CTS compact tensile sample stress intensity factor calculation method under different solder layer thicknesses and Young moduli

Abstract

The invention relates to a CTS compact tensile sample stress intensity factor calculation method under different solder layer thicknesses and Young moduli, and the method comprises the steps: carrying out the finite element simulation calculation of a stress intensity factor of a stress field parameter before a crack of a CTS sample model under different loading angles, solder layer thicknesses and Young moduli based on an interaction integration method; the fracture parameter values are subjected to least square fitting by using an empirical formula, and a corresponding empirical formula is obtained. The method can be used for predicting the fracture performance of the CTS compact tensile sample structure with cracks, and the formula is simple and easy to use; the method is suitable for different loading angles, solder layer thicknesses and Young modulus conditions, and the stress intensity factor of the sample can be quickly and accurately calculated only by measuring the limit load of the sample; the reliability evaluation precision of the CTS compact tensile sample structure containing the cracks can be effectively improved, and safety and economic risks caused by improper evaluation can be reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of fatigue crack propagation of tensile specimens, relates to the calculation of stress intensity factors of tensile specimens, and specifically relates to a method for calculating stress intensity factors of CTS compact tensile specimens under different solder layer thicknesses and Young's moduli. Background Art

[0002] The CTS compact tensile specimen structure is convenient for carrying out I-II composite fatigue crack growth tests, so it is often used to carry out related tests with the CTS compact tensile specimen structure and its corresponding fixtures. However, most of the research based on the CTS compact tensile specimen is based on the change of the stress intensity factor of homogeneous materials at different loading angles, and there is almost no research on the effect of different solder layer thickness and solder layer Young's modulus on the stress intensity factor at different loading angles. However, these two factors significantly affect the fracture behavior of the CTS compact tensile specimen material. Therefore, current research makes it impossible to accurately evaluate the reliability and manage the life of heterogeneous welded specimens, which introduces greater safety and economic risks.

[0003] In order to solve the current problems, numerical analysis methods are often used to calculate the stress intensity factor under different loading angles. However, the results reported so far only consider the stress intensity factor of homogeneous materials under different loading angles and structural dimensions, which cannot be applied to heterogeneous welding materials, and there is no calculation formula for the stress intensity factor based on different solder layer thicknesses and Young's model.

[0004] In summary, it is urgent to adopt numerical analysis methods to solve the stress intensity factor of CTS compact tensile specimens under different loading angles, different solder layer thicknesses and Young's modulus, develop a calculation formula for the stress intensity factor, and ultimately achieve accurate calculation of the fracture toughness of CTS compact tensile specimens. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method for calculating the stress intensity factor of a CTS compact tensile specimen under different solder layer thicknesses and Young's modulus. Based on the interaction integral method, a finite element simulation calculation is performed on the stress intensity factor of the crack front stress field parameters of the CTS compact tensile specimen model under different loading angles, solder layer thicknesses and Young's modulus. The fracture parameter values ​​are fitted by the least squares method using an empirical formula, and the corresponding empirical formula is obtained.

[0006] The present invention solves the technical problem by the following technical solutions:

[0007] A method for calculating stress intensity factor of CTS compact tensile specimens under different solder layer thicknesses and Young's moduli, the method comprising the following steps:

[0008] 1) The finite element analysis software Abaqus was used to establish a three-dimensional finite element model of the CTS compact tensile specimen with cracks, and the Young's modulus E0 and E of the anisotropic materials were input, where E0 is the Young's modulus of the specimen, E is the Young's modulus of the solder layer, and the Poisson's ratio γ0 was set up. The loading points were set up at the centers of the two loading pin holes of the CTS compact tensile specimen, and the coupling constraints between the loading points and the fixture were set up by means of motion coupling constraints. The external loads P were applied to the upper and lower loading points respectively.

[0009] 2) The 20-node simplified integration unit C3D20R is used to mesh the three-dimensional finite element model, and the focus ring mesh is used to encrypt the crack tip and introduce singular units;

[0010] 3) Using the Abaqus built-in solver, the stress intensity factor K at the center of the crack front under different loading angles, solder layer thicknesses and different Young's moduli is obtained. i ;

[0011] 4) For the stress intensity factor under different ratios of solder layer thickness to sample thickness L / B, polynomial fitting is performed on the data using equations (1) and (2) respectively, and the relationship between the loading angle β and the ratio of the Young's modulus of the solder layer to the Young's modulus of the sample E / E0 and the normalized stress intensity factor is established:

[0012]

[0013] where Y Ⅰ and Y ⅠⅠ are the SIF components K under the two fracture modes respectively. I and K II Normalized stress intensity factor of

[0014] β is the loading angle;

[0015] a1-e1 and a2-e2 are fitting parameters.

