Method for calculating residual stress of 95% aluminum oxide based on indentation cracks

Abstract

A 95% alumina residual stress calculation method based on indentation cracks comprises the following steps: determining a test area and a test point position of 95% alumina, the test area covering a plurality of crystal grains; carrying out a Vickers indentation experiment at the position of the measuring point; the method comprises the following steps of: acquiring indentation cracks in a test area, counting the indentation cracks, measuring all the indentation cracks which crack near the tip of an indentation, classifying the cracks according to the size relationship between the crack length l and the indentation radius a, and calculating the projection lengths of the Palmqvist cracks in the horizontal direction and the vertical direction according to the condition that the cracks are Palmqvist cracks when l is less than 1.5 a, and the cracks are Radio-median cracks when l is less than 1.5 a; and obtaining the residual stress of 95% Al2O3 based on a calculation model between the projection length of the Palmqvist crack and the residual stress.

Description

Technical Field

[0001] The invention relates to the technical field of material residual stress determination, and in particular to a method for calculating 95% aluminum oxide residual stress based on indentation cracks. Background Art

[0002] Brazing, as a common method for bonding ceramics to metals, has been widely used in mechanical, aerospace, microelectronics and other fields. Due to the large difference in thermal physical properties between metals and ceramics, large residual stress is often generated during the brazing cooling process, often causing cracking and failure on the ceramic side.

[0003] At present, researchers mostly use qualitative methods to control residual stress, but none of them accurately characterize the micro-area stress on the ceramic side. The indentation crack method has become one of the test technologies that can characterize the micro-area stress of ceramics due to its simple test, high spatial resolution, and the ability to measure non-equibiaxial residual stress in principle. Marshall and Lawn, based on the assumption that the Vickers indentation crack is semi-elliptical, proposed the hypothesis that the crack length shortens due to compressive stress and lengthens due to tensile stress, thereby affecting the measurement of fracture toughness, and established the calculation relationship between the fracture toughness measurement value and the residual stress. Where K IC is the fracture toughness measurement value; ξ is the dimensionless correction factor introduced into the formula; E and H represent the hardness and elastic model of the material being tested, respectively; P is the Vickers indentation load; c represents the length from the center of the Vickers indentation to the end of the crack; σ R is the residual stress, and ψ is the crack shape geometry factor. However, this calculation relationship only considers the relationship between crack length and stress, and does not take into account the diversity of the crack system, the uncertainty of the stress field under the indenter, the test scale (when the test scale is small enough, the surface microstructure and crystal orientation of the material will affect the length of the test crack), and there are many calculation parameters, which are difficult to accurately measure in experiments. Therefore, its effectiveness in practical applications remains to be discussed. Summary of the invention

[0004] The present invention provides a 95% aluminum oxide residual stress calculation method based on indentation cracks and a system thereof, which can accurately and conveniently obtain the micro-area residual stress of the surface of 95% Al2O3.

[0005] On the one hand, the present invention discloses a method for calculating residual stress of 95% alumina based on indentation cracks, comprising the following steps:

[0006] S1: Determine the test area of ​​95% aluminum oxide and its measuring point location;

[0007] S2: Perform Vickers indentation test at the measuring point;

[0008] S3: Obtain the indentation cracks in the test area and make statistics on the indentation cracks;

[0009] S4: The residual stress of 95% Al2O3 is obtained based on the calculation model between the projection length of the Palmqvist crack and the residual stress.

[0010] Preferably, in S3,

[0011] All indentation cracks that crack near the indentation tip are measured. The measured values ​​include the indentation radius a, crack length l, and crack extension direction θ. Based on the difference in the shape of the crack surface, the cracks are classified according to the relationship between the crack length l and the indentation radius a. When l is less than 1.5a, it is a Palmqvist crack, otherwise it is a Radial-median crack. The projection lengths of the Palmqvist crack in the horizontal and vertical directions are calculated.

[0012] Preferably, in S4,

[0013] The calculation model is: l = 3.03 + 0.00524 × σ,

[0014] Where σ is the residual stress, unit is MPa; l is the crack projection length perpendicular to the direction of action of σ, unit is μm.

[0015] Preferably,

[0016] The pressing load is low load 0.49kgf, and the holding time is 20s.

[0017] Preferably,

[0018] The crack surface opens and displaces under the action of normal tensile stress, thereby achieving crack extension.

[0019] Preferably,

[0020] The test area covers a plurality of dies.

[0021] Preferably,

[0022] The test area avoids intercrystalline voids, intracrystalline pores, grain breakage and grain boundaries.

[0023] Preferably,

[0024] The Vickers indentation test is carried out using a Vickers indenter.

[0025] Preferably,

[0026] The indentation crack expansion mode is an opening type expansion.

[0027] Preferably,

[0028] The residual stress is projected onto the crack surface in the normal direction. Its projection component acts as an additional force to the normal tensile stress to promote or hinder the expansion of the crack.

[0029] Preferably,

[0030] The crack is projected in the horizontal and vertical directions, and the non-equibiaxial residual stress is calculated based on the crack projection length.

