A method, system, device and medium for predicting mechanical and thermal performance parameters based on microstructure of a weld

Abstract

A kind of method, system, device and medium based on mechanical and thermal performance parameter prediction of weld microstructure, method: to the weld sample containing void defect, do scanning experiment, carry out image threshold segmentation and three-dimensional reconstruction to scanning image to obtain the area ratio and volume ratio of void in weld, obtain ideal weld geometric model according to the size of weld containing void defect, do difference set operation, obtain the geometric model of weld containing void defect, establish the mechanical and thermal model of void defect weld under different void content, obtain the change relationship of equivalent young's modulus, equivalent thermal conductivity and its change amount of weld containing void defect with void area ratio, apply temperature load to the geometric model of weld containing void defect, obtain the stress-strain response curve and temperature distribution of weld under different void content, realize mechanical and thermal performance prediction;System, device and medium are used to realize a kind of method based on mechanical and thermal performance parameter prediction of weld microstructure;The accuracy of electronic equipment performance prediction is improved.

Description

Technical Field

[0001] This invention belongs to the field of electronic packaging technology, and specifically relates to a method, system, device and medium for predicting mechanical and thermal performance parameters based on the microstructure of solder joints. Background Technology

[0002] Electronic packaging structures are subject to temperature, electrical stress, humidity, and vibration during service, leading to stress relaxation, material aging, and void defects within the structure, resulting in performance degradation or even failure. Solder joints play a supporting and electrical connection role in the packaging structure. Under high current density, current density concentration occurs within the solder joints. Under the influence of temperature gradients, stress gradients, and electron wind, atoms migrate within the solder joints, leading to electromigration voids. During the reflow soldering process, the volatilization of flux and solder paste, substrate surface treatment, and intermetallic compounds formed at the solder joint and copper interface can all contribute to voids, causing decreased conductivity, increased thermal resistance, degraded mechanical properties, and reduced dielectric constant. This results in decreased output performance of electronic devices, even functional failure, and changes in system response characteristics. Therefore, determining the mechanical and thermal parameters of defective solder joints is beneficial not only for predicting the fatigue life of electronic devices but also for reliability assessment.

[0003] Typically, the mechanical and thermal properties of defective solder joints are determined using electron microscopy (SEM) and numerical finite element (FEM) simulations to study the size, distribution, and performance of voids. Scanning electron microscopy (SEM) is a common method for observing the microstructure of materials. It allows observation of cross-sectional information of the solder joint after secondary processing, including cross-sectional dimensions, the morphology and distribution of micron-level voids, and inferences about the structural changes of defects at a specific cross-section. FEM, on the other hand, involves simplifying the number and shape of voids, making two-dimensional assumptions about the three-dimensional solder joint model, simulating the geometric model of the defective solder joint in a computer, and applying physical fields such as structure and temperature to predict its mechanical and thermal properties. However, both SEM and FEM cannot accurately reflect void distribution and calculate solder joint performance, and they can easily damage the internal structure of the solder joint, causing irreversible damage.

[0004] In his 2018 dissertation, "Reliability Study of CSP Packaged LED Flip Chip Solder Layer," Jiang Chengshuo sliced ​​samples that had undergone high-temperature and high-humidity accelerated aging tests. He then used a scanning electron microscope to observe the distribution and size of voids and employed finite element simulation to model the performance of the void solder layer. The simulation assumed that the solder layer was two-dimensional and the voids were spherical. The study investigated the effects of different void ratios, void locations, and void distributions on the mechanical and thermal properties of the solder layer. However, the slicing process used to observe voids damaged the structure of the solder layer, and the void distribution in each cross-section was inconsistent, failing to accurately reflect the morphology and geometric model of the voids inside the solder layer. Furthermore, the two-dimensional and spherical assumptions could not accurately reflect the impact of voids on the mechanical and thermal properties of the solder layer. In addition, the method lacked quantitative analysis of the changes in mechanical and thermal properties with void area, thus failing to provide reliable data support for subsequent research.

[0005] Patent application CN201510417524.5 discloses a method for detecting solder joint void defects based on laser pulse excitation simulation. It employs a finite element modeling method for the heat conduction of solder joints with void defects, and a numerical solution algorithm for the heat conduction problem and its inverse under constant laser pulse heat flux density and natural convection excitation conditions. The numerical solution algorithm is embedded into the finite element model of solder joint heat conduction to establish a model of the variation law of solder joint void defect size with infrared temperature. Based on this model, online detection of solder joint void defects is achieved. However, this patent only analyzes the influence of voids on the thermal properties of solder joints, lacking structural analysis of the voids inside the solder joint and quantitative analysis of the impact of the void area on the thermal conductivity. Therefore, it cannot provide data support for other research.