[0016] Moreover, the structural dimensions of the CTS compact tensile specimen in step 1) are specifically:

[0017] The specimen width W is 40 mm;

[0018] The sample length H is 40 mm;

[0019] The specimen thickness B is 4 mm;

[0020] The crack is in the middle of the specimen, and the crack length a is 20 mm;

[0021] The thickness of the fixture is 4B = 16 mm

[0022] The loading angles β are 0°, 15°, 30°, 45°, 60°, 75° and 90° respectively.

[0023] Moreover, the stress intensity factor results of the two fracture modes in step 3) are normalized to the same form, and the formula is:

[0024]

[0025] Where: K i is the stress intensity factor output by the software, Y i is the normalized stress intensity factor, the normalization factor σ nom As an evaluation index of the external load level, the loading level is maintained at σ nom =10MPa The calculation formula is as follows:

[0026]

[0027] The advantages and beneficial effects of the present invention are:

[0028] 1. The present invention provides a calculation formula for the stress intensity factor under different loading angles, solder layer thicknesses and solder layer Young's modulus for a cracked CTS compact tensile specimen, which can be used to predict the fracture performance of a cracked CTS compact tensile specimen structure. The formula is simple and easy to use.

[0029] 2. The calculation formula of the stress intensity factor provided by the present invention is applicable to CTS specimens with cracks under different loading angles, solder layer thicknesses and Young's modulus conditions. The stress intensity factor of the specimen can be quickly and accurately calculated by simply measuring the ultimate load of the specimen.

[0030] 3. The calculation formulas of stress intensity factors provided by the present invention can effectively improve the reliability evaluation accuracy of the CTS compact tensile specimen structure with cracks. Compared with traditional methods, they are simple and easy to use, which helps to reduce the safety and economic risks caused by improper evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a geometrical schematic diagram of the CTS compact tensile specimen of the present invention;

[0032] Figure 2 The flow chart of the preparation of the CTS compact tensile specimen of the present invention is as follows;

[0033] Figure 3 The load displacement curve diagram obtained by the test of the present invention;

[0034] Figure 4 It is the finite element mesh diagram of the CTS compact tensile specimen of the present invention;

[0035] Figure 5 It is a normalized K1 curve diagram at the center of the crack front calculated by the finite element method of the present invention;

[0036] Figure 6 It is a normalized K2 curve diagram at the center of the crack front edge calculated by the finite element method of the present invention;

[0037] Figure 7 This is the fracture toughness diagram of the sample calculated by the present invention. DETAILED DESCRIPTION

[0038] The present invention is further described in detail below through specific examples. The following examples are only illustrative and not restrictive, and the protection scope of the present invention cannot be limited thereto.

[0039] A method for calculating stress intensity factor of CTS compact tensile specimens under different solder layer thicknesses and Young's moduli is innovative in that the steps of the method are:

[0040] 1) The finite element analysis software Abaqus was used to establish a three-dimensional finite element model of the CTS compact tensile specimen with cracks. The Young's modulus E0, E and Poisson's ratio ν0 of the anisotropic materials were input. The loading points were established at the centers of the two loading pin holes of the CTS compact tensile specimen. The coupling constraints between the loading points and the specimen fixture were established by means of motion coupling constraints. The external loads P were applied to the upper and lower loading points respectively.

[0041] 2) The 20-node simplified integration unit C3D20R is used to mesh the three-dimensional finite element model, and the focus ring mesh is used to encrypt the crack tip and introduce singular units.

[0042] 3) Using the Abaqus built-in solver, the stress intensity factor K at the center of the crack front under different loading angles, solder layer thicknesses and different Young's moduli is obtained. i ;

[0043] 4) For the stress intensity factor under different ratios of solder layer thickness to sample thickness L / B, polynomial fitting is performed on the data using equations (1) and (2) respectively, and the relationship between the loading angle β and the ratio of the Young's modulus of the solder layer to the Young's modulus of the sample E / E0 and the normalized stress intensity factor is established:

[0044]

[0045] Where: Y Ⅰ and Y ⅠⅠ is the normalized stress intensity factor;

[0046] β is the loading angle;

[0047] a1-e1 and a2-e2 are fitting parameters, see Table 1 and Table 2 for details.

