Narrow Results

For a set ${𝒟}$ of connected graphs, a spanning subgraph $F$ of a graph $G$ is called an ${𝒟}$-factor if each component of $F$ is isomorphic to a member of ${𝒟}$. In this paper, we obtain a sufficient condition with regard to tight toughness, isolated toughness and binding number bounds to guarantee the existence of a $\{K_{1,1},K_{1,2},C_n|n\ge 3\}$-factor, two sufficient conditions to guarantee the existence of a $P_{\ge 3}$-factor in a bipartite graph and some sufficient conditions for $\{K_{1,j}|1\le j\le k\}$-factor deleted graph and a $P_{\ge 2}$-factor deleted graph.

A new category of hard nanocomposite coatings with adjustable improved hardness or enhanced toughness consisting of nanocrystalline (nc-) titanium nitride grains embedded in an amorphous (a-) metallic intergranular nickel phase i.e. nc-TiN/a-Ni type has been produced and investigated. Coatings were deposited at 573K on different substrates using a reactive dual ion beam sputtering (RDIBS) technique. A composite Ti-Ni target was sputtered with 1.2 keV Ar⁺ ions and the growing films were bombarded with a mixture of 50 eV Ar⁺+N²⁺+N⁺ ions. XRD, nanoindentation, high load indentation and pin-on-disk tests were used to characterize structural and mechanical properties. By adjusting Ni content enhanced hardness or toughness is obtained with an important improvement in wear resistance corresponding to the coatings exhibiting the highest toughness than highest hardness.

During the mid 1990s earthquakes in Northridge, California, and Kobe, Japan, illustrated a lack of understanding of the behaviour of structural steels exposed to seismic loads. Under this type of load regime, structural steel members are subjected to fully plastic load cycles and unexpectedly brittle failures may result.

A method for determining the accumulation of damage through cyclic pre-straining is proposed. Toughness, as defined by the area under the true stress strain curve, is used as an indicator of the level of damage that the steel has suffered and from this some idea of its remaining capacity to further deform can be determined.

Observations during the testing of these samples have indicated that there is a transition in the failure mode from a fatigue type failure, with a progressively growing crack, to an overload failure, in which the steel fails due to a lack of ability to further deform. Similar transitions have been noted by other researchers in the field. Analysis of the test results seems to show differences in the damage accumulation behaviour that may be used to identify when this transition in failure modes may occur.

The $S$ phase (Al₂CuMg) is an important strengthening phase for the Al–Zn–Cu–Mg alloys, which are widely used in the aerospace and transportation industries. First-principles calculations based on the density functional theory were used to investigate the effects of doping V, Nb, Cd, Ag, Ge and Sb elements on the $S$ phase. The results demonstrate that Ag atom can spontaneously dope into the $S$ phase. Ge and Sb doping can improve the toughness and plasticity of the $S$ phase. And doping Ge, V or Nb can reduce the anisotropy of the Al₂CuMg phase. The hardness of the Nb, V, Cd and Ag doped structures become larger than that of the pristine structure. The results of orbital hybridization in the partial density of states (PDOS) and the distribution in electron density difference (EDD) confirmed that the effect of doping elements and Al atoms has the greatest impact on the performance of the system, and the strength of the covalent bond of the system affects the main aspects of brittleness. This study provides a better theoretical understanding of the doped $S$ phase, providing guidance for improved composition design and performance optimization of Al–Zn–Cu–Mg alloys.

We present an algorithm for testing the inscribability of a trivalent polyhedron or, equivalently, testing the circumscribability of a simplicial polyhedron. Our algorithm, which runs in linear time and uses only low-precision integer arithmetic, is based on a purely combinatorial characterization of inscribable trivalent polyhedra.

We review experiments concerning the quantitative morphology of the fracture surfaces of various materials, at different length scales, using different techniques. These experiments could separate "universal" morphological parameters from material-dependent ones. We show how these results have been at the basis of theoretical developments on crack propagation and damage in heterogeneous materials.

