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.     

Dilatational bands in rubber-toughened polymers

A theory is advanced to explain the effects of rubber particle cavitation upon the deformation and fracture of rubber-modified plastics. The criteria for cavitation in triaxially-stressed particles are first analysed using an energy-balance approach. It is shown that the volume strain in a rubber particle, its diameter and the shear modulus of the rubber are all important in determining whether void formation occurs. The effects of rubber particle cavitation on shear yielding are then discussed in the light of earlier theories of dilatational band formation in metals. A model proposed by Berg, and later developed by Gurson, is adapted to include the effects of mean stress on yielding and applied to toughened plastics. The model predicts the formation of cavitated shear bands (dilatational bands) at angles to the tensile axis that are determined by the current effective void content of the material. Band angles are calculated on the assumption that all of the rubber particles in a band undergo cavitation and the effective void content is equal to the particle volume fraction. The results are in satisfactory agreement with observations recorded in the literature on toughened plastics. The theory accounts for observed changes in the kinetics of tensile deformation in toughened nylon following cavitation and explains the effects of particle size and rubber modulus on the brittle-tough transition temperature.     

Sand–rubber mixtures undergoing isotropic loading: derivation and experimental probing of a physical model

The volume of scrap tyres, an undesired urban waste, is increasing rapidly in every country. Mixing sand and rubber particles as a lightweight backfill is one of the possible alternatives to avoid stockpiling them in the environment. This paper presents a minimal model aiming to shed light on the relevant physical parameters governing the evolution of the void ratio of sand–rubber mixtures undergoing an isotropic compression loading, where the mixtures consist of various volume ratios of rubber. It is based on the idea that, when pressure is applied, the rubber particles deform and partially fill the porous space of the system, leading to a decrease of the void ratio with increasing pressure. We show that our simple approach is capable of reproducing experimental data obtained with sand and rubber of similar particle size distributions up to mixtures composed of 50% of rubber. The effect of the particle shape and size on the model parameters is discussed.     

The effect of particle distribution on damage formation in particulate reinforced metal matrix composites deformed in compression

Image analysis results are reported on the generation of damage in particulate reinforced metal matrix composites during compressive deformation. The technique allows the automated collection of data on the incidence of particle fracture and void formation in the matrix as a function of important microstructural parameters such as local particle volume fraction and particle size. There is a strong relationship between damage and the local volume fraction of the reinforcement proving that damage formation is accentuated in regions of particle clustering. With the SiC reinforced materials examined, there was observed to be a change in dominance of damage mechanism from particle fracture at low local volume fractions to void formation in the matrix within strongly clustered regions. The results are compared with finite element (FE) modelling of the compressive deformation of clustered particles using a simple cluster of equi-spaced particles. The FE results suggest that plastic flow is generally inhibited in clustered regions. In certain highly clustered configurations shielding is such that flow does not occur in the heart of the cluster even at high levels of average plastic strain. The modelling suggests that the change in dominance of damage mechanism is related to the dramatic increase in tensile hydrostatic stresses in the matrix with higher levels of particle clustering.     

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.     

Improved fracture toughness and fatigue life of carbon fiber reinforced epoxy composite due to incorporation of rubber nanoparticles

In this study, core–shell rubber (CSR) nanoparticles with approximate particle size of 35 nm were used as a modifier for the epoxy polymer. The effects of various CSR contents in the epoxy matrix on mode I interlaminar fracture toughness, tensile strength, and fatigue life of the carbon fabric reinforced epoxy (CF/EP) composites were investigated. The experimental results showed that the mode I interlaminar fracture toughness at crack initiation and propagation significantly improved by 71.21 and 58.47 %, respectively, when 8.0 wt% CSR was dispersed in the epoxy matrix. The fatigue life of the modified CF/EP composites at all of CSR contents dramatically increased 75–100 times longer than that of the unmodified CF/EP composites at high cycle fatigue while tensile strength slightly increased by about 10 %. Field emission scanning electron microcopy (FESEM) observations of the fracture surfaces were conducted to explain failure mechanisms of CSR addition to the CF/EP composites. The evidences of the rubber nanoparticle debonding, plastic void growth, and microshear banding were credited for delaying the onset of matrix crack, and reducing the crack growth rate, as a result, attributed to increase in the mechanical properties of the CF/EP composites.     

Role of the rubber particle and polybutadiene cis content on the toughness of high impact polystyrene

High impact polystyrene (HIPS) is a classical reactor polymer blend produced by in situ polymerization of styrene in solution with polybutadiene rubber. The importance of the particle size and rubber crosslink density on the particle cavitation capability and the controlling of toughening mechanisms in the styrenic matrix is well established in current literature. In the present work, the role of the rubber particle on the HIPS toughness has been investigated for two commercial grades with low and high cis polybutadiene. Transmission electron microscopy (TEM) was employed for observation of particle size distribution and digital imaging applied for quantitative analysis of the micrographs. Measurements of apparent volume fraction and average particle size were determined in TEM images for both grades, while the gel content and swelling index were employed to evaluate the effect of the polybutadiene cis isomer on the rubber crosslink density. Grade morphology and crosslink effects on mechanical properties were assessed by slow three-point bending and uniaxial tensile testing. The results illustrate that polybutadiene cis content in HIPS grades has strong influence on the mechanical properties, particularly affecting yielding and energy to failure. Accordingly, it was observed that HIPS grades with equivalent average particle size and apparent volume fractions present a much higher energy to failure and a lower yield stress with high cis content polybutadiene when compared to their lower cis polybutadiene counterparts.     

