Let t be a positive real number. A graph is called t-tough if the removal of any vertex set S that disconnects the graph leaves at most |S|/t components. The toughness of a graph is the largest t for ...which the graph is t-tough. A graph is minimally t-tough if the toughness of the graph is t and the deletion of any edge from the graph decreases the toughness. A graph is chordal if it does not contain an induced cycle of length at least 4. We characterize the minimally t-tough chordal graphs for all t≤1/2. As a corollary, a characterization of minimally t-tough interval graphs is obtained for t≤1/2.
•Compressive properties with inclusion of crumb rubber aggregate into plain and steel fibre concrete were studied.•Compression toughness improved by addition of crumb rubber to plain and steel fibre ...concrete.•ACI equation could be used directly to obtain modulus of elasticity for rubberized steel fibre concrete.•Crumb rubber could be satisfactorily utilized with steel fibre into concrete under compression loading.
In this study, the compression toughness of steel fibre concrete (SFC) with the inclusion of crumb rubber by partial replacement of fine aggregate was investigated. Crumb rubber was incorporated at different percentages of 5%, 10%, and 15% by volume. The compression properties (compression strength, modulus of elasticity and stress–strain diagrams) showed a possible interaction between steel fibre and crumb rubber to enhance such properties of concrete.
Results obtained showed improvement in the compression toughness by increase of crumb rubber content up to 15% and change into the behaviour of normal concrete to ductile instead of brittle. The toughness index and the specific compression toughness of concrete specimens indicated crumb rubber could be satisfactorily utilized with steel fibre to present a good performance under compressive loading and to keep the environment clean and healthy by recycling of waste tire.
An electronic (e‐) skin is expected to experience significant wear and tear over time. Therefore, self‐healing stretchable materials that are simultaneously soft and with high fracture energy, that ...is high tolerance of damage or small cracks without propagating, are essential requirements for the realization of robust e‐skin. However, previously reported elastomers and especially self‐healing polymers are mostly viscoelastic and lack high mechanical toughness. Here, a new class of polymeric material crosslinked through rationally designed multistrength hydrogen bonding interactions is reported. The resultant supramolecular network in polymer film realizes exceptional mechanical properties such as notch‐insensitive high stretchability (1200%), high toughness of 12 000 J m−2, and autonomous self‐healing even in artificial sweat. The tough self‐healing materials enable the wafer‐scale fabrication of robust and stretchable self‐healing e‐skin devices, which will provide new directions for future soft robotics and skin prosthetics.
An extremely tough and water‐insensitive self‐healing elastomer crosslinked through multistrength hydrogen bonding interactions is described. The resultant crosslinking network in polymer film realizes exceptional mechanical properties such as notch‐insensitive high stretchability (1200%), a high toughness of 12 000 J m−2, and autonomous self‐healing even in artificial sweat. The tough self‐healing materials enable the wafer‐scale fabrication of robust and stretchable self‐healing e‐skin devices.
Beside their high mechanical strength, duplex stainless steels are a suitable choice in highly corrosive environments. These types of steels are used in steel bridges more and more frequently exposed ...to low temperatures and fatigue loads. However, for low temperature applications, it must be guaranteed that brittle fracture is avoided since duplex stainless steel shows a toughness-temperature relationship similar to that of carbon steel. For this reason, in the frame of the German national FOSTA research project “P 1390”, comprehensive investigations have been started into the material selection of duplex stainless steel to avoid brittle fracture considering the fracture mechanic based background of EN 1993-1-10. For this purpose, Charpy-V impact tests and fracture toughness tests have been systematically carried out for various duplex stainless steels in order to create the basis for the development of toughness requirements for new duplex classes. The validity of the already existing Master Curve concept and the applicability of the transition temperature correlation for duplex stainless steels based on experimental fracture toughness and Charpy-V impact tests have been investigated. The aim of this contribution is to present first results of these investigations.
