CN109388820A - Determine that irregular temperature follows the finite element simulation method that solder joint damage under section accumulates complete rule - Google Patents
Determine that irregular temperature follows the finite element simulation method that solder joint damage under section accumulates complete rule Download PDFInfo
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- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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Abstract
Determine that irregular temperature follows the finite element simulation method that solder joint damage under section accumulates complete rule the present invention provides a kind of, method includes the following steps: S1, finite element simulation pre-treatment；S2, finite element simulation is carried out to solder joint under different temperatures load, S4, S3, finite element simulation post-processing determine the solder joint uneven cumulative damage expression formula that irregular temperature is followed under section.The present invention is based on solder joint fatigue Crack Damage model using the uneven cumulative damage rule that emulation mode determines, reality is more bonded based on the rule that statistic law obtains compared to tradition, not equality of temperature is considered simultaneously follows the influence of section overlay order bring, as a result more accurate, error can control within 8%, substantially reduce error range.
Description
Technical field
The invention belongs to Reliablility simulation research field, provides in particular a kind of irregular temperature of determination and follow solder joint under section
The finite element simulation method of the complete rule of damage accumulation follows the damage under section more particularly to the temperature in phased mission systems
Accumulation.
Background technique
Current welding spot reliability research is mostly heat premised on solder joint is under the temperature cycles section of standard rule
Fatigue problem, however the real work of electronic product is under a very complicated system, it usually needs it completes by multiple and different ranks
The task of Duan Zucheng.Phased mission systems contain multiple, nonoverlapping, the continuous stage, and system needs in each stage
Being completed for task is different, the stress being subjected to and environmental condition difference, therefore the experienced of electronic equipment is not standard
Temperature follow section, but section is followed by the irregular temperature that multiple stages form, and it is electricity that solder joint heat fatigue occurs under the environment
The dominant mechanism of sub- product failure.Studying the solder joint Thermal Fatigue Damage Accumulation that irregular temperature is followed under section is accurate estimated electricity
The important channel in sub- product failure service life.
The research for following solder joint Thermal Fatigue Damage under section to irregular temperature in engineering only simply cuts open irregular Wen Xun
Face splits into several standard temperature and follows section, carries out accumulation calculating using the linear rule of Miner.And facts proved that, using Miner
Linear rule follows the solder joint Thermal Fatigue Damage under section to irregular temperature and carries out linear accumulation, as a result has relatively large deviation.For
Irregular temperature in phased mission systems follows section, considers that a kind of new uneven cumulative damage rule, the rule contain not
Determining parameter needs to be determined by experiment.However, every group of experiment can only determine the parameter value of a kind of size and material solder joint,
For obtain different sizes and material solder joint damage equation parameter value, need to do a large amount of experiment, lead to experimental period
It is longer, costly.Thermal fatigue behavior of the finite element simulation analog solder joint under load effect, irregular temperature are followed under section
Finite element simulation can be used for response condition of the simulating solder joint under physical condition, for damage position and the fatigue longevity for predicting solder joint
Life provides reference.The finite element simulation of solder joint can be formed with experimental method and be verified, and the shortcomings that can overcome the disadvantages that experimental method, be passed through
Solder joint Thermal Fatigue Damage accumulates Finite Element Simulation Analysis, can follow the cumulative rule of damage under section to carry out the irregular temperature of solder joint
Parameter fitting provides more data, finally determines that irregular temperature follows the complete rule of damage accumulation under section.
Summary of the invention
It is an object of the invention to be directed to the solder joint of different sizes and material, followed for the irregular temperature of determination non-thread under section
Property damage accumulation rule in parameter, provide a kind of finite element simulation method, analysis obtains welding spot size and material to unknown ginseng
Uneven cumulative damage rule is expanded and obtains complete form by several influences.Miner linear accumulation method is substituted using the rule
Computation of damage cumulation is then carried out, so that reliability prediction is more accurate, it is as a result horizontal closer to the real reliability of product.