[0031] Preferably,

[0032] 95% alumina forms a ceramic material.

[0033] On the other hand, the present invention also discloses a 95% aluminum oxide residual stress calculation system based on indentation cracks, comprising:

[0034] A determination device for determining a test area of ​​95% aluminum oxide and a location of a measurement point thereof;

[0035] An experimental device, which is used to perform a Vickers indentation test at a measuring point;

[0036] A statistical device is used to obtain the indentation cracks in the test area and make statistics on the indentation cracks.

[0037] A calculation device is used to obtain the residual stress of 95% Al2O3 based on a calculation model between the projected length of the Palmqvist crack and the residual stress.

[0038] Compared with the prior art, the present invention has the following advantages: the present invention realizes the calculation of non-equibiaxial residual stress; the present invention does not need to measure the fracture toughness of the material, and reduces the calculation parameters that are difficult to measure in the experiment, effectively reducing the complexity of the experiment. The present invention can more conveniently and accurately use the Vickers indenter to complete the characterization of the non-equibiaxial residual stress on the surface of 95% Al2O3. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] By reading the detailed description of the preferred specific embodiments below, various other advantages and benefits of the present invention will become clear to those of ordinary skill in the art. The drawings in the specification are only for the purpose of illustrating the preferred embodiments and are not considered to be limitations of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative work. Moreover, the same reference numerals are used to represent the same components throughout the drawings.

[0040] In the attached picture:

[0041] Figure 1 It is a schematic diagram of the indentation morphology characterization method of the present invention;

[0042] Figure 2 Schematic diagram of the Palmqvist crack and Radial-median crack model of the present invention;

[0043] Figure 3 This is a schematic diagram of the effect of prestress on the projection length of Palmqvist crack under low load according to the present invention;

[0044] Figure 4 This is a morphology diagram of single crystal aluminum oxide (sapphire);

[0045] Figure 5 This is the morphology of polycrystalline alumina;

[0046] Figure 6 It is 4J33 / 95%Al2O3 brazed joint;

[0047] Figure 7 A schematic diagram of a stress loading tool and an alumina loading method in one embodiment of the present invention;

[0048] Figure 8 A schematic diagram of a Vickers indentation test of aluminum oxide in a prestressed state in one embodiment of the present invention;

[0049] Fig. 9 This is a schematic diagram of MISE stress distribution results under biaxial tension in one embodiment of the present invention;

[0050] Fig.10 A schematic diagram of stress distribution results in horizontal and vertical directions under equibiaxial loading in one embodiment of the present invention;

[0051] Fig.11 A schematic diagram of a four-point bending loading scheme for a sandwich structure in one embodiment of the present invention;

[0052] Fig.12 It is a schematic diagram of the stress field distribution results in the horizontal direction of the sandwich structure in four-point bending in one embodiment of the present invention;

[0053] Fig.13 This is a schematic diagram of stress distribution in the horizontal direction of Path 1 in one embodiment of the present invention;

[0054] Fig.14 Schematic diagram of the indentation distribution results (C plane) at different stress levels in sapphire;

[0055] Fig.15 Schematic diagram of the indentation morphology (C plane) of sapphire under different stress states;

[0056] Fig.16 Schematic diagram of the relationship between the indentation crack length on the C plane of sapphire and stress;

[0057] Fig.17 The indentation distribution diagram of different indentation loads and different indentation angles on C-plane and A-plane sapphire;

[0058] Fig.18 Schematic diagram of the indentation crack morphology at different indentation angles (sapphire C plane, 0.98kgf);

[0059] Fig.19 Schematic diagram of the indentation crack morphology at different indentation angles (sapphire C plane, 0.49 kgf);

[0060] Fig. 20 Schematic diagram of the relationship between crack length, indentation load, and indentation angle (sapphire C plane);

[0061] Fig.21 Schematic diagram of the indentation crack morphology at different indentation angles (sapphire A plane, 0.98kgf);

[0062] Fig. 22 Schematic diagram of the indentation crack morphology at different indentation angles (sapphire A plane, 0.49 kgf);

[0063] Fig.23 Schematic diagram of the common microstructure in 95% Al2O3;

[0064] Fig.24 Schematic diagram of the effect of prestress on the projection length of different types of Vickers cracks under high load / low load;

[0065] Fig.25 Schematic diagram of EBSD scanning results and grain size distribution of brazed joints;

[0066] Fig.26 This is a schematic diagram of the stress test area of ​​the brazed joint;

[0067] Fig. 27 Schematic diagram of the residual stress measurement scheme of the brazed ceramic side based on the indentation crack method;

[0068] Fig.28 Schematic diagram of the residual stress distribution (indentation crack method) of 95% Al2O3 in a brazed joint.

