Fracture behaviour of thermoplastic acrylic resins and their … · 2017. 4. 29. · acrylic resins and their relevant unidirectional carbon fibre composites: rate and temperature

Dipartimento di Chimica, Materiali e Ingegneria Chimica

“Giulio Natta”

Doctoral program in Materials Engineering, XXIX Cycle

Fracture behaviour of thermoplastic

acrylic resins and their relevant

unidirectional carbon fibre composites:

rate and temperature effects

Doctoral dissertation of Tommaso Pini

Supervisor Prof. Roberto Frassine Tutor Prof. Francesco Briatico Vangosa

“ho capito solo valigia”

(V. Gassman)

i

Abstract

Fracture behaviour of novel acrylic thermoplastic resins to be used as

matrices for composite materials was studied. These resins, one plain

and one toughened with rubber, are suitable to prepare composite

materials adopting a reactive processing technique such as infusion

moulding, overcoming in this way the issues typical of thermoplastic

composites production. The matrices were investigated at small

strains, yield and fracture, taking into account the influence of

displacement rate and temperature on the mechanical response. Small

strain behaviour was investigated with Dynamic Mechanical Analysis

in a three-point bending configuration, adopting the time temperature

equivalence postulate to reduce data obtained from tests conducted at

different temperatures to one single reference temperature. Uniaxial

tensile tests were performed to investigate yielding behaviour while

fracture was studied with Double Torsion and Double Cantilever Beam

techniques for matrices and composites respectively. In all cases, tests

were conducted at different displacement rates and temperatures and

the time temperature was applied so as to obtain fracture toughness

vs. crack propagation speed and yield stress vs. time to yield master

curves. The results from fracture tests showed that Williams’

ii

viscoelastic fracture theory was suitable to predict fracture toughness

dependence on crack propagation speed in the case of the plain resin,

while in the case of the toughened resin a dependence opposite to that

expected was found. This trend was attributed to different deformation

mechanisms occurring at the crack tip at different conditions of strain

rate and temperature. The process zone ahead the crack tip was then

studied more in depth adopting Single Edge Notched Bending

configuration and performing Digital Image Correlation analysis.

Results showed that, concerning the plain resin, the size of the process

zone was approximately constant with respect to the temperature. The

results obtained for the toughened resin on the other hand, confirmed

that the size of the process zone was actually different at different

temperatures. The damage mechanisms in the toughened resin were

investigated studying the changes in volume occurring during tensile

tests at different conditions of temperature and displacement rate. A

change of mechanism at different testing conditions was found.

Fracture behaviour of the toughened resin was also studied in double

notched four-point bending configuration from which a fully developed

yet intact process zone at the crack tip can be obtained. The optical

observation of the process zone at the crack tip obtained in different

conditions of temperature and displacement rate confirmed the change

in the damage mechanisms. This was associated with different amounts

iii

of energy dissipated thus explaining the trend observed in the fracture

toughness vs. crack propagation speed curve for the toughened resin.

Concerning the fracture behaviour of the composites, in order to better

understand the transfer of toughness from matrix to composites, both

the crack initiation and propagation stages were analysed. At crack

initiation the toughening contribution of the fibres is limited, compared

to that during crack propagation, and therefore the main fracture

toughness contribution is given by the matrix. It was found that in the

case of the plain matrix based composites the fracture toughness was

higher than that of the matrix, while in the case of the toughened

matrix based composites it was smaller. This result can reasonably be

explained with the physical constraint induced by the presence of the

fibres on the development of the process zone ahead the crack tip in

the case of the toughened composites. In the case of the plain matrix,

in which the dimensions of the process zone are smaller, the matrix

toughness seems to be fully transferred to the composite. During the

propagation stage, it was found that the fracture toughness was higher

than that of the relevant matrix, for both matrices. The additional

toughening effect given by the fibres was found to be dependent on

crack propagation speed, probably due to time dependent matrix-fibre

interfacial strength.

v

Sommario

Il comportamento a frattura di resine acriliche termoplastiche di

recente sviluppo da impiegare come matrici in materiali composite è

stato studiato. Le resine in questione, una tal quale e una tenacizzata

con gomma, possono essere impiegate per produrre materiali composite

con un processo di tipo reattivo come ad esempio l’infusione, andando

in questo a modo a risolvere tutte le problematiche tipiche della

fabbricazione di materiali compositi a matrice termoplastica. Le

matrici sono state studiate a piccole deformazioni, a snervamento e a

frattura considerando l’effetto della velocità di sollecitazione e della

temperatura sulla risposta meccanica del materiale. Il comportamento

a piccole deformazioni è stato investigato tramite analisi dinamico-

meccanica in configurazione di flessione a tre punti, facendo ricorso al

postulato di equivalenza di tempo e temperatura per traslare i risultati

ottenuti a diverse temperature. Il comportamento a snervamento è

stato studiato mediante test di trazione uniassiale mentre la per quanto

riguarda la frattura sono state impiegate le configurazioni di prova di

doppia torsione e doppia trave incastrata rispettivamente per le matrici

e i composite. Nei vari casi, i test sono stati condotti a varie

temperature e velocità di spostamento e, applicando l’equivalenza di

tempo e temperature si sono ottenute curve maestre di tenacità a

vi

frattura in funzione della velocità di propagazione della cricca e di

sforzo di snervamento in funzione del tempo di snervamento. I risultati

ottenuti dalle prove di frattura hanno evidenziato l’applicabilità della

teoria della frattura viscoelastica di Williams nel prevedere la

dipendenza della tenacità a frattura dalla velocità di propagazione

della cricca per quanto riguarda la resina tal quale, mentre nel caso

della resina tenacizzata è stata ottenuta una dipendenza opposta a

quella attesa. La forma della curva è stata ritenuta dovuta ai differenti

meccanismi di deformazione agenti di fronte all’apice della cricca nelle

diverse condizioni di velocità e temperatura. La zona di processo

davanti l’apice della cricca è stata quindi studiata nel dettaglio con

l’analisi di correlazione digitale delle immagini in configurazione di

flessione a tre punti con singolo intaglio. I risultati hanno evidenziato

come nel caso della resina tal quale la zona di processo avesse sempre

le stesse dimensioni al variare della temperature. Nel caso della resina

tenacizzata si è visto come la zona di processo variasse in dimensioni

al variare della temperatura. I meccanismi di danneggiamento della

resina tenacizzata sono stati quindi studiati andando a misurare le

variazioni di volume nel material a differenti velocità di spostamento

e a differenti temperature. È stato verificato un cambio nei meccanismi

agenti. Il comportamento a frattura della resina tenacizzata è stato

ulteriormente studiato utilizzando la configurazione di prova di

flessione a quattro punti con doppio intaglio grazie alla quale si possono

vii

ottenere zone di processo completamente sviluppate davanti all’apice

della cricca. Osservando le zone di processo ottenute in differenti

condizioni di velocità di spostamento e di temperatura è stato

effettivamente riscontrato un cambio di meccanismo di

danneggiamento. Questo cambio di meccanismo è accompagnato da

una variazione di energia dissipata e quindi in questo modo è possibile

spiegare la dipendenza della tenacità a frattura rispetto alla velocità di

propagazione della cricca ottenuta per la resina tenacizzata.

Per quanto riguarda il comportamento a frattura dei composite, si sono

studiate sia la fase di innesco che di propagazione della cricca, in modo

da poter comprendere meglio il trasferimento di tenacità dalla matrice

al composito. All’innesco il contributo tenacizzante delle fibre è molto

limitato rispetto alla fase di propagazione della cricca, quindi il

maggior contributo alla tenacità a frattura è dovuto alla matrice. Nel

caso dei composite realizzati con la resina tal quale la tenacità era più

elevata di quella della matrice mentre nel caso della resina tenacizzata

il composito è risultato meno tenace della matrice. Questo risultato

può essere spiegato con l’effetto di confinamento indotto dalle fibre

sulla zona di processo che, nel caso della resina tenacizzata, risulta

essere più grande. Nel caso della matrice tal quale la zona di processo

è piccola, la tenacità della matrice è completamente trasferita nel

composito. Durante la fase di propagazione della cricca la tenacità a

frattura dei composite è risultata più alta di quella delle matrici, in

viii

entrambi i casi. Il contributo tenacizzante dovuto alle fibre è risultato

essere dipendente dalla velocità di propagazione della cricca,

probabilmente a causa della dipendenza dal tempo della resistenza

interfacciale fibra-matrice.

ix

Table of contents 1 Introduction and motivation ................................ 1

1.1 References ...................................................................... 3

2 Theoretical background ........................................ 6

2.1 Linear Elastic Fracture Mechanics (LEFM) ................... 6

2.1.1 Process zones ........................................................................ 12

2.2 Viscoelastic fracture ..................................................... 14

2.3 Rubber toughened polymers ......................................... 16

2.3.1 Damage mechanisms in homopolymers ................................. 17

2.3.2 Damage mechanisms in toughened polymers ........................ 18

2.4 References .................................................................... 23

3 Experimental details ......................................... 25

3.1 Materials and samples preparation ............................... 25

3.2 Test methods and data reduction analysis ................... 29

3.2.1 Dynamic Mechanical Analysis .............................................. 29

3.2.2 Tensile tests .......................................................................... 31

3.2.3 Fracture tests on neat polymers ........................................... 33

3.2.3.1 Double Torsion ............................................................... 33

3.2.3.2 Single Edge Notched Bending ........................................ 39

3.2.3.3 Double Notched Four Point Bending ............................. 41

3.2.3.4 Notching ......................................................................... 43

3.2.4 Fracture tests on composites ................................................ 45

x

3.2.5 Digital Image Correlation ..................................................... 47

3.3 References .................................................................... 49

4 Results and discussion ...................................... 53

4.1 Fracture behaviour of matrices .................................... 53

4.1.1 Viscoelastic effects on fracture ............................................. 53

4.1.2 Analysis of deformation mechanisms in the process zone ..... 70

4.1.3 Damage mechanisms in the rubber toughened resin ............ 80

4.1.4 Damage mechanisms at the crack tip in the rubber toughened

resin .............................................................................................. 89

4.2 Fracture behaviour of composites ................................. 98

4.3 References ................................................................... 117

5 Conclusions ..................................................... 123

5.1 References ................................................................... 125

xi

Index of figures Fig. 2.1-1 General loaded body with a crack. From [1] ...................... 8

Fig. 2.1-2 General crack tip contour. From [1].................................. 10

Fig. 2.1-3 Crack loading modes ......................................................... 11

Fig. 2.1-4 Crack tip polar coordinate system. From [6] .................... 12

Fig. 2.3-1 Regions of progressive damage in the vicinity of the crack

tip. From [18] .................................................................................... 22

Fig. 3.1-1 Liquid monomer casting ................................................... 26

Fig. 3.1-2 Tan vs. temperature curves for Elium (blue) and Elium

Impact (red). Arrows indicate the positions of the peaks

corresponding to glass transitions ..................................................... 27

Fig. 3.1-3 Infusion moulding technique. From Arkema website ........ 28

Fig. 3.2-1 Tensile specimen ............................................................... 31

Fig. 3.2-2 Double torsion test configuration ...................................... 34

Fig. 3.2-3 Double torsion compliance calibration curves at 23 °C and

1 mm/min for Elium (blue) and Elium Impact (red). Specimens

dimensions were 120x45x6 mm. Solid lines are linear fittings

representing the term /C a ........................................................... 36

Fig. 3.2-4 Double torsion specimen load-plane deformation. From [14]

......................................................................................................... 38

Fig. 3.2-5 Single Edge Notched Bending specimen ............................ 40

Fig. 3.2-6 Double Notched Four-Point Bending specimen ................ 41

Fig. 3.2-7 DN-4PB specimen after loading with a propagated crack

(left) and a fully developed process zone (right) ............................... 42

xii

Fig. 3.2-8 Position of the slice cut from the DN-4PB specimens after

testing .............................................................................................. 43

Fig. 3.2-9 Notch root in Single Edge Notched Bending specimen ..... 44

Fig. 3.2-10 Composite sheet from infusion moulding with the

direction of the fibres, position of the starter film and cuts for the

final specimens ................................................................................. 45

Fig. 3.2-11 Double Cantilever Beam specimen ................................. 46

Fig. 4.1-1 Effect of corrective factors for large displacement for Elium

(blue) and Elium Impact (red). Dashed lines are original data, solid

lines are corrected data .................................................................... 54

Fig. 4.1-2 Fracture toughness vs. crack propagation speed isothermal

curves for Elium ............................................................................... 55

Fig. 4.1-3 Fracture toughness vs. crack propagation speed master

curve at the reference temperature of 23 °C for Elium. Solid line is a

power law fitting .............................................................................. 55


curves for Elium Impact ................................................................... 56


curve at the reference temperature of 23 °C for Elium. Dashed line is

a visual aid ....................................................................................... 56

Fig. 4.1-6 Storage modulus vs. frequency isothermal curves for Elium

......................................................................................................... 58


Impact .............................................................................................. 58

Fig. 4.1-8 Storage modulus vs. frequency master curves at the

reference temperature of 23 °C for Elium (blue) and Elium Impact

(red) ................................................................................................. 60

xiii

Fig. 4.1-9 Relaxation modulus vs. time curves at the reference

temperature of 23 °C for Elium (blue) and Elium Impact (red). Solid

lines are power law fittings ............................................................... 61

Fig. 4.1-10 Stress-strain curves at different temperatures from tensile

tests at constant displacement rate of 1 mm/min for Elium ............. 62

Fig. 4.1-11 Stress-strain curves at different temperatures from tensile

tests at constant displacement rate of 1 mm/min for Elium Impact 63

Fig. 4.1-12 Yield stress vs. time to yield isothermal curves for Elium

......................................................................................................... 64


