The introduction, originally in 2009, by the FAA of a ‘slow growth’ approach to the certification of polymer-matrix fibre composites has focused attention on the experimental data and the analytical tools needed to assess the growth of delaminations under cyclic-fatigue loads. Of direct relevance is the fact that fatigue tests on aircraft composite components and structures reveal that no, or only little, retardation of the fatigue crack growth (FCG) rate occurs as delamination/impact damage grows. Therefore, of course, the FCG data that are ascertained in laboratory tests, and then employed as a material-allowable property to design and life the structure, as well as for the development, characterisation and comparison of composite materials, must also exhibit no, or only minimal, retardation. Now, in laboratory tests the double-cantilever beam (DCB) test, using a typical carbon-fibre reinforced-plastic (CFRP) aerospace composite, is usually employed to obtain fracture-mechanics data under cyclic-fatigue Mode I loading. However, it is extremely difficult to perform such DCB fatigue tests without extensive fibre-bridging developing across the crack faces. This fibre-bridging leads to significant retardation of the FCG rate. Such fibre-bridging, and hence retardation of the FCG, is seen to arise even for the smallest values of the pre-crack extension length, ap − a0, that are typically employed. The results from the DCB tests also invariably exhibit a relatively large degree of inherent scatter. Thus, a methodology is proposed for predicting an ‘upper-bound’ FCG curve from the laboratory test data which is representative of a composite laminate exhibiting no, or only very little, retardation of the FCG rate under fatigue loading and which takes into account the inherent scatter. To achieve this we have employed a novel methodology, based on using a variant of the Hartman-Schijve equation, to access this ‘upper-bound’ FCG rate curve, which may be thought of as a material-allowable property and which is obtained using an ‘A basis’ statistical approach. Therefore, a conservative ‘upper-bound’ FCG curve may now be calculated from the DCB laboratory test data for material development, characterisation and comparative studies, and for design and lifing studies.@en

Silica nanoparticles possessing three different diameters (23, 74 and 170 nm) were used to modify a piperidine-cured epoxy polymer. Fracture tests were performed and values of the toughness increased steadily as the concentration of silica nanoparticles was increased. However, no significant effects of particle size were found on the measured value of toughness. The toughening mechanisms were identified as (i) the formation of localised shear-band yielding in the epoxy matrix polymer which is initiated by the silica nanoparticles, and (ii) debonding of the silica nanoparticles followed by plastic void growth of the epoxy matrix polymer. These mechanisms, and hence the toughness of the epoxy polymers containing the silica nanoparticles, were modelled using the Hsieh et al. approach (Polymer 51, 2010, 6284-6294). However, it is noteworthy that previous modelling work has required the volume fraction of debonded silica particles to be measured from the fracture surfaces but in the present paper a new and more fundamental approach has been proposed. Here finite-element modelling has demonstrated that once one silica nanoparticle debonds then its nearest neighbours are shielded from the applied stress field, and hence may not debond. Statistical analysis showed that, for a good, i.e. random, dispersion of nanoparticles, each nanoparticle has six nearest neighbours, so only one in seven particles would be predicted to debond. This approach therefore predicts that only 14.3% of the nanoparticles present will debond, and this value is in excellent agreement with the value of 10-15% of those nanoparticles present debonding which was recorded via direct observations of the fracture surfaces. Further, this value of about 15% of silica nanoparticles particles present debonding has also been noted in other published studies, but has never been previously explained. The predictions from the modelling studies of the toughness of the various epoxy polymers containing the silica nanoparticles were compared with the measured fracture energies and the agreement was found to be good.@en

