Sensitivity Analysis of SAC 305 Solder Polycrystal Mechanical Parameters and Predicted Fatigue Lifetime with Different Grain Structures

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript conducts a meso-scale analysis of lead-free SAC305 solder polycrystals using DAMASK to model grain structure and emulate mechanical loading, aiming to address the limitation of homogeneous material models in finite element-based lifetime estimation. Its main innovation lies in quantifying the significant impact of microstructural parameters on solder joint reliability, providing support for the development of more accurate virtual lifetime estimation methods. Nevertheless, I sincerely hope that the authors will approach this paper with enhanced diligence and attention to detail, and address the following fundamental problems:

1. In the Abstract section, there are some grammatical errors such as ““a lot of case” and “an accurate results”.
2. The manuscript mentions the Oxford-UMAT framework as an FE simulation tool for crystal plasticity (Line82-83) but does not briefly compare its advantages and disadvantages with DAMASK (the tool ultimately used in the study). Thus, a brief comparison with Oxford-UMAT would better justify the tool selection.
3. The manuscript first states "12 different cases of crystal orientation are investigated" (Line135-136) and then mentions "Respect to the different Euler angles 13 different simulations are done"(Line139-140), resulting in an inconsistency between the numbers 12 and 13. Briefly explain the reason for the number to avoid confusing readers.
4. There is a grammatical error in Line164: "the loadcase created for the simulations in every case is a 810 seconds long shearing force" – since "810" starts with a vowel sound, "a" should be replaced with "an".
5. Fig. 2 (a), (c), (e) are Mises stress-strain curves and Fig. 2 (b), (d), (f) are hysteresis curves, but their x-axis (horizontal axis) values are not uniform, lacking comparability. Additionally, what does "Strain [1]" in the x-axis mean, and why is the "[1]" added?
6. In Line 272-273: "it needs to be proven experimentally with physical tests that how the failure criteria will change in the case of changing of the orientation" has an awkward structure – "that how" should be adjusted to "how" to streamline the sentence. Please revise the sentence structure to make the expression more concise and clearer.
7. In Line265&311, there may be an obvious numerical error in the statement "60,200%" this may be be a typo. I think it should be 60.2%, rather than 60,200%.
8. The manuscript improperly applies the journal template: Sections from Section 6 "Patents" to the "Abbreviations" section either remain incomplete or are not tailored to the study; additionally, Appendix A.1 and Appendix B are listed but contain no substantive content.
9. In Section 4, the comparison with the latest peer-reviewed studies is insufficient—currently, only References [6] and [19] are cited to support the discussion on grain orientation and solder joint microstructure, while other relevant recent studies are not integrated into the discussion.
10. The manuscript acknowledges that experimental validation is necessary to address the limitations of existing simulation methods (e.g. Line324-325: "more detailed simulations needed to be done and needed to be validated with measurements") and mentions the difficulty of experiments as a reason for adopting simulation. However, it fails to propose any specific experimental measurement methods. Given that the manuscript references "Electron backscattered diffraction (EBSD) measurement" in Section 1.2 (Line123-124) for grain orientation assessment, it is recommended to supplement specific experimental approaches (e.g., EBSD for microstructure characterization, thermal cycling fatigue tests for lifetime verification) to make the validation proposal more concrete, rather than providing a vague statement.

Author Response

Dear Respected Reviewer,

I have attached the rebuttal letter with the answers to the reviewers question in .pdf format.

Best Regards,
Antal Bakonyi

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript addresses an interesting and relevant topic related to the microstructural effects on the fatigue life of SAC305 solder joints using crystal plasticity simulations. The study is technically coherent and the use of DAMASK and Neper is appropriate for mesoscale modeling. However, the paper in its current form requires substantial improvements before being suitable for publication.

1. Novelty and context: The introduction provides background but lacks a clear identification of the research gap and the specific contribution of this work compared to recent literature. Emphasize what is new in your study.
2. Methods: Provide full details of the simulation parameters (constitutive model, material constants, mesh resolution, time steps, solver settings, convergence criteria). Clarify how the periodic boundary conditions and RVE dimensions influence the results.
3. Validation: The study remains purely numerical. Even a qualitative or literature-based comparison would strengthen confidence in the results.
4. Figures and tables: Many figures are redundant, lack scales or legends, and are difficult to interpret. Consider merging or simplifying them to improve readability.
5. Discussion and conclusions: The discussion is mostly descriptive. Please deepen the interpretation of trends and their physical meaning for real solder joints.
6. Formatting: The manuscript still contains MDPI template placeholders (Funding, Ethics, etc.) that must be removed or completed properly.
   
   
   • What is the main question addressed by the research?
     
         The paper investigates how the grain orientation and grain size distribution of SAC305 solder influence its mechanical response and predicted fatigue lifetime. The study is based entirely on crystal plasticity simulations (using DAMASK and Neper) and aims to explore how microstructural anisotropy affects the fatigue life of solder joints under cyclic shear loading.
     
     
   • Do you consider the topic original or relevant to the field? Does it address a specific gap in the field? Please also explain why this is/ is not the case.
     
         The topic is certainly relevant to the field of electronics reliability and materials engineering, especially as lead-free solders remain a key research area. However, the originality of this work is rather limited. Similar studies using crystal plasticity or finite element approaches have already explored the influence of grain orientation on SAC alloys for instance: https://doi.org/10.1109/ECTC51909.2023.00353 https://doi.org/10.1016/j.jmrt.2023.11.113 This paper repeats a comparable type of analysis without introducing clear methodological innovation or new experimental validation. It does provide some additional data on how increasing grain number tends to make the response more isotropic, but this finding is already qualitatively well established in the literature.
     
