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.     

Mechanisms of energy dissipation during impact in toughened polyamides: a SEM analysis

The development of dissipative mechanisms during the fracture of toughened polyamides is investigated by SEM. A preliminary fractographic analysis is carried out on the ductile fracture surfaces of water conditioned PA 6 specimens. Extensive yielding gives rise to a wide development of shear bands and rumples, depending on the local stress conditions. Then, the stress whitened regions under the ductile fracture surfaces of rubber toughened HI-PA 6 specimens are analysed by SEM. This is made possible by means of a simple technique for the cryogenic dissection of ductile fracture surfaces: sections are cut both transversally and longitudinally with respect to the ductile crack growth direction. Under the ductile fracture surfaces extensive cavitation occurs around the rubbery particles, following preferential and definite shear directions. The presence of cavitation is correlated with the distance below the ductile surfaces. The rumpled morphologies can be directly correlated with cavitation and shear bands occurring inside the whitened regions below ductile fractures. Both the orientation of shear bands on the fracture surfaces of water conditioned PA6 and the cavitation-shear yielding morphologies developed inside the fractured PA-rubber blends comply with an octahedral shear model, common to other polymers (rubber toughened epoxies, for instance) and to ductile metals.     

Toughening mechanisms in elastomer-modified epoxies

Some brittle epoxies can be toughened significantly by the addition of an elastomeric phase. A great deal of controversy still exists on the nature of the toughening mechanisms. In this work tensile dilatometry at constant displacement rates was used to determine whether voiding, crazing or shear banding are the deformation mechanisms. Diglycidyl ether-bisphenol A epoxies toughened by various levels of several types of carboxyl-terminated butadiene nitrile liquid rubber were studied. The results indicate that at low strain rates the rubber particles simply enhance shear deformation. At sufficiently high strain rates the rubber particles cavitate and subsequently promote further shear deformation. No indication of crazing as an important toughening mechanism is found. No significant effect of rubber particle size or type can be ascertained.     

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.     

Effects of loading rate and temperature on tensile yielding and deformation mechanisms of nylon 6-based nanocomposites

Tensile tests were conducted on nylon 6/organoclay nanocomposites, with and without POE-g-MA rubber particles, over a range of temperatures and strain rates 10⁻⁴–10⁻¹ s⁻¹. It was shown that the 0.2% offset yield strength varied with both temperature and strain rate which could be described by the Eyring equation thus providing results on the activation energy and activation volume for the physical processes involved. In addition, their tensile deformation mechanisms were characterized using the tensile dilatometry technique to differentiate the dilatational processes (e.g., voiding/debonding caused by the organoclay and rubber particles or matrix) and shear yielding (e.g., matrix with zero volume change). Dilatometric responses indicated that the presence of POE-g-MA rubber particles did not alter the shear deformation mode of neat nylon 6. In contrast, the presence of organoclay layers changed the tensile yield deformation behavior of nylon 6 matrix from dominant shear yielding to combined shear yield plus dilatation associated with delaminations of nanoclay platelets. In nylon 6/organoclay/POE-g-MA ternary nanocomposite, the volume strain response indicated that the POE-g-MA rubber particles promoted shear deformation and suppressed delamination of the organoclay layers. Supports for the deformation mechanisms deduced from the tensile dilatometry tests were corroborated by optical microscopy and transmission electron microscopy micrographs of the studied materials.     

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.     

Morphology and toughening mechanisms in clay-modified styrene-butadiene-styrene rubber-toughened polypropylene

Clay-modified styrene-butadiene-styrene (SBS) rubber is utilized to toughen polypropylene (PP). The SBS rubber is found to have good compatibility with clay particles. SBS rubber helps to finely disperse clay particles in PP matrix. Mode-I fracture mechanisms are investigated using optical microscopy and transmission electron microscopy techniques. Rubber particle cavitation and matrix shear yielding are found to be the main toughening mechanisms in PP/SBS system. In the case of PP/SBS/clay system, widespread rubber particle cavitation, which appears to be facilitated by the presence of clay particle inclusions inside the SBS rubber particles, takes place in the PP matrix. This, in turn, leads to the formation of a bigger shear yielded zone in PP matrix. As a result, an enhanced toughness is observed.     

