Fatigue crack propagation in triblock copolymer toughened epoxy nanocomposites.
Epoxy resins serve as polymer matrices in composites for demanding applications in e.g. engineering, aeronautics, and energy economic sectors since many years. They are a special class of high performance polymers with a good processability and combine excellent mechanical properties with high adhesive strength, low shrinkage and water absorption, as well as high thermal and chemical stability caused by their crosslinked structure . By knowing the involved chemistry, the user can vary and adapt these properties over a wide range of temperatures and therefore control structural features or the degree of crosslinking . A drawback coming along with the molecular crosslinking is the inherently brittle nature of epoxy resins, which causes low fracture toughness and a poor resistance to fatigue crack propagation. Various strategies have thus been developed to overcome this problem [3-5], e.g. the modification by phases of compliant nature.
One of the first extensive research studies on toughening of epoxy was done by Sultan and McGarry . They successfully added a carboxyl terminated liquid butadiene rubber (CTBN) to a bisphenol A based epoxy precursor and were able to drastically increase its fracture toughness. Later, research focused on the variation of the type of rubbery epoxy modifier, e.g. amine terminated butadiene acrylonitrile  and hydroxy! terminated butadiene acrylonitrile , as well as the toughening by thermoplastic modifiers, such as Poly(phenylene oxide)  and the examination of the involved fracture mechanisms [10, 11]. The effect of rubbery toughened epoxy thermosets on the fatigue crack propagation (FCP) behaviour was deeply investigated by Azimi and Hertzberg [12-14]. They were able to show that rubber modified epoxies undergo a transition in the FCP behaviour at a dynamic stress intensity level where the plastic zone size of the crack tip exceeds the modifier's particlc size, and due to the activation of mechanisms such as cavitation and shear yielding of the matrix the resistance to FCP was improved. This is in accordance with the findings of Karger-Kocsis and Friedrich , who described the main toughening mechanisms for a CTBN toughenend anhydride system during fatigue crack propagation as rubber cavitation and subsequent shear-yielding of the matrix. However, the introduction of rubber modifiers usually lead to both, a loss in glass transition temperature [T.sub.g] and a reduction of strength and elastic modulus of the thermoset .
A fairly new approach to toughen epoxy resins while maintaining the level of mechanical properties and [T.sub.g] is the introduction of block-copolymers (BCP) as a second phase [16-24]. This concept was successfully applied by Bates et al. by using amphiphilic BCP [25, 26], which were assembled via a living chain-growth method [27, 28], These BCPs are composed of at least two chemically different constituents generating polymeric macromoleculcs of various compositions, such as diblock (AB), triblock (ABA, ABC), multiblock, and alternating compositions or even tapered ones . In contrast to liquid rubbers BCP offer the ability to obtain a variety of nanosized structures in thermosets, e.g. spherical and cylindrical micelles, vesicles, and other (dis-) continuous structures [26, 29, 30]. Thereby, nanostructuring can occur in at least two ways and combinations thereof [31, 32]: (1) via a thermodynamically driven self-assembling of the macromolecules prior to curing [33, 34], and (2) a reaction induced phase separation mechanism (RIPS) during the curing process [35-39].
Applying BCP as toughening agents for epoxy polymers offers a new route for developing nanocomposites. Assembling the BCP nanostructure is a complex process which depends on various parameters. Understanding and controlling these allows the tailoring of a specific BCP-epoxy morphology. Parameters are e.g. the BCP-composition (AB, ABA. etc.), the type and length of blocks, the block/length ratio, as well as the type and nature of the epoxy precursor and the curing agent . Furthermore, the curing process, i.e. curing temperature and time play an important role . The resulting material structure, the BCP phase morphology and size  as well as its bonding to the matrix  can significantly influence the fracture mechanical properties of epoxy.
Recently, Kishi et al.  introduced a BCP (PMMA-blockPBnA-block-PMMA) into a phenol novolac cured epoxy (DGEBA) to examine the nanophase structuring of the system. They showed that the formation of the BCP nanophases was controlled by the molecular weight of the immiscible blocks as well as by the length ratio of the different blocks. No effect of the gelling time on the type of created nanostructures was observed and thus, it was concluded that the heterogeneous nanostructure was rather formed via self-assembling than via the RIPS mechanism. On the other hand, Romeo et al. (39| clearly demonstrated an influence of the cure cycle on the final nanostructure of a PS-block-PMMA toughened epoxy. Asada et al.  examined the microphase separation using the same system as Kishi et al. , and via in situ small-angle X-ray scattering they found that microphase separation occurred in two steps: first the BCP organized in micellic structures via self-assembly in the uncured epoxy, and in a second step the BCP grew in size, and their distance to each other increased until the miscible PMMA blocks were finally assembled in the epoxy network. In this case, it was believed that the PMMA chain length mainly controlled the reorganization process.