Impact .............................................................................................. 64

Fig. 4.1-14 Yield stress vs. time to yield master curves at the

reference temperature of 23 °C for Elium (blue) and Elium Impact

(red). Solid lines are power law fittings ............................................ 65

Fig. 4.1-15 Relaxation modulus vs. time curves at the reference

temperature of 23 °C for Elium (blue) and Elium Impact (red). Solid

lines are power law fittings. Plus (+) symbols refer to results from

tensile tests. ...................................................................................... 67

Fig. 4.1-16 Shift factors obtained building master curves of

conservative modulus, yield stress and fracture toughness for Elium69

Fig. 4.1-17 Shift factors obtained building master curves of

conservative modulus, yield stress and fracture toughness for Elium

Impact .............................................................................................. 69

Fig. 4.1-18 Load vs. displacement curves for Elium (blue) and Elium

Impact (red) tested at 23 °C and 5 mm/min. Crosses symbols

indicate the initiation point taken from video recordings ................. 71

Fig. 4.1-19 Crack tip reference system .............................................. 72

xiv

Fig. 4.1-20 Displacement v in direction normal to crack plane around

the crack tip for Elium Impact (5 mm/min, 23 °C) ......................... 73

Fig. 4.1-21 Measurement method for the displacement () in

correspondence of the crack plane .................................................... 74

Fig. 4.1-22 Displacement, at crack plane vs. distance from crack

tip, crack tip opening displacement and length of the process zone for

Elium Impact (5 mm/min, 23 °C) .................................................... 75

Fig. 4.1-23 Displacement, at crack plane vs. distance from crack

tip for Elium Impact at crack initiation and during several stages of

crack propagation (5 mm/min, 23 °C) ............................................. 76

Fig. 4.1-24 Crack tip opening displacement at different crack lengths

for Elium (E) and Elium Impact (EI) .............................................. 76

Fig. 4.1-25 Crack tip opening displacement at different temperatures

for Elium (blue) and Elium Impact (red) ......................................... 77

Fig. 4.1-26 Process zone length () at different temperatures for

Elium (blue) and Elium Impact (red) .............................................. 78

Fig. 4.1-27 Fracture toughness vs. initiation time master curves at

the reference temperature of 23 °C for Elium (blue) and Elium

Impact (red). Solid symbols come from (3.19), open symbols from

(4.6) ................................................................................................. 80

Fig. 4.1-28 Volumetric vs. linear strain for Elium Impact

(temperature 23 °C, displacement rate 10 mm/min). Measured

volumetric strain is represented in orange and the black line

represents the stress-strain curve ..................................................... 82

Fig. 4.1-29 Volumetric vs. linear strain at different temperatures for

Elium Impact (displacement rate 1 mm/min). Dashed line represent

curves having slope equal to 1 and 0 ................................................ 83

xv

Fig. 4.1-30 Volumetric vs. linear strain at different displacement rates

for Elium Impact (temperature 60 °C). Dashed line represent curves

having slope equal to 1 and 0 ........................................................... 84

Fig. 4.1-31 Volumetric contributions vs. linear strain for Elium

Impact (temperature 23 °C, displacement rate 10 mm/min).

Measured volumetric strain is represented in orange, elastic

contribution in blue, crazing/cavitation contribution in red and the

black line represents the stress-strain curve ...................................... 85

Fig. 4.1-32 Crazing/cavitation strain component vs. total strain at

different temperatures for Elium Impact (displacement rate 1

mm/min) .......................................................................................... 86

Fig. 4.1-33 Shear yielding strain component vs. total strain at

different temperatures for Elium Impact (displacement rate 1

mm/min) .......................................................................................... 87

Fig. 4.1-34 Crazing/cavitation strain component vs. total strain at

different displacement rates for Elium Impact (temperature 60 °C) . 87

Fig. 4.1-35 Shear yielding strain component vs. total strain at

different displacement rates for Elium Impact (temperature 60 °C) . 88

Fig. 4.1-36 Process zone length () at different temperatures for

Elium Impact. Measurements from DIC (red solid squares), DN-4PB

tests performed at 1 mm/min (black solid squares) and DN-4PB tests

performed at 10 mm/min (black open squares) ................................ 90

Fig. 4.1-37 Process zones of Elium Impact tested at 10 mm/min and

different temperatures. ...................................................................... 91

Fig. 4.1-38 Process zones of Elium Impact tested at 1 mm/min and

different temperatures. ...................................................................... 92

Fig. 4.1-39 Process zone of polypropylene impact copolymer. Fig. 4(e)

from [19] ........................................................................................... 94

xvi

Fig. 4.1-40 Craze in cast PMMA. Image 3(a) from [27] ................... 95

Fig. 4.1-41 Process zones of Elium Impact tested at 40 °C, 10 and 0.1

mm/min. .......................................................................................... 96

Fig. 4.1-42 Process zone of an epoxy resin. Fig. 7(a) from [17] ........ 97

Fig. 4.2-1 Double Cantilever Beam test load vs. displacement curves

for Elium (blue) and Elium Impact (red) (20 mm/min, 0 °C). Crosses

indicate the VIS initiation points. Specimen thickness is different for

the two materials. ............................................................................ 99

Fig. 4.2-2 R-curve for Elium-based composite (20 mm/min, 23 °C) 100

Fig. 4.2-3 R-curve for Elium Impact-based composite (20 mm/min,

23 °C) ............................................................................................. 100

Fig. 4.2-4 Crack length vs. time curve for Elium-based composite (20

mm/min, 23 °C) ............................................................................. 101


curves for Elium-based composite .................................................. 102


curves for Elium Impact-based composite ...................................... 102


curves at the reference temperature of 23 °C for Elium (solid

symbols) and Elium-based composite (open symbols). Solid line is a

power law fitting, dashed line is a visual aid. Different symbols refer

to different test temperatures ......................................................... 104


curves at the reference temperature of 23 °C for Elium Impact (solid

symbols) and Elium Impact-based composite (open symbols). Dashed

line are visual aids. Different symbols refer to different test

temperatures .................................................................................. 104

xvii

Fig. 4.2-9 Ratio of composites and their relevant matrices fracture

toughness vs. crack propagation speed for Elium (blue) and Elium

Impact (red) ................................................................................... 106

Fig. 4.2-10 (a) Fracture surface of Elium based composite, tested at a

displacement rate of 20 mm/min and a temperature of 60 °C. (b)

Elium based composite, 20 mm/min - 0 °C. (c) Elium Impact based

composite, 20 mm/min - 60 °C. (d)Elium Impact based composite, 20

mm/min - 0 °C. White vertical rectangular stripes are the stitches

used to weave the unidirectional carbon fibres. .............................. 108

Fig. 4.2-11 (a) Fracture surface of Elium-based composite, tested at a

displacement rate of 20 mm/min and a temperature of 60 °C. (b)

Elium based composite, 20 mm/min - 0 °C. (c) Elium Impact based

composite, 20 mm/min - 60 °C. (d)Elium Impact based composite, 20

mm/min - 0 °C. Magnification 1000 x ............................................ 110


the reference temperature of 23 °C for Elium-based (blue) and Elium

Impact-based composites (red). Different symbols refer to different

test temperatures ............................................................................ 112


the reference temperature of 23 °C for Elium (solid symbols) and

Elium-based composite (open symbols). Different symbols refer to

different test temperatures .............................................................. 113


the reference temperature of 23 °C for Elium Impact (solid symbols)

and Elium Impact-based composite (open symbols). Different

symbols refer to different test temperatures ................................... 113

Fig. 4.2-15 Ratio of composites and their relevant matrices fracture

toughness vs. crack initiation time for Elium (blue) and Elium

Impact (red) ................................................................................... 114

xviii

Fig. 4.2-16 (a)Cross section of Elium-based composite. (b) Cross

section of Elium Impact-based composite. The dark area is the resin-

rich region on which the average value of CTOD of each matrix is

reported .......................................................................................... 116

1

1 Introduction and

motivation

Continuous fibre composite materials are nowadays largely used in all

those applications in which specific strength, stiffness and low weight

are desired features, for example in the aerospace and other

transportations fields.

Polymeric composites can be divided in two main families: those which

have thermoset resins as matrices and those based on thermoplastic

resins. Thermoplastic composites present several advantages in

comparison with thermosetting ones: they have higher values of

toughness and ductility, the parts can be welded and recycled and

there are not shelf life related issues. On the other hand, processing of

thermoplastic composites can be difficult, due to their high melt

viscosity, and dedicated techniques have to be implemented [1–3]. A

yet another solution to overcome the issues related to the high melt

viscosity is to adopt a reactive processing technique based on in situ

polymerization. Infusion moulding, which was adopted in this work, is

an example of this type of processing methods. The fibres are

impregnated by the liquid monomers and then the polymerization

reaction takes place after the complete impregnation of the fibres.

T. Pini – Fracture of thermoplastic acrylic resins and composites

2

Similarly, the unreinforced samples can be produced by casting the

monomers in a closed mould.Equation Chapter (Next) Section 1

One of the most common reason of failure of a composite is

delamination, caused by the onset and the propagation of a crack in

the matrix-rich region between two adjacent laminae. A crack can be

generated by the presence of a geometric feature of the component or

a defect which in its turn can be due to manufacturing process or

exercise stresses. Around such defects there is an intensification of the

stresses which may lead to crack onset and propagation and,

ultimately, to catastrophic fracture.

When designing adopting a damage tolerant approach it is obviously

fundamental to predict crack onset and propagation. The problem can

be studied in the framework defined by linear elastic fracture

mechanics (LEFM) [4–8] which is suitable also for anisotropic

materials such as composites [9] and to materials which present some

nonlinear features but globally behave as linear elastic.

Since a crack in a composite will propagate in the matrix region

between two plies, the resistance to crack propagation is strongly

related to matrix properties [10]. In the light of this, the present work

was devoted to matrix characterization in order to have a full

knowledge of it when investigating composite materials. The materials

under study were polymers, hence the dependence on time of their

mechanical properties had to be taken into account. The viscoelastic

Introduction and motivation

3

behaviour of both the matrices and composites was investigated,

adopting time-temperature superposition principle, and the influence

of loading rate and temperature was taken into account during fracture

as well. Viscoelastic fracture theories [11–13] treat the problem as in

LEFM but considering the time dependence of the parameters involved

and relate, for crack propagation, fracture toughness with crack

propagation speed.

Another key aspect in fracture of polymers is toughening. The practice

of adding rubber particles in a glassy polymer to increase fracture

toughness, at expenses of modulus and strength, is nowadays common

also in the industry [14] and imposes some considerations when

evaluating the fracture behaviour.

In the present work a rubber toughened polymer and a composite

based on the same polymer as matrix were studied (as long as their

untoughened equivalent); chapter 2 reports the theoretical background

of the work, chapter 3 explains the experimental part of it and then

the results are discussed in the chapter 4. Chapter 5 concludes the

work.

1.1 References

[1] N. Bernet, V. Michaud, P.-E. Bourban, and J.-A. . Månson, “Commingled yarn composites for rapid processing of complex

T. Pini – Fracture of thermoplastic acrylic resins and composites

4

shapes,” Composites Part A: Applied Science and Manufacturing, vol. 32, no. 11, pp. 1613–1626, Nov. 2001.

[2] F. Henninger and K. Friedrich, “Thermoplastic filament winding with online-impregnation. Part A: process technology and operating efficiency,” Composites Part A: Applied Science and Manufacturing, vol. 33, no. 11, pp. 1479–1486, Nov. 2002.

[3] A. Offringa, “Thermoplastic composites: rapid processing applications,” Composites Part A: Applied Science and Manufacturing, vol. 27, no. 4, pp. 329–336, Jan. 1996.

[4] T. L. Anderson, Fracture Mechanics: Fundamentals and Applications, Second Edition. CRC Press, Boca Raton, 1995.

[5] A. A. Griffith, “The Phenomena of Rupture and Flow in Solids,” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 221, pp. 163–198, 1921.

[6] G. R. Irwin, “Analysis of stresses and strains near the end of a crack traversing a plate,” Journal of Applied Mechanics, vol. 24, pp. 361–364, 1957.

[7] J. R. Rice, “A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks,” Journal of Applied Mechanics, vol. 35, pp. 379–386, 1968.

[8] J. G. Williams, “Introduction to linear elastic fracture mechanics,” in Fracture Mechanics Testing Methods for Polymers, Adhesives and Composites, Elsevier, Amsterdam, 2001, pp. 3–10.

[9] J. G. Williams, “Application of fracture mechanics to composite materials,” K. Friedrich, Ed. Elsevier, Amsterdam, 1989, pp. 3–38.

[10] W. L. Bradley, “Application of fracture mechanics to composite materials,” K. Friedrich, Ed. Elsevier, Amsterdam, 1989, pp. 159–187.

Introduction and motivation

5

[11] W. Bradley, W. J. Cantwell, and H. H. Kausch, “Viscoelastic Creep Crack Growth: A Review of Fracture Mechanical Analyses,” Mechanics of Time-Dependent Materials, vol. 1, pp. 241–268, 1997.

[12] R. Frassine, M. Rink, A. Leggio, and A. Pavan, “Experimental analysis of viscoelastic criteria for crack initiation and growth in polymers,” International Journal of Fracture, vol. 81, pp. 55–5, 1996.

[13] J. G. Williams, “Applications of linear fracture mechanics,” in Failure in Polymers, Springer-Verlag, Berlin, 1978, pp. 67–120.

[14] C. B. Bucknall, “The physics of glassy polymers,” R. N. Howard and R. J. Young, Eds. Chapman and Hall, London, 1997, pp. 363–412.

