Thermosetting Polymers Part 13 potx

13.2–13.3 the principles of toughening of thermosets by ber particles, and the role of morphologies, interfacial adhesion, composi-tion, and structural parameters on the toughening effec

The two methods of improving the macroscopic toughness of sets are similar to those used for amorphous or semicrystalline thermoplas-tics: (i) plasticization and (ii) amplification of deformation mechanisms viathe generation of a heterogeneous structure.

thermo-The plasticizer addition is a relatively simple technique A misciblelow-Tgcompound is added to the formulation, so as to produce a decrease

in both the glass transition temperature and the yield stress, and a sponding improvement in the fracture resistance These drawbacks are verysevere for thermosets, and generally this method is not used for tougheningpurposes

corre-The most frequently applied methods for improving toughness are theaddition of preformed particles or the in-situ formation of dispersed rubbery

or thermoplastic particles in the thermoset matrix(Chapter 8)

In Secs 13.2–13.3 the principles of toughening of thermosets by ber particles, and the role of morphologies, interfacial adhesion, composi-tion, and structural parameters on the toughening effect are analyzed.Section 13.4 is devoted to the use of initially miscible thermoplastics fortoughening purposes The effect of core-shell rubber particles is discussed

rub-in Sec 13.5 and, rub-in Sec 13.6, miscellaneous ways of toughenrub-ing thermosets(liquid crystals, hybrid composites, etc.), are analyzed

13.2 TOUGHENING OF THERMOSETS

Epoxy networks are the most widely studied materials, due to their known chemistry Consequently, many studies are devoted to epoxy net-works as model networks, although the principles and models developed can

well-be applied to other thermosets

The principles of toughening have been described by Kinloch (1989),Mu¨lhaupt (1990), Huang et al (1993b), and McGarry (1996) The roles ofparticles during both the initiation and propagation of the crack may beanalyzed separately

13.2.1 Role of the Inclusions in the Initiation Step

(Before the Appearance of an Intrinsic Defect

or Crack)

a Modification of the Stress Field

For a single rubber particle in an infinite uniaxial tensile stress field, it wasdemonstrated that there is a stress concentration effect with a factor around

2, at the particle equator(Fig 13.1)

This is only valid for particles with a modulus lower than the matrix

On the other hand, in the case of glass beads in polymers the stress centration occurs at the poles

con-If the particle is bonded firmly to the matrix (we will discuss this pointlater), the initial uniaxial tension stress is changed into a triaxial tensionstress field, due to the low rubber incompressibility The stress field aroundrubbery particles is not the same as that around a void

Increasing the concentration of particles (roughly for a volume tion approaching 10%), the stress concentration effects of neighboring par-ticles can overlap (Fig 13.2) Therefore, a large volume fraction of thematrix supports an average load higher than the applied load and canyield This stress concentration effect increases when the volume fraction

frac-of dispersed particles increases or the interparticle distance decreases

As shear yielding is the main deformation mechanism of the network,

it is clear that the presence of rubber particles favors the yielding of the

matrix But also, due to incomplete phase separation(Chapter 8),a fraction

of rubber remains dissolved in the matrix and contributes to the decrease of

Tg and
y Yielding can then occur at lower applied loads

The introduction of rubber particles increases the fracture energy ofthe networks at room temperature, but also decreases the temperature of theductile–brittle transition (Van der Sanden and Meijer, 1993) This ductile–brittle transition is strongly dependent on the nature (and Tg) of the rubber-rich phase and the amount of rubber dissolved in the matrix The lowestductile–brittle transition is obtained with butadiene-based copolymers(Tg
80C), compared with butylacrylate copolymers (Tg
40C)

b Internal Cavitation and Debonding

Due to the difference of expansion coefficients between the particles and thematrix, different kinds of stress fields may be developed (Raghava, 1987).Rubbery and thermoplastic particles are placed in a hydrostatic tension

F 13.2 Stress field overlap between rubber particles

stress field (8–12 MPa) (Sec 13.3.2 d), while glass beads are placed in acompressive stress field (15–20 MPa) The ratio of the bulk modulus,

K ¼ E=3ð1  2Þ, over the shear modulus, G, is around 1000 for a rubberand close to 1 for a glassy polymer

If the adhesion between particles and matrix is good, rubber particlesinternally cavitate when a load is applied

