A diffraction method for measuring residual stress in complex materials

Abstract

The present invention relates to the technical field of residual stress diffraction testing, and more specifically, to a method for measuring residual stress in complex materials using diffraction technology. The present invention only requires measuring the strain of the matrix phase to obtain the overall stress of the material. The specific steps are: first, obtaining the average bulk modulus #imgabs0# and average shear modulus #imgabs1# of the complex material to be tested; then, using a micromechanical model, calculating the diffraction elastic constants of specific crystal planes of the matrix phase of the complex material; and then, through X-ray or neutron diffraction measurements of the matrix phase strain of the complex material and calculation of the stress of the complex material, the overall stress of the material can be determined. The present invention provides simple testing and highly reliable results.

Description

Technical Field

[0001] The present invention relates to the technical field of residual stress diffraction testing, and in particular to a method for measuring the residual stress of a complex material using diffraction technology. Technical Background

[0002] With the increasing demand for lightweight and functional structures in the aerospace and military industries, the use of advanced composite materials in large aircraft, spacecraft, satellites, rockets, and missiles has continued to increase, gradually expanding from non-load-bearing components to primary load-bearing components. For example, satellite bearing cylinders are now entirely made of composite materials; solid rocket engines are also largely composite. The A380, a superjumbo, comprises 25% of its structural weight in composite materials. Its major carbon fiber composite components include the center wing box, wing ribs, fuselage skin panels, aft fuselage section, tail section, floor beams, rear pressure frame, and vertical stabilizer. The Boeing 787's use of composite materials has attracted even greater attention. Composite materials account for 50% of its structural weight. The fuselage and wings utilize carbon fiber-reinforced laminates instead of aluminum alloys, while the engine nacelles, horizontal and vertical stabilizers, rudders, and wingtips utilize carbon fiber-reinforced sandwich panels. The US F-22, a fourth-generation fighter jet, also utilizes composite materials for 25% of its structural weight. The Airbus A40M large military transport aircraft also makes extensive use of composite materials in its manufacturing, enabling it to boast a payload exceeding that of any existing large transport aircraft. Therefore, the use of composite materials and structures has been an inevitable and realistic trend in the development of aerospace, military industry and other fields over the past few decades.

[0003] Residual stress in materials and their components significantly impacts their fatigue strength, corrosion resistance, dimensional stability, and service life. This impacts numerous industries, including machinery manufacturing, water conservancy, electric power, aerospace, military, nuclear industry, petrochemicals, metallurgy, and transportation. For example, significant residual stress in the beam frames of large aircraft can severely impact component processing accuracy and lead to serious consequences such as cracking. Internal residual stresses generated during the manufacturing of turbine disks and blades, as well as their coatings, in aircraft engines operating at extremely high temperatures can cause component deformation during operation, impacting gas turbine performance and efficiency, and even leading to premature failure. In high-speed rail train bodies, significant residual stresses are present when welding high-strength aluminum alloy beams to the train cars. This can lead to significant stress corrosion cracking during operation, significantly impacting the train's service life. Therefore, accurately characterizing the internal stress conditions of these components under extreme manufacturing and service conditions is a crucial prerequisite for developing high-end components and evaluating their performance. Furthermore, further analysis of the material's underlying stress distribution, load transfer, and stress concentration is crucial for the development of new materials and the manufacture of new components.

[0004] There are many methods for stress measurement, including stress release method, magnetic method, ultrasonic method and diffraction method. Most of the above engineering materials are complex phase materials. The current diffraction method for measuring stress of complex phase materials is to measure the strain of the two phases separately and then multiply it by the corresponding diffraction elastic constant and volume fraction weighted. The specific expression is

[0005] (1)

[0006] In the formula represents the stress of the complex material, 、 and represent the volume fraction of the matrix phase, diffraction elastic constant, and strain, respectively; 、 and where represents the volume fraction, diffraction elastic constant, and strain of the second phase, respectively. This method, on the one hand, fails to consider the interaction between the two phases of the composite material, affecting the accuracy of the stress calculation. On the other hand, when the second phase content in the composite material is low or the diffraction peak corresponding to the second phase is weak, the second phase strain cannot be accurately measured, thus restricting the precise measurement and calculation of stress and strain in the composite material. Summary of the Invention

[0007] Based on the above problems, the present invention provides a new method for measuring the residual stress of complex phase materials using the diffraction method. The stress of the entire material can be obtained by simply measuring the strain of the matrix phase. The specific expression is

[0008] (2)

[0009] In the formula represents the stress of the complex material, and represent the diffraction elastic constant and strain of the “new” crystal plane of the matrix phase (hkl), respectively.

