Application of the Phase Field Approach for Crack Propagation in Viscoelastic Solid Materials under Thermal Stress: A Case Study of Solder Fracturing
DOI:
https://doi.org/10.37934/arnht.28.1.94108Keywords:
Phase field model, Thermal fracturing, Viscoelasticity, Solder cracking, Adaptive mesh refinementAbstract
To date, solder has been a crucial component for interconnecting circuit boards (PCBs) and electronic components in the electronics industry. However, solder faces certain challenges, such as cracking due to thermal changes. This paper investigates solder cracking under thermal expansion. We employ a phase field model to study crack propagation under thermal stress in a square domain and in solder with a fillet shape. The model is based on those proposed by Takaishi-Kimura and Alfat, where the stress and strain tensors are modified to account for variations in the temperature field. In this study, we consider the solder material to be viscoelastic, while the other materials are treated as homogeneous and isotropic. A numerical example is computed using the adaptive mesh finite element method, with the code implemented in FreeFEM software. The results of this study are in good agreement with previous numerical and experimental findings.
Downloads
References
Anam, Khairul, Anindito Purnowidodo, and Hastono Wijaya. "The Effect of Fluid Temperature and Crack Size toward Stress Intensity Factor on Geothermal Pipe Installations." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 54, no. 1 (2019): 27-36.
Sokolnikoff, I. S., and E. S. Sokolnikoff. "Thermal stresses in elastic plates." Transactions of the American Mathematical Society 45, no. 2 (1939): 235-255. https://doi.org/10.1090/S0002-9947-1939-1501989-8 DOI: https://doi.org/10.1090/S0002-9947-1939-1501989-8
Tanaka, Hirokazu, Yuuichi Aoki, and Shigeharu Yamamoto. "The mechanism of solder cracking." Report 2 in ESPEC Technology Report (1997): 1997.
De Vries, J. W. C., M. Y. Jansen, and W. D. Van Driel. "On the difference between thermal cycling and thermal shock testing for board level reliability of soldered interconnections." Microelectronics Reliability 47, no. 2-3 (2007): 444-449. https://doi.org/10.1016/j.microrel.2006.05.009 DOI: https://doi.org/10.1016/j.microrel.2006.05.009
Lee, W. W., L. T. Nguyen, and Guna S. Selvaduray. "Solder joint fatigue models: review and applicability to chip scale packages." Microelectronics reliability 40, no. 2 (2000): 231-244. https://doi.org/10.1016/S0026-2714(99)00061-X DOI: https://doi.org/10.1016/S0026-2714(99)00061-X
Chen, S. C., Yi-Cheng Lin, and C. H. Cheng. "The numerical analysis of strain behavior at the solder joint and interface in a flip chip package." Journal of Materials Processing Technology 171, no. 1 (2006): 125-131. https://doi.org/10.1016/j.jmatprotec.2005.06.061 DOI: https://doi.org/10.1016/j.jmatprotec.2005.06.061
Richardson, Casey L., Jan Hegemann, Eftychios Sifakis, Jeffrey Hellrung, and Joseph M. Teran. "An XFEM method for modeling geometrically elaborate crack propagation in brittle materials." International Journal for Numerical Methods in Engineering 88, no. 10 (2011): 1042-1065. https://doi.org/10.1002/nme.3211 DOI: https://doi.org/10.1002/nme.3211
Kimura, Masato, Takeshi Takaishi, Sayahdin Alfat, Takumi Nakano, and Yoshimi Tanaka. "Irreversible phase field models for crack growth in industrial applications: thermal stress, viscoelasticity, hydrogen embrittlement." SN Applied Sciences 3, no. 9 (2021): 781. https://doi.org/10.1007/s42452-021-04593-6 DOI: https://doi.org/10.1007/s42452-021-04593-6
Ambati, Marreddy, Tymofiy Gerasimov, and Laura De Lorenzis. "A review on phase-field models of brittle fracture and a new fast hybrid formulation." Computational Mechanics 55 (2015): 383-405. https://doi.org/10.1007/s00466-014-1109-y DOI: https://doi.org/10.1007/s00466-014-1109-y