If the adhesion is low, debonding at the rubber particle–matrix face can occur In both cases voids are formed and this reduces the degree ofstress triaxiality in the surrounding matrix and favors the further growth ofshear bands

inter-Internal cavitation was proved by comparison of the initial particlediameter with the diameter measured on a fracture surface (Huang et al.,1993b) An increase of about 20–70% of the initial volume was found,depending on the temperature This voiding process participates in theenergy consumption and is the cause of the stress whitening effect observed

on deformed samples

In the case of thermoplastic particles, because the bulk modulus isequivalent to that of the matrix, no cavitation is observed

c Initiation of Matrix Shear Yielding

As discussed inChapter 12,crazing does not occur in thermosets; therefore,the only possible response of the matrix to a load is to promote localizedshear yielding between particles

A considerable amount of energy is stored in the sample before theappearance of the first crack In this step, the rubbery particles act – aftercavitation or debonding – as triggers for the generation of shear bands in thematrix (Huang and Kinloch, 1992b)

Using finite element stress analysis, Huang et al (1993b) demonstratedthat shear bands must appear at 45, between voids formed in a previousstep As there are many particles, a network of shear bands is generated inthe deformed sample (Yee and Pearson, 1986) Their growth generates theappearance of the first crack

13.2.2 Role of the Particles during Crack Propagation

As a result of the increase in stress and/or strain, shear bands develop in alarge fraction of the sample but, at a certain point, a crack appears andstarts to propagate Several mechanisms for energy absorption, associatedwith the presence of particles, become active during crack propagation

a Crack-Bridging Mechanism

The crack-bridging mechanism is illustrated inFig 13.3 The particles arestretched between the edges of the propagating crack, increasing the fractureenergy This mechanism needs a good adhesion between matrix and parti-cles However, because of the very low modulus of rubber, and in spite ofthe high failure strain, the dissipated energy in such a mechanism is low:

5–10% of the total energy (Kunz-Douglass et al., 1980)

In the case of thermosets toughened with thermoplastics particles (Sec.13.4), this mechanism may be of a considerable importance because of theintrinsic toughness and/or ductility of these particles

b Increase of the Fracture Surface

The presence of particles can modify the fracture surface from a mirror-likesurface (for a brittle material), to a rough stress-whitened surface Theroughness can act as a multiplication factor for the absorbed energy.Sometimes, steps of height (h) are created when the crack jumps over aparticle This leads to the presence of tails issuing from particles, on fracturesurfaces The fracture energy may be expressed by

 ¼ matrix
1  

þk h

where dcis the interparticle distance (center to center), k is a constant, and

 is the volume fraction of particles Furthermore, the particle–matrixdecohesion gives an additionnal surface and increases the fracture energy

F 13.3 Illustration of crack-bridging mechanism

Lange (1970) gives a quantitative description of the critical energyrelease rate supplied by this mechanism:

GIc¼GIcmatrixþ2TL

where TL is a constant (called the line tension) and dp is the interparticledistance (surface to surface) For particles with the same diameter, anincrease in their volume fraction leads to a decrease in dpand an increase

in GIc On fracture surfaces observed by SEM (scanning electron scopy), the presence of a crack-pinning mechanism is revealed by featuressuch as river markings

micro-The crack-pinning mechanism is not very efficient with low-modulusparticles such as rubbers But with stiff thermoplastics (Sec 13.4), or withhigh-modulus particles such as inorganic fillers, this mechanism may have

more and more blunted as a result of the formation of a plastic zone and thedecohesion of particles The stress concentration effect at the crack tipbecomes lower, and the crack is slowed down and even stopped, for thecase of stick-slip propagation(Fig 12.4).

e Crack Deflection

During a fracture-mechanical test performed in mode I, the crack gates in this mode from a macroscopic point of view But the crack can bedeflected locally by the rubbery particles and can also propagate in mode II

propa-As for isotropic materials, GIIc is generally higher than GIc; an artificialincrease of the macroscopic GIcvalue will be then evidenced

f Conclusion

An improvement in the toughness of thermosets can be favored by rubber orthermoplastic particles, which operate both in crack initiation and propaga-tion mechanisms The different toughening mechanisms can act simulta-neously and can be modeled quantitatively