[0006] In their paper "The Influence of Electromigration on the Morphology and Shear Performance of Cu3Sn Solder Joints" published in "Hot Working Technology 2020, 49(11)", Xu Liufeng, Li Xiaoyan, et al. applied different current densities to the samples and observed the micromorphology of the solder joints at different times using a scanning electron microscope. They also measured the shear strength of the solder joints using a testing machine. The conclusion was that the evolution process of the solder joint voids was: honeycomb voids - elongated voids - crack-like defects. The shear strength of the solder joints decreased continuously as the void area increased. This research method, which observes the solder joint voids through an electron microscope, cannot reflect the three-dimensional structure of the entire void and can only reflect local information. The experimental method was used to study the shear performance of the solder joints under different void contents. Since the size of the samples is on the micrometer scale, the measurement of shear performance using a testing machine will produce certain errors, and there is no quantitative analysis of the void area and shear performance. Summary of the Invention

[0007] To overcome the shortcomings of the prior art, the present invention aims to propose a method, system, device, and medium for predicting the mechanical and thermal performance parameters of solder joints based on the microstructure of solder joints. By obtaining the area and volume of voids within the solder joint and the changes in the mechanical and thermal properties of the solder joint with the void content, the mechanical and thermal performance parameters of the microstructure of defective solder joints can be predicted. This method improves the accuracy of predicting the mechanical and thermal performance parameters of solder joints without damaging the internal structure of the solder joints.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints includes the following steps:

[0010] Step 1: Perform a CT scan experiment on the weld sample containing void defects to obtain a two-dimensional scan image;

[0011] Step 2: Import the scanned image from Step 1 into the visualization software Avizo for image thresholding and 3D reconstruction to obtain the size of the weld joint with void defects, the geometric model of the void, the volume of a single void within the weld joint, and the area of ​​a single void.

[0012] Step 3: Based on the dimensions of the weld joint with void defects, the area of ​​a single void within the weld joint, and the volume of a single void obtained in Step 2, calculate the total area and total volume of voids within the weld joint, and obtain the void area ratio and volume ratio within the weld joint;

[0013] Step 4: Based on the dimensions of the weld joint with void defects from Step 2, perform a geometric 3D model to obtain the ideal weld joint geometric model. Then, perform a difference operation between the void geometric model and the ideal weld joint geometric model to obtain the weld joint geometric model containing void defects. The specific process is as follows:

[0014] G t =G d -G v

[0015] In the formula, G t G d G v These represent the geometric model of a weld joint containing void defects, the geometric model of an ideal weld joint, and the geometric model of a void, respectively.

[0016] Step 5: Based on the results obtained in Step 4, establish mechanical and thermal models of void defect welds with different void contents. Using the stress-strain response relationship and Fourier's thermal conductivity law, obtain the equivalent Young's modulus and equivalent thermal conductivity of the welds with different void contents.

[0017] Step 6: Combining the void area ratio and volume ratio in the solder joint from Step 3 with the equivalent Young's modulus and equivalent thermal conductivity of the solder joint under different void contents from Step 5, we obtain the equivalent Young's modulus, equivalent thermal conductivity, and the relationship between the changes in equivalent Young's modulus and equivalent thermal conductivity and the void area ratio of the solder joint with void defects.

[0018] Step 7: Apply a temperature load to the geometric model of the weld joint containing void defects, and combine the results of Step 6 to obtain the stress-strain response curves and temperature distribution of the weld joint under different void contents, so as to predict the mechanical and thermal properties of the weld joint.

[0019] In step 1, a CT scan experiment is performed on the weld sample containing void defects. Based on the different densities of voids and weld matrix in the weld, two-dimensional images of different gray levels are obtained by X-ray irradiation. Combined with scanning data from different directions, the geometric model of the entire weld containing void defects is obtained. The two-dimensional grayscale image is obtained after the scan is completed.

[0020] The specific process of obtaining the dimensions of the weld joint containing void defects, the void geometry model, the void area, and the void volume in step 2 is as follows:

[0021] Step 2.1: Threshold segmentation processing, that is, based on the difference in grayscale between the substrate of the solder joint containing void defects and the voids within the solder joint, the Top-Hat algorithm is used to determine the boundaries between the substrate of the solder joint containing void defects and the voids, thereby obtaining the size of the solder joint containing void defects and the geometric model of the voids. The size of the solder joint containing void defects specifically refers to the diameter and height of the solder joint.

[0022] Step 2.2: Assume the voids within the solder joint are spherical, that is, treat irregularly shaped voids as equivalent spheres of the same volume. Use the visualization software Avizo to obtain the volume of a single void, and then calculate the equivalent sphere radius of the void within the solder joint. Use the equivalent radius of the void within the solder joint to obtain the area of ​​a single void within the solder joint. The specific calculation process is as follows:

[0023]

[0024]

[0025] In the formula, V i R represents the volume of a single cavity within a solder joint. i A represents the equivalent radius of the void within the solder joint. i It represents the area of ​​a single cavity within the weld joint.

[0026] The specific process of step 3 is as follows:

[0027] Step 3.1: The total area and volume of voids within a solder joint are calculated by summing the areas and volumes of all voids within a single solder joint. The calculation process is as follows:

[0028]

[0029]

[0030] In the formula, A a V a Let n represent the total area and total volume of all voids within the solder joint, respectively, and let n represent the number of voids within the solder joint.