     
   • What does it add to the subject area compared with other published material?
     
         The main value of the work lies in offering a consistent comparison between single-crystal and polycrystal simulations with varying grain counts. This might be useful for future calibration of simplified models. Still, the scientific contribution would be stronger if the authors quantified these effects (for example, through sensitivity indices or correlations) and discussed how they could be applied in practical lifetime prediction for solder joints.
     
     
   • What specific improvements should the authors consider regarding the methodology?
     
     
   • Clearly specify the material parameters used for β-Sn (slip systems, hardening law, rate sensitivity, etc.).
   • Include mesh resolution, time step size, solver details, and convergence criteria to ensure reproducibility.
   • Explain the loading setup, including how the shear strain rate corresponds to actual thermal cycling conditions.
   • Discuss the implications and limitations of using periodic boundary conditions and cubic RVEs.
   • If possible, add validation or comparison with published experimental or numerical results to establish credibility.
   • Clarify how the lifetime models (Darveaux and Blattau) were calibrated and why those constants were selected.
    
   • Are the conclusions consistent with the evidence and arguments presented and do they address the main question posed? Please also explain why this is/is not the case.
     
         The conclusions summarize the numerical findings correctly, showing how increasing grain number reduces anisotropy. However, they remain descriptive and do not critically interpret the mechanisms or practical implications. The conclusions are consistent with the presented data but only partially answer the main research question, as the discussion lacks quantitative interpretation and broader relevance to real solder joints.
     
     
   • Are the references appropriate?
     
         Yes. The references are recent and relevant to the field, covering key works on lead-free solder behavior and crystal plasticity modeling. However, the authors rely on them descriptively; a more critical comparison with the most recent studies would improve the contextualization and highlight novelty.
     
     
   • Any additional comments on the tables and figures.
     
         Several figures are redundant or overly similar (e.g., Figures 5–7) and could be merged. Some axes lack units, legends, or clear scales. Image contrast and labeling should be improved for readability. Tables contain useful data but should include units and more informative captions. Overall, graphical presentation needs refinement to meet journal standards.

Overall, the work has potential scientific value but needs significant revision in structure, language, and presentation to meet publication standards.

Comments on the Quality of English Language

The English language should be carefully revised to improve clarity and consistency. The manuscript contains several grammatical and syntactical inaccuracies as well as repetitive or imprecise phrasing. A thorough linguistic revision is recommended to enhance overall readability.

Author Response

Dear Respected Reviewer,

I have attached the rebuttal letter with the answers to the reviewers question in .pdf format.

Best Regards,
Antal Bakonyi

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In this paper, crystal plasticity finite element simulations are done to prove the impacts of the solder material anisotropic behavior to the mechanical behavior and to the estimated lifetime in the case of emulated thermal cycling as shear load cycling. Two different computer tests are presented in this paper based on Darveaux and Blattau estimations.

Some shortcoming and missing of the paper are the following:

1. The order for references is broken in the paper text.
2. The brief description of the subsequent text of the paper should be presented at the end of Introduction.
3. Formulae (1), (2): Where are the deformation characteristics F_e, F_i, F_p found in the text and where (1), (2) used in the paper?
4. (Line 211): What consideration was used to select a shear strain rate?
5. (Line 239): What considerations were used to select constants K₁ = 0, K₂ = 0, K₃ = 0.744833, K₄ = 1? If the constants were selected in advance, then the formulas (5) – (7) lose their meaning and should be replaced with new formulas that consider the constants indicated above.
6. What overall sample geometric sizes were used in the simulation, if a cube size was 100 μm (Line 204) and the final crack length was 500 μm (Line 240)?
7. Formula (8): its form on the paper is irrational. Where the parameters ∆τ and ∆y defined in the text?
8. Page 7: There is irrational text location.
9. Where are formulae in the text, defining the dependence σ_xy vs ϵ _xy (see Figs. 2, 6 – 8, A2)?

Comments on the Quality of English Language

There are numerous English mistakes, therefore, the paper in a whole should be carefully checked and revised. Some examples:

(Line 137): “Electron backscattered diffraction (EBSD) measurement are usually translated…”

(Lines 179, 180): “…every individual crystallites…”

(Lines 202, 203): “…the orientation of the grains are randomly distributed.”

(Line 219): “…there are three different simulation…”

(Line 230): “…two different fatigue model is introduced.”

(Line 253): “…results is presented.”

(Lines 383, 384): “Two different case of test are presented…”

Author Response

Comments and Suggestions for Authors

In this paper, crystal plasticity finite element simulations are done to prove the impacts of the solder material anisotropic behavior to the mechanical behavior and to the estimated lifetime in the case of emulated thermal cycling as shear load cycling. Two different computer tests are presented in this paper based on Darveaux and Blattau estimations.

Some shortcoming and missing of the paper are the following:

Q1: The order for references is broken in the paper text.

Answer: The order of references were broken due to a missed step in the compile process of LaTeX. The order of references are fixed. Very thanks.

Q2: The brief description of the subsequent text of the paper should be presented at the end of Introduction.

Answer: Thank you very much for your remark. We have provided a short summarization of the subsequent text at the end of the introduction chapter.