13.3 RUBBER TOUGHENING OF THERMOSETS

13.3.1 Fracture Modeling of Rubber-Modified Epoxy

Networks

The fracture modeling of rubber-modified thermosets was developed byHuang and Kinloch (1992a), Kinloch and Guild (1996), Huang et al.(1993b), and Yee et al (2000)

Huang et al (1993b) proposed a two-dimensional plane strain model,which was successfully used to identify the stress field around the rubberyparticles and to simulate the initiation and growth of shear bands betweenrubbery particles A model was proposed to quantify the different mechan-isms GIcof the rubber-modified network was written as

where GIcnis the fracture energy for the neat network and is the additionalenergy dissipated per unit area due to the presence of rubber particles It isgiven by

where
Gr is the contribution of particle bridging,
Gsis the contributionfrom plastic shear banding, and
Gv is due to plastic-void growth in thematrix The other possible contributions were not taken into account

According to Kunz-Douglass et al (1980),
Gr may be calculated as

Gv is proportional to the void growth and plasticity parameters ofthe matrix

The model was successfully applied to rubber-modified epoxy works, taking into account both the test temperature and the rate effect

net-(Fig 13.5)

Furthermore, the model makes it possible to separate the tions of the three toughening mechanisms as a function of temperature(Fig.13.6).At high temperatures, the crack-bridging mechanism plays a minorrole; the void-growth mechanism is very sensitive to temperature and can becompletely suppressed at low temperatures Shear yielding is the mainmechanism, except at very high test temperatures where cavitation playsthe major role The contribution of shear yielding depends on the differencebetween the test temperature and Tg, as discussed in Chapter 12

(&) and the experimental results (&) at different test rates and temperatures

of a rubber-toughened epoxy (Huang and Kinloch, 1992a, with kind sion from Kluwer Academic Publisher.)

permis-13.3.2 Influence of Network Structure and

Morphology on Fracture Properties of Epoxy

Networks

As discussed in the previous section, the toughening effect depends both onthe matrix, where the shear bands are propagating, and the rubbery phase,which induces cavitation and crack bridging

In this section, the influence of in-situ formed rubber particles is cussed, while the influence of preformed particles is analyzed in Sec 13.5.For epoxy networks modified by liquid reactive rubbers, it is not soeasy to discuss these parameters separately, because they are interdependent.For example, an increase in the acrylonitrile content of the carboxy-termi-nated butadiene acrylonitrile rubber (CTBN) induces a size reduction of therubbery domains but also a higher miscibility with the epoxy-rich phase,leading to a higher amount remaining dissolved in the matrix at the end ofcure (Chapter 8).It is not possible to separate the influence of these twoeffects on toughness

mechan-isms in epoxy networks versus temperature: (&) rubber bridging; (*) shearyielding; and (~) cavitation (From the results of Huang et al:, 1993b.)

a Influence of the Volume Fraction of Rubber

In a first approximation, GIc depends linearly on the amount of dispersedphase up to a 20–25% volume fraction (Yee and Pearson, 1986; Verche`re etal., 1993; McGarry, 1996)

The use of an in-situ phase-separated rubber produces a decrease inboth the Young’s modulus and the yield stress(Fig 13.7).Therefore, highrubber volume fractions cannot be used for structural applications (highstresses, long-time creep, etc.) A stiffness–toughness compromise has to

be considered But, in any case, the initial volume fraction of rubber cannot

be higher than crit, to avoid phase inversion, leading to a rubbery matrixwith thermoset inclusions(Chapter 8) Another limiting factor may be thecost of the liquid reactive rubbers

b Influence of Particle Size and Particle Size Distribution

It is generally observed that rubber particles are effective for tougheningpurposes when their sizes are in the 0.1–10 m diameter range For a givenvolume fraction of the rubbery phase, there is a critical particle size belowwhich toughening occurs and above which there is no significant effect Thecritical size is related to the interparticle distance, which, in fact, is the mainparameter affecting the toughening effect for both thermoplastics (Wu,1985) and thermosets (Van der Sanden and Meijer, 1993) To keep the

rubber-modified epoxy networks Rubber ¼ CRBN: carboxy-terminated butadieneacrylonitrile random copolymer (Reprinted with permission from Pearson,

1993, Copyright 2001 American Chemical Society.)

critical interparticle distance constant, the critical particle size must increasewith the volume fraction of dispersed phase.