Dean et al.  systematically investigated the toughening effect of diblock copolymers in a bisphenol A based epoxy resin cured by a tetrafunctional aromatic amine. They were able to correlate the strain energy release rate to the phase structure of the BCP and found that the fracture toughness increased when the size to distance ratio of the formed vesicles increased. Also, small concentrations of BCP were able to significantly improve fracture toughness of the system. The formed vesicles encapsulated a given volume fraction of epoxy and "artificially" increased the size of the phase separated structure. Declet-Perez et al.  investigated fracture mechanisms induced by a rubbery (PEO-block-PEP-block-PEO) and a glassy core-type (PEOblock-PS-block-PEO) triblock copolymer, and they showed that the rubbery-core BCP cavitated first and then caused subsequent shear yielding of the matrix, whereas the glassy-core BCP did not cavitate but rather deformed until failure of the surrounding matrix occured.
A study by Fischer et al.  provided information on the effect of an acrylic triblock copolymer on the fatigue crack propagation behaviour of an one-component epoxy system. They compared the effect of an ABA type BCP and a thermoplastic polyhydroxyether modifier with a concentration of 10 wt%. Both modifiers significantly increased the resistance to FCP compared with the neat epoxy. but the BCP reached the highest critical stress intensity factor range [DELTA][K.sub.Ic] without compromising the glass transition temperature.
There is still a lack of knowledge of systematically gained data about the influence of nanophase BCP on the fatigue crack propagation resistance of epoxy resins. To gain a deeper understanding of the reinforcing effects and the energy dissipating mechanisms introduced by these already commercially available triblock copolymers, their influence on the fatigue crack propagation was systematically studied and correlated with structural features of fractured surfaces in this work.
Materials and Synthesis
The materials used in this study were a bisphenol-A-based epoxy resin (DGEBA, D.E.R. 331 from DOW, epoxy equivalent weight: 187 g/eq), which was cured by a cycloaliphatic amine curing agent (3,3'-dimethyl-4.4'-diaminodicyclohexylmethane, HY 2954 from Huntsman, amine equivalent weight: 60 g/eq) and modified by a poly(methylmethacrylate-block-butylacrylateblock-methylmethacrylate) triblock copolymer (Nanostrength M53, from Arkema, in the following named BCP). The modifier is an ABA type block copolymer consisting of two epoxymiscible PMMA blocks ([T.sub.g] [approximately equal to] 120[degrees]C) surrounding a ductile, central and epoxy-immiscible block of PBuA ([T.sub.g] [approximately equal to] - 30[degrees]C), which is supposed to phase separate . The ductile PBuA block content is about 50% .
The systems were prepared by systematically varying the BCP concentration from 0.5 to 10 wt%. The DGEBA epoxy resin was gently mixed with the specific amount of BCP in a dissolver aggregate (Dispermat, VMA Getzmann GmbH) at 90[degrees]C, until a homogenous solution was reached and optical transparency was observed. The dissolution time varied with the modifier's concentration. Then, the EP/BCP mixture was stirred for at least another 45 min at 80 rpm. After cooling the mixture down to room temperature, a stoichiometric amount of curing agent was added and stirred thoroughly for 15 min at 200 rpm. Finally, the mixture was cast into steel molds previously coated with INDROSIL 2000 release agent. The samples were then cured in two steps for 8 h at 70[degrees]C and 16 h at 125[degrees]C. The neat epoxy reference material was processed in the same way.
To obtain a neat BCP test specimen for dynamic mechanical analysis the BCP powder was pressed using a P300M platepress (Dr. Collin GmbH, Ebersberg, Germany) at 180[degrees]C for 5 min under ambient pressure followed by pressing the sample for 1 min at 100 bar.
Flexural Properties. To characterize the mechanical properties of the different systems, three point bending tests were carried out at room temperature according to the standard EN ISO 178 using a Zwick 1474 testing machine with 5 kN load cell. The deformation rate was set to 2 mm/min and the distance between the supports to 64 mm. Displacement was measured by the movement of the machine crosshead. The sample geometry was 80 mm in length, 10 mm in width and 4 mm in thickness. At least five valid tests were performed of each EP/BCP system.