The present invention is implemented as follows:
Determine that irregular temperature follows the finite element simulation that solder joint damage under section accumulates complete rule the present invention provides a kind of
Method, method includes the following steps:
S1, finite element simulation pre-treatment, specifically includes the following steps:
S11, the component part and packing forms for determining finite element 3 d structure model, determine model meshes division mode；
S12, the multiple groups solder joint for choosing different sizes and material, and determine each material parameter；
S13, determine the boundary condition that structure under packaging model applies, the boundary condition include symmetrical boundary condition,
Median surface displacement coupling boundary condition and origin fixed-end boundary condition；
S14, temperature load, the temperature loading include that irregular temperature follows section, decomposes the first standard temperature obtained
It follows section and the second standard temperature follows section；
S2, finite element simulation is carried out to solder joint under different temperatures load, specifically includes the following steps:
S21, any one group of solder joint is chosen, establishes the finite element 3 d structure model of chip；
S22, apply different boundary conditions to chip on 3 d structure model；
S23, irregular temperature follows section, the first standard temperature follows section is applied to chip respectively under every arbitrary boundary conditions and the
Two standard temperature follow section；
S3, finite element simulation post-processing, specifically includes the following steps:
S31, the finite element simulation based on S2 determine the plastic strain cloud charts of selected group solder joint, according to selected group of weldering
The plastic strain cloud charts of point determine the minimum plastic strain, maximum plastic strain and strain variation range of solder joint；
S32, mechanics strain and the relationship of the resistance-strain of solder joint thermal damage and the electricity of multiple groups solder joint for determining solder joint layer
Resistance rate；
S33, cross-sectional area, solder joint height, solder joint length and the temperature change for determining the selected group of solder joint emulated,
Selected group solder joint resistance value is calculated, added in series is carried out to selected group of solder joint resistance value, obtains the resistance of each daisy chain
Simulation value, and calibrated according to the corresponding resistance value measured of testing of selected group of solder joint to the resistance value obtained is emulated, and
3 d structure model after to calibration；
S34, using 3 d structure model after check, remaining all groups solder joint is emulated, and obtain emulation data；
S4, the solder joint uneven cumulative damage expression formula that irregular temperature is followed under section is determined, specifically includes the following steps:
S41, the form for determining the solder joint uneven cumulative damage rule that irregular temperature is followed under section；
S42, parameter a and ruler in the corresponding uneven cumulative damage rule of the solder joint of multiple groups difference size and material are determined
Very little parameter b value；
The influence and dimensional parameters b of S43, the material for determining different solder joints and size to parameter a value and dimensional parameters b value
With the relationship of material constant；
S44, final solder joint uneven cumulative damage rule is determined.
Preferably, chip finite element 3 d structure model is encapsulated using BGA form in S11, finite element 3 d structure model
Including solder joint, chip, five part of substrate, plastic packaging layer and PcB layer, wherein solder joint is octahedral unit, chip, substrate, plastic packaging
Layer and PcB layer be hexahedral element.
Preferably, the mechanics of solder joint layer strains the relationship following expression with the resistance-strain of solder joint thermal damage in S32:
εR=(SR0+kρ0ΔT)(Fp+Ffp+FΔT),
Wherein:
εRFor the resistance-strain of solder joint, ρ is the resistivity of solder joint, R0Not apply initial resistance value when temperature follows section, S
For the cross-sectional area of solder joint, h is solder joint height, and L is solder joint length, and N is recurring number, and Δ T is Wen great little, and index β usually takes
0.5, the k recycle ratio to be in maximum stress in a cycle period, γminFor minimum strain value, Δ γ is plastic strain variation
Range, C are material constant, and for the eutectic solder being widely used, C takes 0.16, and by solving equation group, solder joint can be obtained
Resistance R value, so that it is determined that the resistivity of the solder joint of different materials.
Preferably, the form for determining that irregular temperature follows uneven cumulative damage rule under section in S41 is as follows:
Wherein N is that irregular temperature follows recurring number estimated value when chip sample under section reaches failure；N1For the first standard
Temperature follows recurring number when chip sample under section reaches failure；N2When following that chip sample reaches failure under section for the second standard temperature
Recurring number；A, b is parameter to be fitted, a, b and N1、N2Relational expression it is as follows:
Wherein n1And n2It is that chip sample reaches identical damage in the case where the first standard temperature follows section and the second standard temperature follows section
Recurring number when amount.
Preferably, it can be derived that each group solder joint follows section and the second standard in the first standard temperature according to emulation data in S42
Temperature follows recurring number N when failing under section1、N2, and in whole simulation process, the first standard temperature follows section and the second standard
Temperature follows a series of recurring number n when solder joint damage amount is identical under section1、n2, further according to parameter a, b and N obtained in S411、N2、
n1、n2Relational expression the simulation result of multiple groups difference size, material and material parameter solder joint is intended using least square method
It closes, obtains the match value of parameter a and b.
Preferably, further include in S43 determining solder joint elasticity modulus and solder joint influence of the fatigue strength coefficient to parameter b
Curve, wherein parameter b value reduces with the increase of solder joint elasticity modulus and fatigue strength coefficient.