Q3: Formulae (1), (2): Where are the deformation characteristics F_e, F_i, F_p found in the text and where (1), (2) used in the paper?

Answer: Thank you for your comment. F_e , F_i and F_p are only introduced in the base equation of crystal plasticity modelling, then the plastic flow L_p equation is written. These equations is a brief introduction to the crystal plasticity, we have cited the DAMASK research paper here, where these variables is derived there in detail.

Q4: (Line 211): What consideration was used to select a shear strain rate?

Answer: In our paper we selected the shear strain rate to emulate a thermal cycle from the literature [Ha et al. (2023): „Enhanced solder fatigue life of chip resistor by optimizing solder shape”  https://doi.org/10.1016/j.microrel.2023.114994]. To calculate the actual shear strain rate loading on a BGA we used Blattau analythic fatigue model [Blattau, N. and Hillman, C. “An Engelmaier Model for Leadless Ceramic Chip Devices with Pb-free Solder (2006),” IPC/JEDECLead Free Conference, Santa Clara, CA]., where we calculated what would be the Δy (horizontal thermal expansion mismatch) at the given temperature range, with the given BGA chip and PCB dimensions and material parameters. From Δy with the ramp up and ramp down time the shear strain rate can be calculated. The BGA chip code was RTL9068AAD-V2-CG, which consisted 9x9 solder balls. The Δy is calculated from the CTE (coefficient of thermal expansion) regarding to the [Blattau, N. and Hillman, C. “An Engelmaier Model for Leadless Ceramic Chip Devices with Pb-free Solder (2006),” IPC/JEDECLead Free Conference, Santa Clara, CA] between the two BGA edge in the temperature range which is defined in [Ha et al. (2023): „Enhanced solder fatigue life of chip resistor by optimizing solder shape”  https://doi.org/10.1016/j.microrel.2023.114994]. The strain rate is easily calculated by dividing the calculated Δy with the the ramp time of the temperature cycle. From these steps the 0.0025 1/sec strain rate can be achieved.

Thank you very much for your remark.

Q5: (Line 239): What considerations were used to select constants K₁ = 0, K₂ = 0, K₃ = 0.744833, K₄ = 1? If the constants were selected in advance, then the formulas (5) – (7) lose their meaning and should be replaced with new formulas that consider the constants indicated above.

Answer:  Thank you for your comment. The values of K₁ and K₂ is selected as zero, based on the literature of [Ha et al. (2023): „Enhanced solder fatigue life of chip resistor by optimizing solder shape”  https://doi.org/10.1016/j.microrel.2023.114994]. The following statement based on the literatures of:

[C. Cai, J. Xu, H. Wang, S.B. Park, A comparative study of thermal fatigue life of eutectic sn-bi, hybrid sn-Bi/SAC and SAC solder alloy BGAs, Microelectron. Reliab. 119 (2021), 114065. ]

[E.B. Romdhane, P. Roumanille, A. Gu´ edon-Gracia, S. Pin, P. Nguyen, H. Fr´ emont, Early microstructural indicators of crack initiation in lead-free solder joints under thermal cycling, in: 2021 IEEE 71st Electronic Components and Technology Conference (ECTC), IEEE, 2021, June, pp. 2293–2301. ]

[C. Han, B. Song, Development of life prediction model for lead-free solder at chip resistor, in: 2006 8th Electronics Packaging Technology Conference, IEEE, 2006, December, pp. 781–786. ]

[H.S. Ng, T.Y. Tee, K.Y. Goh, J.E. Luan, T. Reinikainen, E. Hussa, A. Kujala, Absolute and relative fatigue life prediction methodology for virtual qualification and design enhancement of lead-free BGA, in: Proceedings Electronic Components and Technology, 2005. ECTC'05, IEEE, 2005, May, pp. 1282–1291.]

Statement: „Number of cycles crack initiated, N0 is negligible for the solder joint in chip resistor due to relatively smaller number, which is less than 10% of the life time, comparing crack propagation”

For the correct interpretation of Darveaux equation I kept the formulas of (5)-(7) in the written format, and I adjustted the text with the reason for the selection of the values for K₁ and K₂.

Q6: What overall sample geometric sizes were used in the simulation, if a cube size was 100 μm (Line 204) and the final crack length was 500 μm (Line 240)?

Answer: The RVE cube size was chosen to be 100 μm. but in the case of the boundary condition this RVE cube is periodically repeating in every direction as Figure 1 depicts.

The final crack length is the length of crack path on the crack surface of the solder joints. In our case we have chosen for sample the 500 μm size, because it is a common size in the case of BGA joints for the diameter on the critical crack zone. Thank you very much for your comment we have adjusted the text to make clearer explanation.

[Ben Romdhane, E. Microstructural Approach To Evaluate The Reliability Of Lead-Free Electronic Assemblies In Thermome- 483 chanical Fatigue. PhD thesis, Bordeaux University, Bordeaux, France, 2022. Supervised by Frémont H. and Guedon-Gracia, 484 A]

 

Q7: Formula (8): its form on the paper is irrational. Where the parameters ∆τ and ∆y defined in the text?

Answer: Equation (8) comes from the Blattau fatigue model defined in the literature [Blattau, N.; Hillman, C. An Engelmaier Model for Leadless Ceramic Chip Devices with Pb-free Solder. In Proceedings of the 528 IPC/JEDEC Lead Free Conference, Santa Clara, CA, March 2006; pp. 1–14.]. The ∆τ and ∆y are defined below the equation in the text. We have adjusted the text and made clearer definition for the parameters, and introduced the Blattau fatigue model in a more detailed way. Thank you very much for your comment.