[0031] Step 3.2: Based on the diameter and height of the weld joint with void defects obtained in Step 2.1, the diameter and height of the ideal weld joint are obtained, and then the projected area and total volume of the ideal weld joint are obtained. The area and volume of voids within the weld joint are dimensionless. The area ratio of voids within the weld joint is equal to the sum of the projected areas of all voids in the weld joint divided by the projected area of ​​the ideal weld joint. The volume ratio of voids within the weld joint is equal to the sum of the volumes of all voids in the weld joint divided by the total volume of the ideal weld joint. The specific calculation process for the area ratio and volume ratio of voids within the weld joint is as follows:

[0032]

[0033]

[0034] In the formula, Ra and Rv represent the area ratio and volume ratio of the voids within the solder joint, respectively, and Ar v Ar s Vol represents the area of ​​the void within the solder joint and the total area of ​​the ideal solder joint, respectively. v Vol s These represent the volume of the void within the solder joint and the total volume of the ideal solder joint, respectively.

[0035] The specific process of step 5 is as follows:

[0036] Step 5.1: Based on the geometric model of the weld joint containing void defects, simulate the stress on the weld joint containing void defects using a uniaxial tensile mechanical model. By measuring the stress-strain response of the weld joint containing void defects, obtain the equivalent Young's modulus of the weld joint with void defects under different void contents. The calculation process is as follows:

[0037]

[0038] In the formula, σ represents normal stress, ε represents normal strain, and E represents Young's modulus;

[0039] Step 5.2: Based on the geometric model of the solder joint containing void defects, a heat source is set for the solder joint boundary. By measuring the temperature difference between the upper and lower boundaries, the equivalent thermal conductivity of the void defect solder joint under different void contents is calculated using Fourier's law of thermal conductivity. The calculation process is as follows:

[0040]

[0041] In the formula, q represents the heat flux density and k represents the thermal conductivity.

[0042] Step 6 is described in detail below:

[0043] Step 6.1: The calculation process for the changes in equivalent Young's modulus and equivalent thermal conductivity is as follows:

[0044]

[0045]

[0046] In the formula, Cy and Ck represent the changes in the equivalent Young's modulus and equivalent thermal conductivity of the weld joint containing void defects, respectively. bump k bump These are represented as Young's modulus and thermal conductivity of an ideal weld joint, respectively.

[0047] Step 6.2: Calculate the equivalent Young's modulus, equivalent thermal conductivity, and their changes as a function of the void area ratio for weld joints with void defects. Express the equivalent Young's modulus, equivalent thermal conductivity, and their changes as polynomial functions of the void area ratio. The calculation process is as follows:

[0048]

[0049]

[0050] Cy = Poly(Ra)

[0051] Ck = Poly(Ra)

[0052] In the formula, Let represent the equivalent Young's modulus and equivalent thermal conductivity of the weld joint containing void defects, respectively; Ra represents the void area ratio; and Poly represents a polynomial function of Ra.

[0053] The specific process of step 7 is as follows:

[0054] Step 7.1: Apply a temperature load to the geometric model of the weld joint containing void defects to obtain the stress-strain response curves and temperature distribution of the weld joint under different void contents. The temperature field calculation process of the weld joint is as follows, using a structural field and temperature field coupling method:

[0055]

[0056] In the formula, ρ represents density, and c p Let Q(t) represent heat capacity, and Q(t) represent the heat source.

[0057] Step 7.2: The weld joint structural field is simulated using the Anand viscoplastic constitutive relation to model the mechanical behavior of the weld joint under thermal conditions. The thermal strain calculation process is as follows:

[0058] ε T =α·ΔT

[0059] In the formula, ε T Let α represent thermal strain, α represent the coefficient of thermal expansion, and ΔT represent the temperature gradient.

[0060] A system for predicting mechanical and thermal performance parameters based on the microstructure of solder joints includes:

[0061] Solder joint void analysis module: Perform CT scan experiments on solder joint samples with void defects to obtain two-dimensional scan images. Import the scan images into the visualization software Avizo for image thresholding and three-dimensional reconstruction to obtain the size of the solder joint with void defects, the void geometric model, the volume of a single void in the solder joint and the area of ​​a single void. Calculate the total area and total volume of voids in the solder joint to obtain the void area ratio and volume ratio in the solder joint.

[0062] The module for establishing a solder joint model is as follows: Based on the size of the solder joint containing void defects, the ideal solder joint geometric model is obtained. Then, the difference operation is performed between the obtained void geometric model and the ideal solder joint geometric model to obtain the solder joint geometric model containing void defects.

[0063] Mechanical and thermal performance prediction module: Mechanical and thermal models of void defect welds with different void contents are established respectively. Using the stress-strain response relationship and Fourier's law of thermal conductivity, the equivalent Young's modulus and equivalent thermal conductivity of the welds with different void contents are obtained. Combining the void area ratio and volume ratio in the weld, the equivalent Young's modulus, equivalent thermal conductivity, and the changes in equivalent Young's modulus and equivalent thermal conductivity with the void area ratio of the weld with void defects are obtained. Temperature load is applied to the geometric model of the weld with void defects to obtain the stress-strain response curves and temperature distribution of the welds with different void contents, thereby realizing the prediction of the mechanical and thermal properties of the welds.

[0064] A device for predicting mechanical and thermal performance parameters based on the microstructure of solder joints includes:

[0065] Memory: Used to store a computer program that implements a method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints;

[0066] Processor: Used to implement a method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints when executing the computer program.

[0067] A computer-readable storage medium storing a computer program that, when executed by a processor, enables a method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints.

