Fracture and toughening mechanisms of silica- and core–shell rubber-toughened epoxy at ambient and low temperature

A Young’s modulus of 3.14 GPa was measured for the control epoxy (Table 2), which is identical to the value reported by Masania et al. [38] for this epoxy polymer.

When silica nanoparticles were added to the epoxy, the modulus generally increased with the increased amount of particles added in (Table 2). This is as expected because silica has a much higher modulus, of 70 GPa [39], compared to that of the epoxy (3.14 GPa). The significance of the increases in modulus will be discussed with the results of the analytical modelling in the “Tensile modulus prediction” section. Tensile strength information is given in Table 3, and shows that the tensile strength is independent of the silica nanoparticle wt%, as expected due to the small size of the particles.

The addition of CSR particles increased the Young’s modulus of the epoxy up to 5 wt%, where a value of 3.90 GPa was measured (Table 2). It may be expected that the addition of the CSR particles would reduce the Young’s modulus of the specimens, because the rubber core will have a much lower modulus than that of the epoxy. However, the small increases in the modulus values indicate that the PMMA shell has a higher modulus compared to the epoxy and this causes the overall increase.

There was a significant reduction in the modulus value when the concentration of CSR was increased from 5 wt% to 10 wt%. This is due to agglomeration of the CSR particles, as could be seen on the fracture surfaces, which had a different appearance compared to the other wt% of CSR, and as will be discussed below with the results from the SEM imaging (“Core–shell rubber-modified epoxy” section). This indicates that the optimum concentration of CSR particles is below 10 wt%. The tensile strength (Table 3) reduces with increasing wt% of CSR due to the relatively large size of the particles, which act as defects and cause premature failure of the epoxy.

The hybrids containing equal wt% of silica and core–shell rubber particles did not show significant changes in their tensile properties compared to the addition of silica only (Table 2). The increases were within the experimental error, confirming that the addition of CSR only gives a relatively small increase in modulus due to the presence of the PMMA shells. The use of 10 wt% of CSR in the hybrid gave a decrease in the modulus, which is likely to be due to agglomeration as for the epoxy with 10 wt% of CSR only.

For the control epoxy, a fracture energy of G_c = 68 J/m² was measured using SENB tests at room temperature (Table 4). This agrees within experimental error with the value of 77 J/m² quoted in the literature for this epoxy by Hsieh et al. [21]. This confirms that the unmodified epoxy is very brittle.

When the 20-nm silica nanoparticles were added to the epoxy, there was an approximately linear increase in fracture energy as the wt% of silica increases up to 15 wt% (Table 4). However, at low silica contents, the increase in fracture energy is greater than linear, indicating that the silica nanoparticles are more effective at toughening at low contents. The significant increase at low silica content is of interest, as this has not been reported in previous work where the smallest content of silica nanoparticles used was 4 wt%, e.g. [21, 37, 40], and this will be discussed further with the results of the predictive modelling. At 15 wt% of silica and above, the fracture energy values reach a plateau at approximately 220 J/m² (Fig. 1). These values agree well with those quoted in the literature [21, 37].

The addition of CSR particles to the epoxy gives a small increase in fracture energy to 96 J/m² (Table 4). However, there is a notable plateau as the fracture energy barely increases when the wt% of CSR particles is increased, and a maximum fracture energy of 108 J/m² was measured using 10 wt% of CSR (Fig. 2). Thus, the increases in fracture energy values for the intermediate wt% of CSR were not significant. Some agglomeration of the CSR particles occurs, which may reduce the toughening effect.

The CSR particles are not individual particles but are aggregates of much smaller particles (of about 300 nm in diameter). As these particles are relatively small, they will be relatively difficult to cavitate [41]. If they are poorly bonded to other particles in the aggregate, then the triaxial stresses within the plastic zone may be insufficient to cause cavitation and hence some of the potential toughening mechanisms are not activated. The small particles are not surrounded by epoxy, so the toughening mechanisms which rely on deformation of the epoxy can be expected to not be fully operative. Thus, the toughening effect is smaller than might be expected for core–shell rubber particles.

