THE MATRIX: EVOLUTIONS II Pearl Sullivan Composites and Adhesives Group Department of Mechanical Engineering University of Waterloo IPR 28 th Annual Symposium, 16 May 2006
Scope: Multi-scale Analyses Atomic/Nanoscale Micro-scale Macro-scale Structural meters 10 10 10 9 10 8 10 7 10 6 10 5 10 4 10 3 10 2 10 1 10 0 10 1 10 2 materials science engineering applied mechanics [Adapted from Broek, 1974] Structure + mechanics are critically linked to function at all scale lengths. Performance depends on : Inherent polymer structure (materials selection) Processing Mechanical/thermal loading on part design Environmental effects
Polymeric Materials Program THERMOSETS Advanced Composites Adhesives THERMOPLASTICS Amorphous Semi-crystalline Network 3-D Structure Amorphous - discrete linear chains Semi-crystalline ordered packing in amorphous matrix
PART I: Thermoset Program Transitions During Cure of a Thermoset Polymerization Cross-linking 3-D Network Modulus, E E g T g E dv Temperature
GOAL: A Unified Model for Modulus Development during Thermoset Cure Phase Transformations Relaxed Modulus, E Cure Kinetics Unrelaxed Modulus, E g Viscoelastic Mechanical Properties Glass Transition Temperature () [ ] n ER t = E + Eg E e i exp i = 1 t τ i Relaxation Time Spectra, E R
Case I. Composite Patch Repair of Metallic Structures CF-18 Y470.5 Bulkhead Thermoset Adhesives Program Team: Drazen Djokic (MScE) Angela Rogers (PhD) Pearl Sullivan X-19 Repair Patch In collaboration with Dr. Andrew Johnston The Institute of Aerospace Research, Ottawa
Project Objectives Investigate residual stress development during patch repair Characterize adhesive cure kinetics during cure process Develop simulation model (viscous-elastic) for predicting: Specimen deformation Cured adhesive interface Substrate in tension Patch in compression Specimen Warpage *, δ *exaggerated deformation
WARPAGE MEASUREMENT Single-sided repair Pre-cured unidirectional carbon fibre/epoxy patch Aluminum substrate FM 73 film adhesive [0 10 ] 304.8 mm 101.6 mm 101.6 mm 50.8 mm Scale: 50 mm Cantilever-Specimen Contact Point Composite Patch Fixture Instrumented Cantilever Beam Al Substrate Al 2024-T3 Substrate Pre-Cured Composite Patch, AS4-3501/6 [0 ] 10 + 1 ply of FM 73 0.20mm 1.50mm 3.30mm Adhesive Film, 1 ply FM 73 Djokic, D. et. al. American Society for Composites Annual Meeting, Austin, Texas, Sept 2000, 12 pgs.
DSC for Cure Kinetics Determination Perform a dynamic temperature scan on uncured and partially cured specimens with DSC. Calculate T g from the heat flow data for each sample. Calculate the degree of conversion for each specimen. Heat Flow (W/g) Tg Temperature ( C) T g Q res α c T g = A 1 + B 1 α + C 1 α 2 α < α c T g = A 2 + B 2 (α - α c ) + C 2 (α α c ) 2 for α > α c
Analytical Models: Cure Kinetics Equation An existing semi-empirical empirical model (Kamal( and Sourour,1973) dα dt 1.85 1.8 = K + K α α α 2 f 1 Rate of Cure, dα/dt (1/min) 0.04 0.03 0.02 0.01 Model Predictions and Experimental Measurements Temperature dependent reaction rate constants: T=95 C T=120 C K K 1 1 = 1.38 10 = 6.62 10 Degree of Cure, α Experiment Model 11 4 exp exp 0.00 0.0 0.2 0.4 0.6 0.8 1.0 Rate of Cure, dα/dt (1/min) 0.12 0.10 9.353 10 0.08 RT 0.06 0.04 3.694 10 4 4 0.02 0.00 RT0.0 0.2 0.4 0.6 0.8 1.0 Degree of Cure, α Experiment Model
E (GPa) 2.5 2.0 E( T E (GPa) 1.5 2.5 1.0 2.0 0.5 Analytical Models: Viscoelastic Response DMA Stress Relaxation Test Data: Relaxation Modulus: 1.5 0.0 20 0 50 100 150 200 250 300 350 400 1.0 C ( α 0.5, t, α) = E Shift Function: ( α) + 0.0-1.0-0.5 0.0 0.5 1.0 1.5 2.0 2.5 Log(t) (min) 2 E ( α) E 30 C 45 C 60 C 75 C 90 C 105 C 120 100 Time -Temperature Superposition: ) log( a T ) = C ( α ) + 2 1 Time (min) T Relaxation Time: u 80 60 40 E (GPa) log( τ) = 3.512 3.073 1 1. 0.735 333 α + α α ( α) Temperature ( C) 2.5 2.0 1.5 2.5 105 C α=0.99 1.0 α=0.95 2.0 α=0.87 0.5 α=0.74 1.5 Model (α=0.99) Model (α=0.95) 0.0 Model (α=0.87) 1.0-2 0 2 4 6 8 Model 10 (α=0.74) 12 E (GPa) exp 0.5 a T t ( T, α) τ( α) Log(ξ) (min) Log (ξ) (min) 30 C 45 C 60 C 75 C 90 C Master Curves, Model and Experimental Results: 0.0-2 0 2 4 6 8 10 12 0.19
Temperature [ C] 120 100 80 60 40 20 Results: Single-Step Cure Cycles 0 50 100 150 200 Time [min] Test 1: T cure =121 C, t hold =60 min 3.0 2.5 2.0 1.5 1.0 0.5 0.0-0.5 Specimen warpage, δ [mm] Specimen Warpage, δ model [mm] 3.0 2.5 2.0 1.5 1.0 0.5 0.0 25 45 65 85 105 125-0.5 T gf = 100 C -1.0 T SF(sim.) = 99.6 C Temperature [ C] Experiment Model T SF(exp.) = 102.2 C Negligible warpage during heating and isothermal hold Non-linear warpage until 100 C (T( gf ) Djokic, D. et. al. Composites A:Applied Sci and Manuf. Vol 33(2), 2001, pp. 277-288.
