Role of blend morphology in rubber-toughened polymers

The influence of blend morphology on mechanical behaviour of rubber-toughened polymers was investigated. Diglycidyl ether of bisphenol A epoxies toughnened by core-shell rubber particles were employed as the model systems. The blend morphology was varied by changing the composition of the shell of particles, the curing agent, and the extent of agitation prior to casting. It is shown that the most uniform dispersion of particles is obtained when the shell of the modifiers contains reactive groups. In the absence of the reactive groups and when a slow curing agent is employed, however, a highly connected microstructure is obtained. It was found that a blend with a connected microstructure provides significantly higher fracture toughness compared to a similar blend containing uniformly dispersed particles. The reason for this observation is that the connected morphology enables the shear bands to grow further from the crack tip and thus consume more energy before fracture occurs. Also, the yield strength in uniaxial tensile testing is significantly lower in the blend with the connected morphology. Therefore, it should contribute to a larger plastic zone size.     

Modelling of overall plastic deformation in rubber-toughened polymers

Summary. In this paper, we provide a constitutive model for overall (macroscopic) plastic deformation behavior in a rubber-toughened polymer blend. A porous plasticity theory is employed as a basis for the constitutive modeling. In our investigation, the polycarbonate (PC) is chosen as a matrix material of polymer blend. First, the true uniaxial stress-strain relation for PC, which is an important part of the constitutive model, is carefully measured. Secondly, finite element analyses of neck propagation in a tensile specimen of PC are performed to test the efficiency of the introduction of the accurately measured true stress-strain relation into the model. Then, in order to investigate local and average deformation behavior of the matrix material (PC) around cavitated rubber particles in polymer blend, an axisymmetric unit cell analysis is carried out. Finally, finite element analyses of the neck propagation in a tensile specimen of a rubber-toughened PC are performed, and the numerical results are compared to experimental results. It is revealed that the present constitutive model has the ability to well reproduce the behavior of a rubber-toughened polymer blend with rather small volume fraction of rubber particles, which is up to about 10%. However, for blends with larger volume fraction of the rubber particles, the discrepancy between the computational and the experimental results increases. Several possibilities of enhancing the model are discussed.     

Analytical modelling of mechanical properties for rubber-toughened polymers

Using a new quasi-sphere model, an analytical method is presented to determine the material properties and stress concentration factors of rubber-toughened polymers. The calculation is simple and the closed form results fit quite well with experimental data and various results using the finite element method. This simple and efficient method can be easily used to calculate a huge amount of results to fit the requirement of engineering. Also, this type of modeling can provide a better understanding of deformation mechanisms for development of this important composite material.     

Crack-tip damaged zones in rubber-toughened amorphous polymers: a micromechanical model

The various stages of crack propagation in rubber-toughened amorphous polymers (onset and arrest, stable and unstable growth) are governed by the rate of energy dissipation in the cracktip damaged zone; hence the relationship between the applied stress intensity factorK ₁ and the damaged zone size is of utmost importance. The size of the crack-tip damaged zone has been related toK ₁ via a parameter which is characteristic of the material in given conditions: this factor is proportional to the threshold stress for damage initiation in a triaxial stress field, and has been denoted by ^*. Theoretical values of ^* have been calculated by means of a micromechanical model involving the derivation of the stresses near the particles and the application of damage initiation criteria. The morphology, average size and volume fraction of the rubbery particles have been taken into account together with the nature of the matrix. The calculated values of ^* have been successfully compared with the experimental ones, for a wide set of high-impact polystyrenes (HIPS) and rubber-toughened poly(methyl methacrylate) (RTPMMA).Nomenclature PS; HIPS polystyrene; high-impact polystyrene - PMMA; RTPMMA poly(methyl methacrylate); rubber-toughened PMMA - MI; CS/H; CS/R particle morphologies (multiple inclusion; hard core - rubber shell; rubber core - rigid shell) - K _r;K _g bulk moduli of rubber and glassy materials - G _r;G _g shear moduli of the same materials - v _p particle volume fraction - L mean centre-to-centre distance between neighbouring particles - B; H; W standard names for the dimensions of the compact tension specimen - R _y size of the crack-tip plastic zone in a homogeneous material - h half thickness of the crack-tip damaged zone - r; polar coordinates around the crack tip (Fig. 1) - r;r _p distance from particle centre; particle radius - p normalized distance from the particle (Equation 5) - K ₁;K _1c;K _1p stress intensity factor; critical values ofK ₁ at the onset of and during crack growth - G _1c plane strain energy release rate - _y yield stress in uniaxial tension - _th macroscopic threshold stress for the onset of local damage initiation in a composite material - ^* characteristic parameter (Equation 3) - ⁰; ₁ ⁰ ; ₂ ⁰ ; ₃ ⁰ applied stress tensor and its three principal stresses - ⁰ uniaxial applied stress - ; ₁; ₂; ₃ local stress tensor and its three principal stresses - A tensor which elements are the ratios of those of over those of ⁰ (Equation 4) - v Poisson's coefficient of the matrix - g triaxiality factor of the crack-tip stress field - _e; _p Mises equivalent stress; dilatational stress (negative pressure) - I ₁;I ₂ invariants of the stress tensor - U ₁;U ₂ material parameters for argon and Hannoosh's craze initiation criterion (Equation 12)     

