CN109388820B - Finite element simulation method for determining integral rule of weld spot damage accumulation under irregular temperature cycle profile - Google Patents
Finite element simulation method for determining integral rule of weld spot damage accumulation under irregular temperature cycle profile Download PDFInfo
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Abstract
The invention provides a finite element simulation method for determining a complete rule of weld spot damage accumulation under an irregular temperature cycle profile, which comprises the following steps: s1, finite element simulation pretreatment; and S2, performing finite element simulation on the welding spot under different temperature loads, S3, performing finite element simulation post-processing, and S4, determining a nonlinear damage accumulation expression of the welding spot under an irregular temperature cycle profile. The nonlinear damage accumulation rule determined by the simulation method is based on a welding spot fatigue crack damage model, is more practical compared with the rule obtained by the traditional statistical method, simultaneously considers the influence caused by the superposition sequence of different temperature cycle profiles, has more accurate result, can control the error within 8 percent, and greatly reduces the error range.
Description
Technical Field
The invention belongs to the field of reliability simulation research, particularly provides a finite element simulation method for determining a complete rule of weld spot damage accumulation under an irregular temperature cycle profile, and particularly relates to damage accumulation under the temperature cycle profile in a multi-stage task system.
Background
The current research on the reliability of the welding point mostly aims at the problem of thermal fatigue of the welding point under the temperature cycle profile of a standard rule, however, the actual work of electronic products is under a very complex system and usually needs to complete a task consisting of a plurality of different stages. The multi-stage task system comprises a plurality of non-overlapping continuous stages, the tasks required to be completed in each stage of the system are different, the stress and the environmental conditions are different, therefore, the experienced temperature of the electronic equipment is not a standard temperature cycling profile, but an irregular temperature cycling profile consisting of a plurality of stages, and the occurrence of thermal fatigue of welding spots in the environment is a main mechanism for failure of electronic products. The research on the accumulation rule of the thermal fatigue damage of the welding spot under the irregular temperature cycle profile is an important way for accurately predicting the fault life of the electronic product.
In engineering, the research on the thermal fatigue damage of the welding spot under the irregular temperature cycle profile is only to simply split the irregular temperature cycle profile into a plurality of standard temperature cycle profiles and carry out cumulative calculation by utilizing a Miner linear rule. However, the fact proves that the linear accumulation of the thermal fatigue damage of the welding spot under the irregular temperature cycle profile is carried out by applying the Miner linear rule, and the result has larger deviation. For irregular temperature-cycle profiles in a multi-stage mission system, a new non-linear damage accumulation rule is considered, which contains undetermined parameters and needs to be determined experimentally. However, each set of experiment can only determine the parameter value of the welding spot of one size and material, and a large number of experiments are needed to obtain the parameter values of the welding spot damage accumulation equation of different sizes and materials, which results in longer experiment period and higher cost. The finite element simulation can simulate the thermal fatigue behavior of the welding spot under the action of load, and the finite element simulation under the irregular temperature cycle profile can be used for simulating the response condition of the welding spot under the actual condition, so that reference is provided for predicting the damage position and the fatigue life of the welding spot. The finite element simulation of the welding spot can form verification with an experimental method, the defects of the experimental method can be overcome, more data can be provided for parameter fitting of a damage accumulation rule under an irregular temperature cycle section of the welding spot through the finite element simulation analysis of the thermal fatigue damage accumulation of the welding spot, and finally a complete damage accumulation rule under the irregular temperature cycle section is determined.
Disclosure of Invention
The invention aims to provide a finite element simulation method for determining parameters in a nonlinear damage accumulation rule under an irregular temperature cycle profile aiming at welding spots of different sizes and materials, so that the influence of the welding spot size and the material on unknown parameters is analyzed, and the nonlinear damage accumulation rule is expanded to obtain a complete form. The damage accumulation calculation is carried out by applying the rule instead of a Miner linear accumulation rule, so that the reliability prediction is more accurate, and the result is closer to the real reliability level of the product.