Preferably, the relationship of parameter b value and solder joint elasticity modulus and welding material fatigue strength coefficient, such as following formula
It is shown,
B=c1+c2E+c3σf
Wherein, c1、c2、c3For predetermined coefficient, c1=3.28, c2=-0.034, c3=-1.56, E is solder joint elasticity modulus,
σfFor welding material fatigue strength coefficient.
Preferably, irregular temperature is followed shown in uneven cumulative damage method following expression final under section in S44:
A~N (2.803,0.031242)
B=c1+c2E+c3σf
c1=3.28, c2=-0.034, c3=-1.56
Wherein, E is solder joint elasticity modulus, σfFor welding material fatigue strength coefficient.
Compared with prior art, the invention has the following advantages:
1. the uneven cumulative damage rule that the present invention is determined using emulation mode, can make up the experimental method period it is long,
Costly disadvantage.
2. the damage accumulation rule that the present invention obtains is based on solder joint fatigue Crack Damage model, compared to tradition based on system
The rule that meter method obtains more is bonded reality.
3. the rule form that the present invention obtains is simpler, just compared to the uneven cumulative damage rule of forefathers' research
Parameter in application, expression formula is all readily available, while considering different section overlay order brings influences, as a result more
It is accurate to add.
4. the linear rule of common Miner in engineering, error is up to 20% or more, and the Nonlinear Cumulative that the present invention obtains
Rule error can control within 8%, substantially reduce error range.
5. the present invention follows the solder joint heat fatigue under section for irregular temperature, consider solder joint different materials and size to damage
The influence of accumulation proposes that complete uneven cumulative damage rule, accumulation calculated result are more accurate using emulation mode.
Detailed description of the invention
Fig. 1 is finite element 3 d structure model of the invention；
Fig. 2 is the boundary condition that the structure in embodiment under packaging model applies；
Fig. 3 is that total irregular temperature in embodiment follows section；
Fig. 4 is that the first standard temperature in embodiment follows section；
Fig. 5 is that the second standard temperature in embodiment follows section；
Fig. 6 is the plastic strain cloud charts of the single solder joint in embodiment；
Fig. 7 is the connecting mode of the chip daisy chain in embodiment；
Fig. 8 be embodiment in T1 simulation value and measured value with recurring number change curve；
Fig. 9 be embodiment in T2 simulation value and measured value with recurring number change curve；
Figure 10 be embodiment in T3 simulation value and measured value with recurring number change curve；
Figure 11 is the parameter a value of the different size different materials solder joints in embodiment；
Figure 12 is the distribution of the parameter a in embodiment；
Figure 13 is the parameter b value of the different size different materials solder joints in embodiment；
Figure 14 is the relational graph of the solder joint elasticity modulus and parameter b in embodiment；
Figure 15 is the fatigue strength coefficient of the solder joint in embodiment and the relational graph of parameter b；And
Figure 16 is the equation image of parameter b value and the relationship of solder joint elasticity modulus and fatigue strength coefficient in embodiment.
Specific embodiment
Below with reference to the attached drawing exemplary embodiment that the present invention will be described in detail, feature and aspect.It is identical attached in attached drawing
Icon note indicates element functionally identical or similar.Although the various aspects of embodiment are shown in the attached drawings, unless special
It does not point out, it is not necessary to attached drawing drawn to scale.
Determine that irregular temperature follows the finite element simulation that solder joint damage under section accumulates complete rule the present invention provides a kind of
Method, method includes the following steps:
S1, finite element simulation pre-treatment, specifically includes the following steps:
S11, the component part and packing forms for determining finite element 3 d structure model, determine model meshes division mode；
S12, the multiple groups solder joint for choosing different sizes and material, and determine each material parameter；
S13, determine the boundary condition that structure under packaging model applies, the boundary condition include symmetrical boundary condition,
Median surface displacement coupling boundary condition and origin fixed-end boundary condition；
S14, temperature load, the temperature loading include that irregular temperature follows section, decomposes the first standard temperature obtained
It follows section and the second standard temperature follows section；
S2, finite element simulation is carried out to solder joint under different temperatures load, specifically includes the following steps:
S21, any one group of solder joint is chosen, establishes the finite element 3 d structure model of chip；
S22, apply different boundary conditions to chip on 3 d structure model；
S23, irregular temperature follows section, the first standard temperature follows section is applied to chip respectively under every arbitrary boundary conditions and the
Two standard temperature follow section, wherein irregular temperature, which follows section also known as combination temperature, follows section, the first standard temperature follows section and the second mark
Quasi- temperature, which follows section and follows section by the combination temperature, decomposes to obtain.
