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.     

Plane-stress fracture of polycarbonate films

The use of the specific essential work of fracture, W _e, to characterize fracture of polycarbonate films is described. It is shown that the plane-stress specific essential work of fracture for polycarbonate film can be obtained from single-edge-notched-tension specimens, by extrapolating the straight-line relationship between the total work of fracture, W _f, and ligament length, L, to zero ligament length. From the data, it seems that, for a given film thickness, W _e is almost independent of the specimen width but increases with increasing thickness. The non-essential work of fracture as obtained from the slope of a W _f versus L plot showed no significant width dependence, and for the majority of thicknesses it was almost invariant with thickness, indicating that the shape of the outer plastic zone surrounding the fracture process zone is almost invariant with the dimensions of the test specimen.     

Temperature and deformation rate dependence of the work of fracture in polycarbonate (PC) film

Single edge notched polycarbonate (PC) specimens of thickness 0.175 mm were pulled to complete fracture at temperatures between 25°C and 100°C and at loading rate values of 2, 5 and 50 mm/min. A duckbill-shaped yielded zone was formed ahead of the crack tip in all the specimen tested. Propagation of the crack within the yielded zone was always stable. The method of essential work of fracture (EWF) was used to study the effects of temperature and loading rate on fracture toughness. The specific essential work of fracture, w _e, was found to be independent of both temperature and loading rate. The non-essential work of fracture, w _p, increased with increasing temperature but showed no systematic variation with respect to loading rate. Moreover, plastic constraint factor, m, also increased with increasing temperature. A linear temperature dependence was obtained for both w _p and m giving the extrapolated values of w _p = 0 and m = 0.5 at –23°C.     

Effect of temperature on fracture properties of an amorphous poly(ethylene terephthalate) (PET) film

Fracture behaviour of an amorphous polyethylene terephthalate (PET) film with a glass transition temperature (T _g ) of 72°C and a thickness of 0.21 mm was studied between 23 and 70°C using Double Edge Notched Tension (DENT) specimens. Within this temperature range, DENT specimens fractured by ductile tearing of the ligament region after ligament region had been fully yielded. The load-displacement curves obtained for different ligament lengths were geometrically similar to one another. On the basis of these, Essential Work of Fracture (EWF) methodology was used to determine fracture toughness of the PET film as a function of temperature. A linear relationship was obtained between the total specific work of fracture, w _f , and ligament length, L, at temperatures under consideration. Results showed that specific essential work of fracture, w _e , is independent of temperature but the specific non-essential work of fracture ( w _p ) increases with increasing temperature and drops in value near the glass-transition temperature. A linear relationship was also found for yielding (w _y ) and necking/tearing (w _nt ) components of w _f as a function of ligament length. The specific essential work components were found to be temperature dependent and whilst component w _ey decreased component w _ent increased with increasing temperature. The contribution of w _ent to w _e was substantially greater than that of w _ey at all temperatures.     

On the essential work of fracture of linear low-density-polyethylene. I. Precision of the testing method

The precision (i.e. the repeatability) of the essential work of fracture (EWF) method in determining the fracture parameters of a highly extendible linear low-density-polyethylene film is investigated. In order to minimize any interference from external variables, a random data collection procedure is adopted to extract, from a large data set, various EWF samples with sizes ranging from 11 to 150 data points. Two different notching procedures have been considered, involving different tools (scalpel or razor blade) and cutting methodologies.The notching procedure has only a marginal influence in terms of the correlation coefficient of the linear regression and standard error on the specific essential work of fracture (w_e). However, the mean of w_e values is markedly affected by the notching procedure, being its influence on the specific non-essential work of fracture (βw_p) parameter relatively lower. The dispersion of the w_e and βw_p data around their mean values decreases as the sample size increases, with a trend clearly affected by the notching procedure.     

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.     

Factors affecting work of fracture of uPVC film

Essential work of fracture (EWF) approach was used to evaluate the fracture toughness of uPVC film. It was found that the specific essential work of fracture, (w_e) is independent of specimen width, specimen gauge length, loading rate and test temperature, but dependent on the geometry of the test specimens. Test temperature and geometry were the only testing parameters affecting the specific non-essential work of fracture (w_p) in a very significant way. The plastic zone shape factor () was found to be very sensitive to both the geometry and temperature. It was established that both w_e and w_p could be partitioned into components that are linked to yielding (i.e. w_e,y and _yw_p,y) and necking/tearing (i.e. w_e,nt and _ntw_p,nt) processes. The only testing parameter that affected w_e,y was test temperature, whereas w_e,nt was affected by test temperature as well as geometry. All testing parameters used in this study affected the values of _yw_p,y and _ntw_p,nt.     

