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.     

Fracture characterization of ductile polymers through methods based on load separation

The applicability of load separation property based methods of determining J–R curves of ductile polymers is analysed in this work. Two methods are analysed: the load normalization method and the S_pb method. The load normalization method is based on the use of a plastic deformation dependent function which has an explicit functional form, H, whereas the S_pb method is based on the S_pb parameter, which was defined as the calculated load ratio between two specimens, one having a growing crack and the other with a non-propagated crack. The obtained J–R curves have been compared with those obtained experimentally in order to study the applicability and accuracy of both methods. Although both methods have been shown to be applicable, the load normalization method is the most accurate and the easiest to apply.     

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.     

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.     

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.     

Influence of morphology on the fracture toughness of isotactic polypropylene

An adaptation of the fracture toughness test method, the J-integral technique, is described within the general framework of polymer fracture behavior. It is shown that there is a strong interaction between different morphological parameters in the way they affect the fracture behavior of isotactic polypropylene (iPP). The fracture toughness decreases with increasing crystallinity at a fixed spherulite size. The fracture toughness also decreases slightly with increasing spherulite size at a constant crystallinity, but this may not be a pure spherulite size effect. The use of a nucleating agent results in a very fine spherulitic structure but facilitates crack growth and reduces the material toughness beyond the crack initiation stage. This suggests that the material behavior is dictated by the increase in crystallization temperature caused by the presence of the nucleating agent and not by the change in spherulite size. © 1995 John Wiley & Sons, Inc.     

Numerical Simulation of Crack Growth in Polyethylene Composites by Means of the Cohesive Zone Model

Summary: The cohesive zone model is used for the numerical simulation of crack growth in homogeneous specimens made of two different grades of polyethylene (PE) as well as in PE-bimaterials. The material data and the shapes of the cohesive function are deduced from experimental data by Ivankovic et al., Eng. Fract. Mech. 71, 2004, 657–668 and Ting et al., Polym. Eng. Sci. 46, 2006, 763–777. Fracture toughness parameters are evaluated from the simulated load versus displacement curves. The results show a significant influence of the arrangement of the two PE-grades in the bimaterial specimens, caused by both the different material properties and the different characteristic parameters of the cohesive function.     

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).     

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.     

Environmental stress cracking of low-density polyethylene in normal alcohols

Fracture mechanics was used to investigate the environmental stress cracking of low-density polyethylene with 4.0 melt flow index. Annealed samples were prepared; a single edge notch was made and then the samples were fractured under constant load in four different liquid alcohols. The relation between the stress intensity factor K and the crack speed a˙ has been investigated. The log a˙ vs. logK curves are influenced not only by temperature but also by the alcohol used as the environment. This influence has been studied in detail. The conclusions are as follows: the crack speed at high K is determined by the diffusion mechanism, and this mechanism cannot be explained in terms of hydrodynamics but can be explained in terms of thermally activated molecular motion. On the other hand, the crack speed at low K is strongly related to the plasticization and the stress relaxation of the crack tip material.     

Effect of repetition nanoindentation of GaN epilayers on a‐axis sapphire substrates

In this work, gallium nitride (GaN) epilayers were deposited on a‐axis sapphire substrate by means of metal organic chemical vapor deposition (MOCVD). Berkovich nanoindentation was used to explore the repetition pressure‐induced impairment of the GaN film. The observation of load‐displacement vs stress‐strain curves concludes that basal slip is implicated in the deformation on the A plane GaN. The increase in the hardness (H) and elastic modulus (E) was determined from cyclic nanoindentation, and resulted in a crack due to the formation of incipient slip bands and/or the to‐and‐fro motion of mobile dislocation. It is indicated that the generation of individual dislocation and residual deformation of the GaN films are showed by CL mapping analysis. From the morphological studies, it is revealed that the crack was found by means of atomic force microscope (AFM) technique at nine loading/reloading cycles even after the indentation beyond the critical depth on the residual indentation impression. Copyright © 2010 John Wiley & Sons, Ltd.     

Application of the load separation criterion in J-testing of ductile polymers: A round-robin testing exercise

Round robin tests carried out under the direction of the Technical Committee 4 of the European Structural Integrity Society (ESIS TC4) have shown that, for determining the fracture resistance of ductile polymers at low loading rates, the multi-specimen methodology based on the construction of the material crack growth resistance curve often does not provide reliable data due to the uncertainties associated with the measurement of crack advancement (Δa). With the aim of strengthening this multi-specimen methodology, the ESIS TC4 attention has been recently focused on the analysis of a testing scheme based on the load separation criterion, which does not require the measurement of Δa.The present work gives the results of a multi-laboratory round-robin testing exercise carried out by ESIS TC4 in order to assess the degree of reproducibility of the fracture parameters obtainable with the application of this load separation criterion based testing scheme. Encouraging results have been obtained.     