There was a steady increase in fracture energy when the wt% of silica/CSR particles added into the epoxy increases (Fig. 3). The hybrid with 10 wt% of silica and CSR particles showed the largest improvement in fracture energy, but no synergy was found, i.e. there was no extra increase due to the addition of both types of particles. The agglomeration observed for the CSR-modified epoxies was also seen for the silica/CSR hybrid specimens, and this could explain why no synergy occurs. Indeed, the hybrids show similar fracture properties as when using one type of particle and this suggests that this combination of particles does not have a significant effect in improving the fracture energy of the epoxy.

The low-temperature SENB tests gave higher fracture energy values than at room temperature for the unmodified epoxy, and the values were higher when the temperature was lower; see Figs. 1, 2 and 3. At room temperature, an average fracture energy of 68 J/m² was measured, increasing to 93 J/m² at − 40 °C and 126 J/m² at − 80 °C.

For the silica-modified epoxy, the results of the low-temperature SENB tests are shown in Fig. 1. There was a significant increase in the measured fracture energy at all wt% of silica when tested at − 80 °C compared to the room-temperature tests. The increase was more significant with a high wt% of silica nanoparticles, as a nearly 50% increase in fracture energy was measured (e.g. for 25.4 wt% of silica the room-temperature fracture energy is 223 J/m², compared with 349 J/m² at − 80 °C). At − 40 °C, there was no significant difference in the fracture energies compared to the room-temperature values (Fig. 1) as the standard deviations overlap.

The results of the low-temperature SENB tests of the CSR-modified epoxy are shown in Fig. 2. The fracture energy is approximately doubled for most of the specimens tested at − 80 °C when compared to the room-temperature tests. There was an increasing trend in fracture energy when the wt% of particles increased. This trend was also seen for the tests performed at − 40 °C, but the fracture energy values were very similar to the room-temperature results for all wt%. There was a plateau when the wt% of CSR particles added in was high (at 10 wt%). This suggests that the high wt% use of CSR is not the optimum for toughening and that using a medium-to-lower wt% (2–5 wt%) would be most appropriate, as increasing the wt% further has no additional toughening effect. This indicates that the agglomeration which occurs at 10 wt% also influences the G_c value.

The trend for an increase in fracture energy with increase in wt% of particles used was notable in the hybrid silica/CSR specimens for all temperature conditions (Fig. 3). However, the magnitude of the increase in fracture energy for the low-temperature tests was not as significant as with the use of only one type of particle. The fracture energy values were similar to those using CSR only, which were smaller than the silica results. The optimum amount of hybrid particles at low temperature is 10 wt% (i.e. 10 wt% of CSR plus 10 wt% of silica), as this concentration gave the highest fracture energy.

At room temperature, the fracture energy increases with the increase in wt% of particles, and no synergy was found with the use of hybrid silica/CSR particles.

At low temperature, the lower temperature (− 80 °C) gave higher fracture energy values for most specimens. This trend of increasing fracture energy with increasing wt% of particles is clearer and more significant when compared to room-temperature results. This showed that the effect of toughening was more significant when the materials experienced more brittle failure at lower temperatures [31, 42, 43].

The measured fracture energies are compared with analytical modelling predictions [21, 37, 44] in the “Analytical modelling” section.

The fracture surfaces of the SENB unmodified epoxy specimens tested at room temperature were compared with the low-temperature fracture surfaces, and no significant differences were found between the different conditions. The surfaces were relatively smooth, with river lines parallel to the direction of local crack propagation, indicating that little energy is absorbed during fracture. A scanning electron microscope image of the fracture surface of the unmodified epoxy at room temperature is shown in Fig. 4.

SEM images of the fracture surfaces of the silica-modified epoxy are shown in Fig. 5. Individual silica nanoparticles can be seen, and some possible voids can also be found in some images; see Fig. 5c for example. With silica particles of 20 nm in diameter, the voids formed by debonding of the epoxy from the silica followed by plastic void growth would be expected to be about 35 nm in diameter. This is because the void will grow until the circumferential strain is equal to the strain to failure measures from plane strain compression tests. Thus, the void grows until the void diameter = particle diameter x (1 + strain to failure), where the strain to failure measured in plane strain compression is 0.75 [21]. The smallest voids found in Fig. 4a were 33 nm in diameter, indicating that the observed voids were formed by debonding and void growth.

