Critical Stress Intensity Factor Research Articles

Attapulgite-MXene Hybrids with Ti3C2Tx Lamellae Surface Modified by Attapulgite as a Mechanical Reinforcement for Epoxy Composites.

As a member of two-dimensional (2D) materials, MXene is an ideal reinforcement phase for modified polymers due to its large number of polar functional groups on the surface. However, it is still relatively difficult to modify any functional groups on the surface of MXene at present, which limits its application in enhancing some polymers. Herein, one-dimensional (1D) attapulgite (ATP) nanomaterials were introduced onto the surface of MXene to form ATP–MXene hybrids, which successfully improved the mechanical properties of the epoxy composites. ATP with appropriate content can increase the surface roughness of the MXene lamellae to obtain better interface interaction. Therefore, remarkable enhancement on the mechanical property was achieved by adding M02A025 (0.2 wt % MXene and 0.25 wt % ATP), which is the optimum composition in the hybrids for composite mechanical properties. Compared to neat epoxy, the tensile strength, flexural strength and critical stress intensity factor (KIC) of M02A025/epoxy are increased by 88%, 57%, and 195%, respectively, showing a high application prospect.

Fatigue and fracture toughness of electron beam welded joints of aluminum alloy 6156 (Al–Mg–Si) for aerospace applications

AbstractThe mechanical behavior of AA6156 electron beam welded joints and the effect of artificial aging heat treatments on the fracture‐related properties were investigated. The fatigue test results of the welded joints presented lower fatigue endurance limit by approximately 60%, when compared to the base material. Fracture resistance results showed that the critical stress intensity factor (Kcr) was essentially decreased (~32%) in the as‐welded condition. Heat treatment before welding presented a 15% increase in Kcr for 4 h of artificial aging, while a decrease in Kcr was noticed for prolonged isothermal heat treatment prior to welding. By applying post welding heat treatments, all investigated isothermal heat treatment conditions resulted in decreasing Kcr. Tensile test results of the welded joints showed that an almost 40% increase of the yield stress can be achieved with appropriate post welding heat treatment, on the expense of only 10% decrease in Kcr.

Evaluation of fracture processes under shear with the use of DIC technique in fly ash concrete and accurate measurement of crack path lengths with the use of a new crack tip tracking method

The paper proves how the innovative optical and contactless DIC technique can be used for the examination of fracture processes in concrete with fly ash under shear loading. Critical stress intensity factor KIIc and the characteristics of the cracks occurring in the loaded specimens were investigated by two measuring devices. A new proposed concept allowed to assess the fracture toughness of the composite by the direct testing of the material with an initial defect, i.e. directly in the crack propagation area.The article also presents an original, sophisticated solution for measuring the actual length of crack path (ALCP) in the material with the use of the crack tip tracking (CTT) method. The measurement of the ALCP, using the CTT method, allowed to prove that unmodified concrete are characterised by greater brittleness, whereas composites made on the basis of the binary binder behave as quasi-plastic materials in the fracture process.

Stress intensity factors for micro- and macroscale bimaterial cantilevers and bend specimens

Bilayered materials with different properties play an important role in several fields of engineering to improve the mechanical, thermal, electrical, magnetic characteristics of structures. In order to determine the fracture toughness of such bimaterials, experimental measurements must be combined with numerical calculations, which is a tremendous effort. Therefore, a procedure is presented which enables a simple determination of the (critical) stress intensity factor for bimaterial bend specimens. The procedure is applicable for nano- to macroscale cantilevers and three-point bend specimens consisting of linear-elastic or elastic-plastic film and substrate materials. By finite element computations, the procedure is verified for a wide range of Young's moduli combinations, layer heights, and crack lengths. Possible limitations of the procedure are worked out. Practical applications for concrete bimaterial systems are presented, as well as the usage as a failure assessment tool.