 

Q8: Page 7: There is irrational text location.

Answer: We have checked our manuscript and we did not see any irrational text location. However, we have made adjustments on this page regarding to your previous comments Q7.

 

Q9: Where are formulae in the text, defining the dependence σ_xy vs ϵ _xy (see Figs. 2, 6 – 8, A2)?

Answer: The loads are defined in subchapter 2.4. The most important Crystal Plasticity equations which gives the relation between e_xy and sigma_xy are written in (1), (2), (3), (4). To introduce the CP theory and its equations in detail would greatly increase the size of this research. Moreover, the resultant dependence on the mentioned figures can not be defined with an equations, because the dependence is highly impacted on the grain morphology and grain ODF (orientation distribution functions). DAMASK documentation research paper and a book about Crystal Plasticity equations is cited in this paper.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

In the contact technology of electronic components, and not only with the removal of lead from the contact alloy, but the problem of mechanical strength as a function of the number of grains per unit volume of alloy has also remained unstudied and unanalyzed in various conditions (shear and temperature)
In the context of the above, the work presented clarifies very well the behavior of contact alloys from the point of view of the grains (2..16) in the alloy per unit volume under shear stresses.
The behavior of contacts at various temperatures (- 40 degrees Celsius...+ 300 degrees Celsius) remains unstudied and could be the subject of another work by the authors, taking into account the research in the field of Silicon Carbide components

Author Response

Thank you very much for your comment. We will take your advice. In our future works we want to study the effect of the temperature change on the material parameters.

Author Response File: Author Response.pdf

Reviewer 5 Report

Comments and Suggestions for Authors

1) The motivation for conducting a sensitivity analysis on SAC305 is relevant; however, the novelty of the present work is not sufficiently distinguished from existing sensitivity studies on solder alloys. The authors should clearly articulate what new physical insight or methodological advancement this study provides.

2) The description of the crystal plasticity constitutive model lacks sufficient detail to allow reproducibility. Key equations, parameter definitions, and underlying assumptions should be explicitly stated rather than referenced indirectly.

3) The procedure used for generating the different grain structures is not described in enough detail. It is unclear whether the microstructures are statistically representative of real SAC305 joints or idealized constructs.

4) The mesh convergence study is briefly mentioned but not convincingly demonstrated. Quantitative evidence of convergence for stress, strain, and fatigue indicators should be supplied.

5) The physical basis for selecting the specific ranges of mechanical parameters in the sensitivity analysis is not adequately justified. It is unclear whether these ranges correspond to experimentally observed variability.

6) The interaction between anisotropy and grain morphology is discussed qualitatively, but the paper lacks quantitative metrics to assess this interaction rigorously.

7) The fatigue life prediction methodology relies heavily on model parameters whose calibration process is not sufficiently documented. The authors should provide the experimental origin or calibration strategy for these parameters.

8) The statistical robustness of the sensitivity results remains questionable, as the number of realizations per grain structure appears limited. The uncertainty associated with random microstructure generation should be assessed.

9) The authors employ a fatigue indicator parameter (FIP), yet its physical interpretation in relation to actual damage mechanisms in SAC305 is only superficially discussed.

10) The boundary conditions imposed in the finite element model may strongly influence the predicted fatigue life. A justification of these conditions in relation to realistic solder joint service conditions is needed.

11) The thermal–mechanical loading profile appears idealized. It is unclear whether the applied thermal cycling conditions reflect real operating environments of electronic assemblies.

12) The manuscript does not clearly differentiate between elastic anisotropy and plastic anisotropy effects in the reported sensitivity outcomes.

13) Several figures present trends without any error bars or statistical dispersion, making it difficult to assess variability and confidence in the results.

14) The validation of the numerical predictions against experimental fatigue life data is insufficient. At minimum, a qualitative comparison with existing experimental datasets should be included.

15) The resolution of grain orientation distribution functions (ODFs) and their influence on fatigue scatter is not analyzed in depth.

16) The computational cost of the proposed framework is not discussed. This is critical for assessing the practical applicability of the method in industrial design.

17) The authors conclude that certain parameters dominate fatigue life sensitivity; however, this conclusion is not supported by a formal global sensitivity analysis (e.g., Sobol indices).

18) The paper lacks a clear discussion on how grain size distribution, rather than only grain shape, influences fatigue damage accumulation.

19) Several assumptions are made regarding rate-dependent behavior, yet the implications of strain-rate sensitivity on the sensitivity ranking are not explored.

20) The interpretation of crack initiation based solely on FIP localization may be overly simplistic and should be discussed in the context of known crack nucleation mechanisms in SAC305.

21) The role of intermetallic compounds (IMCs) at grain boundaries and their effect on local stress concentration is entirely neglected, despite their known relevance in solder fatigue.

22) The comparison between different grain structures is presented mainly in relative terms; absolute fatigue life values and their consistency with reported experimental lifetimes should be discussed.

23) The manuscript would benefit from a clearer separation between model input uncertainty and inherent microstructural variability.

24) The sensitivity analysis appears to be predominantly local rather than global. The limitations of this approach should be explicitly acknowledged.

25) Some parameters are varied independently despite potential physical coupling (e.g., hardening modulus and saturation stress). This may lead to non-physical parameter combinations.