Specimen Warpage, δ exp. [mm] Experiment 3.0 2.5 2.0 1.5 1.0 0.5 82 C,4hr 77 C, 6hr Results: Single-Step Cure Cycles 104 C, 1hr 121 C, 1hr 0.0 25 45 65 85 105 125 125-0.5 T SF T cure T SF T gf -1.0 Temperature [ C] Specimen Warpage, δ model [mm] Model 3.0 3.0 2.5 2.0 1.5 104 C,1hr 1.0 82 C,4hr 121 C, 1hr 0.5 77 C, 6hr 0.0 25 45 65 85 105 125-0.5 T SF T cure T SF T gf Temperature [ C] -1.00
Next Steps 1. Patch repair model for multi-step cure can be improved by: Including diffusion effects in cure kinetics model Including viscoelastic response within gelation-vitrification range 2. Modulus development needed: Integrate models into FE code
Comparison of Models 0.015 0.002 0.001 dα/dt (min -1 ) 0.010 0.005 Experimental Model 3 Model 4 Proposed Model 0.000 0.85 0.90 0.95 0.000 0.0 0.2 0.4 0.6 0.8 1.0 Degree of Conversion (α)
Refined Cure Kinetics Model d k m ( ) n ( ) n α α 1 1 1- α + k 2 α m2 2 1 1-a = dt 1 + exp C - c [ ( α α )] This model: Suggests that chemical curing is primarily the result of a combination of two autocatalytic reactions; Includes a diffusion factor in the denominator. Rogers, A. and Lee-Sullivan, P., Polymer Engineering and Science Vol. 43(1), Jan 2003, pp 14-25
Case II. Dimensional Stability of Microelectronic Bonds Epo-tek H20E two-part epoxy Silver filled; sub micron-size Electrically Conductive Adhesive (ECA) Thermally conductive Applications: Microelectronics Optoelectronics
Cure Conversion with Time 1.2 1 0.8 Degree of Cure (%) 0.6 80 90 100 110 120 0.4 0.2 0 0 50 100 150 200 250 300 350 400 Time (min)
Cure kinetics for Electrically Conductive Adhesive (ECA) 120 deg. Iso Cure (6h) 0.006 0.005 0.004 da/dt 0.003 0.002 0.001 Run 1 Run 2 Run 3 Iterative Model 0-0.001 0 0.2 0.4 0.6 0.8 1 a(t) Garvin, M. and Lee-Sullivan, P., Canadian Themal Analysis Meeting, Toronto, May 2006
Tg Advancement with Degree of Cure Tg advancement with DOC 90 80 70 60 Tg ( o C) 50 40 30 20 10 0 97.00% 97.50% 98.00% 98.50% 99.00% 99.50% 100.00% DOC (%)
Ultimate Goal of Thermoset Cure Modeling Program n E ( t, T, α) = E ( T, α) + E ( T, α) E ( T, α) e exp R g i 1 i= a t ( T, ) T, ατi α For application in computational modeling: adhesive bonding processes composite processing microelectronic assembly, e.g. underfill, encapsulation
Part II : Thermoplastic Program Goals Characterize time-, temperature- and moisture effects on stability of thin-walled moldings Creep and Stress Relaxation Develop phenomenological model to predict the intrinsic viscoelastic constitutive behaviour (e.g. time-dependent bulk modulus).
Post-Molding Dimensional Stability Does your part warp after molding? Case 1: Polypropylene (PP) Cooling rate effects on part warpage during injection molding
Post-molding thin-wall warpage Warpage in thin-walled plates due to unsymmetrical residual stress during uneven cooling Can be minimized through part-cavity design and processing conditions
Measuring Post-Molding Warpage using Coordinate Measuring Machine Circularity was calculated from 50 measurements: D0 Deviation = diameter/ d Flatness was calculated from 150 measured points on the surface: D1, D2, D3 Deviation = height/ d Disk diameter, d ~ 10 in
1.6 Circularity Flatness 1.4 Average Circularity Average Flatness 0.60 Circularity and Flatness (mm) 1.2 1 0.8 0.6 0.4 0.2 With lower 5 L/min cooling rate: Lower Warpage Lower Warpage Variability 0.50 0.40 0.30 0.20 0.10 Deviation from Round and Flat (%) 0 0.00 0 10 20 30 40 50 60 Warpage after one week after molding 27
Evolution of Warpage over 1 Week Increasingly more warpage as the part ages for higher cooling rate 1.200 Flatness 30 L/min 0.450 Circularity 30 L/min Flatness and Circularity (mm) 1.000 0.800 0.600 0.400 0.200 Flatness 5 L/min Circularity 5 L/min 30 C 30 F 5 0.400 0.350 0.300 0.250 0.200 0.150 0.100 Deviation from Round and Flat (%) 0.050 0.000 0.000 0 1 2 3 4 5 6 7 Days after Molding 28