Fracture characterization of high-density polyethylene pipe materials using the J-integral and the essential work of fracture

In this paper, fracture mechanics concepts are reviewed and their relevance to examine the toughness of highly deformable materials such as high-density polyethylene (HDPE) pipe materials is discussed. Using two different specimen configurations (single edge notched bending and compact tension), it was found that the $J-R$ approach is unable to give pertinent indications on fracture toughness of HDPE. Alternatively, applying the essential work of fracture approach to double edge notched tension specimen, seems a more appropriate way to measure the fracture strength of HDPE and therefore to analyze the fracture process of such materials. Nevertheless, the severe necking occurring at the crack tip and in the plastic zone makes difficult the crack growth measurement, which clearly depends on the strain state and on the stress triaxiality level.     

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.     

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.     

Detection of crack nucleation in sheet metalforming by monitoring infrared radiation

In the present work a method is described for the early detection of large plastic strains localisation and subsequent crack nucleation in sheet metalforming. The method is based on the monitoring of the infrared radiation emitted from the material during stretching. It is concluded that the point of the final crack nucleation can be located in the very early stages of stretching, when overall mean strains are insignificant (less than 20% of the yielding strain of the material).     

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.

     

The essential work of plane stress ductile fracture

In a ductile material, the total work of fracture is not a material constant and linear fracture mechanics is inappropriate. The work performed in the end region at the tip of a crack, where the fracture process takes place, is considered the essential work of fracture, and a constant for a particular sheet thickness. It is shown that this essential work can be estimated from deep edge notched tension specimens by extrapolating the straight line relationship between the work of fracture and ligament length to zero ligament length.

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Résumé Dans un matériau ductile, le travail de rupture n'est pas constant quel que soit le matériau, et la théorie linéaire élastique de la rupture n'est pas appropriée.Le travail effectué dans la région la plus en avant de l'extrémité de la fissure, ou le processus de rupture prend place, est considéré comme le travail essentiel de rupture et est une constante pour une épaisseur particulière de tôle. On montre que ce travail essentiel peut être estimé à partir d'éprouvettes encochées latéralement par des entailles profondes, en extrapolant la relation linéaire existant entre le travail de rupture et la longueur du ligament en direction d'une longueur égale à zéro.

     

Plane-stress essential work of ductile fracture for polycarbonate

The effect of specimen geometry, specimen size and the specimen orientation on the essential work of fracture for polycarbonate is investigated. Two different test geometries, namely the single-edge notched tension and double-edge notched tension specimens, are used to evaluate the essential work of fracture for crack propagation. It is shown that the specific essential work of fracture for crack propagation,w _e is independent of the test piece geometries and the size of the test piece. It seems that for a given sheet thickness,w _e is a fundamental material property being independent of the specimen geometry and size. The value ofw _e does change with the orientation of the initial notch with respect to the melt flow direction. The straight-line relationships between the total specific work of fracture,w _f, and ligament length,L, breaks down when the ligament length to specimen thickness ratio is less than about three, because the fracture data fall in the plane stress-plane strain transition region. A plane strain specific essential work of fracture,w _le|, was obtained by extrapolating the best regression line of the data to a zero ligament. For the initial notch in the melt flow direction, values forw _e andw _le, were approximately 28 and 3 kJ m^–2, respectively. The specific essential work of initiation,w _le was about 4.3 kJ m^–2 ·J _R curves (J-a curves) were also obtained and it is shown that the intercept and the slope of theJ _r curve, i.e.J _C and dJ/da, are related tow _e and the slope of thew _f versus ligament plot.     

On the essential work of fracture in polymer–metal multilayers

Polyethylene terephtalate (PET) metallized with aluminium by physical vapour deposition was investigated through classical physical chemistry techniques and mechanical characterization. The amount of aluminium altered the amount of crystallinity of the PET substrate, but appeared unrelated to the mechanical properties obtained with regular tensile test. In contrast, the essential work of fracture (EWF), as obtained with Cotterell tests, permitted to better discriminate the perforation resistance. It is shown that increasing the amount of crystallinity within the PET linearly reduced the EWF.     

The essential work of fracture for tearing of ductile metals

A simple energy balance analysis is presented for the tearing of ductile sheet metals using the trousers test. It is shown that the specific essential work of fracture (w _e ) for tearing can be estimated by extrapolating the straight line relationship between the tearing force per unit thickness and the trousers leg width to zero leg width. There are two contributions to the specific essential work of fracture: one is due to the localised plastic shearing work in a zone contiguous with the torn edges (w _e1 ) and the other is the final out-of-plane tearing work (w _e2 ).

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Résumé En utilisant le Trousers Test, on présente une analyse simple d'équilibre énergétique dans le cas du déchirement de feuilles métalliques ductiles. On montre qu'il est possible d'estimer le travail spécifique de rupture en déchirement w _e en extrapolant la relation linéaire qui lie la force de déchirement par unité d'épaisseur et la largeur de l'échantillon caractéristique entre une valeur 0 et une valeur donnée. Deux éléments contribuent au travail spécifique essentiel de rupture, l'un est dû au travail de cisaillement plastique local dans une zone contigue aux bords de l'arrachement (w _e1 ) et l'autre est le travail de déchirement final hors du plan de la feuille (w _e2 ).

     

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).     

