Essential work of fracture,crack tip opening displacement,and J-integral relationship for a ductile polymer film

A unique set of double-edge notched tension specimens of a Polyethylene Terephthalate Glycol-modified film was tested in mode I, plane stress. The load was registered on a universal testing machine. The displacements, ligament lengths, and video frames were recorded by a Digital Image Correlation system. With these registered data, the essential work of fracture, J-integral, and crack tip opening displacement (CTOD) fracture concepts have been applied. The onset of crack initiation was through a complete yielded ligament. The analysis showed that the intrinsic specific work of fracture, w_e, is the specific energy just up to crack initiation, which is an initiation value. w_e has both a coincident value and the same conceptual meaning as J_o, the J-integral at the onset of crack initiation. The relationship between J_o and CTOD is also determined. The influence on the notch quality when the specimens were sharpened by two different procedures, femtosecond laser ablation and razor blade sliding, was analysed in detail.     

Refined fixture design for effective essential work of fracture toughness characterization of m-LLDPE thin films

Characterization of Mode-I fracture toughness of ductile polymeric thin films is nontrivial. Proper specimen preparation and experimental procedures are required to ensure in-plane tensile loading. In this study, a custom-built double-edge notched tensile test fixture was employed to characterize the Mode-I essential work of fracture (EWF) toughness of metallocene linear low-density polyethylene (m-LLDPE) films. Effects of specimen geometry, strain rate and film orientation on the specific essential work of fracture, w_e, and the specific non-essential work of fracture, w_p, were investigated. Results indicate both EWF parameters are independent of the crosshead speed, gauge length (distance between upper and lower clamps) and specimen width within the ranges tested. w_e is significantly higher for thinner films and for crack propagation perpendicular to the blown film machine direction (MD). The usefulness of EWF for evaluating m-LLDPE fracture toughness is discussed.     

Determination and comparison of the plane stress essentialwork of fracture of three polyesters PET, PPT and PBT

The essential work of fracture (EWF) method has been used to study the relationship between molecular structure and thin film fracture toughness for three ductile polyesters at ambient temperature. The fracture toughness of PPT is of particular interest. Successful fracture characterisation of thin film polyesters has been achieved by the EWF method using double edge notched tension (DENT) specimens. The specific essential work of fracture, w _e, for polyethylene terephthalate (PET), polypropylene terephthalate (PPT) and polybutylene terephthalate (PBT) films is found to be 35.54±2.56, 41.03±3.23 and 31.34±8.60 kJ m^–2, respectively. Differential scanning calorimetry (DSC) has been employed to investigate the crystallinity of the polymers concerned and the effect of this on their EWF values.     

Fracture Behaviour and Deformation Mechanisms of Polyimide/Silica Hybrids

Films of particulate polyimide-silica hybrids were produced by a sol-gel process and were examined in terms of morphological structure and fracture properties at different temperatures, varying from 20 to 250 °C. The fracture toughness characteristics were studied by the “Essential Work of Fracture” method using double edge-notched specimens of different ligament lengths. The results showed that the fracture toughness, expressed through the essential (w_e) and non-essential work of fracture (βw_p) parameters increased when submicron silica particles were dispersed in the polyimide matrix. In particular, it was found that both w_e and βw_p increased with temperature to a larger extent than the parent polyimide. This enhancement in the fracture toughness was attributed to extensive cavitations and shear yielding originating at the particle interface and within the matrix.     

Determination and comparison of the essentialwork of fracture (EWF) of two polyester blends

The fracture toughness of blends of polypropylene terephthalate (PPT) with polyethylene terephthalate (PET) and polybutylene terephthalate (PBT) were investigated. Binary blends were prepared comprising 10:90, 30:70, 50:50, 70:30 and 90:10 mass/mass%. The fracture toughness was determined for each blend using the essential work of fracture (EWF) method and thin film double edge notched tension (DENT) specimens. The specific essential work of fracture, w _e, values obtained for blends of PET/PPT ranged from 27.33 to 37.38 kJ m^–2 whilst PBT/PPT blends yielded values ranging from 41.78 to 64.23 kJ m^–2. Differential scanning calorimetry (DSC) was employed to assess whether or not crystallinity levels influence the mechanical properties evaluated. The fracture toughness of PPT deteriorated with PET incorporation. However, high we values exceeding that of pure PPT were obtained for PBT/PPT blends across the composition range studied.     

