A graph G is called a $(P_{\geq n},k)$ -factor-critical covered graph if for any $Q\subseteq V(G)$ with $|Q|=k$ and any $e\in E(G-Q)$ , $G-Q$ has a $P_{\geq n}$ -factor covering e. We demonstrate that (i) a $(k+1)$ -connected graph G with at least $k+3$ vertices is a $(P_{\geq 3},k)$ -factor-critical covered graph if its toughness $t(G)>{(2+k)}/{3}$ ; (ii) a $(k+2)$ -connected graph G is a $(P_{\geq 3},k)$ -factor-critical covered graph if its isolated toughness $I(G)>{(5+k)}/{3}$ . Furthermore, we show that the conditions on $t(G)$ and $I(G)$ are sharp.

The materials chosen to make thermal engines, spacecrafts, or human implants cannot fail in an unpredictable way to guarantee the users' well-being. These applications can benefit from the use of ceramics because of their temperature resistance, corrosion resistance, or hardness. Although parts based on ceramic matrix composites and zirconia are already in use, a more recent ceramic with a structure inspired from seashells provides an attractive combination of ease of processing, high strength, and high toughness. These nacre-like aluminas are made of aligned micron-sized monocrystalline platelets joined together by a mix of mineral secondary phase and nanoparticles. The review's first objective is to provide a picture of what these newly developed bioinspired ceramics are capable of within today's ceramic and nacre-inspired composites landscape. I will also extract from the results the links between process/microstructure/performance to better understand the potential of these materials in terms of toughness and strength increase. Finally, I will present the challenges that are ahead to eventually reproduce the exceptional fracture behavior observed in nacre.

Coarsening mechanism of precipitations was investigated in a weld metal of Alloy 617 during long-term aging at 750 °C, and its effect on impact toughness was clarified distinctly. The needle-like M6C phases at the grain boundary nucleated and coarsened at 2000 h and then presented a stable size with aging to 8000 h. Spherical γ′ phase grew rapidly with the rate of 0.0121 nm/h when aged at 1000 h; then, its ripening rate (RR) reduced to 0.0033 nm/h at 8000 h and stabilized around it. The coarsening of M6C and γ′ was, respectively, controlled by interface diffusion and volume diffusion with the coarsening rate constant of 7.865 × 10−20 m2/s and 1.519 × 10−27 m3/s. Interaction of M6C and γ′ could facilitate their coarsening and cause dramatic decrease in toughness at the early stage. At aging to 8000 h and more, the lower RR of needle-like M6C phases and γ′ phases helped to form stable toughness at a later stage.

Thermal cycling of planar solid oxide cell (SOC) stacks can lead to failure due to thermal stresses arising from differences in thermal expansion of the stack’s materials. The interfaces between the cell, interconnect, and sealing are particularly critical. Hence, understanding possible failure mechanisms at the interfaces and developing robust sealing concepts are important for stack reliability. In this work, the mechanical performance of interfaces in the sealing region of SOC stacks is studied. Joints comprising Crofer22APU (preoxidized or coated with MnCo2O4 or Al2O3) are sealed using V11 glass. The fracture energy of the joints is measured, and the fractured interfaces are analyzed using microscopy. The results show that choosing the right coating solution would increase the fracture energy of the sealing area by more than 70%. We demonstrate that the test methodology could also be used to test the adhesion of thin coatings on metallic substrates.

Natural structural materials (NSMs) such as nacre, teeth, bones and crustacean exoskeleton are usually made of weak biomaterials arranged in specific structural design imparting them remarkable mechanical characteristics. Such hierarchical structural layouts found in nature encourage designing of mechanically desirable synthetic structural materials (SSMs). Among variety of natural hierarchical layouts, this paper specifically focuses on helicoidal architectural design found in the tough dactyl club of mantis shrimp. We first decode the mechanics behind helicoidal microstructural design and document the development of impact resistant macroscale helicoidal architectured synthetic structural materials (HA-SSMs). Next, near-field electrospinning technique (NFES)- both melt (polycaprolactone) and solution (polyvinylidene fluoride) type has been discussed in detail, as a novel method for developing lab scale 3D biomimetic HA-SSMs in micro-nanoscale. Further, the effect of the helical arrangement, size of substructures and surface treatment on strength and toughness of NFES fabricated HA-SSMs samples is analysed.