Similar results were found for the samples containing 5, 10, 15 and 25.4 wt% of silica nanoparticles. Some particles can be seen on the fracture surfaces, with some debonding and void growth of particles (Fig. 5a–c). When the wt% of particles was low, the surfaces appear relatively brittle and smooth as expected due to the low toughness. When the wt% of particles used was high, more particles can be seen on the fracture surfaces. The particles initiate toughening mechanisms and hence increase the roughness of the surface, so at high wt% the surfaces become very rough.

SEM images of the fracture surfaces of the CSR-modified epoxies are shown in Fig. 6. The CSR particles were distinct from the epoxy matrix at low wt%, as the epoxy is smooth and brittle and the CSR particle aggregates appear as light-coloured rough patches through which the crack propagates. At high wt%, the surface becomes much rougher and it is harder to distinguish the matrix from the CSR particle aggregates. Some agglomeration of the CSR particles can be seen on the fracture surfaces; see Fig. 6b for example.

The CSR particles are aggregates, typically 50 μm in diameter, of small CSR particles which are about 300 nm in diameter, as shown at higher magnification in Fig. 7. These small (primary) CSR particles cavitated during fracture to leave a void within the shell, as indicated by the dark circles within the light rings in Fig. 7b.

The aggregates of CSR particles were not observed to debond from the epoxy matrix, as no dark ring that would indicate a cavity formed by debonding was present around the aggregates; see Figs. 6 and 7a. Although the aggregates are much larger than the diameter of the plastic zone, evidence of toughening mechanisms such as crack pinning or crack deflection was not observed on the fracture surfaces as the crack propagated through the aggregates.

SEM images of fracture surfaces of the silica/CSR hybrid-modified epoxy are shown in Fig. 8, and a higher-magnification image is shown in Fig. 9. The agglomerates of CSR particles can be readily identified in the silica/CSR hybrid-modified epoxy images, but it is much harder to identify the silica nanoparticles due to their small size and the roughness of the fracture surfaces. River lines are present on the surfaces (see Fig. 8b for example) which are typical for crack propagation in brittle polymers due to the crack being slowed when it propagates through an aggregate of CSR particles.

The main toughening mechanisms identified using SEM in the silica-modified epoxy were debonding of the silica nanoparticles and subsequent void growth of the epoxy polymer. For the CSR-modified epoxy, particle cavitation was the main toughening mechanism, followed by void growth of the epoxy. A synergy effect was not found with the addition of silica/CSR hybrid particles, but the toughening mechanisms identified for the single particle-modified epoxies were also observed for the hybrids. Shear band yielding has been observed extensively in previous studies [21, 38, 45] using this epoxy and with the addition of the same silica nanoparticles, so it can be readily concluded that shear band yielding will also occur in the present work.

The Halpin–Tsai model predicts the modulus, E, of a particle-modified material using [46]:where E_u is the Young’s modulus of the matrix, v_f is the volume fraction of particles, ζ is the Halpin–Tsai geometry factor, which is equal to 2 for spherical particles [21, 26, 37], and η can be written as:where E_p is the modulus of the particles (70 GPa for the silica nanoparticles) and E_u is the modulus of the unmodified epoxy (3.14 GPa, as measured in the present work). The hybrid-modified epoxy predictions assume that the modulus for the hybrid-modified epoxy is equal to the sum of the increases due to the addition of each particle type.

The predicted modulus values of the silica-modified epoxies are shown in Fig. 10. Most of the predicted modulus values agree very closely to the measured values. There was a linear increase in modulus in the predictions when the wt% of silica nanoparticles increased, and the gradient of the linear increase was very similar to that measured experimentally. This shows that the Halpin–Tsai model works well for the silica-modified epoxy. It also confirms that the assumption that the modulus of the silica nanoparticles is equal to that of bulk silica (i.e. E_p = 70 GPa) [39] is reasonable.

