Microstructure dependent viscoplastic damage modelling of tin-lead solder

Journal of the Mechanics and Physics of Solids

Volumn 54, Issue 12, 2006, Pages 2621-2651

  Ubachs, R L J M ^a   Schreurs, P J G ^a   Geers, M G D ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Microstructure dependency; Nonlocal damage; Phase field; Solder; Viscoplastic

Indexed keywords

MICROSTRUCTURE DEPENDENCY; NONLOCAL DAMAGES; PHASE FIELDS; VISCOPLASTIC DAMAGES;

EUTECTICS; LEAD ALLOYS; MATHEMATICAL MODELS; MICROSTRUCTURE; TIN ALLOYS; VISCOPLASTICITY;

SOLDERING ALLOYS;

EID: 33749632846     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2006.05.001     Document Type: Article

References (75)

1. Akay H., Paydar N., and Bilgic A. Fatigue life predictions for thermally loaded solder joints using a volume-weighted averaging technique. J. Electronic Packaging 119 (1997) 228-235
2. Amagai M. Chip scale package (csp) solder joint reliability and modeling. Microelectr. Reliab. 39 4 (1999) 463-477
3. Amagai M., Watanabe M., Omiya M., Kishimoto K., and Shibuya T. Mechanical characterization of Sn-Ag-based lead-free solders. Microelectr. Reliab. 42 (2002) 951-966
4. Anand L. Constitutive relations for hot working of metals. J. Plasticity 1 (1985) 213-231
5. Anderson T., Guven I., Madenci E., and Gustafsson G. The necessity of reexamining previous life prediction analyses of solder joints in electronic packages. IEEE Trans. Components Packaging Technol. 23 3 (2000) 516-520
6. Basaran C., and Chanderoy R. Mechanics of Pb40/Sn60 near-eutectic solder alloys subjected to vibration. Appl. Math. Modell 22 (1998) 601-627
7. Basaran C., and Chanderoy R. Using finite element analysis for simulation of reliability tests on solder joints in microelectronic packaging. Comput. Struct. 74 (2000) 215-231
8. Basaran C., and Jiang J. Measuring intrinsic elastic modulus of Pb/Sn solder alloys. Mech. Mater. 34 (2002) 349-362
9. Basaran C., and Tang H. Implementation of a thermodynamic framework for damage mechanics of solder interconnects in microelectronic packaging. International J. Damage Mech. 11 (2002)
10. Basaran C., Desai C., and Kundu T. Thermomechanical finite element analysis of problems in electronic packaging using the disturbed state concept. Part I: Theory and formulation. J. Electr. Packaging 120 1 (1998) 41-47
11. Bažant Z., and Pijaudier-Cabot G. Nonlocal continuum damage localization instability and convergence. J. Appl. Mech. 55 (1988) 287-293
12. Bird J., Mukherjee A., and Dorn J. Quantitative Relation Between Properties and Microstructure (1969), Israel University Press, Jerusalem pp. 255-342
13. Boers S., Schreurs P., and Geers M. Operator-split damage-plasticity applied to groove forming in food can lids. Internat. J. Solids and Struct. 42 (2005) 4154-4178
14. Bonda N., and Noyan I. Deformation inhomogeneity and representative volume in Pb/Sn solder alloys. Metall. Trans. A 23A (1992) 479-484
15. Cahn J., and Hilliard J. Free energy of a nonuniform system, I: Interfacial energy. J. Chem. Phys. 28 2 (1958) 258-267
16. Canumalla S., Mathew S., and Saha S. Damage evolution in Sn62Pb36Ag2 solder of a chip scale package under a monotonic shear stress. Electronic Components and Technology Conference (2003), IEEE, New York
17. Cheng Z., Wang G., Chen L., Wilde J., and Becker K. Viscoplastic Anand model for solder alloys and its application. Soldering Surf. Mount Technol. 12 2 (2000) 31-36