Dynamic Mechanical Analysis. Viscoelastic properties and the effect of BCP on the phase separation behaviour and [T.sub.g] of the thermoset were investigated by dynamic mechanical analysis (DMA, Q800, TA Instruments) in tensile setup at a frequency of f = 10 Hz. The rectangular specimens measured 30 mm in length. 5 mm in width and 2 mm in thickness. The temperature was varied from -100[degrees]C up to 250[degrees]C with a heating rate of 1[degrees]C/min. The glass transition temperature was determined at the peak value of the mechanical damping tan [delta].
Fracture Toughness. The critical stress intensity factor [K.sub.Ic] and the critical strain energy release rate [G.sub.Ic] were determined using a Zwick 1474 testing machine, according to ASTM E5045. Compact tension (CT) samples (Fig. 1) were used, where W is given by the mold geometry to W = 31.2 mm. The thickness B was set to 6 mm to ensure a state of plane strain at the crack tip and to be able to apply linear elastic fracture mechanics theory (LEFM). The test velocity was set to 1 mm/min and a preliminary force [F.sub.v] =2 N was applied. The displacement was measured by the movement of the machine crosshead. For statistical evaluation 8 samples of each EP/BCP system were examined.
To determine the crack opening displacement (COD) a sharp notch was introduced into the samples by razor blade tapping (cf. ). The initial crack length ao for each specimen was measured on the fractured surface after the test by light microscopy, coupled to an electronic caliper. To be accounted for a valid measurement the crack length had to satisfy the ratio 0.45 [less than or equal to] [a.sub.0]/W [less than or equal to] 0.55. The strain energy release rate [G.sub.Ic] was calculated using the modulus [E.sub.f], obtained from three-point bending tests for plane strain conditions according to Eq. 1.
[G.sub.Ic] = [K.sup.2.sub.Ic]/[E.sub.f]] * (1-[v.sup.2]) (1)
The Poisson ratio was v=0.34.
Fatigue Crack Propagation. The resistance to fatigue crack propagation was determined using a Bose Electroforce 3550 with a 1 kN load cell, which was digitally adjusted to a maximum load of 200 N. The test procedure and data evaluation followed the ESIS TC 4 test protocol , with the stress intensity factor range [DELTA] K calculated according Eq. 2. The frequency was set to f = 5 Hz sinusoidal loading. The load ratio R represents the ratio of the minimum applied load to the maximum applied load for any given load cycle, and it was set to R = [F.sub.min]/ [F.sub.max] = 0.2. The maximum force was chosen to satisfy the relation [DELTA]K[congruent to][K.sub.Ic]/2.
[DELTA]K = [DELTA]F/B*[square root of W] f([alpha]) = [F.sub.max] - [F.sub.min]/B * [square root of W] f ([alpha]) (2)
The test sample geometry and preparation were the same as for the static fracture toughness (cf. Fig. 1).
The crack opening displacement COD was measured using a clip-on crack propagation-extensometer by Sandner Messtechnik GmbH at the position [X.sub.V0] = -0.25W at the front of the CT-specimens. The crack shape factor f([alpha]=a/W) was then calculated using Eq. 3 with the coefficients [c.sub.i] provided in Ref. 47.
[alpha] = a/W = [c.sub.0] + [c.sub.1] + [c.sub.2] [([U.sub.x]).sup.2] + [c.sub.3] [([U.sub.x]).sup.3] + [c.sub.4] [([U.sub.x]).sup.4] + [c.sub.5][([U.sub.x]).sup.5] (3)
[U.sub.x] = 1/[square root of ([BE.sub.f]COD/F) + 1 (4)
The term [U.sub.x] was calculated using Eq. 4, where B is the sample width, [E.sub.f] is the elastic modulus, COD is the crack opening displacement, and F the applied force.
Fractographic Examinations. Fatigue fracture surface analyses were performed by scanning electron microscopy (SEM) using a Zeiss Supra 40VP at various magnifications, deploying SE and Inlens detectors. The accelerating voltage was 5 kV. The fracture surfaces were sputtered with a gold-palladium layer at I = 40 mA for 70 seconds (Balzers Sputter Coater SCD050). All images were taken ahead of the initial crack tip. Image], image analysis software was deployed to analyze the dimensions of features of fracture surfaces, e.g. BCP phase sizes.
RESULTS AND DISCUSSION
To characterize the mechanical performance of the neat epoxy and the BCP modified systems, three-point-bending tests were carried out. The test results are summarized in Table 1 and Fig. 2. The flexural modulus Ef of the reference system was measured to [E.sub.f,EP] = 2,630 MPa and decreases slightly with increasing BCP concentration. The soft block phase is thereby presumably reducing the modulus and accordingly flexural strength [[sigma].sub.f] from [[sigma].sub.f,EP]=126 MPa to roughly [[sigma].sub.f,10%] = 90 MPa for the modified system with 10 wt% BCP. Interestingly, by the introduction of 6 wt% into the neat resin a sudden drop of modulus and strength can be observed. This behaviour was previously reported by Chen and Taylor  for a BCP toughened anhydride cured epoxy system. They related the drop of modulus and strength to the formation of a phase-inverted microstructure, although this effect was first observed at a higher BCP concentration of 12 wt%.