As the effective modulus of the CSR particles is unknown, this value was back-calculated from fitting to the experimental results at low CSR contents, and a value of E_p = 8.0 GPa was obtained. The predicted modulus values of the CSR-modified epoxy are shown in Fig. 11. The agreement becomes poor when the wt% of particles is increased, and there is a reduction in the measured modulus at 10 wt% of CSR, which is due to clustering of the particles. (Note that 10 wt% was the highest possible wt% of CSR that can be added to the resin as the viscosity became too high at larger CSR contents.) The predicted value suggests that a higher modulus could be obtained with a better distribution of particles at 10 wt% CSR.

Although the rubber core of the CSR particles will have a low modulus when compared to the epoxy, the modulus of the CSR-modified epoxy increases with wt%. This indicates that a stiffer shell is present, and the PMMA shell of the CSR particles has a modulus higher than that of the epoxy.

The predicted modulus values for the silica/CSR hybrid-modified epoxy are shown in Fig. 12. The hybrid predictions were made by adding the modulus increase contributed from the predictions for each of the two particle types. A similar pattern of results was found in the hybrid-modified epoxy predictions compared to the individual particles when compared to the experimental results, with reasonable agreement at low particle contents. There is also a drop in the modulus for the 10 wt% silica/CSR hybrid specimens, as was observed for the 10 wt% CSR specimens due to the presence of agglomerates.

The predicted modulus values generally agreed extremely well with the experimental findings. The silica-modified epoxy predictions agreed best with the experimental results. The modulus of the CSR-modified epoxy was expected to be lower than the modulus of the unmodified epoxy, because the modulus of rubber is lower than epoxy. However, the PMMA shell of the CSR particles increases the modulus, and hence slightly increased modulus values were found for the CSR-modified epoxy. This pattern continues for the silica/CSR hybrid-modified epoxy. Where a drop in the modulus was measured, when using 10 wt% of CSR, this was observed to be due to clustering of the particles.

The fracture energies of the modified epoxies can be predicted using the Huang and Kinloch model, which considers that the contributions from the various toughening mechanisms can be added to the fracture energy of the unmodified epoxy. The overall fracture energy can be written [47] as:where G_u is the fracture energy of the unmodified epoxy and Ψ is the sum of the overall toughening contributions from the particles.

Considering the toughening mechanisms, shear band yielding occurs when particles are added to this epoxy, as shown by Hsieh et al. [21]. This is the case for both the silica nanoparticles and the core–shell rubber particles. For rubber-modified epoxies, the rubber particles may cavitate to create voids, which then increase in diameter by plastic deformation of the epoxy [48]. For silica-modified epoxies, the particles can debond to create voids, which then grow by plastic deformation of the epoxy [49]. These processes absorb energy and hence increase the toughness.

There will be a contribution to Ψ from each of the identified toughening mechanisms. The increase in fracture energy due to shear banding is ΔG_s, the contribution from debonding (or cavitation) of particles is ΔG_db, and that from plastic void growth is ΔG_v [50]. Hence:

Debonding occurs for hard particles, while cavitation occurs for soft particles [37], but both processes create a void which is then able to grow. However, it has been shown that debonding or cavitation does not contribute significantly to the energy absorption [37] and hence can be ignored, i.e. ΔG_db = 0 J/m². Therefore, Eq. 7 becomes [47]:

The contributions of shear band yielding and void growth can be calculated using the equations [47, 50] below.

The fracture energy contribution of shear band yielding, ΔG_s, is given [37, 47] by:where v_f is the volume fraction of particles, σ_ycu is the compressive yield stress, γ_fu is the compressive failure strain of the unmodified polymer (measured from plane strain compression tests) and [47, 50]:where r_p is the radius of the particles, and the radius of the plastic zone, r_y, is given by:where K_sp is the maximum stress concentration around a particle, µ_m = 0.2 is a material constant, and r_pzu is the radius of plastic deformation zone of the unmodified epoxy, as discussed below. The value of K_sp is a function of the volume fraction of particles, v_f, and can be expressed [37] as:

The values of the compressive yield stress, σ_ycu, and the compressive failure strain, γ_fu, are taken from Hsieh et al. [21] (Table 5).