18. Conrad H., Guo Z., Fahmy Y., and Yang D. Influence of microstructure on the plastic deformation kinetics fatigue crack growth rate and low-cycle fatigue of solder joints. J. Electr. Mater. 28 9 (1999) 1062-1070
19. Ding, Y., Wang, C., Mingyu, L., Han-Sur, B., 2004. Aging effects on fracture behavior of 63Sn37Pb eutectic solder during tensile tests under the SEM. Mater. Sci Eng. A 384(1-2), 314-323.
20. Dreyer W., and Müller W. A study of the coarsening in tin/lead solders. Internat. J. Solids Struct. 37 (2000) 3841-3871
21. EU, 2003. Directive 2002/95/EC of the European Parliament and of the Council of 27 January 2003 on the restriction of the use of certain hazardous substances in electrical and electronic equipment. Official J. Euro. Union 37, 19-23.
22. Frear D. Thermomechanical fatigue of solder joints: a new comprehensive test method. IEEE Trans. Composites, Hybrids, and Manufacturing Technology 12 4 (1989) 492-501
23. Frear D., Burchet S., Neilsen M., and Stephens J. Microstructurally based finite element simulation on solder joint behaviour. Soldering Surf. Mount Technol. 9 1 (1997) 39-42
24. Frear D., Grivas D., and Morris Jr. J. A microstructural study of the thermal fatigue failures of 60Sn-40Pb solder joints. J. Electr. Mater. 17 (1988) 171-180
25. Glema A., Łodygowski T., and Perzyna P. Interaction of deformation waves and localization phenomena in inelastic solids. Comput. Methods Appl. Mech. Eng. 183 (2000) 123-140
26. Geers M., Ubachs R., and Engelen R. On the numerical modelling of ductile damage with an implicit gradient-enhanced formulation. Revue Européenne des Eléments Finis 10 2/3/4 (2001) 173-192
27. Geers M., Ubachs R., and Engelen R. Strongly non-local gradient-enhanced finite strain elastoplasticity. Internat. J. Numer. Methods Eng. 56 (2003) 2039-2068
28. Goodman, P., Strudwick, P., Skipper, R., 2004. Technical adaptation under Directive 2002/95/EC (RoHS)-Investigation of exemptions, Reliability and Failure analysis ERA Report 2004-0603, ERA Technology.
29. Guo, Z., Conrad, H., 1993. Computer modeling of isothermal low-cycle fatigue of Pb-Sn solder joints, In: Electronic Components and Technology Conference, vol. 47. IEEE, pp. 831-838.
30. Gurson A. Continuum theory of ductile rupture by void nucleation and growth: Part I-Yield criteria and flow rule for porous ductile media. J. Eng. Mater. Technol. Transac. ASME 99 (1977) 1-15
31. Hacke P., Sprecher A., and Conrad H. Microstructure coarsening during thermo-mechanical fatigue of Pb-Sn solder joints. J. Electr. Mater. 26 7 (1998) 774-782
32. Ju S., Kuskowski S., Sandor B., and Plesha M. In: Schroeder S., and Mitchell M. (Eds). Fatigue of Electronic Materials, STP-1153 (1994), American Society for Testing and Materials, Philadelphia 1-21
33. Jung K., and Conrad H. Microstructure coarsening during static annealing of 60Sn40Pb solder joints: I Stereology. J. Electr. Mater. 30 10 (2001) 1294-1302
34. Jung K., and Conrad H. Microstructure coarsening during static annealing of 60Sn40Pb solder joints: II Eutectic coarsening kinetics. J. Electr. Mater. 30 10 (2001) 1303-1307
35. Kanchanomai C., and Mutoh Y. Temperature effect on low cycle fatigue behavior of Sn-Pb eutectic solder. Scripta Materialia 50 1 (2004) 83-88
36. Kanchanomai C., Miyashita Y., and Mutoh Y. Low cycle fatigue behavior and mechanisms of a eutectic Sn-Pb solder 63Sn/37Pb. Internat. J. Fatigue 24 (2002) 671-683
