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Utfv..rilt ol Auctland ttbnr1l u{GnrrruNc mRArv

Application of the Double Torsion Specimen to the Study of

Fracture in Fibre Reinforced Plastics

w

Niven Rhyr Brown

A

thesis

submitted in partial fulfilment of the requirements for the

degree

of

Doctor of Philosophy (Engineethg)

Deparhent of Mechanical Engineering

School

of Engineering

University

of

Auckland Auckland, New Zealand

November

L993

Abstract

The increasing use

of fibre

reinforced polymers

in

structural components often requires an accurate assessment

of

the strength

of

the component. The strength

of

composite materials is usually based on the strength

of

an

individual

lamina.

This is then

combined

in a

manner depending

on the orientation of the

plies

within

the

laminate.

The actual

failure

process is often ignored

in this type

of analysis. Composite failure is the result

of

damage accumulation from a number

of failure

modes,

in particular, fibre failure, matrix failure and failure of

the interface between the fibres and

matrix.

Measurement

of

the interfacial strength requires specialised testing techniques

in

order to obtain accurate characterisation of the interfacial failure processes.

This research uses

of

configurations.

a double torsion specimen reinforced

with

fibres

in

a number The testing techniques developed

allow the

interaction

of

a

matrix

crack

with

fibres,

matrix

crack

with

fibres, resulting

in

the

failure of

the

interface.

Finite element analysis has been used

to

gain an

insight into

the deformation mechanisms.

A

compliance change analysis has been developed so that the load

in

the fibres can

be

calculated.

Results

from the finite

element analysis

confirm the

analytical procedures

and

show that,

for

the

fibre/resin

combination tested, the interface has a lower fracture toughness than the matrix

material.

The interaction between

the

fibres

and matrix

shows

that the

mechanism

of fibre bridging inhibits

the

propagation of matrix cracks. This produces an apparent

increase

in

the toughness

of

the composite system.

To confirm the failure processes occurring, the technique of acoustic emission has been used

to monitor the

development

of the

specimen

failure. In line with

other workers,

it

is shown that matrix failure produces

low

amplitude events and interfacial failure produces

mid

amplitude events. Fibre failure

did not

occur to any significant degree. This thesis shows how the contribution from the presence

of an interface

affects

the fracture of

composite

materials and how, via

the

reinforced double torsion

specimen,

this contribution can be

measured. and interpreted.

llt

Acknowledgements

The

production of this

thesis

would not

have been possible had

it not

been for the time and effort of many people. Some of them may not be mentioned here by name,

but

their contribution has not been forgotten.

In

particular,

I would

like to express my gratitude to the following:

o My supervisor, George Moltschaniwskyj, for his support

^and

encouragement throughout the course of this work. His

patience, thoughtfulness,

wisdom

and conscientiousness have been a source

of

great

inspiration. Without his invaluable

supervision

and many hours

sPent discussing

fibres,

fracture,

fishing

and

front-foot

cover

drives, this

thesis

would

not have been possible. ^{Thank you.}

I

Associate Professor Debes Bhattacharyya

for his

patience, enthusiasm and diligence

in

co-supervising this research work.

o Mr

^{Terry Boyd and his team}

of

technicians

for

their invaluable assistance in the experimental aspects of this work.

t

^The

University

Grants Committee

for their

financial assistance

in

the form of a Postgraduate Scholarship.

r The Yacht

^Research

Unit,

Strength

of Materials Laboratory and

Maskell Productions

Ltd

for

providing

financial support.

o

Adhesive Technologies

Ltd,

Dow Chemicals and

High

Modulus

NZ Ltd

for

providing

materials and technical advice.