[0068] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0069] 1. The microstructure of solder joint voids is obtained by CT scanning experiments. Unlike the assumed random spherical model in the prior art, the present invention can accurately determine the mechanical and thermal performance parameters of defective solder joints based on the geometric model and position distribution of these real microstructures, effectively improving the accuracy of fatigue life model results for electronic devices.

[0070] 2. This invention uses difference operations to obtain a true geometric model of a weld joint containing void defects. Compared with the method of directly establishing the weld joint structure, it can not only clearly see the morphology of the void inside the weld joint, but also reduce the number of model meshes and improve computational efficiency.

[0071] 3. This invention establishes the relationship between the void area ratio and the mechanical and thermal performance parameters of the solder joint. Compared with using the void volume ratio, it is easier to predict and characterize the performance of defective solder joints through simple resistance measurement experiments, providing a new approach for evaluating the performance of defective solder joints.

[0072] In summary, this invention obtains the microstructure of solder joints through CT scanning, calculates the area and volume of voids using the spherical equivalent method, obtains a true geometric model of the solder joint based on difference operations, and uses mechanical and thermal models to obtain the equivalent Young's modulus and equivalent thermal conductivity of the solder joint. Based on the total void area, it obtains the relationship between mechanical and thermal performance parameters and the void area ratio. Variable loads are applied to the equivalent model to obtain stress and temperature distribution, thereby enabling the prediction of mechanical and thermal performance parameters of defective solder joints and improving the accuracy of predicting the performance of electronic devices. Attached Figure Description

[0073] Figure 1 This is a flowchart of the method of the present invention.

[0074] Figure 2 This is a three-dimensional reconstruction of the weld joint containing void defects in this invention.

[0075] Figure 3(a) shows the geometric model of the cavity.

[0076] Figure 3(b) shows the geometric model of an ideal weld joint.

[0077] Figure 3(c) shows the geometric model of a weld joint containing void defects.

[0078] Figure 3(d) shows the mesh refinement diagram near the void.

[0079] Figure 4(a) shows the relationship between the Young's modulus of the defective weld and its variation and the ratio of the void area.

[0080] Figure 4(b) shows the relationship between the thermal conductivity of the defective weld joint and its change and the ratio of the void area.

[0081] Figure 5 This is a stress-strain response and temperature curve of a defective weld joint according to the present invention. Detailed Implementation

[0082] The present invention will now be described in further detail with reference to the accompanying drawings.

[0083] See Figure 1 A method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints, comprising:

[0084] Step 1. Obtain two-dimensional scan images of the weld sample containing void defects using X-ray CT scanning;

[0085] Step 1.1: Based on micron-level computed tomography technology, the BGA solder joint area is cut from the packaged circuit board. The cutting size is 15mm×15mm, the radius of the solder joint is 260um and the height is 160um. There are 6 solder joints, the solder joint material is SnAgCu305, and each solder joint has void defects.

[0086] Step 1.2: The solder joint area was scanned using a Zeiss Xradia 520versa CT scanner with a resolution of 1.6 μm / pt. Based on the different densities of voids and substrate within the solder joint, two-dimensional images of different grayscale were obtained after X-ray irradiation. After scanning in different directions, the geometric model of the entire solder joint was obtained. The scan resulted in a two-dimensional grayscale image of 984 × 10¹³ pixels.

[0087] Step 2. Import the scanned image from Step 1 into the visualization software Avizo for image thresholding and 3D reconstruction to obtain the size of the weld joint with void defects, the geometric model of the void, the area of ​​a single void, and the volume of a single void.

[0088] Step 2.1: Import the 2D grayscale image obtained from the CT scan into the visualization software Avizo for image thresholding. Thresholding involves using the Top-Hat algorithm to determine the boundaries between the substrate and the voids based on the different grayscale values ​​of the solder joint substrate and the voids within the solder joint. The threshold selection must satisfy the requirement that the void area ratio corresponds to the experimentally measured voltage change, thereby obtaining the true 3D microstructure of the solder joint substrate and voids. The 3D geometric image of the solder joint containing void defects obtained after 3D reconstruction is shown below. Figure 2 As shown;

[0089] Step 2.2: To simplify the analysis of the location, area, and distribution of voids, a spherical assumption is made for the void defects, that is, irregularly shaped void defects are equivalent to spheres of the same volume. The volume of a single void is obtained using the visualization software Avizo, and then the equivalent sphere radius of the void within the solder joint is calculated. The area of ​​a single void within the solder joint is obtained using the equivalent radius of the void within the solder joint. The specific calculation process is as follows:

[0090]

[0091]

[0092] In the formula, V i R represents the volume of a single cavity within a solder joint. i A represents the equivalent radius of the void within the solder joint. i This represents the area of ​​a single cavity within the solder joint;

[0093] Step 3. Calculate the total area and volume of the weld joint voids to obtain the void area ratio and volume ratio;

[0094] Step 3.1: Based on the area and volume of a single void obtained using the sphere equivalence method, sum the areas and volumes of all voids within a single solder joint to calculate the void area ratio and volume ratio and their impact on the mechanical and thermal properties of the solder joint. The formulas for the total area and total volume of all voids within a single solder joint are as follows:

[0095]

[0096]

[0097] In the formula, A a V a Let n represent the total area and total volume of all voids within the solder joint, respectively, and let n represent the number of voids.