37. Kanchanomai C., Miyashita Y., and Mutoh Y. Strain-rate effects on low cycle fatigue mechanism of eutectic Sn-Pb solder. Internat. J. Fatigue 24 (2002) 987-993
38. Leo P., Lowengrub J., and Jou H. A diffuse interface model for microstructural evolution in elastically stressed solids. Acta Metall. 46 6 (1998) 2113-2130
39. Liu X., and Plumbridge W. Thermomechanical fatigue of Sn-37 wt% Pb model solder joints. Mater. Sci. Eng. A 362 1-2 (2003) 309-321
40. Matin M., Vellinga W., and Geers M. Quantitative microscopy of microstructural evolution in eutectic solders subjected to static thermal load. In: Ernst L., Zhang G., Dudek R., and deSaintLeger O. (Eds). Thermal and Mechanical Simulation and Experiments in Micro-Electronics and Micro-Systems. EuroSIME 2003 (2003), Shaker Publishing, Aix-en-Provence 111-116
41. Mediavilla, J., Peerlings, R., Geers, M., 2006a. Discrete crack modelling of ductile fracture driven by nonlocal softening plasticity. Internat. J. Numer. Methods Eng. 66(4), 661-688.
42. Mediavilla, J., Peerlings, R., Geers, M., 2006b. An integrated continuous-discontinuous approach towards damage engineering in sheet metal forming processes. Eng. Fracture Mech. 73(7), 895-916.
43. Mediavilla, J., Peerlings, R., Geers, M., 2006c. A nonlocal triaxiality-dependent ductile damage model for finite strain plasticity. Comput. Methods Appl. Mech. Eng. 195(33-36), 4617-4634.
44. Mei Z., Morris J.J., Shine M., and Summers T. Effects of cooling rate on mechanical properties of near-eutectic tin-lead solder joints. J. Electr. Mater. 20 (1991) 599-608
45. Miao H.-W., and Duh J.-G. Microstructure evolution in Sn-Bi and Sn-Bi-Cu solder joints under thermal aging. Mater. Chem. Phys. 71 (2001) 255-271
46. Needleman A., Tvergaard V., and Hutchinson J. Void Growth in Plastic Solids (1992), Springer, New York
47. Ni Y., He L., and Yin L. Three-dimensional phase field modeling of phase separation in strained alloys. Mater. Chem. Phys. 78 (2002) 442-447
48. Oyane M., Sato T., Okimoto K., and Shima S. Criteria for ductile fracture and their applications. J. Mech. Working Technol. 4 (1980) 65-81
49. Peerlings R., De Borst R., Brekelmans W., and de Vree J. Gradient enhanced damage for quasi-brittle materials. Internat. J. Numer. Methods Eng. 39 19 (1996) 3391-3403
50. Peerlings R., Geers M., De Borst R., and Brekelmans W. A critical comparison of nonlocal and gradient-enhanced softening continua. Internat. J. Solids Struct. 38 (2001) 7723-7746
51. Peerlings R., Massart T., and Geers M. A thermodynamically motivated implicit gradient damage framework and its application to brick masonry cracking. Comput. Methods Appl. Mech. Eng. 193 30-32 (2004) 3403-3417
52. Perzyna P. Fundamental problems in visco-plasticity. Recent Advances in Applied Mechanics (1966), Academic Press, New York
53. Perzyna, P., 1971. Thermodynamic theory of viscoplasticity. In: Advances in Applied Mechanics, vol. 11. Academic Press, New York, pp. 313-354.
54. Perzyna P. On constitutive modelling of dissipative solids for plastic flow, instability and fracture. In: Sawczuk A., and Bianchi G. (Eds). Plasticity today: Modelling, Methods and Applications (1985), Elsevier Applied Science Publishers, Amsterdam 657-679
55. Rice J., and Tracey D. On the ductile enlargement of voids in triaxial stress fields. J. Mech. Phys. Solids 17 (1969) 201-217
56. Rynemark M., Nylen M., and Hutchinson B. On the fatigue of solder subjected to isothermal cyclic shear. Scripta Metallurgica Mater. 28 (1993) 349-353