. Auckland Electric Power Board (now trading

as

Mercury Energy),

and

particularly Mr Kevin Mooney, for the use of their

acoustic emission equipment.

t Industrial

Research

Ltd for employing me over the final

stages

of

^this

project. In

particular,

Mr

Graeme Finch for his

flexibility in

accommodating me and

for

allowing me to avail myself of their computing facilities.

o

The undergraduate project students

who

have assisted

in

the experimental work:

Mike

Boyd,

Phil

Steeghs, Peter Dudson and Shane Williamson.

1V

The staff,

visiting

fellows and

my

colleagues at the

University of

Auckland

for making

postgraduate

study an unforgettable experience. I would

especially

like to

thank the members

of

the E-team,

fly

office cohabitants,

the gang of five: Richard, Mike, Mark and David, and,

especially, ffiY composites colleague

Mark. All

have helped to shape me

in

various ways.

A

^special thank

you to

those who begging

of

Macintosh time: Lynley,

and Trish.

have tolerated

my

using,

borrowing

or

Henry

and Barb, and,

ultimately,

Mike

Untold

thanks must go

to my

^parents and

family for bringing

me

up

and supporting

in

a plethora of ways.

And

the

final

acknowledgeu,*ent must go to my wife,

Lynette.

Her love, and encouragement

(and our Kucing) have been my inspiration over

the duration of my doctoral studies. _Je t'aime.

Tm.a.gLna.tion

is ntore.

itttporta.nt

tfta.n

RnoLutEf,i,cJg.tft

"4-LBER"T

EXNSTEXN

Contents

Title page Abstract

Acknowledgements Contents

List of Symbols List of Figures List of Tables

1. Introduction

Table of Contents

vl

i ii iii vi viii

xi xvii

Page

1

5 7 7 15 18 22 24 24 27 33 35 35 38 4L 50 50 60 62 2.

Review

2.1.

Fracture mechanics

2.1..'1.. Fracture concepts

2.1.2. Fracture toughness measurement 2.1,.3. Fracture of polymers

2.1,.4. Fracture

of

non-homogeneous materials 2.2. Composite strength and failure

2.2.I.

Description of failure processes 2.2.2. Strength models for composites 2.2.3. Determination of properties 2.3. Theory of debonding

2.3.1,. Stresses on the interface 2.3.2. Interfacial failure

2.3.3. Methods for testing the interface

2.4.

Acoustic emission for composites

2.4.I.

Overview

2.4.2. Discrimination of failure modes

2.4.3. Strength determination using acoustic emission

The Double Torsion

Test

3.1.

Description of technique

3.1.1. Features of the double torsion-specimen 3.L.1.1. Specimen geometry

3.L.1.2. Mode of failure

3.1.1.3. Crack shape and velocity

3.1..2. Analysis of the unreinforced specimen

3.1..3. Double torsion testing on reinforced specimens 3.1,.4. Specimen configurations

66 68 68 69 71 74

u

87 92

3.

Contents

3.2.

vii

3.3.

3.4.

Determination of interfacial properties 3.2.1,. Compliance change method 3.2.2. Fibre pull-out analysis 3.2.3. Energy methods Finite element modelling

3.3.1. Previous attempts at modelling 3.3.2. Reasons for finite element analysis 3.3.3. Description of model

Experimental procedure for double torsion testing 3.4.1.. Experimental equipment

3.4.2. Specimen preparation

97 98

t04

L07 115 115

1r9 L20 123 123 L28

130 131 132

1,43

156

1.61, 1,61,

168 175 184 184 187 194

197

207

270

212

239

24t

243

4. Experimental

Results

and Analysis

4.2.

4.3.

5. Discussion 6. Conclusion

7. Recommendations

8.