Cavitation Instabilities in Plastics and Rubber-Modified Plastics

Spherical void expansion in plastics and rubber-modified plastics is investigated under radial traction conditions. The plastics are modeled as elastic-plastic pressure-sensitive materials and the rubbers are modeled as nonlinearly elastic materials. First, the growth of a spherical void in an infinite plastic matrix is investigated under remote radial traction conditions. The results show that the cavitation stress of the plastic decreases significantly as the pressure sensitivity increases. Then, the growth of a spherical void located at the center of a spherical rubber particle in an infinite plastic matrix is investigated under remote radial traction conditions. The results indicate that without any failure criteria for the rubber, the cavitation stress does not exist when the void is small and the rubber is characterized by high-order strain energy functions. However, when a failure criterion for the rubber is considered at a finite stretch ratio, the results show that the cavitation stress for the plastic with the rubber particle becomes close to that for the plastic without the rubber particle. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mechanisms of cavitation over a range of temperatures in rubber-toughened PSAN modified with three-stage core-shell particles

In situ straining on a transmission electron microscope (TEM) stage has been used to study deformation mechanisms in a blend of poly(styrene-co-acrylonitrile) (PSAN) with PMMA/acrylate-rubber/PMMA core-shell particles, over a range of temperatures. Thin sections were tested at -20, 23 and 60°C at a constant tensile strain rate of 0.05% s-1. Cavitation was observed at all three temperatures. At -20°C, the main deformation mechanisms were crazing of the PSAN matrix and fibrillation of the acrylate rubber. At 23°C, crazing and shear yielding of the PSAN occurred simultaneously, with more extensive fibrillation of the rubber particles and drawing of material from the PMMA cores. This disruption of thermoplastic core material indicates that high stresses are generated within the modifier particles. At 60°C, crazing could no longer be detected: shear yielding of the matrix and cavitation of the rubber particles were the main mechanisms of deformation. This revised version was published online in November 2006 with corrections to the Cover Date.     

Toughening mechanism for a rubber-toughened epoxy resin with rubber/matrix interfacial modification

For a rubber-toughened piperidine-DGEBA epoxy resin, the interface between the rubber particle and the epoxy resin matrix was modified by an epoxide end-capped carboxyl terminated butadiene and acrylonitrile random copolymer (CTBN). The end-capping epoxides used were a rigid diglycidyl ether of bisphenol-A (Epon 828), a short-chain flexible diglycidyl ether of propylene glycol (DER 736), and a long-chain flexible diglycidyl ether of propylene glycol (DER 732). The microstructures and the fracture behaviour of these rubber-modified epoxy resins were studied by transmission electron microscopy and scanning electron microscopy. Their thermal and mechanical properties were also investigated. In the rubber-modified epoxy resins, if the added CTBNs were end-capped by a flexible diglycidyl ether of propylene glycol (DER 732 or DER 736) before curing, the interfacial zone of the undeformed rubber particle, the degree of cavitation of the cavitated rubber particle on the fracture surface and the fracture energy of the toughened epoxy resin were all significantly increased. The toughening mechanism based on cavitation and localized shear yielding was considered and a mechanism for the interaction between cavitation and localized shear yielding that accounts for all the observed characteristics is proposed.     

Three-dimensional elastoplastic finite element modelling of deformation and fracture behaviour of rubber-modified polycarbonates at different triaxiality

A periodic face-centred cuboidal cell model is provided to account for inter-particle interaction, and a particle-crack tip interaction model is developed to study the interaction between a blunting model I crack tip and the closest array of initially spherical rubber particles in an effective medium. Three-dimensional elastoplastic finite element analysis has been preformed to study the deformation and fracture behaviour of rubber-modified polycarbonates. The effective elastoplastic constitutive relation is derived by the method of homogenisation and local stress and strain distributions are obtained to explore the role of rubber cavitation in the toughening process at different stress triaxiality. 3D elastoplastic finite element results are compatible with experimental observations, that is, rubber particles can act as stress concentrators to initiate crazing or shear yielding in the matrix but they behave differently from voids at high triaxiality. Rubber cavitation plays an important role in the toughening process under high tensile triaxial stresses.     

