Fatigue crack growth under active cycling conditions is simulated using the cohesive zone modeling concept within the framework of the Finite Element Method. To this end, a cyclic cohesive zone model based on a damage evolution equation is extended onto the case of transient thermal loading conditions and is implemented into ANSYS. The thermal and mechanical interaction of the cohesive surfaces is taken into account for both open and closed crack states. By incorporating the temperature dependence of the cohesive zone model parameters, the model is also extended onto cases of nonisothermal fatigue. To speed-up fatigue simulations, the cyclic cohesive zone model is equipped with the cycle jump technique based on direct iteration of the damage evolution equation. The implemented thermomechanical cyclic cohesive zone model is applied to a problem of interfacial debonding between two layers of a power metallization stack subjected to the active thermal cycling.

1. Simulation of a fatigue crack
problem in electronic devices using
cohesive zone modelling approach
Bala Karunamurthy. KAI Kompetenzzentrum Automobil-
und Industrieelektronik GmbH, Villach.
Grygoriy Kravchenko. ILSB, TU Wien
ACUM’15. Vienna

2. Copper

3. What happens in the chip?
Source: Wikipedia
(V Kosel, KAI)
Active device  Heat dissipation
Crack
Heat
Si

4. surface of the sun: 63 W/mm2
How much heat is generated?
(M Nelhiebel, KAI)

5. Si
Cu
Thermally
Induced
Cyclic
Stresses
Thermal
Cycling
Inhom. Mech.
Properties
Temp.
Gradients

6. Global Model
1st Sub-Model
2nd Sub-Model Deformed State Accumulated PS
Electrical  Thermal  Mechanical
(V Kosel, KAI)

7. The 3 Questions
1. Where crack would initiate?
2. Which direction it will grow?
3. What is the growth rate?

8. How do we predict fatigue damage?
1. Stress or strain based approach
2. Energy based approach
Critical plane: physically sound and can predict orientation of
fatigue or crack plane
Damage Growth model
- Plastic work per cycle
- Total strain energy
density per cycle

9. Fatigue cracks form
- on planes of maximum shear strain amplitude &
the maximum normal stress acting on this plane
FIP:Fatemi-Socie
K ~ Material constant; 1

10. Crack growth modelling
CTOD
FPZ is required
- Measurement difficulties
- Mixed loads & Interface
J-Integral
based on deformation theory of plasticity
- small plastic zones
- Near crack tip stress field
Cohesive Zone Model
- well suited for our applications
- creep-fatigue; oxidation assisted cracking etc

11. Traction-Separation Law (TSL)
• relation between tractions and
separations
• separation energy (critical energy
release rate)
• monotonic CZM: no damage increment
inside the envelope (grey area)
• tractions, separations
• damage D = [0; 1]
Cohesive Zone Modelling

12. TM-CCZM
• Hysteresis on loading-unloading
• Damage accumulation in each cycle
• Fatigue crack propagation
Damage evolution law (Bouvard, 2009)
• Extended for Transient thermal
- parameters A, m, T0, n, δc
Traction – separation relations
parameters α, Kn
7 parameters in total for 2D (temperature
dependent)
Cyclic Cohesive Zone Modelling
“A cohesive zone model for fatigue and creep–fatigue crack growth in single crystal superalloys” Bouvard,
2009. International Journal of Fatigue

13. Cycle Jump Technique
ANSYS USERINTER Subroutine
Based on direct iteration of
damage evolution
Thermo-mechanical Cyclic Cohesive Zone Model (TM-CCZM) implemented in
contact formulation as user subroutine
Heat Transfer in CZ

14. Crack growth in semiconductor device
Heat Flux

15. Acknowledgements:
Funding bodies:
Austrian Research Promotion Agency (FFG, Project No. 846579)
and the Carinthian Economic Promotion Fund (KWF, contract
KWF-1521/26876/38867).
KAI & Infineon Technologies AG.
Prof. Heinz Pettermann, ILSB, TU Wien
Contact: bala.karunamurthy@k-ai.at