The stress-whitened damage zone of PVC blends

The stress-whitened damage zone that formed ahead of a semicircular notch during slow tensile loading has been measured from optical micrographs of translucent blends of poly(vinyl chloride) (PVC) with experimental chlorinated polyethylene (CPE) resins. When the zone was small, the plane strain condition applied and from the elastic stress distribution a constant mean stress condition was found at the boundary of the crescent-shaped zone. The critical mean stress did not depend on the chlorine content or the chlorine distribution of the experimental CPE resin used in the blend. While the critical mean stress decreased as the amount of CPE in the blend was increased, the critical volume strain, calculated from the bulk modulus, was independent of composition and was thought to be the controlling parameter for stress-whitening. When the zone was larger, the shape was qualitatively described by concepts of stress redistribution in the presence of a plastic zone ahead of the notch. Macroscopic flow and necking were only detected near the maximum in the stress-displacement curve.     

Toughening of polystyrene by natural rubber-based composite particles: Part III Fracture mechanisms

Impact testing has allowed the toughness of PS blends to be correlated with the morphology of the dispersed rubber phase, which was a natural rubber (NR) in particle form, coated with a shell of polystyrene (PS) or polymethylmethacrylate (PMMA). PS subinclusions were also introduced into the NR core. The impact resistance of the prepared PS blends began to rise steeply at a particle content of about 18 wt %. Transmission electron microscopy (TEM) in combination with osmium tetroxide staining techniques, allowed direct analysis of the crazing and cavitation processes in the composite natural rubber particle-toughened PS blends. Bulk samples were studied at high and slow deformation speeds. Different deformation mechanisms were effective, depending on the location of the observed stress-whitened zone relative to the notch tip. The apparent fracture mechanisms in rubber-toughened PS blends were also studied by scanning electron microscopy. PS blends containing polydisperse natural rubber-based particles or monodisperse poly(n-butylacrylate)-based particles, and commercial high-impact polystyrene, were compared. This revised version was published online in November 2006 with corrections to the Cover Date.     

Nylon-6/rubber blends

The stress field around a rubber particle and a cavitated particle in a nylon/rubber blend has been studied using an analytical and a finite element approach. Attention was paid to the influence of the mechanical properties of the dispersed phase and the applied stress state. The results show that the choice of the bulk modulus of the elastomer is crucial. It appeared that especially with a triaxial stress, the Von Mises stress increased strongly upon cavitation (a more than five-fold increase close to the particle) while the hydrostatic stress only increased slightly. Also, the stresses in particles in the neighbourhood of a cavity have been calculated. Stresses in particles lying in or close to the equatorial plane of the cavity were higher than stresses in the other particles. Therefore, propagation of cavitation is most likely to occur perpendicular to the applied stress.     

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.     

The effect of load level on the mechanism of fatigue crack propagation in ABS

The fatigue crack propagation (FCP) mechanism of an ABS was examined under tension-tension loading as a function of load level. The crack was always preceded by a damage zone consisting of assemblies of stress-whitened lines. Crack growth was predominantly through the root damage line, with occasional jumps into neighbouring lines. These jumps occurred most frequently in the medium load level test. Transmission electron microscopy (TEM) analyses showed the damage within the stress-whitened lines to consist of elongated, and occasionally ruptured, rubbery domains at the specimen surface, with the appearance of extensive crazes bridging their interstices toward the mid-thickness. The craze intensity (size and number) increased with decreasing load level. The crazes manifested themselves on the fracture surface as a patch morphology, which was increasingly pervasive with decreasing load level. In the rougher region that followed, ductile tearing of the matrix is believed to be promoted by rubber cavitation and the merging of crazes. Normal fatigue striations indicate crack advance by greater fractions of the damage zone length at higher load levels.     

