A method for calculating residual stress of 95% alumina based on indentation crack

Abstract

A 95% alumina residual stress calculation method based on indentation crack, in the method, the test area of 95% alumina and the position of the measuring point are determined, the test area covers multiple grains; the Vickers indentation experiment is carried out at the measuring point position; the indentation crack in the test area is obtained, and the indentation crack is counted, wherein all the indentation cracks near the indentation tip are measured, the cracks are classified by the size relationship between the crack length l and the indentation radius a, and the cracks are classified according to the size relationship between the crack length l and the indentation radius a, and the cracks are classified according to the size relationship between the crack length l and the indentation radius a, and the cracks are classified according to the size relationship between the crack length l and the indentation radius a, and the cracks are classified according to the size relationship between the crack length l and the indentation radius a, and the cracks are classified according to the size relationship between the crack length l and the indentation radius a, and the cracks are classified according to the size relationship between the crack length l and the indentation radius a, and the cracks are classified according to the size relationship between the crack length l and the indentation radius a, and the cracks are classified according to the size relationship between the crack length l and the indentation radius a, and the cracks are classified according to the size relationship between the crack length l and the indentation radius a, and the cracks are classified according to the size relationship between the crack length l and the indentation radius a, and the cracks are classified according to the size relationship between

Description

Technical Field

[0001] This invention relates to the field of residual stress measurement technology, and in particular to a method for calculating the residual stress of 95% alumina based on indentation cracks. Background Technology

[0002] Brazing, as a common method for bonding ceramics and metals, has been widely used in fields such as machinery, aerospace, and microelectronics. However, due to the significant differences in thermophysical properties between metals and ceramics, large residual stresses are often generated during the cooling process of brazing, which often leads to cracking failure on the ceramic side.

[0003] Currently, researchers mostly use qualitative methods to control residual stress, but none of them accurately characterize the micro-stress on the ceramic side. The indentation crack method, with its simplicity, high spatial resolution, and the ability to measure non-uniform biaxial residual stress, has become one of the testing techniques capable of characterizing micro-stress in ceramics. Marshall and Lawn, based on the assumption that Vickers indentation cracks are semi-elliptical, proposed that the crack length shortens with compressive stress and lengthens with tensile stress, thus affecting the measurement of fracture toughness. They also established the relationship between the measured fracture toughness and the calculated residual stress. Where K IC ξ is the fracture toughness measurement; ξ is the dimensionless correction factor introduced into the formula; E and H represent the hardness and elastic model of the tested material, 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 ψ represents residual stress, while ψ is the geometric factor of crack shape. However, this calculation relationship only considers the relationship between crack length and stress, without taking into account the diversity of crack systems, the uncertainty of the stress field under the indenter, the test scale (when the test scale is small enough, the microstructure of the material surface and crystal orientation will affect the length of the test crack), and many calculation parameters, which are difficult to accurately measure in experiments. Therefore, its effectiveness in practical applications is still debatable. Summary of the Invention

[0004] This invention provides a method and system for calculating residual stress in 95% alumina based on indentation cracks, which can accurately and easily obtain the micro-area residual stress on the surface of 95% Al2O3.

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

[0006] S1: Determine the test area and test point locations for 95% alumina;

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

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

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

[0010] Preferably, in S3,

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

[0012] Preferably, in S4,

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

[0014] In the formula, σ is the residual stress, in MPa; l is the crack projection length perpendicular to the direction of σ, in μm.

[0015] Preferred,

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

[0017] Preferred,

[0018] The crack surface undergoes opening displacement under normal tensile stress, thereby enabling crack propagation.

[0019] Preferred,

[0020] The test area covers multiple grains.

[0021] Preferred,

[0022] The test area avoids intergranular pores, intragranular pores, grain fragmentation, and grain boundaries.

[0023] Preferred,

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

[0025] Preferred,

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

[0027] Preferred,

[0028] The residual stress is projected onto the normal direction of the crack surface, and its projected component acts as an additional force of the normal tensile stress, either promoting or hindering crack propagation.

[0029] Preferred,

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

[0031] Preferred,

[0032] 95% alumina forms ceramic materials.

