Technische Universität Berlin Fakultät für Verkehrs- und Maschinensysteme, Institut für Mechanik Lehrstuhl für Kontinuumsmechanik und Materialtheorie,

Technische Universität BerlinFakultät für Verkehrs- und Maschinensysteme , Institut für Mechanik

Lehrstuhl für Kontinuumsmechanik und Materialtheorie, Prof. W.H. Müller

Copyright © Prof. Dr. rer. nat. W.H. Müller, e-mail: [email protected], 2003 1

Institute of Mechanics

Chair for Continuum Mechanics

and Materials Theory

Our Mission:

“The modeling of the behavior

of engineering structures

made of complex materials”




Interface Fracture at Diffusion-Bonded Zones of the MCC

Probabilistic Fracture Mechanicsfor Brittle Materials

Morphological Changes in the Microstructureof Solders, Ceramics, Superalloys

10 10 10 10 100 -2 -4 -6 -8 m

Reliability of Injection Molded Rear Lights made of PMMA

Thermal Stressesin Microelectronic

Components

Interface and Matrix Crackingin Particle and FibreReinforced Materials




Micromorphological Change in Solders and its Impact on Mechanical Properties:

Experiments and Computer Simulations

by

W. H. Müller

and

W. Dreyer, R.L. Reuben

Weierstraß-Institut fürAngewandte Analysis und Stochastik




Contents• Motivation: Of solders and their ailments

• Problem definition: mechanics & thermodynamics of

changes in microstructure

• Computer simulations

• The quest for reliable material parameters












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°CMELF miniature resistor and solder joints before and after 3000 temperature cycles

Micromorphology of Materials: Aging of Eutectic SnPb Solder




Eutectic SnPb Deposited on Copper, Cooled in a Muffle Furnaceand Aged Using a Heating Cartridge

Thermostatic Control

Thermocouple Cartridge HeaterSolder




Eutectic SnPb Deposited on Copper, cooled in a Muffle Furnaceand Aged Using a Heating Cartridge

• Formation of Lamellae




Scanning Electron Microscope (SEM) Analysis0 h 22 h




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












Phase Field Model I: Mechanical aspects, objectives

Effective method for calculating stresses / strains:

for solids with complex microstructuresubjected to external stresses/strains subjected to eigenstrains (e.g., thermal / lattice mismatch)

Equations

Mechanical equilibrium:

Hooke’s law:

Kinematic relations:

0

j

ij

x

*klklijklij C

i

j

j

iij x

u

x

u

2

1




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

,00

i

i

x

J

t

c

,2

1 *2

0

klklkllk

klj

iji cxx

ca

cxMJ

ijM

klaTijij *

ijklC

SPt

S

klklkllk

klS Sxx

Sb

SP *

2

2

1~












Aging at low temperature (time frame ):• h905.0~

Aging at high temperature (time frame ) :• min51

Experimental result• Aging at RT after (a) 2 h, (b) 17 d and (c) 63 d: (a) After solidification, (b) 3 h, and (c) 300 h at 125°C:




Aging at low temperature (with different CTE‘s):•

Then switch to high temperature:•

Aging at high temperature with isotropic surface tensions:•




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:•

MPa5




Aging at high temperature with thermal w/o external load:•

Aging at high temperature with thermal load and horizontal tension :• MPa5




• Computer simulation of the aging process









Documents

Technische Universität Berlin Fakultät für Verkehrs- und Maschinensysteme, Institut für Mechanik Lehrstuhl für Kontinuumsmechanik und Materialtheorie,