RF magnetron-sputtered CrCuN coatings with ultra-low Cu content (0.53–2.1 at.%) were deposited using Cr${}_{97}$Cu₃ target (at.%) by changing the substrate negative bias from 0V to $-$200V. The CrNiN coatings with different nickel contents (0, 2.92 and 8.79 at.%) were sputtered by different-component Cr–Ni alloy targets (Cr, Cr${}_{95}$Ni₅ and Cr${}_{80}$Ni${}_{20}$, in at.%). The effect of bias and alloying element content on coating toughness was investigated by nanoindentation. The results show that all the coatings have unsatisfied toughness because of $H$/$E^{*}<0.1$. With increasing bias, the toughness of CrN and CrCuN coatings improves basically due to grain refinement caused by high bias effect. Under the same bias, although CrCuN coatings have finer grains, their toughness is still lower than that of CrN coatings because of inadequate copper coverage degree as a result of ultra-low copper content. On the contrary, once there is an appropriate alloying element content of 2.92 at.% Ni, the toughness of CrNiN coatings increases with the nickel content due to relatively higher Ni coverage degree.

This work focused on the mechanical and corrosion behaviors of electroplated nickel on heat-treated low carbon steel serving as an alternative to austenitic stainless steel for the yam beater in a yam pounding machine. Four standard samples were prepared for electrodeposition from the steel samples by heating to a temperature of 920°C with a 60-min holding time. One of the samples was air-cooled while the remaining three were quenched in H₂O and later tempered at 450°C, 550°C and 650°C for 60min. After the heat treatment process, the ultimate tensile strength, toughness, and microhardness of the samples were obtained. Nickel electrodeposition was later carried out on the heat-treated mild steel using Watt standard bath concentration. Optical Microscopy (OM) and Scanning Electron Microscope equipped with energy dispersion spectroscopy (SEM/EDS) were used for the characterization of the heat-treated and nickel-electrodeposited samples. More so, the electrochemical behavior of the nickel-plated samples was studied in a yam fluid environment using the potentiodynamic polarization technique. X-ray fluorescence (XRF) was used to analyze the chemical and oxide composition of the samples. The results showed that among all the heat treatment operations, the sample heat-treated at 920°C and tempered at the highest tempering temperature of 650°C gave the highest toughness value (102MJ/m³) when compared with stainless steel at 124MJ/m³. The sample heat-treated at 920°C and tempered at 550°C displayed a corrosion rate of 0.022182mm/yr as against the stainless steel sample with a value of 0.0031864mm/yr. From the analysis, the nickel deposited on the heat-treated samples enhanced corrosion resistance in the yam fluid. XRF analysis of the yam before pounding, after processing with nickel electroplated, and stainless beaters shows the content of nickel as 0.0941%, 0.109%, and 0.1113%, respectively. It was concluded that the materials for the yam pounding beater, therefore, perform better if they were both heat-treated and nickel-plated. Invariably, stainless steel could be successfully replaced with heat-treated and nickel-plated mild steel for use as a yam pounding beater.

Purpose: The aim of this study is to investigate deterioration in mechanical integrity of the collagen network of bovine bone formed by non-enzymatic glycation (NEG), a process that mimics aging by microindentation technique. Methods: Young and old bovine cortical bone specimens were rested in solutions for four weeks for the process of NEG and were grouped as ribosylated and non-ribosylated. A series of indentations were made on bone specimens weekly for each of 3-masses of 50 g, 100 g and 200 g for 10 s to detect the effect of indentation load and for each of five durations of 5 s, 10 s, 20 s, 30 s for 100 g to study the effect of indentation duration. The applied load was increased to 300 g, 500 g, 1000 g and 2000 g for 10 s to be able to make microcracks. Specimens were tested in the wet and dry state to study the effects of hydration on microhardness measurement. Results: Loads of 50 g, 100 g and 200 g for 10 s were able to differ ribosylated bone from non-ribosylated bone for the young and old bovine bones. Microhardness values increased with increasing incubation period. Microhardness of dry specimens were found to be statistically higher than that of wet specimens. Presence of extrinsic toughening mechanisms including crack bridging due to uncracked ligaments and collagen fibers were directly observed by scanning electron microscope (SEM). Ribosylated bone was found to have lower number of collagen bridging compared to non-ribosylated bovine bone. Conclusion: Microhardness test by these are able to discriminate non-modified collagen structure from modified collagen. On the other hand, it is found that microindentation was not able to discriminate the degree of NEG.

