Load separation principle in determination of J-R curve for ductile polymers: Suitability of different material deformation functions used in the normalization method

The load separation principle states that the load, P, can be represented as the multiplication of two independent functions: A crack geometry function, G(a), and a material deformation function, H(v). The principle constitutes the theoretical basis for the single-specimen J-integral experiment and the incremental calculation of J-integral crack growth resistance (J-R) curves. The normalization method is a new method, which assumes load separation and uses characteristic deformation properties of materials to relate load, displacement and crack length in a functional form. From the deformation material function or “material key curve”, J-R curve can be developed from a single precracking experiment. This investigation deals with the applicability of the load separation criterion to evaluation of ductile fracture mechanics parameters in rubber-modified polystyrene, polypropylene, rubber-modified PMMA, ABS resin and high-density polyethylene in the bending configuration. Different mathematical relationships for the deformation function (power law function, LMN function and combined power law straight line relationship) have been proposed and compared. The resulting J-R curves are in good agreement with those obtained by the traditional multiple-specimen technique. The results presented here imply that the use of a single load-displacement method for evaluation of J-integrals for ductile polymers is possible and hence also the normalization method can be used for evaluation of J-R curves from a single-test record.     

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).     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Effect of molecular relaxations on the fracture behavior of poly(vinyl chloride)

The fracture toughness of PVC has been measured by using three-point bend specimens tested over a wide range of strain rate and temperature. A method has been described of deriving fracture load indirectly by measurement of stiffness from a preliminary “low blow” test in instrumented impact testing. Some limitations of the method, when used with semi-ductile material of low stiffness, have been discussed. Fracture toughness results have also been evaluated by an alternative energy method, which is however more suitably applied to the lower speed impact test. The curves of K_1c versus temperature for PVC contain a weak maximum at a temperature below T_g, the location of which varies with testing speed. The position of the maximum in the time–temperature field has been compared with the locus of the β damping peak derived from mechanical (flexural vibrations, torsion pendulum) and dielectric loss measurements, with reasonable agreement. Static toughness was higher than dynamic, and this correlated with fracture surface appearance, thereby indicating a real difference in toughness probably associated with crack tip craze development.     

Finite element modelling of mode I delamination specimens by means of implicit and explicit solvers

The simulation of delamination using the Finite Element Method (FEM) is a useful tool to analyse fracture mechanics. In this paper, simulations are performed by means of two different fracture mechanics models: Two Step Extension (TSEM) and Cohesive Zone (CZM) methods, using implicit and explicit solvers, respectively.TSEM is an efficient method to determine the energy release rate components G_Ic, G_IIc and G_IIIc using the experimental critical load (P_c) as input, while CZM is the most widely used method to predict crack propagation (P_c) using the critical energy release rate as input.The two methods were compared in terms of convergence performance and accuracy to represent the material behaviour and in order to investigate their validity to predict mode I interlaminar fracture failure in unidirectional AS4/8552 carbon fibre composite laminates.The influence of increasing the loading speed and using mass scaling was studied in order to decrease computing time in CZ models.Finally, numerical simulations were compared with experimental results performed by means of Double Cantilever Beam specimens (DCB).Results showed a good agreement between both FEM models and experimental results.     

Characterizing fracture energy of proton exchange membranes using a knife slit test

