SAMPE 2016_PREDICTING STRESS RELAXATION BEHAVIOR

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