However, the strain at maximum stress [[epsilon].sub.f] of the reference system was found to be [[epsilon].sub.f,EP] = 8.1%. The addition of up to 6 wt% ([[epsilon].sub.f,6%] = 7.5%) of the BCPs into the epoxy resin did not significantly reduce ductility of the cured samples, even though scattery data for 2 and 4 wt% was observed. At higher concentrations of 8 wt% and 10 wt% BCP though, ductility of the EP/BCP-systems decreased to [[epsilon].sub.f,8%] = 5.2% and [[epsilon].sub.f,10%] = 6.6%, respectively.
Dynamic Mechanical Analysis
Dynamic mechanical analysis (DMA) was used to examine the viscoelastic properties of both the reference, i.e. the neat epoxy and the neat block copolymer, as well as the toughened EP/BCP systems. The resulting mechanical damping tan [delta] and the storage modulus E' are depicted in Fig. 3a and b as a function of temperature T. Figure 3a shows two distinct peaks of the neat BCP. which can be associated with the relaxation of the rubbery PBuA blocks ([T.sub.g,PbuA] = -30[degrees]C) and the stiff PMMA blocks ([T.sub.g,PMMA] = 120[degrees]C). The [alpha]-transition, i.e. glass transition temperature of the epoxy reference system, is located at ~175[degrees]C, and it shifted to higher values when BCP was added (cf. Table 1). However, [T.sub.g] of the EP/BCP systems decreased again at BCP concentrations above 2 wt%. It is believed that the BCP first cause a shift to higher [T.sub.g] because they might serve as additional crosslinks in the polymer network, while the reduction of [T.sub.g] above 2 wt% might be related to an increasing compatibility and bonding of the PMMA blocks to the epoxy matrix. The highest [T.sub.g] of ~183[degrees]C, i.e. a shift by 8[degrees]C, was measured for EP/BCP (2 wt%), and it decreased to ~181[degrees]C for EP/BCP (10 wt%). Similar results were indeed obtained by Bashar et al. , who incorporated triblock copolymers (PMMA-block-PBuA-block-PMMA) into an amine cured bisphenol A based epoxy resin. Thereby, [T.sub.g] of the modified system increased by about 3[degrees]C compared with the neat reference material. Bashar et al. ascribed the slight shift to experimental uncertainties. Figure 3a also shows that the glass transition of the immiscible PBuA phase in the EP/BCP systems overlaps with the [beta]-relaxation peak of the neat epoxy (ca. -57[degrees]C). With increasing BCP concentration the related PBuA peak becomes more pronounced, and shifts to higher temperatures. The simultaneous reduction of [T.sub.g] of the EP/BCP systems and the rising [T.sub.g] of the PBuA-rich phase with the BCP concentration, indicates an increasing compatibility of the immiscible components in the EP/BCP systems . The latter will be confirmed in the following sections by investigating the related changes in the morphology.
At about 140[degrees]C, a shoulder in the tan S curve is apparent for the neat epoxy, and it becomes even more pronounced for the EP/BCP systems. The occurrence of such a shoulder can be ascribed to at least two effects which might even overlap: (1) the systems undergo a post-curing since segmental motions in the epoxy network allow unreacted functional groups reacting with each other, and (2) the relaxation process of PMMA segments in the epoxy-rich phase became more prominent due to higher absolute content of PMMA blocks.
The neat BCP storage modulus E' in the range from -100[degrees]C to -45[degrees]C is similar to the E' of the neat epoxy (Fig. 3b). Then E' drops when approaching the [T.sub.g] of the PBuA-rich phase, and once again, when reaching the [T.sub.g] of the PMMA-rich phase. Closely examining the EP/BCP systems, the glass transition of the PBuA phase can be distinguished, most pronounced in EP/BCP (10 wt%). The glass transition of PMMA, however, as seen in the neat BCP sample, is barely visible in the EP/BCP systems, which indicates a good compatibility of PMMA blocks to EP. The glass transition temperatures of the EP/BCP systems are rather shifted to higher temperatures and overlap with that of the neat epoxy For all EP/BCP systems a further increase in temperature leads to a drop of E' to a rubbery plateau located at the same level as the neat epoxy. It does not drop to the niveau of the neat BCP ([less than or equal to] 1 MPa). This confirms the presence of a continuous epoxy phase without phase inversion of the EP/BCP systems.
