Critical Stress Intensity Factor Research Articles

Effects of translaminar edge crack and fiber angle on fracture toughness and crack propagation behaviors of laminated carbon fiber composites

Abstract In this study, the translaminar fracture toughness of carbon fiber laminated composites with different layer sequences was investigated experimentally and numerically for different crack directions. In the numerical study, first of all, the critical stress intensity factor was determined by using the M-integral method. Three-dimensional model and M-integral analysis were achieved in the ANSYS finite element package program. The non-local stress fracture criterion was used to in order to find failure curves of the materials. Then, in order to find the crack propagation directions numerically, the solid model was transferred to the LS-DYNA program and progressive failure analysis was performed. Fracture toughness decreased by 9.92 % with the change of crack angle from 15° to 90°. As the fiber angle changed from 0° to 45°, it decreased by 9.17 %. The biggest error between the experimental and numerical study results was found at α = 45°, with a rate of 12.3 %.

Chitosan toughened epoxy resin by chemical cross-linking: Enabling excellent mechanical properties and corrosion resistance

There is a growing demand for the development of epoxy resin modified with biomaterials, aiming to achieve high toughness. Herein, chitosan crosslinked epoxy resin (CE) was synthesized by diisocyanate as a bridge. With 4,4′-diamino-diphenylmethane (DDM) as the curing agent, thanks to the unique cross-linking structure of the CE resin and the presence of carbamate groups, the cured CE/DDM exhibited superior properties compared to commercially available epoxy resin (E51). The tensile strength of the cured CE-3/DDM reached 90.17 MPa, the elongation at break was 11.2 %, and the critical stress intensity factor (KIC) measured 1.78 MPa m1/2. These values were 21.4 %, 151.6 %, and 81.6 % higher than those of the cured E51/DDM, respectively. It is worth noting that the addition of biomass material chitosan did not reduce the thermal stability of the resin. Additionally, the CE coatings on the metal substrate exhibited exceptional corrosion resistance, as evidenced by higher impedance values in electrochemical impedance spectroscopy (EIS) and polarization voltages in the Tafel curve compared to those of the E51 coating. This study opens up a novel approach to modifying epoxy resin with biomass materials with high toughness and corrosion resistance, without sacrificing other performance.

Nanocomposite fracture analysis: Aligned Fe3O4-GNP nanoplatelets’ effects on KIC, GIC, CTODc, and fracture mechanisms in epoxy matrices

Epoxy nanocomposites are crucial in aerospace, enhancing structural performance, reducing weight, and improving fuel efficiency across various applications. They ensure safety, reliability, and optimal performance in critical aerospace systems. Optimizing fracture properties like crack growth resistance (KIC), critical stress intensity factor (GIC), and critical crack tip opening displacement (CTODc), is vital for safety, durability, and innovation, especially in epoxy nanocomposites under extreme conditions. This study examines how random Graphene Nanoplatelets (GNP) and aligned Fe3O4-GNP nanoplatelets impact the fracture resistance of epoxy nanocomposites. It analyzes various fracture properties and crack propagation mechanisms following ASTM D5045-99 standards for CT specimen toughness tests using a COD gauge, focusing on nanoparticle alignment and wt% loading effects. Neat epoxy has a KIC of 0.94 MPa m1/2, increasing to 1.20 with 0.600 wt% GNP. Aligned Fe3O4-GNP peaks at 1.49. the baseline GIC starts at 209 J/m2 and rises to 301 J/m2 with 0.600 wt% GNP, and notably to 419J/m2 with aligned Fe3O4-GNP. Aligned Fe3O4-GNP significantly enhances fracture properties by modifying stress distribution at primary crack fronts through mechanisms such as deflection, branching, and twisting. These findings offer crucial insights for improving epoxy nanocomposites in aerospace, ensuring increased safety, reliability, and performance in critical components.

Research on Crack Propagation of Nitrate Ester Plasticized Polyether Propellant: Experiments and Simulation.