S3, finite element simulation post-processing, specifically includes the following steps:
S31, the finite element simulation based on S2 determine the plastic strain cloud charts of selected group solder joint, according to selected group of weldering
The plastic strain cloud charts of point determine the minimum plastic strain, maximum plastic strain and strain variation range of solder joint；
S32, mechanics strain and the relationship of the resistance-strain of solder joint thermal damage and the electricity of multiple groups solder joint for determining solder joint layer
Resistance rate；
S33, cross-sectional area, solder joint height, solder joint length and the temperature change for determining the selected group of solder joint emulated,
Selected group solder joint resistance value is calculated, added in series is carried out to selected group of solder joint resistance value, obtains the resistance of each daisy chain
Simulation value, and calibrated according to the corresponding resistance value measured of testing of selected group of solder joint to the resistance value obtained is emulated, and
3 d structure model after to calibration；
S34, using 3 d structure model after check, remaining all groups solder joint is emulated, and obtain emulation data；
S4, the solder joint uneven cumulative damage expression formula that irregular temperature is followed under section is determined, specifically includes the following steps:
S41, the form for determining the solder joint uneven cumulative damage rule that irregular temperature is followed under section；
S42, parameter a and ruler in the corresponding uneven cumulative damage rule of the solder joint of multiple groups difference size and material are determined
Very little parameter b value；
The influence and dimensional parameters b of S43, the material for determining different solder joints and size to parameter a value and dimensional parameters b value
With the relationship of material constant；
S44, final solder joint uneven cumulative damage rule is determined.
Preferably, chip finite element 3 d structure model is encapsulated using BGA form in S11, finite element 3 d structure model
Including solder joint, chip, five part of substrate, plastic packaging layer and PcB layer, wherein solder joint is octahedral unit, chip, substrate, plastic packaging
Layer and PcB layer be hexahedral element.
Preferably, the mechanics of solder joint layer strains the relationship following expression with the resistance-strain of solder joint thermal damage in S32:
εR=(SR0+kρ0ΔT)(Fp+Ffp+FΔT),
Wherein:
εRFor the resistance-strain of solder joint, ρ is the resistivity of solder joint, R0Not apply initial resistance value when temperature follows section, S
For the cross-sectional area of solder joint, h is solder joint height, and L is solder joint length, and N is recurring number, and Δ T is Wen great little, and index β usually takes
0.5, the k recycle ratio to be in maximum stress in a cycle period, γminFor minimum strain value, Δ γ is plastic strain variation
Range C is material constant, and for the eutectic solder being widely used, C takes 0.16, and by solving equation group, solder joint can be obtained
Resistance R value, so that it is determined that the resistivity of the solder joint of different materials.
Preferably, the form for determining that irregular temperature follows uneven cumulative damage rule under section in S41 is as follows:
Wherein N is that irregular temperature follows recurring number estimated value when chip sample under section reaches failure；N1For the first standard
Temperature follows recurring number when chip sample under section reaches failure；N2When following that chip sample reaches failure under section for the second standard temperature
Recurring number；A, b is parameter to be fitted, a, b and N1、N2Relational expression it is as follows:
Wherein n1And n2It is that chip sample reaches identical damage in the case where the first standard temperature follows section and the second standard temperature follows section
Recurring number when amount.
Preferably, it can be derived that each group solder joint follows section and the second standard in the first standard temperature according to emulation data in S42
Temperature follows recurring number N when failing under section1、N2, and in whole simulation process, the first standard temperature follows section and the second standard
Temperature follows a series of recurring number n when solder joint damage amount is identical under section1、n2, further according to parameter a, b and N obtained in S411、N2、
n1、n2Relational expression the simulation result of multiple groups difference size, material and material parameter solder joint is intended using least square method
It closes, obtains the match value of parameter a and b, the elasticity modulus and fatigue strength coefficient of different materials can directly be looked by Materials Handbook
?.
Preferably, further include in S43 determining solder joint elasticity modulus and solder joint influence of the fatigue strength coefficient to parameter b
Curve, wherein parameter b value reduces with the increase of solder joint elasticity modulus and fatigue strength coefficient.
Preferably, the relationship of parameter b value and solder joint elasticity modulus and welding material fatigue strength coefficient, such as following formula
It is shown,
B=c1+c2E+c3σf
Wherein, c1=3.28, c2=-0.034, c3=-1.56, E is solder joint elasticity modulus, σfIt is strong for welding material fatigue
Spend coefficient.c1,c2,c3For predetermined coefficient, numerical value is obtained by being fitted to solve.
Preferably, irregular temperature is followed shown in uneven cumulative damage method following expression final under section in S44:
A~N (2.803,0.031242)
B=c1+c2E+c3σf
c1=3.28, c2=-0.034, c3=-1.56
Wherein, E is solder joint elasticity modulus, σfFor welding material fatigue strength coefficient.