57. Shen Y., Li W., and Fang H. Phase structure and cyclic deformation in euetectic tin-lead alloy: a numerical analysis. Trans. ASME 123 (2001) 74-78
58. Shen Y., Abell K., and Garrett S. Effects of grain boundary sliding on microstructural evolution and damage accumulation in tin-lead alloy. Int. J. Damage Mech. 13 3 (2004) 225-240
59. Sluys L., and De Borst. Dispersive properties of gradient-dependent and rate-dependent media. Mech. Mater. 18 (1994) 131-149
60. Stam F., and Davitt E. Effects of thermomechanical cycling on lead and lead-free (SnPb and SnAgCu) surface mount solder joints. Microelectronics Reliability 41 (2001) 1815-1822
61. Steinmann P. Formulation and computation of geometrically non-linear gradient damage. Internat. J. Numer. Methods Eng. 46 (1999) 757-779
62. Towashiraporn P., Gall K., Subbarayan G., and McIlvanie B. Power cycling thermal fatigue of Sn-Pb solder joints on a chip scale package. Internat. J. Fatigue 26 (2004) 497-510
63. Tvergaard V. Material failure by void growth to coalescence. Adv. Appl. Mech. 27 (1990) 83-151
64. Ubachs, R., Schreurs, P., Geers, M., 2003. Microstructure evolution of tin-lead solder. In: Ernst, L., Zhang, G., Dudek, R., de Saint Leger, O. (Eds.), Thermal and Mechanical Simulation and Experiments in Micro-Electronics and Micro-Systems, EuroSIME 2003. Aix-en-Provence, France, pp. 1-7, cd-rom.
65. Ubachs R., Schreurs P., and Geers M. A nonlocal diffuse interface model for microstructure evolution of tin-lead solder. J. Mech. Phys. Solids 52 8 (2004) 1763-1792
66. Ubachs R., Schreurs P., and Geers M. Phase field dependent viscoplastic behaviour of solder alloys. Internat. J. Solids and Struct. 42 9/10 (2005) 2533-2558
67. Van der Sluis O., Schreurs P., and Meijer H. Effective properties of a viscoplastic constitutive model obtained by homogenisation. Mech. Mater. 31 (1999) 743-759
68. Vianco P., Burchet S., Neilsen M., Rejent J., and Frear D. Coarsening of the Sn-Pb solder microstructure in constitutive model-based predictions of solder joint thermal mechanical fatigue. J. Electr. Mater. 28 11 (1999) 1290-1298
69. Voyiadjis G., Abu Al-Rub R., and Palazotto A. Thermodynamic framework for coupling of non-local viscoplasticity and non-local anisotropic viscodamage for dynamic localization problems using gradient theory. Int. J. Plasticity 20 (2004) 981-1038
70. Wang G., Chen Z., Becker K., and Wilde J. Applying Anand model to represent the viscoplastic behaviour of solder alloys. J. Electr. Packaging 123 (2001) 247-253
71. Wang W., and Sluys L. Formulation of an implicit algorithm for finite deformation viscoplasticity. Internat. J. Solids Structures 37 (2000) 7329-7348
72. Wang W., Sluys L., and De Borst R. Viscoplasticity for instabilities due to strain softening and strain-rate softening. Internat. J. Numer. Methods Eng. 40 (1997) 3839-3864
73. Yang X., and Nassar S. Constitutive modelling of time-dependent cyclic straining for solder alloy 63Sn-37Pb. Mech. Mater. 37 (2005) 801-814
74. Zhang, X., Lee, S.-W., 1998. Thermal fatigue life prediction for solder joints with the consideration of damage evolution. In: 1998 IEEE/CPMT Electronics Packaging Technology Conference, pp. 279-285.
75. Zhu J., Chen L., Shen J., and Tikare V. Coarsening kinetics from a variable-mobility Cahn-Hilliard equation: Application of a semi-implicit Fourier spectral method. Phys. Rev. E 60 4 (1999) 3564-3572