Evaluation of fracture toughness of ABS polymers via the essential work of fracture (EWF) method

The essential work of fracture (EWF) method was employed to determine the fracture toughness of SAN/PB-g-SAN blends with the compositions of 65/35–0/100. It was found that the plane stress EWF approach is applicable for different SAN/PB-g-SAN blends. During EWF tests, three different types of load–displacement curves were recorded, depending on the blend composition. For the samples containing rubbery phase of 35–65 wt% crack growth occurred immediately after full ligament yielding. Further increase in rubber content and for the samples with 75 and 85 wt% of rubbery phase, the onset of crack growth was preceded by the formation of necking zone in the form of a sharp load drop after full ligament yielding. For the sample with the composition of 0/100, strain hardening behavior was observed without any sign of neck formation. The specific essential work of fracture (EWF) w _e increased at first with the increase of PB-g-SAN wt% and then decreased with further increasing amount of rubbery phase. The maximum value of w _e was observed for the blend with 75 wt% of PB-g-SAN. The specific non-essential work of fracture βW _p increased with increasing of rubbery phase concentration. The analyzing of yielding and necking/tearing components of essential and non-essential parameters showed that for the samples containing 55 wt% and higher of rubbery phase, w_\texte,nt \succ w_\texte,y w_{\text{e,nt}} \succ w_{\text{e,y}} and b_\textnt w_\textp,nt \succ b_\texty w_\textp,y \beta_{\text{nt}} w_{\text{p,nt}} \succ \beta_{\text{y}} w_{\text{p,y}} , indicating that a majority of fracture energy was dissipated in the necking and tearing stages of fracture process. Finally, it is shown that w _e values can be predicted via COD values.     

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.     

Essential and Non-essential Work of Fracture of PI/SiO<Subscript>2</Subscript> Hybrid Thin Films

Essential work of fracture (EWF) analysis is used to study the effect of the silica doping level on fracture toughness of polyimide/silica (PI/SiO₂) hybrid films. By using double-edge-notched-tension (DENT) specimens with different ligament lengths, it seems that the introduction of silica additive can improve the specific essential work of fracture (w _e ) of PI thin films, but the specific non-essential work of fracture (βw _p ) will decease significantly as the silica doping level increasing from 1 to 5 wt.%, and even lower than that of neat PI. The failure process of the fracture is investigated with online scanning electron microscope (SEM) observation and the parameters of non-essential work of fracture, β and w _p , are calculated based on finite element (FE) method.     

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.     

Fracture strength and adhesive strength of hydroxyapatite-filled polycaprolactone

Fracture toughness and tear strength of hydroxyapatite (HAP)-filled poly(ε-caprolactone) (PCL) with increasing HAP concentration were studied. The toughness was assessed in terms of essential work of fracture (EWF). Adhesive strength between HAP and PCL interfaces was evaluated using T-peel testing. The adhesion between the two components was found to be relatively strong. Double edge notched tension (DENT) and trousers test specimens were used for the EWF tests. The effect of HAP phase in PCL on the fracture and tearing toughness was investigated. The results obtained from the EWF tests for the HAP-filled PCL complied with the validity criteria of the EWF concept, namely, (1) geometric similarity for all ligament lengths; (2) fully yielded ligament and (3) plane-stress fracture condition. Values for specific essential work of fracture (w _e ) and specific plastic work of fracture (βw _p ) were found to decrease with increase in HAP concentration. The testing procedure showed promise in quantifying the tearing resistance and rising R-curve behavior common in natural materials and it can be extended to other biomaterials that exhibit post-yield deformation. A quantitative assessment based on fracture mechanics of the adhesive strength between the bioactive interfaces plays an important role for continued development of tissue replacement and tissue regeneration materials.     

Thickness effect on fracture in high impact polystyrene

The effect of thickness on the fracture behaviour of a high-impact polystyrene containing approximately 7% rubber is studied. For thicknesses below 10 mm plane stress ductile tearing occurs and deep edge notched tension specimens are used to obtain the specific essential work of fracture (w _e) in plane strain. Mixed mode plane strain-plane stress fracture is predominant in single-edge notched tension specimens with thicknesses above 10 mm. By assuming that the plane stress layers are given by the overall fracture toughness (K _c) a modified bimodal fracture analysis based on linear elastic fracture mechanics concepts is presented to analyse the experimental results. The plane strain fracture toughnessG _c1 (=K _c1 ² /E) is in good agreement withw _e. It is shown thatK _c1 for HIPS is larger than that of the polystyrene matrix alone due to the toughening effect of the rubber at the crack tip vicinity.     

Application of the essential work of fracture method in ranking the performance in service of high-density polyethylene resins employed in pressure pipes

High-density polyethylene resins have increasingly been used in the production of pipes for water- and gas-pressurized distribution systems and are expected to remain in service for several years, but they eventually fail prematurely by creep fracture. Usual standard methods used to rank resins in terms of their resistance to fracture are expensive and non-practical for quality control purposes, justifying the search for alternative methods. Essential work of fracture (EWF) method provides a relatively simple procedure to characterize the fracture behavior of ductile polymers, such as polyethylene resins. In the present work, six resins were analyzed using the EWF methodology. The results show that the plastic work dissipation factor, βw _p , is the most reliable parameter to evaluate the performance. Attention must be given to specimen preparation that might result in excessive dispersion in the results, especially for the essential work of fracture w _e .     