The fracture energy contribution from plastic void growth, ΔG_v, is given [37, 47] by:where v_fv is the volume fraction of voids, v_f is the volume fraction of particles, µ_m is a material constant, σ_ycu is the compressive yield stress of the unmodified polymer and r_pzu is the radius of plastic zone at fracture. The stress concentration factor for voids, K_v, depends on the volume fraction of particles, v_f, and can be expressed [37] as:

The values required for the modelling are quoted in Table 5.

It has been reported that generally 100% of the rubber particles cavitate, but cavitation is easier for soft and large particles, so small particles or those with a stiffer rubber core may not cavitate [24].

For silica-modified epoxies, previous work has shown that if debonding does occur, not all of the silica nanoparticles will undergo debonding. Experimental measurements have shown that between 10 and 15% of the silica nanoparticles debond [21, 51]. This has been confirmed by theoretical work by Bray et al. [51] which showed that debonding is highly affected by the distances between particles. This work showed that once a silica particle debonds then its nearest neighbours can no longer debond due to the changes in the stress state around the particles. The theoretical prediction is that only 1/7 of the randomly dispersed nanoparticles would be able to debond [21, 51]. Thus, only 14.3% of the silica nanoparticles will be able to undergo debonding and subsequent void growth.

Three different cases are therefore modelled in the present work:

For the silica-modified epoxy in the present work, the toughening mechanisms of shear band yielding and plastic void growth of the epoxy polymer after particle debonding are expected to result [52].

It is very difficult to measure the volume fraction of voids from SEM of the fracture surfaces, especially for the silica nanoparticles, due to the small diameter of the particles. However, it is possible to predict the void diameter, and hence the volume fraction of voids, v_fv, can be calculated by assuming that a void will grow until the circumferential strain equals the failure strain measured from plane strain compression tests of the unmodified epoxy. The predicted radius of a void is given by [51]:where \( \gamma_{\text{fu}} \) is the failure strain measured in the plane strain compression test and \( r_{\text{p}} \) is the particle radius. This makes the analytical modelling truly predictive. If the volume fraction of voids was measured from the fracture surfaces, then the fracture tests would need to be performed before the modelling can be done, so the results are not properly predictive.

Localised plastic deformation is often the main energy dissipation mechanism in brittle materials. With the use of linear elastic fracture mechanics (LEFM), the radius of the plane strain plastic deformation zone is required for the prediction of the fracture energy using the equations above and can be found from the equations below [53, 54].

For the unmodified epoxy, the radius of the plane strain plastic deformation zone, r_pzu, is given by:where E_u is the modulus, G_cu is the fracture energy, v is the Poisson’s ratio and σ_ytu is the tensile yield stress of the unmodified epoxy.

For the nanoparticle-modified epoxy, the radius of the zone is given by:where \( \mu_{\text{m}} \) is the coefficient of increase in shear yield stress with hydrostatic pressure, which for epoxy is between 0.175 and 0.225. The value of K_vm depends on the volume fraction of particles, v_f, and can be expressed as [55]:

The parameters used in the equations are listed in Table 5.

The fracture energy predictions for the silica-modified epoxy are compared with the measured values in Fig. 13. The 14.3% of void growth with shear predictions agree best with the experimental results when compared with the other assumptions used, which confirms that shear band yielding does occur although it cannot be observed using the scanning electron microscope. Note that the 100% void growth predictions are not shown in Fig. 13 as they greatly overestimate the fracture energy, as expected. The measured values agree very well with those by Hsieh et al. [37]. The predictions from the present work are slightly lower than those from Hsieh et al. due to the lower measured fracture energy of the unmodified epoxy.