[0048] Table 1 Normalized K ICalculate the parameters a1-e1 in formula (1)

[0049]

[0050]

[0051] Table 2 Normalized K II Calculate the parameter a2-e2 in formula (2)

[0052]

[0053] The structural dimensions of the CTS compact tensile specimen in step 1) are specifically:

[0054] The specimen width W is 40 mm;

[0055] The sample length H is 40 mm;

[0056] The sample thickness B is 4 mm

[0057] The crack is in the middle of the specimen, and the crack length a is 20 mm;

[0058] The thickness of the fixture is 4B = 16 mm

[0059] The loading angles β are 0°, 15°, 30°, 45°, 60°, 75° and 90° respectively.

[0060] The stress intensity factor results of the two fracture modes in step 3) are normalized to the same form, and the formula is:

[0061]

[0062] Where: K i is the stress intensity factor output by the software, Y i is the normalized stress intensity factor, the normalization factor σ nom As an evaluation index of the external load level, the loading level is maintained at σ nom =10MPa The calculation formula is as follows:

[0063]

[0064] Take the nano Tech-LT-SS model nano silver solder paste produced by NBE Technology of the United States as an example, use the method proposed by the present invention to obtain its accurate fracture performance. Through the uniaxial tensile fracture test, the basic mechanical properties of nano silver are measured: Young's modulus E1, E2, E3 and E4 are 16.7GPa, 15.3GPa, 14GPa and 12.7GPa respectively, and the limit load F1, F2, F3 and F4 are 1280N, 1100N, 800N and 520N respectively.

[0065] Next, the fracture performance of nano silver solder paste will be accurately predicted according to the method of the present invention.

[0066] 1) Sample design and processing

[0067] The test uses a compact tensile shear CTS specimen designed by Richard and its matching loading device, the loading device is in the form of Figure 1 The dried sample block is aligned and bonded to another substrate, and then sintered on a manual hot press produced by CARVER. During the sintering process, the temperature is raised to 280°C at a certain heating rate, and the pressure is 10MPa at this temperature and kept for 1h. The sintering process is as follows: Figure 2 As shown, the solder layer was then cooled to room temperature in the furnace. The solder layer thickness was measured to be 0.1 mm.

[0068] 2) Fracture test process

[0069] The ground and polished CTS specimens were clamped on the M-3000 testing machine. Since it was a high-temperature fracture test, the temperature in the test box needed to be raised to the test value, and the test loading was carried out after heating and keeping warm in the high-temperature box for 20 minutes. The fracture test used displacement loading with a loading rate of 0.01 mm / s. During the fracture test, a high-temperature resistant lens was used to track the entire process of static fracture of the CTS specimen. In order to study the effect of different Young's moduli on fracture properties, type I loading (α=90°C) fracture tests were carried out on sintered silver CTS specimens at 25°C, 75°C, 125°C and 175°C. The load-displacement curves obtained from the experiment are shown in the figure below. Figure 3 shown.

[0070] 3) Experimental data processing

[0071] Two types of data are collected during the experiment: one is the photos of the sample surface taken by the camera, and the other is the text data collected by the MTS testing machine, including time, load, opening displacement, etc. The flexibility C is obtained by the ratio of displacement to load, and finally, the flexibility and crack length corresponding to each moment are obtained.

[0072] 4) Finite element method to establish the relationship between stress intensity factor, solder layer thickness and Young's modulus