6

2 Theoretical background

2.1 Linear Elastic Fracture Mechanics

(LEFM) Equation Chapter (Next) Section 1

Fracture mechanics is the theoretical approach based on continuum

mechanics that studies the growth and the propagation of cracks in

materials, defining intrinsic material properties that account for the

fracture behaviour. The macroscopic failure can be predicted, once the

crack or generic flaws (geometrical discontinuities, inclusions, holes,

microcavities) dimensions are known, based on the assumption that a

defect does not change material properties per se but actually modifies

locally the stress field induced by the external load. The intensification

of these stresses may reach a critical threshold for which the defect

starts to propagate inside the material, resulting in the fracture

process.

The basic assumptions are [1], [2]:

All materials contain flaws, cracks or inhomogeneities starting

from which fracture can initiate and propagate causing failure.

The growth of a crack can be characterised as the energy per

unit area necessary to produce new fracture surface, which is

the crack resistance R.

Theoretical background

7

The first assumption excludes the possibility of having perfect

materials, while the second implies that a criterion for fracture can be

found considering the problem in terms of energy balance (it is not the

only criterion).

We consider a sheet of uniform thickness B, in which a crack of length

a is propagating remaining similar to itself, meaning that the change

of crack area is given by

dA B da (2.1)

For a crack that propagates at constant speed a the energy balance

during a time interval dt can be written as

e d s kU U U U BRa (2.2)

where eU is the time derivative of the external work, dU is the time

derivative of the energy dissipated in processes not related to the

creation of new surfaces, sU is the time derivative of the stored elastic

energy and kU is the time derivative of the kinetic energy. Linear

elastic fracture mechanics assumes, in the static case, that all

dissipative phenomena are embodied in R and that kinetic energy

contribution is negligible.

It is possible to define the energy release rate parameter G as

1 e sdU dU

GB da da

(2.3)

T. Pini – Fracture behaviour of acrylic resins and composites

8

This quantity can be considered the driving force for crack

propagation. Combining (2.2) and (2.3) we obtain, at fracture

G R (2.4)

R is the critical value of G for which there is fracture propagation and

is therefore usually indicated with Gc. G may be derived for a body of

thickness B containing a crack of length a which has an applied load

P giving a deflection u (Fig. 2.1-1).

Fig. 2.1-1 General loaded body with a crack. From [1]

We can write

edU Pdu (2.5)

1

2sdU du dP

P uda da da

(2.6)

Considering the derivative of compliance C with respect to crack length

a

2

1dC du u dP

da P da P da (2.7)

then, combining (2.3), (2.5), (2.6) and (2.7) we obtain the general

expression derived by Irwin and Kies [3]


9

2

2

P CG

B a

(2.8)

which is valid for both constant load and constant displacement. The

term /C a depends on material properties and specimen geometry

and can be derived experimentally.

The loading can be applied to the cracked body as stresses over a

boundary instead of a being a concentrated load. In this case the

external work is evaluated as integrals over a contour surrounding

the crack tip (Fig. 2.1-2) and we can write the following expression for

G:

n ss n s

du duG W dy dS

dx dx

(2.9)

in which n, s, un and us are the normal and shear stress and

displacements where Ws is the strain energy density. This is the

expression of the contour integral expression described by Rice [4],

usually denoted as J for non-linear elastic materials and it becomes G

in the elastic case. and it is true for any elastic system and it is

applicable also in the case of laminates.


10

Fig. 2.1-2 General crack tip contour. From [1]

Another fracture criterion can be found considering the problem as the

intensification of the stress at the crack tip. The stress distribution

around the crack tip has the same for all loadings but its intensity

depends on load and geometry. The parameter that quantifies the

stresses at the crack tip is K, the stress intensity factor. Confining the

attention to Mode I crack loading (Fig. 2.1-3) and adopting the

coordinated system reported in Fig. 2.1-4 the stresses around the crack

tip are given

( )2

Iij ij

Kf

r

(2.10)

The stress along the crack plane ( 0 ) and in direction normal to it

is equal to

2

Iyy

K

r

(2.11)

It is possible to observe that the stress becomes infinite for 0r ,

therefore it is not possible to adopt a fracture criterion based on the


11

stress at the crack tip. However, the product yy r is finite and a

critical value of stress intensity factor KIc, can be taken as an elastic

criterion for fracture.

Fig. 2.1-3 Crack loading modes

Irwin [5] established a relationship between the stress intensity factor

KI and the strain energy release rate G:

2

'IK

GE

(2.12)

where 'E E for plane stress and 2' / (1 )E E for plane strain with

E and being the Young’s modulus and the Poisson’s ratio

respectively. This way G and KI are interchangeable and the critical

KIc fracture criterion is identical to a critical strain energy release rate

GIc.

However, since it is not always possible define stress intensity factors

for interlaminar fracture in composites, in this work it will be adopted

the strain energy release rate G to describe the fracture behaviour.


12

Fig. 2.1-4 Crack tip polar coordinate system. From [6]

2.1.1 Process zones

The elastic stresses introduced above reach an infinite value when the

distance from crack tip reaches zero. If that was the real case, in the

presence of a defect and in whichever load conditions a crack would

propagate due to the infinite stress. Actually, it is necessary to consider

some non-linearity in the material which will yield before reaching the

crack tip. The validity of LEFM holds only if the dimension of the

zone in which there are plastic deformations is limited with respect to

the dimensions of the linear elastic continuum of the body. These

conditions are referred as small scale yielding.


13

Irwin proposed [5] a model for a circular process zone based on an

elastoplastic behaviour of the material. The distance in the crack plane

at which the stress (plane) is equal to yield stress y is obtained by

(2.11) and is equal to

2

1

2I

yy

Kr

(2.13)

In order to have the same force balance as in the case of pure elastic

solution, the dimension of the zone must be increased in order to obtain

a redistribution of the stresses:

2

12 I

p yy

Kr r

(2.14)

In the case of polymers, the process zone is often not circular but more

a co-linear extension of the crack length. The model adopted in this

case is the one proposed by Dugdale [7] for which the extension of the

process zone in the case of plane stress is given by

2

8I

py

Kr

(2.15)

Without considering the model chosen to describe it, the dimension of

the process zone is influenced by stress state: along the thickness of a

plate the stress goes from being plane at the free surface to fully triaxial

(plane strain) in the centre. Adopting, for example, the Von Mises

criterion it can be demonstrated that the extension of the process zone


14

is larger in the case of plane stress than in the case of plane strain, for

both modes I and II. This holds for both Irwin’s and Dugdale’s models.

The plastic deformations are related to the capability of resisting to

crack growth; therefore, the dimension of the process zone will

translate into values of fracture toughness higher in the case of plane

stress in comparison with those relevant to plane strain state. The

measured fracture toughness will be an average of these values, so in

order to get a result that can be considered a property of the material

a mainly plane strain state should be obtained by choosing a proper

geometry. It must be noticed that it is also the most conservative case.

2.2 Viscoelastic fracture

In LEFM analysis the material is assumed to be linear elastic.

Polymers, however, are viscoelastic materials. Several theories were

formulated in the past years to describe the fracture behaviour of such

materials. In this work the theory proposed by Williams [8–10] was

adopted. The basic assumptions are that the material is linear and only

slightly viscoelastic; if this is the case, linear elastic equations can be

employed replacing the parameters with their time-dependent

counterparts.


15

Another key assumption is that the crack tip opening displacement is

constant over the time window considered. Fracture toughness can be

expressed as

( ) ( )Ic c yG t t (2.16)

where c the crack tip opening displacement and y the yield stress.

Substituting the relationship between KI and G (2.12) and equation

(2.16) into the process zone model proposed by Dugdale (2.15), this

becomes

2

2 2 2 28 8 (1 ) 8 (1 )Ic Ic c

py y y

K G E c Er

(2.17)

The dependence on time of the quantities has now to be taken into

account. Both the yield stress and relaxation modulus are functions of

time and can be described with the following power laws:

0( ) nE t E t (2.18)

0( ) my t t (2.19)

A simplification, often made but not adopted here, is to consider the

yield strain constant with time which implies that the yield stress and

the modulus have the same time dependence. The expression for the

length of the process zone is then

0 02 2

0 0

( )8 (1 ) 8 (1 )

nn mc c

p m

c E t c Er t t

t

(2.20)


16

It is often useful to relate the fracture toughness and the crack

propagation speed. The time scale is chosen as the time necessary to a

crack that moves at constant speed to go through the process zone:

prta

(2.21)

Substituting (2.20) into (2.21), solving for t and then substituting into

(2.16) we obtain the relationship between the fracture toughness and

the crack propagation speed:

1

0 10 2

08 (1 )

mmn m

c n mIc c

c EG c a

(2.22)

or, if we consider only the dependence on crack propagation speed:

' 1

mn n m

IcG a a (2.23)

In the case of crack initiation, this is not supposed to grow up until a

certain incubation time ti. The relationship between fracture toughness

and incubation or initiation time is simply given by (2.16) and can be

written as:

( ) ( )Ic i c y iG t t (2.24)

2.3 Rubber toughened polymers

Multiphase materials are usually developed in order to obtain

properties superior to those of the single components. Often, the

increase of a certain property causes the reduction of another, but


17

generally a combination with the right balance properties can be found

[11].

A common approach to enhance toughness in glassy brittle polymers

is to finely disperse rubbery domains in them. The presence of the

rubber particles obviously modifies the general behaviour of the

material and introduces different mechanism with respect to the

unmodified polymer. Hence, in order to fully understand the damage

mechanisms of a toughened polymer is better to recall also those of the

untoughened polymers.

2.3.1 Damage mechanisms in homopolymers

Processes involving plastic deformation in homogenous polymers are

essentially two: shear yielding and crazing [12], [13].

Shear yielding is a deformation process in which the distortion occurs

without notable changes in volume. In crystalline materials shear

yielding occurs on specific slip planes while shear processes are less

localized in the case of non-crystalline polymers. Shear yielding can

take place diffusively or through the formation of localized shear bands

depending on the polymer. Shear bands, birefringent and visible under

polarized light, should propagate in a direction forming an angle of 45°

with the load direction according to yield criteria. The actual direction


18

in the case of polymers differs from this value due to the dependence

of yield stress on the hydrostatic pressure.

Crazing is a phenomenon that involves, under an applied tensile load,

the creation of several micro voids which is accompanied by a change

in volume and in refractive index of the material. These voids, instead

of coalescing and becoming a crack, are stabilized by highly oriented

fibrils of polymeric material which prevent widening of the holes. The

yielded region is oriented perpendicular to load direction, resembles a

crack but it is highly different and is called a craze. Since the fibrils

connecting the faces of a craze are highly oriented, crazes can still carry

load even if around 75% of their volume is made of void. The basic

sequence of crazing initiation is [14]: local plastic deformation in the

surrounding of a defect with build-up of lateral stresses, nucleation of

void to release triaxial constraint and void coalescence. Crazes then

will grow via meniscus instability up until fibrils rupture which leads

to crack propagation.

2.3.2 Damage mechanisms in toughened polymers

The presence of the rubber particles acts in several different ways to

increase the toughness of the plain matrix. Also, the toughening effect

is related and influenced by many parameters such as particle size and

distribution, matrix composition, rubber content and adhesion


19

between matrix and particles. For sure, the presence of a rubbery phase

introduces other mechanisms and modifies those seen for

homopolymers in 2.3.1

The main mechanisms in a toughened polymer are multiple crazing,

particle cavitation and shear yielding of the matrix [12], [15–17]. The

different mechanisms occur depending on different material properties

but also on different load conditions.

Multiple crazing in the matrix is both initiated and controlled by

the rubber particles. Under tensile load, crazes are initiated at particles

equators, where the maximum principal stresses are located and then

propagate in direction perpendicular to load direction until an obstacle,

such as another particle, is encountered. The result is a large number

of small crazes, in contrast with the small number of larger crazes that

is found in the plain polymer. The relatively large volume of material

affected by dense crazing accounts for the stress whitening and the

higher energy absorption.

Cavitation of rubber particles is the growth of microvoids when a

critical volume strain is reached. It is generally accepted that

cavitation of the particles itself does not involve high amount of energy

absorbed but it is still a key mechanism in polymers toughening due

to its role in promoting matrix plasticity.


20

Shear yielding in the matrix is a mechanism similar to that observed

in untoughened polymers. However, in toughened polymers shear

yielding is promoted by cavitation of rubber particles, since after

cavitation the triaxial stress state is released and the matrix undergoes

plane stress conditions. This favours shear yielding in the matrix

surrounding the rubber particles while the triaxiality is more craze-

prone stress state.

Although cavitation of rubber particles may also involve some amount

of energy dissipation itself, its main role in toughening is the activation

of shear yielding which is the major energy absorbing mechanism. All

the mechanisms above may occur simultaneously in a toughened

polymer and the contribution of each mechanism depends on several

parameters such as rubber particles size, dispersion and concentration

and also temperature and rate conditions.

Béguelin [18] proposed, for a material very similar to that studied in

this work, a sequence of damage development that can be summarized

in the following steps:

The increase of remote stress causes the initiation and growth

of cavities at the poles of rubber particles. The resulting increase

of stress in the matrix surrounding the particles leads to

initiation of microcrazes at particle equators. The crazes start

to propagate in the matrix region between the particles, with a


21

constant stress acting on the craze fibrils as in unmodified

polymers

Crazes keep on growing in a direction perpendicular to load.

The craze growth is stopped when a neighbouring particle is

encountered. The particles are therefore now connected by a

craze network which allows for crazes to thicken.

Crazes start to branch and deviate from a direction

perpendicular to load and propagate at an angle more or less

equal to 45° in direction of the poles of the neighbouring

particles. Portions of material isolated from each other in a web

of voids are created, therefore the triaxiality of stress at crack

tip is relieved and the shear of the matrix is facilitated. Finally,

the crack propagates breaking the fibrils of the crazes.