MODELLING FOR TRANSCRYSTALLINE AND INTERCRYSTALLINE FRACTURE BY VOID NUCLEATION AND GROWTH

A criterion has been formulated for transcrystalline and intercrystalline fracture caused by the evolution of voids located both in a grain and on grain boundaries. The criterion is based on the idea of plastic collapse for a unit cell that is a regular structural mezovolume of polycrystalline material. The criterion does not require the introduction of any empirical parameters, such as critical void size, critical size of ligament between voids and critical void volume fraction, which are used in most models.
Modelling has been performed for void nucleation and growth in a grain and on grain boundaries for elastic–plastic deformation and under creep conditions. A scheme is proposed to describe the transition from transcrystalline to intercrystalline cavitation fracture as a function of strain rate and temperature.
The effect of stress triaxiality on the critical strain and the lifetime for both transcrystalline and intercrystalline fracture has been investigated. A comparison of the results predicted by the suggested criterion with available empirical data has been performed.     

The effect of dispersed paint particles on the mechanical properties of rubber toughened polypropylene composites

The influence of dispersed paint particles on the mechanical properties of rubber toughened PP was investigated. The matrix was basically a hybrid of PP, rubber and talc. Model systems with spherical glass bead filled matrix were also studied to examine the effect of filler shape and size. Properties like tensile strength, strain at break, impact strength, and fracture toughness were influenced by the dispersed inclusions. Tensile strength at yield decreased linearly according to Piggott and Leinder's equation. Strain at break decreased more drastically with paint particles than glass beads, revealing that irregularly shaped particles offered greater stress concentrations. The tensile strength and strain at break were less influenced by the size of paint particles whereas a slight decrease in the modulus values was observed with decreasing particle size. Impact strength and fracture toughness also decreased with increasing filler fraction. Lack of stress transfer between filler and matrix aided in reduction of impact strength. Decrease in fracture toughness was influenced by volume replacement and constraints posed by fillers. The size of paint particles had little effect on the impact strength and fracture properties at the filler concentration levels used in this investigation.     

Cavitation instability in rubber with consideration of failure

Cavitation instability in rubber is investigated by examining spherical void expansion in rubber particles under dead-load traction conditions. Spherical symmetry is assumed to simplify the governing equations in order to gain qualitative understanding of cavitation phenomenon. A simple strain failure criterion for rubber is proposed to demonstrate the effect of rubber failure on cavitation phenomenon. When the strain failure criterion is considered, the results show that, as in neo-Hookean materials, critical cavitation stresses exist for Mooney-Rivlin materials and for nonlinearly elastic materials characterized by a third-order strain energy function.     

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.     

Fracture resistance of a glass-fibre reinforced rubber-modified thermoplastic hybrid composite

Toughening mechanisms in a hybrid amorphous thermoplastic composite containing both distributed rubber particles and rigid glass fibres have been investigated. Tensile properties were measured for a range of materials with varying rubber particle and glass-fibre contents, and different rubber particle sizes. Fracture toughness was characterized by separating the overall fracture into its initiation and propagation components. Deformation and fracture modes at crack tips were optically characterizedin situ during loading. The results indicate that both initiation and propagation toughness are enhanced by rubber particle additions to the glass-fibre reinforced composite. Synergistic effects between glass fibres and rubber particles are identified: for example, glass fibres inhibit crazing at rubber particles, and rubber particles tend to promote crazing at fibre/matrix interfaces and also void initiation at fibre ends. Toughening mechanisms are discussed in the light of available models.     

Fracture and fatigue of bonded rubber blocks under compression

Fracture and fatigue failure of bonded rubber cylinders are discussed. Under large compressive forces, two modes of fracture are possible: splitting open of the free surface and tearing at or near the bonded edges; tearing energy T for the latter case is estimated. Under cyclic compression, the probable fracture mode of rubber is by crack propagation, leading to the bulged volume breaking away. The corresponding tearing energy is calculated. To predict the fatigue life, the rate of crack growth dc/dn is assumed to be proportional to T². A life prediction equation is thus obtained, of the form: load cycle N = (K/g)⁵, where K is a constant, about 10 for a typical soft natural rubber compound, and g is the maximum shear strain set up at the edges of the bonded surfaces.     