To understand the fracture properties of the nitrate ester plasticized polyether (NEPE) propellant, single-edge notched tension (SENT) tests were carried out at room temperature (20 °C) under different tensile rates (10-500 mm/min). The mechanical response, crack morphology, evolution path, and crack propagation velocity during the fracture process were studied using a combination of a drawing machine and a high-speed camera. The mode I critical stress intensity factor KIc was calculated to analyze the tensile fracture toughness of the NEPE propellant, and a criterion related to KIc was proposed as a means of determining whether the solid rocket motors can normally work. The experimental results demonstrated that the NEPE propellant exhibited blunting fracture phenomena during crack propagation, resulting in fluctuating crack propagation velocity. The fracture toughness of the NEPE propellant exhibited clear rate dependence. When the tensile rate increased from 10 mm/min to 500 mm/min, the magnitude of the critical stress intensity factor increased by 62.3%. Moreover, numerical studies based on bond-based peridynamic (BBPD) were performed by modeling the fracture process of the NEPE propellant, including the crack propagation speed and the load-displacement curve of the NEPE propellant. The simulation results were then compared with the experiments.

Experimental research on the fracture of Laminated bamboo lumber using compact tension specimens based on the net section method and digital image correlation technique

This investigation evaluates the significance of thickness (B) and initial crack length-to-width ratio (α) on the fracture toughness of Laminated bamboo lumber (LBL) compact tension (CT) specimens under mode Ⅰ fracture conditions. The digital image correlation (DIC) technique is employed to analyse the result, while the net section method is utilised to determine the critical strain energy release rate (GIc). The fracture mode observed in LBL is characterised as brittle fracture, and the critical stress intensity factor (KIc) of CT specimens achieved a maximum value of 25.58 MPa·mm1/2. The fracture energy, calculated by the net section method, was determined by analysing the crack extension length (ae) of the CT specimen obtained by the DIC technique. This study aims to establish the mathematical connection between GIc, ae, and critical load (PQ) in terms of the strain energy release rate context, which offers an innovative approach to analysing GIc data of CT specimens subjected to mode I fracture. The calculated value for GIc was determined to be 12.18 J/mm2.

Fracture of four semi-regular lattices regulated by T-stress in modified boundary layer models

The development of additive manufacturing technology has promoted the rise of various lattice metamaterials, and evaluating their fracture properties is critical for both application and safety. Here, by conducting finite element simulations on four types of elastic-brittle semi-regular lattices (kagome, snub-trihexagonal, elongated-triangular, and snub-square), we indicate that the fracture toughness of lattice metamaterials is not solely determined by the crack-tip singular term, i.e., the critical stress intensity factor, but is also influenced by the non-singular T-stress term. T-stress regulates fracture toughness by modulating geometrical distortions and force-carrying modes of lattice bars around the crack front. This regulation effect depends on the lattice topology and becomes weaker under mixed-mode loading. As the relative density of lattices decreases, T-stress can force elastic buckling of bars around the crack front, which may deteriorate the fracture toughness. Additionally, positive T-stress tends to promote the crack deflection and negative T-stress tends to inhibit. Our results offer new insights into the structure-property relationships in the presence of T-stress, which may contribute to design the geometry of micro/nano-lattice metamaterials.

Enhancement fracture behavior of sustainable cementitious composites using synergy between fly ash (FA) and nanosilica (NS) in the assessment based on digital image processing procedure

The present study has investigated the strength properties and fracture toughness of concrete composites reinforced 5 % nanosilica (NS) by adding different contents of fly ash (FA), i.e.: 0 %, 15 % and 25 %. The evaluated fracture toughness, under three-point flexural loads, were critical stress intensity factor (KIcS) and critical crack tip opening displacement (CTODc). Digital image processing procedure was used in this studies. It was stated that both the 5 % addition of NS and the total share of the nanomodifier with FA grains in the composition of the concrete mix significantly improve the strength properties of concretes, as well as their fracture toughness under first model of cracking in linear and non-linear terms. Moreover, it was observed that in concrete containing only NS the fracture process was clearly delayed and relatively short, whereas crack patterns in this composite were almost perfectly straight with significant crack width. On the other hand, in concretes icorporating NS + FA crack patterns were strongly curved (frequently with branching) with few microcracks in the vicinity of the main cracks. Concretes including FA and NS can be used in the execution of specific types of reinforced concrete structures subjected to fatigue or dynamic loads, e.g. bridge structures or industrial buildings.