[0010] In the present invention It can be expressed as ( ),Right now ( )and are the diffraction elastic constants and strains of the “new” crystal plane of the matrix phase (hkl). The corresponding elastic constitutive equation is:

[0011] (2-1)

[0012] In the formula represents the measured corresponding force, represents the (hkl) crystal plane diffraction elastic constant, Represents the strain in different directions of the (hkl) crystal plane. When i=j, it represents the principal strain, and i≠j represents the combined strain.

[0013] This paper uses micromechanics theory and a self-consistent method to calculate the effect of the second phase on the stress state of the matrix phase under uniaxial tension, and converts this effect into the effect of the diffraction elastic constant. This establishes a theoretical calculation model for the diffraction elastic constant of complex materials, and derives a "new" diffraction elastic constant for the matrix phase. The matrix phase strain is also obtained using the diffraction method.

[0014] The diffraction method for strain measurement is mainly based on Bragg's law:

[0015] When a beam with a wavelength of When X-rays hit the surface of a crystal, they will be reflected at a specific angle ( ) receives the peak of X-ray reflected light, which is the X-ray diffraction phenomenon. The diffraction angle The wavelength of X-rays , the diffraction crystal plane spacing d follows the famous Bragg law: .like Figure 6 shown.

[0016] Bragg's law establishes a definite relationship between the diffraction angle that can be accurately measured macroscopically and the interplanar spacing of the material. The elastic strain corresponding to the stress in the material is characterized by the relative change in the interplanar spacing. When it exists, the interplanar spacing d changes with the relative orientation of the crystal plane and the stress. According to Bragg's law, the corresponding diffraction angle It will also change.

[0017] The basic principle of measuring residual stress by neutron diffraction is similar to that of the X-ray method, which also determines the strain ε by measuring the change in the interplanar spacing d. Unlike X-ray diffraction, which can only measure the surface stress of the sample, the neutron beam has stronger penetrating power and can obtain diffraction information within a larger range of the sample's internal space.

[0018] The neutron diffraction method determines the change of d value by the time of flight method. According to Bragg's law: , assuming that the interplanar spacing changes under stress , then the material lattice strain can be expressed as:

[0019] (1-1)

[0020] In the time-of-flight mode, due to the scattering angle is fixed, the neutron flight time , so the elastic strain can be obtained from formula (1-1):

[0021]

[0022] In the formula is the flight time of neutrons in the unstressed sample, is the interplanar spacing of the sample in a stress-free state.

[0023] The present invention provides a new method for measuring residual stress of complex phase materials using a diffraction method, comprising the following steps:

[0024] Step 1

[0025] Obtain the average bulk modulus of the complex phase material to be tested by measuring or looking up and the average shear modulus ; In the present invention, the average bulk modulus of the composite material and the average shear modulus It can be measured in a variety of ways, the most commonly used method being the pulse excitation method.

[0026] The present invention adopts the pulse excitation method to measure the average bulk modulus of the composite material and the average shear modulus The following steps are included:

[0027] Prepare the sample according to the national standard and obtain the sample mass, length, width, and thickness; place the sample horizontally on two horizontally tensioned platinum wires, with the excitation point and signal collection point at two opposite corners of the sample, and collect the bending vibration frequency and torsional vibration frequency;

[0028] Substitute the collected bending vibration frequency and torsional vibration frequency into the formula to obtain the dynamic Young's modulus E, shear modulus G, and bulk modulus K; if the test material is a complex material, then K and G are equivalent to the average bulk modulus of the complex material. and the average shear modulus ;

[0029] Calculation of elastic modulus E:

[0030] (3)

[0031] Where:

[0032] E=dynamic Young's modulus, unit: Pa,

[0033] m=sample mass, in g,

[0034] b=sample width, in mm,

[0035] L=sample length, in mm,

[0036] t = sample thickness, in mm,

[0037] = fundamental resonant frequency of the bending rod in Hz,

[0038] Calculation of shear modulus G:

[0039] (4)

[0040] Where:

[0041] G = shear modulus, in Pa,

[0042] = torsional vibration frequency, in Hz,

[0043] B is the shape parameter ;

[0044] A is the parameter obtained through experience. ;

[0045] Calculation of bulk modulus K:

[0046] (5)

[0047] In specific applications, the dynamic Young's modulus measurement method of refractory materials specified in GB / T30758-2014 is adopted; the outside micrometer specified in GB / T1216-2018 is adopted.

