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Institute of Mechanics Chair for Continuum Mechanics and Materials Theory

Institute of Mechanics Chair for Continuum Mechanics and Materials Theory. Our Mission: “The modeling of the behavior of engineering structures made of complex materials”. Weierstraß-Institut für Angewandte Analysis und Stochastik. by W. H. Müller and W. Dreyer, R.L. Reuben.

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Institute of Mechanics Chair for Continuum Mechanics and Materials Theory

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  1. Institute of MechanicsChair for Continuum Mechanics and Materials Theory Our Mission: “The modeling of the behavior of engineering structures made of complex materials”

  2. Weierstraß-Institut für Angewandte Analysis und Stochastik by W. H. Müller and W. Dreyer, R.L. Reuben Micromorphological Change in Solders and its Impact on Mechanical Properties: Experiments and Computer Simulations

  3. Contents • Motivation: Of solders and their ailments • Problem definition: mechanics & thermodynamics of changes in microstructure • Computer simulations • The quest for reliable material parameters

  4. Contents • Motivation: Of solders and their ailments • Problem definition: mechanics & thermodynamics of changes in microstructure • Computer simulations • The quest for reliable material parameters

  5. Micromorphology of Materials: Aging of Eutectic SnPb Solder SMT solder joints: Formation of interface cracks Microstructural coarsening Ball Grid Arrays and solder ball before and after 4000 temperature cycles Aging at RT after (a) 2h, (b) 17d and (c) 63d (a) After solidification, (b) 3h and (c) 300 h at 125°C MELF miniature resistor and solder joints before and after 3000 temperature cycles

  6. Eutectic SnPb Deposited on Copper, Cooled in a Muffle Furnaceand Aged Using a Heating Cartridge Solder Thermocouple Cartridge Heater Thermostatic Control

  7. Eutectic SnPb Deposited on Copper, cooled in a Muffle Furnaceand Aged Using a Heating Cartridge • Formation of Lamellae

  8. Scanning Electron Microscope (SEM) Analysis 0 h 22 h

  9. Aging of Air-Cooled SnAg Deposited and Aged Using aCopper Block with Heating Cartridge • Temperatur 180°C  spheroidisation 0 h 18 h 24 h 40 h

  10. Contents • Motivation: Of solders and their ailments • Problem definition: mechanics & thermodynamics of changes in microstructure • Computer simulations • The quest for reliable material parameters

  11. Equations Mechanical equilibrium: Hooke’s law: Kinematic relations: Phase Field Model I: Mechanical aspects, objectives Effective method for calculating stresses / strains: for solids with complex microstructure subjected to external stresses/strains subjected to eigenstrains (e.g., thermal / lattice mismatch)

  12. Phase Field Model II: Thermodynamic aspects Diffusion equation / equation for order parameter: Extended diffusion flux / production density of the order parameter: Fick (1855) Cahn-Hilliard (1958) strain-energy density (1996) Physically based material parameters: diffusions / mobility coefficients specific Gibbs free energy “surface tensions” thermal expansion coefficients elastic coefficients

  13. Contents • Motivation: Of solders and their ailments • Problem definition: mechanics & thermodynamics of changes in microstructure • Computer simulations • The quest for reliable material parameters

  14. Aging at low temperature (time frame ): Aging at high temperature (time frame ) : Experimental result (a) After solidification, (b) 3 h, and (c) 300 h at 125°C: Aging at RT after (a) 2 h, (b) 17 d and (c) 63 d:

  15. Aging at low temperature (with different CTE‘s): Then switch to high temperature: Aging at high temperature with isotropic surface tensions:

  16. Aging at high temperature with thermal w/o external load: Aging at high temperature with thermal load and vertical tension : Further aging at low temperature after switching-off the external load:

  17. Aging at high temperature with thermal w/o external load: Aging at high temperature with thermal load and horizontal tension :

  18. Computer simulation of the aging process

  19. Contents • Motivation: Of solders and their ailments • Problem definition: mechanics & thermodynamics of changes in microstructure • Computer simulations • The quest for reliable material parameters

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