References

4.L. Finite element modelling

4.L.L. Element and mesh verification

4.1,.2. Modelling of fibre reinforced specimens 4.1.3. Comparison

with

experimental results Double torsion testing

4.2.1. Unreinforced specimens

4.2.2. Developmental fibre configurations

4.2.3. Experimental calculation of interfacial properties Acoustic emission testing

4.3.L. Experimental technique 4.3.2. Acoustic emission results

4.3.3. Discussion of acoustic emission results

9. Appendices

Appendix A Appendix B

Appendix C

Appendix D Appendix E

Appendix F

Appendix G

Stress intensity factor equations

Typical graphs from acoustic emission testing Results from fracture toughness testing

Typical load

plot

from double torsion testing Choice of gauge for crack opening displacement measurement

Finite element

input

file Typical experimental data

223 223 227 23L 238

List of Symbols

List of Symbols

crack length, half crack length for centre notched plate area of fracture, cross-sectional area

nominal crack velocitv

B

^thickness

c

^crack length of embedded fibre

C

^compliance

COD

crack opening displacement

d

^{fibre diameter}

E

Young's Modulus

F pull-out

^force,

work

^{done by} load, strength parameter

G

shear modulus

G

strain energy release rate

h

length used to determine crack shape factor

K

^stress intensity factor

K

torsional stiffness constant

I

^length of debond

L

specimen length, embedded fibre length

n

subcritical crack growth parameter

N

^number of cycles

P

^{load on specimen,} load on fibres

r

fibre radius, radial coordinate, distance from crack tip

R

interfibre distance

Ro

crack resistance characteristic

f

crack

front

translational velocity

S

^{ultimate shear stress,} crack shape factor

t

^thickness

T

applied moment

tn

^{thickness at notch}

u

displacement

U

strain energy

v

displacement perpendicular to the crack surface

v

crack velocity

v1r1

a

A

a

units

m m2 m.s-1 m m m.N-1 m m

Pa

N,I,

^-

Pa

Pa.m m Pa.{m m4 m

I

N

m m Pa.m m.s-1 Pa, - m

N.m

m m

N.m

m m.s-1

List of Symbols

wm W X X' v Y Y'

moment arm from load-point to support

width

of double torsion specimen, energy ultimate tensile strength

in

the fibre direction ultimate compressive strength

in

the fibre direction load-point displacement

ultimate tensile strength

in

the transverse direction ultimate compressive strength

in

the transverse direction

Greek characters

1X

m m,

I

Pa Pa

m

Pa Pa

6,a

Eg

o x e

v

I : t

0

1

2 6

I II u

c

d

f

FE

i

t

load-point displacement

crack opening displacement at crack front

stress shear stress

angle of twist, angle coordinate Poisson's ratio

angle to base of crack front translational speed local crack speed normal to crack front

strain

m m

Pa Pa

radians

radians

m.s-1

Subscripts / superscripts

initial

position

reference to section L, reference to fibre direction reference to section 2, reference to transverse direction reference to in-plane shear

mode

I

fracture mode

II

fracture mode

III

fracture

critical mode, reference to cracked half specimen reference to debond

reference to fibre

reference

to finite

element solution contracted notation index

contracted notation index

List of Symbols

L

^reference

to

^ligamerrt

m

teference to matrix, refer.ence to mid-side nodes

P

^{reference to load}

s

^referenee

to

^{in-plane shear}

t total

v

^reference

ts

^{vertex nodes}

x

cartesian cosrdinate, reference to fibre direcfion

y

^cartesian co-ordinate, reference

to

tr.ansverse direction

x

List of Figures

List of Figures

2.1,.

^The

Griffith

criterion. a) Cracked plate

with

fixed ends and applied stress

o;

b) Elastic energy for crack lengths a and a+da.

2.2.

Cracked plate

with

loads free to move.

2.3.

^{Stresses about a crack}

in

^{an infinite plate.}

2.4.

Crack loading ^modes.

2.5.

^{Standard fracture} toughness specimens: a) three-point bend ^test, and b) compact tension ^test.

2.6.

Fracture toughness specimen where the crack grows

into a

compressive region: a) Brazilian specimen, and b) double-cleavage

drilled

compression specimen.

2.7.

Controlled crack growth specimens: a) double-cantilever beam specimen, and b) double torsion specimen.

