CN113720679B - Method for testing mechanical constitutive equation of micron-size electronic solder - Google Patents

Method for testing mechanical constitutive equation of micron-size electronic solder Download PDF

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Publication number
CN113720679B
CN113720679B CN202110843401.3A CN202110843401A CN113720679B CN 113720679 B CN113720679 B CN 113720679B CN 202110843401 A CN202110843401 A CN 202110843401A CN 113720679 B CN113720679 B CN 113720679B
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solder
micro
stress
displacement
strain
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CN113720679A (en
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秦红波
丁超
秦薇
雷楚宜
杨道国
张国旗
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Guilin University of Electronic Technology
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Guilin University of Electronic Technology
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/08Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N3/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/02Details
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02Details not specific for a particular testing method
    • G01N2203/06Indicating or recording means; Sensing means
    • G01N2203/067Parameter measured for estimating the property
    • G01N2203/0676Force, weight, load, energy, speed or acceleration
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/02Details not specific for a particular testing method
    • G01N2203/06Indicating or recording means; Sensing means
    • G01N2203/067Parameter measured for estimating the property
    • G01N2203/0682Spatial dimension, e.g. length, area, angle

Abstract

The invention discloses a method for testing a mechanical constitutive equation of micron-size electronic solder, which uses a mechanical stretching experiment to obtain a load and displacement relation curve of a nickel wire and a micro-welding spot sample, and then combines simple data post-processing to obtain a real stress and strain relation of the micron-size solder in the micro-welding spot.

Description

Method for testing mechanical constitutive equation of micron-size electronic solder
Technical Field
The invention relates to the technical field of welding spot mechanics test, in particular to a micrometer-size electronic solder mechanics constitutive equation test method.
Background
In the field of microelectronics, most of failures of electronic components are caused by failures of welding spots, and researchers at home and abroad generally adopt experimental and simulation methods to study the mechanical behaviors of the welding spots so as to provide technical guidance for improving the reliability of the welding spots. Compared with an experimental research method, the simulation method can obtain the magnitude and distribution of mechanical parameters such as stress, strain, fracture and the like in the material, so that the failure mechanism of the welding spot can be deeply analyzed. With the recent development of high-density packages, the size of the solder joints has already reached the micrometer size (760 micrometers to 10 micrometers). The solder (solder) is the main component of the solder joint, and when the mechanical finite element simulation is performed on the solder part in the solder joint structure, the constitutive equation of the solder must be input. Constitutive equations are mathematical models reflecting macroscopic properties of a substance, and are functional expressions between stress and strain.
To obtain the stress-strain relationship of the micro-joint material, researchers typically use conventional tensile experiments on a universal tester to measure the solder stress-strain relationship. However, conventional tensile experiments employed bulk as-cast solders (typically in the order of centimeters) of large size. Research shows that after the size of the brazing filler metal reaches the micron level, the crystal state, the organization structure and the mechanical property of the brazing filler metal are changed drastically compared with those of a large brazing filler metal sample, namely, obvious size effect exists, and the mechanical property measured based on the large brazing filler metal sample cannot reflect the stress and strain relation of the micron-sized material.
Therefore, it is difficult to obtain the stress-strain relationship of the solder in the micro solder joints by the conventional tensile test method. Researchers at home and abroad develop a method for combining nanoindentation technology and finite element inversion analysis to obtain a mechanical constitutive equation of the solder. However, this method is extremely cumbersome, requires precise expensive equipment (nanoindenters), has high test costs and theoretical thresholds, and is not easy to operate. This makes it very difficult for researchers to develop mechanical simulations of the micro-pad structure.
Disclosure of Invention
The invention aims to provide a method for testing a mechanical constitutive equation of micron-size electronic solder, and aims to solve the technical problems that the stress and strain relation of solder in a micro-welding spot is difficult and complicated to obtain in the prior art.