Silica nanoparticles possessing three different diameters (23, 74 and 170 nm) were used to modify a piperidine-cured epoxy polymer. Fracture tests were performed and values of the toughness increased steadily as the concentration of silica nanoparticles was increased. However, no significant effects of particle size were found on the measured value of toughness. The toughening mechanisms were identified as (i) the formation of localised shear-band yielding in the epoxy matrix polymer which is initiated by the silica nanoparticles, and (ii) debonding of the silica nanoparticles followed by plastic void growth of the epoxy matrix polymer. These mechanisms, and hence the toughness of the epoxy polymers containing the silica nanoparticles, were modelled using the Hsieh et al. approach (Polymer 51, 2010, 6284-6294). However, it is noteworthy that previous modelling work has required the volume fraction of debonded silica particles to be measured from the fracture surfaces but in the present paper a new and more fundamental approach has been proposed. Here finite-element modelling has demonstrated that once one silica nanoparticle debonds then its nearest neighbours are shielded from the applied stress field, and hence may not debond. Statistical analysis showed that, for a good, i.e. random, dispersion of nanoparticles, each nanoparticle has six nearest neighbours, so only one in seven particles would be predicted to debond. This approach therefore predicts that only 14.3% of the nanoparticles present will debond, and this value is in excellent agreement with the value of 10-15% of those nanoparticles present debonding which was recorded via direct observations of the fracture surfaces. Further, this value of about 15% of silica nanoparticles particles present debonding has also been noted in other published studies, but has never been previously explained. The predictions from the modelling studies of the toughness of the various epoxy polymers containing the silica nanoparticles were compared with the measured fracture energies and the agreement was found to be good.@en

The present paper considers the general mechanical, fracture and cyclic-fatigue properties of four different epoxy polymers containing various concentrations of well-dispersed silica nanoparticles. Firstly, it was found that, for any given epoxy polymer, their Youngs modulus steadily increased as the volume fraction, vf, of the silica nanoparticles was increased. Modelling studies showed that the measured moduli of the different silica-nanoparticle filled epoxy-polymers lay between upper-bound values set by the Halpin-Tsai and the Nielsen no-slip models, and lower-bound values set by the Nielsen slip model; with the last model being the more accurate at relatively high values of vf. Secondly, the presence of silica nanoparticles always led to an increase in the toughness of the epoxy polymer. However, to what extent a given epoxy polymer could be so toughened was related to structure/property relationships which were governed by (a) the values of glass transition temperature, Tg, and molecular weight, M c, between cross-links of the epoxy polymer, and (b) the adhesion acting at the silica-nanoparticle/epoxy-polymer interface. Thirdly, the two toughening mechanisms which were operative in the epoxy polymers containing silica nanoparticles were identified to be (a) localised shear-bands initiated by the stress concentrations around the periphery of the silica nanoparticles, and (b) debonding of the silica nanoparticles followed by subsequent plastic void-growth of the epoxy polymer. Fourthly, for one formulation the cyclic-fatigue properties have been studied and a significant improvement was found to arise from the addition of the silica nanoparticles. Finally, the toughening mechanisms have been quantitatively modelled and there was good agreement between the experimentally measured values and the predicted values of the fracture energy, Gc, for all the epoxy polymers modified by the presence of silica nanoparticles. The modelling studies have emphasised the important roles of the stress versus strain behaviour of the epoxy polymer and the silicananoparticle/ epoxy-polymer interfacial adhesion in influencing the extent of the two toughening mechanisms, and hence the overall fracture energy, Gc, of the nanoparticle-filled polymers.@en

Epoxy matrix fibre composites have been modified with the addition of rubber and nanosilica particles. Fracture studies conducted on the bulk matrix and composite show a synergistic effect between the nanosilica and rubber, resulting in a 50% increase in bulk fracture energy in an anhydride cured system.@en

Epoxy matrix fibre composites have been modified with the addition of rubber and nanosilica particles. Fracture studies conducted on the bulk matrix and composite show a synergistic effect between the nanosilica and rubber, resulting in a 50% increase in bulk fracture energy in an anhydride cured system.@en

An epoxy resin, cured with an anhydride, has been modified by the addition of silica nanoparticles. The particles were introduced via a sol-gel technique which gave a very well dispersed phase of nanosilica particles, which were about 20 nm in diameter, in the thermosetting epoxy polymer matrix. The glass transition temperature of the epoxy polymer was unchanged by the addition of the nanoparticles, but both the modulus and toughness were increased. The fracture energy increased from 77 J/m 2 for the unmodified epoxy to 212 J/m 2 for the epoxy polymer containing 20 wt.% of nanosilica. The fracture surfaces were inspected using scanning electron and atomic force microscopy, and these microscopy studies showed that the silica nanoparticles (a) initiated localised plastic shear-yield deformation bands in the epoxy polymer matrix and (b) debonded and allowed subsequent plastic void-growth of the epoxy polymer matrix. A theoretical model for these toughening micromechanisms has been proposed to confirm that these micromechanisms were indeed responsible for the increased toughness that was observed due to the presence of the silica nanoparticles in the epoxy polymer.@en