[0033] On the other hand, the present invention also discloses a system for calculating the residual stress of 95% alumina based on indentation cracks, comprising:

[0034] A determining device used to determine the test area and the location of the measuring points for 95% alumina;

[0035] An experimental setup used to perform Vickers indentation experiments at the measuring points;

[0036] A statistical device is used to acquire indentation cracks within the test area and to statistically analyze the indentation cracks.

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

[0038] Compared with existing technologies, this invention has the following advantages: This invention enables the calculation of non-uniaxial biaxial residual stress; it eliminates the need to measure the fracture toughness of the material and reduces the computational parameters that are difficult to determine in experiments, effectively lowering experimental complexity. This invention allows for a more convenient and accurate characterization of the non-uniaxial biaxial residual stress on the surface of 95% Al2O3 using a Vickers indenter. Attached Figure Description

[0039] Various other advantages and benefits of the present invention will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0040] In the attached diagram:

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

[0042] Figure 2 This is a schematic diagram of the Palmqvist crack and Radial-median crack models of the present invention;

[0043] Figure 3 This is a schematic diagram illustrating the effect of prestress on the projected length of Palmqvist cracks under low load according to the present invention.

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

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

[0046] Figure 6 For 4J33 / 95%Al2O3 brazed joints;

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

[0048] Figure 8 This is a schematic diagram of a prestressed Vickers indentation test on alumina in one embodiment of the present invention;

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

[0050] Figure 10 This is a schematic diagram of the stress distribution in the horizontal and vertical directions under equal biaxial loading in one embodiment of the present invention;

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

[0052] Figure 12 This is a schematic diagram of the horizontal stress field distribution of a sandwich structure under four-point bending in one embodiment of the present invention.

[0053] Figure 13 This is a schematic diagram of the horizontal stress distribution along Path1 in one embodiment of the present invention;

[0054] Figure 14 This is a schematic diagram of the indentation distribution (C-plane) in sapphire under different stress levels;

[0055] Figure 15 This is a schematic diagram of the indentation morphology (C plane) of sapphire under different stress states;

[0056] Figure 16 This is a schematic diagram showing the relationship between the length of the indentation crack on the C-plane of sapphire and stress.

[0057] Figure 17 The diagram shows the indentation distribution on sapphire crystals with different indentation loads and indentation angles on planes C and A.

[0058] Figure 18 A schematic diagram of the indentation crack morphology (sapphire C-plane, 0.98 kgf) at different indentation angles;

[0059] Figure 19 A schematic diagram of the indentation crack morphology (sapphire C-plane, 0.49 kgf) at different indentation angles;

[0060] Figure 20 This is a schematic diagram showing the relationship between crack length and indentation load and indentation angle (sapphire C-plane);

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

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

[0063] Figure 23 A schematic diagram of common microstructures in 95% Al2O3;

[0064] Figure 24 This is a schematic diagram illustrating the effect of prestress on the projected length of different types of Vickers cracks under high / low loads.

[0065] Figure 25 This is a schematic diagram showing the EBSD scan results and grain size distribution of the brazed joint;

[0066] Figure 26 Schematic diagram of the stress test area for brazed joints;

[0067] Figure 27 This is a schematic diagram of a method for measuring residual stress on the side of brazed ceramics based on the indentation cracking method.

[0068] Figure 28 This is a schematic diagram of the residual stress distribution (indentation cracking method) of 95% Al2O3 in a brazed joint.

[0069] The present invention will be further explained below with reference to the accompanying drawings and embodiments. Detailed Implementation

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

[0071] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. The terms "comprising" or "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising but not limited to." The following descriptions are preferred embodiments for carrying out the invention; however, these descriptions are for the purpose of understanding the general principles of the specification and are not intended to limit the scope of the invention. The scope of protection of this invention is determined by the appended claims.

[0072] To facilitate understanding of the embodiments of the present invention, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific embodiments. The accompanying drawings do not constitute a limitation on the embodiments of the present invention.

[0073] The method for calculating the residual stress of 95% alumina based on indentation cracks includes the following steps:

[0074] S1: Determine the test area and test point locations for 95% alumina, wherein the test area covers multiple grains;

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

[0076] S3: Obtain indentation cracks within the test area and statistically analyze them. Specifically, measure all indentation cracks that crack near the tip of the indentation. The measured values ​​include the indentation radius a, crack length l, and crack propagation direction θ. Based on the shape differences of the crack surface, classify the cracks according to the relationship between the crack length l and the indentation radius a. The criteria are: if l < 1.5a, it is a Palmqvist crack; otherwise, it is a Radial-median crack. Calculate the projected lengths of the Palmqvist crack (also known as a radial crack) in the horizontal and vertical directions.

