Fuzheng Yang Defense

Investigations on Interface and Interphase Development in Polymer-

Matrix Composite Materials

F. Yang, Ph.D. Candidate

Composites Processing Laboratory

Department of Mechanical Engineering

University of Connecticut

Storrs, Connecticut 06269-3139

Presented at the Ph. D. Oral Defense

July 12, 2002 • Storrs, Connecticut

Composites Processing Laboratory, University of Connecticut

Interface and Interphase in Polymer-Matrix Materials

Debonding and pull-out of fiber

reinforcements from matrix could

occur because of poor Interphase

properties

matrix

fiber“Bad”

interfacial

bonding

“Good”

interfacial

bonding

Interface refers to the interlaminar region between two surfaces

of thermoplastic sheets

Interphase is the region near the fiber surface


Objective

Develop a fundamental description of the phenomena

governing interfacial bonding during thermoplastic

composites processing

Develop a fundamental description of the microscale

mechanisms to predict the interphase formation during

thermosetting composites processing


Thermoplastic Composites Processing

Based on the principle of fusion bonding

Intimate contact is a critical prerequisite in the processing


Intimate Contact

Development of Area Contact at the Interface Due to Flattening of

Asperities on Prepreg Surfaces

Geometric structure is random

Roughness features are found

over a number of length scales

Frequency, [m -1]

10 -1 4

10 -1 2

10 -1 0

10 -8

102

103

104

Po

wer

Spectr

um

, S

(

) [

m-3]

IM7/PIXA-M Tape

S( ) -2.1

D = 1.45

o = 1/Lo

S() ~ 2D-5

This suggests the existence of a

fractal structure in the surface

profiles


Lo

Second Generation: L2 = L1/f = Lo/f2

h1 = ho/f

Fractal Cantor Set Model of Prepreg Surfaces

Captures the multiscale asperity structure found in real surfaces

Parameters of the Cantor Set Surface: D, ho, Lo, f, and s

First Generation: L1 = Lo/f(n)th Generation: Ln = Lo/fn

hn-1 = ho/fn-1

s = 2 new asperities perprevious generation asperity

ho

Lo

L1/3

h1

s = 3 new asperities perprevious generation asperity


Frequency, [m -1]

10 -1 4

10 -1 2

10 -1 0

10 -8

102

103

104

Po

wer

Spectr

um

, S

(

) [

m-3]

IM7/PIXA-M Tape

S( ) -2.1

D = 1.45

FFT

Determination of Cantor Set Surface Parameters

o = 1/Lo

Lo is determined from o

s

; ho is determined from the r.m.s. height: ho = 2s

u

f is determined using relation between linear contact area

Li and displacement u (obtained using volume

conservation of Cantor set surface compression).

Li s u

f ho Lo

S() ~ 2D-5D is determined from the power spectrum:

s is related to D and f using the statistical properties of a

self-affine fractal set (Majumdar, 1996) s f

D/ 2-D


Initial Location of the Contact Surface

Cantor Set Surface Deformation

5oa

15a

15

3oboa4dt

t

0

F =

ˆ

6a

3oboa

dt

da4

3a

3b

dt

da4d

op-pF

b

0

)(

ˆ

Basic deformation process is that of squeeze flow of a 2-D rectangle

a

b

d

F̂

a0

bo

adu

d+

da

dt = 0; u =

a2

12

dp

d

dp

d0

p po

ano

The contact between rough surfaces

modeled as contact between an

equivalent rough surface and a flat

surface

Deformed material flows into the

troughs between the asperities

When (n+1)th generation asperities

deform, asperities of the (n)th and

lower generations retain their shape

anf

an-1o


Dicn t

NbnLo

snan0bn0

Loan

1

fn5

4

hoLo

2f

2nD2D

n4

f 1 2

papp

dt 1

tn1

t

15

n 1

Intimate Contact Model

The results of the squeeze flow of a rectangle can be used recursively

through all the asperity generations in the Cantor set to get the degree of

intimate contact development with time.

