A Physics-Based Process Model for the Co- Cure of Honeycomb Core Sandwich Structures

Transcription

1 A Physics-Based Process Model for the Co- Cure of Honeycomb Core Sandwich Structures M.C. Gill Composites Center University of Southern California Center for Composite Materials University of Delaware Formal Research Update 8 December 2017

2 Overview Contractors: University of Southern California Prof. Steven Nutt, PI Prof. Timotei Centea, Co-I University of Delaware Prof. Suresh Advani, PI Sponsor: NASA Langley Research Center Roberto Cano, Technical Monitor Project Term: Phase 1 11/01, /31, 2017 Phase 2 11/01, /31,

3 Introduction Characterize material properties and behavior that influence bond-line quality for a representative composite (Year 1) 2. Identify key material process structure relationships and formulate equations that capture observed behavior (Year 2) 3. Develop an integrated physics-based process model for co-cure of sandwich structures. 4. Refine and validate model through case studies. 3

4 Phase II Phase I Timeline WORK PACKAGE WP1 1.1 Prepreg 1.2 Film Adhesive 1.3 Honeycomb Core (E+M) WP2 2.1 Governing Equations 2.2 Lab-Scale Studies WP3 3.1 Numerical Implementation 3.2 Lab-Scale Studies 3.3 Demonstrator Studies WP4 4.1 Model Refinement 4.2 Demonstrator Studies YEAR 1 YEAR 2 YEAR 3 YEAR 4 M1.3 M1.1 M1.2 M2.1 M2.2 M3.1 M3.2 M4.1 M3.1 Implement governing equations within numerical process simulation M3.2 Validate numerical process simulation using demonstrator case studies 4

5 Today s Presentation Facesheet Permeability Modeling Facesheet Consolidation Modeling Fillet Formation Model Validation Void Growth Modeling Model Integration 5

6 Modeling Approach Sandwich Panel Facesheet Consolidation Fiber bed compaction Resin pressure Resin loss Network Model Adhesive Bond-Line Formation Fillet formation flow Void formation Core Pressure Evolution Gas transport through skins, interfaces Volatile release Gas pressurization Physics-Based Sub-Models 6

7 Modeling Approach Network Model For Entire Structure 1. Complex Geometry 2. Substantial Number of Material Properties Model for a Few Cells 1. A Few Parameters Characterizing Macroscopic Behavior 2. There Are Only Several Different Volumes (2) and Conductivities (3) 7

8 Gas Flow Through Facesheets Gas Flow Occurs when tunnel is formed Tunneling occurs when: P gas > P resin + P capillary Physical Behavior Pressure differences (between gas pressure, resin pressure, and capillary pressure) force the resin to migrate within the fiber bed. Resulting behavior (transience, flow delays, residual pressure) are not usually predictable using simple Darcy s Law. 8

9 Facesheet Permeability Modeling Implementation of multiphase flow model Liquid phase Brooks & Corey Eq. Burdine Eq. Gas phase Simultaneously solve for effective liquid saturation (S e ) and gas pressure (P g ) Solved over x (finite differences) and t (forward explicit) 9

10 Model Output Over x at current time step Over time Max flow does not occur at max ΔP. Resin takes time to desaturate. 10

11 Pros and Cons of this Approach Pros: More physics-based than previous approaches Can potentially account for delays at high resin viscosities Capable of accurately capturing experimental trends: Cons: Slow to compute May be difficult to integrate into overall co-cure model Two characteristic time scales: 11

12 Consolidation and Bleeding H P a P b The Physics 101: 1. Pressures at Resin Surface P c and P b are Unequal 2. Consequently There Should Be Flow ~ K resin P c P b η T H Resin Bleeds P c 3 Pressure Values Controlled p a >p b p a >p c Resin Bleeds The Physics 102: 1. Fiber Bed Deforms 2. Consequently There Should Be Squeeze Flow Coming Out The Physics 103: 1. Domain Not in Equilibrium 2. Consequently There Must Be Some Traction Along Verticals 12

13 Solution σ = p b p a 1 x H + 2 π 1 1 i sin iπ x Τ H exp i2 π 2 K 0 E η 0 H 2 t p = p b 1 x H + p c x H p 2 1 b p a π sin iπ i x Τ H exp i2 π 2 K 0 E η 0 H 2 t 1 FOR FLOW p = p c p b H + 2 p a p b H 1 cos iπ xτh exp i2 π 2 K 0 E η 0 H 2 t Q cb = K η p c p b H t Q pref2c = p a p b H E π 2 Q cb t c = η 0H 2 π 2 K 0 E = p c p b H π 2 E Q pref2bag = p a p b H E π 2 Assumes Time Long Enough Generally Flows to Bag 13