Biological materials such as bone, teeth, and nacre boast remarkable structures and toughening mechanisms, many of them unmatched by engineering materials. In these materials, fracture toughness is key to fulfill critical structural functions and achieve high strength, reliability, robustness, damage tolerance, and notch performance. In this article, we review and discuss some of the main toughening strategies found in hard biological materials. In particular, we underline a “universal” strategy where well-defined microarchitectures, stiff building blocks, and weak interfaces operate in synergy to resist crack propagation. These natural materials have been inspiring the development of a myriad of synthetic materials that duplicate some of these features at the nanoscale and at larger scales. While recent materials show impressive properties, duplication of the architectures and mechanisms seen in natural materials still presents formidable challenges.

The present work has been carried out in order to investigate the sliding wear performance of a Ni-Cr based alloy, containing boron, carbon, silicon and iron, deposited onto a SAE 1045 steel substrate. The coatings were thermally sprayed by means of a High Velocity Oxy-Fuel system and post heat-treated for one hour at 760°C in an argon atmosphere. The relative sliding performance was evaluated under unlubricated dry conditions at different applied normal loads and sliding velocities, in order to analyze the influence of these parameters on the wear response. Test results are discussed and interpreted on the basis of both microstructural evaluations and mechanical properties measurements. The surface morphology and topography of the wear scars have been studied through of a Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Spectroscopy (EDS) techniques. The results have shown an improved wear resistance of the coated steel samples as compared to the uncoated ones.

In this study, varying contents of ultrafine bamboo-char (UFBC) were introduced into PLA/bamboo particle (BP) biocomposites as new reinforcements to improve the mechanical, thermal, and morphological properties of the biocomposites. The new strategy was aiming to realize the synergistic effects of reinforcement and toughening of poly(lactic acid) (PLA) composites through a simple method without surface modification and other additives. The maximum tensile strength, modulus, and elongation at break of 45.20 MPa, 540.50 MPa, and 7.53% were reached at 5.0 wt% UFBC content, which were slightly lower than those of pure PLA. The maximum modulus of elasticity of the ternary biocomposites was 5316.1 MPa at 5.0 wt% UFBC content, which was approximately 2 times higher than the pure PLA. Impact strength reached a maximum value of 38.56 J/m when the UFBC content was 5 wt%, and improved by 376% compared with pure PLA of 7.88 J/m. Meanwhile, compared with the PLA/BP binary composite of 20.50 J/m, it improved 88%. A concrete-like microstructure system was achieved (i.e., cement, sand, and rebar corresponding to PLA, UFBC, and BP, respectively).

The basic principle of high-entropy alloys (HEAs) is that high mixing entropies of solid-solution phases enhance the phase stability, which renders us a new strategy on alloy design. The current research of HEAs mostly emphasizes mechanical behavior at room and higher temperatures. Relatively fewer papers are focused on low-temperature behaviors, below room temperature. However, based on the published papers, we can find that the low-temperature properties of HEAs are generally excellent. The great potential for cryogenic applications could be expected on HEAs. In this article, we summarized and discussed the mechanical behaviors and deformation mechanisms, as well as stacking-fault energies, of HEAs at low temperatures. The comparison of low-temperature properties of HEAs and conventional alloys will be provided. Future research directions will be suggested at the end.