Thermal effects on fracture of biaxial-oriented poly(ethylene terephthalate) (BOPET) film

The effect of temperature on the fracture behaviour of biaxial-oriented poly(ethylene terephthalate) (BOPET) film was studied using the Essential Work of Fracture (EWF) approach. Fracture tests were performed over the temperature range +25 to +160 °C at the speed of 5 mm/min using double edge notched tension (DENT) specimens. The length of the specimens was either along the machine direction (MD) (0°), transverse direction (TD) (90°) or at 45° to either MD or TD. Ductile tearing of the ligament region was noted over the entire temperature range in all three directions. A linear relationship was found between the specific total work of fracture and the ligament length at all test temperatures. Values of the specific essential work of fracture (w _e) in the MD and TD were similar and smaller than in the 45° direction. Within temperature range 25–140 °C, w _e showed little variation if any with respect to temperature. As expected, the Specific Non-Essential Work of Fracture (βw _p) was temperature dependent. This parameter increased with increasing temperature and reached a maximum around the glass transition temperature of BOPET (T _g ≈ 80 °C). The values of the maxima are respectively 16.15, 20.38 and 17.8 MJm⁻³ for the 0°, 45° and 90°.     

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 behavior and environmental stress cracking resistance (ESCR) of HIPS/PE blends and the effect of compatibilization on their properties

Attempts have been made to study the fracture behavior and environmental stress cracking resistance (ESCR) of HIPS/PE blends. The effect of compatibilization on their properties was also studied. EWF tests were conducted to measure the essential specific work of fracture (w_e) and non-essential specific work of fracture (βw_p). The ESCR of the samples was investigated using a special modified tensile creep test under an aggressive environment (sunflower oil). It was found that EWF methodology could be applied to uncompatibilized and compatibilized HIPS/PE blends as well as HIPS. The essential specific work of fracture of compatibilized HIPS/PE blends was higher than uncompatibilized HIPS/PE blends and pure HIPS, while its non-essential work of fracture was higher than uncompatibilized blends and lower than pure HIPS. The results also showed that the ESCR of HIPS decreases with incorporation of PE, but an effective compatibilization of this blend increases its ESCR even higher than pure HIPS. The different properties of compatibilized and uncompatibilized blends and HIPS, in EWF and ESCR tests, were attributed to the different mechanisms of fracture in these materials. The different mechanisms of fracture were justified using morphological studies performed on fracture surfaces of each sample. SEM images showed that there is a reasonable correlation between mechanisms of fracture and microstructure of the samples.     

Effect of composition on fracture behavior of polypropylene–wollastonite–polyolefin elastomer system

The fracture behavior of polypropylene (PP)–wollastonite–polyolefin elastomer (POE) in the mixed mode region was studied using the essential work of fracture (EWF) method. The relationship between the microstructure and the fracture parameters was analyzed. The effect of wollastonite content on the essential work of fracture and the work of plastic deformation was discussed. The energy dissipation during a double-edge-notched tension (DENT) test was calculated with the EWF method. It was found in the mixed mode region that σ_n increases with shortening of the ligament length region as plastic constraint effect rises and variation of the specific total work of fracture with ligament length was still reasonably linear within the mixed mode region. With increasing wollastonite content, w _e (specific essential work of fracture) increases, while the βw _p (specific non-essential work of fracture) decreases. The measurements of energy dissipation show that improvement in the fracture toughness of PP–wollastonite–POE is mainly due to the increase in crack propagation resistance during the necking and tearing processes after yielding, while the plastic deformation capability of the material depends mainly on the properties of fracture behavior before yielding. It is also found that the impact strength of the material decreases with increasing wollastonite content. However, the composition with high impact strength has lower specific essential energy of fracture and lower long-term fracture resistance, indicating that EWF is a better indicator of long-term fracture properties than the impact strength. DSC results show that the presence of wollastonite hinders crystallization of the PP.     

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 ).

     

Fracture behaviour of polypropylene sheets filled with epoxidized natural rubber (ENR)-treated coal gangue powder

The morphology, deformation and fracture properties of polypropylene sheets filled with untreated and epoxidized natural rubber (ENR)-treated coal gangue powder (CGP) were investigated by scanning electron microscope (SEM) and the essential work of fracture (EWF) method. The results show that ENR obviously improves the dispersion of CGP particles in the PP matrix and the interfacial adhesion between CGP particles and PP matrix with the well-established interfacial layer. It is found that all composites fracture in a ductile manner as ligament yields completely and crack propagates steadily. The fracture toughness (w _e ) of the composites is significantly improved with the complete interfacial layer formed by ENR on the surface of CGP particles. With increasing ENR content, the specific plastic work (w _p ) per volume unit of plastic zone of the composites increases considerably in spite of the restricted plastic deformation of plastic zones. In Addition, the fracture parameters of different stages of tensile process demonstrate that the positive effect of ENR on the fracture performance of the composites is mainly achieved by notably reinforcing crack resistance at the stage of necking-tearing after yielding.