[0048] In specific applications, samples are made according to GB / T30758-2014. The specific requirements for the samples are as follows:

[0049] a) The specimen is a rectangular parallelepiped with a length of not less than 60 mm, and the ratio of length (L), width (b), and thickness (t) is approximately 20:5:1;

[0050] b) The parallelism errors of the specimen length, width and thickness are less than 0.5%, 0.1% and 0.1% respectively;

[0051] c) The surface of the specimen should be smooth and flat, and the edges do not need to be chamfered;

[0052] d) The mass of the sample should not be less than 5g.

[0053] The steps to measure and obtain sample parameters are as follows:

[0054] The sample mass shall be weighed using a balance with an accuracy of 1 mg, and the length, width, and thickness of the sample shall be measured using a vernier caliper in accordance with GB / T 1216. When testing the width and thickness of the sample, the two ends and the middle of the sample shall be measured separately, and the average value shall be taken.

[0055] Place the sample horizontally on two horizontally tensioned platinum wires, with the excitation point and signal collection point at two diagonal corners of the sample, such as Figure 1 As shown, the bending vibration frequency and the torsional vibration frequency are collected.

[0056] Step 2

[0057] Use micromechanics models to calculate the diffraction elastic constants of specific crystal planes of the matrix phase of complex materials;

[0058] The micromechanical model is derived as follows:

[0059] ① Derivation of macroscopic stress and strain of complex materials

[0060] Assume that the material global coordinate system is [S], the test coordinate system is [L], and the direction cosine of the strain direction L3 relative to the material global coordinate system [S] is L3(e, f, g). The angle between L3 and the vertical coordinate axis S1 is , the angle between the horizontal component of L3 and the horizontal coordinate axis S1 is , from which we can get:

[0061] (6)

[0062] Therefore, the strain in direction L3 for:

[0063] (7)

[0064] In formula (7) , , represents the principal strain in the test coordinate system, , , , represents the shear strain in the test coordinate system;

[0065] Substituting (6) into (7) we get:

[0066] (8)

[0067] On the other hand, the relationship between the strain and stress of the material as a whole is calculated by using the elastic compliance of the material [S ij ]The matrix can be expressed as:

[0068] (9)

[0069] In formula (9) , represents the principal strain in the material coordinate system; , , represents the principal stress in the material coordinate system; , , represents the shear strain in the material coordinate system; , , represents the shear stress in the material coordinate system;

[0070] When the material is isotropic and the material as a whole is only subjected to uniaxial tension (σ11=σ0≠0, other stress components are 0) and Φ=0, according to Hooke's law, the corresponding change ε ​​of phase A is A and macro stress σ 0 Satisfy between:

[0071] (10)

[0072] in , is the elastic modulus and Poisson's ratio of phase A in the composite material; Φ represents the angle between the horizontal component of the strain direction L3 and the horizontal coordinate axis S1;

[0073] ②Derivation of microscopic stress and strain of constituent phases of composite materials

[0074] Considering the presence of a spherical second phase A in the matrix of the composite material, the strain field of the spherical L phase within the overall elastic range of the composite material is Should be:

[0075] (11)

[0076] In formula (11) and formula (12), is the average strain field of the complex material; is the strain addition caused by the different elastic constants between the spherical A phase and its external matrix composite material; and the stress σ inside the spherical A phase A According to Eshelby's equivalent isoelastic method, we can get:

[0077] (12)

[0078] In formula (12), C A is the single crystal elastic constant of spherical A phase; is the average elastic constant of the composite material; is the inherent strain of the complex material;

[0079] According to Eshelby inclusion theory:

[0080] (13)

[0081] In formula (13), S E represents the Eshelby tensor; substituting Eq. (12) into Eq. (13) and transforming it, we can obtain:

[0082] (14)

[0083] Since the load strain and load stress of the complex material have the following relationship:

[0084] (15)