Low-Temperature Fracture Toughness Study for Hot Mix Asphalt and Warm Mix Asphalt Under Pure Mode I and II Loading Condition

A linear elastic fracture mechanics method is proposed to investigate the fracture behavior of hot mix asphalt and warm mix asphalt; this method was used in this study to calculated the fracture toughness of hot mix asphalt and warm mix asphalt containing 3% Sasobit at low temperatures (0, − 10, and – 20 °C) and two types of bitumen (60/70 and 85/100). A semi-circular specimen with an edged crack under three-point bending load mode was used to create different loading modes, including pure mode I and pure mode II, to test the fracture toughness. The critical stress intensity factor was calculated using the critical load obtained from the failure test. The shape factor was determined from finite element analysis. The results show that hot mix asphalt has a higher fracture toughness against crack growth than the warm mix asphalt containing Sasobit. In addition, the fracture toughness of asphalt mixture with a penetration grade of 85/100 against crack growth is more than that of the mixture with a penetration grade of 60/70. The minimum fracture toughness of hot mix asphalt and warm mix asphalt occurred in pure mode I loading condition.

Mechanical and Fracture Properties of Polycrystalline Graphene with Hydrogenated Grain Boundaries

Molecular dynamics (MD) is employed to study the mechanical and fracture properties of polycrystalline graphene with hydrogenated grain boundaries. Polycrystalline graphene sheets with an average grain size of 4, 6, and 8 nm are considered. The impact of hydrogenation percentage on the mechanical strength and fracture toughness of polycrystalline graphene sheets is investigated. Polycrystalline graphene with and without an initial crack are considered. The results show that due to the hydrogenation the strength of polycrystalline graphene sheets reduces. The impact of hydrogenation is significantly greater on the strength of polycrystalline graphene without an initial crack. The strength of polycrystalline graphene sheets with hydrogenated grain boundaries decreases with increase in temperature. The impact of temperature on the strength increases with increase in hydrogenation percentage at the grain boundaries. The results also show that the hydrogenation of the polycrystalline graphene affects the crack propagation path. As the hydrogenation percentage of grain boundaries increases, the crack path changes from intragranular to intergranular. Furthermore, the increase in the hydrogenation reduces the critical stress intensity factor of polycrystalline graphene. Such changes in the strength, fracture toughness, and crack path are due to the hydrogen embrittlement of grain boundaries which reduces their fracture energy.

The effects of melt grafted maleated polybutylene succinate on the properties of poly(hydroxybutyrate‐co‐hydroxyhexanoate)/polybutylene succinate blends

AbstractPoly(hydroxybutyrate‐co‐hydroxyhexanoate) (PHBHH)/poly(butylene succinate) (PBS) blends were prepared using a melt blending technique. A compatibilizer of maleated PBS (PBSgMA) was produced using reactive melt grafting by varying the maleic anhydride (MA) monomer concentration ranging from 3 to 10 parts per hundred resin (phr). Fourier‐transform infrared (FTIR) spectroscopy and nuclear magnetic resonance (NMR) spectroscopy analyses confirmed the grafting reaction of the PBSgMA. The PBSgMA was incorporated in the 80PHBHH/20PBS and 50PHBHH/50PBS blends to investigate the effect of maleated compatibilizer on the tensile, flexural, drop weight impact, and water absorption properties of the blends with droplets dispersed and co‐continuous morphology. The incorporation of PBSgMA increased the tensile and flexural strength of both the 80PHBHH/20PBS and 50PHBHH/50PBS blends, where the optimum properties achieved at 5 phr concentration of MA. The drop weight impact test results showed that uncompatibilized and compatibilized 50PHBHH/50PBS blends had higher critical strain energy release rate (Gc) than the neat PHBHH. However, blending and compatibilizing did not have a positive effect on the critical stress intensity factor (Kc) of the neat PHBHH. Scanning electron microscopy (SEM) confirmed the improvement of interfacial adhesion and PBS polymer dispersion in PHBHH/PBS blends when incorporated with 5PBSgMA. The water absorption test results demonstrated that compatibilized blends absorbed slightly more water than uncompatibilized blends due to the presence of hygroscopic carboxyl groups of the PBSgMA. However, water absorption effects were reversible and did not result in severe permanent damage to the blends.