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

[0078] In the formula, σ is the residual stress, in MPa; l is the crack projection length perpendicular to the direction of σ, in μm.

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

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

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

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

[0083] In a preferred embodiment of the method for calculating the residual stress of 95% alumina based on indentation cracks, the indentation crack propagation mode is an opening-type propagation, in which the crack surface undergoes an opening displacement under the action of normal tensile stress, thereby realizing crack propagation.

[0084] In one embodiment, the method for calculating the residual stress of 95% alumina 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 as possible from microstructures (intergranular pores, intragranular pores, grain fragmentation, grain boundaries, etc.).

[0086] Furthermore, the testing technique for 95% Al2O3 residual stress based on indentation cracks according to the present invention further provides the following features:

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

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

[0089] In another embodiment, the present invention also discloses a system for calculating the residual stress of 95% alumina based on indentation cracks, comprising:

[0090] A determining device used to determine the test area and the location of the measuring points for 95% alumina;

[0091] An experimental setup used to perform Vickers indentation experiments at the measuring points;

[0092] A statistical device is used to acquire indentation cracks within the test area and to statistically analyze the indentation cracks.

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

[0094] It should be noted that the 95% alumina referred to in this invention refers to polycrystalline alumina of 95% Al2O3, as well as composite structures containing polycrystalline alumina of 95% Al2O3 (such as the metal-ceramic brazed joint mentioned in the examples), especially materials containing polycrystalline alumina of 95% Al2O3 with a grain size of 5-15 micrometers. These materials include, but are not limited to, composite materials containing polycrystalline alumina of 95% Al2O3. Typically, a 4J33 / 95% Al2O3 brazed joint with Au-Ag-Ge filler metal falls under the scope of the 95% alumina referred to in this invention; however, in this case, 95% alumina more specifically refers to the alumina side of the brazed joint.

[0095] In a more specific example:

[0096] Taking the stress characterization of 95% Al2O3 as an example, the prestress of the 95% Al2O3 sample was accurately applied using finite element simulation. A low-load (0.49 kgf) Vickers indentation test was then performed on the prestressed sample, and the Palmqvist crack projection length was statistically analyzed. Furthermore, the residual stress of the 95% Al2O3 was calculated using the calculation model based on this invention. Table 1 shows the accuracy of the residual stress measurement using this calculation model. Comparing the calculated residual stress value with the prestress, the maximum absolute error is 23.3 MPa, and the relative error is 49.7%. In this embodiment, 23.3 MPa is related to the dispersion of the indentation crack length and the accuracy of the crack length measurement, while 49.7% is related to the relatively low prestress level.

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

[0098]

[0099] In another, more specific embodiment,

[0100] The research focuses on a 4J33 / 95%Al2O3 brazed joint with a purity of up to 99.9996% sapphire, 95% polycrystalline alumina (Al2O3), and Au-Ag-Ge filler metal.

[0101] Sapphire crystals were prepared into square specimens with dimensions of 25×25×0.5mm and circular specimens with a diameter of 50.8mm and a thickness of 0.43mm. All sapphire specimens were double-sided polished, with a surface roughness Ra < 0.5nm. Figure 4 Polycrystalline alumina was processed into a cross-shaped specimen with a cross-sectional dimension of 4×3mm. Figure 5 (a) is provided, and the central area has a rounded transition (1mm radius) to accommodate the prestressed tooling. The brazed joint is as follows: Figure 6 As shown, the size of 95% Al2O3 is 10×7×7mm, and the size of 4J33 is 7×7×7mm.

[0102] Sapphire and polycrystalline alumina were subjected to stress-relief annealing at 1300℃ for 2 hours. Then, polycrystalline alumina was polished with 150nm SiO2 polishing slurry until the surface was smooth and free of scratches. The sapphire test area was marked with ink (no further treatment was required due to high surface quality). The treated sapphire and polycrystalline alumina samples were then used for Vickers indentation experiments.

