Influence of particle size and particle size distribution on toughening mechanisms in rubber-modified epoxies

The principal toughening mechanism of a substantially toughened, rubber-modified epoxy has again been shown to involve internal cavitation of the rubber particles and the subsequent formation of shear bands. Additional evidence supporting this sequence of events which provides a significant amount of toughness enhancement, is presented. However, in addition to this well-known mechanism, more subtle toughening mechanisms have been found in this work. Evidence for such mechanisms as crack deflection and particle bridging is shown under certain circumstances in rubber-modified epoxies. The occurrence of these toughening mechanisms appears to have a particle size dependence. Relatively large particles provide only a modest increase in fracture toughness by a particle bridging/crack deflection mechanism. In contrast, smaller particles provide a significant increase in toughness by cavitation-induced shear banding. A critical, minimum diameter for particles which act as bridging particles exists and this critical diameter appears to scale with the properties of the neat epoxy. Bimodal mixtures of epoxies containing small and large particles are also examined and no synergistic effects are observed.     

Fatigue of rubber-modified epoxies: effect of particle size and volume fraction

A change in crack-tip plastic zone/rubber particle interactions induces a transition in the fatigue crack propagation (FCP) behaviour of rubber-modified epoxy polymers. The transition occurs at a specific K level, K _T, which corresponds to the condition where the size of the plastic zone is of the order of the size of the rubber particles. At K>K _T, rubber-modified epoxies exhibit improved FCP resistance compared to the unmodified epoxy. This is because the size of the plastic zone becomes large compared to the size of the rubber particles and, consequently, rubber cavitation/shear banding and plastic void growth mechanisms become active. At K>K _T, both neat and rubber-modified epoxies exhibit similar FCP resistance because the plastic zone size is smaller than the size of the rubber particles and hence, the rubber cavitation/shear banding and plastic void growth mechanisms are not operating. As a result of these interactions, the use of smaller 0.2 m rubber particles in place of 1.5 m rubber particles results in about one order of magnitude improvement in FCP resistance of the rubber-modified system, particularly near the threshold regime. Such mechanistic understanding of FCP behaviour was employed to model the FCP behaviour of rubber-modified epoxies. It is shown that the near threshold FCP behaviour is affected by the rubber particle size and blend morphology but not by the volume fraction of the modifiers. On the other hand, the slope of the Paris-Erdogan power law depends on the volume fraction of the modifiers and not on the particle size or blend morphology.     

Particle size distribution in rubber modified polyamides 6

Particle size and particle-size distribution in rubber-toughened polyamides 6 (PA6) were determined according to the Schwartz-Saltikov method. The quantitative morphological analysis was performed on microtomed samples of binary and ternary blends containing ethylene-propylene random copolymer (EPR) and functionalized EPR rubber (EPR-g-SA). The blends were obtained according to two different methods: concurrent to the hydrolitic polymerization of caprolactam, and simultaneous melt mixing. The formation of an (EPR-g-SA)-g-PA6 copolymer during blending was assumed to occur in the ternary blends. Correlations between particle size, particle size distribution, preparation method, composition and Izod impact strength of such materials were investigated.     

Rubber particle size and cavitation process in high impact polystyrene blends

The rubber particle size and its volume fraction are recognised as being important factors in determining the yield and fracture behaviour of high impact polystyrene (HIPS). However, correlations between the average particle size and cavitation in the rubber with toughening efficiency have only recently been established theoretically. This work provides further evidence on how the deformation kinetics in HIPS are affected by variations in the average rubber particle size highlighting along the way the role of rubber cavitation in the process. Variations in the average particle size were achieved by melt blending different proportions of two commercial grades of HIPS that had the traditional multiple inclusion particle morphology. Tensile and impact properties of the blends were measured and correlated to morphological parameters determined by quantitative image analysis. It was found that yield and fracture behaviour in tensile and impact test were strongly dependent on the amount of sub-micron particles in the blend. At high rates, toughness drops steeply with particle size. It was proposed that stress at yield and post yield strain hardening are controlled by particle size and rubber stretching respectively. Microfracture analysis by transmission electron microscopy lent support to the arguments presented. This revised version was published online in November 2006 with corrections to the Cover Date.     