Cooperative cavitation in rubber-toughened polycarbonate

Particle cavitation in the stress-whitened zone ahead of a semicircular notch in polycarbonate blended with a core-shell rubber was characterized by transmission electron microscopy. Cavitation of rubber particles at five locations in the stress-whitened zone was correlated with the local stress and strain history. It was found that cavitation initiated some distance ahead of the notch when a mean stress condition was met. Initially, only a fraction of the particles cavitated and these were randomly distributed. Single cavitated particles grew into cavitated domains by cooperative cavitation of nearby particles until cavitation was arrested when shear yielding of the matrix provided an alternative mechanism for relief of strain energy. Far from the notch, where the stress state approached uniaxial tension, cavitated domains grew into linear arrays of cavitated particles. A mechanism of cooperative crazing in microlayer composites of polycarbonate and styrene/acrylonitrile copolymer was adapted to cooperative cavitation of core-shell rubber particles. It was proposed that cooperative cavitation of nearby particles occurred by impingement of a small plastic zone that formed at the equator of a cavitated particle.     

Effect of volume fraction of dispersed rubbery phase on the toughness of rubber-toughened epoxy polymers

Journal of Materials Science Letters -     

Interaction of crazes with pre-existing shear bands in glassy polymers

Shear bands have been grown in bulk specimens of P₃O(poly 2,6 diphenyl 1,4 phenylene oxide) and in thin films of two blends of polystyrene with poly(xylenyl ether). The subsequent interaction of crazes with these shear bands has been characterized by transmission electron microscopy. For the case of shear bands grown under the plane stress conditions of thin films, it is found that the bands act as preferential sites for craze nucleation. A fairly regularly-spaced array of short crazes grows within the shear bands and these crazes may thicken sufficiently to coalesce. When the crazes reach the end of the shear band they emerge and propagate into the unoriented polymer matrix. Within the shear band the craze growth direction does not lie normal to the tensile axis, but is rotated due to the molecular orientation of the shear band. The direction of craze growth is also affected under the plane strain conditions of bulk specimens. In this case the craze is diverted along the shear band before re-emerging into the matrix. Measurements of the craze fibril extension ratio, , within the shear band show an increase over typical values obtained outside the shear band in the same polymer. This high value of leads to an increased likelihood of craze break-down and crack nucleation within the shear band.     

Disclination-dislocation model for the kink bands in polymers and fibre composites

A disclination-dislocation model is proposed for the structure and movement of kink bands in oriented polymers and fibre composites, which describes bending and intermolecular slip inside the bands. It is shown that the band structure consists of special disclination-dislocation defects: slipped kinks. The mechanism of kink-band movement, based on the generation of such defects at the band front, is considered. The self elastic energy of slipped kinks is calculated and analysed in detail.     