Novel resveratrol-based hyperbranched epoxy resin suitable for comprehensive modification of epoxy resins

Hyperbranched epoxy resins are efficient modifiers for epoxy resins but still require simultaneous improvements in terms of thermomechanical/mechanical properties and thermal stability. Herein, a novel resveratrol-based hyperbranched polyether epoxy resin (HBPEER) was designed for all-purpose epoxy resin modification. To this end, hyperbranched polyether with terminal phenolic hydroxyl groups was first synthesized from commercially available 1,6-dibromohexane (A2-type monomer) and resveratrol (B'B2-type monomer). Surface modification with epichlorohydrin was afterward implemented to produce hyperbranched polyether with terminal epoxy groups (HBPEER). Next, various HBPEER-modified epoxy thermosets were prepared and characterized. The results suggested that compared to the neat diglycidyl ether of bisphenol A (DGEBA) thermoset, the 6 wt% HBPEER-modified epoxy thermoset showed an increase in impact strength, elongation at break, critical stress intensity factor (KIC), critical crack propagation energy release rate (GIC), flexural strength, tensile strength, storage modulus, glass transition temperature (Tg), and initial thermal decomposition temperature (Td5%) by 69.6 %, 87.0 %, 32.0 %, 68.2 %, 29.3 %, 37.0 %, 8.1 %, 3.5 %, and 1.6 % respectively. Moreover, the dielectric constant and loss of 6 wt% HBPEER-modified epoxy thermoset decreased by 16.2 % and 16.5 %, respectively. Such comprehensive performance modifications were caused by the combined effects of crosslink density improvement, efficient intramolecular cavity, rigid stilbene units, and flexible aliphatic backbone of HBPEER.

Comparative fracture properties of ambient-cured geopolymer concrete containing four different fibers in mono and hybrid combinations using digital image correlation

This paper presents an investigation on the effects of four different fibers (polypropylene (PP), polyvinyl alcohol (PVA), recycled polypropylene (RPP), and steel (S) fibers) on the fracture behaviour of ambient-cured fly ash geopolymer concrete (GPC). The four fibers were added into GPC by both mono at 1.0% volume and hybrid combinations with steel fiber at 0.5% of each other type of fiber. The full-field strain distribution and the crack mouth opening displacement (CMOD) were monitored by digital image correlation (DIC) technology. The results reveal that adding fibers was effective in enhancing the fracture performance and hindering the cracking behaviour of GPC. Furthermore, 1.0% volume steel fiber exhibited to be most advantageous in enhancing the flexural strength by 100%, flexural toughness by 4000%, fracture energy by 3897%, and critical stress intensity factor by 98.8%. GPC with 1.0% volume PP fiber exhibited a characteristic length of 7909 mm, improving the characteristic length of GPC by about 2925%. Additionally, the CMOD was found to have a strong linear relationship with deflection which is unaffected by other factors. The presence of fibers significantly enhanced the ultimate strain. The steel fibers exhibited better performance in hindering the crack propagation. The fracture process zone (FPZ) characteristics differed between specimens with non-metallic and steel fibers, with the latter exhibiting more tortuous shapes and multiple cracks. Notably, a hybridization of steel and non-metallic fibers proves better than mono non-metallic fibers in improving strength, toughness, and ductility. This research provides valuable insights for concrete design and the selection of appropriate fibers based on specific requirements.

Compatibilization of Polyamide 6/Cyclic Olefinic Copolymer Blends for the Development of Multifunctional Thermoplastic Composites with Self-Healing Capability.

This study investigated the self-healing properties of PA6/COC blends, in particular, the impact of three compatibilizers on the rheological, microstructural, and thermomechanical properties. Dynamic rheological analysis revealed that ethylene glycidyl methacrylate (E-GMA) played a crucial role in reducing interfacial tension and promoting PA6 chain entanglement with COC domains. Mechanical tests showed that poly(ethylene)-graft-maleic anhydride (PE-g-MAH) and polyolefin elastomer-graft-maleic anhydride (POE-g-MAH) compatibilizers enhanced elongation at break, while E-GMA had a milder effect. A thermal healing process at 140 °C for 1 h was carried out on specimens broken in fracture toughness tests, performed under quasi-static and impact conditions, and healing efficiency (HE) was evaluated as the ratio of critical stress intensity factors of healed and virgin samples. All the compatibilizers increased HE, especially E-GMA, achieving 28.5% and 68% in quasi-static and impact conditions, respectively. SEM images of specimens tested in quasi-static conditions showed that all the compatibilizers induced PA6 plasticization and crack corrugation, thus hindering COC flow in the crack zone. Conversely, under impact conditions, E-GMA led to the formation of brittle fractures with planar surfaces, promoting COC flow and thus higher HE values. This study demonstrated that compatibilizers, loading mode, and fracture surface morphologies strongly influenced self-healing performance.