[0103] The 4J33 / 95% Al2O3 brazed joint was sanded until the surface scratches were fine and evenly distributed. Then, it was mechanically polished with diamond polishing paste with a particle size of 2.5 μm until the surface was bright and free of obvious scratches. The sample was then ultrasonically cleaned and dried. Finally, the deformation stress layer on the sample surface was removed by ion thinning, thus completing the sample preparation. EBSD testing was performed on the brazed joint using a Gemini SEM500 to analyze the grain size of the polycrystalline alumina in the joint.

[0104] Design the following prestressing fixture:

[0105] Prestressing fixtures such as Figure 7 As shown in (a), a known stress is pre-applied to the alumina sample via a threaded connection and an S-type tension / compression force sensor. For example, the sensor model is FSKA-2kN, with a maximum range of 2kN and a testing accuracy of 0.1% of the maximum range, i.e., 2N. When loading a sample with a cross-sectional dimension of 4×3mm, this equates to a stress measurement error of 0.6MPa, which meets the experimental requirements. Figure 7 As shown in (b) and (c), both biaxial tension-compression loading 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 using a wire EDM fixture; a single-crystal sapphire sample processed by diamond wire EDM is subjected to uniaxial compression loading.

[0106] Numerical simulation of the prestressed field was conducted:

[0107] Biaxial tension / compression and four-point bending methods were selected to pre-stress ceramic samples with known stress. Considering the small test area and the difficulty of attaching strain gauges, a reliable stress pre-stressing method must satisfy the requirements of simple stress field distribution in the test area and the ability to calculate the pre-stress value using formulas. Through practice, the following method was determined: Abaqus software was used to simulate and analyze the stress field distribution characteristics of the ceramic sample test area under different pre-stressing methods.

[0108] Simulation of biaxial tension and compression stress fields:

[0109] The finite element model specimen dimensions are the same as the actual specimen dimensions, with a single-sided loading arm cross-section of 4×3 mm and a central region fillet radius of 2 mm. The material is 95% Al₂O₃, with an elastic modulus of 350 GPa and a Poisson's ratio of 0.23. C3D8R hexahedral elements are used as the mesh elements, with a mesh edge length of 0.1 mm. During stress field calculation, the two end faces of the cross-shaped specimen in the negative X and Y directions are constrained, and a tensile stress of 100 MPa is applied to each of the remaining two end faces. The stress field characteristics of the central region are then analyzed.

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

[0111] In the four-point bending simulation model of the sandwich structure, the 95% Al2O3 model has dimensions of 25×4×3mm. A 1mm thick 65Mn model is added to each side of the 95% Al2O3 model, and the interface interaction between the two is set to hard contact. Four cylinders, considered rigid bodies, are assembled on both sides of the specimen as support ends and loading ends, respectively. The cylinder radii are the same as those of the actual tooling fixture, both being 1mm. The contact points between the cylinders and the specimen are set to hard contact. The mesh element type is specified as C3D8R hexahedron, with a minimum mesh edge length of 0.15mm. The center of the cylinder serving as the support end is fixed, and a specified displacement is applied to the center of the cylinder at the loading end to achieve four-point bending loading of the alumina.

[0112] Vickers indentation test:

[0113] Indentation experiments were conducted on sapphire and polycrystalline alumina under known prestress using a Vickers HV 1000TPTA microscope. The indentation morphology was characterized using a SOPTOP ICX4IM inverted metallographic microscope, and the Vickers indentation size, crack angle at the tip, and length were statistically analyzed using ImageJ software to support subsequent data analysis. For Vickers indentation experiments on alumina under prestress, please refer to [reference needed]. Figure 8 .

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

[0115] Firstly, the stress field distribution under biaxial tension and compression:

[0116] Figure 9 The MISE stress cloud diagram of a cross-shaped ceramic specimen with a center transition radius of 1 mm under a biaxial tensile stress of 100 MPa shows a rhomboid low-stress region with uniform stress distribution and a stress value of 69 MPa. Figure 10 The stress contour maps of the cross-shaped specimen in the horizontal and vertical directions reveal that the stress distribution is uniform in both directions within a 2×2mm square region centered on the specimen's geometric center, with a stress value of 69MPa in each direction. Therefore, when the cross-shaped specimen with this rounded corner size is subjected to biaxial tensile and compressive loading, the 2×2mm square region at the center is the ideal stress measurement area. This region exhibits uniform stress distribution, a stable stress ratio, and a stress magnitude equal to the applied stress in the corresponding direction divided by √2.

