Polymer pre-notched small punch specimens to evaluate the essential work of fracture (EWF) parameters

Standardized deeply double edge notched tensile specimens (DDEN-T) have been usually used to assess fracture properties in thin polymer plates under plane stress conditions. The methodology is based on a multi specimen technique and is well known as the essential work of fracture (EWF) method. In some special circumstances these standard specimens cannot be machined as could be the case if the material is limited. A possible solution proposed in this paper could be the use of pre-notched small punch test specimens, in which the aim is to establish the feasibility of using pre-notched SPT specimens for evaluating the essential work of fracture parameters. The results obtained with these miniature specimens have been compared with those obtained from standard DDEN-T specimens.     

Influence of femtolaser notch sharpening technique in the determination of essential work of fracture (EWF) parameters

The fracture behaviour of a 0.5 mm thick ethylene-propylene block copolymer is analyzed using the essential work of fracture method, using DENT-type specimens. The influence of three experimental parameters in the technique is evaluated: the effect of the notch sharpening technique, the use of a videoextensometer for monitoring the deformations and the measurement of ligament lengths before or after fracture tests were carried on.The results showed that the femtosecond pulsed laser ablation technique (femtolaser) produced sharp notches with no plastic deformation ahead of the notch tip, which yield smaller specific essential work of fracture (w_e) values than in the cases where the notches were sharpened with razor blades. The use of a videoextensometer has allowed removing the viscoelastic energy from the plastic work, with lower values of βw_p. The measurement of the ligament lengths before or after the test did not affect the results.     

Deformation and fracture of paper during the in-plane fracture toughness testing--Examination of the essential work of fracture method

The essential work of fracture (EWF) method is applied to various machine-made papers. The deforming and fracturing processes of the paper samples during testing is analyzed by means of the thermographic observation. Plastic deformation zone appears in three ways when deep double edge notched tension specimens are strained under in-plane stress: i.e. 1. type (i)--appearing through whole the ligament in a vague manner and developing into a circular (or oval) zone even before or at the maximum load point; 2. type (ii)--appearing from notch tip and amalgamating into a circular (or oval) zone after the maximum load point; and 3. type (iii)--appearing from notch tip and not amalgamating into a circular (or oval) zone until the sheet failure. Specimens with small ligament length (L) are likely to belong to type (i), while those with large L to type (ii) & (iii). Among these three types, type (i) fulfills the original assumption of the EWF method best in terms of the complete ligament yielding before crack initiation. Thus the specific essential work of fracture determined using the linear relation of type (i) should be correct, although the estimated work is a little smaller than that from the linear relation of type (ii) & (iii).     

Impact essential work of fracture toughness of ABS/polyamide-6 blends compatibilized with olefin based copolymers

The impact fracture toughness of acrylonitrile-styrene-butadiene/polyamide-6 (ABS/PA6) blends compatibilized with 5% by weight carbon monoxide modified ethylene-n butyl acrylate-maleic anhydride (EnBACO-MAH) or ethylene-methyl acrylate-glycidyl methacrylate (EMA-GMA) copolymers were examined as a function of blend ratio by standard Charpy tests, Essential Work of Fracture (EWF) Methodology and fracture surface morphologies. The samples were first processed in twin-screw extruder and they were subsequently injection moulded. The incompatibilized blends and neat-PA6 fractured in brittle manner, whereas compatibilized blends fractured in ductile manner. The EWF values yielded a maximum when weight percentages of ABS and PA6 were equal to each other. The values obtained in the case of EnBACO-MAH were higher than that of EMA-GMA regardless of blend composition in EWF tests. The trend of impact strengths observed in standard notched Charpy impact tests was in accordance with that of EWF values of blends. The morphology of the ABS/PA6 blends exhibited differences as a function of the component ratio and compatibilizer type. These differences in topology of the fracture surfaces of the blends were utilized to understand the deformation mechanism, and to correlate the fracture toughness values of the blends.     