Let $n\ge 2$ be an integer. The $[1,n]$-factor of a graph $G$ is a spanning subgraph $F$ if $1\le {deg}_F(x)\le n$ for all $x\in V(G)$, and the $\{K_2,C_i\}$-factor is a subgraph whose each component is either $K_2$ or $C_i$. In this paper, we give the lower bounds with regard to tight toughness, isolated toughness and binding number to guarantee the existence of the $[1,n]$-factors and $\{K_2,C_i|i\ge 4\}$-factors for a graph.

For a family of connected graphs ${ℱ}$, a spanning subgraph $L$ of $G$ is called an ${ℱ}$-factor if each component of $L$ is isomorphic to a member of ${ℱ}$. In this paper, sufficient conditions with regard to tight toughness, isolated toughness and binding number bounds to guarantee the existence of the $\{P_2,C_3,P_5,{𝒯}(3)\}$-factor, $P_{\ge 2}$-factor or $\{P_2,C_{2i+1}|i\ge k\}$-factor for $k\ge 3$ are obtained.

The $\{K_{1,1},K_{1,2},\dots ,K_{1,k},{𝒯}(2k+1)\}$-factor and $\{K_{1,2},K_{1,3},K_5\}$-factor of a graph are a spanning subgraph whose each component is an element of $\{K_{1,1},K_{1,2},\dots ,K_{1,k},{𝒯}(2k+1)\}$ and $\{K_{1,2},K_{1,3},K_5\}$, respectively, where ${𝒯}(2k+1)$ is a special family of trees. In this paper, we obtain a sufficient condition in terms of tight toughness, isolated toughness and binding number bounds to guarantee the existence of a $\{K_{1,1},K_{1,2},\dots ,K_{1,k},{𝒯}(2k+1)\}$-factor and $\{K_{1,2},K_{1,3},K_5\}$-factor for any graph.

For a set ${\mathscr{H}}$ of connected graphs, a spanning subgraph $H$ of a graph $G$ is an ${\mathscr{H}}$-factor if every component of $H$ is isomorphic to some member of ${\mathscr{H}}$. In this paper, we give a criterion for the existence of tight toughness, isolated toughness and binding number bounds in a graph of a strong ${𝒮}$-star factor, $\{1,3,\dots ,2n-1\}$-factor and $f$-star factor. Moreover, we show that the bounds of the sufficient conditions are sharp.

Biocomposites such as bone exhibit synergistic superior mechanical properties compared to its constituents, protein (collagen) and mineral (hydroxyapatite). The importance of properties of constituents at the submicron scale with regard to the toughness and strength of bone is investigated employing a discrete lattice model. The results show that matrix failure as opposed to platelet breakage provides better toughness to the bone. There is a fairly sudden increase in the toughness of bone when the strength of mineral platelet to that of protein crosses a particular critical value. These could provide clues to the preparation of ultra-tough artificial composites and the treatment of diseases related to fragility of bone.

Metallic Al was doped into amorphous carbon (a-C) to form a matrix of a-C(Al) of very low residual stress and high toughness at the expense of some hardness. Nanocrystallites of TiC (nc-TiC) of a few nanometers in size were embedded in this matrix to bring back the hardness. The nanocomposite coating of nc-TiC/a-C(Al) was deposited via co-sputtering of graphite, Ti, and Al targets. Although the nanocomposite coating exhibited a moderately high hardness (about 20 GPa), it possessed extremely high toughness (about 55% of plasticity during indentation deformation) and low residual stress (less than 0.4 GPa), smooth (R_a=5.5 nm), and hydrophobic surface (contact angle with water reaches 100°).