This sequence can be found also moving from the undamaged bulk

material towards the crack tip, as summarized in Fig. 2.3-1 where the

three zones in roman numerals are related to the three steps above.


22

Fig. 2.3-1 Regions of progressive damage in the vicinity of the crack tip. From [18]

In order to assess the contribution of each mechanism to the

toughening process it is a common practice to adopt tensile

dilatometry. The principle is that while cavitation and crazing are

dilatational processes, shear yielding occurs at constant volume. The

major drawback of this method is that when cavitation and crazing

occur simultaneously it is difficult to separate their contribution. Other

methods of distinguishing these mechanisms rely on the birefringence

of shear bands under polarized light [12], [15] and the reversibility of

crazing and shear yielding by heating at temperatures close to glass

transition temperature [11].


23

2.4 References [1] J. G. Williams, “Application of fracture mechanics to composite

materials,” K. Friedrich, Ed. Elsevier, Amsterdam, 1989, pp. 3–38.

[2] J. G. Williams, Fracture mechanics of polymers. Ellis Horwood Ltd., Chichester, 1984.

[3] J. A. Kies and G. R. Irwin, “Critical energy release rate analysis of fracture strength,” Welding Journal Research Supplement, vol. 33, pp. 193–198, 1954.

[4] J. R. Rice, “A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks,” Journal of Applied Mechanics, vol. 35, pp. 379–386, 1968.

[5] G. R. Irwin, “Analysis of stresses and strains near the end of a crack traversing a plate,” Journal of Applied Mechanics, vol. 24, pp. 361–364, 1957.

[6] A. Liu, “Summary of stress-intensity factors,” ASM Handbook, vol. 19, pp. 980–1000, 1996.

[7] D. S. Dugdale, “Yielding of steel sheets containing slits,” Journal of the Mechanics and Physics of Solids, vol. 8, no. 2, pp. 100–104, May 1960.


[9] R. Frassine, M. Rink, A. Leggio, and A. Pavan, “Experimental analysis of viscoelastic criteria for crack initiation and growth in polymers,” International Journal of Fracture, vol. 81, pp. 55–5, 1996.


24


[11] C. B. Arends, “Polymer Toughening,” C. B. Arends, Ed. Marcel Dekker, Inc. New York, 1996, pp. 61–84.

[12] C. B. Bucknall, Toughened Plastics. Springer Science + Business Media, Dordrecht, 1977.

[13] A. M. Donald, “Rubber Toughened Engineering Plastics,” A. A. Collyer, Ed. Springer Science+Business Media, Dordrecht, 1994, pp. 1–28.

[14] E. J. Kramer, “Microscopic and molecular fundamentals of crazing,” in Crazing in Polymers, Springer Verlag, Berlin, 1983, pp. 1–56.

[15] C. B. Bucknall, “The physics of glassy polymers,” R. N. Howard and R. J. Young, Eds. Chapman and Hall, London, 1997, pp. 363–412.

[16] C. B. Bucknall, “Quantitative approaches to particle cavitation, shear yielding, and crazing in rubber-toughened polymers,” Journal of Polymer Science Part B: Polymer Physics, vol. 45, no. 12, pp. 1399–1409, 2007.

[17] I. Walker and A. A. Collyer, “Rubber Toughened Engineering Plastics,” A. A. Collyer, Ed. Springer Science+Business Media, Dordrecht, 1994, pp. 29–56.

[18] P. Béguelin, “Approche expérimentale du comportament mécanique des polymères en sollicitation rapide,” École Polytechnique Fédérale de Lausanne, 1996.

25

3 Experimental details

3.1 Materials and samples preparation

Equation Chapter 3 Section 1

Thermoplastic polymers to be used as matrices in composite materials

gained increasing interest due to the advantages that come from their

employment: the parts can be welded, recycled and, most importantly

from this work point of view, they have higher fracture toughness when

compared to thermosets. Unfortunately, the adaption of composite

materials processing techniques developed for thermosets to

thermoplastic matrices is quite cumbersome. In fact, thermoplastic

polymers have typically a high melt viscosity and fibre impregnation,

complete and without voids, may require high pressure and

temperature. Alternatively, techniques developed for thermoplastic

polymers should be adopted.

The innovation introduced by the novel resins investigated in the

present work is the possibility to produce continuous fibre composites

by reactive processing technologies, avoiding this way all the issues

related to high melt viscosity.

Unreinforced resins samples were produced by casting monomeric

solutions in closed moulds (Fig. 3.1-1) and letting the polymerization


26

reaction take place. Plates of various thicknesses were produced.

Specimens for different tests performed were machined from the plates.

Fig. 3.1-1 Liquid monomer casting

Unidirectional continuous carbon fibre composite samples were

produced adopting an infusion moulding technique, in which the liquid

monomers flow in a sealed vacuum bag in which the fibres were

previously inserted. A schematic view of the technique is shown in Fig.

3.1-3. The number of fibre layers determines the final thickness of the

samples.

The materials studied in the present work were two types of acrylic

thermoplastic resins developed by Arkema company. The resins, one

plain and one toughened with rubber have the tradename of Elium®

and Elium Impact® respectively. The toughened resin was obtained

Experimental details

27

adding an acrylic block copolymer under the tradename of

Nanostrength® (10 wt%).

Elium samples were casted at room temperature and let polymerize for

24 hours at this temperature. Then, a thermal treatment of 1 hour at

80 °C and 1 hour at 120 °C was performed to complete polymerization.

In the case of Elium Impact the polymerization reaction was performed

with a thermal cycle of 5 hours at 80° C and then 1.5 hours at 125 °C.

The glass transition temperature was measured as illustrated in section

3.2.1. The two resins showed very similar glass transition temperatures:

127 °C for Elium and 130 °C for Elium Impact as shown in Fig. 3.1-2.

From the same graph it is also evident the glass transition temperature

of the rubbery phase of Elium Impact at approximately -25 °C.

Fig. 3.1-2 Tan vs. temperature curves for Elium (blue) and Elium Impact (red). Arrows indicate the positions of the peaks corresponding to glass transitions


28

The same resins were adopted in the infusion moulding process.

Polymerization conditions were the same as in the case of neat resins,

in order to obtain comparable properties, Nevertheless, the presence of

carbon fibres changes the thermal conductivity of the material,

therefore the thermal history is not exactly the same. The fibres

adopted were T700 12 K unidirectional continuous carbon fibres and

the composites had a final fibre volume fraction of around 60% by

weight. The sizing of the fibres was the same generally adopted for

vinyl ester resins, as a result of previous studies performed by Arkema

company.

Fig. 3.1-3 Infusion moulding technique. From Arkema website


29

3.2 Test methods and data reduction

analysis

3.2.1 Dynamic Mechanical Analysis

Dynamic Mechanical Analysis (DMA) is a technique used to

investigate the viscoelastic behaviour of materials [1], [2]. It is based

on the evaluation of the phase lag between the applied oscillatory

strain and the measured stress and/or vice versa. At a given frequency,

the behaviour of a material is expressed through a complex dynamic

modulus, in which the real part represents the elastic component

(storage modulus), the imaginary part is the viscous component (loss

modulus) and their ratio is the tangent of the phase angle (tan ). This

technique is usually adopted to study the response of the material as

a function of frequency or can be used to find glass transition

temperature.

In this work both temperature and frequency sweeps were performed

to evaluate glass transition temperature (Tg) and moduli curves

respectively. Temperature sweep test was carried out at fixed

frequency and applied strain and with a temperature rate of 10 °C/min,

measuring tan as a function of temperature. Tg was identified by the

position at which a peak of tan occurs.


30

Storage modulus was measured at different temperatures as a function

of frequency. Isothermal tests were performed allowing the specimen

to reach thermal equilibrium after each temperature increase. Applying

the time-temperature superposition principle master curves were built

for a given reference temperature and the relevant shift factors were

obtained. Vertical shift factors were not taken into account.

All tests were performed on a TA RSA-3 machine adopting a three-

point bending configuration. Test parameters were chosen as follows

for both Elium and Elium Impact resins:

Specimen dimensions: 45x6x2 mm

Applied strain: 0.1 %

For frequency sweeps:

Frequency range: 0.1< <10 Hz

Temperature range: -60< T <110 °C

For temperature sweeps:

Frequency: 1 Hz

Temperature range: -50<T<150 °C

Temperature rate 10 °C/min


31

3.2.2 Tensile tests

Yield was investigated with uniaxial tensile tests carried out at

constant displacement rate on an Instron 1121 dynamometer equipped

with thermostatic chamber. Tests were performed at three

displacement rates (0.1, 1, 10 mm/min) and at four temperatures

between 0 and 60 °C. 2 mm thick sheets of both resins were cut

obtaining dumbbell specimens as in Fig. 3.2-1. Strains were measured

with Digital Image Correlation (DIC) (Section 3.2.5).

Fig. 3.2-1 Tensile specimen

The yield point was chosen as the maximum of the stress strain curve.

Yield stress vs. time to yield curves were obtained at the different

temperatures and then a master curve was built shifting data along

the logarithmic time axis.

In order to adopt DIC analysis a sample preparation procedure was

necessary. Before testing, the specimens were painted white adopting


32

a water based paint in order to avoid any interaction with the material

which could have led to premature failure. The white layer was

necessary in order to achieve high contrast with the fine black speckle

pattern which was then applied.

From the strain field from DIC analysis, it was also possible to evaluate

the volume changes occurring during the tests [3], [4] as

20

1 1 1lat

V

V

(3.1)

where is the longitudinal strain and lat is the lateral contraction,

which was considered the same in both transversal directions.

Considering the region of the stress-strain curve close to the origin it

is possible to evaluate Young’s modulus, E, and Poisson’s ratio, as

/E (3.2)

/lat (3.3)

then the elastic contribution to longitudinal and volumetric strain are

given by

/el E (3.4)

0

(1 2 ) el

el

V

V

(3.5)

Under the assumption that the different contributions to volume strain

are additive and that shearing processes do not involve any change in

volume, it is possible to write the volumetric strain due to crazing

and/or cavitation:


33

0 0 0 0/

(1 2 ) el

cr cav el

V V V V

V V V V

(3.6)

Assuming, as done in [3], [4], that the strain component due to crazing

and/or cavitation, cr/cav, is equal to the relevant volume strain

component and assuming the additivity of strain components, it is

possible to obtain the shear component, sh, of the longitudinal strain

from

/el cr cav sh (3.7)

3.2.3 Fracture tests on neat polymers

Fracture of both resins was investigated adopting several

configurations for different purposes.

3.2.3.1 Double Torsion

In order to obtain the strain energy release rate, GIc, as a function of

crack speed, a , the Double Torsion test configuration was chosen [5],

[6]. The reason is its experimental simplicity and the fact that a stable

crack propagation with constant crack speed can be obtained also with

very brittle materials, like the acrylic plain resin studied here. The test

specimen is a notched rectangular plate with a bottom groove, inserted

in order to prevent the crack from wandering during propagation. The

dimensions of the specimens adopted were 120x45x6 mm and


34

200x70x10 mm with initial notch lengths of 22.5 mm and 30 mm

respectively. The specimen is loaded in a four-point bending

configuration and the torsion on each beam is transferred to the un-

notched ligament until the crack starts to propagate (Fig. 3.2-2).

Fig. 3.2-2 Double torsion test configuration

The fracture toughness is evaluated as

2

2c

Icc

P CG

b a

(3.8)

where Pc is the load during propagation, bc the thickness of the grooved

section and /C a is the derivative of the compliance with respect to

the crack length. This derivative is given by:

2

312

C h

a k Wb

(3.9)


35

Where h is the arm length of the applied moment, 2W is the specimen

width, k1 is a correction factor [7], b is the specimen thickness and is

the shear modulus. It can be observed that the term /C a does not

depend on the crack length, and therefore for given test conditions, in

terms of rate and temperature, it remains constant during the test.

The derivative of the compliance with respect to crack length can be

evaluated with (3.9) or, as was done in this work, with a calibration

method: several specimens with different notch lengths were loaded

within the linear elastic region and the different compliances were

measured. Then plotting such compliances vs. the relevant crack

lengths, a linear relationship was found and /C a was evaluated.

Fig. 3.2-3 shows the compliance calibration curves for the specimens

with dimensions of 120x45x6 mm of both resins. Since specimens of

different dimensions were tested in this work, a compliance calibration

for each geometry adopted was performed. The terms /C a for each

resin and each geometry, evaluated at 23 °C and 1 mm/min, are given

in Tab. 3.2-1 in comparison to those evaluated with equation (3.9), in

which the shear modulus was evaluated from the relaxation modulus

curves, at 23 °C, that will be reported in the next chapter.


36

Fig. 3.2-3 Double torsion compliance calibration curves at 23 °C and 1 mm/min for Elium (blue) and Elium Impact (red). Specimens dimensions were 120x45x6

mm. Solid lines are linear fittings representing the term /C a

/C a

(calibration)

/C a

(eq. (3.9))

Elium (120x45x6 mm) 4.87E-05 N-1 4.43E-05 N-1

Elium Impact (120x45x6

mm) 5.57E-05 N-1 6.33E-05 N-1

Elium (200x70x10 mm) 1.36E-05 N-1 1.43E-05 N-1

Elium Impact (200x70x10

mm) 2.91E-05 N-1 2.47E-05 N-1

Tab. 3.2-1 Compliance derivative with respect to crack length for different geometries at 23 °C and 1 mm/min


37

The value of /C a for the different testing conditions was properly

scaled taking into account the ratio between the compliance of the

specimen of the fracture test and that of the calibration specimen.