The present paper investigates the effect of adding silica nanoparticles to an anhydride-cured epoxy polymer. The formation of 'hybrid' epoxy polymers, containing both silica nanoparticles and carboxyl-Terminated butadiene-Acrylonitrile (CTBNrubber microparticles, is also discussed. The structure/property relationships are considered, with an emphasis on the toughness and the toughening mechanisms. The present work also extends an existing model to predict the toughening effect of the nanoparticles in a thermoset polymer. There was excellent agreement between the predictions and the experimental data for the epoxy containing the silica nanoparticles.@en

The present paper investigates the effect of adding silica nanoparticles to an anhydride-cured epoxy polymer. The formation of 'hybrid' epoxy polymers, containing both silica nanoparticles and carboxyl-Terminated butadiene-Acrylonitrile (CTBNrubber microparticles, is also discussed. The structure/property relationships are considered, with an emphasis on the toughness and the toughening mechanisms. The present work also extends an existing model to predict the toughening effect of the nanoparticles in a thermoset polymer. There was excellent agreement between the predictions and the experimental data for the epoxy containing the silica nanoparticles.@en

The present paper investigates the effect of adding silica nanoparticles to an anhydride-cured epoxy polymer. The formation of 'hybrid' epoxy polymers, containing both silica nanoparticles and carboxyl-Terminated butadiene-Acrylonitrile (CTBNrubber microparticles, is also discussed. The structure/property relationships are considered, with an emphasis on the toughness and the toughening mechanisms. The present work also extends an existing model to predict the toughening effect of the nanoparticles in a thermoset polymer. There was excellent agreement between the predictions and the experimental data for the epoxy containing the silica nanoparticles.@en

The present paper investigates the effect of adding silica nanoparticles to an anhydride-cured epoxy polymer. The formation of 'hybrid' epoxy polymers, containing both silica nanoparticles and carboxyl-Terminated butadiene-Acrylonitrile (CTBNrubber microparticles, is also discussed. The structure/property relationships are considered, with an emphasis on the toughness and the toughening mechanisms. The present work also extends an existing model to predict the toughening effect of the nanoparticles in a thermoset polymer. There was excellent agreement between the predictions and the experimental data for the epoxy containing the silica nanoparticles.@en

The present paper investigates the effect of adding silica nanoparticles to an anhydride-cured epoxy polymer. The formation of 'hybrid' epoxy polymers, containing both silica nanoparticles and carboxyl-Terminated butadiene-Acrylonitrile (CTBNrubber microparticles, is also discussed. The structure/property relationships are considered, with an emphasis on the toughness and the toughening mechanisms. The present work also extends an existing model to predict the toughening effect of the nanoparticles in a thermoset polymer. There was excellent agreement between the predictions and the experimental data for the epoxy containing the silica nanoparticles.@en

The present paper investigates the effect of adding silica nanoparticles to an anhydride-cured epoxy polymer. The formation of 'hybrid' epoxy polymers, containing both silica nanoparticles and carboxyl-Terminated butadiene-Acrylonitrile (CTBNrubber microparticles, is also discussed. The structure/property relationships are considered, with an emphasis on the toughness and the toughening mechanisms. The present work also extends an existing model to predict the toughening effect of the nanoparticles in a thermoset polymer. There was excellent agreement between the predictions and the experimental data for the epoxy containing the silica nanoparticles.@en

