THE MATRIX: EVOLUTIONS II

Transcription

1 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

2 Scope: Multi-scale Analyses Atomic/Nanoscale Micro-scale Macro-scale Structural meters 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

3 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

4 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

5 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

6 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

7 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

8 WARPAGE MEASUREMENT Single-sided repair Pre-cured unidirectional carbon fibre/epoxy patch Aluminum substrate FM 73 film adhesive [0 10 ] mm mm 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 ] ply of FM mm 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.

9 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

10 Analytical Models: Cure Kinetics Equation An existing semi-empirical empirical model (Kamal( and Sourour,1973) dα dt = K + K α α α 2 f 1 Rate of Cure, dα/dt (1/min) Model Predictions and Experimental Measurements Temperature dependent reaction rate constants: T=95 C T=120 C K K 1 1 = = Degree of Cure, α Experiment Model 11 4 exp exp Rate of Cure, dα/dt (1/min) RT RT Degree of Cure, α Experiment Model

11 E (GPa) E( T E (GPa) Analytical Models: Viscoelastic Response DMA Stress Relaxation Test Data: Relaxation Modulus: C ( α 0.5, t, α) = E Shift Function: ( α) Log(t) (min) 2 E ( α) E 30 C 45 C 60 C 75 C 90 C 105 C Time -Temperature Superposition: ) log( a T ) = C ( α ) Time (min) T Relaxation Time: u E (GPa) log( τ) = α + α α ( α) Temperature ( C) C α= α= α= α= Model (α=0.99) Model (α=0.95) 0.0 Model (α=0.87) 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:

12 Temperature [ C] Results: Single-Step Cure Cycles Time [min] Test 1: T cure =121 C, t hold =60 min Specimen warpage, δ [mm] Specimen Warpage, δ model [mm] T gf = 100 C -1.0 T SF(sim.) = 99.6 C Temperature [ C] Experiment Model T SF(exp.) = 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

13 Specimen Warpage, δ exp. [mm] Experiment C,4hr 77 C, 6hr Results: Single-Step Cure Cycles 104 C, 1hr 121 C, 1hr T SF T cure T SF T gf -1.0 Temperature [ C] Specimen Warpage, δ model [mm] Model C,1hr C,4hr 121 C, 1hr C, 6hr T SF T cure T SF T gf Temperature [ C] -1.00

14 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

15 Comparison of Models dα/dt (min -1 ) Experimental Model 3 Model 4 Proposed Model Degree of Conversion (α)

16 Refined Cure Kinetics Model d k m ( ) n ( ) n α α α + k 2 α m 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

17 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

18 Cure Conversion with Time Degree of Cure (%) Time (min)

19 Cure kinetics for Electrically Conductive Adhesive (ECA) 120 deg. Iso Cure (6h) da/dt Run 1 Run 2 Run 3 Iterative Model a(t) Garvin, M. and Lee-Sullivan, P., Canadian Themal Analysis Meeting, Toronto, May 2006

20 Tg Advancement with Degree of Cure Tg advancement with DOC Tg ( o C) % 97.50% 98.00% 98.50% 99.00% 99.50% % DOC (%)

21 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

22 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).

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24 Post-Molding Dimensional Stability Does your part warp after molding? Case 1: Polypropylene (PP) Cooling rate effects on part warpage during injection molding

25 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

26 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

27 1.6 Circularity Flatness 1.4 Average Circularity Average Flatness 0.60 Circularity and Flatness (mm) With lower 5 L/min cooling rate: Lower Warpage Lower Warpage Variability Deviation from Round and Flat (%) Warpage after one week after molding 27

28 Evolution of Warpage over 1 Week Increasingly more warpage as the part ages for higher cooling rate Flatness 30 L/min Circularity 30 L/min Flatness and Circularity (mm) Flatness 5 L/min Circularity 5 L/min 30 C 30 F Deviation from Round and Flat (%) Days after Molding 28