[0098] Step 3.2: Based on the radius and geometric model of the ideal solder joint, its projected area and total volume can be obtained. To better describe the influence of defects within the solder joint on its mechanical and thermal performance parameters, the area and volume of the voids are dimensionless, and the area ratio and volume ratio are used. The area ratio of the solder joint is equal to the sum of the projected areas of all voids in the solder joint divided by the projected area of ​​the ideal perfect solder joint. The volume ratio of the solder joint is equal to the sum of the volumes of all voids in the solder joint divided by the total volume of the ideal perfect solder joint. The calculation formulas are as follows:

[0099]

[0100]

[0101] In the formula, Ra and Rv represent the area ratio and volume ratio of the voids, respectively, and Ar vAr s Vol represents the area of ​​the void and the total area of ​​the solder joint, respectively. v Vol s These represent the volume of the cavity and the total volume of the solder joint, respectively.

[0102] Step 4. Perform a difference operation on the determined void geometry model and the ideal perfect weld point geometry model to obtain the actual weld point geometry model containing void defects;

[0103] Step 4.1: Since voids are the main factor affecting solder joint performance, this example extracts the microscopic features of voids in the solder joint using Avizo software and uses tetrahedral meshes to divide the voids.

[0104] Step 4.2: The ideal solder joint geometric model is obtained by performing 3D geometric modeling based on the solder joint dimensions obtained in Step 2. The void geometric model is also obtained in Step 2. Based on the void geometric model and the ideal solder joint geometric model, the true shape of the solder joint can be obtained through difference operations. The principle behind this is:

[0105] G t =G d -G v

[0106] In the formula, G t G d G v These represent a real solder joint, an ideal perfect solder joint, and a void geometric model, respectively.

[0107] See Figure 3(a), which is the geometric model of the void; Figure 3(b), which is the geometric model of the ideal weld joint; Figure 3(c), which is the weld joint structure with void defects. Tetrahedral meshes are used to divide the void and the substrate. An adaptive mesh is used at the interface between the void and the substrate; Figure 3(d), which is the mesh refinement diagram near the void.

[0108] Step 5. Based on the structure of the weld joint with void defects, establish its mechanical and thermal models respectively. Using the stress-strain response relationship and Fourier's thermal conductivity law, obtain the equivalent Young's modulus and thermal conductivity of the weld joint with defects under different void contents.

[0109] Step 5.1: Based on the structure of the weld joint containing voids, simulate the stress on the weld joint using a uniaxial tensile mechanical model. By measuring the stress-strain response of the defective weld joint, calculate the equivalent Young's modulus of the weld joint with different void contents. The calculation formula is as follows:

[0110]

[0111] In the formula, σ represents normal stress, ε represents normal strain, and E represents Young's modulus;

[0112] Step 5.2: The boundary conditions of the mechanical model are that the lower boundary of the weld joint is fixed and a force load is applied to the upper boundary. At the same time, the mesh independence of the model is verified, and steady-state solution is used to obtain the stress, displacement and strain response of the weld joint.

[0113] Step 5.3: When calculating the equivalent Young's modulus of the weld joint based on the mechanical model, the weld joint in this model is a variable cross-section body. To ensure the accuracy of the calculation results, it is necessary to use the equivalent cross-sectional area for calculation. In addition, since each weld joint is different, to ensure the reasonableness of the results, the equivalent cross-sectional area of ​​each ideal weld joint is calculated separately to obtain the equivalent Young's modulus of the weld joint with defects.

[0114] Step 5.4: Based on the actual microstructure of the solder joint, a heat source is set at the boundary of the solder joint. By measuring the temperature difference between the upper and lower boundaries of the solder joint, the equivalent thermal conductivity of the defective solder joint with different void contents is calculated. The calculation formula is as follows:

[0115]

[0116] In the formula, q represents the heat flux density and k represents the thermal conductivity.

[0117] Step 5.5: When calculating the equivalent thermal conductivity of the defective solder joints based on the heat transfer model, the equivalent cross-sectional area is also required. Therefore, the equivalent cross-sectional area results of each solder joint in Step 5.3 will be used to calculate the equivalent thermal conductivity of the six real solder joints.

[0118] Step 6. Combining the void area ratio and volume ratio in the solder joint from Step 3 with the equivalent Young's modulus and equivalent thermal conductivity of the solder joint under different void contents from Step 5, we obtain the equivalent Young's modulus, equivalent thermal conductivity, and the relationship between the changes in equivalent Young's modulus and equivalent thermal conductivity and the void area ratio of the solder joint with void defects.

[0119] Step 6.1: Based on the volume ratio and area ratio of the six solder joint voids, the fitting curve formula for the volume ratio of solder joint voids as a function of the area ratio can be obtained as follows:

[0120] Rv=0.1447-0.02632×Ra+0.00663×Ra 2

[0121] In the formula, Rv is the volume ratio and Ra is the area ratio;

[0122] Step 6.2: Based on the void area ratio and the corresponding equivalent Young's modulus, the relationship between the mechanical property parameters of the weld joint and the void area ratio can be obtained through the following formula:

[0123]

[0124] In the formula, Let Ra represent the equivalent Young's modulus of the weld joint, Ra represent the void area ratio, and Poly represent the polynomial function of Ra.