The measured increase in fracture energy per wt% of silica added is the greatest at low silica contents, indicating that the silica nanoparticles are most effective at toughening when the well-dispersed particles are surrounded by a significant volume of epoxy which is able to deform plastically and absorb energy. The significant increase at low silica content is of interest, as this has not been reported in previous work where the smallest content of silica nanoparticles used was 4 wt%, e.g. [21, 37, 40]. Fractography has identified the toughening mechanisms for silica-modified epoxy as shear band yielding plus debonding and void growth, supported by finite element modelling which has shown that only 1 in 7 (i.e. 14.3%) of the silica nanoparticles will debond [51]. However, the experimental data lie above the predictions for 14.3% of void growth with shear (Fig. 13), suggesting that when the silica nanoparticles are widely spaced, more than 14.3% may undergo debonding and void growth. Bray et al. [51] calculated that 14.3% of the particles would be expected to undergo debonding when the silica content was high, using 20 wt% of silica for their modelling work. They showed that once one particle debonds, the particles close to the void created would not debond, but that when the particles are well separated debonding will occur, which implies that at low silica contents more (or all) of the silica particles would be expected to debond. Inspection of the relative energies quoted [51] shows that when the epoxy contains 2.5 wt% of silica nanoparticles, the energy required to debond a particle is unaffected by whether other particles have debonded or not. It would therefore be expected that the experimental data for 1 wt% and 2 wt% of silica nanoparticles would agree well with predictions assuming shear band yielding plus debonding and void growth of 100% of the particles. These predictions are shown in Fig. 13, and the agreement is very good. This confirms that at low silica contents all of the particles undergo debonding and void growth, and hence the toughening effect is much more pronounced.

The CSR particles were identified to be composed of aggregates of smaller CSR particles (Fig. 7a), as discussed above. The large aggregates of CSR were not observed to debond from the epoxy matrix, as no dark ring that would indicate a cavity formed by debonding was present around the aggregates; see Figs. 6 and 7a. Indeed, as the large aggregates are approximately 50 μm in diameter they are much larger than the diameter of the plastic zone (which is 5.2 μm for the unmodified epoxy, as calculated using Eq. 16). However, the small CSR particles were observed to undergo cavitation, as shown by the holes within the particle shells on the SEM images of the fracture surfaces. Although void growth may occur, the energy dissipated is relatively low, because the individual CSR primary particles are not surrounded by epoxy polymer and hence the energy dissipated by plastic void growth is much smaller than for well-dispersed particles, e.g. Giannakopoulos et al. [47].

The experimental results show a steep increase in fracture energy when using a small CSR content, and the toughness then remains approximately constant within the experimental error with increasing wt% of CSR. At the higher CSR contents used, the experimental data lie between the predictions for shear band yielding only and those for 14.3% of void growth with shear (Fig. 14). Note that the 100% void growth predictions are not shown in the graph as they are significantly higher than the experimental results. This indicates that the CSR particles are relatively ineffective at toughening, but that some energy is dissipated via the void growth mechanism.

The fracture energy predictions for the silica/CSR hybrid-modified epoxy are shown in Fig. 15. The fracture energy values for the hybrids of silica and CSR were calculated using the sum of the increases in the results of the two particles used, as there was equal wt% of each particle type used in the epoxy. Note that the 100% void growth predictions are not shown in the graph as they are significantly higher than the experimental results. The measured fracture energies are lower than those for the silica-modified epoxy and lie between the predictions for shear band yielding only and those for 14.3% of void growth only (Fig. 15). This indicates that there is no synergy between the particle types for the silica/CSR hybrid-modified epoxy. Indeed, the addition of the CSR particles to the silica-modified epoxy reduces the fracture energy values rather than increasing them. Thus, it can be concluded that the size ratio between the agglomerates of CSR particles and the silica nanoparticles is too large for a synergistic effect, which is seen when micron-sized CTBN particles are used with the silica nanoparticles, as shown in Hsieh et al. [37] and Kinloch et al. [40].

The fracture energy predictions from the Huang and Kinloch model, based on the identified toughening mechanisms, agree well with the experimental results. For the silica-modified epoxy, the predictions for 14.3% of void growth with shear yielding fit best with the experimental results and concur with the previous studies, e.g. [37]. The experimental data for the CSR-modified epoxy were found to lie between the predictions for shear band yielding only and those for 14.3% of void growth with shear, showing that the CSR particles were relatively ineffective. Further, there is no synergy between the particle types for the silica/CSR hybrid-modified epoxy as the size ratio between the agglomerates of CSR particles and the silica nanoparticles appears to be too large for a synergistic effect. For the silica-modified epoxy, the increase in fracture energy per wt% of silica added is the greatest at low silica contents, confirming that more than 14.3% of the particles undergo debonding and void growth at low silica contents, and hence the toughening effect is much more pronounced.