J-testing of polymers via the load separation criterion based ESIS TC4 procedure: Effect of the specimen size

The Technical Committee 4, “Polymers, Polymer Composites and Adhesives”, of the European Structural Integrity Society (ESIS TC4) developed a draft protocol based on the load separation criterion to determine two fracture parameters (an initiation parameter, J_I,lim, and a crack growth parameter, m_s) without the need to measure the crack growth (Δa). This is especially beneficial, since the measurement of Δa is prone to errors. The developed testing scheme displays promising results, as shown in a round-robin testing exercise. To further push this testing scheme, it is necessary to verify the specimen size scaling possibility. Hence, in this work, single edge notched in bending (SE(B)) specimens with different sizes, but geometrically similar, were manufactured. ESIS TC4 testing scheme was successfully applied to specimens with the different sizes, and data of J_I,lim and m_s were obtained. The observed effect of the specimen size on the aforementioned fracture parameters is presented and discussed.     

Essential Work of Fracture of photo-oxidized LDPE/EVA Films

The Essential Work of Fracture approach (EWF) was used to determine how UV-C irradiation alters the fracture behaviour of LDPE/EVA films. Complementary characterization was performed by FTIR, DSC, TOM, and uniaxial tensile testing. The crosslinking reactions that govern photo-oxidation process at initial stage of exposure stiffened the amorphous phase of the polymer, leading to films with enhanced elastic modulus, yield stress and ultimate strength, but impaired strain at break. In the fracture experiments carried out on films irradiated within 0 and 5 days, EWF methodology requirements were met and the corresponding fracture toughness parameters (w_e and βw_p ) turned out to be sensitive to UV-C irradiation. Longer irradiation time triggered the development of microcracks, which not allowed further stable crack growth and invalidated the application of EWF approach.     

Microstructure and fracture behavior of semicrystalline polymer–clay nanocomposites

The relationships between the microstructure and the fracture behavior of three polymer/clay nanocomposites were studied. Two different polymer matrices were chosen, namely polyamide‐6 and polyethylene (compatibilized with PE‐g‐MA or PE‐g‐PEo), to reach very different clay dispersion states. The microstructure was characterized in terms of polymer crystallinity, orientation of the polymer crystalline lamellae, clay dispersion state, and orientation of the clay tactoids. The mechanical behavior was characterized by tensile tests. The essential work of fracture (EWF) concept was used to determine the fracture behavior of the nanocomposites. Both tensile and EWF tests were performed in two perpendicular directions, namely longitudinal and transversal. It is shown that the fracture behaviors of the matrices mainly depend on the polymer crystalline lamellae orientation. For the nanocomposites, the relationships between the matrix orientation, the clay dispersion states, the values of the EWF parameters (w_e and βw_p), and their anisotropy are discussed. The results show that the lower the average clay tactoid thickness, the lower is the decrease of fracture performance for the nanocomposite and the more consumed energy as longer the path of the crack. Besides, a linear dependence of the anisotropy of the EWF parameters of the nanocomposites on the average clay aspect ratio is found. The more exfoliated the structure is, the less pronounced the anisotropy of the EWF parameters. Interestingly, it is thought that the average clay aspect ratio is the parameter representing the clay dispersion state that governs the fracture anisotropy of the nanocomposites (as the elastic properties determined by tensile tests). © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1820–1836, 2008     

Essential work of fracture: An approach to study the fracture behavior of acrylic bone cements modified with comonomers containing amine groups

The fracture behavior of acrylic bone cements modified with comonomers containing amine groups was studied using the essential work of fracture approach. The cements were prepared with either 2-(diethylamino)ethyl-acrylate (DEAEA), 2-(dimethylamino)ethyl-methacrylate (DMAEM) or 2-(diethylamino)ethyl-methacrylate (DEAEM) as comonomer in the liquid phase. Double-Edge-Notched Tensión (DENT) specimens were tested in a universal testing machine at 5 mm/min. The results showed that the essential work (w_e) and nonspecific value of fracture (βw_p) of bone cements modified with all percentages of comonomer were notably increased compared with unmodified bone cement. From Scanning Electron Microscopy (SEM) micrographs, ductile behavior was observed for modified bone cements, i.e. the crack propagation is stable, whereas the unmodified cement exhibited brittle behavior indicating unstable crack propagation. The use of the essential work of fracture approach is suggested to determine the fracture behavior of cements that do not exhibit a linear stress-strain relationship.     