[0085] In formula (15), is the average elastic compliance of the composite material. Substituting Equation (15) into Equation (14) and rearranging it, we can obtain:

[0086] (16)

[0087] In formula (16), I is the unit matrix, let:

[0088] (17)

[0089] Then we have:

[0090] (18)

[0091] In the formula and and S E The average bulk modulus of the composite material at any time and the average shear modulus The tensor expression of the function is:

[0092]

[0093] (19)

[0094]

[0095] Where the average bulk modulus and the average shear modulus The value of can be measured; according to formula (18) and T A From the relational expression, we can see that T A Similar to the elastic compliance of the material, it is the interaction factor of the elastic compliance of each phase of the complex material; as long as the elastic constant of the second phase is given You can find out ;

[0096] In summary, the relationship between the second phase and the applied stress in a composite material is:

[0097] (20)

[0098] ③ Derivation of the calculation formula for the diffraction elastic constant of the component phases in complex materials

[0099] Considering that the second phase is randomly distributed and has the same distribution probability in each orientation in three-dimensional space, when the material as a whole is only subjected to uniaxial stress, the second phase has a certain By averaging the crystal plane strain and comparing it with the macroscopic stress-strain relationship, the calculation formula for the "crystal plane diffraction elastic constant" of phase A of the complex material can be obtained as follows:

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106] (twenty one)

[0107]

[0108]

[0109]

[0110]

[0111]

[0112]

[0113] (twenty two)

[0114] Here, 、 is the average elastic constant of the composite material (macroelastic constant); represents the elastic compliance interaction factor The components of the tensor, Is related to the diffraction crystal plane The relevant crystal plane normal direction cosine, that is,

[0115]

[0116] (twenty three)

[0117]

[0118] Where:

[0119]

[0120] , 、 、 as well as 、 、 is the crystal structure parameter. Combining equations (21), (22), and (23) can be used to obtain the crystal plane diffraction elastic constant, 、 .

[0121] Step 3

[0122] X-ray diffraction measurement or neutron diffraction measurement of matrix phase deformation of complex materials and calculation of stress in complex materials;

[0123] When the diffraction method is used to measure stress, the corresponding elastic constitutive equation is:

[0124] (twenty four)

[0125] In formula (24):

[0126] is the stress tensor of the complex material,

[0127] is the matrix phase (phase A) strain tensor,

[0128] 、 is the diffraction elastic constant of the basic phase (phase A) obtained in step 2;

[0129] For a certain measured strain of the matrix phase in a composite material ,(in , and The direction cosines of the x-axis, y-axis, and z-axis of the test coordinate system can be expressed as The six components of are:

[0130] (25)

[0131] represents the principal strain in the test coordinate system, Indicates the shear strain in the test coordinate system. Therefore, when the principal strain is unknown, it is necessary to measure the strain in at least 6 directions of the matrix phase. , d is an integer from 1 to 6, and 6 linear equations are constructed to solve the strain tensor:

[0132] (26)

[0133] After obtaining the strain tensor, the components of the stress tensor of the complex material can be calculated using formula (25).

[0134] When the principal strain is known, it is only necessary to determine the principal coordinate axes of the matrix phase in the material coordinate system. Strain in three directions The stress state of the composite material can be determined. At this time, the constitutive equation (24) can be simplified to:

[0135] (27a)

[0136] (27b)

[0137] (27c)

[0138] In the formula 、 Represents the principal stress of the complex phase material in the material coordinate system.

[0139] Principles and advantages

[0140] This invention, for the first time, uses micromechanics theory and self-consistent methods to analyze the influence of the second phase on the stress state of the matrix phase under uniaxial tension, and converts it into the influence of the diffraction elastic constant, establishes a theoretical calculation model for the diffraction elastic constant of complex phase materials, and obtains the "new" diffraction elastic constant of the matrix phase. This invention is aimed at a composite material (including a completely new one), and only needs to obtain the average bulk modulus of the complex phase material to be tested. and the average shear modulus Then, a micromechanical model is used to calculate the diffraction elastic constants of specific crystal planes of the matrix phase of the composite material. Subsequently, by measuring the phase deformation of the composite material matrix and calculating the stress of the composite material, the overall stress of the material can be obtained. The present invention is simple to test and the results obtained are highly reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0141] Figure 1 The average bulk modulus of the composite material measured by pulse excitation in Example 1 is and the average shear modulus Schematic diagram of;

[0142] Figure 2 Schematic diagram of macro stress analysis adopted in the present invention;

[0143] Figure 3 This is the XRD pattern of the raw material TC17 used in Example 1;

[0144] Figure 4 This is the metallographic microstructure diagram of TC17 in Example 1.