[0069] The present invention is further explained below in conjunction with the accompanying drawings and embodiments. DETAILED DESCRIPTION

[0070] The following will refer to the attached Figures 1 to 28 Specific embodiments of the present invention are described in more detail. Although specific embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0071] It should be noted that certain words are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different nouns to refer to the same component. This specification and claims do not use the difference in nouns as a way to distinguish components, but use the difference in the functions of the components as the criterion for distinction. As mentioned throughout the specification and claims, "including" or "comprising" is an open term, so it should be interpreted as "including but not limited to". The subsequent description of the specification is a preferred embodiment of the present invention, but the description is based on the general principles of the specification and is not intended to limit the scope of the present invention. The scope of protection of the present invention shall be determined by the attached claims.

[0072] To facilitate understanding of the embodiments of the present invention, further explanation will be given below by taking specific embodiments as examples in conjunction with the accompanying drawings, and each of the accompanying drawings does not constitute a limitation on the embodiments of the present invention.

[0073] The calculation method of 95% aluminum oxide residual stress based on indentation crack includes the following steps:

[0074] S1: Determine a test area of ​​95% aluminum oxide and its measuring point positions, wherein the test area covers a plurality of grains;

[0075] S2: Perform Vickers indentation test at the measuring point;

[0076] S3: Obtain the indentation cracks in the test area and make statistics on the indentation cracks, wherein all the indentation cracks that crack near the indentation tip are measured, and the measured values ​​include the indentation radius a, the crack length l, and the crack extension direction θ. Based on the shape difference of the crack surface, the cracks are classified according to the size relationship between the crack length l and the indentation radius a. When l is less than 1.5a, it is a Palmqvist crack, otherwise it is a Radial-median crack. The projection length of the Palmqvist crack (Palmqvist crack is also called radial crack) in the horizontal and vertical directions is calculated;

[0077] S4: The residual stress of 95% Al2O3 is obtained based on the calculation model between the projection length of the Palmqvist crack and the residual stress. The calculation model is: l = 3.03 + 0.00524 × σ (1),

[0078] Where σ is the residual stress, unit is MPa; l is the crack projection length perpendicular to the direction of action of σ, unit is μm.

[0079] It should be noted that see Figure 2Based on the difference in the shape of the crack surface, the cracks are classified by the relationship between the crack length l and the indentation radius a: when l is less than 1.5a, it is a Palmqvist crack, otherwise it is a Radial-median crack, i.e. a median crack.

[0080] In a preferred embodiment of the method for calculating residual stress of 95% alumina based on indentation crack, 95% alumina forms a ceramic material.

[0081] In a preferred embodiment of the method for calculating the residual stress of 95% alumina based on indentation cracks, the test area avoids intercrystalline pores, intracrystalline pores, grain crushing and grain boundaries.

[0082] In the preferred implementation of the method for calculating the residual stress of 95% alumina based on indentation cracks, the Vickers indentation test is tested using a Vickers indenter, the indentation load is a low load of 0.49 kgf, and the holding time is 20 s.

[0083] In a preferred implementation of the method for calculating the residual stress of 95% alumina based on indentation cracks, the indentation cracks extend in an opening-type manner, and the crack surface undergoes an opening displacement under the action of normal tensile stress, thereby achieving crack extension.

[0084] In one embodiment, the method for calculating the 95% aluminum oxide residual stress based on indentation cracks includes:

[0085] In S1, the test area should cover multiple grains to reduce the influence of crystal orientation on cracks; the test site should be as far away from the microstructure (intercrystalline pores, intracrystalline pores, grain breakage, grain boundaries, etc.) as possible.

[0086] In addition, the testing technology of 95% Al2O3 residual stress based on indentation crack according to the present invention further provides the following features:

[0087] 1. This method uses a Vickers indenter for testing, with a low load of 0.49 kgf and a holding time of 20 seconds;

[0088] 2. The 95% Al2O3 residual stress calculation model established by this method makes the following assumptions: The Vickers indentation crack propagation mode in 95% Al2O3 belongs to the opening type, that is, the crack surface undergoes an opening displacement under the action of the normal tensile stress, thereby achieving crack propagation. The residual stress can be projected in the normal direction of the crack surface, and its projection component promotes or hinders the propagation of the crack as an additional force to the normal tensile stress. The crack is projected in the horizontal and vertical directions, and the non-equibiaxial residual stress is calculated based on the crack projection length.

[0089] In another embodiment, the present invention also discloses a 95% aluminum oxide residual stress calculation system based on indentation cracks, comprising:

[0090] A determination device for determining a test area of ​​95% aluminum oxide and a location of a measurement point thereof;

[0091] An experimental device, which is used to perform a Vickers indentation test at a measuring point;

[0092] A statistical device is used to obtain the indentation cracks in the test area and make statistics on the indentation cracks.

[0093] A calculation device is used to obtain the residual stress of 95% Al2O3 based on a calculation model between the projected length of the Palmqvist crack and the residual stress.