The invention is realized by the following steps:
the invention provides a finite element simulation method for determining a complete rule of weld spot damage accumulation under an irregular temperature cycle profile, which comprises the following steps:
s1, finite element simulation pretreatment, specifically comprising the following steps:
s11, determining the components and the packaging form of the finite element three-dimensional structure model, and determining the mesh division mode of the model;
s12, selecting a plurality of groups of welding points with different sizes and materials, and determining parameters of the materials;
s13, determining boundary conditions applied by a structure under the packaging model, wherein the boundary conditions comprise symmetrical boundary conditions, middle plane displacement coupling boundary conditions and origin fixed-support boundary conditions;
s14, determining a temperature load, wherein the temperature load comprises an irregular temperature cycle profile, a first standard temperature cycle profile and a second standard temperature cycle profile obtained through decomposition;
s2, performing finite element simulation on the welding spot under different temperature loads, and specifically comprising the following steps:
s21, selecting any group of welding spots, and establishing a finite element three-dimensional structure model of the chip;
s22, applying different boundary conditions to the chip on the three-dimensional structure model;
s23, respectively applying an irregular temperature cycle profile, a first standard temperature cycle profile and a second standard temperature cycle profile to the chip under each boundary condition;
s3, finite element simulation post-processing, specifically comprising the following steps:
s31, determining a plastic strain distribution cloud picture of the selected welding spot based on finite element simulation of S2, and determining the minimum plastic strain, the maximum plastic strain and the strain change range of the welding spot according to the plastic strain distribution cloud picture of the selected welding spot;
s32, determining the relationship between the mechanical strain of the welding spot layer and the resistance strain of the thermal damage of the welding spot and the resistivity of a plurality of groups of welding spots;
s33, determining the cross-sectional area, the height, the length and the temperature change of the selected welding spots for simulation, calculating to obtain the resistance values of the selected welding spots, adding the resistance values of the selected welding spots in series to obtain the resistance simulation values of the daisy chains, calibrating the resistance values obtained by simulation according to the experimentally measured resistance values corresponding to the selected welding spots, and obtaining a calibrated three-dimensional structure model;
s34, simulating all the other groups of welding spots by using the checked three-dimensional structure model, and acquiring simulation data;
s4, determining a welding spot nonlinear damage accumulation expression under the irregular temperature cycle profile, and specifically comprising the following steps:
s41, determining the form of a welding spot nonlinear damage accumulation rule under the irregular temperature cycle profile;
s42, determining the values of a parameter a and a size parameter b in a nonlinear damage accumulation rule corresponding to a plurality of groups of welding spots with different sizes and materials;
s43, determining the influence of the materials and the sizes of different welding spots on the value of the parameter a and the value of the size parameter b and the relation between the size parameter b and the material constant;
and S44, determining a final welding spot nonlinear damage accumulation rule.
Preferably, in S11, the chip finite element three-dimensional structure model is packaged in a BGA format, and the finite element three-dimensional structure model includes five parts, i.e., a solder joint, a chip, a substrate, a molding compound layer, and a PcB layer, where the solder joint is an octahedral unit, and the chip, the substrate, the molding compound layer, and the PcB layer are hexahedral units.
Preferably, the relationship between the mechanical strain of the solder joint layer and the resistance strain of the thermal damage of the solder joint in S32 is expressed as follows:
R＝(SR0+kρ0ΔT)(Fp+Ffp+FΔT)，
wherein:
Ris the resistance strain of the solder joint, ρ is the resistivity of the solder joint, R0Is the original resistance value when no thermal cycle is applied, S is the cross-sectional area of the weld, h is the height of the weld, L is the length of the weld, N is the number of cycles, Δ T is the magnitude of the temperature, the index β is typically taken to be 0.5, k is the cyclic ratio at maximum stress during one cycle, γminThe minimum strain value is delta gamma is the plastic strain variation range, C is the material constant, C is 0.16 for widely adopted eutectic solder, and the resistance R value of the welding spot can be obtained by solving the equation system, so that the resistivity of the welding spots of different materials can be determined.
Preferably, the form of the non-linear damage accumulation rule in the irregular temperature cycle profile determined in S41 is as follows:
wherein N is the estimated value of the number of cycles when the chip sample under the irregular temperature cycle profile is failed; n is a radical of1The number of cycles when the chip sample under the first standard temperature cycle profile is failed is defined; n is a radical of2The number of cycles when the chip sample under the second standard temperature cycle profile is failed is defined; a. b is the parameter to be fitted, a, b and N1、N2The relationship of (A) is as follows:
wherein n is1And n2Is the number of cycles that the chip sample reaches the same amount of damage under the first and second standard temperature cycling profiles.
Preferably, in S42, the number of cycles N at which each group of welding points fails in the first standard temperature cycle profile and the second standard temperature cycle profile can be obtained according to the simulation data1、N2And a series of cycle numbers n with the same damage amount of the welding spots under the first standard temperature cycle section and the second standard temperature cycle section in the whole simulation process1、n2According to the parameters a, b and N obtained in S411、N2、n1、n2The simulation results of a plurality of groups of welding spots with different sizes, materials and material parameters are fitted by adopting a least square method to obtain the fitting values of the parameters a and b.
Preferably, S43 further includes determining an influence curve of the elastic modulus of the welding spot and the fatigue strength coefficient of the welding spot on the parameter b, wherein the value of the parameter b decreases with the increase of the elastic modulus and the fatigue strength coefficient of the welding spot.
Preferably, the relation between the value of the parameter b and the modulus of elasticity of the welding spot and the fatigue strength coefficient of the material of the welding spot is as shown in the following expression,
b＝c1+c2E+c3σf
wherein, c1、c2、c3Is a predetermined coefficient, c1＝3.28，c2＝-0.034，c3E is the weld elastic modulus, σ, of-1.56fIs fatigue strength coefficient of welding spot material.