Specific embodiment
For in certain aircraft inertial navigation system that summer executes task, to illustrate that bga device welds in its electronic equipment
The irregular temperature of point follows the finite element simulation method of damage accumulation rule under section.Specific step is as follows for this method:
S1, finite element simulation pre-treatment:
S11, the component part and packing forms for determining finite element 3 d structure model, determine model meshes division mode.
Chip finite element model is encapsulated using the BGA form of 16mm × 16mm, chip size 25mm × 25mm, finite element three-dimensional structure mould
Type includes solder joint, chip, substrate, plastic packaging layer, five part of PcB layer, by the information input ANSYS software of chip, and using sweeping
Plunder technology and solder joint generated into octahedral unit, other parts due to shape scrambling and discontinuity, using hexahedron list
Member.
S12, the multiple groups solder joint for choosing different sizes and material, and determine each material parameter.To inquire into different materials and ruler
The influence of parameter in the very little expression formula to damage accumulation, chooses four kinds of welding materials in the present embodiment, respectively Sn62Pb36Ag2,
The diameter of Sn96.5Ag3cu0.5,60Sn40Pb, 97.5Pb2.5Sn, solder joint are selected as 0.5mm, 0.4mm, 0.25mm and 0.6mm
Four kinds of sizes.Anand viscoplastic constitutive equation parameter and each material parameter are as shown in Table 1 and Table 2.
The Anand parameter of 1 different materials solder joint of table
The material properties parameter of each structure of table 2
S13, determine the boundary condition that structure under packaging model applies, the boundary condition include symmetrical boundary condition,
Median surface displacement coupling boundary condition and origin fixed-end boundary condition.
S14, temperature load, the temperature loading include that irregular temperature follows section, decomposes the first standard temperature obtained
It follows section and the second standard temperature follows section；
S2, finite element simulation is carried out to solder joint under different temperatures load:
S21, any one group of solder joint is chosen, establishes the finite element 3 d structure model of chip.The model group determined according to S11
At part, packing forms and grid dividing mode, the solder joint of diameter 0.5mm material Sn62Pb36Ag2 is chosen, finite element is three-dimensional
Structural model is as shown in Figure 1.
S22, apply different boundary conditions to chip on 3 d structure model.According to S13 determine boundary condition,
Applied respectively on model, as shown in Fig. 2, these condition simulations actual use situation of encapsulating structure, wherein X be X to
Degree-of-freedom Coupling, Y1 are Y-direction Degree-of-freedom Coupling, and Y2 is Y-direction symmetry constraint, and A is fixed constraint.
S23, irregular temperature follows section, the first standard temperature follows section is applied to chip respectively under every arbitrary boundary conditions and the
Two standard temperature follow section.Section is followed according to the irregular temperature that S14 is determined and two standard temperature follow section, is applied to model
On.Specific section is as in Figure 3-5.
S3, finite element simulation post-processing:
S31, the finite element simulation based on S2 determine the plastic strain cloud charts of selected group solder joint, according to selected group of weldering
The plastic strain cloud charts of point determine the minimum plastic strain, maximum plastic strain and strain variation range of solder joint.For
The solder joint of diameter 0.5mm material Sn62Pb36Ag2, takes one of solder joint plasticity cloud charts as shown in Figure 6.Attached drawing mark in figure
Note 2 is solder joint, and it is γ that minimum plastic strain can be obtained from figuremin=130176, maximum plastic strain γmax=
20700000, strain variation range is Δ γ=γmax-γmin=2.06 × 107。
S32, mechanics strain and the relationship of the resistance-strain of solder joint thermal damage and the electricity of multiple groups solder joint for determining solder joint layer
Resistance rate.According to the mechanics strain and solder joint heat of document " thermal damage's electrical measurement of Lead-Free Solder Joint is theoretical and applies " available solder joint layer
The resistance-strain of damage has following theory relation:
εR=(SR0+kρ0ΔT)(Fp+Ffp+FΔT), (1)
Wherein:
Wherein, εRFor the resistance-strain of solder joint, ρ is the resistivity of solder joint, R0Not apply initial resistance when temperature follows section
Value, S are the cross-sectional area of solder joint, and h is solder joint height, and L is solder joint length, and N is recurring number, and Δ T is Wen great little, and index β is usual
Taking 0.5, k is the recycle ratio that maximum stress is in cycle period, usually 0.3, γminFor minimum strain value, Δ γ is
Plastic strain variation range, C are material constant, and for the eutectic solder being widely used, C takes 0.16, by seeking equation group, just
It can obtain the value of solder joint resistance R.