[0094] It should be noted that the 95% alumina referred to in the present invention refers to polycrystalline alumina 95% Al2O3, and the composite structure containing polycrystalline alumina 95% Al2O3 (such as the metal ceramic brazing joint mentioned in the example), especially the material containing polycrystalline alumina 95% Al2O3 and the grain size of polycrystalline alumina 95% Al2O3 is 5 to 15 microns. The materials include but are not limited to composite materials containing polycrystalline alumina 95% Al2O3. Typically, a 4J33 / 95% Al2O3 brazing joint filled with Au-Ag-Ge brazing filler is an object covered by the 95% alumina referred to in the present invention, but in this case, 95% alumina is more inclined to refer to the alumina side of the brazing joint.

[0095] In a more specific example:

[0096] Taking the stress characterization of 95% Al2O3 as an example, combined with finite element simulation, the accurate application of prestress to the 95% Al2O3 sample is achieved; and the prestressed sample is subjected to a low-load (0.49kgf) Vickers indentation test, the Palmqvist crack projection length is statistically calculated, and the residual stress of 95% Al2O3 is further calculated according to the calculation model of the present invention. Table 1 shows the residual stress measurement accuracy of this calculation model. Comparing the residual stress calculation value with the prestress, the maximum absolute error is 23.3MPa and the relative error is 49.7%. In this embodiment, 23.3MPa is related to the dispersion of the indentation crack length and the accuracy of the crack length measurement, and 49.7% is related to the low prestress level.

[0097] Table 1 Residual stress measurement accuracy based on crack projection length

[0098]

[0099] In another more specific embodiment,

[0100] The brazing joints of sapphire with a purity of up to 99.9996%, polycrystalline alumina 95% Al2O3 and 4J33 / 95% Al2O3 with Au-Ag-Ge as the filler material were taken as the research objects.

[0101] Sapphire was prepared into square samples with a size of 25×25×0.5 mm and round samples with a diameter of 50.8 mm and a thickness of 0.43 mm. All sapphire samples were double-sided polished with a roughness of Ra<0.5 nm ( Figure 4 The polycrystalline alumina was processed into a cross-shaped specimen with a cross-sectional size of 4×3 mm ( Figure 5 (a)), and the center area is rounded (radius 1mm) to accommodate the prestressing fixture. Figure 6 As shown, the dimensions of 95% Al2O3 are 10×7×7mm and the dimensions of 4J33 are 7×7×7mm.

[0102] Sapphire and polycrystalline alumina were subjected to stress relief annealing at 1300℃ for 2h, and then the polycrystalline alumina was polished with 150nm SiO2 polishing liquid until the surface was flat and scratch-free. The sapphire test area was marked with ink (no other treatment was required for high surface quality), and the treated sapphire and polycrystalline alumina samples were used for Vickers indentation test.

[0103] The 4J33 / 95% Al2O3 brazed joint was sanded until the surface scratches were fine and evenly distributed, and then mechanically polished with a diamond polishing paste with a particle size of 2.5μm. After the surface was bright and without obvious scratches, the sample was ultrasonically cleaned and dried, and finally the deformation stress layer on the sample surface was removed by ion thinning to complete the sample preparation. The brazed joint was tested by Gemini SEM500 to analyze the grain size of the polycrystalline alumina in the joint.

[0104] Design the following prestressing tooling:

[0105] Prestressing tooling Figure 7 As shown in (a), the alumina sample is pre-stressed with a known stress by means of threaded fit and an S-type tension and compression force sensor. For example, the sensor model is FSKA-2kN, with a maximum range of 2kN and a test accuracy of 0.1% of the maximum range, i.e. 2N. When a sample with a cross-sectional size of 4×3mm is loaded, the stress measurement error is equivalent to 0.6MPa, which meets the experimental requirements. Figure 7 As shown in (b) and (c), biaxial tension and compression loading schemes and uniaxial stress loading schemes can be adopted. In the uniaxial stress loading scheme, a 25×4×3mm polycrystalline alumina strip sample is subjected to four-point bending loading through a wire cutting fixture; a single crystal sapphire sample processed by diamond wire cutting is subjected to uniaxial compression loading.

[0106] Implement numerical simulation of prestress field:

[0107] The biaxial tension and compression and four-point bending methods are used to pre-stress the ceramic with known stress. Considering the small test area and the difficulty of attaching strain gauges, a reliable stress pre-stress method must meet the requirements of simple stress field distribution in the test area and the ability to calculate the pre-stress value through the formula. Through practice, the following method is determined: Abaqus software is used to simulate and analyze the stress field distribution characteristics of the ceramic sample test area under different pre-stress methods.

[0108] About biaxial tension and compression stress field simulation:

[0109] The size of the finite element model specimen is the same as the actual specimen size. The cross-sectional size of the single-side loading arm is 4×3mm, and the radius of the fillet in the center area is 2mm. The material is 95% Al2O3, with an elastic modulus of 350GPa and a Poisson's ratio of 0.23. The grid unit is C3D8R hexahedron, and the grid side length is 0.1mm. When calculating the stress field, the two end faces of the cross-shaped specimen in the negative X and Y directions are constrained, and 100MPa tensile stress is applied to each of the remaining two end faces to analyze the stress field characteristics in the center area.