Relation between work of fracture and fracture toughness of short-fibre reinforced polymers

On the basis of micromechanical failure mechanisms acting in short-fibre reinforced polymers we derive the crack resistance curve (R-rmcurve) as a function of crack extension. With the conditions characterizing the point of crack instability, the critical crack extension and fracture toughness, G_c, are calculated. By comparing G_c to the work of fracture we are able to conclude that, depending on the relevant failure characteristics, two parameters are necessary to describe the failure behaviour—the fracture toughness for crack instability or strength and the work of fracture as the energy necessary to drive the crack through the sample.     

On the essential work of ductile fracture in polymers

The essential work of fracture concept has been extended to cover ductile tearing of polymeric materials that neck before fracture. It is shown that the plane stress specific essential fracture work (w _e) can be obtained from deeply edge-notched tension specimens, containing either single or double notches, by extrapolating the straight line relationship between the total specific fracture work (w _f) and ligament length (l) to zero ligament. In this way, specific essential fracture works have been obtained for nylon 66 and two polyethylenes. It seems that w _eis a material property for a given sheet thickness being independent of specimen geometry. The straight line relationship between w _fand l breaks down when the ligament length to sheet thickness ratio is less than about three, since the fracture data fall in the plane stress-plane strain transition region. However, a plane strain specific essential fracture work can still be obtained by extrapolating the least squares curve of the data to zero ligament provided the thickness satisfies plane strain condition. If this condition is not satisfied a near plane strain value is obtained which is dependent upon thickness. This method is also appropriate for ductile polymers like the rubber modified polystyrenes that craze rather than neck. J _Rcurves have also been obtained for nylon 66 and the polyethylenes. Under strictly J-controlled crack growth conditions, it is shown that the intercept and slope of the J _Rcurve, i.e. J _cand dJ/da, are related to the intercept and slope of the w _fversus l plot. The limited amounts of J-controlled data available have precluded a more definite and general conclusion to be made. But based on what little is available, the comparisons of these two quantities in the J _R-a and w _f-l plots are not unreasonable.

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Résumé On a étudié le concept de travail essentiel de rupture pour couvrir l'arrachement ductile des matériaux polymères qui sont sujets à striction avant la rupture. On montre que le travail essentiel de ruptures (We) spécifique à l'état plan de tension peut être obtenu dans le cas d'éprouvettes de traction à entaille latérale profonde comportant une ou deux entailles, en extrapolant la relation linéaire qui lie le travail total de rupture (Wf) et la longueur de ligament (l) jusqu'à un ligament nul. De la sorte, on a obtenu le travail essentiel de rupture pour du nylon 66 et pour deux poly-éthylènes. I1 semble que We est une propriété du matériau pour une épaisseur de plaque donnée, qui est indépendante de la géométrie de l'éprouvette. La relation linéaire entre Wf et l par par un point de rebroussement lorsque le rapport de la longueur du ligament à l'épaisseur de la tôle devient inférieur à environ trois, ce qui correspond au passage des données de rupture dans la transition contrainte plane-déformation plane. Néanmoins, on peut encore obtenir un travail essentiel de rupture spécifique à l'état plan de déformation en extrapolant par les moindres carrés les données jusqu'à un ligament nul, pour autant que l'épaisseur satisfasse un état plan de déformation. Si cette condition n'est pas satisfaite, on obtient une valeur pour un état voisin de l'état plan de déformation, qui dépend de l'épaisseur. Cette méthode est également utilisable dans le cas des polymères ductiles qui, tels les polistyrènes de la famille des caoutchoucs, sont sujets à effritement.

     

Fracture toughness analysis of O-POSS/PLA composites assessed by essential work of fracture method

Essential work of fracture (EWF) method was employed to investigate the effect of the octavinylisobutyl based polyhedral oligomeric silsesquioxane (O-POSS) addition in poly(lactic acid) (PLA) matrix on the fracture behavior of O-POSS/PLA composites. The 2 mm thick rectangular shaped PLA-matrix composites containing various weight ratios of O-POSS were injection molded after processing in a twin-screw extruder. Constant deformation rate tensile tests at room temperature were performed on double edge notched tensile (DENT) specimens with various ligament lengths. It was found that the addition of O-POSS to PLA improved the toughness. It was observed that a greater energy consumed after the maximum load reached on load–displacement curves for the composites. Optimum additive value was obtained at 7 wt% O-POSS.     