[0117] Secondly, the stress field distribution at four points of bending:

[0118] A four-point bending test was conducted on polycrystalline alumina, and the following formula (2) was established for the horizontal stress σ at any position in the loading area. xx (y) is used for calculation:

[0119]

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

[0121] It should be noted that in practice, we found that issues with wire EDM machining accuracy and assembly errors can easily lead to stress concentration in the vicinity of the loading end of alumina specimens under simple four-point bending, resulting in cracking failure and uneven stress field distribution in the specimen. Using a sandwich structure can significantly improve this situation. Ultimately, we adopted a sandwich structure, which involves adding two 1mm thick 65Mn steel sheets between the alumina specimen and the loading and support ends. Figure 8 A four-point bending loading test was conducted, and it was found that under this structure, the crack was located on the tensile stress side at the center of the alumina loading area, which effectively solved the stress concentration problem.

[0122] To verify the reliability of the sandwich structure, simulation tests were conducted using Abaqus software. We found that the stress field in the loaded region of the alumina sample in the sandwich structure was similar to the stress field of alumina in a simple four-point bending structure. Furthermore, the horizontal stress along the thickness direction Path1 of the loaded region was extracted and plotted together with the theoretical value of the horizontal stress calculated by the above formula (2). Figure 13It can be observed that the horizontal stress approaches 0 in 65Mn and exhibits a linear distribution 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 region of the sandwich structure is in very good agreement with the theoretical distribution calculated by formula (2), indicating that formula (2) is still applicable to the stress field calculation in this region under the sandwich structure.

[0123] It should be noted that the sapphire mentioned in this invention is for the purpose of investigating factors affecting indentation cracks, including prestress and crystal orientation. Uniaxial stress Vickers indentation tests were conducted on sapphire (C-plane) samples with prestresses of 0 MPa, -75 MPa, -124 MPa, -160 MPa, and -196 MPa, respectively. The indentation load was 0.49 kgf, the holding time was 20 s, and the number of indentations at the same stress level was no less than 6. Figure 14 ).Depend on Figure 15 It can be seen that under different stress levels, the Vickers indentation cracks in sapphire (C-plane) all originate from the tip of the indentation and extend outward in a roughly cross shape along the diagonal of the indentation. However, when the prestress reaches -160 MPa, some indentations have fewer than four cracks; when the prestress is further reduced to -196 MPa, white lateral cracks begin to appear between two adjacent cracks in the Vickers indentation. In investigating the effect of prestress on crack length using sapphire, to quantitatively analyze the effect of prestress on indentation crack length, the lengths of all visible cracks originating from the tip of the indentation under the same stress state were measured. i (The subscript i is only used for crack counting). The mean crack length is calculated using formula (3).

[0124]

[0125] In the formula The value represents the average crack size, in μm; M represents the number of cracks.

[0126] Figure 16 The relationship between the average length of the indentation crack in the C-plane of sapphire and the stress is illustrated. The average crack length decreases as the prestress decreases, and a good linear relationship is found between the average crack length and the compressive stress level. Equation (4) is obtained by fitting the two, and the goodness of fit R is... 2 It reached 97.5%.

[0127]

[0128] In the formula, σ represents the prestress, and the unit is MPa.

[0129] Furthermore, to determine the influence of crystal orientation on the morphology of indentation cracks, this invention also selected Vickers indentation experiments on sapphire with different orientation planes (C plane, A plane) under stress-free conditions. Unlike the infinitely centrally symmetric spherical indenter, the Vickers indenter is a regular square pyramid, corresponding to a square indentation cross-section, exhibiting fourfold central symmetry (it coincides with the original shape every 90° rotation around the center). In studying the influence of crystal orientation on indentation cracks (the regular square pyramid Vickers indenter), the relative angle between the indenter's indentation direction and the orientation of the test surface 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 the research conclusions are more representative, different indentation loads were selected for the indentation experiments. Figure 17 As shown, indentation tests were carried out in the C-plane and A-plane of the sapphire crystal, with indentation angles of 0° and 45°, and indentation loads of 0.49 kgf and 0.98 kgf, respectively.

