Specific Total Work Of Fracture Research Articles

Evaluation of specific total work of fracture in polypropylene/ethylene‐propylene diene monomer nanocomposites based on various graphene derivatives: Optimization by response surface methodology technique and correlation with microstructure properties

AbstractThis study presents an experimental design approach for optimization and prediction of specific total work of fracture (wf) in polypropylene/ethylene‐propylene diene monomer (EPDM) nanocomposites based on disparate graphene derivatives including multilayer graphene, few‐layer graphene and graphene oxide. Box–Behnken design and response surface methodology (RSM) were exploited at three levels and four factors to construct a predictive mathematical model for the value of wf. The model predicted that the maximum value of wf (136.7 J/mm2) is achieved by applying dynamically vulcanized system at EPDM content and few‐layer graphene content of 20 wt% and of 0.5 wt%, respectively. In addition, by observing the fracture surfaces of specimens, a direct correlation between RSM predictions and morphology of nanocomposites was established. In this regard, transmission electron microscopy and wide‐angle X‐ray diffraction analyses showed that by using few‐layer graphene, thanks to formation of an exfoliated structure, more energy for the failure of nanocomposites is required which substantiates the model predictions. Scanning electron microscopy observations depicted that the droplets diameter of homogeneous EPDM particle size plays a pivotal role in number of micro‐voids and nano‐voids, which consequently promotes the creation of fibril structure and eventually heightens nanocomposite resistance against the applied load. The optimum status of this phenomenon happens at 20 wt% of EPDM and as the model showed, the value of wf reaches the highest point at this EPDM content. Likewise, by applying dynamic vulcanization, as truly predicted by the model, the formation of multi fibrillar structure led to dissipation of extra energy in nanocomposites inducing a remarkable improvement in the value of wf.

Evaluation of fracture behavior of polyethylene/CaCO3 nanocomposite using essential work of fracture (EWF) approach

The fracture behavior of two series of polyethylene (PE) films, both the unreinforced and reinforced with different amounts of nanoscale calcium carbonate (CaCO3) particles was investigated in this research work by means of the essential work of fracture (EWF) approach under the loading condition of mode I. For this purpose, EWF test was conducted on deeply double edge notched tension (DDENT) specimens; and the essential and non-essential components of fracture work, were estimated using the plots representing the variation of the specific total work of fracture (wf) versus the ligament length of the specimen. The results showed that the crack resistance for the PE/CaCO3 nanocomposites was lower than that of the unreinforced PE, and for the case of nanocomposite samples, the total plastic energy absorbed during fracture increased with increasing CaCO3 content up to 2·5 wt-% and then decreased for nanocomposite samples containing 5 wt-%CaCO3. The plastic zone size decreased with increasing CaCO3 content, whereas the specific plastic work per unit volume increased with increasing weight percent CaCO3. The observed trends were rationalized using the fracture and deformation mechanisms of nanocomposites.

Tearing and Delaminating of a Polymer Laminate

The fracture behaviour of laminated materials was studied in this work. The materials used in this work were low-density polyethylene (LDPE) laminated on polyethylene (PET). The thickness of the LDPE was 27 µm and the PET was 100 µm. Experiments were performed by using a 2-leg trousers specimen to analyse the tearing behaviour of the laminate in relation to the delamination. A clear delamination zone was observed during the crack propagation by tearing. Furthermore, a finite element calculation was performed to simulate the behavior around the crack tip during the tearing. A correlation between adhesion and crack propagation was discussed. Finally, the theory of Essential Work of Fracture (EWF) was used for predicting the specific total work of fracture along the tear path across the plastic zones.

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 σn 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.

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°.

Optimal ligament lengths in impact fracture toughness estimation by the essential work of fracture method

This work presents a statistical analysis of the confidence in fracture parameters of polymers estimated through the essential work of fracture (EWF) methodology under impact conditions. Fracture toughness parameters—essential, w e, and non-essential work of fracture, w p—are obtained from the experimental relationship between specific total work of fracture w f and ligament length of the tested samples l: w e is obtained from the y-intercept and w p from the slope of w f versus l in cases where a linear fit is suitable. The distribution of ligament lengths within a fixed number of samples to be tested under impact loading conditions is determined in order to minimize the uncertainty of the estimated parameters when linear reduction of the data is assumed. The statistical approach applied to two different polymeric materials shows that the uniform ligament length distribution along the ligament range is not the optimal one. We propose an optimal distribution of ligament lengths to be tested that depends on the distribution of error standard deviations of the measured work of fracture along the l-axis.