Lo

N

papp

dt =

tn1

t

4 an0bn0

3

5

1

an5

1

an05

bn0 LnN

Lo

fnsn

an0ho

fn2 f 1

anf ho

fn1 f 1


Experimental Processing Setup


Nondestructive Dic Measurements

DAQ Board

Tank

Stand

Amplifier

Gate

Display

Y-Axis Position

Transducer

Sample

X-Axis Position

Rate Generator

Pulser/Receiver Interlaminar contact wasexamined using an immersionultrasonic C-Scan technique

Degree of Intimate Contact isobtained as the ratio of thecontacting (light gray) areasto the total specimen area.


Data Comparisons—AS4/PEEK(Yang and Pitchumani, J. Materials Sci., 2001)

Lee and Springer [6]Fractal Model

0.0

0.2

0.4

0.6

0.8

1.0

0 100 200 300 400 500 600/0

T = 350 oC

P = 276 kPa

(a)

Time, t [sec]

De

gre

e o

f In

tim

ate

Co

nta

ct,

Dic

100 200 300 400 500 600

T = 350 oC

P = 663 kPa

(b)

0.0

0.2

0.4

0.6

0.8

1.0

0 100 200 300 400 500 600

T = 350 oC

P = 1630 kPa

(c)

Time, t [sec]

De

gre

e o

f In

tim

ate

Co

nta

ct,

Dic


IM7/PIXA-M Thermoplastic Tapes(Yang and Pitchumani, J. Materials Sci., 2001)

1125 kPa 3375 kPa2250 kPa

260oC

300oC

280oC

0 200 400 600 800 1000/0 200 400 600 800 1000/0 200 400 600 800 1000

Time, t [sec]

0.0

0.2

0.4

0.6

0.8

1/0

0.2

0.4

0.6

0.8

1/0

0.2

0.4

0.6

0.8

1.0

Degre

e o

f In

tim

ate

Conta

ct, D

ic


Publications

1. F. Yang and R. Pitchumani, "A Fractal Model for Intimate Contact Development

During Thermoplastic Fusion Bonding," in: Proceedings, 13th Technical

Conference of the American Society for Composites, A. J. Vizzini, ed., pp. 1134-

1146, 1998.

2. F. Yang and R. Pitchumani, "Modeling Interlaminar Contact Evolution During

Thermoplastic Composites Processing Using a Fractal Tow Surface Description,"

ANTEC Conference, Society of Plastics Engineers, pp. 1316-1320, 1999.

3. F. Yang and R. Pitchumani, "Fractal Description of Interlaminar Contact

Development During Thermoplastic Composites Processing," Journal of

Reinforced Plastics and Composites, 20, pp. 536-546, 2001.

4. F. Yang and R. Pitchumani, "A Fractal Cantor Set-based Description of Intimate

Contact Evolution During Thermoplastic Composites Processing," Journal of

Materials Science, 36, pp. 4661-4671, 2001

5. F. Yang and R. Pitchumani, "Interlaminar Contact Development During

Thermoplastic Fusion Bonding," Polymer Engineering and Science, 42, pp. 424-

438, 2002


Minor Chain

t = t1

Polymer Healing (Reptation Theory, de Gennes, 1971)

Interdiffusion of polymer chains across interfacial areas in intimate

contact

t = tR

s

t

M

1/ 4

Dh s

s

t

tR

1/ 4

ISOTHERMAL

[Diffusion]

t

M

1/2

[Random Walk] 1/2


P(s,t ) 1

4f t L2exp

s2

4L2 f t

; f t

dt

tR(T )0

t

Nonisothermal Polymer Healing(Yang and Pitchumani, Macromolecules, 2001)

Define a Probability Density Function, P(s,t), as the

probability of finding a particular chain segment at

position, s, and at time, t, such that: P(s,t )ds 1

t s

2 s

2

P(s,t )ds 2 f t L2 Minor chain length at any time

is obtained as the root mean

squared length

Dh t t

L

1/ 2

dt

tR t 0

t

1/ 4

P

t D

2P

s2

P(s,0) (0)

P(s,t ) P(s,t )

s 0 as s

s: curvilinear coordinateD: reptation diffusivity, f(T)


Nonisothermal Healing Model Validation

0.0

0.2

0.4

0.6

0.8

1.0

0 500 1000 1500 2000 2500 3000

Time, t [sec]

Deg

ree o

f h

ea

ling

, D

h

370 oC

400 oC

Ramp: 250 sec.