Fatigue Crack Propagation of 51CrV4 Steels for Leaf Spring Suspensions of Railway Freight Wagons.

Leaf springs are critical components for the railway vehicle safety in which they are installed. Although these components are produced in high-strength alloyed steel and designed to operate under cyclic loading conditions in the high-cyclic fatigue region, their failure is still possible, which can lead to economic and human catastrophes. The aim of this document was to precisely characterise the mechanical crack growth behaviour of the chromium-vanadium alloyed steel representative of leaf springs under cyclic conditions, that is, the crack propagation in mode I. The common fatigue crack growth prediction models (Paris and Walker) considering the effect of stress ratio and parameters such as propagation threshold, critical stress intensity factor and crack closure ratio were also determined using statistical methods, which resulted in good approximations with respect to the experimental results. Lastly, the fracture surfaces under the different test conditions were analysed using SEM, with no significant differences to declare. As a result of this research work, it is expected that the developed properties and fatigue crack growth prediction models can assist design and maintenance engineers in understanding fatigue behaviour in the initiation and propagation phase of cracks in leaf springs for railway freight wagons.

Influence of solid solution treatment on fatigue crack propagation behavior in the thickness direction of 2519A aluminum alloy thick plates

2519A aluminum alloy thick plates have excellent applications in the military industry due to their superior ballistic resistance and fatigue properties. However, the delamination cracking along the thickness direction of this alloy hinders its further utilization. To address this issue and enhance the fatigue properties of this alloy, the effect of single-stage solid solution treatment (SST) and two-stage solid solution treatment (DST) on the fatigue crack propagation (FCP) behavior in the thickness direction of the alloy was investigated. Compared to the optimum SST, the volume fraction of the secondary phase of the alloy was reduced by 28.6% after DST. The precipitated phases were finer with more uniform distribution, and the volume fraction and number density of the precipitation increased by 47% and 30%, respectively. The DST resulted in a lower fatigue crack growth rate (FCGR) and an increase of 2.92% in the critical stress intensity factor value (ΔKcr). The crack propagation mode of the alloy after SST was inter/transgranular crack propagation, while it was transgranular after DST. The aspect ratio of grain and the number of secondary phases in the alloy decrease after DST. Meanwhile, the grain boundary (GB) precipitation phase spacing, the precipitation-free zone (PFZ) width, and the spacing between the secondary phases increase. These changes result in decreased crack sources in the alloy and reduced the bridging effect of secondary phases on fatigue cracks, thus improving the fatigue performance of the alloy.

Mechanics of crack initiation, propagation and crack grain boundary interaction in bicrystal silicon using near-tip localized stress calculation

Crack propagation and arrest are important phenomena in polycrystalline silicon. This phenomenon considerably affects the effectiveness of solar cells made up of polycrystalline silicon. To understand the crack propagation in polycrystalline silicon, it is essential to study the bicrystal first. Earlier, crack propagation has been studied in bicrystal materials primarily from the perspective of material behaviour. However, the mechanics part is largely missing. In the present work, crack propagation of bicrystal silicon during uniaxial tension has been studied at the atomistic scale. The silicon bicrystal was formed by joining two single crystals: crystal 1 and crystal 2 of different orientations. Various states like crack initiation, propagation, arrest, re-initiation and crack grain boundary (GB) interaction have been analysed using Stress Intensity Factor (SIF), calculated from the local crack tip virial stress field. Considering the effect of crack tip velocity, the dynamic SIFs at crack propagation state have been converted to the SIF of an equivalent static crack using the generalized expression for anisotropic material. It has been found that for the propagation state, crack propagation continues as long as the equivalent static SIF is greater than the critical SIF (CSIF). In crystal 1, crack propagation is along the low CSIF direction. Therefore, the crack did not change its path and propagated along a straight line. On the other hand, when the crack enters to crystal 2, it follows a zigzag path. Both of these observations have been justified in terms of near-tip calculated SIFs.