Melt blending using a twin-screw extruder was used to prepare composites of polypropylene (PP)/organic rectorite (PR). The organic rectorite (OREC) was modified with dodecyl benzyl dimethyl ammonium bromide (1227). Wide-angle X-ray diffraction (WAXD) and transmission electron microscopy were used to investigate the dispersion of OREC in the composites. The d spacings of OREC in PR composites was greater than in OREC itself. The dispersion of OREC particles in the PP polymer matrix was fine and uniform when the clay content was small (2 wt.%). The rheology was characterized using a capillary rheometer. The processing behaviour of the PR system improved as the amount of OREC added increased. Non-isothermal crystallization kinetics were analysed using differential scanning calorimetry. It was shown that the addition of OREC had a heterogeneous nucleation effect on PP, and can accelerate the crystallization. However, only when fine dispersion was achieved, and at lower rates of temperature decrease, was the crystallinity greater. Wide-angle X-ray diffraction and polarized light microscopy were used to observe the crystalline form and crystallite size. The PP in the PR composites exhibited an a-monoclinic crystal form, as in pure PP, and in both cases a spherulite structure was observed. However, the smaller spherulite size in the PR systems indicated that addition of OREC can reduce the crystal size significantly, which might improve the ‘toughness’ of the PP. The mechanical properties (tensile and impact strength) improved when the amount of OREC added was appropriate. Dynamic mechanical analysis showed that the storage modulus (E′) and loss modulus (E″) of the nanocomposites were somewhat greater than those of pure PP when an appropriate amount of OREC was added. Finally, thermogravimetric analysis showed that the PR systems exhibited a greater thermal stability than was seen with pure PP.

Welding was successfully used in the fabrication of low pressure steam turbine rotors for nuclear power plants. In this paper, the local brittle zone of the welded joint in NiCrMoV steel with heavy section was investigated by cross-zone fracture toughness test and the effect of martensite–austenite constituent in the simulated reheated zone of welds with different second peak temperature on toughness was analyzed. The results showed that the crack propagated in unstable manner in the reheated zone of welds where the martensite–austenite constituent promoted the initiation and propagation of the crack. The fine structure of martensite–austenite constituent contained retained austenite, martensite, and martensite–austenite mixture microstructure. The impact toughness deteriorated drastically in the incomplete phase transition zone for the simulated reheated zone of welds related to the formation of mixture microstructure in which large blocky martensite–austenite constituent at prior austenite grain boundaries and inside the grains were distributed in the shape of network.

Ceramic fiber–matrix composites (CFMCs) are exciting materials for engineering applications in extreme environments. By integrating ceramic fibers within a ceramic matrix, CFMCs allow an intrinsically brittle material to exhibit sufficient structural toughness for use in gas turbines and nuclear reactors. Chemical stability under high temperature and irradiation coupled with high specific strength make these materials unique and increasingly popular in extreme settings. This paper first offers a review of the importance and growing body of research on fiber–matrix interfaces as they relate to composite toughening mechanisms. Second, micropillar compression is explored experimentally as a high-fidelity method for extracting interface properties compared with traditional fiber push-out testing. Three significant interface properties that govern composite toughening were extracted. For a 50-nm-pyrolytic carbon interface, the following were observed: a fracture energy release rate of ∼2.5 J/m2, an internal friction coefficient of 0.25 ± 0.04, and a debond shear strength of 266 ± 24 MPa. This research supports micromechanical evaluations as a unique bridge between theoretical physics models for microcrack propagation and empirically driven finite element models for bulk CFMCs.

