Moisture Diffusion Modeling in MAPDL and Solder Joint Modeling in WorkBench

Transcription

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 1

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 2

3 Coupled-Field Enhancements at 14.0 New at 14.0 Diffusion physics and coupled-diffusion analyses Motivation Thermal-diffusion Structural-diffusion Structural-thermal-diffusion Simulation of moisture diffusion Sodium migration in aluminum reduction cells 3

4 Elements for Coupled-Diffusion Analyses PLANE223 2-D 8-node quadrilateral SOLID226 3-D 20-node brick SOLID227 3-D 10-node tetrahedron KEYOPT(1) controls physics DoFs KEYOPT(1)= is structural-diffusion (U+CONC) KEYOPT(1)= is thermal-diffusion (TEMP+CONC) KEYOPT(1)= 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) 4

5 Coupled Effects in Structural-Thermal-Diffusion Analyses (14.0) Thermal strain th ( T T ref ) Structural Thermal expansion NLGEOM Thermal Diffusion strain di ( C Cref ) C - ref moisture expansioncoefficient - " reference"concentration Diffusion 5

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 6

7 Percent Weight Gain Results for 85C/85% RH for 168 Hours 0.35% 0.30% 0.25% 0.20% 0.15% 0.10% 0.05% 0.00% 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. 7

8 Popcorn Modeling Use cohesive zone elements to model delamination Use Solid226 to model thermal/structural/diffusion interaction Thermalstrain th ( T Tref ) INTER204 3-D 16-node interface Structural Thermal expansion NLGEOM Thermal SOLID226 3-D 20-node Brick Diffusion strain di ( C Cref ) C - ref moisture expansioncoefficient - " reference"concentration Diffusion SOLID227 3-D 10-node tetrahedron 8

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/C sat is continuous across material interfaces, so this is the DoF used in moisture diffusion problems. 9

10 New Elements for Diffusion Analysis PLANE238 2-D 8-node quadrilateral SOLID239 3-D 20-node brick SOLID240 3-D 10-node tetrahedron 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) Will be supported by the 22x elements 10

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 Motivation Structural-thermo-electric-diffusion analysis Electrostatic-diffusion analysis Enhance moisture migration analysis Electromigration in solder joints 11

12 Driving Forces of Electromigration Atomic concentration Thermal gradient Electric field Stress gradient c Mass conservation J t * cq Atomic flux J D c 2 kt * Q - heatof transport * Z - effectivecharge - atomic volume 0 T * cz e c kt kt 12

13 More Coupled Diffusion Analyses in 15.0 (Subject to Change) Structural Thermal expansion Thermoelastic damping Plastic heat Thermal Joule heat Diffusion Electric diffusion Electrical 13

14 Solder Joint Modeling in Workbench 14

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

16 Solder Creep Models Combined time hardening/double power Law Found to fit SnAg solder test data well. Anand model Syed, A, Accumulated Creep Strain and Energy Density Based Thermal Fatigue Life Prediction Models for SnAgCu Solder Joints ECTC

17 Strain Energy Density Accumulated creep strain W ave ave Results of interest W V V acc V V Averaging over a small volume prevents singularities. 17

18 Cycles to Failure Calculation Following taken from Syed, Ahmer Accumulated Creep Strain and Energy Density Based Thermal Fatigue Life Prediction Models for SnAgCu Solder Joints, ECTC 2004 C 1 N N C" W 1 f acc f ave Where N f = Cycles to Failure C is a constant dependent on material C = and C = for the Anand model Following taken from R. Darveaux, Effect of Simulation Methodology on Solder Joint Crack Growth Correlation, ECTC 2000 Crack Initiation: Crack Growth: Characteristic life: N da dn 0 W K K 3 1 N 0 K2 W avg K4 W avg a da dn Here, K 1 through K 4 are material parameters a is the joint diameter at the interface ( final crack length ) W is the plastic work per cycle 18

19 Workflow Geometry Split solder region for volumetric averaging Design Modeler 19

20 Workflow Input material properties in engineering data 20

21 Workflow Setup Simulation Check Connections and contacts Create Named Selections To identify location for volume averaging Define four load steps for thermal load (3 cycles) 21

22 Workflow Post Processing APDL Command for volumetric averaging and calculations 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 22

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 23