[0145] Figure 5In-situ neutron diffraction measurement of TC17 titanium alloy under loading to verify the "new" diffraction elastic constants obtained in Example 1.

[0146] Figure 6 Schematic diagram of diffraction test. DETAILED DESCRIPTION

[0147] The technical solution adopted by the present invention is:

[0148] By using micromechanics theory and self-consistent methods, we calculated the influence of the second phase on the stress state of the matrix phase under uniaxial tension and converted it into the influence of the diffraction elastic constant. We established a theoretical calculation model for the diffraction elastic constant of complex phase materials and obtained the "new" diffraction elastic constant of the matrix phase. The specific steps are as follows:

[0149] Step 1

[0150] Measurement of the average bulk modulus of complex materials by pulse excitation method and the average shear modulus ;

[0151] The normative documents used in the measurement are GB / T30758-2014 Measurement method of dynamic Young's modulus of refractory materials and GB / T1216 Outside micrometer;

[0152] Requirements for measuring specimens

[0153] According to GB / T30758-2014, the sample requirements are as follows:

[0154] The specimen is a rectangular parallelepiped with a length of not less than 60 mm, and the ratio of length (L), width (b), and thickness (t) is approximately 20:5:1;

[0155] The parallelism errors of the specimen length, width and thickness are less than 0.5%, 0.1% and 0.1% respectively;

[0156] The surface of the specimen should be smooth and flat, and the edges do not need to be chamfered;

[0157] The mass of the sample should not be less than 5g;

[0158] Test steps

[0159] a) Weigh the specimen using a balance with an accuracy of 1 mg. Measure the length, width, and thickness of the specimen using a vernier caliper that complies with GB / T 1216. Measure the width and thickness of the specimen at both ends and in the middle, and take the average value.

[0160] b) Place the sample horizontally on two horizontally tensioned platinum wires, with the excitation point and signal collection point at two diagonal corners of the sample, such as Figure 1 As shown, the bending vibration frequency and the torsional vibration frequency are collected.

[0161] Calculation of elastic modulus E:

[0162] (3)

[0163] Where:

[0164] E=dynamic Young's modulus, unit: Pa,

[0165] m=sample mass, unit: g,

[0166] b=sample width, unit mm,

[0167] L=sample length, unit: mm,

[0168] t=sample thickness, unit: mm,

[0169] = fundamental resonant frequency of the bending rod, in Hz;

[0170] Calculation of shear modulus G:

[0171] (4)

[0172] Where:

[0173] G=shear modulus, unit Pa,

[0174] = torsional vibration frequency, unit Hz,

[0175] , is the shape parameter,

[0176] , is the empirical correction parameter;

[0177] Calculation of bulk modulus K:

[0178] (5)

[0179] Step 2

[0180] Use micromechanics models to calculate the diffraction elastic constants of specific crystal planes of the matrix phase of complex materials;

[0181] The micromechanical model is derived as follows:

[0182] ① Derivation of macroscopic stress and strain of complex materials

[0183] Assume that the material global coordinate system is [S], the test coordinate system is [L], and the direction cosine of the strain direction L3 relative to the material global coordinate system [S] is L3(e, f, g). The angle between L3 and the vertical coordinate axis S1 is , the angle between the horizontal component of L3 and the horizontal coordinate axis S1 is , from which we can get:

[0184] (6)

[0185] Therefore, the strain in direction L3 for:

[0186] (7)

[0187] In formula (7) , , represents the principal strain in the test coordinate system, , , , represents the shear strain in the test coordinate system;

[0188] Substituting (6) into (7) we get:

[0189] (8)

[0190] On the other hand, the relationship between the strain and stress of the material as a whole is calculated by using the elastic compliance of the material [S ij ]The matrix can be expressed as:

[0191] (9)

[0192] In formula (9) , represents the principal strain in the material coordinate system; , , represents the principal stress in the material coordinate system; , , represents the shear strain in the material coordinate system; , , represents the shear stress in the material coordinate system;