0.0

0.2

0.4

0.6

0.8

1.0

0 1000 2000 3000 4000 5000

Time, t [sec]

Deg

ree o

f h

ea

ling

, D

h

370 oC

400 oC

Ramp: 5500 sec.Interfacial Strength data

Obtained using Lap Shear Test


Coupled Bonding Model

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Db

Dh

Dic

Qu

an

titie

s D

b, D

h, D

ic

Dimensionless time,

(a)

fb

= 2.23

dtdt

tdDttDtDDtD

ft

icfhfhicfb

0

0

timecontact intimate

time healing1

5/1

*

*

appw

b

ptgf

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Qu

an

titie

s D

b, D

h, D

ic

Dimensionless time,

(b)

fb

= 0.83

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Qu

an

titie

s D

b, D

h, D

ic

Dimensionless time,

(c)

fb

= 1.03

The effective bond strength

may be given as

A fusion bonding number is defined

as the ratio between the healing

time and the intimate contact time


Processing Windows For Fusion Bonding

Three processing regimes are quantitatively established for the

thermoplastic material AS4/PEEK

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

0.0 1.0 2.0 3.0 4.0 5.0

fb,min

fb,max

Fu

sio

n B

ond

ing N

um

ber,

Dimensionless Heating Rate, d d

(a)

f b

Healing Limited

Intimate Contact Limited

Equally Dominant

0.0

0.5

1.0

1.5

2.0

2.5

0.0 1.0 2.0 3.0 4.0 5.0

Dimensionless Cooling Rate, -d /d

(b)

Fu

sio

n B

ond

ing

Num

be

r,

f b

Healing Limited

Intimate Contact Limited

Equally Dominant


Publications

1. F. Yang and R. Pitchumani, "A Model for Non-isothermal Healing of

Thermoplastic Polymers During Fusion Bonding," To appear in

Proceedings of the Symposium on Polymer and Composite

Materials Processing, ASME IMECE, New York, NY, November 2001

2. F. Yang and R. Pitchumani, “Healing of Thermoplastic Polymers at

an Interface Under Nonisothermal Conditions," Macromolecules, 35,

pp. 3213-3224, 2002

3. F. Yang and R. Pitchumani, “A Nonisothermal Model for Healing and

Bond Strength Evolution at an Interface during Thermoplastic

Matrix Composites Processing," Polymer Composites, in press,

2002


Objective

Develop a fundamental description of the phenomena governing

interfacial bonding during thermoplastic composites processing

Develop a fundamental description of the microscale

mechanisms to predict the interphase formation during

thermosetting composites processing


Outline

Thermosetting composites curing process

Processing-Interphase-Property relationship

Interphase formation model

Correlation Studies

Summary and future work


Thermosetting Composite Curing

Curing is described by

macroscale thermochemical

models consisting of the

energy equation and the

curing kinetics equation

The presence of fibers in the composites significantly alter the cure

characteristics near the fiber surface via several microscale

phenomena

An interphase region forms with different composition from the bulk

resin, which dramatically influences the overall material propertiesj

Thermosetting composite

materials are processed by

high temperature cure cycles


Processing-Interphase-Property Relationship

Microscale Interphase

Formation Phenomena

Relationship of

Interphase Composition

with

Material Properties

Examples: Modulus, CTE

T

t

Cure

Cycle

Interphase

Composition

Profile

c

x Overall Properties

(Drzal, 1990–1992;

