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In this paper, we study linear complementary pairs (LCP) of codes over finite non-commutative local rings. We further provide a necessary and sufficient condition for a pair of codes (C, D) to be LCP of codes over finite non-commutative Frobenius rings. The minimum distances d(C) and d (D ⊥) are defined as the security parameter for an LCP of codes (C, D). It was recently demonstrated that if C and D are both 2-sided LCP of group codes over a finite commutative Frobenius rings, D ⊥ and C are permutation equivalent in Liu and Liu (Des Codes Cryptogr 91:695–708, 2023). As a result, the security parameter for a 2-sided group LCP (C, D) of codes is simply d(C). Towards this, we deliver an elementary proof of the fact that for a linear complementary pair of codes (C, D), where C and D are linear codes over finite non-commutative Frobenius rings, under certain conditions, the dual code D ⊥ is equivalent to C. [ABSTRACT FROM AUTHOR]

Matrix product (MP) codes over a finite field q , where q a prime power, were first introduced by Blackmore and Norton [MP codes over q , Appl. Algebra Engrg. Comm. Comput. 12 (2001) 477–500]. This paper investigates linear complementary dual (LCD) MP codes over finite commutative Frobenius rings. We derive a necessary and sufficient condition for an MP code to have an LCD. We provide some efficient constructions of LCD MP codes. Finally, we have shown an application on cryptography of LCD codes. [ABSTRACT FROM AUTHOR]

In this paper, we clarify some aspects of LCD codes in the literature. We first prove that non-free LCD codes do not exist over finite commutative Frobenius local rings. We then obtain a necessary and sufficient condition for the existence of LCD codes over a finite commutative Frobenius ring. We later show that a free constacyclic code over a finite chain ring is an LCD code if and only if it is reversible, and also provide a necessary and sufficient condition for a constacyclic code to be reversible. We illustrate the minimum Lee distance of LCD codes over some finite commutative chain rings with examples. We found some new optimal cyclic codes over Z 4 of different lengths which are LCD codes using computer algebra system MAGMA. [ABSTRACT FROM AUTHOR]

In this article, keeping the huge research prospective of the study in mind, we consider the non-commutative ring M 4 (F 2) , the set of all 4 × 4 matrices over the field F 2 and confirm that this ring is isomorphic with the ring F 16 + u F 16 + u 2 F 16 + u 3 F 16 , where u 4 = 0 . Besides, we develop the structure of cyclic codes and their generators over the ring. Also, making use of Gray map from M 4 (F 2) to F 16 4 , we infer that the image of a cyclic code is a linear code. Finally, our findings are authenticated by suitable non-trivial examples. [ABSTRACT FROM AUTHOR]

Here, the scalable synthesis of low-density 3D macroscopic structure of graphene oxide (GO) interconnected with polydimethylsiloxane (PDMS) is reported. A controlled amount of PDMS is infused into the freeze-dried foam to result into a very rigid structure with improved mechanical properties, such as tensile plasticity and toughness. The PDMS wets the graphene oxide sheets and acts like glue between the 2D sheets. Molecular dynamics simulations are used to further elucidate the mechanisms of the interactions of graphene oxide layers with PDMS. The ability of using the interconnecting graphene oxide foam as an effective oil-water separator and stable insulating behavior to elevated temperatures are further demonstrated. The structural rigidity of the sample is also tested using laser impact and compared with GO foam. [ABSTRACT FROM AUTHOR]

The liquid inside a solid material is one of the most common composite materials in nature. The interface between solid–liquid plays an important role in unique deformation. Here, model systems of two polymers (polydimethylsiloxane–polyvinylidenefluoride) are used to make sphere of solid with liquid inside it. [ABSTRACT FROM AUTHOR]

