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.     

Essential work of fracture analysis of the tearing of a ductile polymer film

The fracture behaviour of a 0.5 mm thick ethylene-propylene block copolymer, previously evaluated using the essential work of fracture method, has been analyzed again in more detail, using different plots, allowing the determination of the crack initiation displacement and stress. In such plots is evidenced that the specific essential work of fracture, w_e, corresponds to the energy just up to crack initiation value that can be related with J₀. Also, it has been found a novel relationship between the plastic term, βw_p and the crack initiation stress, σ_i.     

The J-integral fracture toughness of PP/CaCO3 composites

The J-integral method was introduced to investigate the fracture process of PP/CaCO₃ composites. The results showed that the resistance of PP/CaCO₃ composites to crack initiation and propagation was greatly improved with the addition of CaCO₃ filler. Large scale plasticity was caused in PP/CaCO₃ composites, from which a large amount of energy was absorbed by the PP matrix. The reason for the increase in the fracture toughness of PP/CaCO₃ composites was attributed to the partial micro-drawing ahead of the crack tip in the PP matrix, which was formed by the stress concentration caused by the filler particles in the PP matrix and/or by the interfacial debonding between filler particles and the PP matrix. It was indicated that the presence of CaCO₃ filler could augment the ductility of composites locally, resulting in higher fracture energy in the crack initiation and propagation of the PP/CaCO₃ composites in a certain CaCO₃ content range.     

Effects of pre-strain on plane stress ductile fracture in α-brass

The effects of pre-strain on plane stress ductile fracture in a 70/30 alpha brass Austral 207 have been studied using the deep-edge-notched tension (DENT) specimens. The amount of pre-strain varies between 5 and 35%. It is found that both the specific essential work of fracture (w _e) and the critical crack opening displacement (_c) decrease with increasing pre-strain. A simple theory for estimating the specific essential work of fracture in the presence of pre-strain is suggested and it gives good agreement with experimental results. Elongations to fracture in the DENT specimens are also predictable from a simple deformation analysis which considers the plastic elongations due to crack initiation, crack propagation and final stretch of a ligament that has reached a necking strain equal to that in a simple plain tension test. Micro-hardness measurements show that the strain localization is more intense near the fracture surface as the pre-strain level is increased and this is suggested to be an explanation for the low _c values obtained in pre-strained specimens.     

Essential work of fracture compared to fracture mechanics—towards a thickness independent plane stress toughness

The essential work of fracture (EWF) and the J-integral methods were applied in a study of the effect of the thickness on the cracking resistance of thin plates. The paper discusses two themes: (1) the relationships between the two methods or concepts is elucidated, and (2) a new, thickness independent plane stress toughness parameter is proposed. For that purpose, cracked aluminium 6082O thin plates of 1-6 mm thickness were tested in tension until final separation. The EWF, w_e, and the J-integral at cracking initiation, J_i, increase identically with thickness except at larger thickness for which the increase of J_i levels off. J_i reaches a maximum for 5-6 mm thickness whereas w_e keeps increasing linearly with thickness. This difference is related to the more progressive development of the necking zone in front of the crack tip when thickness increases: at large thickness, cracking initiates well before the neck has developed to its stationary value during propagation. A linear regression on the fracture toughness/thickness curve allows partitioning the two contributions of the work of fracture: the plastic work per unit area for crack tip necking and a plane stress work per unit area for material separation. The pertinence of this new measure of the pure plane stress cracking resistance is critically discussed based on a micromechanical model for ductile fracture. The micromechanical void growth model incorporates void shape effects, which is essential in the low stress triaxiality regime.     

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.     

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.     

The crack resistance in polybutylene terephthalate (PBT) at crack initiation and during steady crack growth

The resistance to crack initiation and quasi-static crack propagation is investigated for a polybutylene terephthalate (PBT) using annealed and unannealed three-point bend specimens. The resistance to crack initiation (R _i) is determined based on the generalized locus method which determines the resistance to crack growth including crack initiation utilizing the locus of characteristic points on the load against load-point displacement curves of specimens which differ only in initial crack length. This generalized locus method also enables us to investigate the invariance of the crack resistance value along the locus line. The steady state crack resistance (R _p) during quasi-static crack propagation is determined utilizing the functional relation between total essential energy (U _f) for complete fracture and the initial ligament length. The total essential energy is the sum of the blunting energy and the integration of the resistance to crack propagation with respect to the cracking area. The invariance of the crack initiation resistanceR _i, and the steady state resistanceR _p is discussed based on the experimental results of the annealed and unannealed specimens which show different sizes of crack tip plastic deformation.     

