen first enters the plastic yield state. Then, the stress at the edge of the elastic region in the specimen gradually reaches the yield limit, and the plastic region expands to the center of the cross section. The area of the elastic region in the cross section of the specimen gradually decreases. In this stage, it is assumed that the radius of the elastic region in the cross section decreases linearly with the increase of the number of fatigue cycles. With the continuous increase of the number of fatigue cycles, only a small circle around the center remains as the elastic region of the cross section of the specimen. The specimen as a whole enters the plastic region, and the shear stress is approximately uniformly distributed on the entire cross section.

[0048] The second stage: once the entire cross section of the specimen enters the plastic stage, the plastic region no longer expands. The evolution of damage is manifested as the formation and aggregation of micro-cracks in the plastic zone.

[0049] The third stage: with the continuous increase of the number of fatigue cycles, macroscopic cracks / pores begin to appear in the plastic region, and the damage evolution rate begins to increase. Then, the damage rate continues to increase, the progress of damage accelerates, until the final fracture occurs.

[0050] (2) The principle of the material damage volume calibration method based on M-integral is explained:

[0051] The basis for judging the degree of material defect damage by M-integral is as follows:

[0052] From the physical meaning, the evolution process of damage can be described by the total energy release rate of the material system, and the M-integral represents the energy release rate produced by the self-similar expansion of defects, which means that the M-integral is related to the energy change of the entire defect, and can be used to calibrate the damage of materials and structures. As a mechanical parameter that can represent various micro-defects and their evolution in materials, M-integral plays an important role in material damage and structural integrity evaluation. M-integral can be understood as the total potential energy change between the current configuration and the configuration without any defects, when each defect surface particle reaches the current configuration in a self-similar expansion manner. M-integral has a clear physical meaning for describing the damage of defects in materials, but M-integral has not been applied to calibrate the real damage volume of any defect.

[0053] Based on the above status analysis and M-integral clear physical meaning, based on M-integral, a method for evaluating the damage level of defects is proposed. For various defect topographies, the M-integral value is calculated, and according to the same M-integral representing the same damage level, the volume of the elastic spherical hole with the same M-integral value is used as the equivalent damage volume of the defect. The size of the equivalent damage volume can be used to calibrate the actual damage of various defects. Through the method proposed in the application, the damage level of any defect damage in engineering practice can be uniformly calibrated. The calibration process is simple and convenient, and there is no such report at home and abroad.

[0054] As shown in Figure 2 , the material damage volume calibration method based on equivalent M-integral of the application specifically comprises the following steps:

[0055] Step one, for specific defect configurations in materials, such as cracks, holes, multiple cracks, and multiple inclusions, according to the actual situation of the load, the M-integral of the defect is calculated by selecting the far-field integral path surrounding the defect, and the result is recorded as M D ;

[0056] Step two, according to the analytical proof of the complex potential theory of elasticity mechanics, the analytical expression of the M-integral of the spherical hole defect in the three-dimensional elastic material is obtained as: Where σ is the external load, and E is the elastic modulus of the material.

[0057] Step three, according to the same M-integral value representing the same damage degree, based on the equivalent M-integral method: M D =M Hole , the equivalent damage volume of the defect calculated by the formula M=M Hole is:

[0058]

[0059] Step four, according to the size of the equivalent volume V D of the defect in the material obtained in step three, the damage degree of the material is judged. The larger the equivalent volume V D , the greater the damage degree, and the smaller the equivalent volume V D , the smaller the damage degree. According to the size of the equivalent damage volume, the damage level of the material can be uniformly calibrated.

[0060] As shown in Figure 2 , the application is suitable for various complex defects and defect group damage calibration in materials. The defect equivalent damage volume calibration method based on M-integral can be used in subsequent metal material torsional fatigue damage analysis.

[0061] (3) The stress equivalent method for measuring M-integral is described:

[0062] In order to effectively and conveniently measure the value of M-integral under torsional load, an experimental method is introduced below.