Francfort, Gilles A., and J-J. Marigo. "Revisiting brittle fracture as an energy minimization problem." Journal of the Mechanics and Physics of Solids 46, no. 8 (1998): 1319-1342. https://doi.org/10.1016/S0022-5096(98)00034-9 DOI: https://doi.org/10.1016/S0022-5096(98)00034-9
Bourdin, Blaise, Gilles A. Francfort, and Jean-Jacques Marigo. "Numerical experiments in revisited brittle fracture." Journal of the Mechanics and Physics of Solids 48, no. 4 (2000): 797-826. https://doi.org/10.1016/S0022-5096(99)00028-9 DOI: https://doi.org/10.1016/S0022-5096(99)00028-9
Kimura, Masato, and Takeshi Takaishi. "A phase field approach to mathematical modeling of crack propagation." A Mathematical Approach to Research Problems of Science and Technology: Theoretical Basis and Developments in Mathematical Modeling (2014): 161-170. https://doi.org/10.1007/978-4-431-55060-0_13 DOI: https://doi.org/10.1007/978-4-431-55060-0_13
Miehe, Christian, Martina Hofacker, and Fabian Welschinger. "A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits." Computer Methods in Applied Mechanics and Engineering 199, no. 45-48 (2010): 2765-2778. https://doi.org/10.1016/j.cma.2010.04.011 DOI: https://doi.org/10.1016/j.cma.2010.04.011
Spatschek, Robert, Efim Brener, and Alain Karma. "Phase field modeling of crack propagation." Philosophical Magazine 91, no. 1 (2011): 75-95. https://doi.org/10.1080/14786431003773015 DOI: https://doi.org/10.1080/14786431003773015
Anderson, Daniel M., Geoffrey B. McFadden, and Adam A. Wheeler. "A phase-field model of solidification with convection." Physica D: Nonlinear Phenomena 135, no. 1-2 (2000): 175-194. https://doi.org/10.1016/S0167-2789(99)00109-8 DOI: https://doi.org/10.1016/S0167-2789(99)00109-8
Echebarria, Blas, Roger Folch, Alain Karma, and Mathis Plapp. "Quantitative phase-field model of alloy solidification." Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 70, no. 6 (2004): 061604. https://doi.org/10.1103/PhysRevE.70.061604 DOI: https://doi.org/10.1103/PhysRevE.70.061604
Wang, S-L., R. F. Sekerka, A. A. Wheeler, B. T. Murray, S. R. Coriell, RJea Braun, and GB1245661 McFadden. "Thermodynamically-consistent phase-field models for solidification." Physica D: Nonlinear Phenomena 69, no. 1-2 (1993): 189-200. https://doi.org/10.1016/0167-2789(93)90189-8 DOI: https://doi.org/10.1016/0167-2789(93)90189-8
Kobayashi, Ryo. "Modeling and numerical simulations of dendritic crystal growth." Physica D: Nonlinear Phenomena 63, no. 3-4 (1993): 410-423. https://doi.org/10.1016/0167-2789(93)90120-P DOI: https://doi.org/10.1016/0167-2789(93)90120-P
Tóth, Gyula I., György Tegze, Tamás Pusztai, Gergely Tóth, and László Gránásy. "Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2D and 3D." Journal of Physics: Condensed Matter 22, no. 36 (2010): 364101. https://doi.org/10.1088/0953-8984/22/36/364101 DOI: https://doi.org/10.1088/0953-8984/22/36/364101
Nonomura, Makiko. "Study on multicellular systems using a phase field model." PloS one 7, no. 4 (2012): e33501. https://doi.org/10.1371/journal.pone.0033501 DOI: https://doi.org/10.1371/journal.pone.0033501
Yang, Xiaofeng, Yi Sun, and Qi Wang. "A phase field approach for multicellular aggregate fusion in biofabrication." Journal of biomechanical engineering 135, no. 7 (2013): 071005. https://doi.org/10.1115/1.4024139 DOI: https://doi.org/10.1115/1.4024139
Liu, Chun, and Jie Shen. "A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method." Physica D: Nonlinear Phenomena 179, no. 3-4 (2003): 211-228. https://doi.org/10.1016/S0167-2789(03)00030-7 DOI: https://doi.org/10.1016/S0167-2789(03)00030-7
Jacqmin, David. "Calculation of two-phase Navier–Stokes flows using phase-field modeling." Journal of computational physics 155, no. 1 (1999): 96-127. https://doi.org/10.1006/jcph.1999.6332 DOI: https://doi.org/10.1006/jcph.1999.6332
Shen, C., and Y. Wang. "Phase field model of dislocation networks." Acta materialia 51, no. 9 (2003): 2595-2610. https://doi.org/10.1016/S1359-6454(03)00058-2 DOI: https://doi.org/10.1016/S1359-6454(03)00058-2