If a test is performed at constant displacement rate, the crack

propagation speed may be evaluated with the relationship

c

c

xa

PCP C

a a

(3.10)

where x is the constant crosshead displacement rate. Generally, after

crack onset and a brief transient, the crack propagates at constant load

[8]. In this stage, given the fact that both the derivative of the

compliance with respect to crack length and the load are constant, the

crack propagation speed is constant and it is given by

c

xa

CP

a

(3.11)

Several works present in literature proposed corrections for the original

formulation of the double torsion test analysis [8–14]. In this work the

corrections proposed by Leevers [14] to take into account the error

introduced by large displacement were found to be substantial and

were adopted. Corrected fracture toughness is evaluated as:

22

1[ ( ) ( )]IcG P F G

d v

d D

(3.12)

where F and G are given by:


38

1( )

v d vF

D d D

(3.13)

2

2

2

2

1( )

1

d v v d v d vd D D d D d D

Gd v d vd D d D

(3.14)

The ratio v/D is given by the relationship:

tan (sec 1)v

D (3.15)

where v is the vertical displacement, D is the arm length of the applied

moment (h in (3.9)), is the rotation of each beam and a geometric

factor given by

1 2r r B

D (3.16)

in which r1 and r2 are the radii of the supports and B is the specimen

thickness (b in (3.9)) as in Fig. 3.2-4

Fig. 3.2-4 Double torsion specimen load-plane deformation. From [14]

The first and second derivative of v/D with respect to are then

calculated:


39

2sec (1 sin )d v

d D

(3.17)

2

22 tan sec

d v d v

d D d D

(3.18)

In order to apply the correction also on the crack propagation speed,

an equivalent corrected load was evaluated matching equations (3.8)

and (3.12). The corrected load was then adopted to measure the crack

propagation speed with equation (3.11)

DT tests were performed at different displacement rates and at

temperatures varying from 0 to 60 °C. Tests were performed on an

Instron 1185 dynamometer equipped with a 10 kN load cell and a

thermostatic cabinet and on a MTS 831.50 servo hydraulic machine at

Montanuniversität in Leoben, Austria.

3.2.3.2 Single Edge Notched Bending

Single Edge Notched Bending (SENB) configuration [15], is not ideal

to evaluate crack propagation speed but it is suitable for performing

Digital Image Correlation analysis at the crack tip and investigating

the phenomena occurring at the process zone.

Prismatic specimens of 90x20x10 mm, as in Fig. 3.2-5., were cut from

10 mm thick sheets.


40

Fig. 3.2-5 Single Edge Notched Bending specimen

A notch was carefully introduced with a razor blade up to a depth of

about half width of the specimen (section 3.2.3.4).

The specimens were prepared for DIC analysis as in section 3.2.2, but

in this case the airbrush parameters were set in order to obtain the

finest speckle pattern possible which allowed to choose a smaller subset

size during the analysis and better analyse a more localized zone (see

section 3.2.5).

The fracture toughness was evaluated as

( / )

cIc

UG

h W a W (3.19)

where Uc is the energy evaluated as the area underneath the load-

displacement curve at crack initiation, h is the thickness, W is the

width and is a calibration factor dependent on crack length a. The

expression of the calibration factor is reported in [15], for a span to

specimen width ratio equal to 4 as in the case of the present work.


41

Tests were performed at a displacement rate of 5 mm/min and at

temperatures varying from 0 to 60 °C.

3.2.3.3 Double Notched Four Point Bending

The Double Notched Four-Point Bending (DN-4PB) is a technique

useful to examine the process zones and the mechanisms involved in

the fracture process [16–18]. The principle of this technique is simple:

two nominally identical notches are introduced in the specimen which

is then loaded in a four-point bending configuration (Fig. 3.2-6). Since

the notches are in the region in between the two inner loading points

and since in this region the bending moment is constant, the two crack

tips are subjected to an identical stress field.

Fig. 3.2-6 Double Notched Four-Point Bending specimen

Provided that the distance between the notches is large enough,

process zones are formed at both crack tips upon loading without


42

interacting. In the real case, because the cracks cannot be exactly

identical, one will become critical and will start to propagate, thus

unloading the other crack. The result is the development of a process

zone at the second crack tip without a propagating crack (Fig. 3.2-7).

Fig. 3.2-7 DN-4PB specimen after loading with a propagated crack (left) and a fully developed process zone (right)

This test configuration was adopted to study the process zone of the

rubber toughened resin (Elium Impact). Tests were conducted at

crosshead speeds of 0.1, 1 and 10 mm/min with temperature varying

from 0 to 60 °C. After performing the tests, the specimens were cut in

the middle, in direction normal to the fracture surface and parallel to

crack propagation.


43

Fig. 3.2-8 Position of the slice cut from the DN-4PB specimens after testing

A slice in correspondence of the process zone of the crack which did

not propagate was obtained (Fig. 3.2-8) and then was polished and

mounted on a glass slide with a transparent epoxy in order to prevent

any damage to the thin samples during further machining.

The samples, after reducing the thickness to approximately 200 m,

were finely polished. Finally, a Leica DMLM transmission optical

microscope equipped with crossed-polarizers was adopted to take

micrographs of the process zones.

3.2.3.4 Notching

The notches were introduced in DT, SENB and DN-4PB specimens

via automated “chisel-wise” cutting, with an advancement speed of the

blade into the specimen of about 50 m/s. The final notch root radii


44

obtained were less than 10 m in all cases; an example of notch root

is shown in Fig. 3.2-9. Since the quality of the notch has a strong

influence on the measurement of fracture toughness at crack initiation,

in the case of SENB and DN-4PB specimens the blade was changed

every 5 cuts in order to have sharp notches and obtain reliable

measurements of fracture toughness at crack initiation. In the case of

Double Torsion configuration, the quality of the notch is less important

since the test is designed to investigate the stable crack propagation

stage and not the crack initiation.

Fig. 3.2-9 Notch root in Single Edge Notched Bending specimen


45

3.2.4 Fracture tests on composites

Mode I fracture toughness of composite materials was evaluated

adopting Double Cantilever Beam test configuration. Specimens were

cut from sheets produced by infusion moulding (section 3.1)

.

Fig. 3.2-10 Composite sheet from infusion moulding with the direction of the fibres, position of the starter film and cuts for the final specimens

During the infusion process a thin PTFE film was placed at half

thickness of the laminate on one side, having a width of about 60 mm

to obtain the initial notch. Specimens 190 mm long and 20 mm wide

were cut, parallel to fibre direction, so as to contain the starter film as

in Fig. 3.2-10.

The ends of the specimen containing the film were first sanded and

acetone-wiped, and then aluminium load blocks were bonded using a

bi-component epoxy adhesive, Scotch-Weld™ DP-760 from 3M. The


46

side of the specimen was white painted in order to get a good contrast

and be able to locate the crack tip.

Fig. 3.2-11 Double Cantilever Beam specimen

DCB specimens (Fig. 3.2-11) were tested at different displacement

rates and temperatures. Fracture toughness was evaluated as

3

2 ( | |)Ic

P FG

W a N

(3.20)

where Pc is the load, the displacement, W the specimen width, a the

crack length and , F and N are corrective factors for beam root

rotation, large displacements and load blocks respectively. The

procedure for the evaluation of such parameters is reported in ISO

standard 15024 [19], which was also followed to find the initiation and

propagation values of fracture toughness. Tests were video recorded

and crack propagation speed was determined. Tests were performed on

an Instron 1185 dynamometer equipped with a 10 kN load cell and a


47

thermostatic cabinet and on a MTS 831.50 servo hydraulic machine at

Montanuniversität in Leoben, Austria.

3.2.5 Digital Image Correlation

Digital Image Correlation (DIC) is an optical method based on

tracking and comparing images, allowing to measure full-field

displacements and deformations in many engineering applications. It

is becoming the standard for measuring strains in materials science

since there is no contact with the specimen; on the other hand, a

speckle pattern needs to be painted on the specimen for the analysis

and the test must be video-recorder or photographed, with high

resolution and very fine focus.

The basic operating principle of DIC is to track subsets of speckles on

an image and to find the best match between the subsets in a reference

image and in the deformed image. Each subset should be univocally

distinguishable from others. This is achievable by putting on the

specimen surface a randomly distributed pattern of speckles. The

speckles pattern density and dimensions strongly affect the analysis;

they can be tuned but obviously are influenced by how the pattern is

put on the specimen. In this work the specimens were first painted

white, adopting a water based paint in order to avoid any interaction

with the material which lead to premature failure. This white layer


48

was necessary for the transparent material in this work in order to

achieve high contrast with the fine black speckle pattern which was

then applied by a dual action airbrush. The parameters that need to

be chosen when performing DIC are several and can be summarized

as:

Subset size is the size of the portion of image on which the

correlation is done. A smaller subset allows to have a more

localized information, but since a minimum number of speckles

is necessary for subsets matching, the minimum subset size is

affected by the pattern quality. The data obtained after

correlation is stored in the centre of the subset, hence the closer

it is possible to get to edge of the selected area of interest is half

subset size. This is a critical issue when an evaluation close to

edge is necessary as in case, for example, of a crack tip as in the

three point bending tests. In this case a small as possible subset

size is preferred.

Incremental correlation. In the case of very large

deformations the changes from the un-deformed state could be

severe enough to make image correlation very difficult. In this

case incremental correlation could be adopted, using as

reference image for each frame not the initial image but the one

from the prior frame. This way the correlation is better in the


49

case of large deformations, but there can be a progressive

stacking of errors.

Step size determines the distance between two different

subsets and defines the measurement grid density. The step size

is smaller than the subset size and determines the degree of

overlapping of the subsets. Usually a value of around 25% of

the subset size is chosen.

Filter size determines the number of data points on which the

strain is smoothed. The product of step and filter size is the

virtual strain gauge size.

In this work the pattern quality and DIC parameters were studied in

order to get the best and most reliable results from both tensile (section

3.2.2) and fracture tests (section 3.2.3.2). The software adopted to

perform the analysis was Vic-2D from Correlated Solutions, Inc. and

the results were checked also with the open-source MATLAB based

software Ncorr v.1.2 [20]. More detailed information about Digital

Image Correlation can be found in [21].

3.3 References

[1] R. M. Christensen, Theory of Viscoelasticity: Second Edition. Dover Publications, Mineola, 2010.


50

[2] N. G. McCrum, C. P. Buckley, and C. B. Bucknall, Principles of Polymers Engineering, 2nd edition. Oxford University Press, Oxford, 1997.

[3] O. Frank and J. Lehmann, “Determination of various deformation processes in impact-modified PMMA at strain rates up to 105%/min,” Colloid & Polymer Science, vol. 264, no. 6, pp. 473–481, 1986.

[4] D. Heikens, S. D. Sjoerdsma, and W. J. Coumans, “A mathematical relation between volume strain, elongational strain and stress in homogeneous deformation,” Journal of Materials Science, vol. 16, no. 2, pp. 429–432, 1981.

[5] A. G. Evans, “A method for evaluating the time-dependent failure characteristics of brittle materials - and its application to polycrystalline alumina,” Journal of Materials Science, vol. 7, no. 10, pp. 1137–1146, 1972.

[6] J. O. Outwater and D. J. Gerry, “On the fracture energy of glass,” University of Vermont, 1966.

[7] S. Timoshenko and J. N. Goodier, Theory of elasticity. McGraw-Hill, New York, 1969.

[8] R. Frassine, T. Riccò, M. Rink, and A. Pavan, “An evaluation of double-torsion testing of polymers by visualization and recording of curved crack growth,” Journal of Materials Science, vol. 23, no. 11, pp. 4027–4036, 1988.

[9] M. Ciccotti, “Realistic Finite-Element Model for the Double-Torsion Loading Configuration,” Journal of the American Ceramic Society, vol. 83, no. 11, pp. 2737–2744, 2000.

[10] M. Ciccotti, G. Gonzato, and F. Mulargia, “The double torsion loading configuration for fracture propagation: an improved methodology for the load-relaxation at constant displacement,” International Journal of Rock Mechanics and Mining Sciences, vol. 37, no. 7, pp. 1103–1113, 2000.


51

[11] P. J. Hine, R. A. Duckett, and I. M. Ward, “A double-torsion study of the fracture of polyethersulphone,” Journal of Materials Science, vol. 19, no. 11, pp. 3796–3805, 1984.

[12] P. S. Leevers, “Crack-front shape effects in the double torsion test,” J Mater Sci, vol. 17, no. 9, pp. 2469–2480, 1982.

[13] P. S. Leevers and J. G. Williams, “Material and geometry effects on crack shape in double torsion testing,” J Mater Sci, vol. 20, no. 1, pp. 77–84, 1985.

[14] P. S. Leevers, “Large deflection analysis of the double torsion test,” Journal of Mater Science Letters, vol. 5, no. 2, pp. 191–192, 1986.

[15] “Plastics - Determination of fracture toughness (GIc and KIc) - Linear elastic fracture mechanics (LEFM) approach,” International Organization for Standardization, Geneva, CH, 13586, 2000.

[16] M. L. Arias, P. M. Frontini, and R. J. . Williams, “Analysis of the damage zone around the crack tip for two rubber-modified epoxy matrices exhibiting different toughenability,” Polymer, vol. 44, no. 5, pp. 1537–1546, Mar. 2003.

[17] N. Saad, C. Olagnon, R. Estevez, and J. Chevalier, “Experimental Analysis of Glassy Polymers Fracture Using a Double Notch Four Point-Bending Method,” in European Structural Integrity Society, Elsevier BV, 2003, pp. 27–38.