Effect of β-phase on the fracture behavior of dynamically vulcanized PP/EPDM blends studied by the essential work of fracture approach

The effect of β phase polypropylene (PP), induced by β-nucleating agent (β-NA), on the fracture behavior in dynamically vulcanized thermoplastic elastomers (TPVs) based on dynamically vulcanized PP/ethylene-propylene-diene rubber (EPDM) blend was studied. Differential Scanning Calorimetry (DSC) and Wide-angle X-ray diffraction (WAXD) were employed to study the melting behavior and crystalline structures, and the results indicated that the β-NA induced β phase of PP effectively in TPVs. With the increasing dosage of the β-NA incorporated in, the content of β phase increased while the total crystallinity of the blend kept constant. The fracture behavior of the TPVs with different β phase content was studied with double edge notched tensile loaded specimens (DENT) using the essential work of fracture (EWF) approach. The specific essential work of fracture (w_e) increased with the increasing of β phase content, indicating that the presence of β phase could effectively enhance the fracture toughness of TPVs.     

Relationship between fracture toughness and intrinsic deformation parameters in isotropic and flow‐oriented linear low‐density polyethylene

The fracture toughness of isotropic and flow‐oriented linear low‐density polyethylene (LLDPE) is evaluated by the Essential Work of Fracture (EWF) concept, with a special setup of CCD camera to monitor the process of deformation. Allowing for the molecular orientation, flow‐oriented sample, prepared via melt extrusion drawing, is stretched parallel (oriented‐0°) and perpendicular (oriented‐90°) to its original melt extrusion drawing direction, respectively. The obtained values of specific EFW w_e are 34.6, 10.2, and 4.2 N/mm for the oriented‐0°, isotropic and oriented‐90° sample, respectively. With knowledge of intrinsic deformation parameters deduced from uniaxial tensile tests, moreover, a relationship between specific EFW w_e the ratio of true yield stress to strain hardening modulus σ_ty/G is well established. It means that the fracture toughness of polyethylene is determined by both crystalline and amorphous parts, rather than by one of them. Moreover, the true yield stress seems to be nondecisive factors determining the fracture toughness of polyethylene. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2880–2887, 2006     

Analysis of fracture behaviour of fibre reinforced polypropylene using R-curve concept

Experimental results for investigation of dynamical crack resistance curves in the instrumented Charpy impact test on polypropylene (PP)/glass fibre composites are presented. For this purpose the multiple specimen R-curve method, stop-block technique is used. With the aid of J-integral versus stable crack growth (δa) curves the influence of a special coupler system on crack toughness as resistance against stable crack growth is discussed. It is shown that it is possible to quantify different energy dissipative processes with the new fracture mechanical material value J × T₇ (T₇ - tearing modulus). The problems of determining physical crack initiation values for short fibre composites are discussed. The physical material background for using the ‘plastic hinge’ model to describe the deformation behaviour of PP/glass fibre composites is shown, using the example of selected crack opening displacement (σ) versus δa curves.     

