2. Predicting Stress Relaxation Behavior of
Fabric Composites Using Finite Element
Based Micromechanics Model
Anand Vijay Karuppiah
Graduate Research Assistant
Mentor: Dr. Suresh Keshavanarayana Raju
Wichita State University

3. Contents
Introduction
Literature Review
Finite Element Based
Micromechanics Approach
Results & Discussion
Conclusion

4. 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

5. 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)

6. Finite Element based Micromechanics
Model Approach

7. Literature Review
Plain Weave Architecture
2001(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

8. 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

9. Procedure followed
Step 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

10. 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

11. Step 1:Continue
Design Parameters
α
hf
hW
gw
aias ai as
hm
h
w
L
h
w
L
LT

12. Assembly of Binary Subcells for 8-Harness
Satin Weave Architecture

13. Step 2: (Contact Bodies) Continued
Fill Tows Warp Tows
Neat Resin
FEA Software Used:
MSC Marc v2014
Commercial 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.

14. Fiber Bundle/Tows Weave Architecture of 8-Harness Satin
Unit Cell (RVE) of 5320-8HS Woven fabric (Vf=0.56)

15. Constituents Properties

16. 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

17. Material and Sample Fabrication Cont.
Debulking Scheme
Debulk time: 20 minutes Manufacture Recommended Cure Profile
Stress Relaxation Recorded
Displacement,Temperature
0 t0 t1 t
Time (min)
Thermomechanical loading
stress
0 t0 t1 t
Time (min)
Displacement
Temperature
Test Procedure:

18. 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

19. Master curve Formulation
1
2
( )
log
( )
o
T
o
C T T
a
C T T

 
 
( / )
1
( ) i
n
t
i
i
E t E E e 


  
Prony Series
William Landel Ferry (WLF)
Equation
Step:1 Step:2
Step:3

20. 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

21. Step 4: Estimating the Material Properties
of Viscoelastic Tows/Fiber Bundles
Hexagonal Array of 5320-UD
( / )
( ) ( )
1
( ) M
n
t
ijkl ijkl ijkl M
M
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

22. Step 5: Verification of Model Prediction
Homogenized solid model under
flexural loading
(FEA Model)
Experimentation of 5320-8HS
5320-8HS

23. 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 Symmetry
and analyzing under different load cases

24. 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

25. Results and Discussion

26. Experimental Results
Experimental comparison of Effective Stress relaxation of 5320-8HS and 5320-1 at 140 °C

27. Numerical Results
Stress Relaxation Behavior of 5320-8HS Unit cell under different load cases at 140 °C

28. Comparison of Experimental and Numerical
Results
(a) (b)
Flexural viscoelastic Behavior of 5320-8HS at 140 °C
a) [+-45°] plies b) [+-90°] plies

29. 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

30. 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)

31. Stress contours of Neat Resin region around Fill tow#2 at time of 60s, 500s,
1000s,1500s, 2000s

32. 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

33. 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

34. 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.

35. 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.

36. Questions ?

37. 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) 0.04
Waviness length, ai (mm) 0.768
Tow cross section Flatness,
as (mm) 0.512
Unit Cell Length,LT (mm) 10.56
Resin Thickness, hm (mm) 0.002
Unit Cell Thickness, h (mm) 0.352
Crimp angle (deg) α 12

38. 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

39. Backup slides
Viscoelastic behavior of tows