Essential work of fracture and j-integral measurements for ductile polymers

In the ductile tearing of polymers that neck before failure it is shown that the specific essential fracture work (w_e), consisting of the energies dissipated in forming and tearing the neck, is a material property for a given sheet thickness and is independent of specimen geometry. Work of fracture experiments using both double deep-edge notched (DENT) and deep-center notched tension (DCNT) geometries with different ligament lengths yielded almost identical w_e values for a grade of high-density polyethylene. These measurements for w_e are in fairly good agreement with the theoretical values based on the J integral evaluated along a contour surrounding the neck region near the crack tip. Under J-controlled crack growth conditions, it is shown that J_c obtained by extrapolation of the J_R curve to zero crack growth and the slope dJ/da are identical, respectively, to w_e and 4βw_p obtained from the straight line relationship between the specific total work of fracture (w_f) and ligament length (l).     

A method to evaluate critical J-integral value: Locus method

A method which evaluates the critical J-integral value (J_c) by utilizing the locus of crack initiation points on load-displacement records is presented. This method partitions the fracture energy along the locus line based on an energy rate interpretation. The shape of the locus line depends on both the material and the configuration of the specimen. Since the fracture energy can be partitioned even along a nonlinear locus line, the method is also suitable for highly deformable materials, which usually exhibit a nonlinear locus line. In order to validate this point, a thermoplastic rubber was used for experimental study. The experimental results show that J_c can be evaluated by this method without restricting the ratio of the initial crack length to the specimen width (a/w) or the specimen length provided that the locus line can be located on the load-displacement record.     

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.     

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.     

A finite element method based comparative fracture assessment of carbon black and silica filled elastomers: Reinforcing efficacy of carbonaceous fillers in flexible composites

This study is focused on numerical investigation on fracture behaviors of carbon black (CB) and silica filled elastomeric composites. Finite element analysis (FEA) in compliance with multi-specimen method is used to calculate J-integral and geometry factor of the rubber composites up to a displacement of 20 mm for single edge notch in tension (SENT) and double edge notch in tension (DENT) specimens. An empirical relationship between crack tip opening displacement (CTOD) and crack advancement is established depending on notch to width ratio (NWR). The stress contours across the notches for SENT and DENT specimens is discussed briefly. It is found that fracture propagation resistance of CB filled elastomer is 125% more than that of silica filled elastomer. Although, Silica filled elastomer have good tensile strength and crosslink density but it fails to replace carbon black in terms of fracture properties. The critical J-integral for CB filled elastomer is 18.7% and 32.2% more than silica filled elastomer for SENT and DENT specimens respectively. The effect of specimen type on various fracture properties is also explored. The factor of safety is found to be significantly more in case of CB filled elastomers making them less vulnerable to crack propagation and catastrophic failure.     

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.     

Fracture resistance measurement of fused deposition modeling 3D printed polymers

A method is presented to characterize the fracture resistance and interlayer adhesion of fused deposition modeling (FDM) 3D printed materials. Double cantilever beam (DCB) specimens of acrylonitrile butadiene styrene (ABS) were designed and printed with a precrack at the layers' interface. The DCBs were loaded in an opening mode and the load-displacement curves were synchronized with the optical visualization of the crack tip to detect the critical load at the crack initiation. A finite element model, coupled with J-integral method and fracture surface analysis was then developed to obtain the apparent fracture resistance (J_cr,a) and the interlayer fracture resistance (J_cr,i), as a measure of the interlayer adhesion. The maximum J_cr,i was measured to be 4017 J/m², a value close to the fracture resistance of bulk ABS. Both J_cr,a and J_cr,i increased with the printing temperature. This method can find a great importance in the structural applications of printed materials.     

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.     

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.     

Flow properties of poly(methyl methacrylate) solutions

Viscosity and normal stress behavior were measured for poly(methyl methacrylate) samples of various average molecular weights in diethyl phthalate solution at 30 and 60°C. All samples conformed approximately to the most probable distriution (M?_w/M?_n = 2). Concentrations ranged from 0.113 to 0.38 g/ml, and M?_w from 53,800 to 1,620,000. Despite considerable evidence in the literature of unusual linear viscoelastic behavior for this polymer, its nonlinear properties appear to be rather conventional. The viscosity–shear rate master curve was similar to that found earlier for concentrated solutions of polystyrene and poly(vinyl acetate) of comparable molecular-weight distribution. The viscosity time constant τ_o parallels τ_R, the characteristic time of the Rouse model, although the residual dependence of τ_o/τ_R on concentration and molecular weight appears to be slightly different from that for polystyrene and poly(vinyl acetate). Similar conclusions apply to the recoverable compliance J_e,^o estimated from the normal stress behavior of each solution, and its relationship to the Rouse model compliance J_R.     

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.     

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.     

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.     