Preferably, the final nonlinear damage accumulation method under the irregular temperature cycle profile in S44 is shown by the following expression:
a～N(2.803,0.031242)
b＝c1+c2E+c3σf
c1＝3.28,c2＝-0.034,c3＝-1.56
wherein E is the elastic modulus of the welding spot, sigmafIs fatigue strength coefficient of welding spot material.
Compared with the prior art, the invention has the following beneficial effects:
the invention utilizes the nonlinear damage accumulation rule determined by the simulation method to make up for the defects of long period and high cost of the experimental method.
Secondly, the damage accumulation rule obtained by the method is based on a welding spot fatigue crack damage model, and is more practical compared with the rule obtained by the traditional statistical method.
Compared with the nonlinear damage accumulation rule researched by the predecessor, the rule obtained by the invention has simpler form and is convenient to apply, parameters in the expression are easy to obtain, and the influence caused by the superposition sequence of different sections is considered, so that the result is more accurate.
The error of the Miner linear rule commonly used in engineering can reach more than 20%, and the error of the nonlinear accumulation rule obtained by the invention can be controlled within 8%, so that the error range is greatly reduced.
Aiming at the thermal fatigue of the welding spot under the irregular temperature cycle section, the invention considers the influence of different materials and sizes of the welding spot on the damage accumulation, and provides a complete nonlinear damage accumulation rule by using a simulation method, so that the accumulation calculation result is more accurate.
Drawings
FIG. 1 is a finite element three-dimensional structure model of the present invention;
FIG. 2 is a diagram illustrating boundary conditions imposed by the structure under the encapsulation model in the embodiment;
FIG. 3 is a general irregular temperature cycle profile in an example;
FIG. 4 is a first standard temperature cycle section in the example;
FIG. 5 is a second standard temperature cycle section in the example;
FIG. 6 is a cloud of plastic strain profiles for a single weld spot in an example;
FIG. 7 illustrates an exemplary embodiment of a daisy chain of chips;
FIG. 8 is a graph of simulated values and measured values of T1 according to the number of cycles in the example;
FIG. 9 is a graph of simulated values and measured values of T2 according to the embodiment;
FIG. 10 is a graph of simulated values and measured values of T3 according to the number of cycles in the example;
FIG. 11 is a graph showing a value of a parameter a for different sized pads of different materials in an example;
FIG. 12 shows the distribution of parameter a in the example;
FIG. 13 is a graph showing the b value of the parameter for different sized solder joints of different materials in the example;
FIG. 14 is a plot of weld spot modulus of elasticity versus parameter b for an example embodiment;
FIG. 15 is a graph of fatigue strength coefficient of a weld spot versus parameter b in an example; and
FIG. 16 is an equation image of the relationship between the parameter b value and the elastic modulus and fatigue strength coefficient of the welding spot in the embodiment.
Detailed Description
Exemplary embodiments, features and aspects of the present invention will be described in detail below with reference to the accompanying drawings. In the drawings, like reference numbers can indicate functionally identical or similar elements. While the various aspects of the embodiments are presented in drawings, the drawings are not necessarily drawn to scale unless specifically indicated.
The invention provides a finite element simulation method for determining a complete rule of weld spot damage accumulation under an irregular temperature cycle profile, which comprises the following steps:
s1, finite element simulation pretreatment, specifically comprising the following steps:
s11, determining the components and the packaging form of the finite element three-dimensional structure model, and determining the mesh division mode of the model;
s12, selecting a plurality of groups of welding points with different sizes and materials, and determining parameters of the materials;
s13, determining boundary conditions applied by a structure under the packaging model, wherein the boundary conditions comprise symmetrical boundary conditions, middle plane displacement coupling boundary conditions and origin fixed-support boundary conditions;
s14, determining a temperature load, wherein the temperature load comprises an irregular temperature cycle profile, a first standard temperature cycle profile and a second standard temperature cycle profile obtained through decomposition;
s2, performing finite element simulation on the welding spot under different temperature loads, and specifically comprising the following steps:
s21, selecting any group of welding spots, and establishing a finite element three-dimensional structure model of the chip;
s22, applying different boundary conditions to the chip on the three-dimensional structure model;
s23, applying an irregular temperature cycle profile, a first standard temperature cycle profile and a second standard temperature cycle profile to the chip under each boundary condition, wherein the irregular temperature cycle profile is also called a combined temperature cycle profile, and the first standard temperature cycle profile and the second standard temperature cycle profile are obtained by decomposing the combined temperature cycle profile.
