December, 2011

1

Moisture Diffusion

Modeling in MAPDL and

Solder Joint Modeling in

WorkBench

Prepared by: Matt Sutton, PADT

With Input from Elana Antonova, ANSYS Inc

And Ming Yao Ding, ANSYS Inc

December, 2011

2

Outline

• Coupled-diffusion at 14.0

• Standard diffusion at 14.5

• Electromigration and other coupled-diffusion

applications at 15.0

• Solder Joint Modeling in Workbench

• Conclusions

December, 2011

3

Coupled-Field Enhancements at 14.0

• New at 14.0

– Diffusion physics and coupled-diffusion analyses

• Thermal-diffusion

• Structural-diffusion

• Structural-thermal-diffusion

• Motivation

– Simulation of moisture diffusion

– Sodium migration in aluminum reduction cells

December, 2011

4

Elements for Coupled-Diffusion Analyses

• KEYOPT(1) controls physics DoFs – KEYOPT(1)=100001 is structural-diffusion (U+CONC)

– KEYOPT(1)=100010 is thermal-diffusion (TEMP+CONC)

– KEYOPT(1)=100011 is structural-thermal-diffusion (U+TEMP+CONC)

• Material properties required – MP,DXX (DYY, DZZ) for diffusivity

– MP,CSAT for saturated concentration

– MP,BETX (BETY, BETZ) for coefficients of diffusion expansion

– MP,CREF for reference concentration

– All materials can be temperature-dependent

• Boundary conditions – D,,CONC and IC,,CONC for concentration

– F,,RATE for diffusion flow rate

• Results – Concentration gradient (CG)

– Diffusion flux (DF)

– Diffusion strain (EPDI)

PLANE223

2-D 8-node

quadrilateral

SOLID226

3-D 20-node

brick

SOLID227

3-D 10-node

tetrahedron

December, 2011

5

Coupled Effects in Structural-Thermal-Diffusion Analyses (14.0)

Thermal expansion

NLGEOM

Diffusion

Structural Thermal

ionconcentrat reference"" -

tcoefficien expansion moisture -

strain Diffusion

ref

ref

di

C

CC

)(

)( strain Thermal ref

th TT

December, 2011

6

Example Model From Galloway and Miles.

Geometry and ¼ Symmetry

ANSYS Model

1. ANSYS model consists of solid226 with thermal

and diffusion DOFS

2. Die is modeled with solid70s (thermal only)

3. Material properties are temp dependent

December, 2011

7

Results for 85C/85% RH for 168 Hours

0.00%

0.05%

0.10%

0.15%

0.20%

0.25%

0.30%

0.35%

0 24 48 72 96 120 144 168

Perc

en

t W

eig

ht

Gain

Time (hrs)

Model is run as a transient, but since the temperature is

constant and the thermal time scale is much smaller than

the diffusion time scale, you can turn thermal time

integration off.

Post process to get percent weight gain as a function of

time.

December, 2011

8

“Popcorn” Modeling

• Use cohesive zone elements to model

delamination

• Use Solid226 to model thermal/structural/diffusion

interaction

Thermal expansion

NLGEOM

Diffusion

Structural Thermal

ionconcentrat reference"" -

tcoefficien expansion moisture -

strain Diffusion

ref

ref

di

C

CC

)(

)( ref

th TT strain Thermal

INTER204

3-D 16-node

interface

SOLID226

3-D 20-node

Brick

SOLID227

3-D 10-node

tetrahedron

December, 2011

9

Diffusion Analysis at 14.5

• New at 14.5 – Three high-order elements for a standard diffusion analysis

• PLANE238 – 2D 8-node quadrilateral

• SOLID239 – 3D 20-node hexahedral

• SOLID240 – 3D 10-node tetrahedron

• Motivation – Prior to 14.0, a temperature-concentration analogy was used

to model diffusion

• Valid only for homogeneous materials

– For inhomogeneous materials, a normalized concentration approach is available with the new elements

• Unlike temperature, concentration is discontinuous across material interfaces since it is limited by saturated concentration, which is different for different materials. Normalized concentration =C/Csat is continuous across material interfaces, so this is the DoF used in moisture diffusion problems.

December, 2011

10

New Elements for Diffusion Analysis

• Degrees of freedom

– CONC – concentration or normalized

concentration (if Csat specified)

• Material properties (MP)

– DXX, DYY, DZZ, CSAT

• Surface loads (SF)

– Diffusion flux (DFLUX)

• Body loads (BF)

– Diffusing substance generation rate (DGEN)

• Boundary conditions

– D,,CONC and IC,,CONC for concentration

– F,,RATE for diffusion flow rate

• Results

– Concentration gradient (CG)

– Diffusion flux (DF)

PLANE238

2-D 8-node

quadrilateral

SOLID239

3-D 20-node

brick

SOLID240

3-D 10-node

tetrahedron

Will be supported by

the 22x elements

December, 2011

11

Coupled-Field Enhancements at 14.5/15.0

(Subject to Change)