14 Case Studies Pa: Pb: Pc: 1.00E+06 Pa 1.00E+05 Pa 1.00E+05 Pa Pa: Pb: Pc: 1.00E+06 Pa 0.00E+00 Pa 1.00E+05 Pa Pa: Pb: Pc: 1.00E+06 Pa 0.00E+00 Pa 5.00E+05 Pa Pa: Pb: Pc: 1.00E+06 Pa 1.00E+06 Pa 0.00E+00 Pa Pa: Pb: Pc: 1.00E+06 Pa 0.00E+00 Pa 0.00E+00 Pa This Gives Resin Flow. What About Dimpling? 14

15 Facesheet Consolidation: Radial Geometry Strains ε r = u r ε t = u r /r ε = u r + u r /r p app r Momentum Constitutive Equation σ r + σ r σ t r = 0 σ r = E T ε r p σ t = E L ε t p u r U r =0 Now what we do with the pressure? Usual Consolidation: 1. Make it Hydrostatic 2. No Motion Relative to Reinforcement In Our Case Needs To Flow to 1. Get Resin vs Adhesive Mixing 2. Figure Out Where Volatiles Go 1. They will Follow Resin 15

16 Allowing Resin Flow (Radial) Conventionally: ε ሶ = K p μ p app But We Are only at (1-f): εሶ φ ሶ = (1 Uφ) K p μ p n = 0 v r : Resin Relative To Fiber r We Need to Relate Porosity to Pressure: Mobility Factor φp = p 0 φ 0 p n = 0 u r U r =0 Can We Add the Local Pressure Loss? Is This Getting Too Complex for Practical Purposes Number of Parameters 16

17 Application for Co-Cure P a R P b Needs to Deal with Radius Change Quasi-static: et-> Decrease in Radius Needs Correction P c This Might Predict Dimpling If We Can Characterize In-Plane Prepreg Tensile Behavior 17

18 Conclusions There are Two Flows that Move Resin from Prepreg One Driven by Core and Bag Pressure Dependence Increasing With Time One Driven by Autoclave and Bag Pressure Difference, Constrained by Stiffness of Prepreg We Can Combine Flow With Deformation Brings in Extra Material Parameters We Need To Know Porosity in Facesheets Dimpling of Facesheets Where the Volatiles Go (Pressure Models, Adhesive Porosity) 18

19 Fillet Formation Model Validation s Models steady-state balance of hydrostatic forces 19

20 Fillet Formation Model Validation Symmetric: a=0, 2 parameters (b, g) W= half cell size Non-symmetric: 3 parameters (a, b, g) W= not good descriptor Should use Area(Volume) Non-dimensional parameters: α = facesheet contact angle (0 for symmetric case) b = cell wall contact angle σ g = surface tension = ρgw 2 s = surface tension of adhesive r = adhesive density Non-dimensional outputs: Height = H/W Area = A/W 2 20

21 Fillet Formation Model Validation Solution for Height Parameters used: a = 0 (symmetry) b = 0.5 (or 30 ) g = 1 s = 35 x 10-3 J/m 2 r = 1450 kg/m 3 W = m (for 1/8 in cells) H/W ~ 0.54 Solved for b = 0.5 Model can also solve for fillet area (not shown) 21

22 Fillet Formation Model Validation Baseline case for validation: Co-bond: flat facesheet, only adhesive resin available for fillet formation Ambient core pressure: low void content, no redistribution 9658 UNS: no interaction with support 0.5 mm Other cases considered: Vacuum core pressure: adhesive redistribution 9658 NWG: possible interaction with support Co-cure w/ reticulation and in-bag pressurization: no void content, different initial adhesive distribution 22

23 Avg. Height [mm] Fillet Formation Model Validation Sample Avg. Height % Deviation Comments Baseline (ambient, cobond, 9658 UNS adhesive) mm 17.1% Best agreement of four cases assessed Vacuum in core mm 38.5% Foaming/redistribution causes small fillets High variability 9658 NWG adhesive mm 54.2% Interactions with support appear to restrict flow Co-cure, in-bag pressurization, reticulation Model: H/W = 0.54 H = mm Baseline Vacuum Supported IBP, Reticulated mm 25.1% Reticulation deposits adhesive at cell walls more resin to form fillets Larger cells model prediction should be adjusted, but does it matter? Model provides reasonable prediction for baseline Deviations from baseline cause varying deviations from model 23