26) The discussion section tends to restate results without sufficient mechanistic interpretation grounded in dislocation-based deformation physics.

27) The conclusions currently overgeneralize the findings beyond the specific case of SAC305 and the particular microstructural configurations studied.

28) The manuscript would be significantly strengthened by including a clear roadmap for how the proposed sensitivity framework can guide solder joint design optimization or reliability assessment in practice.

Author Response

Comments and Suggestions for Authors

Q1) The motivation for conducting a sensitivity analysis on SAC305 is relevant; however, the novelty of the present work is not sufficiently distinguished from existing sensitivity studies on solder alloys. The authors should clearly articulate what new physical insight or methodological advancement this study provides.

Answer: Thank you very much for your remark. We have modified the introduction part, where we have explicitly written what is the novelty in our present work, and why our studies are different than other mezo-scale simulations related to the reliability of lead-free solder joints.

Regarding to our goal: „The goal of this paper is not only to simulate the strains and stresses, but to extend the analysis to fatigue lifetime, so the anisotropic differences and microstructural effects can be expressed along the axis of fatigue lifetime” Many of research only investigates the grain morphology or deals only with the virtual lifetime estimation from the given/measured out material parameters from samples from shearing or tensile tests. Our goal was to connect the grain morphology and the grain orientation with the fatigue lifetime estimation. This is a key part to understand which is the desired grain morphology and grain orientation to get the best durability from the solder joint against thermomechanical cyclic loading.

Q2) The description of the crystal plasticity constitutive model lacks sufficient detail to allow reproducibility. Key equations, parameter definitions, and underlying assumptions should be explicitly stated rather than referenced indirectly.

Answer:

The scope of this research was to apply crystal plasticity to the field of reliability and failure of lead-free solder joints in microelectronic devices. Introducing crystal plasticity with larger detailment would greatly increase the size of this paper. For this reason the scientific literatures describing DAMASK crystal plasticity implementations are cited in this study, and the most important and applied equations in the simulations (Hardening model, Slip model) are written in the paper.

However, we are agreeing that the underlying assumptions should explicitly stated in our paper, which we add to our paper (for example: twinning is neglected). Thank you for your remark.

 

3) The procedure used for generating the different grain structures is not described in enough detail. It is unclear whether the microstructures are statistically representative of real SAC305 joints or idealized constructs.

Answer: Thank you very much for your remarks. Indeed, we did not clarify that we used NEPER built in functions to generate „idealized” representative volume elements with different grains. We have extended our paper, where we explicitely written that we have used idealized Voronoi Tessellation for the RVEs.

4) The mesh convergence study is briefly mentioned but not convincingly demonstrated. Quantitative evidence of convergence for stress, strain, and fatigue indicators should be supplied.

Answer: Thank you for your comment. We have made modifications in the description of DAMASK solver options. We have added more informations regarding to the DAMASK built in convergence criteria. We have used default convergence criterias with the spectral solver (https://damask-multiphysics.org/documentation/file_formats/numerics.html)

5) The physical basis for selecting the specific ranges of mechanical parameters in the sensitivity analysis is not adequately justified. It is unclear whether these ranges correspond to experimentally observed variability.

Answer:

Thank you very much for your comment, this is a very important review comment. We have added another section in our 2. Chapter Materials and Methods: 2.2. Grain morphology of SAC305 solder joints.

Regarding to the CP material parameters, they are measured out values for every slip systems. These values are constants during the sensitivity tests.

6) The interaction between anisotropy and grain morphology is discussed qualitatively, but the paper lacks quantitative metrics to assess this interaction rigorously.

Answer:

Thank you very much for your comment. This is a limitation of our research. Regarding to our previous response in 5) we have added an extra section in our paper to investigate grain morphologies.

7) The fatigue life prediction methodology relies heavily on model parameters whose calibration process is not sufficiently documented. The authors should provide the experimental origin or calibration strategy for these parameters.

Answer:

Thank you very much for your comment this is another limitation of our paper, that the uncertainity for the crystal plasticity material parameters is unkown. In the case of Beta-Tin there are few measurement, which gives the plastic parameters for every slip system. The CP phenomenological power law model parameters are from a measurement, and this is cited in the research paper.

[Chakraborty, A.; Eisenlohr, P. A full-field crystal plasticity study on how texture and grain structure influences hydrostatic stress 578 in thermally strained β-Sn films. Journal of Applied Physics 2018, 124, 025302. doi:10.1063/1.5029933.]

8) The statistical robustness of the sensitivity results remains questionable, as the number of realizations per grain structure appears limited. The uncertainty associated with random microstructure generation should be assessed.

Answer: Thank you for your comment. This is a limitation of our study. We have added extra information regarding to the RVE model creation parameters in NEPER software. We have used Voronoi tessellation so the resultant grain shapes was idealized. More realizations would give more accurate results regarding to the uncertainity.

9) The authors employ a fatigue indicator parameter (FIP), yet its physical interpretation in relation to actual damage mechanisms in SAC305 is only superficially discussed.

Thank you for your comment. In both of the cases of the fatigue models the inputs were either the dissipated energy accumulated on a cycle or the maximum stresses and strains. In the case of Darveaux fatigue model there is connection between the crack initiation and crack propagation and between the dissipated energy during thermomechanical cycle. In the case of Blattau fatigue model, the fatigue indicator parameter is also related to the result from the multiplication of stress and strain range.