Chemical composition effects on the fracture of polystyrene-block-poly(methyl methacrylate)block copolymers

The crazing and fracture behaviors of glassy–glassy block copolymers were investigated for polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) diblock copolymers that had similar overall molecular weights but different poly(methyl methacrylate) (PMMA) molar fractions. A liquid chromatography technique was applied to separate as-synthesized PS-b-PMMA [(1) weight-average molecular weight (M_w) = 94,000 g/mol and PMMA molar fraction = 0.35 and (2) M_w = 65,000 g/mol and PMMA molar fraction = 0.28] into three fractions with different chemical compositions. With a copper-grid technique, the fracture behaviors of 0.5-μm-thick PS-b-PMMA films were studied as a function of the applied strain. For the higher M_w PS-b-PMMA samples, the median strains at crazing and fibril breakdown increased with an increase in the PMMA molar fraction from 0.24 to 0.46, corresponding to an increase in the chain entanglements in the PMMA domains. In contrast, for the lower M_w samples, the two values were not significantly changed even when the PMMA molar fraction was varied from 0.16 to 0.35. M_w of the minor component in PS-b-PMMA played a critical role in controlling the fracture behaviors of the block copolymers. Specifically, M_w/M_e of the minor component (where M_e is the molecular weight between entanglements) had to be roughly larger than 2 for the block copolymers to sustain sufficient strains before fracture. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3612–3620, 2006     

Fracture toughness of nylon‐6 blends with maleated rubbers

The fracture toughness of blends of nylon‐6 with maleated ethylene–propylene rubber and maleated styrene/hydrogenated butadiene/styrene triblock copolymer was investigated with a single‐edge‐notched three‐point‐bending instrumented Dynatup test. The blends for which the rubber particle size was less than 0.7 μm fractured in a ductile manner over the whole range of ligament lengths, whereas the blends with particles larger than 0.7 μm showed a ductile‐to‐brittle transition with the ligament length. In this regime, ductile fracture was observed for specimens with short ligaments, whereas brittle fracture was seen for those with long ligaments. The ductile fracture behavior was analyzed with the essential‐work‐of‐fracture model, whereas linear elastic fracture mechanics techniques were used to analyze the brittle fracture behavior. The fact that the ductile fracture energy was larger for the blends with the styrene/hydrogenated butadiene/styrene triblock copolymer than for those with ethylene–propylene rubber was due to the larger dissipative energy density of the blends based on the styrene/hydrogenated butadiene/styrene triblock copolymer. Both the critical strain energy release rate (G_IC) and the plane‐strain critical stress intensity factor (K_IC) increased as the rubber particle size decreased for both blend systems. The G_IC and K_IC parameters had similar values, regardless of the rubber type, when the rubber particle size was fixed. The transition ligament length was near the size criterion for plane‐strain conditions for both blend systems. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1739–1758, 2004     

On the determination of the point of fracture initiation by the load separation criterion in J-testing of ductile polymers

The application of an experimental approach based on the load separation criterion for the determination of the point of fracture initiation in a fracture test on a ductile polymer was critically examined. To this aim, the fracture process outlined by the application of this method was related to that described by the visual analysis of the fracture surfaces obtained in fracture tests on nominally identical specimens, in which different levels of crack extension were produced. The material examined was an acrylonitrile-butadiene-styrene (ABS) resin, and the fracture tests were performed at low loading rate on single-edge notched in bending specimens.The results demonstrated that this load separation criterion based methodology is a promising approach for the determination of the point of fracture initiation, and for material fracture resistance, J_Ic, evaluation. The method also has experimental simplicity and a high degree of repeatability.     

Influences of molecular weight and crystalline structure on fracture behavior of controlled-rheology-polypropylene prepared by reactive extrusion

The molecular weight of ethylene-block-co-polypropylene (co-PP) was adjusted by reactive extrusion with the incorporation of dicumyl peroxide (DCP), and the effect of molecular weight on the crystallization behavior, crystal morphology, and fracture behavior was investigated. It was found that, with increasing DCP content, the molecular weight (MW) decreased and the polydispersity (M_w/M_n) slightly decreased. After modification, the number of spherulites with obscure boundaries increased, and the size of the spherulites was more even due to increasing amount of grafting and micro-cross-linking structures, generated in co-PP degradation, which were acting as nucleating agents. Evaluated by essential work of fracture method, the specific essential work of fracture, w_e, was found to be strongly dependent on the molecular weight, especially, on the number average molecular weight (M_n) linearly, while the specific non-essential work of fracture, βw_p, was enhanced with decreasing z-average molecular weight (M_z), probably owing to the reduction of ultra-high molecular weight component in degraded co-PP.     