•A comprehensive investigation has been started and first results are presented based on Charpy-V impact and fracture toughness tests.•The highest nickel content in 1.4462 resulted in the lowest transition temperature followed by lean duplex 1.4662 and 1.4162.•The 3 °C temperature shift per percent of cold deformation in transition curve according to EN 1993-1-10 appears suitable for tested duplex steels.•Lower fracture toughness values are achieved for the specimens fabricated from thicker plates for both duplex 1.4462 and lean duplex 1.4162.•The results confirm that the transition temperature correlation in accordance with EN 1993-1-10 is valid for the studied duplex stainless steels.•The Master Curve approach presented in ASTM E1921 which was developed for carbon steel material is also valid for the tested duplex stainless steels.
•Investigating the effect of the number of wetting- drying cycles on the fracture toughness of sandstone in natural environment.•Investigating the effect of the number of wetting- drying cycles on ...the fracture toughness of sandstone in acidic environment.•Presenting the relationship between the fracture toughness and the effective porosity for sandstone in natural environment.•Presenting the relationship between the fracture toughness and the effective porosity for sandstone in acidic environment.
Factors such as rainfall and its diffusion into the ground and the subsequent drying cause alternating water–stone interactions leading to loosening of stones in long periods and catastrophic events such as landslides. Accordingly, the effect of these factors on the mode I and mode II fracture toughness of sandstone was investigated. Experiments were conducted on centrally cracked Brazilian disc (CCBD) specimens (chevron notch). The specimens were tested after 0, 1, 4, 8, 16 and 20 wetting–drying cycles (in the neutral (pH = 7) and acidic (pH = 3) environments). In addition to the effect of wetting–drying cycles in the natural environment (pH = 7), the effects of salt weathering and chemical weathering (caused by acidic environment) on the fracture toughness were also investigated. The acidic solution consisted of water, hydrochloric acid and sodium sulfate. The mode I and mode II fracture toughness of the sandstone decreased in both natural and acidic environments with increasing the number of wetting–drying cycles. The sandstone was also evaluated in terms of effective porosity and mineralogy to compare the natural and acidic environments. The results showed the insignificant impact of the acidic environment on the sandstone specimen. The effective porosity of the sandstone specimens also increased with increasing the number of cycles.
Steels manufactured via Laser powder bed fusion (LPBF) usually exhibit a good synergy of strength and ductility due to their ultrafine microstructure. Yet, their toughness, in particular cryogenic ...toughness is intrinsically inferior as the formation of micro-voids and oxide inclusions can hardly be fully prevented during LPBF. In this study, a toughening strategy based on chemically heterogenous metastable austenite was proposed to improve the impact toughness of LPBF manufactured high strength steels. As demonstrated in a maraging stainless steel, cryogenic (-196 °C) impact toughness can be enhanced by three times without a sacrifice of strength via tailoring chemically heterogenous austenite in the strong martensitic matrix. Both experiments and molecular dynamic simulations demonstrate that upon impact deformation chemically heterogenous austenite could transform into martensite in a stepwise manner, which could not only absorb massive energy via deformation induced martensite transformation but also make a contribution to local stress mitigation, crack passivation and deflection. The chemically heterogenous austenite strategy has the potential to be utilized for improving the toughness of other high-strength steels.
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•The results of fracture toughness KIIc of fly ash concrete were validated through DIC method.•There is a correlation between KIIc parameter obtained by using two measuring ...devices.•Fracture processes based on the images of major strain and displacement X were analyzed.•An original solution for measuring the actual length of a crack propagating in the material were presented.•A new sophisticated crack tip tracking (CTT) method was introduced.
This article focuses on the analysis of fracture processes in fly ash (FA) concrete considering the second model of cracking. The basic parameter of fracture mechanics in concrete elements according to Mode II fracture, i.e. KIIc, was determined. Two measuring devices were used in the studies. One of them was the Digital Image Correlation (DIC), which is now a popular and extensively used metrology technique. During the experiments, an attempt was made to validate the results of fracture toughness obtained in strength press tests. The main goal of the studies was to confirm the convergence and determine the discrepancy ranges, between the KIIc results obtained on the MTS 810 press and using the DIC technique. During the investigations a new concept was proposed in the analysis of concrete fracture processes under Mode II using the DIC method, i.e. evaluation the fracture toughness of the composite by the direct testing of the material with an initial defect – in the crack propagation area (Fig. 7b). In addition, it was attempted to determine the usefulness of the DIC system for the analysis of initial cracks development in concrete elements subjected to shear. For this purpose, basing on the images of major strains and displacements in the X direction, an in-depth assessment of the initial cracks growth was made. The article also presents an original, sophisticated solution for measuring the actual length of a propagating crack in the material with the use of the crack tip tracking (CTT) method. Principal strains ε11 were used to visualise the cracks, while their length was determined as the sum of the relative crack increments (generated at successive stages of the loading of the specimen) measured on the XY plane (rel XY).