The resistivity that can determine each material solder joint referring to GB/T 3131-2001, such as the solder joint that material is Sn62Pb36Ag2
Resistivity is 1.41 × 10-7Ω/m。
S33, cross-sectional area, solder joint height, solder joint length and the temperature change for determining the selected group of solder joint emulated,
Selected group solder joint resistance value is calculated, added in series is carried out to selected group of solder joint resistance value, obtains the resistance of each daisy chain
Simulation value, and calibrated according to the corresponding resistance value measured of testing of selected group of solder joint to the resistance value obtained is emulated, and
3 d structure model after to calibration.The model established by S21, be calculated automatically from the cross-sectional area of solder joint, solder joint height and
Solder joint length, temperature change are the variation range of the temperature loading loaded, are post-processed, are calculated in ANSYS APDL
Solder joint resistance value to diameter 0.5mm material Sn62Pb36Ag2 is 4.08 × 10-3The connection of Ω, daisy chain T1, T2, T3 are as schemed
Shown in 7, according to the connection type butt welding point resistance added in series of Fig. 7, the resistance simulation value of each daisy chain is obtained.Pass through school
Standard, each daisy chain simulation value and measured value deviation are within 5%.
S34, using 3 d structure model after check, remaining all groups solder joint is emulated, and obtain emulation data.
Using model after check, carry out simulation analysis again, under three kinds of load-up conditions the simulation value of each group solder joint and with measured value
Deviation controls within 5%, wherein tri- daisy chain emulation of T1, T2, T3 of diameter 0.5mm material Sn62Pb36Ag2 solder joint
Value and measured value with recurring number change curve as seen in figs. 8-10.
S4, the solder joint uneven cumulative damage expression formula that irregular temperature is followed under section is determined:
S41, the form for determining the solder joint uneven cumulative damage rule that irregular temperature is followed under section, such as expression formula (7) institute
Show:
Wherein N is that irregular temperature follows recurring number estimated value when chip sample under section reaches failure；N1 is the first standard
Temperature follows recurring number when chip sample under section reaches failure；When N2 is that the second standard temperature follows that chip sample reaches failure under section
Recurring number；A, b is parameter to be fitted.A, the relationship of b and N1, N2 are as follows:
Wherein n1 and n2 is that chip sample reaches identical damage in the case where the first standard temperature follows section and the second standard temperature follows section
Recurring number when wound amount.
S42, parameter a and ruler in the corresponding uneven cumulative damage rule of the solder joint of multiple groups difference size and material are determined
Very little parameter b value.According to emulation data it can be concluded that recurring number N of each group solder joint when failing under two standard temperature follow section1、N2,
A series of recurring number n and in overall process, when solder joint damage amount is identical under two sections1、n2, further according to a obtained in S41,
B and N1、N2、n1、n2Relational expression the simulation result of the various sizes of solder joint of different materials is intended using least square method
It closes, obtains the match value of parameter a and b, the elasticity modulus and fatigue strength coefficient of different materials can directly be looked by Materials Handbook
, as shown in table 3.
Parameter a and the b match value of 3 four kinds of table, four kinds of material size solder joint
The influence and dimensional parameters b of S43, the material for determining different solder joints and size to parameter a value and dimensional parameters b value
With the relationship of material constant.The a value that different welding materials and size are extracted by table 3 makes the material and ruler of parameter a value and solder joint
Very little relational graph, as shown in figure 11, wherein abscissa is different sizes and different materials.It is obtained by figure, parameter a value is not welded
The material of point and the influence of size.By examining, parameter a meets that normal distribution is as shown in figure 12, the wherein expectation of parameter a
2.803 standard deviation is 0.03124.
The b value that different welding materials and size are extracted by table 3, makes the material of parameter b value and solder joint and the relationship of size
Figure, as shown in figure 13, wherein abscissa is different sizes and different materials.As seen from the figure, the situation certain in welding material
Under, parameter b value is not influenced by the size of solder joint.And draw the elasticity modulus of solder joint and the fatigue strength system of solder joint respectively by table 3
The influence curve of several couples of parameter b, as shown in figs. 14-15, as seen from the figure, parameter b value is with solder joint elasticity modulus and fatigue strength system
Several increases and reduce.Visual parameter b value and elasticity modulus of materials E and fatigue strength coefficient σfIt is related.
According to table 3, elasticity modulus and fatigue strength coefficient and corresponding parameter b value are extracted, as shown in table 4.