S3, finite element simulation post-processing, specifically comprising the following steps:
s31, determining a plastic strain distribution cloud picture of the selected welding spot based on finite element simulation of S2, and determining the minimum plastic strain, the maximum plastic strain and the strain change range of the welding spot according to the plastic strain distribution cloud picture of the selected welding spot;
s32, determining the relationship between the mechanical strain of the welding spot layer and the resistance strain of the thermal damage of the welding spot and the resistivity of a plurality of groups of welding spots;
s33, determining the cross-sectional area, the height, the length and the temperature change of the selected welding spots for simulation, calculating to obtain the resistance values of the selected welding spots, adding the resistance values of the selected welding spots in series to obtain the resistance simulation values of the daisy chains, calibrating the resistance values obtained by simulation according to the experimentally measured resistance values corresponding to the selected welding spots, and obtaining a calibrated three-dimensional structure model;
s34, simulating all the other groups of welding spots by using the checked three-dimensional structure model, and acquiring simulation data;
s4, determining a welding spot nonlinear damage accumulation expression under the irregular temperature cycle profile, and specifically comprising the following steps:
s41, determining the form of a welding spot nonlinear damage accumulation rule under the irregular temperature cycle profile;
s42, determining the values of a parameter a and a size parameter b in a nonlinear damage accumulation rule corresponding to a plurality of groups of welding spots with different sizes and materials;
s43, determining the influence of the materials and the sizes of different welding spots on the value of the parameter a and the value of the size parameter b and the relation between the size parameter b and the material constant;
and S44, determining a final welding spot nonlinear damage accumulation rule.
Preferably, in S11, the chip finite element three-dimensional structure model is packaged in a BGA format, and the finite element three-dimensional structure model includes five parts, i.e., a solder joint, a chip, a substrate, a molding compound layer, and a PcB layer, where the solder joint is an octahedral unit, and the chip, the substrate, the molding compound layer, and the PcB layer are hexahedral units.
Preferably, the relationship between the mechanical strain of the solder joint layer and the resistance strain of the thermal damage of the solder joint in S32 is expressed as follows:
R＝(SR0+kρ0ΔT)(Fp+Ffp+FΔT)，
wherein:
Ris the resistance strain of the solder joint, ρ is the resistivity of the solder joint, R0Is the original resistance value when no thermal cycle is applied, S is the cross-sectional area of the weld, h is the height of the weld, L is the length of the weld, N is the number of cycles, Δ T is the magnitude of the temperature, the index β is typically taken to be 0.5, k is the cyclic ratio at maximum stress during one cycle, γminAnd the delta gamma is the minimum strain value, the plastic strain change range C is the material constant, C is 0.16 for widely adopted eutectic solder, and the resistance R value of the welding spot can be obtained by solving the equation system, so that the resistivity of the welding spots of different materials can be determined.
Preferably, the form of the non-linear damage accumulation rule in the irregular temperature cycle profile determined in S41 is as follows:
wherein N is the estimated value of the number of cycles when the chip sample under the irregular temperature cycle profile is failed; n is a radical of1The number of cycles when the chip sample under the first standard temperature cycle profile is failed is defined; n is a radical of2The number of cycles when the chip sample under the second standard temperature cycle profile is failed is defined; a. b is the parameter to be fitted, a, b and N1、N2The relationship of (A) is as follows:
wherein n is1And n2Is the number of cycles that the chip sample reaches the same amount of damage under the first and second standard temperature cycling profiles.
Preferably, in S42, the number of cycles N at which each group of welding points fails in the first standard temperature cycle profile and the second standard temperature cycle profile can be obtained according to the simulation data1、N2And a series of cycle numbers n with the same damage amount of the welding spots under the first standard temperature cycle section and the second standard temperature cycle section in the whole simulation process1、n2According to the parameters a, b and N obtained in S411、N2、n1、n2The simulation results of a plurality of groups of welding spots with different sizes, materials and material parameters are fitted by adopting a least square method to obtain fitting values of the parameters a and b, and the elastic modulus and the fatigue strength coefficient of different materials can be directly found through a material manual.
Preferably, S43 further includes determining an influence curve of the elastic modulus of the welding spot and the fatigue strength coefficient of the welding spot on the parameter b, wherein the value of the parameter b decreases with the increase of the elastic modulus and the fatigue strength coefficient of the welding spot.
Preferably, the relation between the value of the parameter b and the modulus of elasticity of the welding spot and the fatigue strength coefficient of the material of the welding spot is as shown in the following expression,
b＝c1+c2E+c3σf
wherein, c1＝3.28，c2＝-0.034，c3E is the weld elastic modulus, σ, of-1.56fIs fatigue strength coefficient of welding spot material. c. C1,c2,c3The numerical value of the preset coefficient is obtained by solving through fitting.
Preferably, the final nonlinear damage accumulation method under the irregular temperature cycle profile in S44 is shown by the following expression:
a～N(2.803,0.031242)
b＝c1+c2E+c3σf
c1＝3.28,c2＝-0.034,c3＝-1.56
wherein E is the elastic modulus of the welding spot, sigmafIs fatigue strength coefficient of welding spot material.