S. Subramanian, et al., 1996;

R. W. Rydin et al., 1997)

Macroscale

thermochemical

phenomena

(Palmese, 1992)


Microscale Interphase Formation Phenomena

Factors influencing interphase formation (Drzal, 1986)

Surface roughness of the fiber causes non-uniform deposition of

the matrix components

Surface treatments of the fiber yield chemically and structurally

different regions near fiber surfaces

The presence of thin

monomer coating

The preferential adsorption

of the resin component onto

the fiber surfaces

Focus of the present study is placed on the preferential adsorption

kinetics near fiber surfaces which is the principal governing

mechanism of interphase formation for a given surface treatment and

coating processes etc.


Adsorption-Desorption-Diffusion-Reaction Processes

Epoxy and amine molecules

have two states, i.e., adsorbed

state and bulk state, and mass

exchanges between the two

states

An adsorbed molecule is

considered to deposit on the

bare fiber surface or on top of

the other adsorbed molecule

Molecules in the bulk state may

diffuse within the resin mixture

Chemical reaction takes place

simultaneously with the

adsorption and desorption

processes

Adsorption-desorption-diffusion in

Epoxy/Amine System


Microscale Process Description

dN E, i

dt Ra, E i 1,i Ra,E i,i Ra,E i 1,i Rd ,E i 1,i Rd, E i ,i Rd ,E i 1,i n1kr NE, i

storage adsorption, Ra, E(i ) desorption, Rd, E (i ) reaction

For the reaction, n1 E + n2 A P, consider the mass balance of each

species in the adsorbed and bulk states at the (i)th molecular layer

A set of ODE can be formulated to describe the microscale

adsorption-desorption-diffusion-reaction process, whose solution

yields the concentration profile evolution near the fiber surfaces

1,,1,1,,1,

2

,,,,,,

,12

1,,1,,

iiRiiRiiRiiRiiRiiR

NknL

NNND

dt

dN

EdEdEdEaEaEa

iEr

iEiEiE

AE

iE

{

{

Adsorbed

state

Bulk

state

1,,1,

1,

1,,

,

,1

iii

iERT

E

iiEaEaNNN

NeNNkiiR

Ea

dN A,i

dt Ra, A i 1,i Ra, A i,i Ra, A i 1,i Rd, A i 1,i Rd, A i ,i Rd , A i 1,i n2kr NE,i

storage adsorption, Ra, A( i ) desorption, Rd, A (i ) reaction


Diffusion Limited Reaction

The diffusivity D and reaction rate kr are functions of dimensionless

epoxy concentration, = NE(t)/NE0 , and temperature T

The diffusivity is described by free volume theory (Sanford, 1987)

DEA T, D0exp ED /RT exp bD / f g f T Tg {

The reaction rate kr is controlled by the retarded diffusion process at

later stages of polymer cure

Tg Tg0

Tg

0

Ex /Em Fx /Fm 1 1 1Fx /Fm 1

where the glass transition

temperature, Tg(), is given by the

DiBenedetto equation

kr kr 0exp Ea /RT

1 / Dexp Ea /RT

The parameters D0, bD, fg, f, ED, Tg0, Ex/Em, Fx/Fm, kr0, , and Ea in

the above equations depend on the type of thermosetting system


Non-dimensional Groups

Principal non-dimensional groups of the model are identified as:

Adsorption Damköhler Number g Kr0Ka,E exp[(Ea,E-Ea)/RT0]

Epoxy Desorption Ratio bE Kd,EKa,Eexp[(Ea,E- Ed,E) /RT0]

Amine Adsorption Ratio A Ka,AKa,Eexp[(Ea,E- Ea,A) /RT0]

Amine Desorption Ratio bA Kd,AKa,Eexp[(Ea,E- Ed,A) /RT0]

Diffusion Ratio fEA D0 (Ka,E L2) exp[(Ea,E - ED) /RT0]