Pinhole formation in proton exchange membranes (PEM) may be caused by a process of flaw formation and crack propagation within membranes exposed to cyclic hygrothermal loading. Fracture mechanics can be used to characterize the propagation process, which is thought to occur in a slow, time‐dependent manner under cyclic loading conditions, and believed to be associated with limited plasticity. The intrinsic fracture energy has been used to characterize the fracture resistance of polymeric material with limited viscoelastic and plastic dissipation, and has been found to be associated with long‐term durability of polymeric materials. Insight into this limiting value of fracture energy may be useful in characterizing the durability of proton exchange membranes, including the formation of pinhole defects. In an effort to collect fracture data with limited plasticity, a knife slit test was adapted to measure fracture energies of PEMs, resulting in fracture energies that were two orders of magnitude smaller than those obtained with other fracture test methods. The presence of a sharp knife blade reduces crack tip plasticity, providing fracture energies that may be more representative of the intrinsic fracture energies of the thin membranes. Three commercial PEMs were tested to evaluate their fracture energies (G_c) at temperatures ranging from 40 to 90 °C and humidity levels varying from dry to 90% relative humidity (RH). Experiments were also conducted with membrane specimens immersed in water at various temperatures. The time temperature moisture superposition principle was applied to generate fracture energy master curves plotted as a function of reduced cutting rate based on the humidity and temperature conditions of the tests. The shift with respect to temperature and humidity suggests that the slitting process is viscoelastic in nature. Also such shifts were found to be consistent with those obtained from constitutive tests such as stress relaxation. The fracture energy is more sensitive to temperature than on humidity. The master curves converge at the lowest reduced cutting rates, suggesting similar intrinsic fracture energies; but diverge at higher reduced cutting rates to significantly different fracture energies. Although the relationship between G_c and ultimate mechanical durability has not been established, the test method may hold promise for investigating and comparing membrane resistance to failure in fuel cell environments. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 333–343, 2010     

On the measurement of the fracture resistance of polyacrylamide hydrogels by wire cutting tests

The applicability of wire cutting in determining the fracture resistance, G_c, of polyacrylamide (PAAm) hydrogels, with different polymer contents and mechanical stiffness, was investigated. The various gels were synthesized both in the form of cylindrical and bar-shaped samples. Following the experimental scheme proposed in literature for wire cutting, each hydrogel, in the form of cylindrical specimen, was subjected to wire cutting with wires of different diameters. For each hydrogel, G_c was also separately measured by more conventional fracture tests on notched specimens prepared from the bar-shaped samples.The results demonstrated that, although G_c of the PAAm hydrogels here examined could not be evaluated by the direct application of the simple scheme proposed in literature, wire cutting is a promising approach for the measurement of the fracture resistance of chemical gels with relatively high stiffness, also in consideration of its proven experimental simplicity.     

Effect of BaF2 in the formation of Y2BaCuO5 particles in Y-Ba-Cu-O superconductor

The YBCO superconductor was synthesized with BaF₂. The synthesis temperature of the specimen with BaF₂ was to be considerably lower than that for the unused one. The BaF₂ decomposes during the heat treatment, and does not influence the structure and critical temperature. The critical current density,J _c, in the specimen is 1×10⁸ A/m² at 77 K and 0.5T. However,J _c is actually lower for the QMG specimen because the Y₂BaCuO₅ particles are larger than those of the QMG specimen.     

Slow crack growth in blends of HDPE and model copolymers

The resistance to slow crack growth (SCG) was measured in binary blends of high density polyethylene (HDPE) and 5–10% concentrations of model ethylene-butene random copolymers by measuring the time to failure (t_f) under a constant stress intensity. An increase of t_f with the addition of the copolymer if the copolymer could crystallize and the increase was greater the higher branch density. The copolymer with 117 branches/1000C could not crystallize and therefore its blend had a t_f that was less than that of the HDPE. The fracture energies of the blends as determined by their resistance to SCG were compared with the energy by rapid fracture, J_c, as previously measured by Rhee and Crist. It is concluded that SCG is more sensitive to variations in the microstructure than is rapid fracture and that the differences in SCG behavior can be qualitatively explained in terms of the differences in microstructure of the blends. ©1995 John Wiley & Sons, Inc.     

BASHD‐J‐resolved‐HMBC,an efficient method for measuring proton–proton and heteronuclear long‐range coupling constants

Natural products often possess various spin systems consisting of a methine group directly bonded to a methyl group (e.g. –CH_a–CH_b(CH₃)–CH_c–). The methine proton H_b splits into a broadened multiplet by coupling with several vicinal protons, rendering analysis difficult of ⁿJ_C–H with respect to H_b in the J‐resolved HMBC‐1. In purpose of the reliable and easy measurements of ⁿJ_C–H and ⁿJ_H–H in the aforesaid spin system, we have developed a new technique, named BASHD‐J‐resolved‐HMBC. This method incorporates band selective homo decoupled pulse and J‐scaling pulse into HMBC. In this method, high resolution cross peaks can be observed along the F₁ axis by J‐scaling pulse, and band selective homo decoupled pulse simplified multiplet signals. Determinations of ⁿJ_C–H and ⁿJ_H–H of multiplet signals can easily be performed using the proposed pulse sequence. Copyright © 2013 John Wiley & Sons, Ltd.     

