Predicting Stress Relaxation Behavior of Fabric Composites Using Finite Element Based Micromechanics Model
Anand Vijay KaruppiahGraduate Research AssistantMentor: Dr. Suresh Keshavanarayana Raju Wichita State University
ContentsIntroduction
Literature Review
Finite Element Based Micromechanics Approach
Results & Discussion
Conclusion
Introduction• What is Viscoelasticity ? E.g. Polymers, Fiber Reinforced Composite
• What is stress Relaxation?
• Woven Fabric Composite: E.g. Plain Weave, Satin Weave…etc.• Aerospace Structural Applications:
1. http://www.aerooptimal.com/industries/composite-structures
Stress Relaxation
Problems Faced in Experiments• Stress distribution is Inhomogeneous and unknown• Slippage• Out-of-plane Bending Deformation (Buckling)
Before Loading After Loading
Micro view
Macro view
Uniaxial loading
3-Point Bending (Flexural Loading)
Finite Element based Micromechanics Model Approach
Literature ReviewPlain Weave Architecture2001(Shrotriya ,P et al.)
2012 (Kawai Kwok)
1. “Three-dimensional viscoelastic simulation of woven composite substrates for multilayer circuit boards” by Shrotriya .P et al.2. “Micromechanical modeling of deployment and shape recovery of thin-walled viscoelastic composite space structures” by Kawai Kwok
Assumption
The Unit cell model is idealized to contain a linearly viscoelastic matrix and orthogonally interlaced unidirectional (UD) composite tows (fiber bundles) with waviness and straight regions.
Both fill and warp tows are assumed to contain equal fiber volume fraction.
Cross section of tows are assumed to be a flattened lenticular shape.
Woven Fabric Type: 8-Harness satin Weave
Procedure followedStep 1:Calculating the Design Parameters
• Waviness (Crimp) angle• Aspect ratio of tow cross section• Fiber Volume fraction of Tow• Length of the Unit cell
Microscopic Image of 5320-8HS cross section
Filaments with Resin
Laminate
Tow cross section
Method: Subcell Modeling Approach• The model is assumed to contain
repeating pattern of binary subcells within the unit cell itself.
Software's Used: CATIA V5, Hypermesh v10 and FORTRAN 90.
Step 2: Modeling the Unit cell of 8-Harness Satin Weave
1. Rao .M.P,Pantiuk .M, ”Modeling the Geometry of Satin Weave Fabric Composites”. Journal of Composite Material, Vol. 43, No. 1/2009.
8-Harness Satin Weave
Step 1:Continue
Design Parameters
αhfhW
gwaias ai as
hmh
w
L
h
w
L
LT
Assembly of Binary Subcells for 8-Harness Satin Weave Architecture
Step 2: (Contact Bodies) ContinuedFill Tows Warp Tows
Neat Resin
FEA Software Used: MSC Marc v2014Commercial software
Contact Method followed:Segment-Segment
1.MSC Marc 2011 r1 Reference Manual Vol. B: Element Library, MSC. Software Corporation, Santa Ana, CA, 2011, pp 611.2.MSC Marc 2011 r1 Reference Manual Vol. A: Theory and User Information, MSC. Software Corporation, Santa Ana, CA, 2011, pp 611.
Fiber Bundle/Tows Weave Architecture of 8-Harness Satin
Unit Cell (RVE) of 5320-8HS Woven fabric (Vf=0.56)
Constituents Properties
Material and Sample Fabrication
Material Used: Cytec Cycom 5320-8 HS (Harness Satin) weave fabric prepreg and 5320-1 Pure Epoxy Resin
• Out-of-autoclave material• Dimension: 36mm x 5mm x 0.51mm• Nominal cure temperature: 250F for 1hr• Recommended post-cure temperature:
350F for 2hrs
Stacking Sequence for 5320-8HS• [0/90/90/0]• [+45/-45/-45/+45]
Method used: Stress Relaxation
5320-8HS Prepreg Material
5320-1 Resin
Silicon Mold
Molded 5320-1 Resin Specimen
Material and Sample Fabrication Cont.