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
Taking an airplane inertial navigation system executing a task in summer as an example, a finite element simulation method of a damage accumulation rule under an irregular temperature cycle profile of a BGA (ball grid array) packaging device welding spot in electronic equipment is described. The method comprises the following specific steps:
s1, finite element simulation pretreatment:
and S11, determining the components and the packaging form of the finite element three-dimensional structure model, and determining the mesh division mode of the model. The chip finite element model is packaged in a BGA (ball grid array) mode of 16mm multiplied by 16mm, the size of the chip is 25mm multiplied by 25mm, the finite element three-dimensional structure model comprises five parts of a welding spot, the chip, a substrate, a plastic package layer and a PcB layer, the information of the chip is input into ANSYS software, the welding spot is generated into an octahedral unit by adopting a sweeping technology, and other parts adopt a hexahedral unit due to the irregularity and discontinuity of the shape.
And S12, selecting multiple groups of welding points with different sizes and materials, and determining each material parameter. To investigate the influence of different materials and sizes on parameters in the damage accumulation expression, four solder joint materials, namely Sn62Pb36Ag2, sn96.5ag3cu0.5, 60Sn40Pb, and 97.5pb2.5sn, were selected in this example, and the diameters of the solder joints were selected to be four sizes, 0.5mm, 0.4mm, 0.25mm, and 0.6 mm. The parameters of the Anand viscoplasticity constitutive equation and the parameters of each material are shown in tables 1 and 2.
TABLE 1 Anand parameters for solder joints of different materials
TABLE 2 Material Property parameters for each Structure
And S13, determining boundary conditions applied by the structure under the encapsulation model, wherein the boundary conditions comprise a symmetric boundary condition, a middle plane displacement coupling boundary condition and an origin fixed-support boundary condition.
S14, determining a temperature load, wherein the temperature load comprises an irregular temperature cycle profile, a first standard temperature cycle profile and a second standard temperature cycle profile obtained through decomposition;
s2, carrying out finite element simulation on the welding spots under different temperature loads:
and S21, selecting any group of welding points, and establishing a finite element three-dimensional structure model of the chip. According to the model components, the packaging form and the grid division mode determined in S11, solder joints of Sn62Pb36Ag2 materials with the diameter of 0.5mm are selected, and the finite element three-dimensional structure model is shown in figure 1.
And S22, applying different boundary conditions to the chip on the three-dimensional structure model. And respectively applying the boundary conditions on the model according to the boundary conditions determined by the S13, as shown in FIG. 2, wherein the conditions simulate the practical use condition of the packaging structure, X is the coupling of the X-direction freedom degree, Y1 is the coupling of the Y-direction freedom degree, Y2 is the symmetrical constraint of the Y direction, and A is the fixed constraint.
And S23, respectively applying the irregular temperature cycle profile, the first standard temperature cycle profile and the second standard temperature cycle profile to the chip under each boundary condition. The irregular temperature cycle profile determined at S14 and two standard temperature cycle profiles were applied to the model. The specific cross-sections are shown in fig. 3-5.
S3, finite element simulation post-processing:
and S31, determining a plastic strain distribution cloud picture of the selected welding point based on finite element simulation of S2, and determining the minimum plastic strain, the maximum plastic strain and the strain change range of the welding point according to the plastic strain distribution cloud picture of the selected welding point. One of the welding spot plastic distribution clouds of the welding spots of the Sn62Pb36Ag2 material with the diameter of 0.5mm is shown in FIG. 6. The reference number 2 in the figure is the solder point from which the minimum plastic strain γ can be obtainedmin130176, maximum plastic strain γmax20700000, the strain variation range is delta gammamax-γmin＝2.06×107。
And S32, determining the relation between the mechanical strain of the welding spot layer and the resistance strain of the thermal damage of the welding spot and the resistivity of the multiple groups of welding spots. According to the literature, "theory and application of electrical measurement of thermal damage of lead-free solder joint", the following theoretical relationship between the mechanical strain of the solder joint layer and the resistance strain of the thermal damage of the solder joint can be obtained:
R＝(SR0+kρ0ΔT)(Fp+Ffp+FΔT), (1)
wherein:
wherein the content of the first and second substances,Ris the resistance strain of the solder joint, ρ is the resistivity of the solder joint, R0Is the original resistance value when no thermal cycle is applied, S is the cross-sectional area of the solder joint, h is the solder joint height, L is the solder joint length, N is the cycle number, Δ T is the temperature magnitude, the index β is typically taken to be 0.5, k is the cyclic ratio at maximum stress during one cycle, typically 0.3, γminThe minimum strain value is delta gamma is the plastic strain variation range, C is the material constant, C is 0.16 for widely adopted eutectic solder, and the value of the solder joint resistance R can be obtained by solving the equation system.