Analysis of elastoplastic sharp notches

In this paper the elastoplastic solutions with higher-order terms for apex V-notches in power-law hardening materials have been discussed. Two-term expansions of the plane strain and the plane stress solutions have been obtained. It has been shown that the leading-order singularity approaches the value for a crack when the notch angle is not too large. In plane strain cases the elasticity does not enter the second-order solutions when the notch opening angle is too small. For a large notch angle, the two-term expansions of the plane strain near-tip fields are described by a single amplitude parameter. The plane stress solutions generally contain the elasticity terms. The boundary layer formulations based on the small-strain plasticity theory confirm that a dominance zone exists ahead of the notch tip. Finite element results give good agreement to the asymptotic solutions under both plane strain and plane stress conditions. The second-order terms cannot improve the predictions significantly. The near-tip fields are dominated by a single parameter. Finite element calculations under the finite strain J ₂-flow plasticity theory revealed that the finite strains can only affect local characterization of the asymptotic solution. The asymptotic solution has a large dominance zone around the notch tip. For an apex notch bounded to a rigid substrate the leading-order singularity falls with the notch angle significantly more slowly than in the homogeneous material. It vanishes at the notch angle about 135° for all power-hardening exponents. The elasticity effects enter the second-order solutions when the notch angle becomes large enough. The tip fields are characterized by the hydrostatic stress and the shear stress ahead of the notch.     

Volume change and light scattering during mechanical damage in polymethylmethacrylate toughened with core-shell rubber particles

Mechanical damage was investigated in polymethylmethacrylate toughened with core-shell (hard core) rubber particles. During a tensile experiment, volume changes, light absorption, light scattering and a small strain elastic modulus were recorded. Light scattering was quantitatively related to the number of damaged particles and a fast partial unloading technique allowed determination of the non-elastic part of these changes in material properties. Experiments performed between 10^–5 and 10^–1s^{–1 and between 20 and 70 °C} showed time-temperature transitions. These appeared to be different for each property, and measurement of the activation energy for each parameter enabled microscopic damage mechanisms to be inferred. Three types of microstructural damage were observed: pure matrix plasticity at very low strain rates or high temperatures, rubber cavitation at correlated locations at medium strain rates and temperatures, and disordered cavitation, rubber tearing and matrix plasticity at high strain rates or low temperatures. The experimental mean stress triggering rubber cavitation was compared with the predicted value.     

Craze-like damage in a core-shell rubber-modified epoxy system

Toughening mechanisms of a core-shell rubber-modified epoxy were investigated using various microscopic techniques. It was found that the crack tip damage zone of the rubber-modified epoxy appeared to consist of multiple craze-like damage and massive shear banding using optical microscopy. The craze-like damage was further analysed using transmission electron microscopy (TEM) and actually found to be a collection of line arrays of highly cavitated rubber particles. The matrix material around the cavitated particles appeared to have plastically deformed, while the material outside of the array was undeformed. The structure and physical nature of this highly localized dilatational process are substantially different from those of the commonly known craze. The sequence of events leading to the formation of these craze-like line arrays is discussed.     

不同冲击断裂方式下橡胶粒子形态对HIPS脆韧转变的影响

核-壳型/蜂窝型高抗冲聚苯乙烯(HIPS)树脂在Izod冲击和落锤冲击断裂过程中的脆-韧转变行为不同。透射电镜(TEM)对亚断裂形变区的观察表明,蜂窝型HIPS对落锤冲击作用下的脆韧转变敏感,应力集中能有效引发基体的塑性形变,呈韧性断裂,但在v-notched Izod冲击断裂过程中,却呈脆性;而核-壳型HIPS的冲击断裂性能与之相反。将LDO假说引入冲击破坏研究并结合损伤竞争准数Da和Vincent图探讨了分散相特性及冲击方式对脆韧转变行为的影响。     

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.     

Fracture of notched polycarbonate under hydrostatic pressure

The brittle fracture behaviour and plastic deformation of round-notched polycarbonate bars subjected to three-point bending under hydrostatic pressure have been studied. Below a certain critical pressure, the brittle fracture initiated from an internal craze nucleated at the tip of the local plastic zone ahead of the notch rooT. The position of the nucleation of the craze receded from the tip of the notch with increasing applied pressure. When the pressure was increased over a critical value, general yielding occurred by passage of the plastic zone across the notched cross-section, that is, the brittle to ductile transition took place. A qualitative analysis of the stress distribution within the plastic zone explains that the brittle to ductile transition under hydrostatic pressure occurs when the general yield takes place before a critical stress for brittle crack propagation is reached.     