[18] H.-J. Sue and A. F. Yee, “Study of fracture mechanisms of multiphase polymers using the double-notch four-point-bending method,” Journal of materials science, vol. 28, no. 11, pp. 2975–2980, 1993.

[19] “Fibre-reinforced plastic composites - Determination of mode I interlaminar fracture toughness, GIc, for unidirectionally reinforced materials,” International Organization for Standardization, Geneva, CH, 15024, 2001.


52

[20] J. Blaber, B. Adair, and A. Antoniou, “Ncorr: Open-Source 2D Digital Image Correlation Matlab Software,” Experimental Mechanics, vol. 55, no. 6, pp. 1105–1122, 2015.

[21] H. Schreier, J.-J. Orteu, and M. A. Sutton, Image Correlation for Shape, Motion and Deformation Measurements. Springer-Verlag, Berlin, 2009.

53

4 Results and discussion

4.1 Fracture behaviour of matrices

4.1.1 Viscoelastic effects on fracture

Double torsion test configuration, illustrated in section 3.2.3.1, was

adopted to determine fracture toughness of both resins as a function

of crack propagation rate. Original load-displacement curves and those

corrected to take into account the change in length of moment arm

due to large displacements [1] are shown in Fig. 4.1-1. The corrective

effect is more evident in the case of Elium Impact, which being more

compliant shows larger displacements than Elium. Based on the

corrected curves, crack propagation speed and fracture toughness were

measured, considering the stage in which the load Pc was constant.

Fig. 4.1-2 and Fig. 4.1-4 show fracture toughness, GIc, as a function of

crack propagation speed, a , for the two materials at different

temperatures. Adopting the time-temperature equivalence, master

curves of GIc as function of crack propagation speed were built by

shifting horizontally the data relevant to the different temperatures so

as to superpose to those at the reference temperature of 23 °C. Results

are reported in Fig. 4.1-3 and Fig. 4.1-5.


54

Fig. 4.1-1 Effect of corrective factors for large displacement for Elium (blue) and Elium Impact (red). Dashed lines are original data, solid lines are corrected data

The different behaviour of the two resins investigated is evident: Elium

showed increasing fracture toughness for increasing values of crack

propagation speed as expected from viscoelastic fracture theories [2–5],

while Elium Impact showed a non-monotonic trend.

Results and discussion

55

Fig. 4.1-2 Fracture toughness vs. crack propagation speed isothermal curves for Elium

Fig. 4.1-3 Fracture toughness vs. crack propagation speed master curve at the reference temperature of 23 °C for Elium. Solid line is a power law fitting


56

Fig. 4.1-4 Fracture toughness vs. crack propagation speed isothermal curves for Elium Impact

Equation Chapter (Next) Section 1

Fig. 4.1-5 Fracture toughness vs. crack propagation speed master curve at the reference temperature of 23 °C for Elium. Dashed line is a visual aid


57

The trends obtained for fracture toughness vs. crack propagation speed

were compared with those predicted by Williams’ theory reported in

section 2.2.

Following this theory:

'nIcG a (4.1)

with

'1

mn

n m

(4.2)

In order to obtain n, the exponent of the power law describing the

relaxation modulus, E, dependence on time, t, dynamic mechanical

tests were used.

The conservative component of the dynamic complex modulus (storage

modulus) E’ as a function of frequency obtained at different

temperatures are reported in Fig. 4.1-6 and Fig. 4.1-7 for Elium and

Elium Impact respectively.


58


Fig. 4.1-7 Storage modulus vs. frequency isothermal curves for Elium Impact

Isothermal curves were then shifted horizontally along the frequency

axis to reach superposition, obtaining the master curves at the

reference temperature of 23 °C reported in Fig. 4.1-8. Observing the


59

master curves, it is clear that while the two materials have a similar

dependence of E’ on frequency, Elium Impact showed lower values of

modulus as a consequence of the presence of the rubbery phase. This

result was expected considering that the small strains response of a

rubber-toughened polymer is largely determined by the properties of

the matrix; however, the rubbery phase lowers the stiffness of the

material [6]. Concerning the viscoelasticity of the material this is still

mainly governed by the matrix.

From the storage modulus vs. frequency curves it was possible to

obtain the relaxation modulus as function of time curves. Following

the approach proposed by [7], relaxation modulus can be approximated

as the real part of the complex dynamic modulus, evaluated at

21 / t :

21/( ) '( ) |

tE t E

(4.3)

The curves obtained are reported in Fig. 4.1-9 in double logarithmic

scale. The curves were fitted (solid lines in Fig. 4.1-9), in the range of

times between 10-4 and 106 seconds, with a power law function as

0( ) nE t E t (4.4)

Fitting parameters found are reported in Tab. 4.1-1. From the

measurements of the process zone length (section 4.1.2) and the crack

propagation speeds covered by double torsion tests, the times, t,

characteristic of the fracture process were evaluated and it was verified


60

that they were inside the range of times over which fitting of the

relaxation modulus curves was performed.

Fig. 4.1-8 Storage modulus vs. frequency master curves at the reference temperature of 23 °C for Elium (blue) and Elium Impact (red)


61

Fig. 4.1-9 Relaxation modulus vs. time curves at the reference temperature of 23 °C for Elium (blue) and Elium Impact (red). Solid lines are power law fittings

E0 (GPa) n

Elium 3.66 0.049

Elium Impact 2.47 0.051

Tab. 4.1-1 Fitting parameters of relaxation modulus power law function of time

To obtain the exponent m of the power law describing yield stress, y,

vs. time to yield, ty, yield behaviour of both matrices was determined

performing tensile tests at different rates and temperatures. Examples

of the stress-strain curves obtained at different temperature for a


62

displacement rate of 1 mm/min are given in Fig. 4.1-10 and Fig. 4.1-11

for the two materials.

The influence of temperature on the mechanical response of both

materials is clearly visible and, comparing the curves relevant to the

two resins, it is possible to observe the substantial difference between

them. Elium showed in all test conditions a more brittle behaviour

while for Elium Impact a lower strength and much larger elongations

at break were observed as expected due to the presence of the rubbery

phase.

Fig. 4.1-10 Stress-strain curves at different temperatures from tensile tests at constant displacement rate of 1 mm/min for Elium


63

Fig. 4.1-11 Stress-strain curves at different temperatures from tensile tests at constant displacement rate of 1 mm/min for Elium Impact

The yield point was taken at the maximum of the stress-strain curve.

Yield stress measured at different testing conditions are reported in

Fig. 4.1-12 and Fig. 4.1-13 as a function of the time to yield.


64


Fig. 4.1-13 Yield stress vs. time to yield isothermal curves for Elium Impact


65

Data were then reduced to obtain master curves by shifting isothermal

data along the logarithmic time axis so as to obtain the best

superposition. The master curves for the reference temperature of 23

°C are shown in Fig. 4.1-14. Yield stress dependence on time to yield

was fitted to a power law function

0m

y yt (4.5)

which is also shown in Fig. 4.1-14 by a solid line for each resin.

Parameters of the power law fittings of the experimental data are

reported in Tab. 4.1-2.

Fig. 4.1-14 Yield stress vs. time to yield master curves at the reference temperature of 23 °C for Elium (blue) and Elium Impact (red). Solid lines are

power law fittings


66

0 (MPa) m

Elium 110.15 0.072

Elium Impact 54.98 0.047

Tab. 4.1-2 Fitting parameters of yield stress power law function of time to yield

In order to cross-check the results, the relaxation modulus (Fig. 4.1-9)

was measured from tensile tests too. Tangent modulus and the relevant

time were taken at a fixed strain (1%) at different testing conditions.

The times were shifted adopting the same shift factors obtained

building the yield stress master curves. Results are reported in Fig.

4.1-15 and compared to the relaxation modulus curves obtained from

DMA tests. It can be observed that a good agreement was found,

validating the approximation made in (4.3).


67

Fig. 4.1-15 Relaxation modulus vs. time curves at the reference temperature of 23 °C for Elium (blue) and Elium Impact (red). Solid lines are power law fittings.

Plus (+) symbols refer to results from tensile tests.

Considering the exponents n and m found for relaxation modulus and

yield stress power laws (Tab. 4.1-1, Tab. 4.1-2), it was possible to

evaluate the theoretical value of the exponent n’ of the power law

relating fracture toughness and crack propagation speed (4.2). In Tab.

4.1-3 it is possible to compare the theoretical value and that fitted

from experimental data. In the case of Elium resin a good agreement

was found while in the case of Elium Impact, since the trend was

decreasing and not monotonic, there was no sense in such comparison.

This different behaviour of the two resins is clearly not only linked to

differences in the viscoelastic effects, such as those in the far field

(expressed through the relaxation modulus) and at the crack tip


68

(expressed through the yield stress time dependence), but could rather

be due to some change in the local deformation mechanisms in the

process zone at the crack tip occurring under the different test

conditions.

n’ (th.) n’ (exp.)

Elium (7.4±0.1)10-2 (6.3±0.7)10-2

Elium Impact (4.7±0.2)10-2 -

Tab. 4.1-3 Fracture toughness power law of crack propagation speed exponents. Comparison between William’s theoretical and experimental values

A last observation on the viscoelastic effects on the mechanical

properties of the resins can be made. The shift factors obtained

building the master curves of conservative modulus, yield stress and

fracture toughness are reported in Fig. 4.1-16 and Fig. 4.1-17 as a

function of temperature in an Arrhenius plot. The curves appear

similar for the different levels of deformation, indicating that small

strains, yield and fracture are governed by the same viscoelastic

phenomena, as previously found in [8], [9].


69

Fig. 4.1-16 Shift factors obtained building master curves of conservative modulus, yield stress and fracture toughness for Elium

Fig. 4.1-17 Shift factors obtained building master curves of conservative modulus, yield stress and fracture toughness for Elium Impact


70

4.1.2 Analysis of deformation mechanisms in the

process zone

The size of the process zone was determined from fracture tests

performed adopting Single Edge Notched Bending configuration at four

temperatures and at a single displacement rate, as described in section

3.2.3.2. Tests were video recorded and the onset of crack propagation

was determined by optical observation of the videos. For Elium the

onset was almost coincident with the maximum of the load-

displacement curve, while in the case of Elium Impact crack onset

occurred before the maximum of the curve was reached after which a

short stable crack propagation took place (Fig. 4.1-18). For both

materials after the maximum crack propagation became unstable.


71

Fig. 4.1-18 Load vs. displacement curves for Elium (blue) and Elium Impact (red) tested at 23 °C and 5 mm/min. Crosses symbols indicate the initiation point taken

from video recordings

From the video-recordings of the tests the process zone size was

determined by means of Digital Image Correlation. The displacement

field in the vicinity of the crack tip was measured both at crack

initiation and during crack propagation. The reference system

considered is schematically shown in Fig. 4.1-19. The origin of the

reference system corresponds to the crack tip.


72

Fig. 4.1-19 Crack tip reference system

An example of the DIC results showing the displacement v in the y

direction at crack initiation is reported in Fig. 4.1-20. It is possible to

observe that the displacement shows a large change from the left to

the right sides of the crack tip along the crack plane.


73

Fig. 4.1-20 Displacement v in direction normal to crack plane around the crack tip for Elium Impact (5 mm/min, 23 °C)

This change in the displacement is quantified in Fig. 4.1-21 at a generic

distance x1 from the crack tip. The displacement, , at the crack plane

was so determined: the two branches of the v-displacement vs. y curve

were linearly fitted and was taken as the distance of the two

intercepts.


74

Fig. 4.1-21 Measurement method for the displacement () in correspondence of the crack plane

was measured at several distances from the crack tip, x, and an

example of vs. x curve is showed in Fig. 4.1-22. The value of at the

crack tip, x=0, is the Crack Tip Opening Displacement (CTOD or c).

It is also possible to observe that becomes practically zero at a certain

distance from crack tip. This distance can be considered as a measure

of the length of the process zone .


75

Fig. 4.1-22 Displacement, at crack plane vs. distance from crack tip, crack tip opening displacement and length of the process zone for Elium Impact (5 mm/min,

23 °C)

Curves of vs. x were obtained at during crack propagation, moving

the reference system to the crack tip as in Fig. 4.1-19. It can be

observed from Fig. 4.1-23 that the curves are almost identical,

indicating that the process zone size does not change during crack

propagation.


76

Fig. 4.1-23 Displacement, at crack plane vs. distance from crack tip for Elium Impact at crack initiation and during several stages of crack propagation (5

mm/min, 23 °C)

Fig. 4.1-24 Crack tip opening displacement at different crack lengths for Elium (E) and Elium Impact (EI)

Crack tip opening displacement values measured at several crack

lengths are reported in Fig. 4.1-24 for the two resins and for the


77

different temperatures investigated. It can be observed that for both

resins the value of CTOD was fairly constant for increasing crack

length in all testing conditions. Further, in the case of Elium this value

was the same at different temperatures while for Elium Impact it

increases with temperature. The different behaviour of the two resins

is summarized in Fig. 4.1-25, in which the average values of CTOD as

a function of temperature are plotted.

Fig. 4.1-25 Crack tip opening displacement at different temperatures for Elium (blue) and Elium Impact (red)

In section 4.1 it was shown that Williams’ theory describes well

viscoelastic fracture behaviour of Elium resin; the result in Fig. 4.1-25

is in agreement with this finding since the basic assumption of constant

CTOD is met, while this is not obviously the case for Elium Impact.


78

Further, the values of CTOD in the case of Elium agree well with those

found in literature for similar materials [4], [10], [11].

Fig. 4.1-26 shows the length of the process zone as a function of

temperature for the two resins: as for crack tip opening displacement,

process zone length showed differences between the two resins. In the

case of Elium, is fairly constant, while in the case of Elium Impact

an increasing trend with temperature is observed.