The mechanical behavior of nano-scale metallic glasses was investigated by in situ compression tests in a scanning electron microscope. Platinum-based metallic glass nano-pillars were fabricated by thermoplastic forming. The nano-pillars and corresponding bulk substrate were tested in compression over the range of room temperature to glass transition. Stress-strain curves of the nano-pillars were obtained along with in situ observation of their deformation behavior. The bulk substrate as well as nano-pillars showed an increase in elastic modulus with temperature which is explained by diffusive rearrangement of atomic-scale viscoelastic units. [ABSTRACT FROM AUTHOR]

The influence of Pt layer thickness on the fracture behavior of PtNiAl bond coats was studied in situ using clamped micro-beam bend tests inside a scanning electron microscope (SEM). Clamped beam bending is a fairly well established micro-scale fracture test geometry that has been previously used in determination of fracture toughness of Si and PtNiAl bond coats. The increasing amount of Pt in the bond coat matrix was accompanied by several other microstructural changes such as an increase in the volume fraction of α-Cr precipitate particles in the coating as well as a marginal decrease in the grain size of the matrix. In addition, Pt alters the defect chemistry of the B2-NiAl structure, directly affecting its elastic properties. A strong correlation was found between the fracture toughness and the initial Pt layer thickness associated with the bond coat. As the Pt layer thickness was increased from 0 to 5 µm, resulting in increasing Pt concentration from 0 to 14.2 at.% in the B2-NiAl matrix and changing α-Cr precipitate fraction, the initiation fracture toughness (KIC) was seen to rise from 6.4 to 8.5 MPa·m1/2. R-curve behavior was observed in these coatings, with KIC doubling for a crack propagation length of 2.5 µm. The reasons for the toughening are analyzed to be a combination of material's microstructure (crack kinking and bridging due to the precipitates) as well as size effects, as the crack approaches closer to the free surface in a micro-scale sample. [ABSTRACT FROM AUTHOR]

Fracture toughness measurements at the small scale have gained prominence over the years due to the continuing miniaturization of structural systems. Measurements carried out on bulk materials cannot be extrapolated to smaller length scales either due to the complexity of the microstructure or due to the size and geometric effect. Many new geometries have been proposed for fracture property measurements at small-length scales depending on the material behaviour and the type of device used in service.In situtesting provides the necessary environment to observe fracture at these length scales so as to determine the actual failure mechanism in these systems. In this paper, several improvements are incorporated to a previously proposed geometry of bending a doubly clamped beam for fracture toughness measurements. Both monotonic and cyclic loading conditions have been imposed on the beam to study R-curve and fatigue effects. In addition to the advantages thatin situSEM-based testing offers in such tests, FEM has been used as a simulation tool to replace cumbersome and expensive experiments to optimize the geometry. A description of all the improvements made to this specific geometry of clamped beam bending to make a variety of fracture property measurements is given in this paper. [ABSTRACT FROM PUBLISHER]

Barium cerate is a candidate material for use in solid-oxide fuel cells (SOFC) and other solid-state ionic devices, due to its high proton conductivity in reduced-temperature operating conditions. The present paper investigates the crystal structure, surface and grain morphologies, particle size and distribution, and microstructural defects of both as-synthesized and heat-treated nanoparticles of barium cerate. Crystalline barium cerate was successfully synthesized in nanoparticle form using a relatively low-temperature wet chemistry route using hexamethylenetetramine. X-ray diffraction was carried out to understand the formation of various phases at different stages of processing. The evolution of the morphology and both the size and the shape of nanoparticles, were studied by high-resolution transmission electron microscopy after different heat-treatment temperatures. Nanoparticles are found to exhibit a cubic morphology after synthesis at 80°C, and change to a mixed multi-faceted and equiaxed morphology as annealing temperature is increased to 800°C. Crystallographically oriented surface steps can be observed at the surrounding edges of nanoparticles. Microstructural features, including edge dislocation and low-angle grain boundaries, are observed in some nanoparticles. Possible mechanisms for nanoparticle formation and the effect of annealing temperature on morphological changes are discussed. [ABSTRACT FROM AUTHOR]