Sarkar, Subrato, Indra Vir Singh, and B. K. Mishra. "A Thermo-mechanical gradient enhanced damage method for fracture." Computational Mechanics 66 (2020): 1399-1426. https://doi.org/10.1007/s00466-020-01908-z DOI: https://doi.org/10.1007/s00466-020-01908-z
Alfat, Sayahdin, Masato Kimura, and Alifian Mahardhika Maulana. "Phase field models for thermal fracturing and their variational structures." Materials 15, no. 7 (2022): 2571. https://doi.org/10.3390/ma15072571 DOI: https://doi.org/10.3390/ma15072571
Alfat, Sayahdin. "On energy-consistency principle of PFM for thermal fracturing in thermoviscoelasticity solids and its application for modeling thermal response due to crack growth based on adaptive mesh technique." Computers & Mathematics with Applications 175 (2024): 107-118. https://doi.org/10.1016/j.camwa.2024.09.016 DOI: https://doi.org/10.1016/j.camwa.2024.09.016
Alfat, Sayahdin. "Phase Field Model for Crack Propagation and its Extension to Thermoelasticity and Poroelasticity: Thermal Fracturing, Hydraulic Fracturing, and Desiccation Cracking." PhD diss., Ph. D. thesis, Kanazawa University, 2023.
Billotte, Catherine, Pierre J. Carreau, and Marie-Claude Heuzey. "Rheological characterization of a solder paste for surface mount applications." Rheologica Acta 45 (2006): 374-386. https://doi.org/10.1007/s00397-005-0053-3 DOI: https://doi.org/10.1007/s00397-005-0053-3
Durairaj, R., S. Ramesh, S. Mallik, A. Seman, and N. Ekere. "Rheological characterisation and printing performance of Sn/Ag/Cu solder pastes." Materials & Design 30, no. 9 (2009): 3812-3818. https://doi.org/10.1016/j.matdes.2009.01.028 DOI: https://doi.org/10.1016/j.matdes.2009.01.028
Mukherjee, Subhasis, Mohammed Nuhi, Abhijit Dasgupta, and Mohammad Modarres. "Creep constitutive models suitable for solder alloys in electronic assemblies." Journal of electronic packaging 138, no. 3 (2016): 030801. https://doi.org/10.1115/1.4033375 DOI: https://doi.org/10.1115/1.4033375
Liu, Wenning, and Frank G. Shi. "Effect of the viscoelastic behavior of molding compounds on crack propagation in IC packages." In 52nd Electronic Components and Technology Conference 2002.(Cat. No. 02CH37345), pp. 854-858. IEEE, 2002. 10.1109/ECTC.2002.1008200 DOI: https://doi.org/10.1109/ECTC.2002.1008200
Bui, Huy Duong, and Stéphanie Chaillat. "On a nonlinear inverse problem in viscoelasticity." Vietnam Journal of Mechanics 31, no. 3-4 (2009): 211-219. https://doi.org/10.15625/0866-7136/31/3-4/5649 DOI: https://doi.org/10.15625/0866-7136/31/3-4/5649
Lakes, Roderic S. Viscoelastic Solids (1998). CRC press, 2017.
Weinberg, Kerstin, Tim Dally, Stefan Schuß, Marek Werner, and Carola Bilgen. "Modeling and numerical simulation of crack growth and damage with a phase field approach." GAMM‐Mitteilungen 39, no. 1 (2016): 55-77. https://doi.org/10.1002/gamm.201610004 DOI: https://doi.org/10.1002/gamm.201610004
Halouani, Ayda, Abel Cherouat, Mariem Miladi Chaabane, and Mohamed Haddar. "Modeling and experimental investigation of damage initiation and propagation of LQFP package under thermal cycle." Microsystem Technologies 26 (2020): 3011-3021. https://doi.org/10.1007/s00542-020-04884-9 DOI: https://doi.org/10.1007/s00542-020-04884-9
Hecht, Frédéric. "New development in FreeFem++." Journal of numerical mathematics 20, no. 3-4 (2012): 251-266. https://doi.org/10.1515/jnum-2012-0013 DOI: https://doi.org/10.1515/jnum-2012-0013
Ngaongam, Choosak, and Rapee Ujjin. "FEM Modelling of the Heating Behaviour in Vibrothermography Based on Thermoelastic Damping on Crack Location." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 108, no. 1 (2023): 66-74. https://doi.org/10.37934/arfmts.108.1.6674 DOI: https://doi.org/10.37934/arfmts.108.1.6674
Hillman, Craig, Nathan Blattau, and Matt Lacy. "Predicting Fatigue of Solder Joints Subjected to High Number of Power Cycles." In IPC APEX EXPO Conference Proceedings. 2014.