Micromechanics of rubber–toughened polymers

A new micromechanical model is provided to account for the full interaction between rubber particles in toughened polymers. Three-dimensional large deformation elastic–plastic finite element analysis is carried out to obtain the local stress and strain fields and then a homogenization method is adopted to obtain the effective stress–strain relation. The dependence of the local stress and strain distributions and effective stress–strain relation on phase morphology and mechanical properties of rubber particles is examined under various transverse constraints. The profile for the effective yield surface is obtained at four different particle volume fractions. It is shown that stress triaxiality affects significantly the effective yield stress and the local stress concentrations. Rubber cavitation and matrix shear yielding are two coupled toughening mechanisms; which one occurs first depends on the properties of rubber particles and matrix and the imposed triaxiality. Rubber cavitation plays an important role in the toughening process under high tensile triaxial stresses. Axisymmetric modelling may underestimate, and two-dimensional plane-strain modelling may overestimate, the inter-particle interaction compared with three-dimensional modelling.     

On the elastic properties of rubber toughened Styrenics

Rubber toughened Styrenics represent an interesting model system for a blend containing a soft second phase in the form of dispersed spherical particles. The elastic properties of such a system have been widely examined in the past, both from experimental and theoretical viewpoints, however some questions remain unanswered. In this work an attempt is made to rationalize the field via the proposal of pertinent experimentation followed by a short review and the application of a convincing theoretical model. The elastic properties of rubber toughened Styrenics appear to be reproduced by a diluted model for spherical inclusions, in which the lower bound condition has to be used to describe the elastic properties of the second phase particles. Also, the more phenomenological Nielsen equation closely reproduces the experimental data.These results suggest that the role of stress intensification around the particles in rubber toughened Styrenics has to be reconsidered.Dedicated to Dr Giuseppe Cigna in the occasion of his retirement.     

Effect of rubber particle size on the impact tensile fracture behavior of MBS resin with a bimodal particle size distribution

We performed impact tensile fracture experiments on methylmethacrylate–butadiene–styrene (MBS) resin with small and large particles in a bimodal size distribution, and examined the effects of particle size on fracture behavior by fixing the total rubber content (28 wt%) and the small particle size (about 140 nm), and varying the size of large particles (about 490 nm or 670 nm). Dynamic load P′ and displacement δ′ of single-edge-cracked specimens were measured using a Piezo sensor and a high-speed extensometer, respectively. A P′−δ′ diagram was used to determine external work U _ex applied to the specimen, elastic energy E _e stored in the specimen, and fracture energy E _f for creating a new fracture surface A _s. Energy release rate was then estimated using G _f = E _f/A _s. Values of G _f were correlated with fracture loads and mean crack velocity v _m determined from load and time relationships. We then examined the effect of particle size on G _f and v _m, and results indicated that particle size plays an important role in changing the values of G _f and v _m.     

Particle size measurement of standard reference particle candidates with improved size measurement devices

In order to prepare standard reference particles, experimental and theoretical studies have been conducted on particle size measurement of two kinds of spherical glass beads. The sheath flow- type electrical sensing zone method and the revised sedimentation balance method were used for the measurement. The data were compared with those obtained by the microscopic method with a sample size greater than 10 000. The particle size distributions obtained by use of the sheath flow- type electrical sensing zone method and microscopic method are nearly equal for the two kinds of glass beads. However, deviations of less than 5% were observed between the improved sedimentation balance and microscopic methods. The experimental data of the microscopic method are within the 95% reliability region of the sheath flow-type electrical sensing zone method.     

Particle size determination of a three-component suspension using a laser-scattering particle size distribution analyzer

In this study, a rapid and accurate particle size determination method using a light-scattering particle size analyzer was developed to measure the particle size and size distribution of a suspension containing three solid components: clotrimazole, triamcinolone, and sarafloxacin, which have different refractive indices. To ensure that data represent the size distribution of the primary particles of the suspension, the optimal sonication prior to and during measurement was determined. It was found that the results obtained using the average relative refractive index (RRI) of the three components agreed with the results obtained using three individual RRIs. In addition, the results from two analysts demonstrated good reproducibility of this method. The size distribution data of the suspension were also compared to those of the bulk drugs. The results showed that the median particle size of this three-component suspension is relatively close to that of clotrimazole, which accounts for 80% of solid particles in the suspension. Furthermore, the results obtained using the light-scattering technique were comparable to those obtained using a polarized light microscope equipped with an image analyzer, indicating acceptable accuracy of this technique.     