[0193] When the material is isotropic and the material as a whole is only subjected to uniaxial tension (σ11=σ0≠0, other stress components are 0) and Φ=0, according to Hooke's law, the corresponding change ε ​​of phase A is A and macro stress σ 0 Satisfy between:

[0194] (10)

[0195] in , is the elastic modulus and Poisson's ratio of phase A in the composite material; Φ represents the angle between the horizontal component of the strain direction L3 and the horizontal coordinate axis S1;

[0196] ②Derivation of microscopic stress and strain of constituent phases of composite materials

[0197] Considering the presence of a spherical second phase A in the matrix of the composite material, the strain field of the spherical L phase within the overall elastic range of the composite material is Should be:

[0198] (11)

[0199] In formula (11) and formula (12), is the average strain field of the complex material; is the strain addition caused by the different elastic constants between the spherical A phase and its external matrix composite material; and the stress σ inside the spherical A phase A According to Eshelby's equivalent isoelastic method, we can get:

[0200] (12)

[0201] In formula (12), C A is the single crystal elastic constant of spherical A phase; is the average elastic constant of the composite material; is the inherent strain of the complex material;

[0202] According to Eshelby inclusion theory:

[0203] (13)

[0204] In formula (13), S E represents the Eshelby tensor; substituting Eq. (12) into Eq. (13) and transforming it, we can obtain:

[0205] (14)

[0206] Since the load strain and load stress of the complex material have the following relationship:

[0207] (15)

[0208] In formula (15), is the average elastic compliance of the composite material. Substituting Equation (15) into Equation (14) and rearranging it, we can obtain:

[0209] (16)

[0210] In formula (16), I is the unit matrix, let:

[0211] (17)

[0212] Then we have:

[0213] (18)

[0214] In the formula and and S E The average bulk modulus of the composite material at any time and the average shear modulus The tensor expression of the function is:

[0215]

[0216] (19)

[0217]

[0218] Where the average bulk modulus and the average shear modulus The value of can be obtained by measurement; according to formula (18) and T A From the relational expression, we can see that T A Similar to the elastic compliance of the material, it is the interaction factor of the elastic compliance of each phase of the complex material; as long as the elastic constant of the second phase is given You can find out ;

[0219] In summary, the relationship between the second phase and the applied stress in a composite material is:

[0220] (20)

[0221] ③ Derivation of the calculation formula for the diffraction elastic constant of the component phases in complex materials

[0222] Considering that the second phase is randomly distributed and has the same distribution probability in all orientations in three-dimensional space, when the material as a whole is subjected to only uniaxial stress, the average strain of a certain (h, k, l) crystal plane of the second phase is compared with the macroscopic stress-strain relationship to obtain the calculation formula of the "crystal plane diffraction elastic constant" of phase A of the complex material:

[0223]

[0224]

[0225]

[0226]

[0227]

[0228]

[0229] (twenty one)

[0230]

[0231]

[0232]

[0233]

[0234]

[0235]

[0236] (twenty two)

[0237] Here, 、 is the average elastic constant of the composite material (macroelastic constant); represents the elastic compliance interaction factor The components of the tensor, Is related to the diffraction crystal plane The relevant crystal plane normal direction cosine, that is,

[0238]

[0239] (twenty three)

[0240]

[0241] Where:

[0242]

[0243] , 、 、 as well as 、 、 is the crystal structure parameter. Combining equations (21), (22), and (23) can be used to obtain the crystal plane diffraction elastic constant, 、 .

[0244] Step 3

[0245] X-ray diffraction measurement or neutron diffraction measurement of matrix phase deformation of complex materials and calculation of stress in complex materials;

[0246] When the diffraction method is used to measure stress, the corresponding elastic constitutive equation is:

[0247] (twenty four)

[0248] is the stress tensor of the complex material, is the matrix phase (phase A) strain tensor, 、 is the diffraction elastic constant of the basic phase (phase A) obtained in step 2. For a certain measured strain of the matrix phase in the composite material ,(in , and The direction cosines of the x-axis, y-axis, and z-axis of the test coordinate system can be expressed as The six components of are:

[0249] (25)

[0250] Therefore, when the principal strain is unknown, it is necessary to measure the strain in at least 6 directions of the matrix phase. , d is an integer from 1 to 6, and 6 linear equations are constructed to solve the strain tensor:

[0251] (26)

[0252] After obtaining the strain tensor, the components of the stress tensor of the complex material can be calculated using formula (25).