[0073] The finite element software Abaqus was used to establish a three-dimensional stress model of a CTS compact tensile specimen with cracks. The specimen width W was 40 mm, the specimen length H was 40 mm, the initial crack length a was 0.5W = 20 mm, the specimen thickness B was 0.1W = 4 mm, the loading angles β were 0°, 15°, 30°, 45°, 60°, 75° and 90°, and the solder layer thickness was L. A detailed grid focusing strategy was used at the crack front, which was divided into 15 rings, and each ring was divided into 16 grid units in the circumferential direction. Figure 4 As shown. In the first ring around the crack tip, we used degenerate elements and moved the middle nodes to the position of the quarter point. The purpose of this layout design is to avoid the formation of square root singularities at the crack front. The minimum size of the singular element in the model along the radial direction is 0.01; the minimum radial size of the model is 0.001mm. The mesh reseeding in the thickness direction contains a total of 40 layers of elements, and the number of meshes for each model ranges from 250,000 to 400,000. A series of models were constructed, covering L / B = 0.025, 0.05, 0.1, 0.2, 0.4, 0.8, 1.6, 3.2 and 6.4, and the Young's modulus E of the solder layer was set to 10, 20, 40, 60, 80, 100GPa, and the Poisson's ratio ν0 was 0.34. At the same time, the Young's modulus E0 of the specimen and the fixture remained fixed at 110GPa, and the Poisson's ratio ν0 was 0.34. With these settings, we successfully constructed 378 sets of experimental models. By calculating the experimental model, the normalized stress intensity factor is extracted as Figure 5 and Figure 6 As shown, Figure 5 (a), (b), (c) and Figure 6 (a), (b), and (c) are the normalized K at different E values ​​under L / B = 0.025, 0.05, 0.1, 0.2, 0.4, 0.8, 1.6, 3.2, and 6.4, respectively. I (Type I stress intensity factor) and K II (Type II stress intensity factor) curve. The fitting empirical formulas are as shown in equations (1) and (2).

[0074] Substituting the measured Young's modulus E1, E2, E3 and E4 into equations (1) and (2), the Y corresponding to the CTS compact tensile specimen can be calculated. I and Y II . △K of the sample I and △K II Use the following formula to calculate:

[0075]

[0076] Where: ΔF is the limit load;

[0077] a is the crack length;

[0078] Finally, the calculated △K of the sample is used I and △K II The fracture toughness of the sample was calculated using the following formula:

[0079]

[0080] The fracture toughness of the sample at each loading temperature is calculated as follows: Figure 7 shown.

[0081] Although the embodiments and drawings of the present invention are disclosed for illustrative purposes, those skilled in the art will appreciate that various substitutions, changes and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A method for calculating the stress intensity factor of a CTS compact tensile specimen under different solder layer thicknesses and Young's modulus, characterized by: The steps of the method are: 1) The finite element analysis software Abaqus was used to establish a three-dimensional finite element model of the CTS compact tensile specimen with cracks, and the Young's modulus E0 and E of the anisotropic materials were input, where E0 is the Young's modulus of the specimen, E is the Young's modulus of the solder layer, and the Poisson's ratio γ0 was set up. The loading points were set up at the centers of the two loading pin holes of the CTS compact tensile specimen, and the coupling constraints between the loading points and the fixture were set up by means of motion coupling constraints. The external loads P were applied to the upper and lower loading points respectively. 2) The 20-node simplified integration unit C3D20R is used to mesh the three-dimensional finite element model, and the focus ring mesh is used to encrypt the crack tip and introduce singular units; 3) Using the Abaqus built-in solver, the stress intensity factor K at the center of the crack front under different loading angles, solder layer thicknesses and different Young's moduli is obtained. i ; 4) For the stress intensity factor under different ratios of solder layer thickness to sample thickness L / B, polynomial fitting is performed on the data using equations (1) and (2) respectively, and the relationship between the loading angle β and the ratio of the Young's modulus of the solder layer to the Young's modulus of the sample E / E0 and the normalized stress intensity factor is established: where Y Ⅰ and Y ⅠⅠ are the SIF components K under the two fracture modes respectively. I and K II Normalized stress intensity factor of β is the loading angle; a1-e1 and a2-e2 are fitting parameters.

2. The method for calculating the stress intensity factor of a CTS compact tensile specimen under different solder layer thicknesses and Young's modulus according to claim 1, characterized in that: The structural dimensions of the CTS compact tensile specimen in step 1) are as follows: The specimen width W is 40 mm; The sample length H is 40 mm; The specimen thickness B is 4 mm; The crack is in the middle of the specimen, and the crack length a is 20 mm; The thickness of the fixture is 4B = 16 mm The loading angles β are 0°, 15°, 30°, 45°, 60°, 75° and 90° respectively.

3. The method for calculating the stress intensity factor of a CTS compact tensile specimen under different solder layer thicknesses and Young's modulus according to claim 1, characterized in that: The stress intensity factor results of the two fracture modes in step 3) are normalized to the same form, and the formula is: Where: K i is the stress intensity factor output by the software, Y i is the normalized stress intensity factor, the normalization factor σ nom As an evaluation index of the external load level, the loading level is maintained at σ nom =10MPa The calculation formula is as follows:

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