In order to achieve the above purpose, the method for testing the mechanical constitutive equation of the micron-sized electronic solder adopted by the invention comprises the following steps:
s1: carrying out a tensile experiment on the nickel wire and the micro-welding spot sample to obtain a load and displacement relation curve of the nickel wire and the micro-welding spot sample;
s2: according to the obtained load and displacement relation curve of the nickel wire and the micro-welding spot sample, subtracting the displacement value of the nickel wire with the corresponding length from the displacement value of the micro-welding spot at the same load to obtain the load and displacement relation curve of the brazing filler metal in the micro-welding spot sample;
s3: converting the load and displacement relation curve of the brazing filler metal into an engineering stress and strain relation curve, and then converting the engineering stress and strain relation curve into a real stress and strain relation curve;
s4: linearly fitting a true stress-strain relation curve of the solder in an elastic stage, and fitting the stress-strain relation curve of the solder in a plastic stage by adopting a power function;
s5: and solving an expression of the stress-strain relation of the solder according to fitting results of stress-strain relation curves of the solder in the elastic stage and the plastic stage.
And (3) carrying out a tensile experiment on the nickel wire and the micro-welding spot sample, and obtaining a load and displacement relation curve of the nickel wire and the micro-welding spot sample:
clamping the nickel wire on a dynamic mechanical stretcher, carrying out a uniaxial stretching experiment on the nickel wire by adopting a displacement loading mode, and carrying out linear fitting on load and displacement data in an elastic stage to obtain a load and displacement relation curve in the elastic stage of the nickel wire;
and clamping the micro-welding spot sample on a dynamic mechanical stretcher, uniaxially stretching the micro-welding spot sample until the micro-welding spot sample breaks by adopting a displacement loading mode, and selecting a relation curve before the micro-welding spot reaches the maximum tension to obtain a load and displacement relation curve of the micro-welding spot sample.
In the step of converting the load and displacement relation curve of the brazing filler metal into the engineering stress and strain relation curve:
using sigma nom =F/A 0 Calculating engineering stress sigma at each data point of solder nom Wherein F is the current tensile load, A 0 Is the initial cross-sectional area of the solder;
using epsilon nom =ΔL/L 0 Calculating engineering strain epsilon at each data point of solder nom Wherein DeltaL is the current displacement of the solder, L 0 Is the initial length of the solder.
In the step of converting the engineering stress and strain relation curve into the real stress and strain relation curve:
using sigma=sigma nom (1+ε nom ) Will sigma nom Converting into true stress sigma;
using ε=ln (1+ε) nom ) Will epsilon nom Converting to true strain epsilon.
Fitting a stress-strain relation curve of the plastic stage of the brazing filler metal by adopting a power function, and obtaining an expression of the stress-strain relation of the plastic stage:
using a power function y=ax n And (5) fitting a stress-strain relation curve of the plastic stage of the solder.
The beneficial effects of the invention are as follows: the real stress and strain relation of the micron-sized brazing filler metal in the micro-welding spots can be obtained by combining a mechanical stretching experiment with simple data post-processing, the experimental process is simple, the data processing is easy, and compared with the prior art, the mechanical stretching test method provided by the invention greatly reduces the cost of constitutive relation test.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flow chart of the steps of the method for testing the mechanical constitutive equation of the micron-sized electronic solder of the present invention.
Fig. 2 is a schematic view of the nickel wire of the present invention.
FIG. 3 is a graph of load versus displacement for a nickel wire of the present invention.
FIG. 4 is a schematic diagram of a Ni/SnBi/Ni micro solder joint according to the present invention.
FIG. 5 is a graph of load versus displacement for Ni/SnBi/Ni micro-pads of the present invention.
Fig. 6 is a graph of load versus displacement for the SnBi solder of the present invention.
Fig. 7 is a graph of true stress versus strain for the SnBi solder of the present invention.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative and intended to explain the present invention and should not be construed as limiting the invention.