[ Darveaux, R. Effect of simulation methodology on solder joint crack growth correlation. In Proceedings of the 50th Elec- 583 tronic Components and Technology Conference (Cat. No.00CH37070), Las Vegas, NV, USA, 21-24 May 2000; pp. 1048–1058. 584 doi:10.1109/ECTC.2000.853299. 585 ]

[ Darveaux, R. Effect of Simulation Methodology on Solder Joint Crack Growth Correlation and Fatigue Life Prediction. Journal of 586 Electronic Packaging 2002, 124, 147–154. doi:10.1115/1.1413764]

[Blattau, N. and Hillman, C. “An Engelmaier Model for Leadless Ceramic Chip Devices with Pb-free Solder (2006),” IPC/JEDECLead Free Conference, Santa Clara, CA]

 

 

 

10) The boundary conditions imposed in the finite element model may strongly influence the predicted fatigue life. A justification of these conditions in relation to realistic solder joint service conditions is needed.

Answer: Yes, this is a limitation of the RVE application with periodical boundary condition. In our future work we want to investigate what is the error risen from simulations with periodical boundary condition with more complex boundary conditions in relation to realistic solder joint service condition.

11) The thermal–mechanical loading profile appears idealized. It is unclear whether the applied thermal cycling conditions reflect real operating environments of electronic assemblies.

Regarding to the physical basis for the loading and temperature cycles:

In our paper we selected the shear strain rate to emulate a thermal cycle from the literature [Ha et al. (2023): „Enhanced solder fatigue life of chip resistor by optimizing solder shape”  https://doi.org/10.1016/j.microrel.2023.114994]. To calculate the actual shear strain rate loading on a BGA we used Blattau analythic fatigue model [Blattau, N. and Hillman, C. “An Engelmaier Model for Leadless Ceramic Chip Devices with Pb-free Solder (2006),” IPC/JEDECLead Free Conference, Santa Clara, CA]., where we calculated what would be the Δy (horizontal thermal expansion mismatch) at the given temperature range, with the given BGA chip and PCB dimensions and material parameters. From Δy with the ramp up and ramp down time the shear strain rate can be calculated. The BGA chip code was RTL9068AAD-V2-CG, which consisted 9x9 solder balls. The Δy is calculated from the CTE (coefficient of thermal expansion) regarding to the [Blattau, N. and Hillman, C. “An Engelmaier Model for Leadless Ceramic Chip Devices with Pb-free Solder (2006),” IPC/JEDECLead Free Conference, Santa Clara, CA] between the two BGA edge in the temperature range which is defined in [Ha et al. (2023): „Enhanced solder fatigue life of chip resistor by optimizing solder shape”  https://doi.org/10.1016/j.microrel.2023.114994]. The strain rate is easily calculated by dividing the calculated Δy with the the ramp time of the temperature cycle. From these steps the 0.0025 1/sec strain rate can be achieved.

Thank you very much for your remark.

12) The manuscript does not clearly differentiate between elastic anisotropy and plastic anisotropy effects in the reported sensitivity outcomes.

Answer: Thank you very much for your remark. We have adjusted the discussion parts. We have removed the differentiations between the elastic and plastic parts, because it is not connected closely to our findings, and more simulation data and investiagion would be needed to clearly differentiate between them.

 

 

13) Several figures present trends without any error bars or statistical dispersion, making it difficult to assess variability and confidence in the results.

Answer: Thank you very much for your insightful comment. This is a limitation of our paper. Due to the small number of realization for simulations we have added the result data in table format in the results chapter and in the appendix.

14) The validation of the numerical predictions against experimental fatigue life data is insufficient. At minimum, a qualitative comparison with existing experimental datasets should be included.

Answer: Thank you for your remark. This is a valid limitation of our study. In our future work we will gather datasets from existing experimental results to get a qualitative comparision.

15) The resolution of grain orientation distribution functions (ODFs) and their influence on fatigue scatter is not analyzed in depth.

Answer: Thank you very much. We have adjusted the introduction chapter and the Pole figures section with the new Grain morphology section regarding to the ODFs and their influence on fatigue scatter.

16) The computational cost of the proposed framework is not discussed. This is critical for assessing the practical applicability of the method in industrial design.

Answer: Thank you very much for your comment. Computational cost is not in the scope of this research, thus we have not analyzed the what was the time cost of the simulations.

17) The authors conclude that certain parameters dominate fatigue life sensitivity; however, this conclusion is not supported by a formal global sensitivity analysis (e.g., Sobol indices).

Answer: Thank you very much for your remark. In the state-of-the-art literature, there are a lot of conlusions, which mention or conclude from measurements and simulation that the microstructure of the solder joints plays an important role in the thermomechanic lifetime, due to the Beta-Tin anisotropic mechanical behaviour. At the same time other factors should not be neglected from the sensitivity, for example:

PCB layout design (other Surface Mounted Componenets placements, PCB material parameters) Chip design (geometric sizes and tolerances for copper pad, solder joints etc.) material impurities-voids, manufacture parameters: reflow tolerances, surface finish of copper pads, coating, etc.

We are agreeing that not only the microstructural factor is dominating the fatigue lifetimes.

Thank you very much for your comment again.

 

18) The paper lacks a clear discussion on how grain size distribution, rather than only grain shape, influences fatigue damage accumulation.

