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

Copper

What happens in the chip?

Source: Wikipedia

(V Kosel, KAI)

Active device Heat dissipation

Crack

Heat Si

surface of the sun: 63 W/mm2

How much heat is generated?

(M Nelhiebel, KAI)

Si

Cu Thermally Induced

Cyclic Stresses

Thermal Cycling

Inhom. Mech. Properties

Temp. Gradients

Global Model

1st Sub-Model

2nd Sub-Model Deformed State Accumulated PS

Electrical Thermal Mechanical

(V Kosel, KAI)

The 3 Questions

1. Where crack would initiate?

2. Which direction it will grow?

3. What is the growth rate?

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

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

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

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

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

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

Crack growth in semiconductor device

Heat Flux

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