Monolithic (single layer) glass‐ceramic restorations often fail from chipping and fracture. Using blunt indentation of a model flat porcelain‐like brittle layer bonded onto a dentin‐like polymer support system, a variety of fatigue fracture modes has been identified and analyzed: outer cone, inner cone, and median cracks developing in the near‐contact region at the occlusal surface; radial cracks developing at the internal cementation surface along the loading axis. Our findings indicate that monolithic glass‐ceramic layers are vulnerable to both occlusal surface damage and cementation internal surface fracture. Clinical issues in the longevity of ceramic restorations are discussed in relation to biting force, physical properties of ceramic crowns and luting cement, and thicknesses of ceramic and cement layers. © 2008 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2009 [ABSTRACT FROM AUTHOR]

The roles of indenter material and size in the failure of brittle veneer layers in all‐ceramic crown‐like structures are studied. Glass veneer layers 1 mm thick bonded to alumina layers 0.5 mm thick on polycarbonate bases (representative of porcelain/ceramic‐core/dentin) are subject to cyclic contact loading with spherical indenters in water (representative of occlusal biting environment). Two indenter materials—glass and tungsten carbide—and three indenter radii—1.6, 5.0, and 12.5 mm—are investigated in the tests. A video camera is used to follow the near‐contact initiation and subsequent downward propagation of cone cracks through the veneer layer to the core interface, at which point the specimen is considered to have failed. Both indenter material and indenter radius have some effect on the critical loads to initiate cracks within the local Hertzian contact field, but the influence of modulus is weaker. The critical loads to take the veneer to failure are relatively insensitive to either of these indenter variables, since the bulk of the cone crack propagation takes place in the contact far field. Clinical implications of the results are considered, including the issue of single‐cycle overload versus low‐load cyclic fatigue and changes in fracture mode with loading conditions. © 2006 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater 2006. [ABSTRACT FROM AUTHOR]

A study is made of veneer failure by cracking in all‐ceramic crown‐like layer structures. Model trilayers consisting of a 1 mm thick external glass layer (veneer) joined to a 0.5 mm thick inner stiff and hard ceramic support layer (core) by epoxy bonding or by fusion are fabricated for testing. The resulting bilayers are then glued to a thick compliant polycarbonate slab to simulate a dentin base. The specimens are subjected to cyclic contact (occlusal) loading with spherical indenters in an aqueous environment. Video cameras are used to record the fracture evolution in the transparent glass layer in situ during testing. The dominant failure mode is cone cracking in the glass veneer by traditional outer (Hertzian) cone cracks at higher contact loads and by inner (hydraulically pumped) cone cracks at lower loads. Failure is deemed to occur when one of these cracks reaches the veneer/core interface. The advantages and disadvantages of the alumina and zirconia core materials are discussed in terms of mechanical properties—strength and toughness, as well as stiffness. Consideration is also given to the roles of interface strength and residual thermal expansion mismatch stresses in relation to the different joining methods. © 2006 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2006 [ABSTRACT FROM AUTHOR]

A research program on failure modes induced by spherical indenters in brittle layer structures bonded to polymeric substrates, in simulation of occlusal function in all-ceramic dental crowns, is surveyed. Tests are made on model flat and curved layers bonded onto a dentin-like polymer base, in bilayer (ceramic/polymer) and trilayer (ceramic/ceramic/polymer) configurations. All-transparent systems using glass as a porcelain-like outer or veneer layer and sapphire as a stiff and strong core support layer enable in situ observation of the entire evolution of fracture modes in the brittle layers, from initiation through to failure. With the fracture modes identified, tests are readily extended to systems with opaque polycrystalline dental core ceramics, notably alumina and zirconia. A variety of principal failure modes is identified: outer and inner cone cracks developing in the near-contact region at the top surface; radial cracks developing at the bottom surface along the loading axis; margin cracks from the edges of dome-like structures. All of these modes are exacerbated in cyclic loading by time-cumulative slow crack growth, but inner cones are subject to especially severe mechanical fatigue from hydraulic pumping of water into the crack fissures. Conditions under which each mode may be expected to dominate, particularly in relation to geometrical variables (layer thickness, contact radius) and relative material properties, are outlined. Clinical issues such as crown geometry, overload versus fatigue failure, role of residual stresses in fabrication, etc. are addressed. [ABSTRACT FROM AUTHOR]