Toughness enhancement of polyimides by in situ generation of silica particles

Films of particulate polyimide–silica hybrids were produced by the sol–gel process from solution mixtures of a commercial polyamic acid and pre-hydrolysed tetraethoxysilane. Mechanical properties were evaluated at different temperatures, varying from 20 to 250 °C. The fracture toughness characteristics were studied by the ‘essential work of fracture’ method using double edge-notched specimens of different ligament lengths. The essential ( w e) and the non-essential or plastic work of fracture ( βw p) were estimated from plots of the specific total work of fracture versus ligament length. The results showed that not only the modulus and yield strength but also the fracture toughness increased when submicron silica particles, produced by the sol–gel method, were dispersed in the polyimide matrix. In particular, it was found that both w e and βw p increased with temperature to a larger extent than the parent polyimide. This enhancement in the fracture toughness was attributed primarily to extensive cavitations originating at the particle interface with the matrix.

Tearing resistance of some co-polyester sheets

A three-zone model consisting of initial, evolutionary and stabilised plastic zones for tearing resistance was proposed for polymer sheets. An analysis with the model, based on the essential work of fracture (EWF) approach, was demonstrated to be capable for predicting specific total work of fracture along the tear path across all the plastic zones although accuracy of specific essential work of fracture is subject to improvement. Photo-elastic images were used for identification of plastic deformation sizes and profiles. Fracture mode change during loading was described in relation with the three zones. Tearing fracture behaviour of extruded mono- and bi-layer sheets of different types of amorphous co-polyesters and different thicknesses was investigated. Thick material exhibited higher specific total work of tear fracture than thin mono-layer sheet in the case of amorphous polyethylene terephthalate (PET). This finding was explained in terms of plastic zone size formed along the tear path, i.e., thick material underwent larger plastic deformation than thin material. When PET and polyethylene terephthalate glycol (PETG) were laminated with each other, specific total work of fracture of the bi-layer sheets was not noticeably improved over that of the constituent materials.

Effect of temperature on work of fracture parameters in poly(ether-ether ketone) (PEEK) film

The effect of temperature on plane-stress ductile fracture of an amorphous poly(ether-ether ketone) (PEEK) film of thickness 0.125 mm was studied between 23 and 140 °C using double edge notched tension (DENT) specimens. Within this temperature range, DENT specimens underwent full-ligament yielding prior to final fracture, producing load–displacement curves at various ligament lengths that were geometrically similar to one another at a given temperature. On the basis of these, “essential work of fracture (EWF)” methodology was used to determine the temperature dependence of the fracture toughness of PEEK film. Results showed that specific total work of fracture ( w f) is a linear function of ligament length ( L) over the entire temperature range under consideration. The value of w f at L=0 which is referred to as the “specific essential work of fracture, w e” decreased with increasing temperature. However, below the glass transition temperature, T g (≈140 °C), the amount w e decreased but was less than 10%. The slope of the line w f versus L which is referred to as the “specific non-essential work of fracture, βw p” increased with increasing temperature and showed a significant drop in value at T g. It is shown that w e and βw p are both composite terms, each consisting of a yielding ( w ey, β y w py) and necking/tearing ( w ent, β nt w pnt) components. It is found that w ent≫ w ey and β nt w pnt≫ β y w py, at all temperatures thus indicating that plastic deformation zone is linked mostly to necking/tearing component of the fracture process. Finally, it is shown that temperature dependence of the specific essential work of fracture parameters ( w e, w ey, w ent) can be predicted via crack opening displacement values.

Effect of temperature on fracture toughness of an amorphous poly(ether-ether ketone) film using essential work of fracture analysis

The effect of temperature on plane-stress ductile fracture of an amorphous poly(ether-ether ketone) (PEEK) film of thickness 0.125 mm was studied between 23 and 140 °C using double edge notched tension (DENT) specimens. Within this temperature range, DENT specimens underwent full-ligament yielding prior to final fracture, producing load–displacement curves at various ligament lengths that were geometrically similar to one another at a given temperature. The ‘essential work of fracture’ methodology was used to determine the temperature dependence of the fracture toughness of PEEK film. Results showed that specific total work of fracture ( w f) is a linear function of ligament length ( L) over the entire temperature range under consideration. The value of w f at L=0 which is referred to as the ‘specific essential work of fracture’, w e decreased with increasing temperature. However, below the glass transition temperature, T g (≈140 °C), the decrease in w e was not more than 10%. The slope of the line w f versus L, which is referred to as the ‘specific non-essential work of fracture’, βw p increased with increasing temperature and showed a significant drop in value at T g. It is shown that w e and βw p are both composite terms, each consisting of yielding ( w ey, β y w py) and necking/tearing ( w ent, β nt w pnt) components. It is found that w ent⪢ w ey and β nt w pnt⪢ β y w py, at all temperatures, thus indicating that plastic deformation zone is linked mostly to the necking/tearing component of the fracture process. Finally, it is shown that temperature dependence of the specific essential work of fracture parameters ( w e, w ey, w ent) can be predicted via crack opening displacement values.