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

[0131] The indentation load is 0.98 kgf. Figure 18 When the indentation load is reduced to 0.49 kgf, the distribution of Vickers indentation cracks in the C-plane is similar at different indentation angles. They all originate from the tip of the indentation and extend outward in a cross shape, showing little influence from the indentation angle. Figure 19 At different indentation loads and indentation angles, the crack propagation angle did not change significantly. The average length of the visible crack under different indentation loads and angles was statistically analyzed. Figure 20 It was found that the length of the indentation crack in plane C was not significantly affected by the indentation angle, but was mainly related to the indentation load.

[0132] 2) Indentation cracks in the A-plane of sapphire

[0133] When the indentation load is 0.98 kgf, the indentation crack morphology in the A-plane of the sapphire is as follows: Figure 21 As shown, the crack morphology in this orientation differs significantly from that in the C-plane. Figure 21 As shown in (a), when the indentation angle is 0°, the indentation cracks are classified into three types according to their propagation direction: vertical parallel cracks C1 perpendicular to the c-axis, horizontal cracks M1 perpendicular to the m-axis, and oblique cracks at a certain angle to the m-axis. Statistically, the angle between the oblique crack and the m-axis is 37.6±4.0°, which corresponds to the R1 plane (crystal plane) in the sapphire fracture model. The direction of the crack (with an angle of 38.2° between the normal and the m-axis) is very close, therefore R1 is used to represent the bevel crack. The indentation crack corresponding to a 45° rotation of the indenter is shown below. Figure 21In Figure (b), it can be observed that crack M1 has disappeared and crack C1 has significantly decreased. The main observable cracks are two sets of parallel cracks originating from the tip of the indentation. Statistical analysis revealed that the propagation direction of these two sets of cracks is not a cross-shaped crack extending along the diagonal of the indentation under stress dominance, but rather is actually crack R1 with an angle of 38.3±1.8° to the m-axis and crack R2 with an angle of 59.3±4.0° to the m-axis. When the indentation load is 0.49 kgf ( Figure 22 When the crack morphology is distributed, the same pattern exists.

[0134] Furthermore, it was observed that the crack lengths differed along the propagation direction within the same indentation. We believe this may be related to the indentation stress field and the differences in the fracture energies of crystal planes with different orientations. The propagation process of indentation cracks in α-Al₂O₃ depends on the fracture energy of the crystal plane corresponding to the crack surface and the residual stress perpendicular to the plane. When the indenter is first inserted, the stress at the indentation tip is the greatest, and the crack first appears at this location. The crack propagation direction is determined by the theoretical fracture strength of different orientations and the perpendicular component of the projection of the indentation stress field onto that plane. Figure 21 Taking (a) as an example, the stress field at the tip of the indentation is projected onto each orientation plane. The forces acting perpendicularly on the C and M planes preferentially reach the theoretical fracture strength of the corresponding orientation planes, thus forming C1 and M1 cracks. During crack propagation, the stress in the indentation tip region is released, so no other cracks appear at this location. As the indenter is pressed further down, the stress field at the edge of the indentation away from the tip gradually increases, and C1 and R1 cracks continue to be generated. Since the propagation of the C1 crack releases stress, the R1 crack does not appear on the same side of the indentation as the C1 crack. When the indenter is rotated 45°, the stress components of the indentation stress field acting on the R1 and R2 orientation planes are the largest, so the quasi-cross-shaped cracks composed of R1 and R2 cracks mainly appear in the indentation morphology.

[0135] Further, see Figure 23 It shows the common indentation crack morphology in 95% Al2O3. When the crack extends to intergranular pores or intragranular pores, the crack extension terminates because the energy at the crack tip is completely released. Figure 23 In (c), it was observed that when the crack propagates to the grain boundary, the crack propagation direction may deflect, and it begins to propagate along the grain boundary direction. Furthermore, when the grain at the indentation location has a small dimension along the depth direction, grain fragmentation may occur, as seen in [the diagram]. Figure 23 (d) Therefore, the surface microstructure affects crack propagation, which in turn affects the linear relationship between crack length and stress.

[0136] Therefore, in this invention, when measuring stress, the influence of microstructure should be reduced by reasonably selecting the indentation location. For example, the location should be selected where the crack has not extended to the grain boundary and the grain at the location of the indentation is large in size along the depth direction so that grain breakage will not occur; and the location should be far away from intergranular pores and intragranular pores.