Damage zone development in PVC under a multiaxial tensile stress state

The irreversible deformation mechanisms of poly(vinyl chloride) with a semicircular notch under slow tensile loading have been studied as a function of sheet thickness. Initially, core yielding was observed in the optical microscope as two families of slip lines growing from the notch surface in the centre of the specimen. The size and shape of the core yielding zone could be described by plasticity analysis. A stress-whitened zone subsequently initiated near the tip of the slip line zone. The stress whitening was caused by 1 m voids that were visible in the scanning electron microscope. The mean stress for stress whitening was calculated to be 43.0±1.5 MPa by a plastic stress analysis of a pressure-dependent yield material. By assuming a constant mean stress along the boundary of the stress-whitened zone, the one-dimensional shift of the elastic stress distribution was obtained. At higher stresses, hinge shear and intersecting shear were observed for thick and thin sheet, respectively.     

Nylon-6/rubber blends

The deformation zone of fractured nylon-6/ethylene-propylene rubber specimens was studied using scanning electron microscopy (SEM). In this deformation zone three distinct layers were observed. In the main part of the stress-whitened zone only cavitation was visible. From 150-5 m below the fracture surface, massive plastic deformation was observed. Directly under the fracture surface there was a layer about 3–5 m thick where no cavitation or deformation was visible. This zone without cavitation was only visible when the specimen was fractured at high deformation rates. It is proposed that this top layer consists of material which was molten during fast crack propagation under adiabatic conditions. This hypothesis has been confirmed by model calculations and experiments. When the deformation rate is very high (greater than the impact velocities) plastic deformation is not homogeneous throughout the deformation zone, but confined to layers.     

Corrosion-Facilitating Local Plastic Deformation for α-Ti in Methanol

The effect of corrosion process on facilitating local plastic deformation for α-Ti in methanol has been investigated with the micro-multiplicative moire interferometer technique. The size of plastic zone and the plastic strain ahead of loaded notch have been measured. The results show that the anodic dissolution, or corrosion process itself can enhance the plastic zone and the plastic strain ahead of a loaded notch during stress corrosion of α-Ti in methanol solution     

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.     

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.     

Numerical and experimental studies on the fracture behavior of rubber-toughened epoxy in bulk specimen and laminated composites

To study the toughening mechanisms of liquid rubber (LR) and core-shell rubber (CSR) in bulk epoxy and composite laminate, experimental and numerical investigations were carried out on compact tension (CT) and double-cantilever-beam (DCB) specimens under mode-I loading. The matrix materials were pure epoxy (DGEBA), 15% LR (CTBN) and 15% CSR modified epoxies. Experimental results and numerical analyses showed that both liquid rubber (LR) and core-shell rubber (CSR) could improve significantly the fracture toughness of pure epoxy (DGEBA). However, the high toughness of these toughened epoxies could not be completely transferred to the interlaminar fracture toughness of the unidirectional carbon fibre reinforced laminate. The main toughening mechanism of CSR in bulk epoxy was the extensive particle cavitation, which greatly released the crack-tip triaxiality and promoted matrix shear plasticity. The poor toughness behavior of CSR in the carbon fibre laminate was thought to be caused by the high constraint imposed by the stiff fibre layers. No particle cavitation had been observed in LR modified epoxy and the main toughening mechanism was merely the large plastic deformation near the crack-tip due to the rubber domains in the matrix which results in a lower yield strength but a higher elongation-to-break.     

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.     

On cavitation and macroscopic behaviour of amorphous polymer-rubber blends

Abstract

The macroscopic behaviour of rubber-modified polymethyl methacrylate (PMMA) was investigated by taking into account the microdeformation mechanisms of rubber cavitation. The dependence of the macroscopic stress–strain behaviour of matrix deformation on the cavitation of rubber particles was discussed. A phenomenological elastic-viscoplastic model was used to model the behaviour of the matrix material, while the rubber particles were modelled with the hyperelasticity theory. A two-phase composite material with a periodic arrangement of reinforcing particles of a circular unit cell section was considered. Finite-element analysis was used to determine the local stresses and strains in the two-phase composite. In order to describe the cavitation of the rubber particles, a criterion of void nucleation is implemented in the finite-element (FE) code. A comparison of the numerically predicted response with experimental result indicates that the numerical homogenisation analysis gives satisfactory prediction results.     

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.