Fracture behaviour of polyethylene naphthalate (PEN)

Fracture toughness of a semi-crystalline polyethylene naphthalate (PEN) film of thicknesses 0.050, 0.075 and 0.125mm was measured as a function of temperature and loading rate using both double edge notched tension (DENT) and single edge notched tension (SENT) specimens. The specific essential work of fracture (EWF) and the multi-specimen J-integral methods were used to evaluate fracture toughness. The variation of the specific total work of fracture (wf) with ligament length (L) was linear for ligament lengths between 5 and 15mm. Within this range, wf versus L was independent of thickness at all temperatures but was dependent on both temperature and loading rate. The specific EWF (we) was found to be independent of thickness and loading rate but showed three regions of varying temperature dependence. Between 23 and 80°C (region I) we was essentially independent of temperature but increased with temperature between 80 and 120°C (region II) and decreased with temperature thereafter (region III). At glass transition temperature (i.e. 120°C), we reached a maximum value of 75kJ/m2. The specific non-EWF (βwp) increased with both loading rate and temperature. The greatest change in βwp value with respect to temperature was obtained in region II.The plot of J-integral versus crack extension (Δa) was independent of thickness but was dependent upon temperature. we was found to be equivalent to both J0.2 and J0.

Work of fracture of polystyrene/high density polyethylene blends compatibilized by triblock copolymer

The fracture toughening behavior of polystyrene/high density polyethylene blends compatibilized by 10 wt % of a styrene-ethylene-butylene-styrene triblock copolymer (SEBS) was assessed using single-edge notched tension (SENT) and double-edge notched tension (DENT) specimens of various gauge lengths over a wide range of tensile rates. The fracture of DENT and SENT specimens was completely ductile under the plane-stress condition. A linear relationship was observed between the specific total work of fracture and the ligament length (L) for a given L range. The results showed that the essential work (w e ) was independent of the tensile rate (R) range of 1-30 mm/min, and it then decreased considerably when R was increased to 50 mm/min and above. However, the nonessential work exhibited a rate independent trend behavior. In addition, w e and the specific nonessential work of fracture (βw p ) were basically independent of the gauge length (G), provided that G was greater than the width of the sample. Finally, it was also shown that the w e and βw p values for SENT specimens are obviously greater than those for DENT specimens.

Temperature dependence of essential and non-essential work of fracture parameters for polycarbonate film

Single edge and double edge notched polycarbonate specimens of thickness 0·;375 mm have been pulled to complete fracture at temperatures between 25 and 120°C. Within this temperature range specimens underwent full ligament yielding prior to final fracture, producing load–displacement curves at various ligament lengths that were geometrically similar to one another for a specific geometry. On the basis of these, the method of the essential work of fracture was used to study the effect of temperature on fracture toughness of polycarbonate film. Results showed that a linear relationship exists between specific total work of fracture wt and ligament length L over the entire temperature range under consideration. The slope of the line, which is referred to as the specific non-essential total work of fracture βwp , increased with increasing temperature. However, the interception at L = 0, which is referred to as the specific essential total work of fracture we , showed little variation with respect to temperature. Change of geometry affected both values, although the change in βwp was more significant than that of we , for which change of no more than 10%was attained. Based on the maximum load on the load–displacement curve, wt for double edge notched specimens was partitioned into the specific work of fracture for yielding wy and the specific work of fracture for yielding necking/tearing wnt . Linear relationships were found for both terms as a function of ligament length from which the essential (we,y , we,nt ) and non-essential (βy wp,y , βnt wp, nt ) related work terms were attained. Results showed that the yielding related work terms for polycarbonate decrease, while the necking/tearing related work terms increase, with increasing temperature.

Work of fracture of PBT/PC blend: Effect of specimen size, geometry, and rate of testing

AbstractFracture behavior of PBT/PC blend was studied at room temperature using two specimen geometries (SENT and DENT) and a wide range of specimen sizes and crosshead speeds. It was found that the fracture of all SENT and DENT specimens is completely ductile and stable. A linear relationship was obtained between the specific total work of fracture, wf, and the ligament length, L. Extrapolation of this linear relationship to zero ligament length gave the specific essential work of fracture, we, which for PBT/PC blend was 35 ± 5 kJ/m2 and was almost insensitive to geometry and the dimensions of test specimens as well as testing rate.

Essential work of fracture in polymer films

The fracture behaviour of two polymer films (100 μm thick) has been investigated according to the essential work of fracture (EWF) approach in order to assess the validity of the linear relationship between the specific total work of fracture and the ligament length, postulated to exist by the EWF theory, and examine the transition from plane strain to plane stress conditions. Double edge notched specimens loaded in tension were used; ligaments were varied in the range 0.3 to 45 mm. No linear relationship was found and it was confirmed that a power law can be very accurately fitted to the experimental data. An annealed copper film (100 μm thick) exhibited the same pattern of behaviour.

Essential work of fracture and j‐integral measurements for ductile polymers

AbstractIn the ductile tearing of polymers that neck before failure it is shown that the specific essential fracture work (we), 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 we values for a grade of high‐density polyethylene. These measurements for we 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 Jc obtained by extrapolation of the JR curve to zero crack growth and the slope dJ/da are identical, respectively, to we and 4βwp obtained from the straight line relationship between the specific total work of fracture (wf) and ligament length (l).