The viscoelastic behaviour of this type of BCP is complex and requires further analysis, but here, it shall primarily serve as an indicator for the phase separation behaviour.
To better understand the effect of the BCP on the critical stress intensity factor and the critical energy release rate of the synthesized nanoeomposites, Fig. 4 summarizes the normalized [K.sub.Ic,X]/[K.sub.Ic,EP] and [G.sub.Ic,X]/[G.sub.Ic,EP] values as a function of BCP concentration, respectively. The stress intensity factor [K.sub.Ic] of the neat epoxy was 0.63 Mpa[square root of m], whereas the energy release rate [G.sub.Ic] was calculated as 133 J/[m.sup.2] (see Table 1).
The fracture toughness [K.sub.Ic] and the energy release rate [G.sub.Ic] are continuously increasing as the BCP concentration is increasing. At 6 wt% the energy release rate jumps to 580 J/[m.sup.2] and reaches a kind of plateau at 10 wt% ([G.sub.Ic] 10% = 684 J/[m.sup.2]), which represents a fivefold energy release rate compared with that of the neat epoxy. The strong rise of [G.sub.Ic] may be attributed to the activation of a superior toughening mechanism, due to a change of the EP/BCP morphology. However, the jump in toughness correlates with the drop of mechanical properties at the same concentration.
Fatigue Crack Propagation
The resistance to fatigue crack propagation is typically described by correlating the crack propagation speed, i.e. the crack extension length per load cycle da/dN with the corresponding stress intensity factor range [DELTA]K (cf. Eq. 2). Thereby the stable crack propagation regime can be described by the Paris-Erdogan law (Eq. 5), where a is the crack length, N the number of cycles, C is a material constant and m represents the slope of the curve, also referred to as Paris' law exponent.
da/dN =C[([DELTA]K).sup.m] (5)
A toughening effect of BCP on epoxy would be represented by a reduction of the crack propagation speed da/dN and a higher critical stress intensity factor range [DELTA][K.sub.Ic], which is indicated by a shift of the FCP curves to higher [DELTA]K-values and a decreasing Paris' law exponent m with respect to the neat epoxy. However, the drastically increased [G.sub.Ic] of the EP/BCP systems is not necessarily equivalently transferred to the fatigue performance of the materials. Other stress conditions prevail in a fatigue loading situation than in a quasi-static loading situation, since the crack tip zone and the crack sharpness are not the same. This can lead to different failure mechanisms in static and fatigue loading situations .
Figure 5 depicts FCP curves for the neat epoxy and the various EP/BCP systems. The curves of the modified systems were gradually shifted and tilled with increasing BCP concentration. The Paris' law exponent m was thereby reduced by nearly 50% from [m.sub.EP] = 15.5 to [m.sub.8%] = 8.1 in case of EP/BCP (8 wt%), which represents a significant improvement of the resistance to FCP due to the block copolymers. The effect of shifting the curve to higher [DELTA]K can be recognized by comparing the crack propagation speed at a given stress intensity range, e.g. [DELTA]K = 0.5 Mpa[square root of m]. In this case the crack propagation rate da/dN of the EP/BCP systems was strongly reduced from 925 nm/cycle for the EP/BCP (2 wt%) to only 21 nm/cycle for EP/BCP (10 wt%).
The FCP curve of EP/BCP (2 wt%) started propagating even beyond the instable crack propagation regime of the neat epoxy ([DELTA][K.sub.Ic.EP] [congruent to] 0.39 Mpa[square root of]m]). Increasing the BCP concentration to 6 wt% resulted in another large shift to higher [DELTA]K and a reduction of the slope from to [m.sub.6%] =9.7. The 8 wt% system nearly overlaps with the 6 wt% system, whereby the 10 wt% modified system was shifted again further to higher stress intensity factor ranges. Trend-wise, all the obtained [DELTA][K.sub.Ic] test results (cf. dotted line in Fig. 5 for the neat epoxy and Table 1) are in a good linear agreement with the static stress intensity factor [K.sub.Ic], generally following the relationship [DELTA][K.sub.Ic] = [K.sub.Ic] *(1-R) .
Similar results were reported by Fischer et al.  for a comparable (lower soft block content than in the current study), 10 wt% BCP modified high performance resin. Fischer et al. found that the Paris exponent of the FCP curve strongly declined by about 32% to m = 11 in case of the block copolymer modified system, whereas [DELTA][K.sub.Ic] for instable crack propagation was increased to about 0.89 MPaxm. These results are in good agreement with the data obtained in this study (Table 1).
