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.     

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 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.     

Influence of femtolaser notch sharpening technique in the determination of essential work of fracture (EWF) parameters

The fracture behaviour of a 0.5 mm thick ethylene-propylene block copolymer is analyzed using the essential work of fracture method, using DENT-type specimens. The influence of three experimental parameters in the technique is evaluated: the effect of the notch sharpening technique, the use of a videoextensometer for monitoring the deformations and the measurement of ligament lengths before or after fracture tests were carried on.The results showed that the femtosecond pulsed laser ablation technique (femtolaser) produced sharp notches with no plastic deformation ahead of the notch tip, which yield smaller specific essential work of fracture (w_e) values than in the cases where the notches were sharpened with razor blades. The use of a videoextensometer has allowed removing the viscoelastic energy from the plastic work, with lower values of βw_p. The measurement of the ligament lengths before or after the test did not affect the results.     

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.     

Morphology and crack toughness behaviour of nanostructured block copolymer/homopolymer blends

The crack initiation and propagation behaviour of styrene-butadiene (SB) star block copolymer/polystyrene blends (ST3/PS) forming PS-rich and polybutadiene (PB)-rich nanosized domains by self-assembling have been investigated using the essential-work-of-fracture (EWF) approach. Three morphological transitions have been observed, which are crucial to understand the crack toughness behaviour: (i) 0-30 wt.% PS homopolymer: A co-continuous domain structure of PS-rich and PB-rich domains has been observed. For PS homopolymer fraction (?_PS) < 10 wt.% PS homopolymer (i.e. only pure ST3) the rubbery PB-rich phase forms the major phase and for ?_PS > 10 wt.% the glassy PS-rich phase. (ii) At 40-60 wt.% PS homopolymer, a layer-like morphology is formed where the PS-rich layer thickness is ?50 nm, a critical dimension, which is crucial for understanding the ductile-to-semiductile transition. (iii) For 80 wt.% PS homopolymer, PS-rich phase starts to form the matrix combined with a transition from shear stress dominated (shear yielding) to normal stress dominated behaviour (PS-like crazes). The co-continuous morphology at 20 wt.% and 30 wt.% PS is capable of improving toughness of block copolymers, demonstrated by the observed maximum in the non-essential work of fracture and thus explaining a new way of toughening of polymers while retaining high transparency. The correspondence between the ductile-to-semiductile transition and the change in the shape of plastic zone from circular to elliptical as revealed from strain field analysis could be clearly reaffirmed by the observed transition from shear to normal force induced deformation in the fractured surface analysis of these blends. The conceptual correspondence of βw_p and w_e with T_J and δ_0.2 respectively reveal that resistance against crack propagation (βw_p and T_J) is morphology sensitive while the resistance against crack initiation (w_e and δ_0.2) is matrix sensitive.     

On the application of the damage work density as a new initiation criterion for ductile fracture

In this paper the ‘damage work’ proposed by Chaouadi et al. is used to formulate an energy crack initiation criterion to describe ductile crack initiation. The traditional assessment of structural integrity by the J-integral, a property of elastic-plastic fracture mechanics is compared. Two free-cutting and one structural steel are investigated. The measured values for the critical damage work density at initiation W_di are compared with values for copper and RPV steel. As the fracture mechanical approach is limited to sharp cracks in the material (high-constraint stress state) the present damage mechanics approach is regarded as important as a more general concept closer to reality. While old void growth models of damage mechanics cannot formulate a simple criterion for crack initiation the applied damage work reaches a constant value at initiation W_di which is independent of the stress state during the deformation process. We recommend W_di as a material property of toughness for testing and engineering purposes.     

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.     

High rate toughness of ductile polymers

Impact toughness of two highly ductile polymers: acrylonitrile-butadiene-styrene (ABS) terpolymer and polypropylene block copolymer (PPBC) - was evaluated using the essential work of fracture (EWF) - and a J-R resistance single specimen curve - S_pb techniques. The EWF has proved to be capable of determining toughness from the total fracture energy of several samples differing in initial ligament length and the linear regression of the data. On the other hand, the S_pb method, which is based on the load separation principle, is able of constructing J-R curves by inferring instantaneous crack growth length from the sole comparison between one sharp and one blunt-notched load-displacement traces. Results show that both methodologies can be used under impact conditions when evaluating ABS polymers. However, ABS impact fracture toughness value yielded by the EWF method, w_Ie, was larger than the J_0.2 value obtained from the S_pb method. This difference was imputed to the more progressive development of the necking zone in front of the crack tip under plane strain conditions. On the contrary, for very ductile fracture behavior like that demonstrated by PPBC in which J-controlled conditions were not achieved and hence J-R curves could not be built the EWF appeared as a valuable alternative to characterize impact toughness.     