Debulking SchemeDebulk time: 20 minutes Manufacture Recommended Cure Profile
Stress Relaxation Recorded
Dis
plac
emen
t, Te
mpe
ratu
re
0 t0 t1 t
Time (min)
Thermomechanical loading
s
tress
0 t0 t1 t
Time (min)
Displacement
Temperature
Test Procedure:
Step 3: Experimental determination of Viscoelastic properties of 5320-1 Epoxy Resin
Dynamic Mechanical Analyzer (DMA) Test setup for 5320-1 Pure Epoxy Resin
5320-1 Resin
3-Point Bending Tension
Master curve Formulation
1
2
( )log
( )o
To
C T Ta
C T T
( / )
1
( ) i
nt
ii
E t E E e
Prony Series
William Landel Ferry (WLF) Equation
Step:1 Step:2
Step:3
1.Cytec. CYCOM 5320-1 Epoxy Resin System. Accessed on [12/18/2015]; Available from http;//www.cemselectorguid.com/pdf/CYCOM_5320-1_031912.pdf.2.Cytec. CYCOM T650-35K Carbon Fiber. Accessed on [12/21/2015]; Available from: http://cytec.com/sites/default/files/datasheets/THORNEL_T650-35_052112.pdf
Table 1. Elastic and thermal properties of the fiber and neat resin
i Ei (MPa) (s)1 2.56E+02 2.75E+02
2 2.33E+02 5.41E+03
3 2.35E+02 9.41E+04
4 2.59E+02 1.47E+06
5 3.73E+02 1.38E+07
6 5.86E+02 9.67E+07
7 4.79E+02 8.05E+08
8 3.70E+02 5.58E+09
9 4.72E+02 3.34E+10
i
Table 2. Relaxation times and coefficients of the Prony series for 5320-1 Epoxy Resin
Step 4: Estimating the Material Properties of Viscoelastic Tows/Fiber Bundles
Hexagonal Array of 5320-UD
( / )( ) ( )
1
( ) M
nt
ijkl ijkl ijkl MM
C t C C e
Stiffness matrix:
(Vf 0.77)
a) σ11 Stress contour under 140 C at 2000s
b) σ23 Stress contour under 140 C at 2000s
c) σ12 Stress contour under 140 C at 2000s
e) σ22 Stress contour under 140 C at 2000s
Step 5: Verification of Model Prediction
Homogenized solid model under flexural loading
(FEA Model)
Experimentation of 5320-8HS
5320-8HS
Overall View of Finite Element Analysis
[+-90] & [+-45] Homogenized laminate model
5320-8HS unit cell (RVE) model
Hexagonal array (Vf 0.77)
Fill Tows
Warp Tows
8 Harness interlaced satin weave architecture
Stress Relaxation Behavior of Woven
Fabric
2. Defining the Contact Body for 5320-8HS Unit cell model (Segment-Segment Contact Algorithm)
1. Estimating the Viscoelastic Properties of Fiber Bundle with Known fiber and Resin Properties under different Load cases
3. Verification of Unit cell Model Prediction
3. Applying Kinematic conditions of Periodic Symmetryand analyzing under different load cases
Accuracy of Micromechanical Model(Elastic Behavior)
5320-8HS System EXPERIMENT FEA (Unit Cell) % ERROR
E11 (Msi) 10.1000 10.6938 5.8789
E22 (Msi) 10.2000 10.7015 4.9163
E33 (Msi) -- 1.8019 --
0.0480 0.0448 6.6693
-- 0.4855 --
-- 0.4851 --
G12(Msi) 0.7550 0.7304 3.2532
G23(Msi) -- 0.5723 --
G31(Msi) -- 0.5727 --
23
12
13
Results and Discussion
Experimental Results
Experimental comparison of Effective Stress relaxation of 5320-8HS and 5320-1 at 140 °C
Numerical Results
Stress Relaxation Behavior of 5320-8HS Unit cell under different load cases at 140 °C
Comparison of Experimental and Numerical Results
(a) (b)
Flexural viscoelastic Behavior of 5320-8HS at 140 °C a) [+-45°] plies b) [+-90°] plies
Stress contours for normal load along the warp direction at time of 2000 s a) Fill Tows b) Warp Tows c) 5320-8HS Unit Cell
a) b)
c)
Observation
Stress contours for normal load along the Fill direction at time of 60s, 500s, 1000s,1500s, 2000s
a) Fill Tow#2 b) Warp Tow#2
a) b)
Stress contours of Neat Resin region around Fill tow#2 at time of 60s, 500s, 1000s,1500s, 2000s
Observation: (Contin.)
(a) (b)
a) Distribution of σ31 in 5320-8HS Laminate model at 2000 s b) Variation of σ31 in 5320-8HS Laminate model along the width of the Specimen at 2000 s, 1500 s, 1000 s, 500s,
100 s, 6 s
Conclusion
• Developed Micromechanical model predictions are in good agreement with experimental results.
