The essential work of fracture of polyamide 66 filled with TiO2 nanoparticles

The fracture property of 21-nm TiO₂-nanoparticle filled polyamide 66 was studied based on the essential work of fracture method. An energy-partitioned work of fracture approach was introduced, in which the resistance to crack initiation, w_ini, and the resistance to crack propagation, w_prop, were applied. Double-edge-notched-tension specimens with different original ligament lengths were tested at a constant cross-head speed. The results showed that the essential work term of composites filled with low nanoparticle concentration notably increased, while the plastic work fairly decreased compared to that of neat matrix at room temperature. Fractography analysis suggests a three-stage evolution of crack initiation. The individual nanoparticles acted as stress concentration points, which promoted cavitations and thus induced relatively large local deformation. Thereafter, the tiny cavitations coalesced into sub-micro ones and rapidly grow into micro-voids and crack initiation due to the high-level stress concentration. The plastic work of composites was decreased with increasing nanoparticle fractions, which was due to unavoidably aggregated nanoparticles leading to high level stress concentration that favouring the crack propagation.     

Statistical procedure for improving the precision of the measurement of the essential work of fracture of thin sheets

The precision of the measurement of the essential work of fracture requires an accurate determination of the critical ligament length below which the ligament is in a mixed mode stress state and the failure mechanisms considerably change. A statistical procedure is proposed which allows to determine easily and accurately this critical ligament length. After rejection of the specimens having too small ligament lengths, w_e is obtained by extrapolation of the remaining data for zero ligament length. The number of data points from which w_e is calculated is also shown to strongly influence the precision of the measurement. The procedure is applied to the measurement of the toughness of sheets of Al and Zn alloys and of a low density polyethylene. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

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.     

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.     

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.     

Fatigue strength of carbon steel specimens having an extremely shallow notch

In order to elucidate how the principal dimensions of a notch as small as grains affect the fatigue strength of carbon steel, rotating bending fatigue tests were carried out on annealed 0.45% C steel specimens having an extremely small artificial notch whose depth is either 5 or 10μm. The fatigue processes at notched parts were observed successively.In these extremely shallow notches, the parameter controlling fatigue limits for fracture σ_w was the notch depth, independently of notch sharpness. On the other hand, the crack initiation limits in the notches σ_W1 were determined by a single K_tσ_W1 — χ relation obtained from the tests on ordinary notches, where K_t is the stress concentration factor and χ is the stress gradient at the notch root.These results were studied on the basis of the characteristics of crack initiation process, the stress intensity variations at the crack tip and the stress distribution near the notch root.     

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.     

Fracture initiation of geometrically scaled, notched three-point-bend bars of a low-alloy ferritic steel

The purpose of the experimental work reported in this contribution was to provide data that may serve for the development of scaling rules for ductile fracture at blunt notches. Bending experiments were performed with three sizes of geometrically scaled notched bend specimens of the ferritic pressure vessel material 20MnMoNi55, material number 1.6310 (heat number 69906) using carefully scaled supports, using geometrically similar U-notched bend bars with rectangular cross-sections and scaled blunt notches covering a scale range of 14. Fracture initiation was reliably detected by means of the dc potential drop technique. Comparison of the normalised load versus load-point-displacement curves revealed a significant size effect for the conditions of fracture initiation, with large specimens fracturing at smaller normalised displacements than smaller ones. The energy up to the initiation point normalised to the ligament can be linearly correlated with specimen size, while the energy normalised to the active volume (ligament size multiplied by notch width) consists of two terms: a hyperbolic decay term analogous to the initiation of crack extension in fracture mechanics and a constant term corresponding to the classical size independent plasticity theory. For the smallest specimens investigated the first term amounts to about 28% of the total volume specific work, for the largest specimens there is almost no contribution of the first term.     

State‐of‐the‐art review on extended stress intensity factor concepts

The stress intensity factor concept for describing the stress field at pointed crack or slit tips is well known from fracture mechanics. It has been substantially extended since Williams' basic contribution (1952) on stress fields at angular corners. One extension refers to pointed V‐notches with stress intensities depending on the notch opening angle. The loading‐mode‐related simple notch stress intensity factors K₁, K₂ and K₃ are introduced. Another extension refers to rounded notches with crack shape or V‐notch shape in two variants: parabolic, elliptic or hyperbolic notches (‘blunt notches’) on the one hand and root hole notches (‘keyholes’ when considering crack shapes) on the other hand. Here, the loading‐mode‐related generalised notch stress intensity factors K_1ρ, K_2ρ and K_3ρ are defined. The concepts of elastic stress intensity factor, notch stress intensity factor and generalised notch stress intensity factor are extended into the range of elastic–plastic (work‐hardening) or perfectly plastic notch tip or notch root behaviour. Here, the plastic notch stress intensity factors K_1p, K_2p and K_3p are of relevance. The elastic notch stress intensity factors are used to describe the fatigue strength of fillet‐welded attachment joints. The fracture toughness of brittle materials may also be evaluated on this basis. The plastic notch stress intensity factors characterise the stress and strain field at pointed V‐notch tips. A new version of the Neuber rule accounting for the influence of the notch opening angle is presented.     