[0063] The relationship between M-integral and the change of total potential energy CTPE can be expressed as:

[0064] M = 3CTPE (3)

[0065] The key to measuring M-integral is to find a method to measure CTPE. For a defective cylindrical specimen, the change of total potential energy is as follows:

[0066]

[0067] where L is the length of the specimen, σ θ is the circumferential stress on the elastic integral path, u θ is the circumferential displacement of the elastic integral path under internal load σ θ , σ r is the radial stress on the elastic integral path, u r is the radial displacement of the elastic integral path under internal load σ r .

[0068] In fact, the stress equivalence of the specimen can be decomposed according to the superposition principle, as shown in Figure 3 Since the superposition principle is established in the elastic zone far from the plastic zone, and the M-integral is also calculated on the elastic integral path surrounding all plastic zones, it can be proved that the defective cylindrical specimen can be equivalent to the combination of a continuous body without defects under the same remote load and a defective cylindrical specimen under the same size internal load acting on the elastic integral path. Therefore, assuming that the cross section remains circular after torsion and there is no axial elongation, the total work of the remote load in the defective specimen can be written as

[0069]

[0070] where θ is the torsion angle of the defective specimen, θ1 is the torsion angle of the non-defective specimen, as shown in Figure 3 Comparing equation (4) and equation (5), it can be found that the second term on the right side of equation (5) is CTPE. Therefore, CTPE is equal to the difference between the external work of the defective specimen and the non-defective specimen of the same size. Therefore, the M-integral of the specimen under torsional load can be calculated by the following equation:

[0071] M = 3CTPE = 3T(θ-θ1) (6)

[0072] (4) The experimental process for verifying the metal material torsional fatigue life prediction model based on M-integral is described:

[0073] The detailed process of measuring CTPE is as follows: Figure 4 As shown in the figure. First, the torque-torsion angle curve L0 was obtained by applying a monotonically increasing torque T to the defect-free specimen, as shown in the figure. Second, the specimen underwent a torsional fatigue test. The number of fatigue cycles was N, and the maximum fatigue torque was T. max The minimum fatigue torque is T min Finally, the torque-torsion angle curve L of the defective specimen after N fatigue cycles was recorded by uniaxial torsion testing. N Based on the physical meaning of CTPE, from curves L0 and L... N T = T max T = T min The area enclosed by the shaded area in the diagram is named ΔCTPE. Repeat this measurement process until the specimen fails and breaks, as shown below. Figure 5 and Figure 6 As shown. After N fatigue cycles, the ΔM of the defective specimen can be calculated as: ΔM = 3ΔCTPE. After obtaining the M-integral in the experiment, the equivalent damage volume V can be calculated. D Furthermore, dV can be obtained. D / dN and ΔM / A P The relationship between them.

[0074] (5) The following example of the failure of a DD6 nickel-based alloy under torsional fatigue load further illustrates the torsional fatigue life prediction method for metallic materials based on M-integral of the present invention:

[0075] The stress-strain curve of DD6 nickel-based alloy material was obtained by uniaxial tensile test. The elastic modulus was 198.3 GPa, the yield stress was 340.0 Mp, and the Poisson's ratio was about 0.33.

[0076] Specimen loading in the example Figure 7 As shown. The test section of the specimen was a cylinder with a diameter of 6 mm and a length of 25 mm; torsional fatigue loading was applied to both ends of the specimen using an MTS-858 / 2.5T testing machine. The experiment was conducted in torque control mode, with the maximum torque (T)... max The torque values ​​were 12 Nm and 13 Nm, respectively, with a torque ratio of 0.1 and a frequency of 20 Hz. All experiments were conducted at room temperature.

[0077] fatigue damage rate dV D / dN and the corresponding fatigue driving force ΔM can be calculated using the seven-point incremental polynomial method. The fatigue driving force is defined as the M-integral change per unit area of ​​the plastic zone in the cross-section, i.e., ΔM / A. P Perform dV D / dN and ΔM / A P The logarithmic operation yields the following result: Figure 8 As shown in the figure. It can be seen that the damage evolution rate dVD / dN and ΔM / A P The relationship is logarithmically linear, thus validating the fatigue model in equation (1). The dV values ​​of all specimens... D / dN and driving force ΔM / A P The logarithmic linear relationship between them is roughly the same, meaning it is independent of the magnitude of the torque. The fitting function is as follows: Figure 8 As shown.