Fig. 4.1-26 Process zone length () at different temperatures for Elium (blue) and Elium Impact (red)

From the three-point bending fracture tests also fracture toughness

values at crack initiation were measured. Crack propagation stage was

not investigated with SENB configuration because crack propagation

was unstable in most of the testing conditions examined.


79

Fracture toughness and the relevant initiation times obtained at

different temperatures were shifted along the time axis adopting the

shift factors (Fig. 4.1-16, Fig. 4.1-17) previously found building the GIc

vs. a master curves. Fracture toughness vs. initiation time master

curves at the reference temperature of 23 °C are shown in Fig. 4.1-27.

The two materials, Elium and Elium Impact, exhibited opposite trends

as already observed for propagation stage (section 4.1). A decreasing

trend, such as that observed for Elium resin, is expected from

viscoelastic theories since the dependence on time is given by the

viscoelastic properties of the bulk material.

Further, fracture toughness, GIc, was also evaluated as:

( )Ic c y initG t (4.6)

in which the yield stress was determined at the initiation time adopting

the power law parameters from Tab. 4.1-2 and c is the CTOD at crack

initiation. The values of fracture toughness obtained are also reported

in Fig. 4.1-27: a good agreement between the two procedures can be

observed. This confirms the validity of the CTOD measured by DIC.


80

Fig. 4.1-27 Fracture toughness vs. initiation time master curves at the reference temperature of 23 °C for Elium (blue) and Elium Impact (red). Solid symbols come

from (3.19), open symbols from (4.6)

4.1.3 Damage mechanisms in the rubber

toughened resin

The fracture toughness behaviour observed for Elium Impact as a

function of crack propagation speed cannot be ascribed to purely

viscoelastic effects. It was hypothesized that the trend observed could

be related to different deformation mechanisms occurring at the crack

tip under the different testing conditions.

In order to explore which damage mechanisms can occur in the

toughened resin tensile dilatometry was performed, as previously done

in several works [12–15]. The analysis was conducted also on Elium


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resin, but the results were poor due to the fact that volume strains

were so small that the measurements were very much affected by the

experimental error.

Volumetric strain in Elium Impact was evaluated in tensile tests, as

explained in section 3.2.2 for different conditions of temperature and

displacement rate. An example of a volumetric vs. linear strain curve

is given in Fig. 4.1-28. It can be observed that the curve shows two

changes of slope: the strain corresponding to the second change in slope

coincide with the maximum of the stress-strain curve, at which yield

was taken. The first change in slope of the initial portion of the curve

is actually related to the fact that the material is not perfectly

elastoplastic. The slope of the curves after yielding is related to the

different possible damage mechanisms.


82

Fig. 4.1-28 Volumetric vs. linear strain for Elium Impact (temperature 23 °C, displacement rate 10 mm/min). Measured volumetric strain is represented in

orange and the black line represents the stress-strain curve

The ideal cases of pure crazing and pure shear yielding are associated

to curves having slope equal to 1 and 0 respectively [12], [15] which are

reported as dashed lines for comparison. Also cavitation, as crazing,

gives changes in volume but in smaller amount, therefore the slope

associated is expected to be less than 1. Further, cavitation promotes

shear yielding therefore in real cases all the mechanisms occur

concurrently and it is somehow difficult to distinguish between them

solely from volumetric behaviour. In any case, as the contribution of

shear yielding increases the slope is expected to decrease. The results

obtained at different temperatures and at different rates are reported

in Fig. 4.1-29 and Fig. 4.1-30 respectively. Similar trend of deformation

volume with strain rate was found also by [12], [13], [15], [16]. The


83

experimental curves shown (and also the curves from all the conditions

tested) fall between the ideal cases of slopes equal to 0 and 1, indicating

a concurrent presence of different mechanisms: multiple crazing, shear

yielding and cavitation of the rubber particles.

Fig. 4.1-29 Volumetric vs. linear strain at different temperatures for Elium Impact (displacement rate 1 mm/min). Dashed line represent curves having slope equal to

1 and 0


84

Fig. 4.1-30 Volumetric vs. linear strain at different displacement rates for Elium Impact (temperature 60 °C). Dashed line represent curves having slope equal to 1

and 0

The curves indicate that for higher rates and lower temperatures

multiple crazing prevailed while at lower rates and higher temperatures

there was a predominance of cavitation and shear yielding.

It is also worth to be noticed that the slope of the single curve at

different conditions is not constant but there are slight changes. This

indicates that the different deformation mechanisms coexist but occur

in different moments during progressively increasing deformation, in

agreement with the sequence proposed by Béguelin and discussed in

section 2.3.2.

The volumetric strain can be decomposed in the different contributions

due to different mechanisms as explained in section 3.2.2. Fig. 4.1-31

shows an example of the different contributions to volume change. It


85

can be observed that for small strains the volumetric strain is due only

to elastic contribution, while for increasing deformation the

contribution of crazing and/or cavitation becomes more and more

important. The curve of volumetric strain component due to

crazing/cavitation is given by the difference between the measured

overall volume strain and the elastic volume strain. Obviously, in this

plot the shear yielding is not present since it occurs at constant volume.

Fig. 4.1-31 Volumetric contributions vs. linear strain for Elium Impact (temperature 23 °C, displacement rate 10 mm/min). Measured volumetric strain is represented in orange, elastic contribution in blue, crazing/cavitation contribution

in red and the black line represents the stress-strain curve

The strain components can be obtained from the volumetric strain

components, as explained in section 3.2.2. This way it is possible to

evaluate the contribution of shear yielding too. The strain components


86

relevant to crazing/cavitation and shear yielding at different rates and

temperatures are shown in Fig. 4.1-32 - Fig. 4.1-35.

Fig. 4.1-32 Crazing/cavitation strain component vs. total strain at different temperatures for Elium Impact (displacement rate 1 mm/min)


87

Fig. 4.1-33 Shear yielding strain component vs. total strain at different temperatures for Elium Impact (displacement rate 1 mm/min)

Fig. 4.1-34 Crazing/cavitation strain component vs. total strain at different displacement rates for Elium Impact (temperature 60 °C)


88

Fig. 4.1-35 Shear yielding strain component vs. total strain at different displacement rates for Elium Impact (temperature 60 °C)

As already pointed out by the observation of the slope of the

volumetric vs. linear strain curves, a different contribution of the

different damage mechanisms depending on temperature and

displacement rate was found. A progressive shift from multiple crazing

to cavitation and shear yielding can be observed for increasing

temperatures or decreasing displacement rates.

Since shear yielding is known to be accompanied by higher amount of

energy dissipated in comparison with multiple crazing, the change in

damage mechanism observed from tensile tests could give also an

explanation for the trend observed in the curve of fracture toughness

vs. crack propagation speed reported in section 4.1.1, although it must

be kept in mind that the stress state in the two cases is not the same.


89

4.1.4 Damage mechanisms at the crack tip in the

rubber toughened resin

The different damage mechanisms observed in tensile tests were

considered to be an explanation for the dependence of fracture

toughness, GIc, on crack propagation speed, a , found for the toughened

resin. Nevertheless, the stress state in the case of a tensile test is

different from the one occurring at the crack tip during fracture.

As already done in several works [17–22], the double notched four point

bending technique was adopted to investigate the damage mechanisms

occurring during fracture with the intent of confirming what observed

from tensile tests (Section 4.1.3).

Elium Impact specimens broken in double notched four point bending

test configuration were cut and prepared for optical observation of the

process zone developed in front of the un-propagated crack, as

explained in section 3.2.3.3. Images taken with optical microscopy are

reported in Fig. 4.1-37, Fig. 4.1-38, Fig. 4.1-41. It is possible to observe

that the cracks grew to a certain length before the failure of the

specimen, therefore the actual position of the crack tip was carefully

located at higher magnifications and it is also shown in the figures.

The process zones obtained under different testing conditions are

reported at the same scale to point out the change in length. A measure

of the length of the process zone was estimated and it is reported in


90

Fig. 4.1-36 for the different temperatures and displacement rates

investigated. The first observation is that the length of the process

zones obtained in section 4.1.2 are consistent with those obtained from

the images. The influence of the temperature found from DIC

measurements is confirmed, while the influence of the displacement

rate cannot be appreciated in the range examined.

Fig. 4.1-36 Process zone length () at different temperatures for Elium Impact. Measurements from DIC (red solid squares), DN-4PB tests performed at 1

mm/min (black solid squares) and DN-4PB tests performed at 10 mm/min (black open squares)


91

Fig. 4.1-37 Process zones of Elium Impact tested at 10 mm/min and different temperatures.


92

Fig. 4.1-38 Process zones of Elium Impact tested at 1 mm/min and different temperatures.

The different morphologies, shapes and appearances of the process

zones obtained at different testing conditions suggest that a change in

the damage mechanisms occurring at crack tip during fracture could

be present, as already observed during tensile tests. Unfortunately,

optical observation of the process zones solely does not allow to


93

distinguish the different contributions to fracture toughness given by

the different damage mechanisms.

Qualitative considerations can be made by comparing the images of

the process zone obtained with those present in other works.

Many authors adopted Double Notched Four Point Bending test

configuration to investigate the damage mechanisms in various

toughened polymers [17–22] while other authors investigated materials

similar to the toughened resin here studied, adopting DN-4PB or other

methods to arrest crack propagation [23–27].

Recalling the sequence of damage and the different contributions

proposed by Béguelin (section 2.3.2), similar observation were found

in the work of Jung and Weon [19] for different blends of polypropylene

copolymers. They suggested the presence of both intensive shear

yielding around the crack tip and along the crack wake and a massive

crazing in the region surrounding the shear yielded region. They

hypothesized that the crazing was effective in facilitating the formation

of shear yielding in the matrix. An example of a process zone taken

from this work, showing these two mechanisms, can be found in Fig.

4.1-39.


94

Fig. 4.1-39 Process zone of polypropylene impact copolymer. Fig. 4(e) from [19]

It can be observed that there is a resemblance to the images of the

process zone taken in this work. In particular, the process zone is

similar to those obtained at 23 and 40 °C in Fig. 4.1-37 and at 23 °C

in Fig. 4.1-38.

On the other hand, the process zone obtained at 0 °C and 1 mm/min

(Fig. 4.1-38) is very thin and elongated and it resembles in shape a

craze in an untoughened polymer, such as the neat Poly(methyl

methacrylate) shown in Fig. 4.1-40 [27] in which a crazed process zone

led the crack propagation. This may confirm the hypothesis made in

section 4.1.3 of a predominance of multiple crazing at low

temperatures.


95

Fig. 4.1-40 Craze in cast PMMA. Image 3(a) from [27]

An appearance of the process zone quite different from the others was

found in the specimen tested at low speed and 40 °C. In this case it is

evident the presence of well distinguishable spikes. It is reported in

Fig. 4.1-41 in comparison with the process zone obtained at the same

temperature but at a displacement rate 100 times higher.


96

Fig. 4.1-41 Process zones of Elium Impact tested at 40 °C, 10 and 0.1 mm/min.

The appearance of the process zone resembles that obtained in an

another work [17] which is reported in Fig. 4.1-42.


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Fig. 4.1-42 Process zone of an epoxy resin. Fig. 7(a) from [17]

Two regions can be distinguished: the inner region, closer to crack tip,

in which cavitation of the rubber particles was followed by shear

yielding of the matrix. The second region is the one located ahead the

first and is composed by the bands extending in different directions at

small angles with respect to crack propagation direction. These are

dilatational bands [28] that did not cause yet massive shear yielding of

the surrounding matrix.

The resemblance of the process zone of the material under study here

to that of a different material such as an epoxy in which multiple

crazing mechanism was not observed, confirms somehow the change in

damage mechanisms found from tensile dilatometry.


98

Although the indications obtained from tensile dilatometry concerning

the different damage mechanisms occurring in the toughened material

at different testing conditions seem to be partially confirmed from the

observation of the process zones here reported, further studies are

necessary.

In order to identify and distinguish the different mechanisms occurring

at the crack tip the same process zone reported in this section are

currently being prepared to be observed with Transmission Electron

Microscope.

4.2 Fracture behaviour of composites

Fracture toughness was measured from DCB tests both at crack

initiation and during propagation. The initiation point was taken as

the instant in which the crack was observed to start moving in the

video recordings (VIS point) and it was almost coincident with the

deviation from linearity as in Fig. 4.2-1.


99

Fig. 4.2-1 Double Cantilever Beam test load vs. displacement curves for Elium (blue) and Elium Impact (red) (20 mm/min, 0 °C). Crosses indicate the VIS

initiation points. Specimen thickness is different for the two materials.

GIc was measured as illustrated in section 3.2.4, at crack initiation and

at several different crack extension during propagation, obtaining GIc

vs. crack length a curves (R-curves). Examples of R-curves for the

two materials are reported in Fig. 4.2-2 and Fig. 4.2-3, in which it is

possible to observe that the fracture toughness increases after crack

initiation and then reaches a fairly constant value. The figures indicate

the range of crack extension over which the average value of fracture

toughness GIc was determined.


100

Fig. 4.2-2 R-curve for Elium-based composite (20 mm/min, 23 °C)

Fig. 4.2-3 R-curve for Elium Impact-based composite (20 mm/min, 23 °C)

Crack propagation speed was measured as the slope of the crack length

vs. time curve obtained from video-recordings over the same range of

crack length in which the average value of GIc was determined, as in


101

Fig. 4.2-4. Tests were performed at different displacement rates and

temperatures and the results are reported in Fig. 4.2-5 and Fig. 4.2-6.