• Although the fiber reinforcement improves the mechanical properties of resin, it does not always improve its viscoelastic properties.
• Also, developed micromechanical model can be used to predict the viscoelastic behavior for different various fiber volume fraction.
• Therefore, this in turn reduces a lot of material testing cost and labor.
• Similar procedure can be followed for all woven fabric system
Future Study
• In our current research, we are focusing to validate the master curve generated from the elevated temperatures with micromechanical prediction.
• Also, we are focusing to enhance our computation using Parallel Processing Technique.
References Karami, G., “Finite Element Micromechanics for Stiffness and Strength of Wavy Fiber Composites”. Journal of Composite
Material, Vol. 38, No. 4/2004. Shrotriya, P., Sottos, N., “Viscoelastic response of woven composite substrates”. Composite Science and Technology, Vol.
65, 2005, pp. 621–634. Zhu, Q., Shrotriya, P., Geubelle, P., Sottos, N., “Viscoelastic response of a woven composite substrate for multilayer circuit
board applications”. Composite Science and Technology, Vol. 46, 2003, pp. 394–402. Kawai, K., “Mechanical modeling of deployment and shape recovery of thin-walled viscoelastic composite space structures”.
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2012. Abadi, M.T., “Micromechanical analysis of stress relaxation response of fiber-reinforced polymers”. Composites Science and
Technology 69 (2009): p.1286–1292. MSC Marc 2011 r1 Reference Manual Vol. B: Element Library, MSC. Software Corporation, Santa Ana, CA, 2011, pp 611. MSC Marc 2011 r1 Reference Manual Vol. A: Theory and User Information, MSC. Software Corporation, Santa Ana, CA,
2011, pp 611. Cytec. CYCOM 5320-1 Epoxy Resin System. Accessed on [12/18/2015]; Available from
http;//www.cemselectorguid.com/pdf/CYCOM_5320-1_031912.pdf. Anandvijay, K.R, Suresh, K.R., Kevontrez, K.J., Abhiruchika, S., “An Experimental and Numerical Study of Flexural
Viscoelastic Response of Woven Composite” AIAA, Region V Technical Conference 2016, Ames, IA. Cytec. CYCOM T650-35K Carbon Fiber. Accessed on [12/21/2015]; Available from:
http://cytec.com/sites/default/files/datasheets/THORNEL_T650-35_052112.pdf Kumosa, M., “Micro and Meso-mechanics of 8-HS satin woven fabric composites: part I-Evaluation of elastic behavior”.
Elsevier science Ltd., 2001. Rafic, Y., Hallal, A., et al., Comparative review study on elastic properties Modeling for Unidirectional Composite materials,
Textbook, Chapter 17. INTECH Open Access Publisher, 2012, ISBN: 9535107119. Aliabadi, M.H., “Woven composites”. Computational and Experimental methods in structures-vol.6. London, UK: Imperial
College Press, 2015, ISBN-9781783266173. Rao .M.P,Pantiuk .M, ”Modeling the Geometry of Satin Weave Fabric Composites”. Journal of Composite Material, Vol. 43,
No. 1/2009.
Questions ?
Backup slides
Unit Cell Design Parameters
Mesh Details
Tow Fill warp Resin Total
No. of Elements 864 13824 13824 62472 90120
Element type: Hexahedral, Pentahedral, Tetrahedral
Tow Thickness,g (mm) 0.175
Gap b/w tows, g (mm) 0.04Waviness length, ai (mm) 0.768
Tow cross section Flatness, as (mm) 0.512Unit Cell Length,LT (mm) 10.56
Resin Thickness, hm (mm) 0.002
Unit Cell Thickness, h (mm) 0.352
Crimp angle (deg) α 12
Backup slides X faces Y faces Z faces
Properties X- X+ Y- Y+ Z- Z+
E11 U=0,V and W free
U=cons, V and W free
V=0, U and W free
V=cons, U and W free
W=0, U and V free
W=Wo, U and V free
E22 ,E33 U=0, V and W free
U=cons, V and W free
V=0, U and W free
V=Vo, U and W free
W=0, U and V free
W=cons, U and V free
G12 V=W=0 V=0,W= Wo V=0 V=0 U=V=0 U=V=0
G23 V=W=0 V=Vo ,W= 0 U=W=0 U=W=0 W=0 W=0
Loading and boundary conditions of 8-Harness unit cell in a) XY-Plane and b) XZ-Plane
Boundary Conditions
Backup slidesViscoelastic behavior of tows