[0125] Based on the least squares method of polynomial fitting, the fitting curve of the equivalent Young's modulus of the weld joint as a function of the void area ratio is obtained:

[0126] y=42.7416-0.11768×Ra-0.00214×Ra 2

[0127] In the formula, y is the equivalent Young's modulus, and Ra is the weld joint void area ratio;

[0128] In order to apply the equivalent Young's modulus results to weld joints of different sizes, the relationship between the change in Young's modulus and the void area ratio under different void area ratios was calculated as follows:

[0129] Cy=0.5997+0.27404×Ra+0.00495×Ra 2

[0130] In the formula, Cy is the change in Young's modulus, and Ra is the ratio of the area of ​​the weld void.

[0131] Referring to Figure 4(a), the relationship between the Young's modulus of the defective weld and its change and the void area ratio is shown in the figure. The equivalent Young's modulus decreases quadratically with the increase of the void area ratio, and the change of the equivalent Young's modulus increases quadratically with the increase of the void area ratio.

[0132] Step 6.3: Based on the void area ratio and the corresponding equivalent thermal conductivity, the relationship between the thermal properties of the solder joint and the void area ratio can be obtained through the following formula:

[0133]

[0134] In the formula, Let represent the equivalent thermal conductivity of the solder joint, Ra represent the void area ratio, and Poly represent a polynomial function of Ra.

[0135] The fitting curve of the equivalent thermal conductivity of the solder joint as a function of the void area ratio was obtained by polynomial fitting:

[0136] k=56.675-0.06255×Ra-0.00382×Ra 2

[0137] In the formula, k is the equivalent thermal conductivity, and Ra is the area ratio of the weld joint void.

[0138] To increase the generalizability of the results, the relationship between the change in thermal conductivity and the void area ratio under different void area ratios was calculated as follows:

[0139] Ck=0.56548+0.11025×Ra+0.00669×Ra 2

[0140] In the formula, Ck is the change in thermal conductivity, and Ra is the ratio of the void area of ​​the solder joint;

[0141] Referring to Figure 4(b), the relationship between the thermal conductivity of the defective solder joint and its change and the void area ratio is shown in the figure. The equivalent thermal conductivity decreases quadratically with the increase of the void area ratio, and the change in the equivalent thermal conductivity increases quadratically with the increase of the void area ratio.

[0142] Step 7. Apply a temperature load to the defective weld joint model, and use the equivalent Young's modulus and equivalent thermal conductivity to obtain the stress response curve and temperature distribution of the weld joint, thereby predicting the mechanical and thermal properties of the defective weld joint.

[0143] Step 7.1: Based on the actual working environment of the solder joint, using the coupling method of structural field and temperature field, the calculation formula for the temperature field of the solder joint is as follows:

[0144]

[0145] In the formula, ρ represents density, and c p It is expressed as heat capacity, and Q(t) represents a variable heat source;

[0146] The weld joint structural field is simulated using Anand viscoplastic constitutive relations to model the mechanical behavior of the weld joint under thermal conditions, with thermal strain determined by the following equation:

[0147] ε T =α·ΔT

[0148] In the formula, ε T It is expressed as thermal strain, α as the coefficient of thermal expansion, and ΔT as the temperature gradient;

[0149] Step 7.2: Simulation yields stress response and temperature distribution curves of weld joints under different void contents, as shown in the figure. Figure 5 As shown, the solder joint stress decreases with increasing void area ratio, while the temperature rise increases with increasing void area ratio. The mechanical and thermal properties obtained considering the solder joint microstructure are more consistent with reality and are of great significance for predicting the lifespan of electronic devices and assessing reliability. This indicates that the present invention can explore the influence of the micro-characteristics of solder joint voids on solder joint performance from the real structure and effectively predict the mechanical and thermal properties of solder joints.

[0150] As can be seen from the above embodiments and simulation results, compared with the prior art, the present invention uses the sphere equivalent method to calculate the area and volume of the void, obtains the true geometric model of the solder joint based on the difference operation, uses mechanical and heat transfer models to obtain the equivalent Young's modulus and equivalent thermal conductivity of the solder joint, obtains the relationship between the mechanical and thermal performance parameters and the void area ratio based on the total void area, applies variable load to the equivalent model to obtain stress and temperature distribution, and obtains the results that the equivalent thermal conductivity decreases quadratically with the increase of the void area ratio, and the change in equivalent thermal conductivity increases quadratically with the increase of the void area ratio. It has the characteristic of improving the prediction accuracy of electronic equipment performance without damaging the internal structure of the solder joint.

[0151] A system for predicting mechanical and thermal performance parameters based on the microstructure of solder joints includes:

[0152] Solder joint void analysis module: Perform CT scan experiments on solder joint samples with void defects to obtain two-dimensional scan images. Import the scan images into the visualization software Avizo for image thresholding and three-dimensional reconstruction to obtain the size of the solder joint with void defects, the void geometric model, the volume of a single void in the solder joint and the area of ​​a single void. Calculate the total area and total volume of voids in the solder joint to obtain the void area ratio and volume ratio in the solder joint.