The mechanisms being responsible for this behaviour may be ascribed to extrinsic toughening mechanisms. It is known that crack shielding mechanisms, such as crack deflection and crack pinning, as well as bridging effects, are activated if the plastic zone size is small compared with the hindering obstacles [11, 13, 51]. Such mechanisms would shift the da/dN-[DELTA]K-curve to higher stress intensity factor ranges . Furthermore, at higher AK zone shielding mechanisms, such as cavitation and debonding, may lead to a decrease in the slope m of the curves .
To establish a correlation between fracture mechanical properties and features of the microstructure fractographic studies were performed by SEM.
Figure 6 shows the typical smooth and featureless fracture surface of the brittle neat epoxy. With increasing BCP content from 2, 6, 8 to 10 wt% the visual observation of fracture surfaces portends a rise in surface roughness (Fig. 7A-D). An increase in surface roughness indicates a crack deflection mechanism being present during fatigue crack propagation , and such mechanism would lead to a shift of the FCP-curves to higher [DELTA]K. which correlates well with the experimental results depicted in Figure 5. The EP/BCP (2 wt%) shows a well dispersed, particulate BCP-rich structure in epoxy. At 6 wt% BCP, however, the morphology changes, and the fracture surface is composed of interconnected, isle-like epoxy-rich domains containing spherical BCP-rich inclusions. Although the modifier concentration was further increased from 6 to 10 wt% the morphological structure did not change drastically. A phase inversion was not detected, which is confirmed by the results from DMA tests. Thus, epoxy is the dominating phase throughout all EP/BCP systems in the current study.
By comparing the average size of the BCP-rich particles being present in the different systems, i.e. in the epoxy rich regions, the particle dimensions decrease and reach the nanometer scale when the BCP concentration is raised from 2 wt% ([d.sub.2%] = 336 [+ or -] 77 nm), 6 wt% ([d.sub.6%] = 283 [+ or -] 82 nm), 8 wt% ([d.sub.8%] = 254 [+ or -] 68 nm) to 10 wt% ([d.sub.10%] = 136 [+ or -] 40 nm). The change in microstructure from 2 to 6 wt% as well as the reduction of the BCP phase dimension in epoxy-rich areas of EP/BCP with increasing concentration are further indicators for an increasing compatibility of the BCP with epoxy.
Taking a closer look at the various features and the microstructure of epoxy-rich areas. Fig. 8 provides a more detailed capture of the fatigue fracture surfaces and toughening mechanisms for the 2 wt% and the 10 wt% EP/BCP systems. Figure 8 clearly reveals the formation of a dispersed particulate BCP-rich structure in the 2 wt% systems with dimensions in the submicron range (item A). These particles partially cause crack pinning events (item B), as indicated by small "tails," i.e. fracture steps at the small inclusions occurring in crack propagation direction. Besides, the particles show characteristic lumps in their centre (item A). Such features are also present in EP/BCP (10 wt%) (item C). Indeed, the formation of such particles in BCP toughened epoxies was already reported by other researchers [22, 24, 42). Micrographs taken at higher magnification (Fig. 9) reveal the plastic deformation of BCP-rich particles. Fibrils and cavities were also formed during crack propagation. Furthermore, partial debonding of the particles from the matrix occurs, and particle fracture is visible. Such high plasticity is typical in case of rubbery core-shell-type fillers (cf. ), and so far, it was not observed in BCP modified systems yet. As shown in Fig. 9, item D, the particles adhere well to the surrounding matrix, and thus, fibrils were formed, still retaining some stress transfer between particles and the matrix. The debonding mechanism is associated with the tilting of the FCP-curve and leads to a reduction of the Paris exponent m. The formation of lumps, on the other hand, suggests a bridging mechanism accompanied by particle cavitation, which would reduce the crack driving force and shift the curves to higher AK. The crack pinning mechanism yields the same effect.
The BCP bridging mechanism is schematically depicted in Fig. 10. It is believed that the inclusion is first stretched by the separating crack faces, but it remains adhering to the matrix (Fig. 10a). During a further crack opening more energy is consumed to elongate the rubbery phase and to bridge the crack causing a necking of the particles and partial debonding (Fig. 10b). The BCP are composed of glassy PMMA, with a similar Poisson ratio (v = 0.4) than epoxy , and a rubbery core, having a Poisson ratio of about v = ~0.5. It is therefore assumed that the rubbery portions of the BCP-rich regions deform and allow the particles to cavitate. When torn apart, the inclusion relaxes and bounces back, resulting in a "cup and cone" type of fracture structure (Fig. 10c).