Answer: To investigate different grain shapes and morphologies with different grain growth model is not in the scope of this study. However, in the same time this is a limitation of our study, due to not only the grain size but the grain shapes are a statistical and random parameters even in the case of Voronoi tessellation. As we mentioned earlier we have used the basic NEPER settings for grain size distribution.

We have also add an acknowledgement in the end of the discussion:

„In this study only Voronoi tessellations are used for idealized input geometry, while there is other grain growth models, which are closer to reality and more realistic geometries can give more accurate results, for example the SAC305 solder in BGA joints solidificates with dendritic structure and can give more accurate results.”

[BenRomdhane, E. Microstructural Approach To Evaluate The Reliability Of Lead-Free Electronic Assemblies In Thermome- 543 chanical Fatigue. PhD thesis, Bordeaux University, Bordeaux, France, 2022. Supervised by Frémont H. and Guedon-Gracia, 544 A.]

19) Several assumptions are made regarding rate-dependent behavior, yet the implications of strain-rate sensitivity on the sensitivity ranking are not explored.

Answer: Thank you very much for your comment. Strain-rate sensitivity has really an important effect ont he solder joints thermomechanical lifetime. However, the analysis of strain rate sensitivity is not in the scope of this study.

20) The interpretation of crack initiation based solely on FIP localization may be overly simplistic and should be discussed in the context of known crack nucleation mechanisms in SAC305.

Answer: Thank you very much for your remark. This is an important topic in finite element analysis. Until the present day a mezoscale solver, which can calculate with crack nucleation and propagation combined with grain boundries in 3D is still under developement. Calculating FIP on localized values are truly overly simplistic. For this reason we calculated with the averaged values on the RVEs volume. This type of averaging are used in other virtual lifetime estimation, as [Ha et al. (2023): „Enhanced solder fatigue life of chip resistor by optimizing solder shape”  https://doi.org/10.1016/j.microrel.2023.114994] where sets of volume portions were investigated with averaged dissipated energy values as input for the Darveaux fatigue model.

Moreover, in the case of energy-based fatigue models or in the case of damage-based fatigue model like Darveaux, where the FIP is the dissipated energy density on a certain volume or point, the crack nucleation phase is neglected . In [Ha et al. (2023): „Enhanced solder fatigue life of chip resistor by optimizing solder shape”  https://doi.org/10.1016/j.microrel.2023.114994] the Darveaux is applied with the K₁ and K₂ constants chosen to be zero because of the following statements based on measurements from literatures: „Number of cycles crack initiated, N0 is negligible for the solder joint in chip resistor due to relatively smaller number, which is less than 10% of the life time, comparing crack propagation”

[C. Cai, J. Xu, H. Wang, S.B. Park, A comparative study of thermal fatigue life of eutectic sn-bi, hybrid sn-Bi/SAC and SAC solder alloy BGAs, Microelectron. Reliab. 119 (2021), 114065.]

[ E.B. Romdhane, P. Roumanille, A. Gu´ edon-Gracia, S. Pin, P. Nguyen, H. Fr´ emont, Early microstructural indicators of crack initiation in lead-free solder joints under thermal cycling, in: 2021 IEEE 71st Electronic Components and Technology Conference (ECTC), IEEE, 2021, June, pp. 2293–2301.]

[C. Han, B. Song, Development of life prediction model for lead-free solder at chip resistor, in: 2006 8th Electronics Packaging Technology Conference, IEEE, 2006, December, pp. 781–786. ]

[ H.S. Ng, T.Y. Tee, K.Y. Goh, J.E. Luan, T. Reinikainen, E. Hussa, A. Kujala, Absolute and relative fatigue life prediction methodology for virtual qualification and design enhancement of lead-free BGA, in: Proceedings Electronic Components and Technology, 2005. ECTC'05, IEEE, 2005, May, pp. 1282–1291.]

For this reason the the crack nucleation is not investigated in our study. However, I am agreeing that in the future the crack nucleation mechanism should not be excluded from the virtual lifetime estimation method.

 

 

21) The role of intermetallic compounds (IMCs) at grain boundaries and their effect on local stress concentration is entirely neglected, despite their known relevance in solder fatigue.

Answer:

Thank you very much for your remark. The SAC305 solder joints composed in around 85% are Beta-Sn so the base of modeling was to understand ther primary phase mechanical behaviour under the loading. Modeling IMC boundaries is a very difficult job, since the crystal plastic parameters are not measured out yet, and the IMC between the grains and on the solder-copper pad connections are dynamically changing during the lifetime: IMC layer growth. We written the acknowledgement in our paper, that neglecting the IMCs effect at the grain boundaries is a model inaccuracy.

 

22) The comparison between different grain structures is presented mainly in relative terms; absolute fatigue life values and their consistency with reported experimental lifetimes should be discussed.

Answer: The absolute fatigue lifetime values are very difficult to interpret and compare with other experimental lifetimes, since in the field of microelectronics reliability in the topic of solder joint lifetime estimation, the experiments and the tuning of fatigue models are very test specific. The absolute fatigue lifetimes from experiment can be different due to the different load, different chip geometries, to the different PCB layout, and due to the different soldering and manufacturing processes.

[Depiver, J.A.; Mallik, S.; Amalu, E.H. Thermal fatigue life of ball grid array (BGA) solder joints made from different alloy 526 compositions. Engineering Failure Analysis 2021, 125, 105447,. doi:10.1016/j.engfailanal.2021.105447.]

 

23) The manuscript would benefit from a clearer separation between model input uncertainty and inherent microstructural variability.