The effect of loading rate on mixed mode I/II fracture behavior of adhesively bonded joints: Experimental and numerical approach

In this study, the use of a modified Arcan fixture to investigate the fracture behavior of adhesively bonded Al/Al joints has been discussed under rate-dependent loading in various loading conditions (mode I, mode II, and mixed mode (I/II)). It was observed that the testing speed has a significant effect on the fracture properties of the joints, especially in pure mode, II. The results indicated that failure load was increased for all three loading modes and an increase was also observed for strain energy release rate at all loading conditions. The critical fracture loads obtained from the experimental tests were used to calculate the values of the critical stress intensity factors and strain energy release rates for loading modes I, II, and mixed mode I/II at different loading rates by using the finite element method. It was shown that the values of strain energy release rate for loading mode II were higher than mode I and mixed mode at all loading speeds. Finally, scanning electron microscope analyses (SEM) were used to investigate the effects of loading speed on the failure surfaces of the adhesive in microstructural scales and it was shown that at low loading rates, the number of crazes that cause failure in the adhesive layer increases.

Investigations on morphology, tribology, rheology, thermo-mechanical properties, and EMI shielding of WC/MWCNT nanohybrids in polypropylene

This study is focused to explore the synergism of dual nanofillers (tungsten carbide (WC) and multiwalled carbon nanotubes (MWCNTs)) in melt extruded PP composites. The synergy of fillers in PP enhanced the elastic modulus, tensile strength, and critical stress intensity factor by 141.8%, 35.4%, and 62.6%, respectively, at an optimum filler content of 1 wt% of WC and 2 wt% of MWCNTs. In the hybrid composites, activation energy to initiate thermal decomposition raised by 78% and wear resistance increased by 93%, and the hybrid composites exhibited enhanced reflectivity in the X band region, which contributed to high electromagnetic shielding effectiveness. The improvement in the properties makes the current hybrid composite system an ideal candidate in application sectors where high modulus, energy absorption, and thermal stability are required.

POSS/EHTPB synergistically toughened epoxy resin for cryogenic application

The high brittleness of epoxy resin at cryogenic temperature restricts their wide application in cryogenic engineering. In this study, polyhedral oligomeric silsesquioxane (POSS) with -Si-O-Si- molecular chains were synthesized, and the mechanical properties of diglycidyl ether of bisphenol A (E51 epoxy resin) were significantly enhanced at room temperature (RT) by incorporating a 4% POSS and curing agent 4,4′-diamino-diphenylmethane (DDM) as the E51/POSS/DDM resin system. Subsequently, by adding different contents of epoxidation hydroxyl-terminated polybutadiene (EHTPB) into the E51/POSS/DDM resin system, the EHTPB-E51/POSS/DDM resin system was prepared. The investigation into the impact of EHTPB content on the mechanical properties of EHTPB-E51/POSS/DDM resin system at room temperature (RT) revealed that EHTPB-E51/POSS/DDM resin system with 10% EHTPB exhibited the most favorable results. Specifically, the elongation at break, flexural strength, and critical stress intensity factor (KIC) were measured to be 6.82%, 143.75 MPa, and 1.83 MPa m1/2, respectively. These values demonstrated a notable improvement of 53.3%, 26.9%, and 86.7% compared to those for the E51/DDM resin system. Concurrently, at 77 K, the elongation at break and critical stress intensity factor (KIC) increased by 37.8% and 73.5%, respectively. The toughening mechanism of the prepared EHTPB-E51/POSS/DDM resin system was further explored through resin-curing cross-linking simulation networks and SEM images of the fracture surface of resin samples. The study of EHTPB and POSS synergistically toughened epoxy resin provided a new efficient method to prepare epoxy resins with high toughness at low temperatures.