[0253] When the principal strain is known, it is only necessary to determine the principal coordinate axes of the matrix phase in the material coordinate system. Strain in three directions The stress state of the composite material can be determined. At this time, the constitutive equation (24) can be simplified to:

[0254] (27a)

[0255] (27b)

[0256] (27c)

[0257] In the formula 、 Represents the principal stress of the complex phase material in the material coordinate system.

[0258] Example:

[0259] Test and calculate residual stress of TC17 (α+β phase) titanium alloy (nominal composition Ti-5Al-2Sn-2Zr-4Mo-4Cr);

[0260] Step 1: Elastic modulus test

[0261] The test and calculation object is: TC17 (α+β phase) titanium alloy (nominal composition Ti-5Al-2Sn-2Zr-4Mo-4Cr), which is provided by Baoji Baomei Titanium Metal Materials Co., Ltd., with dimensions of 200×60×30mm. The main chemical composition (Wt%) is shown in Table 1

[0262]

[0263] The sample was subjected to XRD analysis and the structure was observed under a metallographic microscope. Figure 3 , Figure 4 As shown;

[0264] The specimens were processed into blocks of 120 × 40 × 10 mm. The specimens were weighed using a balance with an accuracy of 1 mg. The length, width, and thickness of the specimens were measured using a vernier caliper that complies with GB / T 1216. The width and thickness of the specimens were measured at both ends and in the middle, and the average value was taken.

[0265] After measurement, the actual dimensions of the sample were 121.34 mm in length, 39.34 mm in width, 9.92 mm in thickness, and 204.23 g in mass.

[0266] According to the test method and principle mentioned above, the Young's modulus of TC17 titanium alloy was obtained by pulse excitation method. =110.2GPa, shear modulus =42.1GPa, the bulk modulus is calculated =96.1GPa

[0267] Step 2: Calculation of diffraction elastic constants

[0268] The stiffness coefficient matrix of α phase at room temperature is obtained by first principle calculation and literature search :

[0269]

[0270] The α phase stiffness coefficient matrix and TC17 bulk modulus and shear modulus Substituting into formula (17) and (19), the elastic-flexibility interaction factor is calculated as The values ​​of each component are: t 11 =-0.0009, t 12=0.0005, t 13 =0.0002, t 33 =-0.0006, t 44 =0.0005, t 66 =-0.0033. .

[0271] Substituting the 103 crystal plane into the model calculation, the diffraction elastic constant of the α phase of the TC17 (103) plane can be obtained as follows:

[0272] .

[0273] Step 3: Diffraction strain test and stress calculation of complex titanium alloy

[0274] In-situ neutron diffraction testing was conducted on TC17 titanium alloy at the Advanced Research Reactor (CARR) at the China Institute of Atomic Energy. The α-phase strain of the TC17 titanium alloy was measured by neutron diffraction and multiplied by the diffraction elastic constant obtained in step 2 to obtain the material stress value. This was then compared with the applied stress value to verify the accuracy of the strain measurement and stress calculation method. The specific test process is as follows:

[0275] Measuring specimen: TC17 tensile bar ( ) (Processed from materials provided by Baoji Baomei Titanium Co., Ltd.);

[0276] Measurement steps:

[0277] A) Loading the tensile machine: Use a crane to place the tensile machine in the center of the sample table and load the 6mm diameter TC17 tensile specimen.

[0278] B) Align the optical path using a standard sample to align the center of the sample volume with the theoretical center of the diffraction measurement point. Align the point to be measured on the sample with the diffraction point, and align the vector to be measured with the scattering vector.

[0279] C) Neutron diffraction measurement, based on the selected monochromator (Si (400)), the take-off angle is 74.7°, and the α phase (103) crystal plane is selected as the test crystal plane. The theoretical value of the diffraction angle (2θ) is 76.7°. In order to enhance the diffraction signal, 76.7° is used as the center. The axis of rotation was rotated 5° up and down, in 1° increments, with a 600s probe time at each angle. The tensile device was activated, and tensile stresses of 0.15kN (0MPa), 13.572kN (480MPa), 18.096kN (640MPa), and 23kN (813MPa) were applied to each test point. Testing was performed after the stress state stabilized. The strain values ​​obtained under each stress state are shown in the following table:

[0280]

[0281] D) Stress calculation Since the composite titanium alloy specimen is in uniaxial tension, the axial direction is set to the x-axis direction, and the α-phase diffraction elastic constant of the TC17 (103) surface obtained by the model calculation in step 2 is , And substitute the measured strain value into the stress calculation formula:

[0282]

[0283] in is the measured axial tensile strain of the α phase (103) plane of TC17 titanium alloy, , .