Atomistic aspects of the temperature effect on fracture toughness of a silicon single crystal

The temperature effect on the fracture toughness of a Si single crystal was explored through molecular dynamics simulations over the temperature range of 1–1000 K. A sharp crack model with the (010)[001] (plane)[front] crystallographic system was considered, in which the interatomic force was characterized using the modified embedded atom method potential. The computational experiment of a mode-I fracture was carried out employing the displacement based on the mode-I near tip field, and the fracture toughness was evaluated using the critical stress intensity factor for the onset of crack growth. The results showed that the fracture toughness in the temperature range of 1–750 K slightly decreased with increasing temperature, where the effect of lattice trapping was reduced at the elevated temperature. However, when the temperature was higher than 800 K, the fracture toughness increased resulting from the nucleation of nanovoids in front of the crack tip. Detailed atomistic analysis showed that, in the small-scale yielding limit, the temperature effect on the hydrostatic component of the local crack tip field was important to crack-tip plasticity.

Polypropylene hybrid composites: Effect of reinforcement of sisal and carbon fibre on mechanical, thermal and morphological properties

Abstract Polypropylene (PP)/sisal fibre (SF)/carbon fibre (CF) hybrid composites were prepared by melt blending process at a variable weight percentage (wt%) of carbon: sisal fibre loading (20:10, 15:15, 10:20, and 5:25). MA-g-PP (MgP) as a compatibiliser was used to improve the dispersion of the fibres within the PP matrix. The composites were subjected to mechanical tests to optimize the fibre content of CF: SF. Incorporation of 20 wt% of CF and 10 wt% of SF with 5 wt% MgP resulted in higher mechanical performance of about 67.02 and 112% over that of PP/SF composite. Similarly, the impact strength was found to be optimum which enhanced to the tune of 39.62% as compared with PP/SF composites. Halpin Tsai model was used to compare the theoretical tensile modulus of PP/SF/MgP composites and PP/SF/CF/MgP hybrid composites with experimental evaluated values. Fracture toughness parameters such as K IC (critical stress intensity factor) and G IC (critical strain energy release rate) are determined for PP/SF/MgP composites and PP/SF/CF/MgP hybrid composites and compared by using single edge notch test. DSC study showed higher melting temperature (T m ) of PP/SF/CF/MgP composites as compared to PP revealing the enhancement in thermal stability. TGA/DTG study revealed the synergistic effect of the hybrid composite thus confirming the hybridisation effect of the system. DMA study showed that the hybridisation of CF and SF within the matrix polymer contributes to an increase in the storage modulus (Eʹ). Morphological observation by SEM confirmed that the carbon fibres and sisal fibres are well uniformly dispersed within the PP matrix, in the presence of MgP.

Notch effect on the linear elastic fracture mechanics values of a polysulfone thermoplastic polymer

Users of the most popular procedures for determining the linear elastic fracture mechanics parameters on polymers have noted that the repeatability and reproducibility of the results depend strongly on the quality of the notches generated. In an attempt to provide a better understanding, polysulfone specimens were pre-cracked using classical razor blade methods (tapping and sliding), and also by the femtosecond pulsed laser ablation technique. These specimens were analyzed, and the critical stress intensity factor was determined. The ablated specimens showed very good notch quality, the sharpest crack tip radii, displayed neither mechanical nor thermal damage in front of the crack tip, and were very consistent, providing both a lesser scatter and a statistically significant lower critical stress intensity factor than the razor blade pre-cracked specimens. Finally, some consideration and advice for suitable generation of notches are also given.