Computer modelling of rubber-toughened plastics

A computer model has been developed which shows that high-impact polystyrene (HIPS) surface roughness (gloss) depends heavily on rubber phase volume and rubber particle size distribution parameters. The model has been developed in a series of steps. First, several tools have been created for isolation and display of rubber particles near the surface of computer-generated resins. Next, a technique for choosing surface points has been devised, using an algorithm which allows the surface to be disturbed by any particle near the surface. In step three, a non-linear fit of the surface points produces an abstract surface in the form of a grid. The variability in the array of grid points is a measure of surface roughness. The measured surface roughness of conventional high-impact polystyrene resins correlates to the variables identified by the model. A high percentage of the surface roughness variability has been explained in a correlation using average rubber particle size and rubber phase volume, showing the linear regression approach to be good for prediction of the surface roughness of conventional HIPS resins.     

Computer modelling of rubber-toughened plastics

Coarse models of high-impact polystyrene (HIPS) have been created by computer simulation of the rubber particle spacing in the resin. Interparticle surface-surface distance parameters can be calculated from the models to help explain properties of real materials and predict the properties of hypothetical impact-polystyrene resins. Calculations of the geometric spacing of rubber particles in a group of hypothetical HIPS resins show that a narrow rubber-particle size distribution gives smaller interparticle distance and more reinforcing particles compared to broad distributions for a given average particle size.     

Fracture behaviour of rubber-toughened polymer blends

The fracture toughness of a core-shell rubber modified polycarbonate-copolyester blend was determined by using theJ-integral approach. Single-edge notch bend specimens were tested at room temperature using a crosshead speed of 1 mm min^–1. The resistance curve for the blend was not affected by specimen width, direction of crack growth with respect to mould-flow direction, and sidegrooving. Fractographic analysis suggested that the matrix debonded from the rubber particles thus relieving the triaxial stresses and enabling the matrix to yield more easily. The initiation of crack growth in theJ-tests was observed to occur shortly after the onset of non-linearity in the load-deflection curve. Consequently, an attempt was made to describe fracture in this blend by using linear elastic fracture mechanics.     

A model for particle cavitation in rubber-toughened plastics

An energy-balance criterion for cavitation of rubber particles, which was proposed in an earlier paper [A. Lazzeri and C. B. Bucknall, J. Mater. Sci. 28 (1993) 6799], is developed by including a term for the energy stored in the matrix and released during expansion of the voids. The model relates the critical volume strain at cavitation to the radius of the rubber particle, and to the shear modulus, surface energy and failure strain of the rubber. The effects of temperature, strain rate and type of stress field upon cavitation behaviour and the resulting toughness of the two-phase polymer are discussed in terms of the model.     

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.     

Structure-property relations in an injection-moulded,rubber-toughened,semicrystalline polyoxymethylene

A relationship has been identified between the injection-moulded structure of a rubber-toughened polyoxymethylene (POM), and its mechanical properties. The material used was a commercially available POM (Dupont ST100) which contained 20% to 30% polyurethane rubber within a 50% to 60% crystalline matrix. These percentages were invarient through the thickness. A strong sensitivity towards the development of a core-skin morphology was discovered; microscopy and microhardness techniques revealed the skin depth to be 1200 m. The skin layer was found to consist of individual sheets, 2 to 4 m thick, that were stacked parallel to the plaque face. By contrast, the core contained spherulites, of 100 to 300 m diameter, that surrounded oriented discrete 2 to 4 m thick rubber rods. Morphological differences between the core and skin were reflected in their respective mechanical properties. Tensile response in the skin was ductile, with elongations reaching 300%, while the core exhibited more brittle behaviour (only 25% elongation). In both regions the yield strength was 45 MPa, a value expectedly reduced from the homopolymer (69 MPa) due to the presence of the rubber phase. Fatigue crack propagation response in the skin of the blend was found to be superior to that of the neat resin; however, the core behaviour was a function of orientation. A combination of inferior FCP response and the noticeable presence of a preferred plane of fracture, highlighted the significant weakness of the core material when loaded in a direction transverse to the injection moulding direction.