4 elasticity modulus of table and fatigue strength coefficient and corresponding parameter b value
| Elastic modulus E (GPa) | Fatigue strength coefficient σf(GPa) | Parameter b |
| 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 |
Above data is fitted using Matlab, obtains the pass of parameter b value Yu solder joint elasticity modulus and fatigue strength coefficient
System, such as expression formula (9).Graph of equation picture is as shown in figure 16.
B=c1+c2E+c3σf (9)
Wherein c1=3.28, c2=-0.034, c3=-1.56, E is solder joint elasticity modulus, σfFor welding material fatigue strength
Coefficient, c1,c2,c3For predetermined coefficient, numerical value passes through the multiple groups b value in above table, E value and σfValue, passes through above-mentioned expression
Formula finds out three coefficient solutions using least square method and obtains.
S44, final solder joint uneven cumulative damage rule is determined.The value of parameter a, b in uneven cumulative damage rule
It has been determined that then irregular temperature is followed shown in uneven cumulative damage method such as formula (10) final under section
A~N (2.803,0.031242)
B=c1+c2E+c3σf
c1=3.28, c2=-0.034, c3=-1.56 (10)
Wherein E is solder joint elasticity modulus, σfFor welding material fatigue strength coefficient.The damage accumulation method that the present invention is obtained
It then compares with the linear rule of Miner, experimental result, as shown in table 5.
5 two rules of table and experimental result compare
| Material | Experimental result | The linear rule of Miner | Error | Rule of the present invention | Error |
| 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% |
As it can be seen that the finite element simulation method really reflects external environment when component solder joint place system executes task
The variation of stress, and influence of the welding spot size material to uneven cumulative damage rule is considered, and the rule has been determined
Final expression-form.The uneven cumulative damage rule of complete form more fully, science, rationally, reliability prediction result
Real reliability closer to product is horizontal.
It should be understood that above-described embodiments are merely to illustrate the technical scheme, rather than it is limited
System；Although the present invention is described in detail referring to the foregoing embodiments, those skilled in the art should understand that: its
It can still modify to technical solution documented by previous embodiment, or part of or all technical features are carried out
Equivalent replacement；And these modifications or substitutions, technical solution of various embodiments of the present invention that it does not separate the essence of the corresponding technical solution
Range.
Claims (8)
1. a kind of determine that irregular temperature follows the finite element simulation method that solder joint damage under section accumulates complete rule, feature exists
In: it the described method comprises the following steps:
S1, finite element simulation pre-treatment step, specifically include:
S11, the component part and packaging model for determining finite element 3 d structure model, determine model meshes division mode；
S12, the multiple groups solder joint for choosing different sizes and material, and determine each material parameter；
S13, boundary condition under packaging model is determined, the boundary condition includes symmetrical boundary condition, median surface displacement coupling
Boundary condition and origin fixed-end boundary condition；
S14, temperature load, the temperature loading include that irregular temperature follows section, the first standard temperature follows section and the second mark
Quasi- temperature follows section；
S2, finite element simulation step is carried out to solder joint under different temperatures load, specifically included:
S21, any one group of solder joint is chosen, the finite element 3 d structure model of chip is established for selected group of solder joint；
S22, apply different boundary conditions to chip on the finite element 3 d structure model；
S23, apply that irregular temperature follows section, the first standard temperature follows section and the second mark to chip respectively under every arbitrary boundary conditions
Quasi- temperature follows section；
S3, finite element simulation post-processing step, specifically include:
S31, the finite element simulation based on S2 determine the plastic strain cloud charts of selected group solder joint, according to the plastic strain
Cloud charts determine the minimum plastic strain, maximum plastic strain and strain variation range of solder joint；
S32, mechanics strain and the relationship of the resistance-strain of solder joint thermal damage and the resistivity of multiple groups solder joint for determining solder joint layer；
S33, cross-sectional area, solder joint height, solder joint length and the temperature change for determining the selected group of solder joint emulated are calculated
Selected group solder joint resistance value is obtained, added in series is carried out to selected group of solder joint resistance value, obtains the resistance emulation of each daisy chain
Value, and calibrated according to the corresponding resistance value measured of testing of selected group of solder joint to the resistance value obtained is emulated, and obtain school
3 d structure model after standard；
S34, using 3 d structure model after check, remaining all groups solder joint is emulated, and obtain emulation data；
S4, it determines the solder joint uneven cumulative damage expression formula step that irregular temperature is followed under section, specifically includes:
S41, the form for determining the solder joint uneven cumulative damage rule that irregular temperature is followed under section；
S42, determine that parameter a and size in the corresponding uneven cumulative damage rule of the solder joint of multiple groups difference size and material join
Number b value；
The influence and dimensional parameters b and material of S43, the material for determining different solder joints and size to parameter a value and dimensional parameters b value
Expect the relationship of constant；And
S44, final solder joint uneven cumulative damage rule is determined.