The effect produced by a rubbery phase is based on the followingmechanism:

Mechanical loading ! cavitation in rubber particles ! promotion

of shear bands in matrix ! toughness improvement

To initiate this mechanism, particles must produce an adequate stress centration effect: diameters larger than 0.1–0:2 m are effective for thispurposes Smaller particles cannot store sufficient elastic energy to inducecavitation (Lazzeri and Bucknall, 1993; Dompass and Groeninckx, 1994).The existence of a critical interparticle distance below which a significanttoughening effect is observed is based on shear banding being favored by thestress-field overlap between neighboring particles

con-The maximum particle size for efficient toughening is in the order of5–10 m (Kinloch, 1989; Pearson and Yee, 1991) It has been proved experi-mentally that larger particles are relatively inefficient (Pearson and Yee,1991), although they are expected to be active in crack bridging; however,the contribution of this mechanism to rubber toughening is less than 10% ofthe total fracture energy at room temperature (seeFig 13.6)

It has been assessed that bimodal particle size distributions consisting

of a population of small and large particles may exhibit a better tougheningeffect than unimodal ones, due to a ‘‘synergistic effect’’ (Chen and Yan,1992) But this does not seem to be a general trend (Pearson and Yee, 1991;Grillet et al., 1992)

c Influence of the Matrix Tg

The effect of the matrix Tg on toughness has been analyzed extensively(Levita, 1989; Pearson and Yee, 1989; Van der Sanden and Meijer, 1993).Although the observed effect is usually ascribed to changes in the crosslinkdensity, it is better to regard it as being produced by a change in Tg withrespect to the test temperature, T

Figure 13.8shows that the toughening produced by a dispersed bery phase increases with an increase in the molar mass of the DGEBA(diglycidyl ether of bisphenol A) monomer and a corresponding decrease ofthe matrix, Tg As GIc was measured at room temperature, the mainobserved effect is the decrease in the shear yield stress of the matrix bylowering its glass transition temperature (a decrease of TgT at constantT) This favors shear yielding of the matrix and increases the tougheningeffect The same trend is observed for different rubber volume fractions andalso under impact conditions (Van der Sanden and Meijer, 1993)

rub-Results presented in Fig 13.8 could have been interpreted as an effect

of crosslink density on toughening But this is an incorrect concept, becausecrosslink density can be increased by the use of a low-molar-mass aliphaticdiepoxide This would decrease the matrix Tg and increase its toughenabil-ity, in spite of the increase in crosslink density But also, it may be statedthat at the same TgT, other factors related to the chemical structure, such

as sub-Tg relaxations, will play a role on toughening mechanisms

d Influence of the Interfacial Adhesion

A threshold of interfacial adhesion between both phases is needed to (a)promote the cavitation mechanism and (b) activate the crack-bridgingmechanism For rubbery particles, the former contributes much morethan the latter to the total fracture energy Adhesion is achieved by theuse of functionalized rubbers that become covalently bonded to the matrix.Higher toughness values have been reported by the use of functionalizedrubbers (Kinloch, 1989; Huang et al., 1993b) However, these experimentalresults also reflect the effect of other changes (particle size distribution,

dipheny sulfone) versus the initial DGEBA (diglycidyl ether of bisphenol A):(*) neat systems; (^) with 10% CTBN (27% AN) Rubber ¼ CTBN: carboxy-terminated butadiene acrylonitrile random copolymer (Pearson and Yee,

1989 with kind permission from Kluwer Academic Publisher.)

amount of dissolved rubber, etc.), produced by introducing functionalgroups in the rubber(Chapter 8).

A threshold level of interfacial adhesion is also necessary to produce atriaxial tensile state around rubber particles as the result of the cure process.When the two-phase material is cooled from the cure temperature to roomtemperature, internal stresses around particles are generated due to thedifference of thermal expansion coefficients of both phases If particles can-not debond from the matrix, this stress field magnifies the effect producedupon mechanical loading

Under these conditions, the hydrostatic pressure, p, around a rubberparticle is given by (Raghava, 1987)

A six-fold increase in GIcvalues was obtained for a thermoset based

on DGEBF (diglycidyl ether of bisphenol F) containing 5 wt% of an idized hyperbranched polymer (Boogh et al., 1999) At this small concentra-tion, the decrease of the Young’s modulus and the glass transitiontemperature were not so significant It was suggested that the high toughen-ing capacity of HBP modifiers is induced by the generation of a gradient ofproperties within the phase-separated particles

epox-But other studies showed that increasing the amount of HBP led to adecrease in both the Young’s modulus and the glass transition temperature;

moreover, a linear polyester of the same chemical structure as the HPBproduced a similar toughening effect (Gopala et al., 1999; Wu et al.,1999) Particles with lower sizes than 1 m gave no increase in toughness,while particles of 2–3 m gave nearly the same fracture toughness irrespec-tive of molar mass or thermoplastic architecture.