• Current development

– Support structural material nonlinearities (plasticity,

viscoelasticity)

– Couple diffusion with electric and electrostatic fields

• Structural-thermo-electric-diffusion analysis

• Electrostatic-diffusion analysis

• Motivation

– Enhance moisture migration analysis

– Electromigration in solder joints

December, 2011

12

Driving Forces of Electromigration

• Atomic concentration

• Thermal gradient

• Electric field

• Stress gradient

volumeatomic -

charge effective -

transport of heat -

flux Atomic

onconservati Mass

*

*

*

2

*

0

Z

Q

kT

c

kT

ecZT

kT

cQcDJ

t

cJ

December, 2011

13

More Coupled Diffusion Analyses in 15.0

(Subject to Change)

Thermal expansion

Thermoelastic damping

Plastic heat

Electric diffusion Diffusion

Jo

ule

he

at

Structural Thermal

Electrical

December, 2011

14

Solder Joint

Modeling in

Workbench

December, 2011

15

Solder Creep Models

• Anand’s Viscoplasticity model

– Most popular material

model for solder

– Originally developed for

metal forming applications

R. Darveaux, “Effect of Simulation Methodology on Solder Joint Crack

Growth Correlation”, ECTC 2000

December, 2011

16

Solder Creep Models

• Combined time

hardening/Double power

Law

– Found to fit SnAg

solder test data well.

Syed, A, “Accumulated Creep Strain and Energy Density Based

Thermal Fatigue Life Prediction Models for SnAgCu Solder Joints”,

ECTC 2004

Anand model

December, 2011

17

Results of interest

• Strain Energy Density

• Accumulated creep strain

– Averaging over a small volume prevents singularities.

V

VWWave

V

Vacc

ave

December, 2011

18

• Following taken from Syed, Ahmer

“Accumulated Creep Strain and Energy

Density Based Thermal Fatigue Life

Prediction Models for SnAgCu Solder

Joints”, ECTC 2004

• Where

Nf = Cycles to Failure

C’ is a constant dependent on material

C’=0.0153 and C”=0.0019 for the Anand

model

Cycles to Failure Calculation

1 accf CN 1

"

avef WCN

• Following taken from R. Darveaux, “Effect of Simulation Methodology

on Solder Joint Crack Growth Correlation”, ECTC 2000

• Crack Initiation:

• Crack Growth:

• Characteristic life:

2

10

K

avgWKN

4

3

K

avgWKdN

da

dNda

aNW 0

Here, K1 through K4 are material

parameters

a is the joint diameter at the

interface (‘final crack length’)

W is the plastic work per cycle

December, 2011

19

• Geometry

– Split solder region for

volumetric averaging

– Design Modeler

Workflow

December, 2011

20

• Input material properties in engineering data

Workflow

December, 2011

21

• Setup Simulation

– Check Connections and contacts

– Create Named Selections

• To identify location for volume

averaging

– Define four load steps for thermal

load (3 cycles)

Workflow

December, 2011

22

• Post Processing

– APDL Command for

volumetric averaging

and calculations

Workflow cycletime=4200

*do,AR98,1,3

!--------------------------------------------------

! Read in the result at time=CycleTime*n (end of cycle)

! Select solder part

! Ensure that Named Selection "Solder" exists

!--------------------------------------------------

set,,,,,cycletime*AR98

cmsel,s,Solder

!--------------------------------------------------

! Get accumulated plastic work (nl,plwk) and volume (volu)

!--------------------------------------------------

etable,erase

etable,vsetable,nl,plwk

etable,volu,volu

!--------------------------------------------------

! Multiply acc. plastic work by volume

!--------------------------------------------------

smult,pwtable,volu,vsetable

!--------------------------------------------------

! Sum all values and put in parameters Sx_NAMEy where

! NAME = type of summation

! y = cycle number (1-3)

!--------------------------------------------------

ssum

*get,s_volu%AR98%,ssum,,item,volu

*get,s_plwk%AR98%,ssum,,item,pwtable

!--------------------------------------------------

! Calculate volume-averaged acc. strain energy density (plastic work)

!--------------------------------------------------

s_wavg%AR98%=s_plwk%AR98%/s_volu%AR98%

*enddo

my_solder_wdiff_2_1=s_wavg2-s_wavg1

my_solder_wdiff_3_2=s_wavg3-s_wavg2

December, 2011

23

Conclusions

• Moisture Modeling is now supported at 14.0

– Coupled Diffusion-Structural-Thermal capabilities exist today.

– You can turn on and off which physics you are interested in with

keyopts on the elements

– You can control transient time integration for particular DOFs to

account for disparity in time scales between physics

• More advanced coupling is coming in future releases

– Coupling to support electromigration

– More advanced support for existing couplings

• Solder joint reliability studies can now be performed in WB

virtually natively

– Advanced material property input supported

– Transient workflow is supported.

– Post processing calculations are supplied with simple snippet