The purpose of this work is to study the effect of SiO2- and Al2O3-NPs on the microstructure and mechanical properties of the weld bead (WB) created by a process of Submerged Arc Welding (SAW) between two AISI 1025 steel plates. Also it was necessary consider the chemical compositions of slags and burned fluxes, in order to determine the elements that are deposited and contribute in the final microstructure of WB. The welding materials to form each WB were a M12K electrode, a commercial fused flux (CFF) and AISI 1025 steel plates bevelled at 45°. In addition SiO2- or Al2O3-NPs an ethylic alcohol mixture were applied directly to the beveled surfaces, just before the SAW process, which was carried out according to the AWS A5.17 norm. Microstructural and phase changes at the Heat Affected Zone (HAZ) and Welding Zone (WZ) were analysed by metallographic Optical and Scanning Electron Microscopies. The mechanical properties of the WBs were determined through Tensile, Charpy impact and Vickers Hardness tests. By means of metallography of WBs, it was determined that the length of the AF needles increases in 113 and 183 % when adding SiO2- or Al2O3-NPs, respectively. Related to the mechanical properties of the WB, the tensile and yield strength decreases with both additions, SiO2- or Al2O3-NPs. The microhardness at WZ was found to decrease by adding such oxide-NPs. Moreover, the impact energy absorbed by the WBs increases approximately by 83 or 57% due to SiO2- or Al2O3-NPs addition, respectively.

The effect of specimen thickness on fracture toughness and fracture mechanism was investigated in bulk columnar-grained Cu with preferentially oriented nanoscale growth twins. Below a critical specimen thickness of ∼1.0 mm, plane stress state prevailed ahead of the crack tip and the fracture initiation toughness J C decreased with decreasing thickness. Above the critical thickness, J C decreased with increasing thickness until approaching an intrinsic thickness-independent value when the crack front was mainly under plane strain condition. Under plane strain condition, threading dislocations were majorly activated to glide along the nanotwin channels and to produce severe stress concentrations when they piled-up against grain boundaries (GBs). As a result, intergranular cracking mediated the failure of the nanotwinned Cu. On the contrary, under plane stress condition, dislocations slipping-transfer across twin boundaries (TBs) or partial dislocations gliding at TBs were activated to accommodate the plastic deformation. Consequently, stress intensification at GBs was plastically relaxed through enhanced detwinning and shear banding, which suppressed the intergranular fracture and promoted transgranular shear fracture.

Room-temperature fracture along the (111) plane of silicon is probed at the micron-scale using chevron notched cantilever beams that enable stable crack growth before unstable fracture in successful tests. The main experimental observation is that a growing crack can extend and arrest at different stress intensity factor values within the same specimen. The present data thus provide evidence of variations in the effective Si fracture toughness along the path of a growing crack. This effect could be explained by variations in the extent of limited cracktip plasticity along the crack path. The present work also shows that the microscopic chevron notch test is, from an experimental point of view, an inconvenient method to probe the fracture toughness of silicon because it is difficult with silicon to nucleate a crack at the chevron tip at loads low enough to allow for subsequent stable crack growth.

In the present study, the effect of heat treatment on microstructure and mechanical properties of gas tungsten arc (GTA) welded 15CDV6 high strength low alloy steel is discussed. Experiments were carried out based on Taguchi L9 orthogonal array to weld 15CDV6 plate of thickness 3.7 mm. The input parameters considered in this work were current, voltage, and welding speed. Tensile strength, microhardness, and impact strength were measured as performance characteristics. Post weld heat treatment was carried out on the weldments to study its effect on the properties of weldments and microstructures were characterized using optical microscope and the X-ray diffraction analysis revealed the presence of MO2C and VC precipitates in the weld. Post weld heat treatment of the GTA welded samples and base metal successfully produced properties required for aerospace applications.

Since the discovery of glass-ceramics by Stookey in the 1950s, there has been increasing demand for glass-ceramics with high strength and toughness for medical, structural, and consumer electronics markets. This article reviews recent developments in composition, microstructure, and mechanical properties of glass-ceramics, with an emphasis on their mechanical performance. It reveals that glass-ceramics with strength and toughness comparable to structural ceramics, such as Al2O3, have been successfully developed. Meanwhile, efforts are being devoted to creating glass-ceramics with further improved damage resistance. With inspiration from natural materials such as jade, baddeleyite, bone, and nacre, glass-ceramics with unique microstructures and properties have been obtained. Further progress is needed in the design of novel compositions, microstructures, and phase assemblages to activate multiple toughening mechanisms in glass-ceramics for significant improvements in strength and toughness.