Lin, Jian, Yongping Lei, Zhongwei Wu, and LanLi Yin. "Comparison investigation of thermal fatigue and mechanical fatigue behavior of board level solder joint." In 2010 11th International Conference on Electronic Packaging Technology & High Density Packaging, pp. 1179-1182. IEEE, 2010. https://doi.org/10.1109/ICEPT.2010.5582756 DOI: https://doi.org/10.1109/ICEPT.2010.5582756
Lall, Pradeep, Mohd Nokibul Islam, John Evans, Jeffrey C. Suhling, and Tushar Shete. "Damage mechanics of electronics on metal-backed substrates in harsh environments." IEEE Transactions on Components and Packaging Technologies 29, no. 1 (2006): 204-212. https://doi.org/10.1109/TCAPT.2006.870390 DOI: https://doi.org/10.1109/TCAPT.2006.870390
Ima, T. "Estimating the thermal fatigue life of lead-free solder joints." Yamaha Motor Tech Rev 49 (2013): 43-47.
Sitek, Janusz, Aneta Araźna, Kamil Janeczek, Wojciech Stęplewski, Krzysztof Lipiec, Konrad Futera, and Piotr Ciszewski. "Influence of thermal cycling on reliability of solder joints executed on long and metal core PCBs." Soldering & Surface Mount Technology 27, no. 3 (2015): 120-124. https://doi.org/10.1108/SSMT-03-2015-0009 DOI: https://doi.org/10.1108/SSMT-03-2015-0009
Alfat, Sayahdin. "New Frameworks of PFM for Thermal Fracturing in The Linear Thermoelasticity Solids Based on a Microforce Balance Approach." (2023). https://doi.org/10.21203/rs.3.rs-3776383/v1 DOI: https://doi.org/10.21203/rs.3.rs-3776383/v1
Li, Yicong, Tiantang Yu, Chen Xing, and Sundararajan Natarajan. "Crack growth in homogeneous media using an adaptive isogeometric fourth-order phase-field model." Computer Methods in Applied Mechanics and Engineering 413 (2023): 116122. https://doi.org/10.1016/j.cma.2023.116122 DOI: https://doi.org/10.1016/j.cma.2023.116122
Biot, Maurice Anthony. "Thermoelasticity and irreversible thermodynamics." Journal of applied physics 27, no. 3 (1956): 240-253. https://doi.org/10.1063/1.1722351 DOI: https://doi.org/10.1063/1.1722351
Abouelregal, Ahmed E., Fahad Alsharari, S. S. Alsaeed, Mohammed Aldandani, and Hamid M. Sedighi. "A semi-analytical approach for thermoelastic wave propagation in infinite solids subject to linear heat supply using two-phase lag theory." Continuum Mechanics and Thermodynamics (2024): 1-18. https://doi.org/10.1007/s00161-024-01324-1 DOI: https://doi.org/10.1007/s00161-024-01324-1
Shen, Rilin, Haim Waisman, and Licheng Guo. "Fracture of viscoelastic solids modeled with a modified phase field method." Computer Methods in Applied Mechanics and Engineering 346 (2019): 862-890. https://doi.org/10.1016/j.cma.2018.09.018 DOI: https://doi.org/10.1016/j.cma.2018.09.018
Yin, Bo, Johannes Storm, and Michael Kaliske. "Viscoelastic phase-field fracture using the framework of representative crack elements." International Journal of Fracture 237, no. 1 (2022): 139-163. https://doi.org/10.1007/s10704-021-00522-1 DOI: https://doi.org/10.1007/s10704-021-00522-1
Downloads
Published
How to Cite
Issue
Section