Toughening of polyester resins by rubber modification

The microstructures of two polyester resin systems, with reactive liquid rubber additions incorporated, were investigated using electron microscopy. Fracture surface morphologies of failed fracture toughness specimens were examined using scanning electron microscopy. The fine structures of unfractured toughened resins were examined by imaging ultra thin sections in the transmission electron microscope. Three of the four rubber additives investigated produced, upon curing, a dispersion of second-phase rubber-rich particles in the polyester resin matrix. The fourth additive, which was more compatible with polyester than the other three, did not produce any detectable particle dispersion upon curing, even at relatively high concentrations. The fine structures of the particle distribution were found to be highly dependent upon both rubber and resin formulations. Rubber additions modified the mode of fracture observed in double torsion tests of polyester resins, from continuous crack propagation to slip-stick, and distinctive changes in fracture surface morphology were observed. In zones of crack arrest and slow stable crack growth, crack blunting occurred and highly deformed structures were seen on the fracture surface. In one system, this zone was split into two distinct regions, due to crack blunting and the initiation of new, sharp cracks. In zones of rapid crack growth, there was no evidence of crack blunting. The amount of crack blunting was highly dependent upon speed of testing.     

Nanoscale fracture analysis by atomic force microscopy of EPDM rubber due to high-pressure hydrogen decompression

The relationship between internal fracture due to high-pressure hydrogen decompression and microstructure of ethylene–propylene–diene–methylene linkage (EPDM) rubber was investigated by atomic force microscopy (AFM). Nanoscale line-like structures were observed in an unexposed specimen, and their number and length increased with hydrogen exposure. This result implies that the structure of the unfilled EPDM rubber is inhomogeneous at a nanoscale level, and nanoscale fracture caused by the bubbles that are formed from dissolved hydrogen molecules after decompression occurs even though no cracks are observed by optical microscopy. Since this nanoscale fracture occurred at a threshold tearing energy lower than that obtained from static crack growth tests of macroscopic cracks (T _s,th), it is supposed that nanoscale structures that fractured at a lower threshold tearing energy (T _nano,th) than T _s,th existed in the rubber matrix, and these low-strength structures were the origin of the nanoscale fracture. From these results, it is inferred that the fracture of the EPDM rubber by high-pressure hydrogen decompression consists of two fracture processes that differ in terms of size scale, i.e., bubble formation at a submicrometer level and crack initiation at a micrometer level. The hydrogen pressures at bubble formation and crack initiation were also estimated by assuming two threshold tearing energies, T _nano,th for the bubble formation and T _s,th for the crack initiation, in terms of fracture mechanics. As a result, the experimental hydrogen pressures were successfully estimated.     

Mechanical properties and fracture behaviors of epoxy composites with multi-scale rubber particles

In this work, we developed a strategy to balance the toughness and thermal resistance of epoxy composites by incorporating the multi-scale rubber particles. Two types of rubber i.e. the phase-separation-formed submicron liquid rubber (LR) and preformed nano-scale powered rubber (PR) particles were chosen as tougheners. It was found that the combination of these multi-scale rubber particles not only provides superior efficiency in enhancing the impact resistance of epoxy composites, but also results in balanced glass transition temperature. In particular, the highest gain in impact strength was obtained for the ternary composites containing 9.2 wt% submicron liquid rubber and 9.2 wt% nano-sized powered rubber which were ∼112% higher than the maximum enhancements of ∼49% and ∼66% for the corresponding binary composite systems with the single-phase rubber, respectively. The damage zone observation and fracture surface analysis suggested that the combined use of multi-scale particles was effective to promote matrix plastic deformation including void growth and shear banding induced by the improved rubber cavitation/debonding, which is likely responsible for the highly improved impact resistance of the ternary composites.     

Prediction of ductile fracture using isotropic and kinematic hardening rules including void nucleation

A formulation combining kinematic translation and isotropic expansion for a yield surface based on Gurson–Tvergaard function is used to describe void growth. By adopting a criterion of internal necking of the ligaments between voids, fracture strains for tensile bars made of conventional alloys and powder metal compacts—with micromechanical parameters mostly identified from experiments—are predicted according to kinematic, isotropic and mixed hardening models. Fracture strains predicted by the kinematic‐hardening model are in closer agreement with experiments whereas those estimated according to isotropic‐hardening model are overestimated. The consideration of either step‐like or continuous void nucleation models indicates its great influence on fracture strains and emphasizes a further need to quantify the statistical parameters involved in these models.     

Particle toughening of polymers by plastic void growth

An analysis is given for the toughening of particle filled polymers assuming that plastic void growth around debonded, or cavitated particles is the dominant energy absorbing mechanism. The controlling parameter is the debonding (or cavitation) surface energy which triggers the growth of a plastic void around the particle which in turn enhances the toughness. Literature data are examined for particles ranging from 0.01 to 25 μm in radius in thermoset resins and it is found that the surface work for very small particles is the surface work of adhesion while for larger sizes it is some fraction of the matrix toughness. This larger debonding energy is found to be proportional to the particle radius. Large toughness increases are predicted, and observed, in the nano-range, i.e. 0.01 μm which are shown to require good particle dispersion and high matrix ductility. More modest increases are predicted at the micron scale but these are more robust.     

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.