A new approach for measurement of the fracture toughness using the edge cracked semi-cylinder disk (ECSD) concrete specimens

In this paper, a new approach for measurement of the fracture toughness of concrete using the edge cracked semi-cylinder disk (ECSD) specimens has been rendered. The critical stress intensity factor (fracture toughness) of concretes was determined by using the edge cracked semi-cylinder disk (ECSCD) type specimens. The normalized Mode I stress intensity factor of concrete was measured and estimated through a new formula. The versatile finite element method (FEM) was used to derive this appropriate formula and the Mode I fracture toughness of the specimens determined with a reasonable accuracy. In the laboratory, the notched Brazilian disks (NBD) were tested to evaluate the accuracy of the ECSCD method. A discrete element analysis of the ECSCD tests was also carried out to numerically simulate these experiments and validate the accuracy of the fracture toughness values. Finally, very good agreements gained by comparing the crack extension patterns obtained from the experimental tests with the numerical simulations’ results. However, the toughness values obtained through ECSCD experiments were lower than those measured from the NBD tests. This is due to the smooth distribution of tensile stress around the notch in the ECSCD concrete specimens.

Quasi-static and dynamic fracture behavior of lead zirconate titanate: A study of poling and loading rate

In this study, coupon specimens of both poled and de-poled lead zirconate titanate (PZT) are examined under quasi-static and stress-wave loading conditions. Mode-I crack initiation and fracture behavior is examined using ultra high-speed imaging in conjunction with 2D digital image correlation on symmetrically impacted specimens. Measured displacement fields ahead of the dynamically loaded crack tip are used to extract the critical stress intensity factor (KICd) at initiation and are compared with quasi-static SENT fracture toughness tests. Results demonstrate that under static conditions, the difference between poled and de-poled specimens is not statistically significant, however under dynamic conditions, poled samples exhibited a 70% greater fracture toughness compared to the de-poled specimens. To verify the increase was not due to thermal degradation of material mechanical properties during the de-poling process, re-poled specimens were also prepared and examined under dynamic fracture loading conditions. In general, impulsively loaded samples exhibited greater fracture toughness compared to their quasi-statically loaded counterparts, regardless of the poling. Specifically, the critical stress intensity factor increased seven to tenfold compared to static fracture toughness values, with poled samples exhibiting the greatest toughness of all samples explored. In terms of rate, the increase in fracture toughness under dynamic conditions likely comes from microcracking and potentially phase transformations at the crack tip. In terms of poling, the increase in fracture toughness is likely due to a bulk manifestation of ferroelastic toughening, where dynamic domain reorientation provides crack tip shielding.

A convenient method for the strength evaluation of cracked functionally graded material plates under different loadings

As functionally graded material (FGM) plates are widely used in engineering and industrial fields, the fracture strength evaluation of the cracked FGM plate becomes increasingly important. However, due to the gradation of the mechanical properties of FGM, few analytical methods are simple and available. In this paper, a convenient strength evaluation method for the cracked FGM plates under different loadings is proposed in terms of the stress intensity factor (SIF) appearing at a crack tip. This method uses the stable relationship of singular stress fields between FGM and homogeneous material to greatly simplify the complex SIF calculation process of the cracked FGM plate. The results show that the SIFs of FGM plates under tension, bending, and three-point bending (experiment) can be obtained conveniently and accurately by using two simple formulas, and the trends of critical SIF can also be investigated directly even if the SIF solution of the homogeneous plate (reference problem) is unknown. Comparisons with the published theoretical and experimental results indicated that the present method is reliable, precise, and practical to determine SIF and perform strength prediction.