[0110] Simulation of four-point bending stress field of sandwich structure:

[0111] The size of the 95% Al2O3 model in the four-point bending simulation model of the sandwich structure is 25×4×3mm, and a 65Mn model with a thickness of 1mm is added on both sides of the 95% Al2O3 model, and the interface interaction between the two is set to hard contact. Four cylinders regarded as rigid bodies are assembled on both sides of the specimen as the support end and the loading end respectively. The radius of the cylinder is the same as that of the actual fixture, both of which are 1mm. The contact position between the cylinder and the specimen is set to hard contact. The grid unit type is specified as C3D8R hexahedron, and the minimum size of the grid edge length is 0.15mm. The center of the cylinder as the support end is fixed, and the specified displacement is applied to the center of the cylinder at the loading end to realize the four-point bending loading of alumina.

[0112] Vickers indentation test:

[0113] The indentation experiment was carried out on sapphire and polycrystalline alumina with known pre-stress using the Weiyi HV 1000TPTA. The indentation morphology was characterized using the SOPTOP ICX4IM inverted metallographic microscope, and the software ImageJ was used to calculate the Vickers indentation size, crack angle and length at the tip to support subsequent data analysis. The Vickers indentation experiment of alumina with pre-stress can be found in Figure 8 .

[0114] Furthermore, the following specific results on the prestress field of Al2O3 samples were obtained:

[0115] First, the stress field distribution of biaxial tension and compression:

[0116] Fig. 9 The MISE stress cloud diagram of a cross-shaped ceramic specimen with a central transition radius of 1 mm under an equibiaxial tensile stress of 100 MPa shows a diamond-shaped low-stress area with uniform stress distribution and a stress value of 69 MPa. Fig.10 The stress cloud diagram of the cross-shaped specimen in the horizontal and vertical directions shows that the stress distribution in the horizontal and vertical directions is uniform in the 2×2mm square area at the geometric center of the specimen, and the stress value is 69MPa. Therefore, when the cross-shaped specimen with this fillet size is subjected to biaxial tension and compression loading, the central 2×2mm square area is an ideal stress measurement area, where the stress distribution is uniform, the stress ratio is stable, and the stress magnitude is the stress applied in the corresponding direction divided by √2.

[0117] Second, the stress field distribution of four-point bending:

[0118] A four-point bending test was performed on polycrystalline alumina, and the following formula (2) was established to express the horizontal stress σ at any position in the loading area: xx (y) is calculated:

[0119]

[0120] Where P is the loading load, unit N; w and h are the width and thickness of the specimen, respectively, in mm; L and l are the distances between the support point and the loading point of the four-point bending fixture, respectively, in mm; y is the neutral plane distance, in mm.

[0121] It should be noted that in practice, we found that the wire cutting processing accuracy and assembly error problems easily lead to stress concentration in the area near the loading end of the alumina specimen under simple structure four-point bending, which is prone to cracking failure. The actual stress field distribution of the specimen is uneven, and the sandwich structure can significantly improve it. Finally, we adopted the sandwich structure, that is, adding two 1mm thick 65Mn ( Figure 8 ) conducted a four-point bending loading experiment and found that under this structure, the crack was located on the tensile stress side of the center of the alumina loading area, which effectively solved the stress concentration problem.

[0122] In order to verify the reliability of the sandwich structure, Abaqus software was used to perform simulation tests. We found that the stress field in the loading area of ​​the alumina specimen in the sandwich structure is similar to the stress field of the alumina in the simple four-point bending structure. The horizontal stress on the path Path1 along the thickness direction of the loading area was further extracted and plotted together with the theoretical value of the horizontal stress calculated by the above formula (2). Fig.13It can be found that the horizontal stress approaches 0 in 65Mn and is linearly distributed in the alumina region. Due to the continuity of stress, there is a narrow stress transition zone near the interface between the two materials. More importantly, the simulated stress distribution in the alumina loading area of ​​the sandwich structure is very consistent with the theoretical distribution calculated by formula (2), which shows that formula (2) is still applicable to the calculation of the stress field in this area under the sandwich structure.

[0123] It should be noted that the object of the present invention, sapphire, is to explore the factors affecting indentation cracks, including the study of prestress and crystal orientation. Uniaxial stress Vickers indentation tests were carried out on sapphire (C plane) samples with prestress of 0MPa, -75MPa, -124MPa, -160MPa and -196MPa, respectively. The indentation load was 0.49kgf, the holding time was 20s, and the number of indentations at the same stress level was not less than 6 ( Fig.14 ).Depend on Fig.15 It can be seen that the Vickers indentation cracks of sapphire (C plane) at different stress levels all start from the indentation tip and basically extend outward in a cross shape along the diagonal direction of the indentation. However, when the prestress reaches -160MPa, the number of cracks in some indentations is less than 4; when the prestress is further reduced to -196MPa, white lateral cracks begin to appear between two adjacent cracks of the Vickers indentation. In the process of using sapphire to investigate the effect of prestress on crack length, in order to quantitatively analyze the effect of prestress on indentation crack length, the length l of all visible cracks starting from the indentation tip under the same stress state is measured. i (The subscript i is only used to count cracks.) The mean crack length is calculated as shown in formula (3).