Modes of deformation in rubber-modified thermoplastics during tensile impact

Real-time small-angle X-ray scattering (RTSAXS) studies were performed on a series of rubber-modified thermoplastics. Scattering patterns were measured at successive time intervals as short as 1.8 ms and were analysed to determine the plastic strain due to crazing. Simultaneous measurements of the absorption of the primary beam by the sample allowed the total plastic strain to be computed. The plastic strain due to other deformation mechanisms, e.g. particle cavitation and macroscopic shear deformation was determined by the difference. Samples of commercial thicknesses can be studied at high rates of deformation without the inherent limitations of microscopy and its requirement of thin samples (i.e., plane strain constraint is maintained on sample morphology). Contrary to the conclusions drawn from many previous dilatation-based studies, it has been demonstrated that the strain due to non-crazing mechanisms, such as rubber particle cavitation, and deformation of the glassy ligaments between rubber particles, occurs before that due to crazing mechanisms. Crazing accounts for at most only half of the total plastic strain in HIPS (high impact polystyrene) and ABS (rubber-modified styrene-acrylonitrile copolymer) materials. The proportion of strain attributable to crazing can be much less than half the total in thermoplastic systems with considerable shear yield during plastic deformation. The predominant deformation mechanism in polycarbonate-ABS blends is shear in the PC (polycarbonate) with associated rubber gel particle cavitation in the ABS. This cavitation means that there appears to be a direct relationship between gel particle rubber content in the ABS and toughness of the blend. The mechanism is the same whether the tensile stress is in the direction parallel or perpendicular to the injection-moulded orientation, with simply less total strain being reached before fracture in the weaker perpendicular direction. Crazing, although the precursor to final fracture, occurs after the predominant mechanism and contributes only a few per cent to the total plastic deformation.     

Pre-yield tensile set of a semi-crystalline polymer,its blend and composite

Tensile set was studied at low strains on polypropylene, aliphatic polyketone, rubber toughened blends and CaCO₃ particle toughened composites. The rubber in the rubber toughened blends had a particle size of 0.7 μm. The CaCO₃ particles had a size of 0.7 μm and had been coated with stearic acid. Step-cyclic loading was applied in 1% strain incrementals at a strain rate of 10⁻² s⁻¹. The maximum strain applied was 20%. The temperature of the test bar was studied with an infra-red camera. Pre-yield deformation is normally assumed to take place in a nonlinear elastic manner. However, for polypropylene and polyketone elastoplastic deformation starts at low strains. For PP the onset of tensile set is at very low strains and increases with strain. The tensile set at the yield point was only 50% and at the drawing strain 100%. Polyketone had a similar tensile set development but shifted to slightly higher strains. Here too the tensile set at the yield point was about 50% and at the drawing strain 100%. The temperature of the non yielded material was found to rise in polyketone a 7 °C. The rubber toughened blends had at low strains a higher tensile set, but after the yield strain the set was similar to the base polymer. At 5% strain the tensile set increased with rubber content. The sub micron CaCO₃ particle toughened composites increased the tensile set too. The tensile set is a simple technique for studying the pre-yield behaviour of multi phase systems.     

Studies on the growth of voids in amorphous glassy polymers

Numerical studies are presented of the localized deformations around voids in amorphous glassy polymers. This problem is relevant for polymer–rubber blends once cavitation has taken place inside the rubber particles. The studies are based on detailed finite element analyses of axisymmetric or planar cell models, featuring large local strains and recent material models that describe time-dependent yield, followed by intrinsic softening and subsequent strain hardening due to molecular orientation. The results show that plasticity around the void occurs by a combination of two types of shear bands, which we refer to as wing and dog-ear bands, respectively. Growth of the void occurs by propagation of the shear bands, which is driven by orientational hardening. Also discussed is the evolution of the local hydrostatic stress distribution between voids during growth, in view of possible craze initiation. © 1998 Kluwer Academic Publishers     

Internal structure of rubber particles and craze break-down in high-impact polystyrene (HIPS)

Polystyrene can be substantially toughened by the addition of rubber particles, their role being to act as craze initiators permitting substantial plastic deformation to occur prior to fracture. The internal structure of these particles is variable: typically the smaller (1 m) particles are solid rubber and the larger particles contain sub-inclusions of polystyrene. Thin films of a toughened high-impact polystyrene (HIPS) suitable for optical and transmission electron microscopy (TEM) have been prepared, and the interplay between the internal structure of the particles and the crazes they generate has been examined by TEM. It is found that as crazes form around the solid rubber particles, significant lateral contraction occurs accompanying their elongation in the tensile direction. As this contraction proceeds, decohesion occurs just beneath the particlecraze interface, resulting in the formation of a void. This void will grow under increasing stress, leading to premature failure of the craze. In contrast to this behaviour, occluded particles can accommodate the displacements due to crazing by local fibrillation of the rubber shell which surrounds each sub-inclusion, without the formation of large voids. Consequently, the occluded particles do not act as sites for early craze break-down. These results suggest that the optimum morphology for rubber particles in HIPS will consist of a large number of small PS occlusions, each surrounded by a thin layer of rubber, in which case the size of the inherent flaws introduced during crazing will be minimized.     