Fatigue properties and fatigue fracture mechanisms of SiC whiskers or SiC particulate-reinforced aluminium composites

Fatigue properties and fracture mechanisms were examined for three commercially fabricated aluminium matrix composites containing SiC whiskers (SiC_w) and SiC particles (SiC_p) using a rotating bending test. The fatigue strengths were over 60% higher for SiC_w/A2024 composites than that for the unreinforced rolled material, while for the SiC_p/A357 composites, fatigue strengths were also higher than that for the unreinforced reference material. For the SiC_p/A356 composites at a volume fraction of 20%, the fatigue strength was slightly higher than that of the unreinforced material. Fractography revealed that the Mode I fatigue crack was initiated by the Stage I mechanism for the SiC_w/A2024 and SiC_p/A357 composites, while for the SiC_p/A356 composite, the fatigue crack initiated at the voids situated beneath the specimen surfaces. On the other hand, the fatigue crack propagated to the whisker/matrix interface following the formation of dimple patterns or the formation of striation patterns for SiC_w/A2024 composites, while for the SiC_p/A356 and SiC_p/A357 composites the fatigue crack propagated in the matrix near the crack origin and striation patterns were found. Near final failure, dimple patterns, initiated at silicon carbide particles, were frequently observed. Mode I fatigue crack initiation and propagation models were proposed for discontinuous fibre-reinforced aluminium composites. It is suggested that the silicon carbide whiskers or particles would have a very significant effect on the fatigue crack initiation and crack propagation near the fatigue limit.     

A review of the J and I integrals and their implications for crack growth resistance and toughness in ductile fracture

The application of the J and the I-integrals to ductile fracture are discussed. It is shown that, because of the finite size of the fracture process zone (FPZ), the initiation value of the J-integral is specimen dependent even if the plastic constraint conditions are constant. The paradox that the I-integral for steady state elasto-plastic crack growth is apparently zero is examined. It is shown that, if the FPZ at the crack tip is modelled, the I-integral is equal to the work performed in its fracture. Thus it is essential to model the fracture process zone in ductile fracture. The I-integral is then used to demonstrate that the breakdown in applicability of the J-integral to crack growth in ductile fracture is as much due to the inclusion in the J-integral of progressively more work performed in the plastic zone as it is to non-proportional deformation during unloading behind the crack tip. Thus J _R -curves combine the essential work of fracture performed in the FPZ with the plastic work performed outside of the FPZ. These two work terms scale differently and produce size and geometry dependence. It is suggested that the future direction of modelling in ductile fracture should be to include the FPZ. Strides have already been made in this direction.     

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.     

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.     

Nanoparticle-induced enhancement in fracture toughness of highly loaded epoxy composites over a wide temperature range

The fracture toughness of an epoxy molding compound (EMC) has been enhanced over a wide temperature range by the addition of a very low volume fraction of silica nanoparticles to the EMC filled with micro-silica particles, which induces macroscopic crack deflection and plastic deformation in front of the crack tip. To evaluate the fracture toughness (G _IC) of these materials, the single edge notched bending (SENB) test was performed for a wide range of temperatures (from ambient temperature to 230°C). The fracture toughness of the nano-silica filled EMCs was found to be improved in this temperature range by as much as a factor of two. Investigation of the fracture surfaces revealed that the micro-silica particles are covered with deformed matrix materials, which implies that the silica nanoparticles induced the crack to move into the interface between the micro-silica particles. Fractography results suggest that the silica nanoparticles act as surface modifiers of the micro-silica particles, which results in crack deflection and plastic deformation.     

Work of fracture of high impact polystyrene (HIPS) film under plane stress conditions

Essential work of fracture methodology was used to determine plane-stress ductile fracture toughness of high impact polystyrene film of thickness 0.26 mm. Results obtained indicated that specific essential work of fracture, w _e, is independent of loading rate, and for certain specimen sizes, independent of both gauge length and width of the specimen. On the other hand, w _e was found to be affected by the temperature, molecular anisotropy and the geometry of the test specimens. Reasonable estimate of w _e was obtained via crack opening displacement value.     