Limitations of elastic definitions in Al-Si-Mg cast alloys with enhanced plasticity: linear elastic fracture mechanics versus elastic-plastic fracture mechanics

Linear elastic fracture mechanics describes the fracture behavior of materials and components that respond elastically under loading. This approach is valuable and accurate for the continuum analysis of crack growth in brittle and high strength materials; however it introduces increasing inaccuracies for low-strength/high-ductility alloys (particularly low-carbon steels and light metal alloys). In the case of ductile alloys, different degrees of plastic deformation precede and accompany crack initiation and propagation, and a non-linear ductile fracture mechanics approach better characterizes the fatigue and fracture behavior under elastic-plastic conditions.To delineate plasticity effects in upper Region II and Region III of crack growth an analysis comparing linear elastic stress intensity factor ranges (ΔK_el) with crack tip plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) is presented. To compute plasticity corrected stress intensity factor ranges (ΔK_pl), a new relationship for plastic zone size determination was developed taking into account effects of plane-strain and plane-stress conditions (“combo plastic zone”). In addition, for the upper part of the fatigue crack growth curve, elastic-plastic (cyclic J based) stress intensity factor ranges (ΔK_J) were computed from load-displacement records and compared to plasticity corrected stress intensity factor ranges (ΔK_pl). A new cyclic J analysis was designed to compute elastic-plastic stress intensity factor ranges (ΔK_J) by determining cumulative plastic damage from load-displacement records captured in load-control (K-control) fatigue crack growth tests. The cyclic J analysis provides the true fatigue crack growth behavior of the material. A methodology to evaluate the lower and upper bound fracture toughness of the material (J_IC and J_max) directly from fatigue crack growth test data (ΔK_FT(JIC) and ΔK_FT(Jmax)) was developed and validated using static fracture toughness test results. The value of ΔK_FT(JIC) (and implicitly J_IC) is determined by comparing the plasticity corrected elastic fatigue crack growth curve with the elastic-plastic fatigue crack growth curve. A most relevant finding is that plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) are in remarkably good agreement with cyclic J analysis results (ΔK_J), and provide accurate plasticity corrections up to a ΔK corresponding to J_IC (i.e. ΔK_FT(JIC)). Towards the end of the fatigue crack growth test (above ΔK_FT(JIC)) when plasticity is accompanied by significant tearing, the cyclic J analysis provides a more accurate way to capture the true behavior of the material and determine ΔK_FT(Jmax). A procedure to decouple and partition plasticity and tearing effects on crack growth rates is given.Three cast Al-Si-Mg alloys with different levels of ductility, provided by different Si contents and heat treatments (T61 and T4) are evaluated, and the effects of crack tip plasticity on fatigue crack growth are assessed. Fatigue crack growth tests were conducted at a constant stress ratio, R = 0.1, using compact tension specimens.     

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.     

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.     

Evaluation of dynamic fracture toughness KId by Hopkinson pressure bar loaded instrumented Charpy impact test

A novel method for measuring the dynamic fracture toughness, K_Id, using a Hopkinson pressure bar loaded instrumented Charpy impact test is presented in this paper. The stress intensity factor dynamic response curve (K_I(t)−t) for a fatigue-precracked Charpy specimen is evaluated by means of an approximate formula. The onset time of crack initiation is experimentally detected using the strain gauge method. The value of K_Id is determined from the critical dynamic stress intensity factor at crack initiation. A K_Id value for a high-strength steel is obtained using this method at a stress-intensity-factor rate () greater than 10⁶ MPa .     

Super-toughening polyamide-612 by controlling dispersed phase domain size: Essential work of fracture assessment

A new pathway to super-toughen polyamide-612 (PA-612) by incorporating domains of soft poly(octene-co-ethylene)-g-maleic anhydride (POE-g-MA) via melt blending leading to more than ∼1100% increase in notched Izod impact strength vis-à-vis fracture toughness enhancement is demonstrated. Fourier transform infra red (FTIR) studies showed effective phase interactions between PA-612 and POE-g-MA whereas dynamic mechanical analysis (DMA) revealed a reduction in loss-peak intensity at ∼45 °C with increase in the soft phase fraction. The optimal dependence of fracture-toughness (in plane-stress) on domain-size (D_n) of dispersed-phase in the form of a reduction in resistance to crack initiation indicated by essential work of fracture (w_e) and linear increase in resistance to crack propagation indicated by non-essential work of fracture (βw_p) of the blends ⩾10 wt% of POE-g-MA content is correlated to an increase in domain-size ⩾∼0.3 μm. Fracture surface morphology indicated crazing to be responsible for the transition in fracture behavior, i.e. remarkable toughening of PA-612 at the critical rubber phase domain size range of ∼0.2–0.3 μm.     

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.     

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.     

Influence of threshold parameters on cleavage fracture predictions using the Weibull stress model

This study explores applications of three-parameter Weibull stress models to predict cleavage fracture behavior in ferritic structural steels tested in the transition region. The work emphasizes the role of the threshold parameters (_th and _{w – min}) in cleavage fracture predictions of a surface crack specimen loaded predominantly in tension for an A515-70 pressure vessel steel. A recently proposed procedure based upon a toughness scaling methodology using a modified Weibull stress (^* _w) extends the calibration scheme for the Weibull modulus, m, to include the threshold parameters. The methodology is applied to calibrate the Weibull stress parameter for the tested material and then to predict the toughness distribution for the surface crack specimen. While the functional relationship between ^* _w and m suggests a strong effect of the threshold stress, _th, on the calibrated m-parameter, the results show a remarkably weak dependence of fracture predictions on _th as does the dependence of fracture predictions on _w–min for this 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.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K _IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K ^H _IC for a single hydride platelet at the crack tip has been also estimated.