Microdeformation mechanisms in rubber toughened PMMA and PMMA-based copolymers

The classical method of toughening polymethylmethacrylate (PMMA) is to incorporate composite rubber particles into the homopolymer matrix. This approach has been extended in the present work by (i) combining rubber toughening with chemical modification of the matrix or (ii) introduction of the rubber modifier via PMMA-b-polybutylacrylate (PBA)-b-PMMA triblock copolymers. Significant improvements in fracture toughness at low speeds were observed in notched compact tension tests when the ductility of the rubber toughened PMMA matrix was improved by copolymerization, and comparable levels of toughness were achieved in the block copolymers. However, both types of material showed a transition to more brittle behavior at impact speeds, associated with increased localization of the crack tip deformation. Physical interpretations for this behavior and the scope for further optimization of the fracture response are discussed.     

The role of cavitation and debonding in the toughening of core–shell rubber modified epoxy systems

Epoxy systems EPN/BA and EPN/DDS having significantly different cross-link densities have been modified using core–shell rubber particles. The toughening mechanisms have been investigated and the results show that cavitation and particle–matrix debonding play different roles in the low and high cross-link density epoxy resins. This revised version was published online in November 2006 with corrections to the Cover Date.     

Elastic properties of rubber particles in toughened PMMA: ultrasonic and micromechanical evaluation

Ultrasonic measurements and micromechanical models are used to evaluate elastic properties of rubber particles dispersed in toughened polymers. Ultrasonic phase velocities and attenuation spectra of rubber-toughened poly(methyl methacrylate) (PMMA) with different rubber particle fractions are measured for longitudinal as well as transverse waves. The ultrasonic properties of rubber-toughened PMMA are found to depend markedly on the rubber particle fraction. The bulk and shear moduli determined from the measured velocities are in turn used to estimate those moduli of the particles based on existing micromechanics models, namely the three-phase model and the Hashin–Shtrikman upper and lower bounds. The bulk modulus of the particle estimated by the three-phase model is found to be in close agreement with the result of previous investigators. Implications of the Hashin–Shtrikman bounds for the particle moduli are also examined.     

Particle shape effects on particle size measurement for crushed waste glass

Recently, narrow particle size distributions, as measured by sieve analysis, of crushed waste glass were used as a replacement for Portland cement in concrete. Their chemical reactivity was successfully studied as a function of this measure of particle size. Differences between sieve analysis and laser diffraction measures of particle size prompted this current re-analysis. Extremely careful sieving was used to divide the crushed waste glass particles into 0–25 μm, 25–38 μm, and 63–75 μm sieve size ranges, but laser diffraction did not agree with these particle size cutoffs. We use these same materials to try and understand the discrepancies between particle size as measured by laser diffraction and sieve analysis by using X-ray computed tomography followed by spherical harmonic analysis to measure the three-dimensional particle shape and size, as well as the length (L), width (W), and thickness (T) of each particle. We show how laser diffraction and X-ray CT results, along with sieve analyses, can be quantitatively related for these crushed waste glass particles in the approximate size ranges considered. In contrast to previous speculation, the particle width W does not have to correspond closely to the sieve opening – the correspondence depends on overall particle shape. In addition, we demonstrate how many particles are needed to analyze in order to achieve stable averages and distributions of the L/W, W/T, and L/T aspect ratios, which approximately define particle shape. These results have implications for how particle size is measured and interpreted in the cement and concrete and other industries.     

发泡剂粒径对硅橡胶泡沫材料性能的影响研究

以硅橡胶为基体材料,采用发泡剂H制备硅泡沫材料.研究了不同发泡助剂对发泡剂H分解温度的影响,以及发泡剂粒径对硅泡沫材料密度、硬度、力学性能、压缩性能和泡孔大小及其分布状态的影响规律.结果表明:发泡剂H与发泡助剂尿素的比例为1:1时,两者之间具有良好的匹配性;在发泡剂粒径对硅泡沫材料性能的影响方面,随着发泡剂粒径的减小,硅泡沫材料的密度、硬度、拉伸强度和40％压缩应变下的压缩应力值逐渐变大,当发泡剂粒径达到300目时,上述性能参数达到最大值,之后又出现下降趋势;其中,原始目数和较大目数下制备的硅泡沫材料的性能变化情况相似.同时,采用SEM技术对不同发泡剂粒径时硅泡沫材料的泡孔大小和分布状态进行了分析.     