Tailored adhesion at polymer/nonpolymer interfaces

In this investigation, block copolymers of deuterated polystyrene (dPS) and poly (2-vinylpyridine) (PVP) have been used to modify the adhesion at polystyrene/soda lime glass interfaces. The fracture energy, G_s of these interfaces was measured using an asymmetric double cantilever beam specimen. The failure mechanism was investigated using forward recoil spectrometry (FRES) and Rutherford backscattering spectrometry (RBS). The areal density, ∑ of the dPS-PVP block copolymer at the two fracture surfaces, as well as the fraction of the dPS block on the PS side of the fractured sample are measured directly by FRES. The fraction of the PVP block on the glass side of the interface can be found by quaternizing the PVP with methyl iodide and then using RBS to measure the amount of iodine on each fracture surface. Short dPS blocks (N_dPS < 175) do not entangle effectively with the PS homopolymer and only very small increases in G_c can be achieved as the dPS block pulls out of the interface. If the dPS block is long (N_dPS ? 175) and if ∑ is large, crazes can develop in the PS ahead of the crack. The crazed interface fails at low ∑ by breaking the block copolymer close to the styrene/vinylpyridine link. At higher ∑, if the PVP block is relatively short (N_PVP = 95), the crazed interface fails by the PVP block being pulled off the glass. If both the PVP and dPS blocks are long (? 175), the G_c increases rapidly with increases in ∑, but the interface becomes so strong that the glass on the thinner side of the test specimen breaks. The dPS block and the PVP block are found on opposite sides of the fracture surface with most of the PVP on the glass and most of the dPS on the PS side of the interfaces. Finally, if the glass surface is modified by coating it with a self-assembled hydrophobic monolayer produced from chlorodimethyloctadecylsilane (CDMOS), the interface becomes very weak and fails by pull-off of the PVP from the CDMOS-coated glass. Using these results it is possible to tailor the interfacial adhesion to produce a desired G_c within a wide range of possible values. © 1994 John Wiley & Sons, Inc.     

Dynamic fracture testing of polymethyl-methacrylate (PMMA) single-edge notched beam

Dynamic fracture in single-edge notched polymethyl-methacrylate (PMMA) beams have been investigated by three-point-bending impact testing with a drop-weight machine. A high-speed camera combined with the digital image correlation (DIC) method is used to capture the impact-induced crack initiation and propagation, as well as the beam deformation fields and the open mode strain at the original notch tip. The crack propagation length is recorded and the instantaneous crack velocity is calculated. Furthermore, the dynamic fracture toughness K_Id is quantified from the loading-displacement relations at different impact velocities. The effects of the impact velocity and impact energy on dynamic fracture toughness, fracture initiation strain, as well as the corresponding influences on the fracture propagation velocity, are discussed.     

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.     

Reversible nonlinear conduction behavior for high‐density polyethylene/graphite powder composites near the percolation threshold

The reversible nonlinear conduction (RNC) behavior of high‐density polyethylene/graphite powder composites with various graphite powder volume concentrations slightly above the threshold has been studied. The relationships between the current density (J) and electric field (E) of the composites, as shown in J(E) curves, can be well described by the scaling functions of J/J_c ～ (E/E_c) when E < E_c and J/J_c ～ (E/E_c) when E > E_c, where J_c is the crossover current density and E_c is the crossover electric field. The results indicate that J_c scales with the linear conductivity σ₀ as J_c ～ σ. It is believed that the macroscopic RNC is a combined result of the microscopic conduction processes, involving electronic transporting along carbon chains and tunneling or hopping across thin polymer bridges. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2833–2842, 2001