[0124]

[0125] In the formula It represents the mean value of cracks in μm; M represents the number of cracks.

[0126] Fig.16 The relationship between the average length of the sapphire C-plane indentation crack and stress is shown. The average crack length becomes shorter as the prestress decreases, and it is found that there is a good linear relationship between the average crack length and the compressive stress level. The two are fitted to obtain formula (4), and its fitting degree R 2 Reached 97.5%.

[0127]

[0128] Where σ is the prestress, unit is MPa.

[0129] Furthermore, in order to determine the effect of crystal orientation on the indentation crack morphology, the present invention also selects to conduct Vickers indentation experiments on different orientation planes (C plane, A plane) of sapphire in a stress-free state. Unlike the spherical indenter with infinite central symmetry, the Vickers indenter is a regular tetrahedron, and the corresponding indentation cross-sectional shape is a square, with four-fold central symmetry (every 90° rotation around the center coincides with the original shape). To study the effect of crystal orientation on indentation cracks (regular tetrahedron Vickers indenter), the relative angle between the indenter insertion direction and the test surface orientation should actually be considered. We define the indentation angle as the angle between the diagonal direction of the Vickers indenter and the m-axis of the sapphire. In addition, to ensure that the research conclusions are more representative, different indentation loads are selected for the indentation test. Such as Fig.17 As shown, indentation tests were carried out in the C plane and A plane of sapphire, with the indentation angles of 0° and 45°, and the indentation loads of 0.49 kgf and 0.98 kgf, respectively.

[0130] 1) Indentation crack in the C plane of sapphire

[0131] The press load is 0.98kgf ( Fig.18 ), the distribution of the Vickers indentation crack in the C plane at different indentation angles is similar, all starting from the indentation tip and extending outward in a cross shape, and is not greatly affected by the indentation angle. Fig.19 ), the crack extension angle did not change significantly. The average length of visible cracks under different indentation loads and indentation angles ( Fig. 20 ), it is found that the C-plane indentation crack length is less affected by the indentation angle and is mainly related to the indentation load.

[0132] 2) Indentation crack in sapphire A plane

[0133] When the indentation load is 0.98 kgf, the indentation crack morphology in the sapphire A plane is as follows Fig.21 As shown in Figure 2, it is found that the crack morphology of this orientation is significantly different from that of the C plane. Fig.21 As shown in (a), when the indentation angle is 0°, the indentation cracks are divided into three categories according to their extension direction: vertical parallel cracks C1 perpendicular to the c-axis, horizontal cracks M1 perpendicular to the m-axis, and bevel cracks at a certain angle to the m-axis. According to statistics, the angle between the bevel crack and the m-axis is 37.6±4.0°, which is consistent with the R1 plane (crystal plane) in the sapphire fracture model. The normal direction is very close to the m-axis (the angle between the normal and the m-axis is 38.2°), so R1 is used to represent the bevel crack. The corresponding indentation crack after the indenter rotates 45° is shown in Fig.21In (b), it can be found that the M1 crack disappears and the C1 crack is greatly reduced. The cracks that can be observed are mainly two groups of parallel cracks starting from the indentation tip. According to statistics, the extension direction of these two groups of cracks is not a cross crack extending along the diagonal direction of the indentation under the dominance of stress, but actually the R1 crack with an angle of 38.3±1.8° to the m-axis and the R2 crack with an angle of 59.3±4.0° to the m-axis. When the indentation load is 0.49kgf( Fig. 22 ), the crack morphology distribution shows the same rule.

[0134] In addition, it can be found that the crack propagation direction and the corresponding crack length are different in the same indentation. We believe that this may be related to the indentation stress field and the difference in crystal plane fracture energy between different orientation planes. The expansion process of the indentation crack in α-Al2O3 depends on the crystal plane fracture energy corresponding to the crack plane and the residual stress perpendicular to the plane. When the indenter is just beginning to press in, the stress at the indentation tip is the largest, and the crack first appears at this position at the indentation tip. The crack propagation direction is determined by the theoretical fracture strength of the different orientation planes and the vertical component of the projection of the indentation stress field onto the plane. Fig.21 Taking (a) as an example, the stress field at the tip of the indentation is projected onto each orientation plane, and the force acting perpendicularly on the C plane and the M plane preferentially reaches the theoretical fracture strength of the corresponding orientation plane, so C1 and M1 cracks are formed. During the crack propagation process, the stress in the tip area of ​​the indentation is released, so no other cracks appear at this position. As the indenter is pressed further downward, the stress field at the edge of the indentation away from the tip gradually increases, and C1 cracks and R1 cracks continue to appear. Since the expansion of the C1 crack releases stress, the R1 crack does not appear on the same side of the indentation at the same time as the C1 crack. When the indenter is rotated 45°, the stress component of the indentation stress field acting on the R1 and R2 orientation planes is the largest, so the quasi-cross crack composed of R1 and R2 cracks mainly appears in the indentation morphology.