[0153] The module for establishing a solder joint model is as follows: Based on the size of the solder joint containing void defects, the ideal solder joint geometric model is obtained. Then, the difference operation is performed between the obtained void geometric model and the ideal solder joint geometric model to obtain the solder joint geometric model containing void defects.

[0154] Mechanical and thermal performance prediction module: Mechanical and thermal models of void defect welds with different void contents are established respectively. Using the stress-strain response relationship and Fourier's law of thermal conductivity, the equivalent Young's modulus and equivalent thermal conductivity of the welds with different void contents are obtained. Combining the void area ratio and volume ratio in the weld, the equivalent Young's modulus, equivalent thermal conductivity, and the changes in equivalent Young's modulus and equivalent thermal conductivity with the void area ratio of the weld with void defects are obtained. Temperature load is applied to the geometric model of the weld with void defects to obtain the stress-strain response curves and temperature distribution of the welds with different void contents, thereby realizing the prediction of the mechanical and thermal properties of the welds.

[0155] A device for predicting mechanical and thermal performance parameters based on the microstructure of solder joints includes:

[0156] Memory: Used to store a computer program that implements a method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints;

[0157] Processor: Used to implement a method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints when executing the computer program.

[0158] A computer-readable storage medium storing a computer program that, when executed by a processor, enables a method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints.

Claims

1. A method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints, characterized in that, Includes the following steps: Step 1: Perform a CT scan experiment on the weld sample containing void defects to obtain a two-dimensional scan image; Step 2: Import the scanned image from Step 1 into the visualization software Avizo for image thresholding and 3D reconstruction to obtain the size of the weld joint with void defects, the geometric model of the void, the volume of a single void within the weld joint, and the area of ​​a single void. Step 3: Based on the dimensions of the weld joint with void defects, the area of ​​a single void within the weld joint, and the volume of a single void obtained in Step 2, calculate the total area and total volume of voids within the weld joint, and obtain the void area ratio and volume ratio within the weld joint; Step 4: Based on the dimensions of the weld joint with void defects from Step 2, perform a geometric 3D model to obtain the ideal weld joint geometric model. Then, perform a difference operation between the void geometric model and the ideal weld joint geometric model to obtain the weld joint geometric model containing void defects. The specific process is as follows: In the formula, , , These represent the geometric model of a weld joint containing void defects, the geometric model of an ideal weld joint, and the geometric model of a void, respectively. Step 5: Based on the results obtained in Step 4, establish mechanical and thermal models of void defect welds with different void contents. Using the stress-strain response relationship and Fourier's thermal conductivity law, obtain the equivalent Young's modulus and equivalent thermal conductivity of the welds with different void contents. Step 6: Combining the void area ratio and volume ratio in the solder joint from Step 3 with the equivalent Young's modulus and equivalent thermal conductivity of the solder joint under different void contents from Step 5, we obtain the equivalent Young's modulus, equivalent thermal conductivity, and the relationship between the changes in equivalent Young's modulus and equivalent thermal conductivity and the void area ratio of the solder joint with void defects. Step 7: Apply a temperature load to the geometric model of the weld joint containing void defects, and combine the results of Step 6 to obtain the stress-strain response curves and temperature distribution of the weld joint under different void contents, so as to predict the mechanical and thermal properties of the weld joint. The specific process of step 7 is as follows: Step 7.1: Apply a temperature load to the geometric model of the weld joint containing void defects to obtain the stress-strain response curves and temperature distribution of the weld joint under different void contents. The temperature field and structural field coupling method is used to calculate the temperature field of the weld joint as follows: In the formula, Represented as density, Expressed as heat capacity, Indicated as a heat source; k Indicates a heat conduction system; Step 7.2: The weld joint structural field is simulated using the Anand viscoplastic constitutive relation to model the mechanical behavior of the weld joint under thermal conditions. The thermal strain calculation process is as follows: In the formula, Represented as thermal strain, It is expressed as the coefficient of thermal expansion. This is represented as a temperature gradient.

2. The method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints according to claim 1, characterized in that, In step 1, a CT scan experiment is performed on the weld sample containing void defects. Based on the different densities of voids and weld matrix in the weld, two-dimensional images of different gray levels are obtained by X-ray irradiation. Combined with scanning data from different directions, the geometric model of the entire weld containing void defects is obtained. The two-dimensional grayscale image is obtained after the scan is completed.

3. The method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints according to claim 1, characterized in that, The specific process of obtaining the dimensions of the weld joint containing void defects, the geometric model of the void, the volume of a single void within the weld joint, and the area of ​​a single void in step 2 is as follows: Step 2.1: Threshold segmentation processing, that is, based on the difference in grayscale between the substrate of the solder joint containing void defects and the voids within the solder joint, the Top-Hat algorithm is used to determine the boundaries of the substrate of the solder joint containing void defects and the voids, thereby obtaining the size of the solder joint containing void defects and the geometric model of the voids. The size of the solder joint containing void defects specifically refers to the diameter and height of the solder joint. Step 2.2: Assume the voids within the solder joint are spherical, that is, treat irregularly shaped voids as equivalent spheres of the same volume. Use the visualization software Avizo to obtain the volume of a single void, and then calculate the equivalent sphere radius of the void within the solder joint. Use the equivalent radius of the void within the solder joint to obtain the area of ​​a single void within the solder joint. The specific calculation process is as follows: In the formula, This represents the volume of a single cavity within the solder joint. This represents the equivalent radius of the void within the solder joint. This represents the area of ​​a single void within the weld joint.