Criteria for cavitation of rubber particles: Influence of plastic yielding in the matrix

The principles of the cavitation criteria for rubber particles in polymeric matrices are briefly reviewed. Although these criteria are based on a linear elastic analysis, it is shown that it is possible to extend them to take into account the elastic-plastic behaviour of the matrix. In this objective, the representative volume element of a periodic material was meshed and computations were performed using a finite element method. The results reported in this paper focus mainly on cavitation under uniaxial tension and examine the influence on the hydrostatic stress in the rubber particles of different parameters such as the volume fraction of rubber, the plastic behaviour of the matrix or the ratio of the elastic moduli. In all cases, plastic yielding in the matrix leads to saturation of the hydrostatic stress in the rubber phase. It is also shown that the history of cavitation barely influences the progression of plasticity in the matrix.     

Polymers toughened with rubber microspheres: an analytical solution for stresses and strains in the rubber particles at equilibrium and rupture

Large strains in rubber toughened polymers cause void formation and growth in the rubber particles and yielding in the matrix. Void formation usually precedes plasticity in the matrix around the particle and previous papers have proposed models for the relationship between rubber surface energy, volume strain energy and void growth. In this paper, it is shown that another volume criterion must also be satisfied arising from the fact that in all these models, no decohesion is allowed at the particle-matrix interface. A fracture mechanics approach, where linear and nonlinear elasticity are assumed for the matrix and the rubber particle, respectively, is used to define a void formation criterion depending on the rubber fracture surface energy. After formation, the stability of the void is examined, taking into account the volume conservation between matrix and particle and the stress due to surface tension when the void size is very small. A size effect is observed, indicating that voids cannot grow in small particles. The required value of fracture energy in a particle on a microscopic scale is discussed.     

Role of rigid nanoparticles and CTBN rubber in the toughening of epoxies with different cross-linking densities

Experimental investigations were conducted to characterize the fracture behaviours of Bisphenol A diglycidyl ether (DGEBA) epoxies modified with rigid nanoparticles (nanosilica or halloysite) and a reactive liquid carboxylterminated butadiene–acrylonitrile (CTBN) liquid rubber to identify toughening mechanisms and toughenability in the cured epoxies with different cross-linking densities. The epoxy was cured using three different hardeners, a heterocyclic amine (piperidine), a cycloaliphatic polyamine (Aradur 2954) and an aromatic amine [4,4′-Diaminodiphenyl sulfone (DDS)] to form nanocomposites with different cross-linking densities. It was found that both the hybrid particles, nanosilica with CTBN rubber and halloysite with CTBN rubber, were effective additives that clearly increased the fracture toughness of the three epoxy composites. In particular, the use of halloysite nanoparticles as additives for the epoxies showed greater potential than nanosilica to increase strength and modulus due to the reinforcing effect of the halloysite nanotubes (HNTs). The epoxy systems cured with the hardeners (Aradur 2954 and DDS), which generated relatively high cross-linking densities, evidenced inferior toughenability of the hybrid particles, compared with the epoxy systems cured using the hardener (piperidine), which produced lower cross-linking densities. The CTBN rubber formed dissimilar domains in different epoxy systems, features which were attributed to the different toughenability of the hybrid particles in the systems due to variations in the dominant toughening mechanisms involved.     

Interlayer toughened unidirectional carbon prepreg systems: effect of preformed particle morphology

A new production process was used to change the surface morphology and reduce the water sensitivity of a commercial preformed rubber particle used for interlayer composite toughening. These particles were incorporated in a model epoxy resin and impregnated into unidirectional carbon fibers. The mode II fracture toughness of a laminate made with experimental particles was 250% higher than the control system and 100% higher than a laminate made with the commercial preformed rubber particles. The new particles were also found to reduce the damage area resulting from impact; however, the ultimate laminate compression strength after impact was lower for the experimental particle modified composite than the commercial particle modified laminate. The composites were also subjected to hot–wet conditions and the initial water absorption rate was less for the experimental particle modified laminates than the laminate containing the commercial material. Yet, after 6400 h, the laminates made with experimental particles were found to absorb more water than the other materials.