The invention discloses a method for testing a mechanical constitutive equation of micron-sized electronic solder, which comprises the following steps:
s1: carrying out a tensile experiment on the nickel wire and the micro-welding spot sample to obtain a load and displacement relation curve of the nickel wire and the micro-welding spot sample;
s2: according to the obtained load and displacement relation curve of the nickel wire and the micro-welding spot sample, subtracting the displacement value of the nickel wire with the corresponding length from the displacement value of the micro-welding spot at the same load to obtain the load and displacement relation curve of the brazing filler metal in the micro-welding spot sample;
s3: converting the load and displacement relation curve of the brazing filler metal into an engineering stress and strain relation curve, and then converting the engineering stress and strain relation curve into a real stress and strain relation curve;
s4: linearly fitting a true stress-strain relation curve of the solder in an elastic stage, and fitting the stress-strain relation curve of the solder in a plastic stage by adopting a power function;
s5: and solving an expression of the stress-strain relation of the solder according to fitting results of stress-strain relation curves of the solder in the elastic stage and the plastic stage.
Specifically, in the step of carrying out a tensile experiment on the nickel wire and the micro-welding spot sample to obtain a load and displacement relation curve of the nickel wire and the micro-welding spot sample:
clamping the nickel wire on a dynamic mechanical stretcher, carrying out a uniaxial stretching experiment on the nickel wire by adopting a displacement loading mode, and carrying out linear fitting on load and displacement data in an elastic stage to obtain a load and displacement relation curve in the elastic stage of the nickel wire;
and clamping the micro-welding spot sample on a dynamic mechanical stretcher, uniaxially stretching the micro-welding spot sample until the micro-welding spot sample breaks by adopting a displacement loading mode, and selecting a relation curve before the micro-welding spot reaches the maximum tension to obtain a load and displacement relation curve of the micro-welding spot sample.
Specifically, in the step of converting the load and displacement relation curve of the brazing filler metal into the engineering stress and strain relation curve:
using sigma nom =F/A 0 Calculating engineering stress sigma at each data point of solder nom Wherein F is the current tensile load, A 0 Is the initial cross-sectional area of the solder;
using epsilon nom =ΔL/L 0 Calculating engineering strain epsilon at each data point of solder nom Wherein DeltaL is the current displacement of the solder, L 0 Is the initial length of the solder.
Specifically, in the step of converting the engineering stress-strain relationship curve into the true stress-strain relationship curve:
using sigma=sigma nom (1+ε nom ) Will sigma nom Converting into true stress sigma;
using ε=ln (1+ε) nom ) Will epsilon nom Converting to true strain epsilon.
Specifically, a power function is adopted to fit a stress-strain relation curve of the plastic stage of the solder, and an expression of the stress-strain relation of the plastic stage is obtained in the steps of:
using a power function y=ax n And (5) fitting a stress-strain relation curve of the plastic stage of the solder.
Specific examples:
this example is the constitutive equation for testing micron-sized SnBi solder in a micro-solder joint sample.
The nickel wire is a commercial pure nickel wire with the length of 10cm and the diameter of 500 mu m. Since commercial nickel wires are not linear, the nickel wires need to be straightened first in order to meet the experimental requirements. However, residual stress is generated during the straightening process, so that the straightened nickel wire needs to be annealed at 660 ℃ for 10 minutes. Then, the annealed linear nickel wire was cut into 2cm pieces for a drawing experiment of the nickel wire and a micro-welding spot sample was prepared. Next, the nickel wire welded end surfaces were sanded in special jigs using 400#, 800#, 1500#, 2000#, 3000# and 5000# series sandpaper and were finished with Al 2 O 3 And polishing by using the particle polishing solution. And (3) welding the two nickel wires with SnBi brazing filler metal in a reflow soldering mode on a special fixture, wherein the welding height is controlled to be 500 mu m, and forming a linear welding spot of the Ni/SnBi/Ni sandwich structure after welding.