0

20

40

60

80

100

-20 0 20 40 60 80 100 120

PA

CM

20

Vo

lum

e P

erc

enta

ge

Distance from Fiber Surface, [nm]

(b)

0

10

20

30

40

50

60

70

80

0 1000 2000 3000 4000

ModelArayasantiparb, et al., [51]

PA

CM

20

Vo

lum

e P

erc

enta

ge

Distance from Fiber Surface, [nm]

(a)

Correlation With Experimental Data

g5.9,bE = 1162.0, A = 28900.0, bA = 809.0, fEA = 3.5 X109

The model predictions are correlated to

interphase concentration profiles measured by

Arayasantiparb, et al., 2001 using electron

energy-loss spectroscopy (EELS) in a scanning

transmission electron microscope (STEM)


Publications

1. F. Yang and R. Pitchumani, “Modeling of Interphase Formation on Unsized

Fibers in Thermosetting Composites," in Proceedings of ASME Heat

Transfer Division, ASME-HTD-366-3, 329-337, 2000.

2. F. Yang and R. Pitchumani, “Kinetics of Interphase Formation in

Thermosetting Composites," To appear in Proceedings of 16th Technical

Conference of the American Society for Composites, Blacksburg, VA,

September 2001.

3. F. Yang and R. Pitchumani, “Studies on Fiber/Matrix Interphase

Development in Thermosetting Matrix Composites," in Proceedings of

12th International Heat Transfer Conference, September, 2002.

4. F. Yang and R. Pitchumani, “A Kinetics Model for Interphase Formation in

Thermosetting-Matrix Composites," Journal of Applied Polymer Science,

Submitted, 2002.


Summary

Two fractal models of intimate contact development based on a

fundamental description of the microscale geometry and the

relevant physical phenomena. The model parameters can be

determined directly from surface profile measurements,

eliminating the need for adjustable parameters.

A rigorous mathematical treatment and analysis of the healing

process is provided, starting from a fundamental description of

the reptation process under nonisothermal conditions.

Interphase evolution in thermosetting materials is described by

a kinetics approach, which fills a critical void in the tailoring of

interphase via cure cycle selection.


Future Work

INTERPHASE MODELING

The EELS (or other?) method may be used to different material

systems and temperatures to obtain a comprehensive data set

for determining the kinetics parameters.

The kinetics parameters (e.g., kdE and kdA) in this study may

additionally be related to the thermodynamic parameters (e.g.,

interaction energies between the fiber surface and the resin

components).

The interphase formation model may be combined with

macroscopic thermochemical models to establish the influence

of the cure cycle on the interphase formation.

POLYMER HEALING

The dependencies of the reptation diffusivity on other factors

(e.g., molecular weight distribution, concentration) may be

incorporated to provide a more general solution of polymer

healing.


Acknowledgements

This research was funded by NSF (Grant No. CTS-

9912093), ONR (Contract No. N00014-96-1-0726), and

AFOSR (Grant No. F496200110521).

I am grateful to my advisory committee: Professors Ranga

Pitchumani, Baki Cetegen, Wilson Chiu, Montgomery

Shaw, and Matthew Begley.

I also want to thank: Peter Boardman, Tom Mealy, Jim

Clougherty, Xiaosheng Guan.


Nonisothermal Healing Model Validation (PEEK)

Te

mpe

ratu

re, T

[ oC]

0.0

0.2

0.4

0.6

0.8

1.0

355

360

365

0 1000 2000 3000 4000 5000 6000 7000

DataCurrent Model [Eqn. (52)]

Deg

ree o

f he

aling

, D

h

(a)

Time, t [sec]

PEEK

Te

mpe

ratu

re, T

[ oC]

0.0

0.2

0.4

0.6

0.8

1.0

355

360

365

0 1000 2000 3000 4000 5000 6000 7000 8000D

eg

ree o

f he

aling

, D

h

(b)

Time, t [sec]

PEEK

Fuzheng Yang Defense

Documents

Transcript of Fuzheng Yang Defense