[0137] In summary, prestress and indentation load significantly affect crack length, while indentation angle and crystal orientation jointly influence crack distribution, with crystal orientation playing a dominant role. Specifically, the indentation crack surface changes due to different surface orientations, and cracks preferentially propagate along orientations with lower bonding strength. Microstructure, on the other hand, exerts a random influence on cracks by deflecting crack propagation direction and halting 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, with the principle of avoiding random influence of microstructure on cracks.

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

[0141] It should be noted that the formula (1) mentioned above was finally determined by fitting in the following way, rather than in any easily conceivable manner:

[0142] The projected lengths of indentation cracks corresponding to two loads under different stress states were statistically analyzed and plotted. Figure 24 It can be seen that under an indentation load of 0.98 kgf, the projected lengths of both the Radial-median and Palmqvist cracks have no obvious linear relationship with the stress. Under an indentation load of 0.49 kgf, it can be clearly observed that the projected lengths of both the Radial-median and Palmqvist cracks generally increase with the decrease of compressive stress. In addition, the projected length of the Palmqvist crack under tensile stress is longer than that under stress-free stress. The projected lengths of the two types of cracks are linearly fitted with the prestress, and the calculation formulas (5) for the crack length of the Radial-median crack under different stress states and (6) for the crack length of the Palmqvist crack under different stress states are obtained. The goodness of fit R of formula (5) is... 2 The fitting accuracy R is only 0.44, indicating a large fitting error, making it unsuitable for predicting residual stress in polycrystalline alumina; while the fitting accuracy R of formula (6) is much higher. 2 The value of 0.93 indicates a good linear relationship between the Palmqvist crack projection length and residual stress, which 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] In the formula, σ is the residual stress, in MPa; l is the crack projection length perpendicular to the direction of σ, in μm.

[0146] Combination Figure 2 and 24 Based on the practical application of this invention, the following explanation is given for the results showing no obvious linear relationship between crack length and stress under high load conditions and a poor linear relationship between the projected length of the Radial-median crack (i.e., the median crack) and stress under low load conditions: Calculations were made of the Vickers indentation size containing cracks under different indentation loads. Under high load (0.98 kgf), the indentation radius 'a' is 4.41 μm, the average projected length of the Radial-median crack (i.e., the median crack) is 8.20 μm, and the average projected length of the Palmqvist crack (i.e., the radial crack) is 3.80 μm. Therefore, the Vickers indentation size containing cracks is 16–25 μm. Under low load (0.49 kgf), the indentation radius is 3.05 μm, the average projected length of the Radial-median crack (i.e., the median crack) is 5.43 μm, and the average projected length of the Palmqvist crack (i.e., the radial crack) is 3.15 μm. Correspondingly, the Vickers indentation size containing cracks is 12–17 μm. Cracks under high load conditions are significantly larger and more likely to be influenced by microstructure during propagation. Therefore, under high load (0.98 kgf), there is no obvious linear relationship between the projected length of either type of Vickers crack and stress. Furthermore, it was found that Palmqvist cracks nucleate only on the surface and propagate laterally, while Radial-median cracks are formed by the connection of Palmqvist cracks propagating on the surface and Median cracks propagating simultaneously in all directions. This inconsistency in propagation direction reduces the linear relationship between the projected length of Radial-median cracks and stress.

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

[0148] It should be noted that the calculation model for residual stress in polycrystalline alumina established in this invention can be applied to characterize the micro-stress on the ceramic side of brazed joints. In this application example, before conducting the Vickers indentation test, we also performed an EBSD test on the brazed joint. Statistical analysis of the results revealed that the average size of the polycrystalline alumina grains in the joint area was between 5 and 15 μm. Figure 25The grain size is consistent with that of the cross-shaped polycrystalline alumina, which ensures the smooth application of the computational model. Subsequently, the residual stress in the region 100 μm from the metallization / ceramic interface at the center of the joint surface was tested. Figure 26 Considering the influence of the low-load (0.49 kgf) crack indentation size and the microstructure of the polycrystalline alumina surface on the test location, the test area was determined to be a 100 × 200 μm rectangle on the ceramic side of the joint center (adjacent to the brazing interface). The stress measurement scheme is as follows: Figure 27 As shown in (a), a Vickers indentation experiment was performed on Al2O3 grains within the test area with an indentation load of 0.49 kgf and a holding time of 20 s (the indentation is marked in red). The test point was selected based on the condition that the grain surface was flat and far from the microstructure (intergranular pores, intragranular pores, and grain boundaries).