The resistivity of each material solder joint can be determined by referring to GB/T3131-2001, for example, the solder joint resistivity of Sn62Pb36Ag2 is 1.41 multiplied by 10-7Ω/m。
S33, determining the cross-sectional area, the height, the length and the temperature change of the selected welding spots for simulation, calculating to obtain the resistance value of the selected welding spots, adding the resistance values of the selected welding spots in series to obtain the resistance simulation value of each daisy chain, calibrating the resistance value obtained by simulation according to the experimentally measured resistance value corresponding to the selected welding spots, and obtaining the calibrated three-dimensional structure model. Automatically calculating the cross section area, height and length of the welding spot through the model established by S21, wherein the temperature change is the change range of the loaded temperature load, carrying out post-treatment in ANSYS APDL, and calculating the welding spot resistance value of the Sn62Pb36Ag2 material with the diameter of 0.5mm to be 4.08 multiplied by 10-3Ω, daisy chains T1, T2, and T3 are connected as shown in fig. 7, and the resistance simulation values of the respective daisy chains are obtained by adding the pad resistances in series according to the connection method of fig. 7. Through calibration, the deviation between the simulation value and the measured value of each daisy chain is within 5 percent.
And S34, simulating all the other groups of welding points by using the checked three-dimensional structure model, and acquiring simulation data. By using the checked model and performing simulation analysis again, the simulation values and the deviations from the actual measured values of the welding spots of each group under the three loading conditions are controlled within 5%, wherein the change curves of the simulation values and the actual measured values of the three daisy chains of T1, T2 and T3 of the welding spots of the Sn62Pb36Ag2 material with the diameter of 0.5mm along with the cycle number are shown in FIGS. 8-10.
S4, determining a welding spot nonlinear damage accumulation expression under the irregular temperature cycle profile:
s41, determining the form of the welding spot nonlinear damage accumulation rule under the irregular temperature cycle profile, as shown in expression (7):
wherein N is the estimated value of the number of cycles when the chip sample under the irregular temperature cycle profile is failed; n1 is the number of cycles at which the chip sample reached failure in the first standard temperature cycling profile; n2 is the number of cycles at which the chip sample reaches failure in the second standard temperature cycling profile; a. b is the parameter to be fitted. a. b is related to N1 and N2 as follows:
wherein n1 and n2 are the number of cycles that the chip sample reaches the same amount of damage at the first standard temperature cycling profile and the second standard temperature cycling profile.
And S42, determining the values of the parameter a and the size parameter b in the nonlinear damage accumulation rule corresponding to a plurality of groups of welding spots with different sizes and materials. According to the simulation data, the cycle number N of each group of welding points when the welding points fail under two standard temperature cycle profiles can be obtained1、N2And a series of cycles n with the same amount of damage to the solder joints under the two cross sections during the whole process1、n2Then a, b and N obtained in S411、N2、n1、n2The least square method is adopted to fit simulation results of welding spots of different materials and different sizes to obtain fitting values of parameters a and b, and the elastic modulus and the fatigue strength coefficient of different materials can be directly found through a material manual, as shown in table 3.
TABLE 3 fitting values of parameters a and b for four sizes of four materials
And S43, determining the influence of the materials and the sizes of different welding spots on the values of the parameter a and the size parameter b and the relation between the size parameter b and the material constant. The values of a for different solder joint materials and sizes are extracted from table 3, and a graph of the relationship between the values of the parameters a and the materials and sizes of the solder joints is made, as shown in fig. 11, where the abscissa is the different sizes and different materials. From the figure, the value of the parameter a is not influenced by the material and the size of the welding spot. The parameter a was tested to fit a normal distribution as shown in fig. 12, where the expected 2.803 standard deviation for parameter a is 0.03124.
The b values of different solder joint materials and sizes are extracted from table 3, and a relation graph of the parameter b value and the solder joint materials and sizes is made, as shown in fig. 13, wherein the abscissa is different sizes and different materials. As can be seen from the figure, under the condition of a certain welding spot material, the value of the parameter b is not influenced by the size of the welding spot. And the influence curves of the elastic modulus of the welding spot and the fatigue strength coefficient of the welding spot on the parameter b are respectively drawn by the table 3, as shown in fig. 14-15, it can be seen that the value of the parameter b decreases with the increase of the elastic modulus and the fatigue strength coefficient of the welding spot. The value of the visible parameter b, the elastic modulus E and the fatigue strength coefficient sigma of the materialfAnd (4) correlating.
According to table 3, the modulus of elasticity and the fatigue strength coefficient and the corresponding value of parameter b are extracted, as shown in table 4.