Furthermore, since the crack propagates from left to right (Fig. 10), plastically deforming the inclusion, the drawn phase (cones) is oriented off-centre in crack propagating direction (cf. Fig. 9, item E, F) and remains plastically deformed at the end of the fractured inclusion. Similar types of fracture morphologies in CTBN modified epoxies were already described by Pearson and Yee , but not yet for BCP toughened epoxies.
In contrast, EP/BCP (10 wt%) shows an even higher resistance to FCP but contains much smaller, even nano-sized inclusions in the epoxy-rich domains (Fig. 8, item C). It is believed that the dispersed spherical BCP-rich particles in the epoxy-rich domains interact with the surrounding BCP-rich network structure causing a highly enhanced resistance to FCP, similar as suggested by Chen and Taylor  for the static fracture behaviour. The morphological alternation of epoxy-rich regions and BCP-rich domains lets expect different energy dissipating mechanisms: (1) the epoxy rich domains containing submicron to nano-sized inclusions (cf. Fig. 9, item G) cause a toughening due to crack-pinning, plastic deformation, cavitation, debonding and crack bridging, and (2) cohesive fracture of the BCP-rich phase occurs (Fig. 9, item H) with plastic deformation and rupture as dominating mechanisms to increase the resistance to FCP. A combination of both mechanisms is considered to generate toughening in the highly filled EP/BCP compounds. However, even though EP/BCP (10 wt%) exhibited the largest shift to higher [DELTA][K.sub.Ic], the Paris exponent slightly increased to m = 9.3, in comparison with EP/BCP (8 wt%). The latter might be an effect of the reduction of shielding phenomena, since the optimum particle size for efficient toughening depends on the relative size of the plastic zone [11, 13], and hence, the loading situation and the morphology at the crack tip. The inclusion size and the concentration in EP/BCP (8 wt%) may have already reached an optimum value with respect to a particle size to plastic zone size-ratio, impeding a further toughening by zone shielding mechanisms , if the modifier concentration is increased to 10 wt% for the present materials. Furthermore, Azimi et al.  and Karger-Kocsis and Friedrich  stated that an increasing particle volume fraction causes a decreasing Paris exponent in case of rubber particle modified systems. If one assumes a dispersed particle structure with the above mentioned particle sizes, the overall occupied particle volume in the EP/BCP (8 wt%) is still 50% higher than in the epoxy containing 10 wt% BCP. This might be an additional factor worth considering when explaining the increase in FCP slopes from [m.sub.8%] = 8.1 to [m.sub.10%] = 9.3.
This study showed that a small amount of triblock copolymers is able to significantly increase the resistance to fatigue crack propagation (FCP) of epoxy. When increasing the BCP concentration from 2 to 10 wt% a transition in the microstructure occurs as follows: (1) at BCP contents below 6 wt% the characteristic microstructure is given by the epoxy matrix containing phase separated and well dispersed spherical BCP-rich particles, and (2) at BCP contents exceeding 6 wt% the epoxy matrix with BCP-rich particles is accompanied by interconnected BCP-rich domains. The latter structure is most beneficial to gain a high resistance to FCP, while containing spherical BCP inclusions in the dimension of about 250 nm (EP/BCP 8 wt%). The glass transition temperature [T.sub.g] rises by up to 8[degrees]C due to the addition of only 2 wt% BCP. An economically favourable system with high toughness would e.g. contain 6 wt% of BCP, which provides already a reduction of the Paris' law exponent by 37% and an increase in [DELTA][K.sub.Ic] by more than 100%, while only moderately affecting modulus, strength, elongation, and glass transition temperature.
During fatigue crack propagation the homogeneously dispersed spherical BCP-rich particles were found to induce toughening mechanisms such as plastic deformation, fibrillation, cavitation, debonding, and bridging, and thus, these reduce the crack driving force. Furthermore, crack pinning phenomena were detected. Toughening mechanisms in case of compounds with BCP contents higher than 6 wt% were found to be a combination of shielding mechanisms induced by BCP inclusions in the epoxy matrix, and deformation, debonding. and rupture of BCP-rich domains.
Parts of the study were presented at the conference "Times Of Polymers" in Ischia, Italy in June 2016. The authors gratefully acknowledge the provision of Nanostrength M53 by Arkema.
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Andreas Klingler (iD), Bernd Wetzel
Institute for Composite Materials (IVW GmbH), University of Kaiserslautern, Erwin-Schrodinger-StraBe, Build. 58, Kaiserslautern 67655, Germany
Correspondence to: A. Klingler; e-mail: firstname.lastname@example.org
Caption: FIG. I. Specimen geometry and configuration for fracture toughness and fatigue crack propagation test .