24 Fillet Formation Model Validation Summary Preliminary model and baseline case show reasonable agreement, to be refined moving forward Assessment of symmetry assumption (a = 0, normalize w.r.t. W) Assessment of area predictions What deviations from the baseline can we predict? Vacuum: requires modeling of foaming/redistribution, high variability observed Supported adhesive: requires modeling of adhesive-support interaction, but fillet size fairly consistent Reticulation: different initial distribution of adhesive In-bag pressurization: additional pressure applied to resin Co-cure: non-rigid facesheet, requires modeling of facesheet compaction and bleed 24

25 Summary of Bubble Growth Modeling Idea of modeling 1. What is the origin of voids? 2. How do they behave in different applied pressure scenarios? 3. How can they interact with core pressure? Origins of voids Nucleation phenomenon 1 st guess Nucleation Heterogeneous Nucleus at a surface More common than homogeneous nucleation Usually happens before than homogeneous nucleation Heterogeneous Homogeneous Homogeneous formed in the bulk of the liquid Origin is the fluctuating thermal motions in the liquid 25

26 Summary of Bubble Growth Modeling Homogeneous Nucleation Classical Nucleation theory (CNT) The minimum work W min required to form a vapor bubble: W min = σa P v P L V= σ(4πr 2 ) P c ( 4 3 πr3 ) Surface energy needed create the surface of a bubble Reversible work needed for vaporizing molecules W min r = 0 σ 4πr 2 P c 4 3 πr 3 = 0 r = 2σ P c Pc :Critical pressure difference If we consider nucleation is the source of bubbles in the adhesive, r can be our initial radius for growth modeling. But, is it really the origin of voids? Need better observation Or Existing solvent can be the origin of voids 26

27 Summary of Bubble Growth Modeling Growth modeling for single bubble: Single bubble surrounded by adhesive film Radius of film s rim is assumed to be infinite ( bubble radius << distance between bubbles) Relationship between concentration and gas pressure inside the bubble (Henry s Law) Adhesive has initial gas concentration value of C 0 which is related to the atmospheric pressure (C 0 =K h P g0 ) Vacuum case Compression case Compression case Vacuum case 27

28 Summary of Bubble Growth Modeling Interaction of growth model with core pressure Making perforated adhesive is dependent on the thickness of adhesive at the bubble position. Rough estimation : Conservation of mass ( without adhesive squeezing into prepreg ) with unknown d Whenever R gets equal/greater than d it means bubble s surface hit the adhesive perimeter. w wd = න [ x w d] dx d = D w

29 Summary of Bubble Growth Modeling X=w/2 is our critical point in which we have to calculate if bubble hits the Surface of adhesive or not. X=w/2 As the graphs show, after 150s, bubble didn t make the adhesive perforated. 29

30 Growth Model and Mass Conservation Where Do We Get Void Creation? Sends in Void Creation Input: Material Parameters, Cell State(Volatiles Generated, Cure Degree,Dewetting ) Output: P (and T?) in Cells Outflows Updates p, T as Needed (Each Step) If Bubble Bursts, Sends Size of Breech That Modifies Resistances and Volumes Bubble Model 30

31 Volatile Generation Model? Where Do We Get This Model? Volatile Generation Model Input: Material Parameters, Cell State(Volatiles Generated, Cure Degree,Dewetting ) Output: P (and T?) in Cells Outflows? Sends in Void Creation Bubble Growth Model 31

32 Project Team Steven Nutt Professor PI Timotei Centea Research Asst. Prof., Co-I Mark Anders PhD Student Daniel Zebrine PhD Student Suresh Advani Professor Co-PI Pavel Simacek Research Associate Navid Niknafs Kermani PhD Student 32

33 Acknowledgements Funding: NASA Langley Research Center NRA NNL16AA13C Roberto Cano, Brian Grimsley Technical Input: NASA Advanced Composites Project United Technologies Aerospace Systems Materials: Hexcel (Gordon Emmerson, Yan Wang) Cytec Solvay (Scott Lucas, Steve Howard) Henkel (David Leach) Airtech International (Gerry Jackson) 33