2.8.

^{Fibres bridging a} matrix crack. The interface may be intact or debonded.

2.9. Von

^Mises

type failure

envelope

for unidirectional lamina. The

axis intercepts represent the measured tensile and compressive strength

in

the longitudinal and transverse directions. Axes not to scale.

2.10. Maximum

shear stress (Tresca)

condition in strain

space (Hart-Smith

1992b).

2.I1.

^{Stress state of a} discontinuous fibre embedded

in

a matrix.

2.12.

Cook

&

Gordon debonding mechanism: failure

of

the interface ahead of the matrix crack: a) due to tension and b) due to shear.

2.13. Outwater & Murphy debonding

mechanism:

failure of the

interface behind the matrix crack tip.

2.14.

^Fibre

pull-out

notation.

2.15.

Schematic diagram

of

acoustic emission characteristics.

2.L6.

Idealised

(top) and

more realistic propagation

of an

acoustic emission waveform (after Scott

&

Martin 1991).

2.17. Attenuation

map

of

a bidirectional carbon

fibre

panel

at two

detection frequencies (Holroyd & Cox 1986).

2.18.

Features

of

an acoustic emission waveform.

3.L.

Double torsion specimen geometry.

3.2. Various

groove geometries used

with the double torsion

specimen: a)

single V-groove on tension side,

b)

single V-groove on compression side, c) double V-grooves,

and

d) square groove.

3.3. Linear displacement model for crack front modelling: a)

^surface

generators,

and b)

crack

front profiles for various proportions of

^the

maximum crack opening displacement.

x1

List of Figures

xll

3.4.

^{Crack front profiles}

with

^varying depth lower grooves (after Frassine et al.

1988).

(a)

Crack profiles do not superimpose

if

referred to the base-line of the grooves,

while

they

do

^(b)

if

referred

to

^the upper (ungrooved) side.

In

(b) the crack shapes have been shifted horizontally to show agreement.

3.5.

^{Surface markings}

on

^{fracture surface}

for

polyester resin double torsion specimen.

3.6. Identification of

the various crack propagation stages and crack speeds (after Frassine 1988).

3.7.

Definition of parameters for crack shape factor (Leevers 1982).

3.8.

Cross-section

of the double torsion

specimen

showing the crack tip

geometry as defined by Leevers (1982).

3.9.

^{Twisted half of a} double torsion specimen.

3.10. Half

of a double torsion specimen showing the fibre pull-out analogy.

3.11.

Fibre reinforced double torsion specimen: a) fibres

in

the direction of crack growth, and b) fibres at right angles to the crack growth.

3.12.

Fibre configurations

for

the double torsion specimen: a) fibres normal to specimen and crack planes,

b)

fibres

in

plane

of

specimen

but

normal to crack, c) fibres normal to specimen

but

at an angle to crack plane, and d) fibres

in

plane of specimen and

in

line

with

crack plane.

3.13.

Normalised crack opening displacement versus normalised crack length for cracked double torsion specimen.

3.L4.

^{Crack opening} displacement versus normalised crack length

for

cracked double torsion specimen.

3.15.

Crack opening displacement versus normalised crack

length for

double torsion specimen

with

fibres bridging crack.

3.1,6.

Linear crack

tip

of double torsion specimen in polyester resin.

3.17.

Crack opening displacement at fibre plane for various fibre depths: a) near the lower surface and b) at the lower surface.

3.18.

Incremental crack growth showing fracture surface area, AA ₌ t Aa.

3.19. Incremental strain energy, AU, during crack growth via the

load- displacement plot.

3.20. Compliance versus crack length showing extrapolated ligament

compliance, Cg, at a = ^0.

3.21.

Representative

load

versus displacement

plot

showing strain energy

in

ligament.

61

is the

load-point deflection equal

to the

deflection

at

the crack plane and P1 is the equivalent residual load in the ligament.