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.     

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.     

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.     

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.     

Effects of loading rate on the local cleavage fracture stress σf in notched specimens

Four point bending (4PB) notched specimens with different notch sizes are tested at various loading rates at a temperature of −110 °C for a C-Mn steel. An elastic-plastic finite element method (FEM) is used to determine the stress and strain distributions ahead of notches. By accurately measuring the distances of the cleavage initiation sites from the notch roots, the local cleavage fracture stress σ_f is measured. The results show that the local cleavage fracture stress σ_f does not essentially change with loading rate V and notch size. The reason for this is that the cleavage micromechanism does not change in the different specimens at various loading rates. The cleavage micromechanism involves competition of two critical events of crack propagation and crack nucleation in the high stress and strain volume ahead of notch root. The large scatter of σ_f and notch toughness are mainly caused by the different critical events in different specimens.     

Effects of loading rate, notch geometry and loading mode on the local cleavage fracture stress of a C–Mn steel

In this work, notched specimens with two notch geometries were tested in two loading modes (four-point bending (4PB) and three-point bending (3PB)) at various loading rates at a temperature of − 110°C for a C–Mn steel. An elastic–plastic finite-element method (FEM) is used to determine the stress distributions ahead of notches. By accurately measuring the distances of the cleavage initiation sites from the notch roots, the local cleavage fracture stress σ _f is measured. The results obtained and combining with previous studies by the authors show that the local cleavage fracture stress σ _f is closely related to the cleavage fracture mechanism (critical events) in steels. The σ _f values do not change with loading rate, notch geometry and loading mode, as long as the critical event of cleavage fracture does not change at various testing conditions. The σ _f is mainly determined by the steel microstructure, and its scatter is mainly caused by the size distribution of the weakest constituent in steels (ferrite grain or pearlite colony with large sizes and large second phase particles) and the change of the critical events in cleavage process. The σ _f can characterize the intrinsic toughness of steels and may be used in a “local approach” model for assessing integrity of flawed structures. The σ _f values could be measured by both 4PB and 3PB tests.     

Influence of notch root radius on ductile rupture fracture toughness evaluation with Charpy-V type specimens

The blunt notch fracture toughness of four types of carbon-manganese steel (ASTM A516 grade 70) has been determined by J-integral tests on Charpy-V type samples with different values of notch root radius, ρ. J-ρ plots, determined using specimens with a notch depth to width ratio, a/w, equal to 0.5, have shown the existence of a limiting ρ value (ρ_eff) below which applied J-intergral values at fracture initiation are constant. These ρ_eff values have been seen to depend only on second-phase particle distribution and not on their volume fraction or on the steel ferritic grain size. The procedure for deriving J-integral values at the onset of stable crack growth from J resistance curves in the case of notches has also been discussed. Experiments with Charpy specimens with a/w = 0.2 do not allow the derivation of meaningful J-ρ plots. In all cases, a ductile fracture criterion based on the constancy of the notch tip strain at rupture initiation has been proved when ρ >ρ_eff.     

The effect of specimen size on the fracture energy and softening function of concrete

This paper examines the effect of specimen size on the fracture energy of concrete, G_F, as measured using the three-point bending test on pre-notched beams prescribed by RILEM TC-50 [1]. The concept of partial fracture energy is introduced and used to explain the observed size effect. The opening displacement at the top of the notch in the test specimen at the end of the test, ω, is affected by the size of the specimen, which in turn affects the measured value of the concrete fracture energy. In theory, when the specimen is large enough to allow the fracture process zone to develop fully,w _f will reach its critical value,w _c , and the effect of specimen size onG _F will be eliminated. The experimental results included here show that in reality the size of the specimen does affect the measurement ofG _F , even when the size is such that the fracture process zone develops fully. This may be due to local plastic deformation in the area around the loading point, which is particularly significant in larger specimens. It may also be due to differences in the influence of the boundary conditions of the test for different specimen sizes. In addition, a procedure is outlined for the determination of the softening function for concrete based on the fracture energy measured in RILEM tests, in which the specimens are small enough to ensure that the energy measured is actually due to fracture and not plastic deformation.     

Influence of crack tip constraint on void growth in pressure sensitive plastic solids - I: 2D analysis

In this work, the effect of constraint on void growth near a notch tip under mode-I loading is investigated in materials exhibiting pressure sensitive yielding and plastic dilatancy. To this end, large deformation elastic-plastic finite element analyses are performed using a two-dimensional (2D) plane strain, modified boundary layer formulation by prescribing the elastic K − T field as remote boundary conditions. The analyses are conducted for different values of K (or J) and T-stress. The material is assumed to obey a finite strain, Extended Drucker-Prager yield condition. The roles of pressure sensitivity, plastic dilatancy and yield locus shape on the interaction between the notch and a nearby void are studied by examining the distribution of hydrostatic stress and plastic strain in the ligament connecting them as well as the growth of notch and the void. The results show that void growth with respect to J is enhanced due to pressure sensitivity, and more so when the plastic flow is non-dilatational. By contrast, irrespective of pressure sensitivity, loss of crack tip constraint can significantly retard void growth.     

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.