[0284] .

Claims

1. A method for measuring residual stress in complex phase materials using a diffraction method, characterized in that: The method specifically comprises the following steps: Step 1 Obtain the average bulk modulus of the complex phase material to be tested by measuring or looking up and the average shear modulus ; Step 2 Use the micromechanics model to calculate the diffraction elastic constants of specific crystal planes of the matrix phase of complex materials. 、 ; Step 3 X-ray diffraction measurement or neutron diffraction measurement of matrix phase deformation of complex materials and calculation of stress in complex materials; When the diffraction method is used to measure stress, the corresponding elastic constitutive equation is: （24） In formula (24): is the stress tensor of the complex material, is the variable tensor of the matrix phase A, 、 is the diffraction elastic constant of the matrix phase A obtained in step 2; For a certain measured strain of the matrix phase in a composite material ,in , and Respectively represent and test the direction cosines of the x-axis, y-axis and z-axis of the coordinate system, and the strain tensor can be used The six components of are: (25) represents the principal strain in the test coordinate system, Indicates the shear strain in the test coordinate system; therefore, when the principal strain is unknown, it is necessary to measure the strain in at least 6 directions of the matrix phase , d is an integer from 1 to 6, and 6 linear equations are constructed to solve the strain tensor: (26) After obtaining the strain tensor, the components of the stress tensor of the complex material can be calculated using formula (25); When the principal strain is known, it is only necessary to determine the principal coordinate axes of the matrix phase in the material coordinate system. Strain in three directions The stress state of the composite material can be determined; at this time, the constitutive equation (24) can be simplified to: （27a) （27b) （27c) In the formula 、 Represents the principal stress of the complex phase material in the material coordinate system; After obtaining the strain of the matrix phase, it is inserted into formula (2) to obtain the stress of the entire material; (2) In the formula represents the stress of the complex material, and represent the diffraction elastic constant and strain of the "new" hkl crystal plane of the matrix phase, respectively.

2. The method for measuring residual stress of a complex phase material by a diffraction method according to claim 1, characterized in that: Expressed as ( ),Right now ( )and are the diffraction elastic constants and strains of the "new" hkl crystal plane of the matrix phase, respectively; the corresponding elastic constitutive equation is: (2-1) In the formula represents the measured corresponding force, represents the hkl crystal plane diffraction elastic constant, It represents the strain in different directions of the hkl crystal plane. When i=j, it represents the principal strain, and i≠j represents the combined strain.

3. The method for measuring residual stress of complex phase materials by diffraction method according to claim 1, characterized in that: Measurement of average bulk modulus of complex materials using pulse excitation method and the average shear modulus The following steps are included: Prepare the sample according to the national standard and obtain the sample mass, length, width, and thickness; place the sample horizontally on two horizontally tensioned platinum wires, with the excitation point and signal collection point at two opposite corners of the sample, and collect the bending vibration frequency and torsional vibration frequency; Substitute the collected bending vibration frequency and torsional vibration frequency into the formula to obtain the dynamic Young's modulus E, shear modulus G, and bulk modulus K; if the test material is a complex material, then K and G are equivalent to the average bulk modulus of the complex material. and the average shear modulus ; Calculation of elastic modulus E: （3） Where: E=dynamic Young's modulus, unit: Pa, m=sample mass, in g, b=sample width, in mm, L=sample length, in mm, t = sample thickness, in mm, = fundamental resonant frequency of the bending rod in Hz, Calculation of shear modulus G: ( ) （4） Where: G = shear modulus, in Pa, = torsional vibration frequency, in Hz, B is the shape parameter, ; A is the parameter obtained through experience. ; Calculation of bulk modulus K: （5）。 4. The method for measuring residual stress of complex phase materials by diffraction method according to claim 3, characterized in that: The dynamic Young's modulus measurement method of refractory materials in accordance with GB / T30758-2014 is adopted; the outside micrometer in accordance with GB / T1216-2018 is adopted.

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