Improved resistance to crack growth of natural rubber by the inclusion of nanoclay

The effect of nanoclay on the fatigue crack growth behavior was investigated. Fatigue tests were carried out on edge notched specimens under cyclic tension loadings. A power–law dependency between crack growth rate and tearing energy was obtained. Natural rubber (NR) filled with 5 phr organically modified montmorillonite (OMMT) possessed the lowest value of the exponent, b, and the smallest crack growth rate at a given tearing energy, denoting the strongest resistance to crack growth. Strain‐induced crystallization was probed by synchrotron WAXD experiments, showing earliest occurrence and strongest ability of crystallization in NR with 5 phr OMMT due to the better exfoliation and orientation of clay layers. The study on the viscoelastic property by dynamic mechanical analysis indicated that NR filled with 10 phr OMMT had the largest contribution to tearing energy attributed to the viscoelastic dissipation in the viscoelastic region in front of the crack tip. This revealed that the strain‐induced crystallization played a more important role in the crack growth resistance than the viscoelastic dissipation for clay filled rubber. Copyright © 2010 John Wiley & Sons, Ltd.     

The use of load separation criterion and normalization method in ductile fracture characterization of thermoplastic polymers

Load separation is the theoretical basis for the single-specimen J-integral experiment and the incremental calculation of J-integral crack growth resistance (J-R) curves. This criterion has been experimentally studied in nongrowing crack records in several materials, and more recently a new method to extend the applicability to growing crack experiments has been proposed in testing steel. This article examines the applicability of the load separation criterion for evaluating ductile fracture mechanics parameters in rubber-modified polystyrenes and thermally treated polypropylene in the bending configuration. This criterion allows the load to be represented as the multiplication of two independent functions: a material deformation function and a crack geometry function. Its validity is evaluated with both stationary and growing crack experiments. η-factor calculation for smooth and side-grooved specimens was also tried using the simple method of Sharobeam and Landes, in order to identify material dependency. This article also investigates the applicability of the normalization method, based on the load separation criterion for evaluating J-R curves on PP and PS. A simple approach which combines a blunt notched and a precracked specimen experiment is proposed to determine the J-R curve of the materials studied. The resulting J-R curves are compared with multiple specimen results available in the literature for these materials. A good agreement between the J-R curves obtained from this simple method and from the multiple specimen technique was found. © 1996 John Wiley & Sons, Inc.     

Polydispersity effects in polymer self-diffusion measured by small-angle neutron scattering

The small-angle neutron scattering (SANS) method for measuring the self-diffusion coefficient D has been analyzed for effects of polydispersity in degree of polymerization for the case of linear polymers diffusing by reptation. Polydispersities corresponding to M_w/M_n = 1.0?10 were considered. It is shown that in all cases a meaningful effective diffusion coefficient D_e can be obtained from the short time recovery of the SANS intensity. This quantity D_e ≤ 1.3 D(M_w), where D(M_w) is the diffusion coefficient of a monodisperse polymer having molecular weight M = M_w. The method relies on SANS intensities extrapolated to zero scattering angle; realistic extrapolation is shown to give rise to quite acceptable errors on the order of 0.05 D_e.     

Symmetry breaking and electron correlation in O2−, O2, and O2+: A comparison of coupled cluster and quadratic configuration interaction approaches

Potential energy curves are calculated for O₂⁻, O₂, and O₂⁺ at the CCSD, QCISD, CCSD(T), and QCISD(T) levels of theory using aug-cc-pVDZ and aug-cc-pVTZ basis sets with electron correlation built onto inversion symmetry constrained and relaxed UHF wave functions. The spectroscopic constant r_e, w_e, w_e, x_e, D_j, and α_e, are determined from the potential curves using standard second-order perturbation theory expressions and are compared with experimental values to assess the relative accuracy of the theoretical approaches. Comparison of corresponding symmetry-constrained and symmetry-relaxed calculations indicates that the CCSD method is generally superior to CCSD(T), QCISD, and QCISD(T) in recovering from a symmetry-broken reference function. © 1996 John Wiley & Sons, Inc.