4. The method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints according to claim 1, characterized in that, The specific process of step 3 is as follows: Step 3.1: The total area and volume of voids within a solder joint are calculated by summing the areas and volumes of all voids within a single solder joint. The calculation process is as follows: In the formula, , These represent the total area and total volume of all voids within the solder joint, respectively. This represents the number of voids within the solder joint; Step 3.2: Based on the diameter and height of the weld joint with void defects obtained in Step 2.1, the diameter and height of the ideal weld joint are obtained, and then the projected area and total volume of the ideal weld joint are obtained. The area and volume of voids within the weld joint are dimensionless. The area ratio of voids within the weld joint is equal to the sum of the projected areas of all voids in the weld joint divided by the projected area of ​​the ideal weld joint. The volume ratio of voids within the weld joint is equal to the sum of the volumes of all voids in the weld joint divided by the total volume of the ideal weld joint. The specific calculation process for the area ratio and volume ratio of voids within the weld joint is as follows: In the formula, , These represent the area ratio and volume ratio of the voids within the solder joint, respectively. , These represent the area of ​​the void within the solder joint and the total area of ​​the ideal solder joint, respectively. , These represent the volume of the void within the solder joint and the total volume of the ideal solder joint, respectively.

5. The method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints according to claim 1, characterized in that, The specific process of step 5 is as follows: Step 5.1: Based on the geometric model of the weld joint containing void defects, simulate the stress on the weld joint containing void defects using a uniaxial tensile mechanical model. By measuring the stress-strain response of the weld joint containing void defects, obtain the equivalent Young's modulus of the weld joint with void defects under different void contents. The calculation process is as follows: In the formula, Represented as normal stress, Represented as positive strain, Expressed as Young's modulus; Step 5.2: Based on the geometric model of the solder joint containing void defects, a heat source is set for the solder joint boundary. By measuring the temperature difference between the upper and lower boundaries, the equivalent thermal conductivity of the void defect solder joint under different void contents is calculated using Fourier's law of thermal conductivity. The calculation process is as follows: In the formula, Expressed as heat flux density, It is expressed as thermal conductivity.

6. The method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints according to claim 1, characterized in that, Step 6 is described in detail below: Step 6.1: The calculation process for the changes in equivalent Young's modulus and equivalent thermal conductivity is as follows: In the formula, , These represent the changes in the equivalent Young's modulus and equivalent thermal conductivity of the weld joint containing voids, respectively. , These are represented as Young's modulus and thermal conductivity of an ideal weld joint, respectively. Step 6.2: Calculate the equivalent Young's modulus, equivalent thermal conductivity, and their changes as a function of the void area ratio for weld joints with void defects. Express the equivalent Young's modulus, equivalent thermal conductivity, and their changes as polynomial functions of the void area ratio. The calculation process is as follows: In the formula, , These represent the equivalent Young's modulus and equivalent thermal conductivity of the weld joint containing voids, respectively. Expressed as the ratio of void area, Represented as A polynomial function.

7. A system for predicting mechanical and thermal performance parameters based on the microstructure of solder joints, used to implement the method described in claim 1, characterized in that, include: Solder joint void analysis module: Perform CT scan experiments on solder joint samples with void defects to obtain two-dimensional scan images. Import the scan images into the visualization software Avizo for image thresholding and three-dimensional reconstruction to obtain the size of the solder joint with void defects, the void geometric model, the volume of a single void in the solder joint and the area of ​​a single void. Calculate the total area and total volume of voids in the solder joint to obtain the void area ratio and volume ratio in the solder joint. The module for establishing a solder joint model is as follows: Based on the size of the solder joint containing void defects, the ideal solder joint geometric model is obtained. Then, the difference operation is performed between the obtained void geometric model and the ideal solder joint geometric model to obtain the solder joint geometric model containing void defects. Mechanical and thermal performance prediction module: Mechanical and thermal models of void defect welds with different void contents are established respectively. Using the stress-strain response relationship and Fourier's law of thermal conductivity, the equivalent Young's modulus and equivalent thermal conductivity of the welds with different void contents are obtained. Combining the void area ratio and volume ratio in the weld, the equivalent Young's modulus, equivalent thermal conductivity, and the changes in equivalent Young's modulus and equivalent thermal conductivity with the void area ratio of the weld with void defects are obtained. Temperature load is applied to the geometric model of the weld with void defects to obtain the stress-strain response curves and temperature distribution of the welds with different void contents, thereby realizing the prediction of the mechanical and thermal properties of the welds.

8. A device for predicting mechanical and thermal performance parameters based on the microstructure of solder joints, characterized in that, include: Memory: for storing a computer program that implements the method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints as described in any one of claims 1-6; Processor: Used to implement the method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints as described in any one of claims 1-6 when executing the computer program.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, enables the implementation of the method for predicting mechanical and thermal performance parameters based on the microstructure of solder joints as described in any one of claims 1-6.

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