Answer: Thank you very much. We have adjusted our text to make a clearer separation between the uncertainities of the model input and the inherent microstructural variability in the case of NEPER microstructure generating settings.

24) The sensitivity analysis appears to be predominantly local rather than global. The limitations of this approach should be explicitly acknowledged.

Answer: Thank you very much. We have acknowledged that our sensitivity analysis is local and concentrated to few microstructural parameters.

 

25) Some parameters are varied independently despite potential physical coupling (e.g., hardening modulus and saturation stress). This may lead to non-physical parameter combinations.

Answer: The hardening moduli and saturation stress values are given in the appendix for the Beta-Tin material parameters slip-system-wise. These parameters are measured out from the literature. These values are constant and not varied during the simulation. The resultant saturation stress and the hardening moduli

26) The discussion section tends to restate results without sufficient mechanistic interpretation grounded in dislocation-based deformation physics.

Answer: Thank you for you comment. A depth interpretation of the results in dislocation density-based deformation physic is not in the scope of this research. Dislocation density based evaluation is a deeper level interpretation of Crystal Plasticity modeling, than the introduced mezo-scale Crystal plasticity, where the slip resistance values are calculated slip-system wise.

27) The conclusions currently overgeneralize the findings beyond the specific case of SAC305 and the particular microstructural configurations studied.

Answer: Thank you very much for your comment. This is very crucial for the paper. We have adjusted and corrected the discussion and conclusion parts where we have written that these results are only valid for this mesoscale crystal plasticity simulation with the modeling simplifications for RVEs. In addition we have written the shortcoming and limitations of the research.

28) The manuscript would be significantly strengthened by including a clear roadmap for how the proposed sensitivity framework can guide solder joint design optimization or reliability assessment in practice.

Answer: Thank you very much for your remark. We have adjusted the 2. Materials and Methods chapter with a text-based roadmap, how can we consider the solder joint microstructure in lifetime estimation. In the Discussion chapter we also written the results of this sensitivity framework, but with the respect to the limitations of the modeling.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I'm truly pleased to see that the majority of the concerns I pointed out have been duly addressed. Nevertheless, there remains some potential for refining the paper:

1. In my view, the phrase "different grain structure" in the title ought to be converted into its plural counterpart, "different grain structures". Meanwhile, the term "lifetime models" listed in the keywords should be adjusted to its singular version, "lifetime model".
2. It is inappropriate to place a comma "," right after the formula in Equation (9).
3. The data presented in Table 1 would be better visualized in the form of a dot-line graph or a bar chart.
4. All instances of the abbreviation "fig." throughout the text should be consistently replaced with "Fig.".
5. The language used in the paper still requires substantial improvement, as exemplified by the text in Lines 355 - 376.
6. There is a typographical mistake in "60,2%" found in Line 389; it should be corrected to 60.2%.
7. Line 408 should be removed.

Author Response

Dear Reviewer,

Thank you very much for your contribution and for your help to improve the paper quality.

We have attached to this letter the Rebuttal document.

Best Regards,

Antal Bakonyi

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have made significant revision. However, what is the link [?] in Line 267?

Comments on the Quality of English Language

There are numerous English mistakes, therefore, the paper in a whole should be carefully checked and revised. Some examples:

(Line 137): “Electron backscattered diffraction (EBSD) measurement are usually translated…”

(Lines 179, 180): “…every individual crystallites…”

(Lines 202, 203): “…the orientation of the grains are randomly distributed.”

(Line 219): “…there are three different simulation…”

(Line 230): “…two different fatigue model is introduced.”

(Line 253): “…results is presented.”

(Lines 383, 384): “Two different case of test are presented…”

Author Response

Comments and Suggestions for Authors

The authors have made significant revision. However, what is the link [?] in Line 267?

Answer: Thank you, it was the citation of (https://doi.org/10.1016/j.microrel.2023.114994), there was a mistype in the citation. At last we have correctly ordered the citations.

 

Comments on the Quality of English Language

There are numerous English mistakes, therefore, the paper in a whole should be carefully checked and revised. Some examples:

(Line 137): “Electron backscattered diffraction (EBSD) measurement are usually translated…”

(Lines 179, 180): “…every individual crystallites…”

(Lines 202, 203): “…the orientation of the grains are randomly distributed.”

(Line 219): “…there are three different simulation…”

(Line 230): “…two different fatigue model is introduced.”

(Line 253): “…results is presented.”

(Lines 383, 384): “Two different case of test are presented…”

Answer: Thank you very much. We have addressed the grammar problems.

Author Response File: Author Response.pdf

Reviewer 5 Report

Comments and Suggestions for Authors

After careful evaluation of the revised manuscript, I confirm that the authors have thoroughly addressed the major revision comments. The paper has been considerably improved in terms of clarity, technical quality, and scientific rigor. The revisions adequately resolve the previously raised concerns, and the manuscript is now suitable and can be accepted for publication.

Author Response

Comments and Suggestions for Authors

After careful evaluation of the revised manuscript, I confirm that the authors have thoroughly addressed the major revision comments. The paper has been considerably improved in terms of clarity, technical quality, and scientific rigor. The revisions adequately resolve the previously raised concerns, and the manuscript is now suitable and can be accepted for publication.

Answer: Dear reviewer, Thank you very much for your constructive comments and remarks! After we carefully rechecked the paper, made some adjustment on the English of the text.

Author Response File: Author Response.pdf