[0078] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A method for predicting the torsional fatigue life of metallic materials based on M-integral, characterized in that, Includes the following steps: 1) Select a far-field closed integration path C that surrounds the defect in the material, and calculate the three-dimensional M-integral of the defect along the far-field closed integration path C. The result is denoted as M. D ; 2) Let M D Equal to the M-integral of a three-dimensional circular hole defect in an elastic material. Hole ,Right now Where R is equal to the radius of the three-dimensional circular hole in the elastic material, σ is the external load, and E is the elastic modulus of the material; 3) The equivalent volume of defects in the material is denoted as V. D Then, from step 2), we can obtain: Based on the equivalent volume V of defects in the material D The size determines the degree of material damage; 4) Define the fatigue damage evolution rate as dV D / dN, defining the fatigue driving force as ΔM / A P V D The equivalent damage volume of the defect in the material is represented by N, the number of cycles is represented by ΔM, and the M-integral range for each load cycle is represented by A. P dV represents the area of ​​the plastic zone of the cross section. D / dN represents the increment of material damage caused by each fatigue cycle; a torsional fatigue life prediction model for metallic materials based on M-integral is established: dV D / dN=c(ΔM / A P ) m Where c and m are material parameters determined experimentally; 5) Torsional fatigue tests were conducted on metallic material specimens to evaluate the effectiveness of the fatigue model. The fatigue tests showed that the fatigue model can uniformly describe the damage process under torsional fatigue load, from the initiation and aggregation of microcracks to the propagation of macrocracks.

2. The method for predicting torsional fatigue life of metallic materials based on M-integral according to claim 1, characterized in that, In step 1), the three-dimensional M-integral is: Where w = σ ij ε ij / 2 represents the strain energy density; x i σ represents the coordinates of the particle; kj ,ε ij ,u k and represent stress, strain, and displacement, respectively; u k,i For displacement with respect to the relevant coordinate x i The partial differential; δ ij Kronecker notation; n j Let S be the outward normal vector around the closed integral path S of the defect; subscript {} ,j Represents the corresponding physical quantity with respect to coordinate x j The partial derivatives of .

3. The method for predicting torsional fatigue life of metallic materials based on M-integral according to claim 1, characterized in that, In step 1), the defects in the material are one or more of the following: cracks, pores, multiple cracks, or multiple inclusions.

4. The method for predicting torsional fatigue life of metallic materials based on M-integral according to claim 1, characterized in that, In step 3), different defect forms include plastic zones, cracks, pores, and inclusions.

5. The method for predicting torsional fatigue life of metallic materials based on M-integral according to claim 1, characterized in that, In step 3), the damage assessment criteria for different defect types are based on the equivalent volume V. D The value is used to calibrate the magnitude.

6. The method for predicting torsional fatigue life of metallic materials based on M-integral according to claim 5, characterized in that, V D A higher value indicates a greater degree of damage, and vice versa.

7. The method for predicting torsional fatigue life of metallic materials based on M-integral according to claim 1, characterized in that, In step 5), the change in total potential energy CTPE was introduced in the experimental study to measure the value of the M-integral.

8. The method for predicting torsional fatigue life of metallic materials based on M-integral according to claim 7, characterized in that, The relationship between the M-integral and the change in total potential energy CTPE is expressed as: M = 3CTPE.

9. The method for predicting torsional fatigue life of metallic materials based on M-integral according to claim 8, characterized in that, For a defective cylindrical sample, the change in total potential energy is as follows: Where L is the length of the sample, σ θ It is the circumferential stress along the elastic integral path, u θ It is the circumferential displacement σ of the elastic integral path under internal load. θ , σ r It is the radial stress on the elastic integral path, u r It is the radial displacement σ of the elastic integral path under internal load. r .

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