[0135] For further information, see Fig.23 , which shows the common indentation crack morphology in 95% Al2O3. When the crack propagates to the intergranular voids or intragranular pores, the crack propagation stops because the front energy of the crack tip is completely released. Fig.23 In (c), it is observed that when the crack propagates to the grain boundary, the crack propagation direction may deviate and begin to propagate along the grain boundary. In addition, when the grain size along the depth direction of the indentation position is small, the grain may break, as shown in Fig.23 Therefore, the surface microstructure will affect the crack propagation, and thus affect the linear relationship between crack length and stress.

[0136] Therefore, in the present invention, when measuring stress, the indentation position should be reasonably selected to reduce the influence of the microstructure, for example, selecting: an indentation position where the crack has not extended to the grain boundary, and the grain size along the depth direction of the indentation position is large so that the grain will not be broken; and a position away from intercrystalline holes and intracrystalline pores.

[0137] In summary, prestress and indentation load significantly affect crack length, while indentation angle and crystal orientation jointly affect crack distribution, and crystal orientation plays a dominant role. Specifically, the indentation crack surface changes due to different surface orientations, and the crack preferentially propagates along the orientation surface with lower bonding strength. The microstructure has a random effect on the crack by deflecting the crack propagation direction and stopping the crack propagation.

[0138] Therefore, when calculating the residual stress of polycrystalline alumina, i.e. 95% Al2O3,

[0139] First, the test points should be arranged reasonably: the principle is to avoid random effects of microstructure on cracks.

[0140] Secondly, the method of expanding the test area to cover multiple grains and taking the average is adopted to reduce the influence of crystal orientation on cracks.

[0141] It should be noted that the formula (1) mentioned above is determined by the following method and final fitting, rather than any easy-to-think-of method:

[0142] The projection lengths of the indentation cracks corresponding to the two loads under different stress states were statistically analyzed and plotted. Fig.24 It can be seen that under the indentation load of 0.98kgf, the projected lengths of the Radial-median crack and the Palmqvist crack have no obvious linear relationship with the stress. Under the indentation load of 0.49kgf, it can be clearly observed that the projected lengths of the Radial-median crack and the Palmqvist crack increase as the compressive stress decreases. In addition, the projected length of the Palmqvist crack under the tensile stress state is longer than the projected length of the crack under the stress-free state. The projected lengths of the two cracks were linearly fitted with the prestress, and the calculation formula (5) for the crack length of the Radial-median crack under different stress states and the calculation formula (6) for the crack length of the Palmqvist crack under different stress states were obtained, where the fitting degree R of formula (5) is 2 The fitting error is only 0.44, which is not suitable for predicting the residual stress of polycrystalline alumina. 2 As high as 0.93, it shows that the Palmqvist crack projection length has a good linear relationship with the residual stress and can be used to predict the residual stress of polycrystalline alumina.

[0143] l=5.64+0.00638×σ (5)

[0144] l=3.03+0.00524×σ (6)

[0145] Where σ is the residual stress, unit is MPa; l is the crack projection length perpendicular to the direction of action of σ, unit is μm.

[0146] Combination Figure 2 and 24 The practice of the present invention provides the following explanation for the fact that the two crack lengths have no obvious linear relationship with stress under high load conditions and the linear relationship between the projection length of the radial-median crack, i.e., the median crack, and stress is poor under low load conditions: the Vickers indentation size of the crack under different indentation loads is calculated, and the indentation radius a corresponding to the high load (0.98 kgf) is 4.41 μm, the average projection length of the radial-median crack, i.e., the median crack, is 8.20 μm, and the average projection length of the Palmqvist crack, i.e., the radial crack, is 3.80 μm, so the Vickers indentation size of the crack is 16 to 25 μm. The indentation radius corresponding to the low load (0.49 kgf) is 3.05 μm, the average projection length of the radial-median crack, i.e., the median crack, is 5.43 μm, and the average projection length of the Palmqvist crack, i.e., the radial crack, is 3.15 μm, and the corresponding Vickers indentation size of the crack is 12 to 17 μm. The crack size under high load conditions is significantly larger, and the probability of being affected by the microstructure during the expansion process is higher, so there is no obvious linear relationship between the projection length of the two Vickers cracks and stress under high load (0.98kgf). In addition, it was found that the Palmqvist crack only nucleates on the surface and expands in the lateral direction, while the Radial-median crack is formed by the Palmqvist crack that expands on the surface and the Median crack that expands simultaneously in all directions. The inconsistency of the expansion direction reduces the linear relationship between the projection length of the Radial-median crack and stress.

[0147] Therefore, the above-mentioned calculation model based on the projection length of the Palmqvist crack and the residual stress is finally based on the fitting formula (1).