Regarding the use of hyperbranched polymers for toughening poses, it may be concluded that

pur-1 The hyperbranched architecture does not always afford anadvantage in toughness or viscosity compared with low-molar-mass thermoplastic modifiers

2 The nature of the functional groups of the HBP is a significantfactor for the control of viscosity, miscibility with the thermosetprecursors, phase separation during cure, and particle–matrixadhesion

f Conclusions

Regarding the toughening of epoxy networks, it may be stated that Fracture energy is roughly proportional to rubber volume fraction

up to phase inversion

The optimum particle size lies in the range 0.1–10 m and depends

on the interparticle distance that must be lower than a critical value.The claim about the better effect achieved by the generation of abimodal distributions of particle sizes has yet to be proved Interfacial adhesion between particles and matrix is necessary andcan be achieved using reactive rubbers

The toughening effect at room temperature increases with adecrease of the matrix Tg

13.3.3 Rubber Toughening of Vinyl Ester (VE) and

Unsaturated Polyesters (UP)

Different types of modifiers are used in UP formulations to increase ness and also to decrease shrinkage and improve the surface aspect.Poly(vinyl acetate) (PVAc) is very often used for ‘‘low-profile’’ appli-cations At low PVAc contents, the continuous matrix is a polyester networkwith PVAc inclusions Increasing the PVAc amount leads first to a bicon-tinuous structure, and then to a phase-inverted system(Chapter 8).The low-profile action is observed in the concentration range where bicontinuousstructures are formed (Pascault and Williams, 2000) However, the fractureenergy attains a maximum value for lower PVAc concentrations (Bucknall

tough-et al., 1991)

Liquid reactive rubbers were also used for UP and vinyl ester tions (Suspene et al., 1993; Siebert et al., 1996) Increases in fracture energyand fatigue- crack resistance were reported for some systems, although nosignificant improvements were observed for some other systems These dif-ferent behaviors are probably related to the heterogeneous structure of thematrix(Chapter 7).Toughening mechanisms in three-phase systems are notyet well established.

in modulus and yield stress This can be unacceptable for structural andlong-term applications (see Fig 13.7) A second limitation is the lack ofsignificant success in the toughening of high-Tg networks (see Fig 13.8)

Following the requests to increase toughness by keeping a high Tg, forseveral applications (the aerospace industry in particular), high-Tg or semi-crystalline thermoplastics (TP) can be used instead of rubbers to modifythermosetting polymers (Hedrick et al., 1985; Pearson, 1993; Hodgkin etal., 1998; Pascault and Williams, 2000)

The thermoplastic-rich phase may be separated in the course of merization (Sec 13.4.2) or can be incorporated as a dispersed powder in theinitial formulation (Sec 13.4.3) A strong drawback of the in situ-phaseseparation for processing purposes is the high viscosity of the initial solutionwhich results from the much higher average molar mass of the TP comparedwith the liquid rubbers Also, for the same reason, the critical concentration

poly-crit has a smaller value (phase inversion is observed at smaller tions of modifier)

concentra-Different TPs have been used to modify thermosets, such as poly(ethersulfone) (PES), polysulfone (PSF), poly(ether ketone) (PEK), polyetherimide (PEI), poly(phenylene oxide) (PPO), linear polyimides, polyhydan-toin, etc (Stenzenberger et al., 1988; Pascal et al., 1990, 1995; Pascaultand Williams, 2000)

The major trend observed is a modest increase in KIc or GIc by theintroduction of initially miscible thermoplastics This improvement isobtained without any loss in stiffness and thermal properties Some veryhigh improvements in KIc, claimed by some authors, are due to phaseinversion, leading to a thermoplastic matrix with thermoset particles