The production of continuous carbon fibre composites using a fused deposition modelling (FDM) method has addressed the problem of low mechanical performance of raw- or short-fibre reinforced polymer ...parts fabricated by the same process, due to the excellent specific strength and stiffness of continuous fibres. However, one key issue of 3D printed polymers or fibre-reinforced polymers is the formation of microscopic voids between individual filaments and within the filaments during the FDM process. This study aims to quantify the adverse effects of voids on 3D printed continuous fibre-reinforced polymer composites. Optical microscopy and micro-CT are used to quantify the void content in continuous CF/PA6 composites fabricated on a 3D printing platform. As a benchmark, 3D printed CF/PA6 composites with the same printing configurations were further processed by compression moulding (CM) with thickness controlled to achieve the minimum void content. Apart from tensile and three-point bending tests in the longitudinal and transverse directions, the study also evaluated the Mode I interlaminar fracture toughness of CF/PA6 composites. By revealing the substantial adverse effects of the microscopic voids in 3D printed composites, this study articulates the critical importance of developing in-process techniques during 3D printing to decrease the void content within the continuous fibre reinforced composites, for the sake of expanding practical applications of 3D printed continuous fibre composites.
•Scaling effect on mode I notch fracture toughness of graphite specimens is studied.•Original fracture tests are performed on notched SCB specimens at different scales.•PS criterion with two various ...FPZ lengths is employed to estimate the test results.•Notch fracture toughness increases significantly by increasing the specimen scale.•PS criterion with both FPZ lengths can estimate the test results well.
In this paper, the mode I notch fracture toughness of graphite specimens weakened by notches of different shapes is investigated experimentally and theoretically. For this purpose, first, by conducting experiments, the apparent fracture toughness values of cracked semi-circular bending (SCB) graphite specimens with four various radii are determined. Next, numerous fracture experiments are performed on the notched SCB graphite specimens in four various scales. Then, the critical radius of the fracture process zone (FPZ) for the notched graphite specimens is obtained using two various equations already proposed in literature for cracked bodies. A well-known stress-based failure model, namely the point stress (PS) criterion, is employed for estimating the notch fracture toughness values of the specimens tested at different scales, taking advantages of two different critical distance formulas. The results show that the fracture toughness values of various notches obtained from PS criterion are in good agreement with the experimental results. Also, found in this research that the notch fracture toughness is considerably dependent on the nominal dimension (radius) of the specimen, such that, as the specimen radius increases, the mode I notch fracture toughness increases. Furthermore, it is revealed that for the present specimens tested, both the critical distance formulas provide almost identical predictions, suggesting that each of them can be arbitrarily selected for prediction.
Carboxyl terminated butadiene acrylonitrile (CTBN) was added to epoxy resins to improve the fracture toughness, and then two different lateral dimensions of graphene nanoplatelets (GnPs), nominally ...<1μm (GnP-C750) and 5μm (GnP-5) in diameter, were individually incorporated into the CTBN/epoxy to fabricate multi-phase composites. The study showed that GnP-5 is more favorable for enhancing the properties of CTBN/epoxy. GnPs/CTBN/epoxy ternary composites with significant toughness and thermal conductivity enhancements combined with comparable stiffness to that of the neat resin were successfully achieved by incorporating 3wt.% GnP-5 into 10wt.% CTBN modified epoxy resins. According to the SEM investigations, GnP-5 debonding from the matrix is suppressed due to the presence of CTBN. Nevertheless, apart from rubber cavitation and matrix shear banding, additional active toughening mechanisms induced by GnP-5, such as crack deflection, layer breakage and separation/delamination of GnP-5 layers contributed to the enhanced fracture toughness of the hybrid composites.