Increasing the crack resistance of high-strength self-compacting concrete

The object of research is high-strength self-compacting concrete, which does not require additional vibration during laying. One of the most problematic issues of high-strength self-compacting concretes is increased cracking, associated with large shrinkage deformations of such concretes and their fragile destruction.
 A decrease in shrinkage deformations of concrete was established when part of the cement was replaced to mineral additives. This effect is explained by a decrease of the cement content and, accordingly, a decrease of the chemical component of the autogenous shrinkage of concrete, and an increase of the adsorptive binding of capillary moisture by mineral additives, with reduces the physical drying shrinkage of concrete. In this case, the type and dispersion of the used mineral additive can affect to the shrinkage deformations of concrete. A significant decrease in shrinkage deformations when using metakaolin is explained by an increase the amount of ettringite as a result of the reaction of active metakaolin Al2O3 with two-water gypsum of cement. It was found that the replacement of cement to 10 % of mineral additives leads to a decrease in the value of the critical stress intensity factor (SIF), which is compensated by a decrease of the fragility of concrete fracture (an increase of the area of microplastic deformations). At the same time, the type of mineral additive used does not affect to the value of the critical stress intensity factor, but significantly affects to the fragility of fracture of concrete samples. The introduction of 10 % mineral additives (to replace cement) had a positive effect on the retention of flow of self-compacting concrete mixes; the best results according to this criterion were observed when using silica fume, fly ash and limestone. All mineral modifiers, except for silica fume, led to a decrease of the compressive strength of high-strength concretes on all terms of hardening. In the case of the tensile strength of concrete at bending and splitting, with the introduction of silica fume, metakaolin and fly ash, a positive effect was observed compared to the base composition without additives.
 Comprehensive accounting of the results obtained will allow a reasonable approach to the design of high-strength self-compacting concretes with increased crack resistance.

Comparison of anisotropic crack tip behavior in hcp titanium by two-dimensional and three-dimensional atomistic simulations

As three-dimensional (3D) atomistic simulations require much higher computational costs, two-dimensional (2D) atomistic simulations under plane strain condition are widely used to study dislocation emission from the crack tip. In order to study the difference of crack tip behavior in 2D and 3D simulations, both 2D and 3D atomistic simulations of the anisotropic crack tip response in hcp titanium were performed, as well as the comparison of simulation results with linear elastic fracture mechanics (LEFM) predictions. The comparing results find significant discrepancies of the near tip stress fields, incipient crack tip deformation and critical stress intensity factor in 2D and 3D simulations. In consistent with the theoretical predictions, crack tip plasticity is solely contributed by the inclined slip mode with a lower critical stress intensity factor than that for cleavage, otherwise an artificial cleavage behavior may be observed in 2D simulations. In contrast to this, the lower stress triaxiality near the free surface leads to an easier dislocation nucleation in free 3D simulations. Besides, the participation of the oblique slip mode improves crack tip plasticity and facilitates the activation of the inclined slip mode that cannot be activated in 2D simulations. In general, the incipient crack tip behavior observed in 3D simulations shows more consistency with experimental results.

Mechanical characterization of self-compacting steel fiber reinforced concrete using digital image correlation

This paper evaluates the mechanical properties, modulus of elasticity (E) and critical stress intensity factor (KIC), of self–compacting concrete with the addition of hook-ended steel fibers, implementing Digital Image Correlation (DIC) to obtain the horizontal and vertical displacement fields for beams under four-point bending test. Based on the vertical displacements and the crack mouth opening displacement, the values of E and KIC were obtained from an inverse analysis using Timoshenko beam and the fracture model proposed by Griffith-Irwin. The results obtained allowed to conclude that DIC is a valid and efficient alternative for the characterization of materials.

On notch fracture mechanics

Different stress distributions for an elastic behavior are presented as analytical expressions for an ideal crack, a sharp notch and a blunt notch. The elastic plastic distribution at a blunt notch tip is analyzed. The concept of the notch stress intensity factor is deduced from the definition of the effective stress and the effective distance. The impacts of the notch radius and constraint on the critical notch stress intensity factor are presented. The paper ends with the presentation of the crack driving forceJρfor a notch in the elastic case and the impact of the notch radius on the notch fracture toughnessJρ,c. The notch fracture toughnessJρ,cis a measure of the fracture resistance which increases linearly with the notch radius due to the plastic work in the notch plastic zone. If this notch plastic zone does not invade totally the ligament, the notch fracture toughnessJρ,cis constant. This occurs when the notch radius is less than a critical one and there is no need to use the cracked specimen to measure a lower bound of the fracture resistance.