List of Figures

xtll

3.22. Crack shapes modelled by Trantina;

left

to

righil

bilinear 40"+30",

30",45,

and 90o (vertical).

3.23. Crack

shapes used

by Trantina and

Tseng

& Berry

^compared

to

^an

experimental shape.

3.24. Double torsion

crack

profiles for

polyester compared

to

those used by White and Tseng

&

Berry.

3.25.

^20-node quadratic displacement brick.

3.26.

Finite element mesh showing boundary nodes. The X-Y plane is the crack plane and the symmetry plane.

3.27.

Experimental apparatus.

3.28.

^{Apparatus used} to photograph crack opening displacement.

3.29.

^Specimen

with

gauge wire attached.

3.30.

Photograph used to determine the crack opening displacement.

3.31.

^{Apparatus for} casting of double torsion specimens.

4.I. Measurement of a) vertical displacement and b) crack

^opening

displacement on the

finite

element model.

4.2.

Comparison

of

vertical displacement

for

a cantilever plate

with

different boundary conditions.

4.3.

Comparison

of

crack opening displacements

for a

cantilever plate

with

different boundary conditions.

4.4.

Comparison

of vertical

displacement

for different

mesh densities and between 8-node and 2O-node bricks.

4.5.

Comparison

of vertical

displacement

for different

mesh densities

for

8- node bricks showing good convergence.

4.6.

Comparison of vertical displacement

for

different mesh biases

for

l6x6x4 model using 8-node bricks.

4.7.

Comparison of vertical displacement

for

different mesh biases

for

10x4x3 model using 20-node bricks.

4.8.

Comparison

of

experimental crack

profile for

polyester resin and a finite element "curved" profile.

4.9.

^Vertical displacement

for

vertical and "curved" crack fronts.

4,1.0.

Crack opening displacement for vertical and "curved" crack fronts.

4.I1,. Finite

element mesh

with uack tip

elements

to model the crack tip

singularity.

4.I2.

Comparison

of

crack opening displacements

of singularity model

^and

vertical crack front with

20-node elements biased

towards crack tip

(bias=2).

List of Figures

4.13.

Comparison

of vertical

displacement

for singularity model and

8-node and 20-node brick element models.

4.I4

Node plane notation for a 24x6x4 mesh. Nodes are represented

by ..

4.15.

Crack opening displacements for no fibres and

full

plane of fibres at node plane 8.

4.'J.6. Comparison of crack opening

displacements

with fibres at

^various

positions along the bottom of the specimen.

4.17.

Comparison

of

crack opening displacements

for

a

fibre at

the

bottom

of node plane 6 and an unreinforced specimen

with

a moment equal

to

the moment beyond the fibre plane.

4.18.

Variation

in

vertical displacement

with

a single fibre at various positions along the cracked portion

of

the specimen. The fibre is always located at the bottom of the specimen.

4.L9. Variation in

crack opening displacement

with a

single

fibre at

various positions through the thickness

of

the specimen. The

fibre is

always at node plane 8.

4.20.

Variation

of

crack opening displacement through the thickness

for

fibres at different thickness planes.

4.2L.

Variation

in

vertical displacement

with

a single fibre at various positions through the thickness of the specimen.

4.22.

Comparison

of

crack opening displacements

for

a fibre at thickness plane

3 and an

unreinforced specimen

with a

moment equal

to the

moment beyond the fibre plane.

4.23.

Comparison of vertical displacement for vertical plane of fibres (all nodes

tied)

versus one

fibre at

thickness plane

3

(greatest closure

for a

single fibre).

4.24.

Crack opening displacement

for

a fibre at thickness plane 4 and thickness plane

3.

Note

that

the maximum COD

is

less

for

the

fibre

at thickness plane 3.

4.25.

Crack opening displacements for a fibre at thickness plane 4 and a fibre at thickness plane

3 with a fibre load to

cause

the

same moment

in

both

cases.

