Sintered nano-silver full-stage creep deformation and service life prediction method based on entropy increase

Abstract

The invention discloses a sintered nano-silver full-stage creep and life prediction method based on entropy increment, which comprises the following steps: selecting test data of creep-time of sintered nano-silver under different temperatures and different stresses, and extracting creep strain and time, fracture creep and creep fracture time corresponding to the creep strain from the test data; obtaining a curve of damage and time based on the creep strain and the fracture creep corresponding to different time; obtaining a reference damage parameter and a damage index through nonlinear fitting of the relation between the damage and the time based on a definition formula of the damage and the time; and performing creep evolution prediction, creep life prediction and internal porosity evolution prediction of the sintered nano-silver in the creep process in the whole stage of the sintered nano-silver. The method can accurately predict the internal defect evolution and creep property of the sintered nano-silver, and is of great significance to design and reliability prediction of high-power electronic packaging.

Description

Technical Field

[0001] The invention relates to the technical field of creep of sintered nano-silver, and in particular to a method for predicting the full-stage creep and life of sintered nano-silver under different ambient temperatures and stresses. Background Art

[0002] Sintered nanosilver has good thermal conductivity, electrical conductivity and mechanical properties, and is an excellent high-temperature solder for high-power chip packaging. With the application of wide bandgap semiconductor materials in 5G communications, new energy vehicles, military and aviation, the power and junction temperature of devices have increased. In the packaging structure, due to the different thermal expansion coefficients between the components, the thermal stress they bear is uneven, which in turn causes the components in the packaging structure to warp. At this time, the edge of the sintered nanosilver, as a solder layer, is subjected to tensile stress for a long time and faces a severe risk of tensile creep failure. At this time, the creep performance and life of the sintered nanosilver are the key to the reliability of the chip-to-substrate connection. During the sintering process, the solvent in the nanosilver paste is removed, so a large number of pores are generated inside the sintered nanosilver, which makes the creep failure mode of the sintered nanosilver very different from that of traditional solders. The currently commonly used Norton's law can only analyze the steady-state creep rate, and the steady-state creep rate must be used to obtain the creep life through the Monkman–Grant model, and these two models do not have the ability to predict the evolution of internal defects of sintered nanosilver during creep. As a high-power electronic packaging material, accurate prediction of the internal defect evolution and creep properties of sintered nanosilver is of great significance to the design and reliability prediction of high-power electronic packaging. Summary of the invention

[0003] In view of the above-mentioned deficiencies in the prior art, the present invention proposes a full-stage creep and life prediction method for sintered nanosilver based on the entropy increase theory. The method can be used to predict defect evolution, creep evolution curves and creep life of metal materials such as sintered nanosilver during creep failure under different ambient temperatures, different stresses and other working conditions.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] A method for predicting creep and life of sintered nanosilver in all stages based on entropy increase comprises the following steps:

[0006] Step 1: Select the experimental data of creep-time of sintered nanosilver at different temperatures and stresses, and directly extract the creep strain σ from the experimental data. in and its corresponding time t, fracture creep Creep rupture time t r ;

[0007] Step 2: Based on the creep strain and fracture creep corresponding to different times in step 1, obtain the curve of damage D and time t;

[0008] Step 3: Based on the definition of damage and time, the reference damage parameter D is obtained by nonlinearly fitting the relationship between damage and time in step 2. 0 and injury index m;

[0009] Step 4: Predict the creep evolution of sintered nanosilver in all stages, the creep life, and the porosity evolution of sintered nanosilver during the creep process;

[0010] Creep evolution prediction: The fracture creep of sintered nanosilver under the desired working conditions and creep rupture time t r Substitute the following formula and assign different values ​​to the variable time t to obtain the creep at different times under this working condition;

[0011]

[0012] Creep life prediction: Any time t and its corresponding creep strain and creep strain rate Substituting into the following formula, the creep rupture time t is obtained r That is the creep life of sintered nanosilver under the corresponding working conditions;

[0013]

[0014] Prediction of the evolution of internal porosity of sintered nanosilver during creep: Substitute the damage of sintered nanosilver obtained in step 2 into the following relationship between porosity and damage, solve the porosity corresponding to different damages, and obtain the porosity change of sintered nanosilver during creep corresponding to the working condition;

[0015]

[0016] Where P is the porosity and c is the material parameter.

[0017] Furthermore, in step 2, the relationship between damage D and time t is:

[0018]

[0019] Among them, Δs is the entropy change at time t relative to the initial time; Δs cr is the entropy change of the whole creep failure process; s is the entropy of the system at time t; s cr and 0 is the entropy of the system at the moment of fracture and the initial moment;

[0020] The relationship between Δs and creep strain is:

[0021]

[0022] Δs cr The relationship with creep strain is:

[0023]

[0024] Where ρ is the material density, T is the absolute temperature, and σ is the stress.

[0025] Furthermore, in step 3, the definition of damage and time is as follows:

[0026]

[0027] Furthermore, in step 1, the test data covers the entire process from initial loading to creep rupture.