TABLE 4 modulus of elasticity and fatigue Strength coefficient and corresponding values of parameter b
| Modulus of elasticity E (GPa) | Coefficient of fatigue strength sigmaf(GPa) | |
| 30 | 1.97 | -0.867 |
| 30 | 1.97 | -0.856 |
| 30 | 1.97 | -0.853 |
| 30 | 1.97 | -0.848 |
| 35 | 2.25 | -1.163 |
| 35 | 2.25 | -1.209 |
| 35 | 2.25 | -1.171 |
| 35 | 2.25 | -1.221 |
| 32 | 2.01 | -0.925 |
| 32 | 2.01 | -0.936 |
| 32 | 2.01 | -0.944 |
| 32 | 2.01 | -0.935 |
| 40 | 2.55 | -2.072 |
| 40 | 2.55 | -2.108 |
| 40 | 2.55 | -2.097 |
| 40 | 2.55 | -2.143 |
And fitting the data by utilizing Matlab to obtain the relation between the parameter b value and the elastic modulus and fatigue strength coefficient of the welding spot, such as an expression (9). The image of the equation is shown in fig. 16.
b＝c1+c2E+c3σf(9)
Wherein c is1＝3.28，c2＝-0.034，c3E is the weld elastic modulus, σ, of-1.56fIs the fatigue strength coefficient of the material of the welding spot, c1,c2,c3For the preset coefficients, the values are passed through the sets of b, E and σ in the above tablefAnd solving the three coefficients by using a least square method through the expression.
And S44, determining a final welding spot nonlinear damage accumulation rule. The values of parameters a and b in the nonlinear damage accumulation rule are determined, and the final nonlinear damage accumulation method under the irregular temperature cycle profile is shown as the formula (10)
a～N(2.803,0.031242)
b＝c1+c2E+c3σf
c1＝3.28,c2＝-0.034,c3＝-1.56 (10)
Wherein E is the weld elastic modulus, σfIs fatigue strength coefficient of welding spot material. The damage accumulation rule obtained by the present invention was compared with the Miner's linear rule and the experimental results, as shown in Table 5.
TABLE 5 comparison of the two rules with the results of the experiment
| Material | Results of the experiment | Miner's linear law | Error of the measurement | Principles of the invention | Error of the measurement |
| Sn62Pb36Ag2 | 282 | 246 | -12.8％ | 295 | 4.6％ |
| Sn96.5Ag3cu0.5 | 184 | 155 | -15.8％ | 188 | 2.2％ |
| 60Sn40Pb | 232 | 191 | -17.7％ | 234 | 0.8％ |
| 97.5Pb2.5Sn | 338 | 270 | -20.1％ | 344 | 1.8％ |
Therefore, the finite element simulation method truly reflects the change of the external environment stress when the system where the welding spot of the component is positioned executes the task, considers the influence of the welding spot size material on the nonlinear damage accumulation rule, and determines the final expression form of the rule. The complete nonlinear damage accumulation rule is more comprehensive, scientific and reasonable, and the reliability prediction result is closer to the real reliability level of the product.
It should be noted that: the above-mentioned embodiments are only used for illustrating the technical solution of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (8)
1. A finite element simulation method for determining a complete rule of weld spot damage accumulation under an irregular temperature cycle profile is characterized by comprising the following steps of: the method comprises the following steps:
s1, a finite element simulation preprocessing step, which specifically comprises:
s11, determining components and an encapsulation model of the finite element three-dimensional structure model, and determining a model mesh division mode;
s12, selecting a plurality of groups of welding points with different sizes and materials, and determining parameters of the materials;
s13, determining boundary conditions under the packaging model, wherein the boundary conditions comprise symmetrical boundary conditions, middle surface displacement coupling boundary conditions and origin fixed support boundary conditions;
s14, determining a temperature load, wherein the temperature load comprises an irregular temperature cycle profile, a first standard temperature cycle profile and a second standard temperature cycle profile;
s2, carrying out finite element simulation on the welding spots under different temperature loads, and specifically comprising the following steps:
s21, selecting any group of welding spots, and establishing a finite element three-dimensional structure model of the chip aiming at the selected group of welding spots;
s22, applying different boundary conditions to the chip on the finite element three-dimensional structure model;
s23, respectively applying an irregular temperature cycle profile, a first standard temperature cycle profile and a second standard temperature cycle profile to the chip under each boundary condition;
s3, a finite element simulation post-processing step, which specifically comprises:
s31, determining a plastic strain distribution cloud picture of the selected welding point based on finite element simulation of S2, and determining the minimum plastic strain, the maximum plastic strain and the strain change range of the welding point according to the plastic strain distribution cloud picture;
s32, determining the relationship between the mechanical strain of the welding spot layer and the resistance strain of the thermal damage of the welding spot and the resistivity of a plurality of groups of welding spots;
s33, determining the cross-sectional area, the height, the length and the temperature change of the selected welding spots for simulation, calculating to obtain the resistance values of the selected welding spots, adding the resistance values of the selected welding spots in series to obtain the resistance simulation values of the daisy chains, calibrating the resistance values obtained by simulation according to the experimentally measured resistance values corresponding to the selected welding spots, and obtaining a calibrated three-dimensional structure model;
s34, simulating all the other groups of welding spots by using the checked three-dimensional structure model, and acquiring simulation data;
s4, determining a welding spot nonlinear damage accumulation expression under the irregular temperature cycle profile, which specifically comprises the following steps:
s41, determining the form of a welding spot nonlinear damage accumulation rule under the irregular temperature cycle profile;
s42, determining the values of a parameter a and a size parameter b in a nonlinear damage accumulation rule corresponding to a plurality of groups of welding spots with different sizes and materials;
s43, determining the influence of the materials and the sizes of different welding spots on the value of the parameter a and the value of the size parameter b and the relation between the size parameter b and the material constant; and
and S44, determining a final welding spot nonlinear damage accumulation rule.