Caption: FIG. 2. Flexural modulus [E.sub.f], maximum stress [[sigma].sub.max], and strain al max. stress [[epsilon].sub.[sigma],max] of EP/BCP systems at different concentrations.
Caption: FIG. 3. Temperature dependencies of (a, left) tan [delta] and (b, right) storage modulus E for the EP/BCP systems and respective neat references. (Color figure can be viewed at wileyonlinelibrary.com]
Caption: FIG. 4. Stress intensity factor [K.sub.Ic] and energy release rate [G.sub.Ic] of EP/BCP systems at different concentrations.
Caption: FIG. 5. Fatigue crack propagation results (da/dN vs. [DELTA]K) of EP/BCP with different concentrations.
Caption: FIG. 6. Neat epoxy reference, FCP fracture surface.
Caption: FIG. 7. Fatigue fracture surfaces of EP/BCP systems at different concentrations: (A) 2 wt%. (B) 6 wt%, (C) 8 wt%, and (D) 10 wt%.
Caption: FIG. 8. Fatigue fracture surfaces of EP/BCP, left: 2 wt%, right: 10 wt%, A: BCP-rich particle with lump. B: crack pinning event, C: Nano-sized inclusions in epoxy-rich domains showing lumps.
Caption: FIG. 9. Fatigue fracture surfaces of EP/BCP. left: 2 wt%, right: 10 wt%, open arrow: crack propagation direction, D: fibrillation of BCP-rich particles, E/F: off-center orientation of BCP-rich drawn phase in crack propagation direction. G: nano-sized BCP-rich particles, II: cohesive fracture of BCP-rich phase. [Color figure can be viewed at wileyonlinelibrary.com]
Caption: FIG. 10. Schematic "Cup and Cone" fracture mechanism, (a) stretching of BCP-rich particles, (b) elongation of the BCP-rich particles with crack bridging and partial debonding. (c) formation of fibrils and cup and cone type of fracture.
TABLE 1. Overview of (fracture) mechanical and thermal properties of the EP/BCP-syslems. BCP (wt%) [E.sub.f] (MPa) [[sigma].sub.f] (MPa) 0 2,630 [+ or -] 84 126 [+ or -] 1.3 0.5 2,630 [+ or -] 114 122 [+ or -] 3.7 1 2,510 [+ or -] 120 120 [+ or -] 3.0 2 2,520 [+ or -] 124 111 [+ or -] 10 4 2,480 [+ or -] 73 113 [+ or -] 8.7 6 2,320 [+ or -] 59 106 [+ or -] 2.4 8 2,180 [+ or -] 59 86 [+ or -] 11.7 10 2,120 [+ or -] 53 90 [+ or -] 4.9 BCP (wt%) [[epsilon].sub.f, [K.sub.lc] (Mpa [sigma]max] (%) [square root of m]) 0 8.1 [+ or -] 0.1 0.63 [+ or -] 0.06 0.5 7.6 [+ or -] 0.8 0.74 [+ or -] 0.08 1 8.0 [+ or -] 0.2 0.82 [+ or -] 0.09 2 6.1 [+ or -] 1.6 0.90 [+ or -]0.12 4 7.2 [+ or -] 1.4 1.08 [+ or -] 0.06 6 7.5 [+ or -] 0.8 1.23 [+ or -] 0.10 8 5.2 [+ or -] 1.3 1.24 [+ or -] 0.07 10 6.6 [+ or -] 1.1 1.28 [+ or -] 0.10 BCP (wt%) [G.sub.lc] (J/[m.sup.2]) [DELTA][K.sub.Ic] (Mpa[square root of m]) 0 133.0 [+ or -] 32.0 0.39 [+ or -] 0.01 0.5 185.6 [+ or -] 54.9 / 1 235.2 [+ or -] 70.2 / 2 284.5 [+ or -] 103.1 0.59 [+ or -] 0.01 4 417.3 [+ or -] 61.4 / 6 580.4 [+ or -] 115.7 0.80 [+ or -] 0.01 8 627.7 [+ or -] 96.0 0.85 [+ or -] 0.04 10 684.5 [+ or -] 133.8 0.91 [+ or -] 0.01 BCP (wt%) [T.sub.g] ([degrees]C) 0 175 0.5 / 1 / 2 183 4 / 6 182 8 / 10 181
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|Author:||Klingler, Andreas; Wetzel, Bernd|
|Publication:||Polymer Engineering and Science|
|Date:||Jun 1, 2017|
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