Interrelation among Microstructure, Development of Voids and The Fracture Behavior of The Nickel-Iron Chromium Alloy.(Dept.M)

In order to understand the fracture behavior of the fractured tube of the ammonium pipeline in the fertilizer production system. it is necessary to take into considerauon the interrelation among nucrostructure, development of voids and the mechanical behavior of the material from which the tube is made. A study of the influence of microstructures parameters on fracture toughness of the tube material (Nickel-Iron Chromium alloy) has been made. Using the J integral concept. J-resistance curves have been obtained and the influence of strain hardening on fracture toughness has been evaluated. Hence, the tearing instability Concept was applied to investigate the fracture Process. The relationship between critical Stress intensity factor and the microstructural parameters has been taken into account Ductile fracture occuring by the formulation growth and coalescence of voids around the inclusions was described. In addition micro-fractographic culmination has been carried out to establish a possible corrclation between the mechanical properties and the micro mechanisms of fracture.

Epoxidized soybean oil modified using fatty acids as tougheners for thermosetting epoxy resins: Part 2—Effect of curing agent and epoxy molecular weight

AbstractA series of bio‐rubber (BR) tougheners for thermosetting epoxy resins was prepared by grafting renewable fatty acids with different chain lengths onto epoxidized soybean oil at varying molar ratios. BR‐toughened samples were prepared by blending BRs with diglycidyl ether of bisphenol A resins, Epon 828 and Epon 1001F, at different weight fractions and stoichiometrically cured using an amine curing agent, 4, 4′‐methylene biscyclohexanamine (PACM). Fracture toughness properties of the unmodified and BR toughened polymer samples—including critical strain energy release rate (GIc), and critical stress intensity factor (KIc)—were measured to investigate the toughening effect of prepared BRs. It was found that the degree of phase separation and toughening were more controllable relative to similar polymers cured using the aromatic curing agent Epikure W, and the use of higher molecular epoxy resins produces a synergistic effect increasing the toughness much more than similar polymers made with lower molecular weight epoxy resins. Average BR domain sizes ranging from 200 to 900 nm were observed, and formulations with GIc, values KIc as high as 1.0 kJ/m2 and 1.4 MPa m1/2 were attained respectively for epoxy systems with Tg greater than 130°C.

Epoxidized soybean oil modified using fatty acids as tougheners for thermosetting epoxy resins: Part 1

AbstractA series of bio‐rubber (BR) reactive tougheners for thermosetting epoxy resins was prepared by grafting renewable saturated fatty acids of different chain lengths (C6‐C14) onto epoxidized soybean oil (ESO) at varying molar ratios. The tunable nature of the BR systems derives from the architecture and functionality of naturally occurring molecules. Control of BR reactivity and molecular weight by varying the degree of grafting and the chain length of the fatty acid was demonstrated. The BR‐toughened samples were prepared by blending BRs with diglycidyl ether of bisphenol A (DGEBA), Epon 828, and stoichiometrically curing the mixture using an aromatic amine hardener, diethyl toluene diamine (Epikure W). Fracture surface morphology studies showed that tuning of phase separated particle sizes was possible depending on the BR type and weight fraction. The resulting toughening effect was evaluated by measuring the fracture toughness of control and toughened polymer samples. The use of BRs significantly improved the critical strain energy release rate and critical stress intensity factor values of thermosetting polymer samples without significantly reducing Tg and modulus. In addition to toughening and adding renewable content to petroleum‐based thermosetting epoxy systems these new tougheners have low viscosity compared to common alternatives and aid ease of processing.