2. A finite element simulation method for determining a complete rule of weld damage accumulation under an irregular temperature cycle profile according to claim 1, wherein: and S11, packaging the chip finite element three-dimensional structure model in a BGA mode, wherein the finite element three-dimensional structure model comprises a welding spot, a chip, a substrate, a plastic package layer and a PcB layer, the welding spot is an octahedron unit, and the chip, the substrate, the plastic package layer and the PcB layer are hexahedron units.
3. A finite element simulation method for determining a complete rule of weld damage accumulation under an irregular temperature cycle profile according to claim 1, wherein: the expression of the relationship between the mechanical strain of the solder joint layer and the resistance strain of the thermal damage of the solder joint in S32 is as follows:
R＝(SR0+kρΔT)(Fp+Ffp+FΔT),
wherein:
Ris the resistance strain of the solder joint, ρ is the resistivity of the solder joint, R0Is the original resistance value when no thermal cycle is applied, S is the cross-sectional area of the welding spot, h is the height of the welding spot, L is the length of the welding spot, N is the cycle number, Delta T is the temperature, the index beta is 0.5, k is the cycle ratio of the maximum stress in one cycle period and is 0.3, gamma isminAnd (3) determining the minimum strain value, wherein delta gamma is the plastic strain variation range, C is the material constant, C is 0.16 for widely-used eutectic solder, and the resistance R value of the welding spot can be obtained by solving the expression, so that the resistivity of the welding spot of different materials can be determined.
4. A finite element simulation method for determining a complete rule of weld damage accumulation under irregular temperature cycling profiles according to claim 1 or 3, wherein: the form of the non-linear damage accumulation rule in the irregular temperature cycle profile determined in S41 is as follows:
wherein N is a cycle number estimated value when the chip sample under the irregular temperature cycle profile is failed; n is a radical of1The number of cycles when the chip sample under the first standard temperature cycle profile is failed is defined; n is a radical of2The number of cycles when the chip sample under the second standard temperature cycle profile is failed is defined; a. b is the parameter to be fitted, a, b and N1、N2The relationship of (A) is as follows:
wherein n is1And n2Is the number of cycles that the chip sample reaches the same amount of damage under the first and second standard temperature cycling profiles.
5. A finite element simulation method for determining a complete rule of weld damage accumulation under an irregular temperature cycle profile according to claim 4, wherein: in S42, the number N of cycles of failure of each group of welding points under the first standard temperature cycle profile and the second standard temperature cycle profile can be obtained according to the simulation data1、N2And a series of cycle numbers n with the same damage amount of the welding spots under the first standard temperature cycle section and the second standard temperature cycle section in the whole simulation process1、n2According to the parameters a, b and N obtained in S411、N2、n1、n2The simulation results of a plurality of groups of welding spots of different sizes and materials are fitted by adopting a least square method to obtain fitting values of the parameters a and b.
6. A finite element simulation method for determining a complete rule of weld damage accumulation under an irregular temperature cycle profile according to claim 5, wherein: s43 also includes determining the effect curve of the elastic modulus of the welding spot and the fatigue strength coefficient of the welding spot on the parameter b, wherein the value of the parameter b decreases along with the increase of the elastic modulus and the fatigue strength coefficient of the welding spot.
7. A finite element simulation method for determining a complete rule of weld damage accumulation under an irregular temperature cycle profile according to claim 6, wherein: the relation between the parameter b value and the elastic modulus of the welding spot and the fatigue strength coefficient of the welding spot material is shown in the following expression,
b＝c1+c2E+c3σf
wherein, c1、c2、c3Is a predetermined coefficient, c1＝3.28，c2＝-0.034，c3E is the weld elastic modulus, σ, of-1.56fIs fatigue strength coefficient of welding spot material.
8. A finite element simulation method for determining a complete rule of weld damage accumulation under an irregular temperature cycle profile according to claim 1, wherein: the expression of the final nonlinear damage accumulation method of the welding spot under the irregular temperature cycle profile in the S44 is shown as follows:
a～N(2.803,0.031242)
b＝c1+c2E+c3σf
c1＝3.28,c2＝-0.034,c3＝-1.56
wherein E is the elastic modulus of the welding spot, sigmafThe fatigue strength coefficient of the welding spot material is shown, and N is a cycle number estimated value when the chip sample under the irregular temperature cycle profile is failed; n is a radical of1The number of cycles when the chip sample under the first standard temperature cycle profile is failed is defined; n is a radical of2The number of cycles when the chip sample under the second standard temperature cycle profile is failed is defined; a. b is the parameter to be fitted.
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