[0148] It should be noted that after the calculation model of polycrystalline alumina residual stress is established in the present invention, it can be applied to the characterization of micro-region stress on the ceramic side of the brazed joint. In this application example, before the Vickers indentation test, we also conducted an EBSD test on the brazed joint. The statistical analysis of the results showed that the average size of polycrystalline alumina particles in the joint area was between 5 and 15 μm ( Fig.25), which is consistent with the grain size of cross-shaped polycrystalline alumina, which can ensure the smooth application of the calculation model. Then the residual stress in the central area of ​​the joint surface 100μm away from the metallization layer / ceramic side interface was tested ( Fig.26 Considering the influence of the crack indentation size under low load (0.49 kgf) and the microstructure of the polycrystalline alumina surface on the test position, the test area was determined as a 100 × 200 μm rectangle on the ceramic side of the joint center (close to the brazing interface). The stress measurement scheme is as follows Fig. 27 As shown in (a), a Vickers indentation test was performed on the Al2O3 grains in the test area with an indentation load of 0.49 kgf and a holding time of 20 s (the red mark is the indentation). The measurement point location selection criteria are that the grain surface is flat and far away from the microstructure (intergranular pores, intragranular pores and grain boundaries).

[0149] The stress calculation method is as follows: Fig. 27 As shown by the orange dashed line in (a), the indentations in different areas are divided at a horizontal interval of 25 μm. Taking the residual stress at 25 μm from the interface as an example, the length and extension direction of all visible cracks within the range of 0 to 50 μm from the interface are counted. After the Palmqvist cracks are screened out, the length of the cracks with an extension direction close to the X direction is projected in the X direction, the mean value of the horizontal crack projection length is calculated, and the residual stress σ parallel to the brazing weld direction is calculated according to formula (6): yy Similarly, the vertical crack projection length is calculated to calculate the stress σ in the direction perpendicular to the weld. xx .

[0150] The statistical results of the projection lengths of horizontal cracks and vertical cracks and the calculated values ​​of residual stress of 95% Al2O3 are shown in Table 2.

[0151] Table 2 Residual stress distribution in 95% Al2O3

[0152]

[0153] Furthermore, the residual stress distribution of 95% Al2O3 is shown in Fig.28 This shows that the residual stress calculation model of polycrystalline alumina in the present invention successfully characterizes the micro-area residual stress on the ceramic side of the 4J33 / 95% Al2O3 brazed joint. It can be found that the residual stress σ xx The tensile stress is shown near the brazing interface, and the stress value is 82.95MPa. As the distance from the brazing interface increases, σ xx Gradually transition to compressive stress, the transition area from tensile stress to compressive stress is between 25 and 50 μm from the brazing interface. Residual stress parallel to the weld direction σ yy It appears as compressive stress near the brazing interface.

[0154] Although the embodiments of the present invention are described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments and application fields, and the above specific embodiments are only illustrative and instructive, rather than restrictive. A person of ordinary skill in the art can also make many forms under the guidance of this specification and without departing from the scope of protection of the claims of the present invention, all of which belong to the protection of the present invention.

Claims

1. A method for calculating residual stress of 95% alumina based on indentation cracks, characterized in that: The steps include: S1: Determine the test area of ​​95% aluminum oxide and its measuring point location; S2: Perform Vickers indentation test at the measuring point; S3: Obtain the indentation cracks in the test area and make statistics on the indentation cracks. S4: The residual stress of 95% Al2O3 is obtained based on the calculation model between the projection length of the Palmqvist crack and the residual stress.

2. The method for calculating the residual stress of 95% alumina based on indentation cracks according to claim 1, characterized in that: Preferably, the test area covers a plurality of grains.

3. The method for calculating residual stress of 95% alumina based on indentation cracks according to claim 1, characterized in that: The test area avoids intercrystalline voids, intracrystalline pores, grain breakage and grain boundaries.

4. The method for calculating residual stress of 95% alumina based on indentation cracks according to claim 1, characterized in that: The Vickers indentation test is carried out using a Vickers indenter.

5. The method for calculating residual stress of 95% alumina based on indentation cracks according to claim 1, characterized in that: The indentation crack expansion mode is an opening type expansion.

6. A 95% aluminum oxide residual stress calculation system based on indentation cracks, characterized in that: include: A determination device for determining a test area of ​​95% aluminum oxide and a location of a measurement point thereof; An experimental device, which is used to perform a Vickers indentation test at a measuring point; A statistical device is used to obtain the indentation cracks in the test area and make statistics on the indentation cracks. A calculation device is used to obtain the residual stress of 95% Al2O3 based on a calculation model between the projected length of the Palmqvist crack and the residual stress.

7. The 95% aluminum oxide residual stress calculation system based on indentation cracking according to claim 6 is characterized in that: The test area covers a plurality of dies.

8. The 95% aluminum oxide residual stress calculation system based on indentation cracking according to claim 6 is characterized in that: The test area avoids intercrystalline voids, intracrystalline pores, grain breakage and grain boundaries.

9. The 95% aluminum oxide residual stress calculation system based on indentation cracking according to claim 6, characterized in that: The Vickers indentation test is carried out using a Vickers indenter.

10. The 95% aluminum oxide residual stress calculation system based on indentation cracking according to claim 6, characterized in that: The indentation crack expansion mode is an opening type expansion.

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