[0028] Furthermore, the symmetric mean absolute percentage error is used to evaluate the accuracy of the predicted values ​​of the prediction method.

[0029] Furthermore, the selected time t can be at any stage of creep failure and is not limited to the steady-state creep strain.

[0030] Furthermore, the creep life is directly obtained through a small amount of test data.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] The method of the present invention can be used to predict the defect evolution, creep evolution curve and creep life of metal materials such as sintered nanosilver during creep failure under different ambient temperatures, different stresses and other working conditions. For high-power electronic packaging materials, the method can accurately predict the internal defect evolution and creep performance of sintered nanosilver, which is of great significance to the design and reliability prediction of high-power electronic packaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a full-stage creep and life prediction method for sintered nanosilver based on entropy increase;

[0034] Figure 2 It is a comparison chart of the creep evolution prediction and experimental data of sintered nanosilver;

[0035] Figure 3 This is a comparison chart of the creep life prediction of sintered nanosilver with the Monkman–Grant model and experimental data;

[0036] Figure 4 is the symmetric mean absolute percentage error diagram of the creep life prediction of sintered nanosilver and the Monkman–Grant model;

[0037] Figure 5 This is the porosity evolution diagram of nanosilver sintered at 150℃ and 5MPa. DETAILED DESCRIPTION

[0038] In order to enable those skilled in the art to better understand the specific use of a method for predicting the creep and life of sintered nanosilver at all stages based on entropy increase, the specific implementation process and flow chart of the present invention are given below ( Figure 1 ), and attached result diagram, the scope of application of the present invention is not limited to this case.

[0039] The present invention proposes a method for predicting creep and life of sintered nanosilver in all stages based on entropy increase. The method can be used to predict defect evolution, creep evolution curve and creep life of sintered nanosilver and other metal materials in the creep failure process under different ambient temperatures, different stresses and other working conditions. The method comprises the following steps:

[0040] 1. Define the damage variable corresponding to time t as a variable related to entropy:

[0041]

[0042] Among them, Δs is the entropy change at time t relative to the initial time; Δs cr is the entropy change of the whole creep failure process; s is the entropy of the system at time t; s cr and 0 is the entropy of the system at the moment of fracture and the initial moment.

[0043] The relationship between Δs and creep strain is:

[0044]

[0045] Δs cr The relationship with creep strain is:

[0046]

[0047] Where ρ is the material density, T is the absolute temperature, σ is the stress, and ε in is the creep strain, is the strain at creep rupture (fracture strain).

[0048] 2. Define the relationship between damage variable and time as:

[0049]

[0050] Where: D 0 is the reference damage parameter, m is the damage index, t r is the creep rupture time.

[0051] 3. Combining formula (1) and formula (4), the relationship between creep and time can be defined as:

[0052]

[0053] 4. By taking the derivative of formula (5), the creep life relationship can be defined as:

[0054]

[0055] in: is the creep strain rate.

[0056] 5. Define the relationship between porosity and damage as:

[0057]

[0058] Where: P is the porosity and c is the material parameter.

[0059] First step parameter D 0 Determination of m

[0060] 1.1. Select some experimental data of creep-time of sintered nanosilver at different temperatures and stresses. The experimental data in this case are from the reference (G.Chen, XH Sun, P.Nie, YH Mei, GQ Lu, and X.Chen, "High-temperature creep behavior of low-temperature-sintered nano-silver paste films," Journal of Electronic Materials, vol. 41, pp. 782-790, 2012.). The creep test conditions of sintered nanosilver are shown in Table 1. The data need to cover the whole process from initial loading to creep rupture. The creep strain ε is directly extracted from the above experimental data. in and its corresponding time t, fracture creep Creep rupture time t r .

[0061] 1.2. Substitute the creep ε corresponding to different times in 1.1 in and fracture creep Substituting into formulas (1)-(3), the damage-time curve can be obtained.

[0062] 1.3. Use formula (4) to obtain the parameter D by nonlinearly fitting the relationship between damage and time in 1.2: 0 and m. For the sintered nanosilver under the working conditions in Table 1, the parameter D determined by 1.3 0 and m are 0.56 and 0.32 respectively.

[0063] Table 1 Creep condition information of sintered nanosilver

[0064]

[0065] Second step creep evolution prediction implementation case

[0066] 2.1、The parameter D obtained in step 1.3 0 Substitute and m into formula (5), and then calculate the fracture creep of sintered nanosilver under the working condition to be determined: and creep rupture time t r Substitute it into formula (5). By assigning different values ​​to the variable time t in (5), the creep at different times under this working condition can be obtained.

[0067] The creep of sintered nanosilver obtained using formula (5) is compared with the experimental data. Figure 2 As shown, the experimental data comes from the reference (G. Chen, XH Sun, P. Nie, YH Mei, GQ Lu, and X. Chen, "High-temperature creep behavior of low-temperature-sintered nano-silver paste films," Journal of Electronic Materials, vol. 41, pp. 782-790, 2012.), Figure 2 It shows that the prediction results of the present invention match well with the experimental data.