The prepared 2cm annealed nickel wire was clamped on a dynamic mechanical stretcher (DMA) with a clamping distance of 8mm (as shown in fig. 2). Then, a uniaxial tension experiment is carried out on the nickel wire by adopting a displacement loading mode of 0.006mm/min to obtain a load and displacement curve of the 8mm nickel wire, and the load and displacement curve of the elastic stage of the nickel wire is linearly fitted (the result is shown in figure 3).
The micro-pad sample was clamped on the DMA at a clamping distance of 8.5mm (as shown in fig. 4). And the micro-welding spot sample is uniaxially stretched until fracture by adopting a displacement loading mode of 0.006mm/min, so that a load and displacement curve of the 8.5mm micro-welding spot sample is obtained, and a curve before the maximum tension is achieved is obtained (as shown in figure 5).
From the results of fig. 3 and 5, it can be seen that the maximum load applied by the micro-pad sample during the stretch-break is less than the load applied when the nickel wire yields, which indicates that the nickel wires at both ends of the micro-pad sample remain in the elastic deformation stage during the stretching of the micro-pad sample of this example. Moreover, experimental results show that the breaking positions of the Ni/SnBi/Ni micro-welding spot samples of the example are all positioned on the brazing filler metal, the yield strength of the pure nickel wires in the example is 164MPa, and the tensile strength of the SnBi is 48MPa, so that the nickel wires at the two ends are still in an elastic deformation stage when the Ni/SnBi/Ni micro-welding spot samples break.
According to the load and displacement curve of the nickel wire in fig. 3, the displacement value of the nickel wire at any load in the elastic stage can be obtained. Then, referring to fig. 3 and 5, at the same load, the displacement value of the SnBi solder in the micro-welding spot sample is obtained by subtracting the displacement value of the corresponding length of the nickel wire from the displacement value of the micro-welding spot sample. All the data points in FIG. 5 are processed according to the method to obtain the load and displacement curve (shown in FIG. 6) of the SnBi solder in the micro-welding spot sample
From the graph of FIG. 6, use is made of sigma nom =F/A 0 Can calculate the engineering stress sigma of the SnBi solder at each data point nom Wherein F is the current tensile load, A 0 Is the initial cross-sectional area of the solder. By epsilon nom =ΔL/L 0 The engineering strain epsilon of the solder at each data point can be calculated nom Wherein DeltaL is the current displacement of the solder, L 0 Is the initial length of the solder. Since the cross-sectional area of the solder changes greatly after plastic deformation, the passing sigma nom =F/A 0 And epsilon nom =ΔL/L 0 And errors exist in the engineering stress-strain relation and the actual stress-strain relation (sigma-epsilon) of the obtained solder. The present example employs σ=σ, respectively nom (1+ε nom ) And epsilon=ln (1+epsilon) nom ) The obtained engineering stress and strain relationship is converted into a real stress and strain relationship, and the obtained real stress and strain relationship curve is obtained (as shown in fig. 7).
According to the SnBi real stress-strain relationship curve, the stress applied when the residual strain is 0.2% is taken as the yield strength (as shown in FIG. 7). Then, the elastic modulus of the solder can be obtained by carrying out linear fitting on the relation curve of the real stress and the strain in the elastic stage, and simultaneously, the power function y=ax is adopted n Fitting a stress-strain relation curve in a plastic stage to obtain fitting parameters a and nAn expression of the relation between stress and strain in the plastic stage can be obtained. And combining fitting results of stress and strain relation curves of the elastic stage and the plastic stage to obtain a stress and strain relation expression of the SnBi solder in the micro-welding spot sample.