4.26.

Detail at crack

tip

of crack opening displacements for finite element model

with

glass fibre, carbon fibre, and no fibre at crack tip, _{bias =} 2.0.

4.27.

Comparison

of

vertical displacements

for finite

element model

with

^glass

fibre, carbon fibre and no fibre at crack tip.

xrv

List of Figures

xv

4.28.

Crack opening displacement versus normalised crack

length for finite

element analysis and measured values

for

PMMA.

4.29.

Crack opening displacement versus normalised crack

length for finite

element analysis and unreinforced polyester ^resin.

4.30.

^Crack

opening

displacement versus normalised crack

length for finite

element analysis

and

glass reinforced polyester

with the fibres at

the bottom.

4.3L Crack opening

displacement versus normalised crack

length for finite

element analysis

and

glass reinforced polyester

with the fibres at

mid thickness.

4.32.

Cracks at the notch

tip

in polyester resin.

4.33. Fracture surface of PMMA

compact

tension

specimen

showing

the transition between fast and slow fracture.

4.34.

^Graph

of

typical load versus crosshead displacement for polyester double torsion specimen.

4.35.

Debonding near the notch

tip.

Note

how

the

matrix

crack is offset from the razor cut.

4.36.

Debonding along crack

in

double torsion specimen

with

a plane

of

fibres over the top of the specimen.

4.37.

Interference of crack front

with

fibre plane.

4.38.

Crack surrounding fibre bundle.

4.39.

Crack arrested at fibre bundle.

4.40. Crack opening

displacement versus normalised crack

length for

glass reinforced polyester

with

the fibres at mid thickness.

4.4L.

Schematic diagram of apparatus for acoustic emission testing.

4.42.

Number of hits versus amplitude

for

duration

of

test

for

an unreinforced polyester resin.

4.43.

Cumulative hits versus amplitude

for

specified time period.

4.M.

Progression of acoustic emission

with

time.

4.45. Number of hits

versus

amplitude for

reinforced polyester resin loaded twice.

A.1.

^Notation

for

compact tension specimen.

A.2.

^Notation

for

three-point bend specimen.

A.3.

Notation

for

double torsion specimen.

A.4.

^{DCDC stress} intensity factor as a function of

c/R

for various

R/h.

List of Figures

xvl

B.1.

Load versus time for typical acoustic emission ^analysis.

8.2.

^Hits versus time for typical acoustic emission ^analysis.

B.3.

Hits versus amplitude for typical acoustic emission analysis.

8.4.

Counts versus time for typical acoustic emission analysis.

8.5.

Counts versus amplitude for typical acoustic emission analysis.

8.6.

^Hits versus energy for typical acoustic emission ^analysis.

8.7.

^{Duration versus} time for typical acoustic emission ^analysis.

D.1. Load plot for

reinforced double

torsion

specimen

showing load

^drops from crack

initiation

and load variations from debonding.

E.1.

Measurement

of

COD

via clip

gauge: a)

clip

gauge method

with

blocks attached

at

crack plane, and

b) clip

gauge method

with

blocks attached away from the crack plane.

8.2. Comparison of actual and measured gauge sizes for circular

and rectangular ^gauges.

List of Tables

xvll

List of Tables

4.1,.

^{Forces and} moments transferred

by

fibres

for

a single

fibre at

thickness plane 3 and a vertical plane of fibres.

4.2.

^Summary

of

fracture toughness tests on unreinforced polymers.

4.3. Fracture

^{toughness based}

on first crack arrest length and load

after

initiation.

4.4.

^{Results from} the application of a

Griffith

energy approach.

C.1..

Three-point bend test fracture toughness results.

C.2.

Compact tension test fracfure toughness ^results.

C.3.

^{Double cleavage}

drilled

compression test fracture toughness results.

CA.

Double torsion test fracture toughness results.