[0068] Step 3 Creep Life Prediction Implementation Case

[0069] 3.1. Take any time t of sintering nanosilver under the working condition to be determined, and the creep rate at that time and creep strain ε in Substitute the parameter m into formula (6) and solve for t in formula (6): r , which is the creep life of sintered nanosilver under the corresponding working conditions.

[0070] 3.2. The accuracy of the predicted values ​​by a full-stage creep and life prediction method for sintered nanosilver based on entropy increase was evaluated using the symmetric mean absolute percentage error (SMAPE):

[0071]

[0072] in: is the test value of creep life of sintered nanosilver, Model prediction value for the creep life of sintered nanosilver.

[0073] In this case, a full-stage creep and life prediction method for sintered nanosilver based on entropy increase is used to predict the creep life of sintered nanosilver at an ambient temperature of 150°C and stresses of 5, 6, and 7.5 MPa, and the creep life is compared with the experimental data and the creep life obtained by the Monkman–Grant model. Figure 3 As shown, the symmetric mean absolute percentage error is Figure 4 shown.

[0074] The results show that the creep life prediction accuracy of sintered nanosilver obtained by the present invention is significantly higher than that of the Monkman–Grant model. Figure 3 and Figure 4 It is confirmed that the prediction results of the present invention accurately match the experimental data.

[0075] At this point, the advantages of the present invention are embodied in the following two aspects:

[0076] (1) The selected time t can be at any stage of creep failure, unlike the Monkman–Grant model which is restricted to steady-state creep strain.

[0077] (2) Saving a lot of time cost. Traditional creep analysis is used to obtain creep life, which requires a complete creep test and discrete analysis, which consumes a lot of time and manpower costs. However, with the help of the present invention, the creep life can be directly obtained through a small amount of test data.

[0078] Example of prediction of porosity evolution in sintered nanosilver during creep in the fourth step

[0079] 4.1. The parameter c in formula (7) can be obtained by Calculated. Substitute the damage of sintered nanosilver calculated in 1.2 into formula (7). Solve the porosity in formula (7) corresponding to different damages to obtain the porosity change of sintered nanosilver during the creep process corresponding to the working condition. The result is as follows: Figure 5 shown.

[0080] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modification, equivalent replacement and improvement made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for predicting creep and life of sintered nanosilver in all stages based on entropy increase, characterized in that: The steps include: Step 1: Select the experimental data of creep-time of sintered nanosilver at different temperatures and stresses, and directly extract the creep strain ε from the experimental data. in and its corresponding time t, fracture creep Creep rupture time t r ; Step 2: Based on the creep strain and fracture creep corresponding to different times in step 1, obtain the curve of damage D and time t; Step 3: Based on the definition of damage and time, the reference damage parameter D0 and damage index m are obtained by nonlinearly fitting the relationship between damage and time in step 2; Step 4: Predict the creep evolution of sintered nanosilver in all stages, the creep life, and the porosity evolution of sintered nanosilver during the creep process; Creep evolution prediction: The fracture creep of sintered nanosilver under the desired working conditions and creep rupture time t r Substitute the following formula and assign different values ​​to the variable time t to obtain the creep at different times under this working condition; Creep life prediction: Any time t and its corresponding creep strain and creep strain rate Substituting into the following formula, the creep rupture time t is obtained r That is the creep life of sintered nanosilver under the corresponding working conditions; Prediction of the evolution of internal porosity of sintered nanosilver during creep: Substitute the damage of sintered nanosilver obtained in step 2 into the following relationship between porosity and damage, solve the porosity corresponding to different damages, and obtain the porosity change of sintered nanosilver during creep corresponding to the working condition; Where P is the porosity and c is the material parameter.

2. The method for predicting the creep and life of sintered nanosilver in all stages based on entropy increase according to claim 1, characterized in that: In step 2, the relationship between damage D and time t is: Among them, Δs is the entropy change at time t relative to the initial time; Δs cr is the entropy change of the whole creep failure process; s is the entropy of the system at time t; s cr and s0 are the entropies of the system at the moment of rupture and the initial moment; The relationship between Δs and creep strain is: Δs cr The relationship with creep strain is: Where ρ is the material density, T is the absolute temperature, and σ is the stress.

3. The method for predicting the creep and life of sintered nanosilver in all stages based on entropy increase according to claim 1, characterized in that: In step 3, the damage and time are defined as follows:

4. The method for predicting the creep and life of sintered nanosilver in all stages based on entropy increase according to claim 1, characterized in that: In step 1, the test data covers the entire process from initial loading to creep rupture.

5. The method for predicting the creep and life of sintered nanosilver in all stages based on entropy increase according to claim 1, characterized in that: The symmetric mean absolute percentage error was used to evaluate the accuracy of the predicted values ​​of the prediction method.

6. The method for predicting creep and life of sintered nanosilver in all stages based on entropy increase according to claim 1, characterized in that: The selected time t can be at any stage of creep failure and is not limited to the steady-state creep strain.

7. The method for predicting the creep and life of sintered nanosilver in all stages based on entropy increase according to claim 1, characterized in that: The creep life can be directly obtained through a small amount of test data.

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