Fatigue Crack Growth and Fracture of 30 wt% B4C/6061Al Composites

This paper focuses on studying the fatigue crack growth (FCG) characteristics and fracture behaviours of 30 wt% B₄C/6061Al composites fabricated by using powder metallurgy and hot extrusion method. Compact tension (CT) specimens having incisions parallel to the extrusion direction (T‐D) and perpendicular to the extrusion direction (E‐D) were investigated through FCG tests. Results show that, at low/medium stress‐intensity factor range levels (ΔK ≤ 9), crack propagation rate in E‐D specimens is lower than that in T‐D specimens because the elongated B₄C particles parallel to the extrusion direction in E‐D specimens can deflect the crack. The scanning electron microscope micrographs of the fractured surface illustrate that crack mainly propagates in the matrix alloy at the initial stage of its propagation and propagates more remarkably near the particle‐matrix interface with the increase of ΔK value. B₄C particles are also found to be easy to fracture during the rapid crack propagation. Based on fracture analyses, considering the impacts of factors like crack deviation, plastic zone size at the crack tip, and crack driving force, a 2‐D crack propagation model was developed to study the fatigue crack propagation mechanism in the 30 wt% B₄C/6061Al composite.     

Experimental investigation on low cycle fatigue and fracture behaviour of a notched Ni‐based superalloy at elevated temperature

In order to investigate the effects of stress concentration on low cycle fatigue properties and fracture behaviour of a nickel‐based powder metallurgy superalloy, FGH97, at elevated temperature, the low cycle fatigue tests have been conducted with semi‐circular and semi‐elliptical single‐edge notched plate specimens at 550 and 700 °C. The results show that the fatigue life of the notched specimen decreases with the increase of stress concentration factor and the fatigue crack initiation life evidently decreases because of the defect located in the stress concentration zone. Moreover, the plastic deformation induced by notch stress concentration affects the initial crack occurrence zone. The angle α of the crack occurrence zone is within ±10° of notch bisector for semi‐circular notched specimens and ±20° for semi‐elliptical notched specimens. The crack propagation rate decreases to a minimum at a certain length, D, and then increases with the growth of the crack. The crack propagation rate of the semi‐elliptical notched specimen decelerates at a faster rate than that of the semi‐circular notched specimen because of the increase of the notch plasticity gradient. The crack length, D, is affected by both the applied load and the notch plasticity gradient. In addition, the fracture mechanism is shown to transition from transgranular to intergranular as temperature increases from 550 to 700 °C, which would accelerate crack propagation and reduce the fatigue life.     

The energy of crack propagation in carbon fibre-reinforced resin systems

The energy expended during controlled crack propagation in unidirectionally reinforced composites of carbon fibre in a brittle resin matrix has been evaluated in terms of the energy dissipated during fibre-snapping, matrix-cracking and fibre pull-out. The work of fracture, _F, is found to depend principally on the frictional shear stress at the fibre/resin interface opposing pulling out of broken fibres. Differences in _F for carbon fibre/resin composites exhibiting a range of interfacial shear strengths and void contents have been explained with reference to variations in fracture surface topography of the fibrous composites. The effect of environment on properties of the interface and work of fracture was also investigated. The energy required to propagate a crack has been compared with the energy for fracture initiation, _I, using a linear elastic fracture mechanics approach. It was found that fibre pull-out energy is the principal contribution to _F, and _I is similar to the elastic strain energy release rate at the initiation of fracture of a brittle, orthotropic solid. For crack propagation parallel to fibres, _F and _I are similar and not unlike the fracture surface energy of the resin alone. The strength of the interface is important only in so far as it affects the value of _I.     

Crack growth prediction and non-linear analysis for an elasto-plastic solid

In this paper, a variable radius for the plastic zone is introduced and a maximum principal stress criterion is proposed for the prediction of crack initiation and growth. It is assumed that the direction of crack initiation coincides with the direction of the maximum principal stress. The von Mises yield criterion is applied to define the plastic zone, instead of assuming a plastic zone with a constant distance r from the crack tip. An improvement is made to this fracture criterion, and the criterion is extended to study the crack growth characteristics of mixed mode cracks. Based on the concept of frictional stress intensity factor, k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The proposed crack growth model is discussed by comparing the experimental results with those obtained using the maximum principal stress criterion.     

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.     

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.