2. the irregular temperature of determination according to claim 1 follows the finite element simulation that solder joint damage under section accumulates complete rule
Method, it is characterised in that: chip finite element 3 d structure model is encapsulated using BGA form in S11, finite element 3 d structure model
Including solder joint, chip, substrate, plastic packaging layer and PcB layers, wherein solder joint is octahedral unit, chip, substrate, plastic packaging layer and
PcB layers are hexahedral element.
3. the irregular temperature of determination according to claim 1 follows the finite element simulation that solder joint damage under section accumulates complete rule
Method, it is characterised in that: the mechanics strain of solder joint layer is as follows with the expression formula of the relationship of the resistance-strain of solder joint thermal damage in S32
It is shown:
εR=(SR0+kρ0ΔT)(Fp+Ffp+FΔT),
Wherein:
εRFor the resistance-strain of solder joint, ρ is the resistivity of solder joint, R0Not apply initial resistance value when temperature follows section, S is weldering
The cross-sectional area of point, h is solder joint height, and L is solder joint length, and N is recurring number, and Δ T is Wen great little, and index β usually takes 0.5, the k to be
It is in the recycle ratio of maximum stress in one cycle period, usually 0.3, γminFor minimum strain value, Δ γ is plastic strain
Variation range, C are material constant, and for the eutectic solder being widely used, C takes 0.16, and by seeking the expression formula, weldering can be obtained
The value of the resistance R of point, so that it is determined that the resistivity of the solder joint of different materials.
4. according to claim 1 or the irregular temperature of determination described in 3 follows solder joint damage under section and accumulates the limited of complete rule
First emulation mode, it is characterised in that: the following institute of form that irregular temperature follows uneven cumulative damage rule under section is determined in S41
Show:
Wherein, N is that irregular temperature follows recurring number estimated value when chip sample under section reaches failure；N1For the first standard Wen Xun
Recurring number when chip sample reaches failure under section；N2Following when chip sample under section reaches failure is followed for the second standard temperature
Number of rings；A, b is parameter to be fitted, a, b and N1、N2Relational expression it is as follows:
Wherein, n1And n2It is that chip sample reaches identical amount of damage in the case where the first standard temperature follows section and the second standard temperature follows section
When recurring number.
5. the irregular temperature of determination according to claim 4 follows the finite element simulation that solder joint damage under section accumulates complete rule
Method, it is characterised in that: can be derived that each group solder joint follows section and the second standard in the first standard temperature according to emulation data in S42
Temperature follows recurring number N when failing under section1、N2, and in whole simulation process, the first standard temperature follows section and the second standard
Temperature follows a series of recurring number n when solder joint damage amount is identical under section1、n2, further according to parameter a, b and N obtained in S411、N2、
n1、n2Relational expression the simulation result of multiple groups difference size and material solder joint is fitted, is joined using least square method
The match value of number a and b.
6. the irregular temperature of determination according to claim 5 follows the finite element simulation that solder joint damage under section accumulates complete rule
Method, it is characterised in that: further include in S43 determining solder joint elasticity modulus and solder joint fatigue strength coefficient to the shadow of parameter b
Curve is rung, wherein parameter b value reduces with the increase of solder joint elasticity modulus and fatigue strength coefficient.
7. the irregular temperature of determination according to claim 6 follows the finite element simulation that solder joint damage under section accumulates complete rule
Method, it is characterised in that: the relationship of parameter b value and solder joint elasticity modulus and welding material fatigue strength coefficient, such as following expression
Shown in formula,
B=c1+c2E+c3σf
Wherein, c1、c2、c3For predetermined coefficient, c1=3.28, c2=-0.034, c3=-1.56, E is solder joint elasticity modulus, σfFor weldering
Point fatigue of materials strength factor.
8. the irregular temperature of determination according to claim 1 follows the finite element simulation that solder joint damage under section accumulates complete rule
Method, it is characterised in that: irregular temperature follows the following institute of expression formula of solder joint uneven cumulative damage method final under section in S44
Show:
A~N (2.803,0.031242)
B=c1+c2E+c3σf
c1=3.28, c2=-0.034, c3=-1.56
Wherein, E is solder joint elasticity modulus, σfFor welding material fatigue strength coefficient, N is that irregular temperature follows chip sample under section
Reach recurring number estimated value when failure；N1Recurring number when chip sample under section reaches failure is followed for the first standard temperature；N2For
Second standard temperature follows recurring number when chip sample under section reaches failure；A, b is parameter to be fitted.
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