The nickel wires with the micron-sized diameters are hardened and straightened, so that the welding of the two sections of nickel wires is facilitated. And (3) annealing the straightened nickel wire to eliminate residual stress caused by the straightening of the nickel wire, so that the load and displacement curve data of the obtained nickel wire are consistent. The real stress and strain relation of the micron-sized brazing filler metal in the micro-welding spots can be obtained by combining a mechanical stretching experiment with simple data post-processing, the experimental process is simple, the data processing is easy, and compared with the prior art, the mechanical stretching test method provided by the invention greatly reduces the cost of constitutive relation test.
The above disclosure is only a preferred embodiment of the present invention, and it should be understood that the scope of the invention is not limited thereto, and those skilled in the art will appreciate that all or part of the procedures described above can be performed according to the equivalent changes of the claims, and still fall within the scope of the present invention.

Claims (4)

1. The method for testing the mechanical constitutive equation of the micron-size electronic solder is characterized by comprising the following steps of:
s1: carrying out a tensile experiment on the nickel wire and the micro-welding spot sample to obtain a load and displacement relation curve of the nickel wire and the micro-welding spot sample; wherein, the straightened nickel wire is annealed at 660 ℃ for 10 minutes;
s2: according to the obtained load and displacement relation curve of the nickel wire and the micro-welding spot sample, subtracting the displacement value of the nickel wire with the corresponding length from the displacement value of the micro-welding spot at the same load to obtain the load and displacement relation curve of the brazing filler metal in the micro-welding spot sample; wherein, a displacement loading mode of 0.006mm/min is adopted to carry out a uniaxial tension experiment on the nickel wire;
s3: converting the load and displacement relation curve of the brazing filler metal into an engineering stress and strain relation curve, and then converting the engineering stress and strain relation curve into a real stress and strain relation curve;
s4: linearly fitting a true stress-strain relation curve of the solder in an elastic stage, and fitting the stress-strain relation curve of the solder in a plastic stage by adopting a power function;
s5: solving an expression of the stress-strain relation of the solder according to fitting results of stress-strain relation curves of the solder in an elastic stage and a plastic stage;
and (3) carrying out a tensile experiment on the nickel wire and the micro-welding spot sample, and obtaining a load and displacement relation curve of the nickel wire and the micro-welding spot sample:
clamping the nickel wire on a dynamic mechanical stretcher, carrying out a uniaxial stretching experiment on the nickel wire by adopting a displacement loading mode, and carrying out linear fitting on load and displacement data in an elastic stage to obtain a load and displacement relation curve in the elastic stage of the nickel wire;
and clamping the micro-welding spot sample on a dynamic mechanical stretcher, uniaxially stretching the micro-welding spot sample until the micro-welding spot sample breaks by adopting a displacement loading mode, and selecting a relation curve before the micro-welding spot reaches the maximum tension to obtain a load and displacement relation curve of the micro-welding spot sample.
2. The method for testing a mechanical constitutive equation of a micron-sized electronic solder according to claim 1, wherein in the step of converting a load versus displacement curve of the solder into an engineering stress versus strain curve:
using sigma nom =F/A 0 Calculating engineering stress sigma at each data point of solder nom Wherein F is the current tensile load, A 0 Is the initial cross-sectional area of the solder;
using epsilon nom =ΔL/L 0 Calculating engineering strain epsilon at each data point of solder nom Wherein DeltaL is the current displacement of the solder, L 0 Is the initial length of the solder.
3. The method of claim 2, wherein the step of converting the engineering stress versus strain curve into a true stress versus strain curve comprises the steps of:
using sigma=sigma nom (1+ε nom ) Will sigma nom Converting into true stress sigma;
using ε=ln (1+ε) nom ) Will epsilon nom Converting to true strain epsilon.
4. The method for testing a mechanical constitutive equation of a micron-sized electronic solder according to claim 3, wherein the step of fitting a power function to a stress-strain relationship curve of a plastic phase of the solder to obtain an expression of the stress-strain relationship of the plastic phase comprises the steps of:
using a power function y=ax n And (5) fitting a stress-strain relation curve of the plastic stage of the solder.
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