The fracture behaviour of ABS polymers

The fracture behaviour of three different grades of ABS has been investigated over a range of temperature and strain-rates. A two-stage fracture process has been observed consisting of a slow crack propagation region followed by catastrophic failure. The surface features in these two regions have been examined in detail using scanning electron microscopy. In all cases, the fracture initiation site was located at either a surface defect or at an internal inclusion much larger than the average rubber particle size.     

Measuring toughness and the cohesive stress-displacement relationship by the essential work of fracture concept

The complete fracture behaviour of ductile double edge notched tension (DENT) specimen is analysed with an approximate model, which is then used to discuss the essential work of fracture (EWF) concept. The model results are compared with the experimental results for an aluminium alloy 6082-O. The restrictions on the ligament size for valid application of the EWF method are discussed with the aid of the model. The model is used to suggest an improved method of obtaining the cohesive stress-displacement relationship for the fracture process zone (FPZ).     

The Essential Work of Fracture (EWF) method – Analyzing the Post-Yielding Fracture Mechanics of polymers

The Post-Yielding Fracture Mechanics describe the fracture behaviour of pre-cracked films and thin sheets that show yielding phenomenon at the crack tip during fracture. The Essential Work of Fracture method (EWF) has been used for this type of fracture characterization, determining two parameters: the specific work of fracture, w_e related with the real fracture process area, and the specific non-essential work of fracture, w_p that corresponds with the work done in the outer region of the crack tip.The EWF technique has been successfully employed especially with polymers, allowing the study of the influence of many variables in fracture properties, unavailable using other techniques such us K_IC or J_IC determination. In this work, the fundamentals of the technique and examples of application are reviewed, presenting a brief summary of the most relevant contributions of our group to the EWF method.     

Analysis of the essential work of fracture method as applied to UHMWPE

The validity of the basic assumptions behind the method of essential work of fracture (EWF), as applied to ultra-high molecular weight polyethylene (UHMWPE), is evaluated using finite element modelling. To define a suitable model of constitutive behaviour, the mechanical properties of UHMWPE have been measured in both uniaxial tension and compression over a range of strain rates. The observed strain rate dependence of stress, including the observed differences in strain rate sensitivity between tension and compression, is interpreted in terms of a single Eyring process. The constitutive theory is constructed comprising an Eyring process and hyperelastic networks, the latter having responses symmetric with respect to tension and compression. This theory is implemented within a finite element scheme, and used to model fracture measurements made on the same material using double-edge notch tensile specimens. Calculations of the non-essential work and of the extent of the plastic zones are thus made possible. It is concluded that the specific non-essential work is essentially constant, but that the shape factor β, assumed constant in the conventional analysis, varies significantly with ligament length. The implication of this finding on the derived EWF value is evaluated and found to be slight.     

Evaluation of the fracture toughness properties of polytetrafluoroethylene

Polytetrafluoroethylene (PTFE) (Dupont Tradename Teflon) is a common polymer with many structural applications including sheet, gaskets, bearing pads, piston rings and diaphragms. The interest here developed because this polymer is being considered as the major component of a newly proposed `reactive' material with a possible application as a projectile to replace common inertial projectiles. Little mechanical property data is available on this material since it is commonly used only as a coating material with the dominant properties being its low friction coefficient and high application temperature. Previous work (Joyce, 2003) on commercially available sheet PTFE material has demonstrated the applicability of the normalization method of ASTM E1820 (1999), the elastic-plastic fracture toughness standard to develop fracture toughness properties of this material over a range of test temperatures and loading rates. Additional work on the aluminum filled `reactive' derivative of the basic PTFE polymer (Joyce and Joyce, 2004) has also recently been completed. In this work, standard ASTM E1820 fracture toughness specimens machined from sintered pucks of PTFE were tested at four test temperatures and at a range of test rates to determine the J _Ic and J resistance curve characteristics of the PTFE material. The major results are that while crack extension is difficult at standard laboratory loading rates at ambient (21 °C) temperature or above, for temperatures slightly below ambient or for elevated loading rates, a rapid degradation of fracture resistance occurs and cracking occurs in a ductile or even nearly brittle manner.     