On the essential work of fracture of neat and rubber toughened polyamide-66

Essential work of fracture (EWF) tests have been conducted on neat and rubber toughened polyamide-66 in order to measure the essential specific work of fracture (w_e) and the non-essential specific work of fracture (βw_p) parameters. Further, the w_e value has been partitioned into two terms, one related to the specific energy contribution for yielding up to the onset of fracture (w_e,init), and another one representing the subsequent crack propagation process (w_e,prop), respectively. EWF tests performed on neat polyamide-66 specimens conditioned up to various equilibrium moisture contents clearly indicate that w_e markedly increases as the material moisture content rises, and that this trend is mainly associated with the increase of its crack propagation component (w_e,prop), the initiation related term (w_e,init) being practically independent of the humidity level. The inclusion of various amounts (7, 16, and 25 wt%) of rubber particles (a random ethylene-acrylic ester-maleic anhydride terpolymer) into the polyamide-66 matrix induces a large increase of the w_e parameter. It is interesting to observe that the w_e,init and w_e,prop terms display different trends with the rubber content. Most of the toughening effect of the rubber particles can be attributed to a large increase of the propagation-related term, the fracture initiation term decreasing with the rubber content. Finally, the loading rate effects on the fracture behaviour have been investigated for polyamide-66 toughened with 25 wt% rubber. An increase of the loading rate causes an increase of the crack-initiation related term w_e,init, while the crack-propagation related parameter w_e,prop decreases. As a consequence, the specific term w_e shows a non-monotonic trend with the loading rate.     

The essential work of plane stress ductile fracture of a strain-aged steel

The paper reports the results of an experimental investigation on the essential work of fracture of a strain-aged low carbon (0.1% C) temper-rolled 16-gauge sheet steel which has been subjected to pre-strain levels of 2 to 12% and ageing temperatures of 80 and 100C. Deep edge-notched tension specimens were used to determine the specific essential work by extrapolating the straight-line relationship between the specific work of fracture (W _f) and ligament length (I) to zero ligament length. The strain-aged steels at 80 and 100 give approximately the same specific essential fracture work of 0.18 to 0.20 J mm^–2 which is independent of the amount of prestrain. Advancing crack opening displacements (C.O.D.) have also been analysed, which give 0.60 to 0.63 mm for the strain-aged steels. For comparison, the prestrained but unaged steels have a higher essential work of fracture of 0.275 J mm^–2 and a larger C.O.D. of 0.73 mm. It is concluded, therefore, that the causes of strain-ageing embrittlement are primarily due to the reduction of both the essential work of fracture and the advancing C.O.D. at the crack tip end region.     

The essential work of fracture through the wall of a uPVC pipe

The specific essential work of fracture, w _e, has been measured for a relatively thick walled uPVC pipe as a function of position through the wall of the pipe. w _e was highest at the surface of the pipe and decreased significantly at the centre of the pipe wall. The variation in w _e through the wall of the pipe correlated with the processing level of the uPVC material as measured by the critical temperature, T _c. The variability in the measured values of w _e was substantially higher in the centre of the pipe where the processing levels were lower. This was likely to be a result of the variability in the microstructure of the material where poor processing had introduced regions of poor fusion of primary PVC particles.     

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.     

Effect of test conditions on the essential work of fracture in polyethylene terephthalate film

The tear resistance of polyethylene terephthalate film is characterized by the essential work of fracture method in mode I as a function of test speed and temperature. Attempts to extrapolate tearing resistance found by the method of essential work to commercial slitting processes are discussed. Limitations of the essential work of fracture method with regards to specimen size are evaluated. Based on the findings modifications to the test protocol are suggested.     

Mechanical behaviour and essential work of fracture of halloysite nanotubes filled polyamide 6 nanocomposites

Polyamide 6 (PA 6)/halloysite nanotubes (HNT) nanocomposites were prepared by melt-extrusion compounding via masterbatch dilution process. A homogeneous dispersion of HNTs in PA 6 matrix was achieved. Differential scanning calorimetric measurements showed that addition of HNTs into PA 6 matrix enhanced the crystallization temperature and degree of crystallinity, thus indicating an effective nucleation induced by the addition of HNTs. Upon halloysite addition, glass transition temperature, storage modulus, Young modulus, tensile strength and notched Charpy impact strength increased without loss of ductility. For the first time, the essential work of fracture (EWF) concept was used to analyse the toughening and fracture behaviour of PA 6/HNT systems. Significant increase (+38%) of the essential work of fracture of PA 6/HNT nanocomposites was noticed at HNTs contents as low as 4 wt.%.     

Determination of essential work of fracture in EPBC sheets obtained by different transformation processes

1 mm sheets of polypropylene and ethylene-propylene block copolymers (EPBC) have been obtained using different processing methods in order to study the influence of processing induced morphology in the fracture properties of these materials. The processing methods employed were compression moulding (CM), extrusion-calendering (EC) and injection moulding (IM). Additionally, the sheets obtained by extrusion and injection were submitted to an annealing process with the aim to obtain more homogeneous morphologies that would ease their characterization.The morphology has been characterized by different techniques: Polarizing light microscopy (MLP), differential scanning calorimetry (DSC), wide-angle X-ray diffraction scattering (WAXS) and scanning electron microscopy (SEM).The fracture properties were determined by the essential work of fracture (EWF) method for deeply double edge notched specimens (DDENT), since these materials show ductile and post-yielding fracture behaviour. The EWF technique was applied in both the melt flow (MD) and the transversal (TD) directions in the sheets obtained by extrusion and injection moulding.Results show that the sensitivity of the technique allows examining the effect of morphological variations of thin sheets, as well as a better characterization of the orientation level (versus other parameters like yielding stress or elastic modulus obtained by tensile test).