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.     

分散相对高分子合金增韧及脆/韧转变的影响

发生脆／韧转变的合金材料,其刚性体分散相ＣＰＰ在基质形成的静水应力的作用下沿拉抻方向发生了塑性形变。分散相无论是刚性体还是弹性体,在基质形成的静水压应力的作用下均可通过形变吸收能量使合金材料增韧;同时分散相也可作为应力集中剂引发基质产生银纹和屈服剪切带,使合金材料增韧,脆／韧转变过程提前,当分散相模量较时,后一种作用为主。随着分散相模量的增加,前一种作用的影响逐渐增加,并最终转变成为主导作用。     

Effect of hybridization of liquid rubber and nanosilica particles on the morphology, mechanical properties, and fracture toughness of epoxy composites

A liquid carboxyl-terminated butadiene–acrylonitrile copolymer (CTBN) and SiO₂ particles in nanosize were used to modify epoxy, and binary CTBN/epoxy composites and ternary CTBN/SiO₂/epoxy composites were prepared using piperidine as curing agent. The morphologies of the composites were observed by scanning electron microscope (SEM) and transmission electron microscope (TEM), and it is indicated that the size of CTBN particles increases with CTBN content in the binary composites, however, the CTBN particle size decreases with the content of nanosilica in the ternary composites. The effects of CTBN and nanosilica particles on the mechanical and fracture toughness of the composites were also investigated, it is shown that the tensile mechanical properties of the binary CTBN-modified epoxy composites can be further improved by addition of nanosilica particles, moreover, obvious improvement in fracture toughness of epoxy can be achieved by hybridization of liquid CTBN rubber and nanosilica particles. The morphologies of the fractured surface of the composites in compact tension tests were explored attentively by field emission SEM (FE-SEM), it is found that different zones (pre-crack, stable crack propagation, and fast crack zones) on the fractured surface can be obviously discriminated, and the toughening mechanism is mainly related to the stable crack propagation zone. The cavitation of the rubber particles and subsequent void growth by matrix shear deformation are the main toughening mechanisms in both binary and ternary composites.     

Toughening mechanisms of modified unsaturated polyester with novel liquid Polyurethane rubber

Unsaturated polyester (UPE) has been toughened by incorporating novel liquid polyurethane (PU) rubber. PU rubber was synthesized using toluene di-isocyanate and polyols such as poly (propylene glycol) and poly (tetramethylene ether) glycoi, whose molecular weights vary from 650 to 4000. Particle size was varied from 0.1 to 3 m by changing the polyol and the molecular weight of PU rubber, and the effects of particle size on the fracture toughness of PU rubber-modified UPE were investigated. Hydroxyl terminated PU rubber (HTPU) and isocyanate terminated PU rubber (ITPU) were used to study the effects of rubber-matrix adhesion. The toughening mechanisms observed by scanning electron microscope are debonding between rubber and matrix in HTPU-modified UPE, and cavitation in the rubber particle in ITPU-modified UPE. However, shear bands were not observed as UPE is a highly cross-linked thermoset with very short chain length between the cross-links. A 1.9-times increase in fracture toughness of UPE was achieved with the formation of cavitated particles. In order to measure the process zone size at the crack tip, the thin sections of tested double-notched four-point bending specimens were examined by optical microscope.     

Particle cavitation in rubber toughened epoxies: the role of particle size

Rubber toughened epoxies are used in a wide range of applications including adhesives when toughness is a crucial property. It is well known that the cavitation of the rubber particles is an important process to optimise the toughness of such materials. This article describes the development of a predictive model to describe the dependence of rubber particle cavitation on particle size. The model is developed using a combination of experimental observations and finite element simulations. Predictions have been obtained for both uniaxial loading conditions and the triaxial loading conditions expected ahead of a crack. The model has been extended to consider the cavitation of nano-sized ‘rubber’ particles.