Interlaminar fracture toughness of unidirectional DCB specimens: A novel theoretical approach

A novel theoretical approach is presented to calculate the mode I interlaminar fracture toughness (G_Ic) of double cantilever beam (DCB) specimens with low ratio of initial crack length-to-thickness (a₀/2h). This method is based on a sixth-order beam theory, namely Reddy-Bickford beam (RB), on Winkler elastic foundation (WEF) to account for both transverse shear deformation of the beam and local effects at the delamination front (root rotation). RB with only two generalized displacements w and ?; and three boundary conditions at ends and loading points of a shear deformable beam gives more accurate results than the fourth-order Timoshenko beam theory. The accuracy of the proposed method in prediction of initiation G_Ic values is evaluated together with other available models considering the experimental fracture toughness for moderately thick unidirectional E-glass/epoxy DCB specimens with small initial delamination lengths.     

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.     

Isotope Shifts of Nitrogen around 800 nm

The Doppler-limited absorption spectra of ¹⁴N and ¹⁵N atoms were measured around 800 nm using concentration modulation spectroscopy to study their isotope shifts. The nitrogen atoms were generated by discharging molecular nitrogen buffered with helium in a homemade discharge tube. The isotope shifts of four multiplets (3s⁴P_J→3p⁴D_J^o, 3s⁴P_J→3p⁴P_J^o, 3s²D_J→5s²P_J^o, and 3p²P_J^o→5s²D_J^o) were measured and their J-dependent specific mass shifts were observed and discussed.     

On the experimental measurement of fracture toughness in SENT rubber specimens

This work provides a direct comparison of several experimental approaches used in the literature to measure fracture toughness of rubber of rubber using single edge notched in tension (SENT) specimens, with the final aim to provide guidelines for an optimal testing procedure. Digital image correlation measurements were used to get new insights into the fracture process. SENT is experimentally advantageous because of the simple preparation from laboratory plates and the small amount of material required. The most common experimental approaches to measure fracture toughness of rubber rely on the energy release rate, measured by the tearing energy or the J-integral parameters. This work points out the importance of experimental conditions and test procedures: long specimens and short notches are preferred, identification of fracture initiation from the front view is necessary, strain energy density should not be evaluated from un-notched specimens at the critical stretch level, rather alternative strategies are shown in this work.     

Direct fracture toughness determination of a ductile epoxy polymer from digital image correlation measurements on a single edge notched bending sample

This work presents a combined experimental and numerical study on the fracture toughness behaviour of a ductile epoxy resin system. Quasi-static fracture tests using single edge notched bending (SENB) specimens were conducted under room temperature conditions. In addition, the digital image correlation technique was employed to experimentally map the full-field displacements and strains around the notch and crack tip, allowing direct calculation of the J-integral fracture toughness. The magnitude of fracture toughness was found to be 1.52 ± 0.03 kJ/m², showing good consistency with the results measured according to the standard analytical formulations. A numerical model of the single edge notch bending specimen was built to compute the local strain field around the crack tip, together with the fracture toughness parameter. Good agreement was confirmed for both the experimental J-integral fracture toughness and the local surface strains around the crack-tip from the digital image correlation based optical technique, compared to the results obtained by numerical simulation. The fracture surfaces of the samples were examined using an optical microscope to analyze the failed surface morphology and the corresponding failure mechanisms.     

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.     

Morphology and fracture behaviour of polyethylene/Mg-Al layered double hydroxide (LDH) nanocomposites

Fracture behaviour of polyethylene (PE)/Mg-Al layered double hydroxide (LDH) based nanocomposites has been studied by essential work of fracture (EWF) approach. Transmission electron microscopy (TEM and X-ray diffraction (XRD) analysis have been used to investigate the morphological features of these nanocomposites. A maximum in the non-essential work of fracture was observed at 5 wt.% LDH demonstrating enhanced resistance to crack propagation compared to pure PE. Morphological analyses of the nanocomposites show that the dispersed LDH platelets are partially exfoliated and also forms clusters with polymer chains remaining entrapped within. Rheological analyses show that the typical low-frequency Newtonian flow behaviour, as observed in unfilled polymer, shifts to shear-thinning behaviour with increasing LDH concentration. At 5 wt.% LDH a ductile-to-brittle transition has been observed. Fracture surface investigation by SEM reveals the arresting of the plastic crack growth by the LDH particle clusters, which is more significant at 5 wt.% LDH content. At higher LDH concentrations, the number of such particle clusters increases causing decrease in the average distance between them. As a result large-scale plastic deformation of the matrix at higher LDH concentration is effectively arrested favouring small strain failure and this in turn reaffirms the possible existence of a ductile-to-brittle transition. The study in general reveals that the resistance against crack initiation (essential work of fracture: EWF) and crack propagation (non-essential work of fracture: βw_p) in these nanocomposites are structurally correlated with the matrix behaviour and the morphology (state of LDH particle dispersion) respectively.