The present paper considers the mechanical and fracture properties of four different epoxy polymers containing 0, 10 and 20wt.% of well-dispersed silica nanoparticles. Firstly, it was found that, for any given epoxy polymer, their Young's modulus steadily increased as the volume fraction, vf, of the silica nanoparticles was increased. Modelling studies showed that the measured moduli of the different silica-nanoparticle filled epoxy polymers lay between upper-bound values set by the Halpin-Tsai and the Nielsen 'no-slip' models, and lower-bound values set by the Nielsen 'slip' model; with the last model being the more accurate at relatively high values of vf. Secondly, the presence of silica nanoparticles always led to an increase in the toughness of the epoxy polymer. However, to what extent a given epoxy polymer could be so toughened was related to structure/property relationships which were governed by (a) the values of glass transition temperature, Tg, and molecular weight, Mc, between cross-links of the epoxy polymer, and (b) the adhesion acting at the silica nanoparticle/epoxy-polymer interface. Thirdly, the two toughening mechanisms which were operative in all the epoxy polymers containing silica nanoparticles were identified to be (a) localised shear bands initiated by the stress concentrations around the periphery of the silica nanoparticles, and (b) debonding of the silica nanoparticles followed by subsequent plastic void growth of the epoxy polymer. Finally, the toughening mechanisms have been quantitatively modelled and there was good agreement between the experimentally-measured values and the predicted values of the fracture energy, Gc, for all the epoxy polymers modified by the presence of silica nanoparticles. The modelling studies have emphasised the important roles of the stress versus strain behaviour of the epoxy polymer and the silica nanoparticle/epoxy-polymer interfacial adhesion in influencing the extent of the two toughening mechanisms, and hence the overall fracture energy, Gc, of the nanoparticle-filled polymers.@en

The present paper considers the mechanical and fracture properties of four different epoxy polymers containing 0, 10 and 20wt.% of well-dispersed silica nanoparticles. Firstly, it was found that, for any given epoxy polymer, their Young's modulus steadily increased as the volume fraction, vf, of the silica nanoparticles was increased. Modelling studies showed that the measured moduli of the different silica-nanoparticle filled epoxy polymers lay between upper-bound values set by the Halpin-Tsai and the Nielsen 'no-slip' models, and lower-bound values set by the Nielsen 'slip' model; with the last model being the more accurate at relatively high values of vf. Secondly, the presence of silica nanoparticles always led to an increase in the toughness of the epoxy polymer. However, to what extent a given epoxy polymer could be so toughened was related to structure/property relationships which were governed by (a) the values of glass transition temperature, Tg, and molecular weight, Mc, between cross-links of the epoxy polymer, and (b) the adhesion acting at the silica nanoparticle/epoxy-polymer interface. Thirdly, the two toughening mechanisms which were operative in all the epoxy polymers containing silica nanoparticles were identified to be (a) localised shear bands initiated by the stress concentrations around the periphery of the silica nanoparticles, and (b) debonding of the silica nanoparticles followed by subsequent plastic void growth of the epoxy polymer. Finally, the toughening mechanisms have been quantitatively modelled and there was good agreement between the experimentally-measured values and the predicted values of the fracture energy, Gc, for all the epoxy polymers modified by the presence of silica nanoparticles. The modelling studies have emphasised the important roles of the stress versus strain behaviour of the epoxy polymer and the silica nanoparticle/epoxy-polymer interfacial adhesion in influencing the extent of the two toughening mechanisms, and hence the overall fracture energy, Gc, of the nanoparticle-filled polymers.@en

The present paper considers the mechanical and fracture properties of four different epoxy polymers containing 0, 10 and 20wt.% of well-dispersed silica nanoparticles. Firstly, it was found that, for any given epoxy polymer, their Young's modulus steadily increased as the volume fraction, vf, of the silica nanoparticles was increased. Modelling studies showed that the measured moduli of the different silica-nanoparticle filled epoxy polymers lay between upper-bound values set by the Halpin-Tsai and the Nielsen 'no-slip' models, and lower-bound values set by the Nielsen 'slip' model; with the last model being the more accurate at relatively high values of vf. Secondly, the presence of silica nanoparticles always led to an increase in the toughness of the epoxy polymer. However, to what extent a given epoxy polymer could be so toughened was related to structure/property relationships which were governed by (a) the values of glass transition temperature, Tg, and molecular weight, Mc, between cross-links of the epoxy polymer, and (b) the adhesion acting at the silica nanoparticle/epoxy-polymer interface. Thirdly, the two toughening mechanisms which were operative in all the epoxy polymers containing silica nanoparticles were identified to be (a) localised shear bands initiated by the stress concentrations around the periphery of the silica nanoparticles, and (b) debonding of the silica nanoparticles followed by subsequent plastic void growth of the epoxy polymer. Finally, the toughening mechanisms have been quantitatively modelled and there was good agreement between the experimentally-measured values and the predicted values of the fracture energy, Gc, for all the epoxy polymers modified by the presence of silica nanoparticles. The modelling studies have emphasised the important roles of the stress versus strain behaviour of the epoxy polymer and the silica nanoparticle/epoxy-polymer interfacial adhesion in influencing the extent of the two toughening mechanisms, and hence the overall fracture energy, Gc, of the nanoparticle-filled polymers.@en