Wear and friction in glassy polymers: Microscratch on blends of polystyrene and poly (2,6-dimethyl-1,4-phenylene oxide)

The microscopic process of abrasive wear and friction in glassy polymers was studied by using a special microscratch technique. A miscible blend of polystyrene (PS) and poly(phenylene oxide) (PPO) was used. It was found that as the composition varies there seems to exist two wear regimes in the blends controlled by different breakdown mechanisms corresponding to the brittle—ductile transition. Detailed study of the contact loads and SEM micrographs indicate that abrasive wear in the glassy polymers is controlled by microcracking under the asperity contacts. The critical load τ_c for initiating microscopic cracks can be linked to the macroscopic wear via a statistical Weibull model where τ_c is taken to be the mean of a strength distribution function. On the other hand, the friction coefficient was found to be independent of the composition but to vary strongly with the contact load. It approaches zero at the extrapolated zero load, but increases rapidly and eventually levels off with contact load. This behavior can be understood by a simple frictional adhesion model in which the polymer deformation during a frictional contact is analyzed by considering the compressive plastic ploughing and shearing yielding around the asperity contact. The shear strength S_o of the polymer/asperity contacts was found to vary with the normal load. The vertical scratch hardness H_v, which characterizes the spontaneous indentation yielding on the polymer surface, was found to be independent of scratch length and depth, and indeed can be regarded as a material constant. Although both S_o and H_v can accurately describe the frictional behavior of the glassy polymers, they bear no correlation to abrasive wear in the same materials. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1295–1309, 1997     

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.     

Microdeformation in thin films of 3FDA/PMDA polyimide and polyimide nanofoams

Transmission electron microscopy has been used to investigate the microdeformation behavior of thermally imidized thermoplastic pyromellitic dianhydride/1,1-bis(4-amino-phenyl)-1-phenyl-2,2,2 trifluoroethylene (3FDA/PMDA) polyimide films with a T_g of ～ 440°C, prepared by solution casting of a polyamic ester precursor. Failure of the films at room temperature was by unstable cracking at about 5% strain, accompanied by homogeneous shear deformation at the crack tips. As the temperature was raised to above 100°C, zones of mixed shear and crazing were observed, and a stick-slip mode of cracking. Above about 300°C shear was once again the dominant deformation mechanism and the films became fully ductile. In films containing porosity on a scale of a few nanometers, prepared by thermal degradation/imidization of a 3FDA/PMDA/poly α-methyl styrene graft copolymer, film failure at room temperature was also by unstable cracking, but a zone of multiple craze-like features was observed at crack tips, rather than a single shear deformation zone. The increase in extent of this zone of craze-like features as the temperature was raised was again associated with an increase in crack stability. ©1995 John Wiley & Sons, Inc.     

Adhesion of viscoelastic materials to rigid substrates. III. Energy criterion for failure

Measurements are described of the strength of a model adhesive joint subjected to (1) tensile rupture, with the interface containing a small unbonded region of varying size, and (2) pure shear deformation, in the form of a partly unbonded sheet. These, and previous measurements of resistance to peeling separation, are all shown to be consistent with an energy criterion for adhesive failure. The characteristic failure energy per unit area of interface has been determined for the model adhesive material as a function of the effective rate of detachment, over a wide range covering almost the entire spectrum of viscoelastic response. The values obtained are found to increase from levels only slightly higher than thermodynamic considerations would predict, i.e., 10²?10³ ergs/cm², at low rates of crack propagation, up to a value of about 10⁶ ergs/cm² at high rates when the material responds in a glasslike manner. These results suggest that the failure energy has two components: the (reversible) work of adsorption and the (irreversible) work of deformation of the adhesive in effecting separation.     

In Situ tensile tests to analyze the mechanical response,crack initiation,and crack propagation in single polyamide 66 fibers

Single fiber mechanical testing is challenging to perform, especially when the diameter is as small as tens of micrometers. For this reason, real‐time observations of crack propagation mechanisms have been rarely been investigated experimentally. This article presents experimental and numerical investigations of fracture of monofilamentary high performance polyamide 66 fibers. Their engineering stress–strain curves are compared. The mechanisms of failure starting from crack initiation until the final brittle fracture are studied by in situ tests in Scanning Electron and optical microscopes. Finite element modeling at the individual fiber scale has been performed in three‐dimensional (3D), as a reverse engineering method. The compliance method was used to determine the crack depth that triggers the final failure. The fracture toughness was numerically determined using the J‐integral concept, accounting for the geometry of the crack front (3D) together with plastic deformation. 3D meshes were designed especially from postmortem observations. The average value deduced was about 47 ± 7 kJ m^?2, which will be discussed with other estimates using linear elastic fracture mechanics. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 680–690     

Hindered internal rotation in molecular systems: quantum statistics of equilibrium and rate constants in the Wigner function formalism

Summary The quantum statistics of a symmetric hindered internal rotator in a molecule or molecular complex is developed within the Wigner function formalism. Different shapes of the rotational barrier are considered. The partition function and the thermodynamic functions are given as Wigner-Kirkwood series expansions in terms of powers of Planck's constant squared. One gets simple closed expressions containing the modified Bessel functionsJ ₀ andJ ₁ of the argumentiV ₀/2kT whereV ₀ is the barrier height. Some problems concerning the evaluation of equilibrium and rate constants of chemical reactions are discussed.Supported by the Alexander von Humboldt-Stiftung     

Effect of anisotropic deformation on the differential scanning calorimetry response of polymer glasses

Large anisotropic deformation affects the physical state of a polymer glass, where the changes in the state of material are revealed by performing a differential scanning calorimetry (DSC) experiment. Previously, the deformation was applied to polymers well below their glass transition temperatures, and it was found that uniaxial compressive loading–unloading resulted in a broad exothermic peak on the DSC trace. Here we report on the effect on the subsequent DSC response of a deformation experiment performed in uniaxial extension on a ductile 50:50 co-polymer poly(BMA-co-MMA) (PBMA/MMA). The deformation of up to 80% strain was applied at T_g − 30°C and T_g − 40°C, that is, closer to T_g than in the previous work. Unlike in the well below T_g deformation case, the DSC trace contains an endothermic peak followed by an exothermic peak. The magnitude of the endothermic peak as well as the asymptotic glassy heat capacity increase with the amount of mechanical work performed during the deformation cycle.