The role of substrate modulus on critical loads to initiate and propagate radial cracks to failure in curved brittle glass shells on compliant polymeric substrates is investigated. Flat glass disks are used to drive the crack system. This configuration is representative of dental crown structures on dentin support in occlusal contact. Specimens are fabricated by truncating glass tubes and filling with epoxy‐based substrate materials, with or without alumina filler for modulus control. Moduli ranging from 3 to 15 GPa are produced in this way. Critical loads for both initiation and propagation to failure increase monotonically with substrate modulus, by a factor of two over the data range. Fracture mechanics relations provide a fit to the data, within the scatter bands. Finite element analysis is used to determine stress distributions pertinent to the observed fracture modes. It is suggested that stiffer substrate materials offer potential for improved crown lifetime in dental practice. © 2006 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 2006 [ABSTRACT FROM AUTHOR]

A study is made of top-surface cracks induced in brittle trilayers by cyclic indentation with a hard sphere in water. The trilayers consist of an external brittle layer (veneer) fused to an inner stiff and hard ceramic support layer (core), in turn adhesively bonded to a thick compliant base (substrate). These structures are meant to simulate essential aspects of dental crowns, but their applicability extends to a range of engineering coating systems. The study follows on from like studies of brittle monoliths and brittle-plate/soft-substrate bilayers. Competing fracture modes in the outer brittle layer remain the same as before: outer and inner cone cracks and radial cracks, all of which form in the near-contact zone and propagate downward toward the veneer/core interface. Inner cone cracks and radial cracks are especially dangerous because of their relatively steep descent through the outer layer as well as enhanced susceptibility to mechanical fatigue. Experiments are conducted on model glass/alumina/polycarbonate systems, using video cameras to record the fracture evolution in the transparent glass layer in situ during testing. Each fracture mode can lead to failure, depending on the maximum contact load and other variables (plate thickness, sphere radius). The potentially beneficial role of a stiff intervening core is discussed, along with potentially deleterious side effects of residual thermal-expansion-mismatch stresses. [ABSTRACT FROM AUTHOR]

A preceding study of the competition between fracture modes in monolithic brittle materials in cyclic loading with curved indenters in liquid environments is here extended to brittle layers on compliant substrates. The fracture modes include outer and inner cone cracks and radial cracks that initiate from the near-contact zone and penetrate downward. Outer cone cracks are driven by stresses from superposed Hertzian and plate flexure fields; inner cone cracks also grow within these fields but are augmented by mechanical driving forces from hydraulic pumping into the crack fissures. Radial cracks are augmented by mechanical driving forces from developing quasiplasticity zones beneath the indenter. Basically, the crack-growth rates are governed by a crack velocity relation. However, the hydraulic and quasiplastic mechanical forces can cumulate in intensity with each cycle, strongly enhancing fatigue. Plate flexure generates compressive stresses at the top surface of the brittle layer, somewhat inhibiting the initiation, and tensile stresses at the lower surface, strongly enhancing the far-field propagation. The tensile stresses promote instability in the crack propagation, resulting in through-thickness penetration (failure). Experiments on a model bilayer system consisting of glass plates bonded to thick polycarbonate bases are presented as an illustrative case study. In situ observations of the crack evolution from initial growth to failure reveal that each fracture mode can dominate under certain test conditions, depending on plate thickness, maximum load, and sphere radius. Implications concerning the failure of practical layer systems, notably dental crowns, are discussed. [ABSTRACT FROM AUTHOR]

