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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