Complexity of crack front geometry enhances toughness of brittle solids

Brittle solids typically fail by growth and propagation of a crack from a surface flaw. This process is modelled using linear elastic fracture mechanics, which parameterizes the toughness of a material by the critical stress intensity factor, or the prefactor of the singular stress field. This widely used theory applies for cracks that are planar, but cracks typically are not planar, and instead are geometrically complex, violating core tenets of linear elastic fracture mechanics. Here we characterize the crack tip kinematics of complex crack fronts in three dimensions using optical microscopy of several transparent, brittle materials, including hydrogels of four different chemistries and an elastomer. We find that the critical strain energy required to drive the crack is directly proportional to the geodesic length of the crack, which makes the sample effectively tougher. The connection between crack front geometry and toughness has repercussions for the theoretical modelling of three-dimensional cracks, from engineering testing of materials to ab-initio development of novel materials, and highlights an important gap in the current theory for three-dimensional cracks.

A general micromechanics-based model for precipitate strengthening and fracture toughness in polycrystal high entropy alloys

High-entropy alloys (HEAs) usually exhibit exceptional mechanical properties attributed to one of important core effects for serious lattice strain to impede dislocation motion compared to the traditional alloys. However, their roles on the quantitative measurement for precipitate strengthening and fracture toughness are lack using the existing physical model. Here, we propose a mechanistic modelling to study effect of heterogeneous strain caused by lattice distortion on the precipitate strengthening and fracture toughness in the HEAs, and then verify this role using atomic simulation. The results indicate that the lattice distortion and precipitate synergistically impede the grain boundary migration, increasing the strength. In the dilute alloy with a low lattice distortion, the grain boundary migration process is less sensitive to the precipitate size. The stress field generated by the lattice distortion relieves the stress concentration at the crack tip under external force. This in turn alleviates the accumulation of dislocations and reduces the probability of crack extension. Furthermore, the heterogeneous strain caused by lattice distortion counteracts some of the applied stress and raises the critical stress for crack extension, which enhances the plasticity and the critical stress intensity factor. The developed unified model would be applicable to high entropy ceramics in similar scenario.

Non-equilibrium nature of fracture determines the crack paths

Local kinetic processes during crack growth are non-equilibrium and discrete and thus cannot be resolved in the framework of continuum thermodynamics. Atomistic modeling using existing empirical or machine-learning force fields also fails to offer satisfactory solutions for the lack of sufficient accuracy in predicting the energetics of strong lattice distortion and edge cleavage during fracture. The problem is addressed here by using a high-fidelity neural network-based force field for fracture (NN-F3) that covers the space of strain states up to material failure and the non-equilibrium, intermediate states at the crack tip. Atomistic simulations using NN-F3 reveal spatial complexities from lattice-scale kinks to sample-scale crack patterns in 2D crystals such as graphene, which evolve along the process of crack growth. The non-uniform lattice distortion and undercoordination of cleaved edges at the crack front play critical roles in the fracture process. The fracture toughness by cleaving specific edges thus cannot be quantified by their energy densities with relaxed atomic-level structures, which, however, have been widely used in the literature. Instead, the fracture patterns, the critical stress intensity factors corresponding to the kinking events, and the energy densities of edges in the intermediate, unrelaxed states offer reasonable measures for the fracture resistance and its anisotropy, which can be determined from experimental or simulation data with the atomic-level resolution. The findings conform well with recent experimental observations.

Investigation of Multi-Factor Stress Corrosion Cracking Failure of Safe-End Feedwater Lines of Submarine Power System.

The corrosion process under the complex safe-end feedwater line conditions was investigated via experimental lab testing and numerical simulation. The corrosion of safe-end feedwater lines was controlled through the combination of galvanic corrosion, residual stress, and flow velocity. Firstly, galvanic corrosion occurred once the 20 steel was welded with 316L stainless steel. The pitting corrosion could be observed on the 20 steel side of the weld joint. Secondly, a vortex flow was detected around the welding bump and within the pits. The growth of the pits was accelerated in both the vertical and horizontal directions. Finally, under the residual stress condition, the stress intensity factor (K) at the bottom of the pits was easier to reach than the critical stress intensity factor (KISCC). Then, pitting was transformed into stress corrosion cracking which then propagated along the weld line. Therefore, the critical factor inducing the failure of safe-end feedwater lines was the combined action of galvanic corrosion, residual stress, and flow velocity.