[0149] The stress calculation method is as follows: Figure 27 As shown by the orange dashed line in (a), the indentations in different regions are divided at 25 μm horizontal intervals. Taking the residual stress at a distance of 25 μm from the interface as an example, the length and propagation direction of all visible cracks within the range of 0 to 50 μm from the interface are statistically analyzed. After screening out the Palmqvist crack, the crack length with the propagation direction close to the X direction is projected towards the X direction. The average length of the crack projection in the horizontal direction is calculated, and the residual stress σ parallel to the brazed weld direction is calculated according to formula (6). yy Similarly, by statistically analyzing the vertical crack projection length, the stress σ in the direction perpendicular to the weld can be calculated. xx .

[0150] The statistical results of the projected lengths of horizontal and vertical cracks and the calculated 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 [the image / data]. Figure 28 This demonstrates that the polycrystalline alumina residual stress calculation model of the present invention successfully characterizes the micro-region residual stress on the ceramic side of the 4J33 / 95% Al2O3 brazed joint. It can be observed that the residual stress σ perpendicular to the weld direction... xx Tensile stress is observed near the brazing interface, with a stress value of 82.95 MPa. This stress increases with distance from the brazing interface. xx The stress gradually transitions to compressive stress, with the transition zone from tensile stress to compressive stress located between 25 and 50 μm from the brazed interface. The residual stress σ parallel to the weld direction... yy It manifests as compressive stress near the brazing interface.

[0154] Although embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art can make many other forms based on the guidance of this specification and without departing from the scope of protection of the claims of the present invention, and all of these are within the scope of protection of the present invention.

Claims

1. A method for calculating the residual stress of 95% alumina based on indentation cracks, characterized in that, Includes the following steps: S1: Determine the test area and test point locations for 95% alumina; S2: Perform Vickers indentation test at the measuring point; S3: Obtain the indentation cracks within the test area and perform statistical analysis on the indentation cracks. S4: The residual stress of 95% Al2O3 was obtained based on a calculation model of the relationship between the projected length and residual stress of the Palmqvist crack. The test area avoided intergranular pores, intragranular pores, grain fragmentation, and grain boundaries. Based on the shape difference of the crack surface, the crack length was less than 1.5 times the indentation radius. For Palmqvist cracks, the calculation model is as follows: (1), In the formula This represents residual stress, with a value range of -150 to 100, in MPa. To and The projected length of the crack perpendicular to the direction of action, in μm, with an indentation load of 0.49 kgf (low load). The indentation crack propagation mode is an opening-type propagation, where the crack surface undergoes opening displacement under normal tensile stress, thereby achieving crack propagation.

2. The method for calculating the residual stress of 95% alumina based on indentation cracks as described in claim 1, characterized in that, The test area covers multiple grains.

3. The method for calculating the residual stress of 95% alumina based on indentation cracks as described in claim 1, characterized in that, The Vickers indentation test is performed using a Vickers indenter.

4. A system for calculating the residual stress of 95% alumina based on indentation cracks, performing the method of any one of claims 1-3, characterized in that, include: A determining device used to determine the test area and the location of the measuring points for 95% alumina; An experimental setup used to perform Vickers indentation experiments at measuring points; A statistical device is used to acquire indentation cracks within the test area and to statistically analyze the indentation cracks. The computing device, which uses a computational model based on the relationship between the projected length and residual stress of a Palmqvist crack to obtain the residual stress of 95% Al2O3, is as follows: (1), In the formula Residual stress, in MPa; To and The projected length of the crack perpendicular to the direction of action, in μm.

5. The system for calculating residual stress in 95% alumina based on indentation cracks as described in claim 4, characterized in that, The test area covers multiple grains.

6. The system for calculating residual stress in 95% alumina based on indentation cracks as described in claim 4, characterized in that, The test area avoids intergranular pores, intragranular pores, grain fragmentation, and grain boundaries.

7. The system for calculating residual stress in 95% alumina based on indentation cracks as described in claim 4, characterized in that, The Vickers indentation test is performed using a Vickers indenter.

8. The system for calculating residual stress in 95% alumina based on indentation cracks as described in claim 4, characterized in that, The indentation crack propagation mode is an opening-type propagation.

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