The competition between fracture modes in monolithic brittle materials loaded in cyclic contact in aqueous environments with curved indenters is examined. Three main modes are identified: conventional outer cone cracks, which form outside the maximum contact; inner cone cracks, which form within the contact; and median–radial cracking, which form below the contact. Relations describing short-crack initiation and long-crack propagation stages as a function of number of cycles, based on slow crack growth within the Hertzian field, are presented. Superposed mechanical driving forces—hydraulic pumping in the case of inner cone cracks and quasiplasticity in the case of median–radials—are recognized as critically important modifying elements in the initial and intermediate crack growth. Ultimately, at large numbers of cycles, the cracks enter the far field and tend asymptotically to a simple, common relation for center-loaded pennylike configurations driven by slow crack growth. Crack growth data illustrating each mode are obtained for thick soda-lime glass plates indented with tungsten carbide spheres in cyclic loading in water, for a range of maximum contact loads and sphere radii. Generally in the glass, outer cone cracks form first but are subsequently outgrown in depth as cycling proceeds by inner cones and, especially, radial cracks. The latter two crack types are considered especially dangerous in biomechanical applications (dental crowns, hip replacements) where ceramic layers of finite thickness are used as load-bearing components. The roles of test variables (contact load, sphere radius) and material properties (hardness, modulus, toughness) in determining the relative importance of each fracture mode are discussed. [ABSTRACT FROM AUTHOR]

The competition between fracture modes in monolithic brittle materials loaded in cyclic contact in aqueous environments with curved indenters is examined. Three main modes are identified: conventional outer cone cracks, which form outside the maximum contact; inner cone cracks, which form within the contact; and median-radial cracking, which form below the contact. Relations describing short-crack initiation and long-crack propagation stages as a function of number of cycles, based on slow crack growth within the Hertzian field, are presented. Superposed mechanical driving forces--hydraulic pumping in the case of inner cone cracks and quasiplasticity in the case of median-radials--are recognized as critically important modifying elements in the initial and intermediate crack growth. Ultimately, at large numbers of cycles, the cracks enter the far field and tend asymptotically to a simple, common relation for center-loaded pennylike configurations driven by slow crack growth. Crack growth data illustrating each mode are obtained for thick soda-lime glass plates indented with tungsten carbide spheres in cyclic loading in water, for a range of maximum contact loads and sphere radii. Generally in the glass, outer cone cracks form first but are subsequently outgrown in depth as cycling proceeds by inner cones and, especially, radial cracks. The latter two crack types are considered especially dangerous in biomechanical applications (dental crowns, hip replacements) where ceramic layers of finite thickness are used as load-beating components. The roles of test variables (contact load, sphere radius) and material properties (hardness, modulus, toughness) in determining the relative importance of each fracture mode are discussed. [ABSTRACT FROM AUTHOR]

It has long been held that bulk silicon is immune from fatigue. We present contrary evidence demonstrating severe fatigue in macroscale cracks produced in cyclic loading of single-crystal silicon with a sphere indenter. The key ingredient is a component of shear stress acting on the cracks during contraction and expansion of the contact circle. This gives rise to frictional sliding at the crack walls, dislodging and ejecting slabs of material and debris onto the silicon surface. The damage expands with continued cycling, leading to progressive degradation of the surface. The results have implications concerning the function of silicon-based devices. [ABSTRACT FROM AUTHOR]

High entropy alloys (HEAs) have attracted widespread interest due to their unique properties at many different length-scales. Here, we report the fabrication of nanocrystalline (NC) Al0.1CoCrFeNi high entropy alloy and subsequent small-scale plastic deformation behavior via nano-pillar compression tests. Exceptional strength was realized for the NC HEA compared to pure Ni of similar grain sizes. Grain boundary mediated deformation mechanisms led to high strain rate sensitivity of flow stress in the nanocrystalline HEA. [ABSTRACT FROM AUTHOR]