The present paper considers the mechanical and fracture properties of four different epoxy polymers containing 0, 10 and 20wt.% of well-dispersed silica nanoparticles. Firstly, it was found that, for any given epoxy polymer, their Young's modulus steadily increased as the volume fraction, vf, of the silica nanoparticles was increased. Modelling studies showed that the measured moduli of the different silica-nanoparticle filled epoxy polymers lay between upper-bound values set by the Halpin-Tsai and the Nielsen 'no-slip' models, and lower-bound values set by the Nielsen 'slip' model; with the last model being the more accurate at relatively high values of vf. Secondly, the presence of silica nanoparticles always led to an increase in the toughness of the epoxy polymer. However, to what extent a given epoxy polymer could be so toughened was related to structure/property relationships which were governed by (a) the values of glass transition temperature, Tg, and molecular weight, Mc, between cross-links of the epoxy polymer, and (b) the adhesion acting at the silica nanoparticle/epoxy-polymer interface. Thirdly, the two toughening mechanisms which were operative in all the epoxy polymers containing silica nanoparticles were identified to be (a) localised shear bands initiated by the stress concentrations around the periphery of the silica nanoparticles, and (b) debonding of the silica nanoparticles followed by subsequent plastic void growth of the epoxy polymer. Finally, the toughening mechanisms have been quantitatively modelled and there was good agreement between the experimentally-measured values and the predicted values of the fracture energy, Gc, for all the epoxy polymers modified by the presence of silica nanoparticles. The modelling studies have emphasised the important roles of the stress versus strain behaviour of the epoxy polymer and the silica nanoparticle/epoxy-polymer interfacial adhesion in influencing the extent of the two toughening mechanisms, and hence the overall fracture energy, Gc, of the nanoparticle-filled polymers.@en

The present paper considers the mechanical and fracture properties of four different epoxy polymers containing 0, 10 and 20wt.% of well-dispersed silica nanoparticles. Firstly, it was found that, for any given epoxy polymer, their Young's modulus steadily increased as the volume fraction, vf, of the silica nanoparticles was increased. Modelling studies showed that the measured moduli of the different silica-nanoparticle filled epoxy polymers lay between upper-bound values set by the Halpin-Tsai and the Nielsen 'no-slip' models, and lower-bound values set by the Nielsen 'slip' model; with the last model being the more accurate at relatively high values of vf. Secondly, the presence of silica nanoparticles always led to an increase in the toughness of the epoxy polymer. However, to what extent a given epoxy polymer could be so toughened was related to structure/property relationships which were governed by (a) the values of glass transition temperature, Tg, and molecular weight, Mc, between cross-links of the epoxy polymer, and (b) the adhesion acting at the silica nanoparticle/epoxy-polymer interface. Thirdly, the two toughening mechanisms which were operative in all the epoxy polymers containing silica nanoparticles were identified to be (a) localised shear bands initiated by the stress concentrations around the periphery of the silica nanoparticles, and (b) debonding of the silica nanoparticles followed by subsequent plastic void growth of the epoxy polymer. Finally, the toughening mechanisms have been quantitatively modelled and there was good agreement between the experimentally-measured values and the predicted values of the fracture energy, Gc, for all the epoxy polymers modified by the presence of silica nanoparticles. The modelling studies have emphasised the important roles of the stress versus strain behaviour of the epoxy polymer and the silica nanoparticle/epoxy-polymer interfacial adhesion in influencing the extent of the two toughening mechanisms, and hence the overall fracture energy, Gc, of the nanoparticle-filled polymers.@en

The present paper concentrates on the effect of adding silica nanoparticles to epoxy polymers, which are the basis of modern structural adhesives. The formation of 'hybrid' epoxy polymers, containing both silica nanoparticles and carboxyl-terminated butadiene-acrylonitrile (CTBN) rubber microparticles, is also discussed. The structure/property relationships are considered, with an emphasis on the toughness and the toughening mechanisms.@en