Fig. 4.2-4 Crack length vs. time curve for Elium-based composite (20 mm/min, 23 °C)


102

Fig. 4.2-5 Fracture toughness vs. crack propagation speed isothermal curves for Elium-based composite

Fig. 4.2-6 Fracture toughness vs. crack propagation speed isothermal curves for Elium Impact-based composite


103

Isothermal curves were then shifted horizontally along the logarithmic

crack speed axis to obtain master curves. The shift factors obtained

building the master curves of the relevant matrices (Fig. 4.1-16, Fig.

4.1-17) were adopted since the viscoelasticity of the composite is

governed by the time dependence of matrix properties. Moreover, in

the case of Elium based composites, the isothermal curves are more or

less horizontal therefore shifting them to obtain superposition was

impossible.

GIc vs a master curves of the two composite materials are shown in

Fig. 4.2-7 and Fig. 4.2-8, together with that of their relevant matrices.

The fracture toughness of both composites is higher than that of the

relevant matrix along the whole range of crack propagation speeds

investigated as found in [9], [29]. This is not a general result, the

opposite was found in [8], [30]. In the case of Elium Impact the

dependence of fracture toughness on crack propagation speed for the

composite reflects that of the matrix, while in the case of Elium the

composite fracture toughness seems to be fairly constant irrespective

of crack propagation rate.

The values of fracture toughness obtained for the composite based on

the toughened resin are comparable to those found in literature for

high performance composites such as carbon

fibre/polyetheretherketone [9], [31].


104

Fig. 4.2-7 Fracture toughness vs. crack propagation speed master curves at the reference temperature of 23 °C for Elium (solid symbols) and Elium-based

composite (open symbols). Solid line is a power law fitting, dashed line is a visual aid. Different symbols refer to different test temperatures

Fig. 4.2-8 Fracture toughness vs. crack propagation speed master curves at the reference temperature of 23 °C for Elium Impact (solid symbols) and Elium

Impact-based composite (open symbols). Dashed line are visual aids. Different symbols refer to different test temperatures


105

In order to better compare the fracture behaviour of matrices and their

relevant composites during propagation, the results of Fig. 4.2-7 and

Fig. 4.2-8 were reported as ratios between GIC of composites and that

of their relevant matrices. Since the composites and matrices data did

not share the same exact crack propagation speeds, a simple

interpolation procedure was applied to obtain the fracture toughness

of composite materials at the crack propagation speeds occurring for

the matrices. Results are reported in Fig. 4.2-9. As already pointed

out, composites turned out to be more crack resistant than the

matrices, over the entire range of crack propagation speed considered.

It is also evident that the amount of increase in toughness obtained in

the composite is dependent on crack propagation speed.


106

Fig. 4.2-9 Ratio of composites and their relevant matrices fracture toughness vs. crack propagation speed for Elium (blue) and Elium Impact (red)

This result can be explained with a rate dependent contribution of the

fibre-related mechanisms to the fracture toughness of the composite.

In particular, a different contribution of fibre bridging at different

temperatures and displacement rates was observed by naked eye

during the tests. From the analysis of the fracture surfaces it was

observed the different increase in fracture toughness at different testing

conditions is related to:

different amount of fibres bridging the crack during propagation

as can be seen in Fig. 4.2-10. Portions of specimens were cut

from the region over which the average value of fracture

toughness was determined and they were investigated with

stereomicroscope at low magnification and the images are


107

reported in Fig. 4.2-10. It can be qualitatively observed that,

for both materials but in particular for Elium based composite,

the amount of fibres that rise from the surface is higher in the

specimens that were tested at 60 °C rather than in those tested

at 0 °C. This results suggests that fibre bridging mechanism

occurred more extensively at the higher temperature tested.

Also, it seems that the difference in abundance of fibre bridging

was more pronounced in the case of Elium-based composite


108

Fig. 4.2-10 (a) Fracture surface of Elium based composite, tested at a displacement rate of 20 mm/min and a temperature of 60 °C. (b) Elium based composite, 20

mm/min - 0 °C. (c) Elium Impact based composite, 20 mm/min - 60 °C. (d)Elium Impact based composite, 20 mm/min - 0 °C. White vertical rectangular stripes are

the stitches used to weave the unidirectional carbon fibres.


109

different strength of the interface between fibre and matrix. Fig.

4.2-11 shows the images of the samples taken with a Cambridge

Stereoscan 360 Scanning Electron Microscope. These images

give an indication of the strength of the matrix-fibre interface.

In the case of Elium based composites fibres appear almost

completely naked, in both conditions of temperature, indicating

a quite poor interfacial strength. Elium Impact based

composites, on the other hand, showed a better interfacial

strength with a higher amount of matrix still attached to the

fibres indicating a cohesive fracture in the matrix rather than a

failure of the interface.

The results of Fig. 4.2-9 can be explained qualitatively with the

combination of these aspects of fibre bridging and the toughness of the

matrix. The decreasing trend of the ratio with crack propagation speed

is due to the large variation of the amount of fibre bridging as crack

speed increases, while the interfacial strength does not change

substantially with crack speed. The higher value of the ratio for Elium

is related to the higher relative contribution to toughness given by the

fibre related mechanisms.


110

Fig. 4.2-11 (a) Fracture surface of Elium-based composite, tested at a displacement rate of 20 mm/min and a temperature of 60 °C. (b) Elium based composite, 20

mm/min - 0 °C. (c) Elium Impact based composite, 20 mm/min - 60 °C. (d)Elium Impact based composite, 20 mm/min - 0 °C. Magnification 1000 x


111

During crack propagation there is a contribution to fracture toughness

coming from both the matrix and the fibres. In order to better

understand the contribution of matrix toughness to that of the relevant

composite it is useful to investigate the crack initiation stage [32], [33].

At initiation, in fact, the contribution of the fibre related mechanisms,

in particular fibre bridging, is negligible. Fracture toughness of the

composite is therefore mainly related to the transfer of matrix

toughness.

Fracture toughness of the composites was measured at crack initiation

(at VIS point) for several conditions of temperature and displacement

rate. A short pre-cracking was introduced in order to discard the effect

of the starter film. As already done for crack propagation data, the

isothermal data points were shifted by the relevant matrix shift factors.

The master curves obtained of fracture toughness vs. initiation time

for both composites are reported in Fig. 4.2-12, in which it is possible

to observe that the two materials showed an opposite dependence of

fracture toughness on time as already found for the matrices.


112

Fig. 4.2-12 Fracture toughness vs. initiation time master curves at the reference temperature of 23 °C for Elium-based (blue) and Elium Impact-based composites

(red). Different symbols refer to different test temperatures

Comparing the curves of each composite with that of its relevant

matrix (Fig. 4.2-13, Fig. 4.2-14), it is clear that the matrix and the

composite show a similar dependence of GIc,init on initiation time. It

also turns out that in the case of Elium, the composite shows a higher

fracture toughness than that of the matrix, while in the case of Elium

Impact the opposite occurs.


113

Fig. 4.2-13 Fracture toughness vs. initiation time master curves at the reference temperature of 23 °C for Elium (solid symbols) and Elium-based composite (open

symbols). Different symbols refer to different test temperatures

Fig. 4.2-14 Fracture toughness vs. initiation time master curves at the reference temperature of 23 °C for Elium Impact (solid symbols) and Elium Impact-based composite (open symbols). Different symbols refer to different test temperatures


114

Also at crack initiation, as already done for crack propagation, the

ratio between the toughness of composites and that of the matrices

was considered. Results are reported in Fig. 4.2-15.

Fig. 4.2-15 Ratio of composites and their relevant matrices fracture toughness vs. crack initiation time for Elium (blue) and Elium Impact (red)

It is possible to observe a different behaviour between the two

materials. In the case of Elium based composite the ratio is still greater

than one while in the case of Elium Impact the matrix turned out to

be tougher than the composite. In other words, the matrix toughness

is fully transferred into the composite in the case of the plain resin. In

the case of the toughened resin, the transfer of toughness into the

composite is only partial. Similar results have been obtained in other

works [8], [9]. This behaviour has been related to the interaction


115

between the process zone developing in the resin rich region in which

the crack propagates and the fibres of the adjacent plies. In the case

of brittle matrices, the process zone is small and its development is not

affected by the presence of the fibres. Hence the matrix toughness is

transferred fully into the composite. In the case of more tough matrices

the process zone is larger and its development is hindered by the

physical constraint exerted by the fibres, with the result of a partial

transfer of the matrix toughness to the composite. In order to validate

these assumptions, the unbroken part of DCB specimens was cut

perpendicularly to the fibre direction and the cross sections were

polished and observed with an optical microscope (Fig. 4.2-16). The

thickness of the matrix layer between plies of fibres was then compared

with the values of crack tip opening displacement found for the two

matrices. CTOD can be taken as the dimension of the process zone in

the direction perpendicular to the crack plane.


116

Fig. 4.2-16 (a)Cross section of Elium-based composite. (b) Cross section of Elium Impact-based composite. The dark area is the resin-rich region on which the

average value of CTOD of each matrix is reported

In the case of Elium the average of CTOD constant values was adopted

while in the case of Elium Impact the minimum value, measured at 0

°C, was adopted. Fig. 4.2-16 shows that the dimension of the process


117

zone of Elium is way smaller than the distance between the fibres,

while in the case of Elium Impact even the minimum CTOD measured

is comparable with the thickness of resin-rich region.

It is also evident from the image, and it was also verified observing the

composite in several regions, that the thickness of the resin-rich region

is different between the two materials. Since the fibres adopted are the

same, this difference may be due to the different rheological properties

of the resins adopted as matrices. Further investigation on this could

lead to thicker resin layers in the composite based on Elium Impact,

resulting in a higher transfer of the matrix toughness.

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[27] M. Todo, K. Takahashi, P.-Y. B. Jar, and P. Béguelin, “Toughening Mechanisms of Rubber Toughened PMMA,” JSME International Journal Series A, vol. 42, no. 4, pp. 585–591, 1999.

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5 Conclusions

The present work was mainly oriented to the investigation of the

fracture behaviour during crack propagation of two thermoplastic

acrylic resins, one plain and one rubber toughened, and their relevant

composites. These resins offer the advantage, with respect to most

thermoplastic matrices for composites, of being processed in a similar

way to thermoset matrices.

The first part of the work was devoted to the investigation of the

matrices relating fracture toughness and crack propagation speed. The

behaviour of the untoughened resin was well described by Williams’

viscoelastic fracture theory, thus indicating that the time dependence

of fracture toughness was governed by the viscoelastic properties of the

material, i.e. the relaxation modulus and the yield stress.

In the case of the toughened material a more in-depth analysis turned

out to be necessary to describe the fracture behaviour. The damage

mechanisms occurring at the crack tip were thought to be the reason

of the dependence of fracture toughness on crack propagation speed

obtained. They were investigated with several techniques (DIC,

dilatometry and optical observation) and a change in the damage

mechanisms occurring under different conditions of displacement rate

and temperature was found.


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The second main topic of this work was the fracture behaviour of

composite materials prepared adopting the same resins discussed above

as matrices.

The fracture toughness of the composites was found to be higher than

that of their relevant matrices, for both matrices, over the range of

crack propagation speed considered. The values of fracture toughness

found, especially in the case of the toughened matrix, were remarkable

if compared to other classes of composite materials.

In order to better understand the delamination process, further studies

on the composites were conducted. The fracture toughness of a

composite material comes from the contribution of matrix and fibre-

related mechanisms. The latter were found to be time dependent and

they were studied investigating the fracture surfaces with optical and

scanning electron microscopy.

The mechanism of matrix toughness transfer into the composite was

highlighted and studied at crack initiation stage. It was found that in

the case of the toughened resin the presence of the fibres altered the

development of the process zone restricting the transfer of matrix

toughness. In the case of the plain resin there was not interaction

between the fibres and the process zone of the matrix layer. Therefore,

the matrix toughness was fully transferred into the composite.

The results obtained in this work confirmed the applicability of these

composite materials to several applications: the fracture toughness

Conclusions

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values and the range of service temperature make them valuable,

especially considering the fact that they are thermoplastic materials

with all the advantages that the adoption of this class of materials

involves

Part of this work was presented at the 21st European Conference on

Fracture and it was published in the conference proceedings [1]. The

article can be found in the Appendix to this work

5.1 References

[1] T. Pini, F. Briatico-Vangosa, R. Frassine, and M. Rink, “Time dependent fracture behaviour of a carbon fibre composite based on a (rubber toughened) acrylic polymer,” Procedia Structural Integrity, vol. 2, pp. 253–260, 2016.

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Appendix – Publication

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Ringraziamenti Le prime persone che vorrei ringraziare sono il mio relatore, Prof.

Roberto Frassine, e il mio tutor, Prof. Francesco Briatico, per il

costante supporto durante lo svolgimento del lavoro che ha portato

alla scrittura di questa tesi. Ringrazio inoltre tutti gli altri docenti del

nostro gruppo di ricerca per l’aiuto, i consigli e il confronto quotidiano.

In particolare ringrazio la Prof.ssa Marta Rink per tutto quello che ha

fatto per me.

Ringrazio mia madre, mio padre, mia sorella e tutta la mia famiglia

per esserci stati sempre.

Saluto i miei colleghi e amici Francesco, Marco, Davide, Andrea,

Natalia, Stefano, Jacopo, Giancarlo, Marco, Nadia e Carla.

Ovviamente un saluto va a tutti gli amici, vecchi e nuovi, di Roma e

di Milano.

I switch back to english to thank Pierre Gerard from the Groupement

du Recherche du Lacq for all the support provided. I also would like

to thank Prof. Gerald Pinter and Steffen Stelzer from

Montanuniversität of Leoben for their kindness and their help.

Documents

Fracture behaviour of thermoplastic acrylic resins and their … · 2017. 4. 29. · acrylic resins and their relevant unidirectional carbon fibre composites: rate and temperature