The main subject of this work is about the effect of T-ZnOw on the toughness and stiffness of polystyrene (PS). In order to avoid the rupture of T-ZnOw during the melt processing, T-ZnOw/PS composites were obtained via the combination of solution blending and injection moulding methods. Although the tensile strength of the composites decreases slightly, the impact strength and tensile modulus increase with the increase of the T-ZnOw content in the matrix. The stiffness and toughness of the composites are enhanced simultaneously. SEM results of the impact-fractured surface show more polymer avulsions, ridges and micro-cracks formed in the T-ZnOw/PS composites, companied with pullout of T-ZnOw from PS matrix and local yielding of PS matrix around T-ZnOw during the impact processing. The possible reasons for the toughness increment of T-ZnOw/PS composites are attributed to the interfacial debonding, pullout of T-ZnOw from PS matrix, anchoring effect of T-ZnOw's special three dimensional structure, local yielding of PS matrix and the formation and propagation of micro-cracks.

Living tissues work with fantastic functions in soft and wet gel-like state. Thus, hydrogels have attracted much attention as excellent soft and wet materials, suitable for making artificial organs for medical treatments.However, conventional hydrogels are mechanically too weak for practical uses. We have created double network (DN) hydrogels with extremely high mechanical strength in order to overcome this problem. DN gels are interpenetrating network (IPN) hydrogels consisting of rigid polyelectrolyte and soft neutral polymer. Their excellent mechanical properties cannot be explained by the standard fracture theories. In this paper, we discuss about the toughening mechanism of DN gels in accordance with their characteristic behavior, such as large hysteresis and necking phenomenon. We also describe the results on tissue engineering application of DN gels.

A coarse-grained molecular dynamics (MD) simulation approach based on a widely used fuse model is developed to study the mechanical behaviors of hierarchical brick and mortar bio-composites made from hard minerals and soft polymers. Massively parallel MD simulations are performed to investigate the toughness enhancement and the effect of stochastic variations in brick strength in representative bio-composites. Our simulations indicate that the hierarchical structure of bio-composites not only plays a key role in toughness optimization, but also reduces the sensitivity of the structure to biomineral imperfections. This work demonstrates a simple and efficient simulation platform for designing novel biomimetic materials.

Interfacial behavior in the microstructure and the plastic deformation in the protein matrix influence the overall mechanical properties of biological hard tissues. A cohesive finite element model has been developed to investigate the inelastic mechanical properties of bone-like biocomposites consisting of hard mineral crystals embedded in soft biopolymer matrix. In this study, the complex interaction between plastic dissipation in the matrix and bonding properties of the interface between minerals and matrix is revealed, and the effect of such interaction on the toughening of bone-like biocomposites is identified. For the case of strong and intermediate interfaces, the toughness of biocomposites is controlled by the post yield behavior of biopolymer; the matrix with low strain hardening can undergo significant plastic deformation, thereby promoting enhanced fracture toughness of biocomposites. For the case of weak interfaces, the toughness of biocomposites is governed by the bonding property of the interface, and the post-yield behavior of biopolymer shows negligible effect on the toughness. The findings of this study help to direct the path for designing bioinspired materials with superior mechanical properties.

Covalent adaptable network (CAN) in thermoset epoxy shows good recyclability due to its bond exchange reactions (BERs), which result in low mechanical strength and toughness. Many experimental studies on using the semi-crystalline structures and ions with the CAN have shown to improve the mechanical strength and toughness of these thermoset epoxies. However, their toughening mechanisms and coupling effects have not been well understood. Herein, we propose an extended Maxwell model to explore toughening mechanisms and coupling effects of the semi-crystallization process and formation of ion phases on CANs, which enables the thermoset epoxy with hybrid chemomechanical yielding. A constitutive stress–strain relationship is formulated to characterize the mechanical toughening and hybrid chemomechanical yielding behavior, where the first stage of yielding is originated from the effect of ions on amorphous phases, and the second stage of yielding is due to the coupling effect of semi-crystallization and formation of ions. The proposed models have been verified using the experimental results, and provide a fundamental approach to understanding the toughening mechanisms and coupling effects of semi-crystallization and ions in thermoset epoxy.