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A Revised Anand Constitutive Model for Lead Free Solder That Includes Aging Effects

[+] Author Affiliations
Mohammad Motalab, Munshi Basit, Jeffrey C. Suhling, Pradeep Lall

Auburn University, Auburn, AL

Paper No. IPACK2013-73232, pp. V001T05A009; 20 pages
  • ASME 2013 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems
  • Volume 1: Advanced Packaging; Emerging Technologies; Modeling and Simulation; Multi-Physics Based Reliability; MEMS and NEMS; Materials and Processes
  • Burlingame, California, USA, July 16–18, 2013
  • Conference Sponsors: Electronic and Photonic Packaging Division
  • ISBN: 978-0-7918-5575-1
  • Copyright © 2013 by ASME


Traditional finite element based predictions for solder joint reliability during thermal cycling accelerated life testing are based on solder constitutive equations (e.g. Anand viscoplastic model) and failure models (e.g. energy dissipation per cycle model) that do not evolve with material aging. Thus, there will be significant errors in the calculations with lead free SAC alloys that illustrate dramatic aging phenomena. In this study, we have developed a revised set of Anand viscoplastic stress-strain relations for solder that include material parameters that evolve with the thermal history of the solder material. The effects of aging on the nine Anand model parameters have been examined by performing stress-strain tests on SAC305 samples that were aged for various durations (0–6 months) at temperature of 100 C. The stress-strain data were measured at three strain rates (.001, .0001, and .00001 1/sec) and five temperatures (25, 50, 75, 100, and 125 C). The mechanical tests have been performed using both water quenched (WQ) and reflowed (RF) samples (two unique specimen microstructures). In the case of the water quenched samples, there is rapid microstructural transitioning during the brief time that occurs between placing molten solder into the glass tubes and immersing the tubes in water bath. On the other hand, the reflowed samples are first cooled by water quenching, and then sent through a reflow oven to re-melt the solder in the tubes and subject them to a desired temperature profile matching that used in PCB assembly.

As expected, the observed mechanical properties of water quenched samples were better (higher in magnitude) than the corresponding mechanical properties of the reflowed samples. Although the differences in elastic modulus between the water quenched and reflowed samples are small, significant differences are present for the yield and ultimate tensile stresses (for each aging condition). For both the water quenched and reflowed specimens, significant degradation of the mechanical properties has been observed with aging. Using the measured stress-strain and creep data, mathematical expressions have been developed for the evolution of the Anand model parameter with aging time. Our results show that 2 of the 9 constants remain essentially constant during aging, while the other 7 show large changes (30–70%) with up to 6 months of aging. The revised Anand constitutive equations for solder with aging effects have also been incorporated into commercial finite element codes (ANSYS and ABAQUS).

Copyright © 2013 by ASME



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