New energy partitioning approach to the measurement of plane-strain fracture toughness of high-density polyethylene based on the concept of essential work of fracture

This study explores three approaches to determining plane-strain fracture toughness of high-density polyethylene (HDPE), based on the concept of essential work of fracture (EWF). The first approach adopted the traditional method that uses total energy consumed in the testing to determine the plane-strain fracture toughness. The second and the third approaches used energy-partitioning principles to exclude the energy consumption in a later stage of the testing from the calculation of the EWF value. The 2nd approach used a new energy partitioning scheme that excluded the energy consumed at the last stage of plastic deformation; and the 3rd approach was based on an existing energy partitioning scheme proposed by another group, to exclude the energy consumption after the maximum load was reached. The results show that only the 2nd approach generates the EWF value that is independent of the specimen thickness. The paper recommends that the 2nd approach be the most suitable method for determining the plane-strain fracture toughness for ductile polymers like HDPE.     

The effect of rate on the impact fracture toughness of polymers

The determination ofG _cfor a polyethylene and PTFE from a conventional energy measuring impact test is described, together with the use of plastic zone and slow crack growth corrections. The rate of the test is changed by two decades by varying the specimen dimensions andG _cas a function of loading time is determined. A remarkably strong time dependence (t ^–0.42) is observed and this is discussed in terms of loss processes in the craze region at the crack tip.

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Résumé On décrit la détermination deG _cpour un polyéthylène et un PTFE à partir d'un essai conventionnel d'impact et d'une mesure de l'énergie, ainsi que l'utilisation des corrections pour la zône plastique et pour la croissance lente de la fissure. La vitesse caractéristique de l'essai est modifiée de deux ordre de grandeur en faisant varier les dimensions de l'éprouvette, et on détermine ainsiG _cen fonction du temps de mise en charge. Une remarquable dépendance du temps est observée, et cette particularité est discutée sous forme d'un processus de perte dans la zône particulière située à la pointe de la fissure.

     

The work of fracture in semiductile polymers

The work to fracture in tension double-notched samples of some semiductile polymeric materials (rigid PVC, Orgalloy and Ultranyl) has been measured as a function of the ligament length. It was established that the work of fracture was proportional to the extent of the plastic zone that developed in the ligament area during crack propagation. It is proposed that the total energy density is made up of two terms, one distributed all over the plastic zone and the other localized in the vicinity of the fracture path. It is then shown that a linear relationship exists between the specific work of fracture and the ligament size, provided the height of the plastic zone linearly depends on the ligament length. The linear extrapolation of the specific work of fracture to nil ligament, yields a value that coincides with J _IC and therefore can be treated as a critical parameter. It is also shown that, at large ligaments, the dependence of the specific work of fracture on the ligament length reflects the post-yield behaviour of the material and it is influenced by the tendency of the height of the plastic zone to level off. Consequently, no specific meaning can be given to quantities obtained, according to the essential work of fracture theory, in the large ligament region, e.g. ligaments larger than three to five times the sample thickness.     

Modified essential work of fracture model for polymer fracture

The well-known essential work of fracture model, describing the linear relationship between fracture energy and un-cracked ligament length, is further extended to allow for any non-linearity in the relationship as this can potentially lead to a large error in determination of the essential work of fracture. Two different polymers, described in the literature, were chosen to show how the essential work of fracture of a polymer can still be determined in cases when a non-linearity exists in the relationship between fracture energy and ligament length. The new model specifies the condition under which the linear relationship exists, and the condition under which the non-linearity needs to be considered.