Two B.sub.2CO phases (oP8' with sp.sup.2-sp.sup.3 hybridization coexist and mP16 with unitary sp.sup.3 hybridization) were predicted via structure searching and stability analysis. The study of ...formation enthalpy reveals that high pressure (HP) technology performed maybe an important method for synthesis. oP8' and mP16 both have large mechanical modulus and they are typical materials with high hardness. Pressure has a positive correlation with its mechanical modulus. The simulated tensile stress-strain relationship reveals that the maximum stress that oP8' can bear is 64.7 GPa in the direction 100, and the maximum tensile is 0.24. Among all isoelectronic with diamond (IED) B-C-O phases, oP8' has the smallest gap and mP16 has the widest gap. With pressure increasing, for B.sub.2CO phases with high symmetry and composed of sp.sup.3 hybridization, their band gaps all increases monotonically; for B.sub.2CO phases composed by sp.sup.3-sp.sup.2 hybridization coexist or with low symmetry like mP16, their band gaps increased first and then decreased.
Most Tensor Problems Are NP-Hard HILLAR, Christopher J; LIM, Lek-Heng
Journal of the ACM,
11/2013, Volume:
60, Issue:
6
Journal Article
Peer reviewed
Open access
We prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list includes: determining the feasibility of a system of bilinear ...equations, deciding whether a 3-tensor possesses a given eigenvalue, singular value, or spectral norm; approximating an eigenvalue, eigenvector, singular vector, or the spectral norm; and determining the rank or best rank-1 approximation of a 3-tensor. Furthermore, we show that restricting these problems to symmetric tensors does not alleviate their NP-hardness. We also explain how deciding nonnegative definiteness of a symmetric 4-tensor is NP-hard and how computing the combinatorial hyperdeterminant is NP-, #P-, and VNP-hard.
A eutectic alloy in the LaB.sub.6-VB.sub.2 system was obtained by the cold crucible method. The ratio of components in the initial powder mixture was 40:60 mol%. Two-phase eutectic regions in the ...structure of the alloy are observed and are an LaB.sub.6 matrix filled with cylindrical VB.sub.2 fibers up to 2 mum in diameter or extended VB.sub.2 crystals with a complex cross-section and an equivalent diameter of up to 10 - 15 mum. The Vickers hardness and the fracture toughness were determined. The relationships between these characteristics and the load on the indenter, the direction of load application, and the type of eutectic structure were established. The maximum value of crack resistance (8.6 MPa·m.sup.1/2) and high hardness (20.0 GPa) were recorded for an alloy with a rod eutectic structure when a 2-N indenter load was applied parallel to the crystallographic c axis of VB.sub.2. The greatest hardening effect at loads of both 2 N and 30 N, expressed in a combination of high hardness (20.5 GPa at 2 N and 20.0 GPa at 30 N) and crack resistance (6.5 MPa·m.sup.1/2 at 2 N and 4.9 MPa·m.sup.1/2 at 30 N), was demonstrated by an alloy with a coarse conglomerate eutectic structure.
Oxide-dispersion- and hard-particle-strengthened (ODS) laser-cladded single-layer multi-tracks with a Ni-based alloy composition with 20 wt.% μm-WC particles and 1.2 wt.% nano-Ysub.2Osub.3 addition ...were produced on ultra-high-strength steel in this study. The investigation of the composite coating designed in this study focused on the reciprocating friction and wear workpiece surface under heavy load conditions. The coating specimens were divided into four groups: (i) Ni-based alloy, nano-Ysub.2Osub.3, and 2 μm-WC (2 μm WC-Y/Ni); (ii) Ni-based alloy with added 2 μm-WC (2 μmWC/Ni); (iii) Ni-based alloy with added 80 μm-WC (80 μmWC/Ni); and (iv) base metal ultra-high-strength alloy steel 30CrMnSiNi2A. Four conclusions were reached: (1) Nano-Ysub.2Osub.3 could effectively inhibit the dissolution of 2 μm-WC. (2) It can be seen from the semi-space dimensionless simulation results that the von Mises stress distribution of the metal laser composite coating prepared with a 2 μm-WC particle additive was very uniform and it had better resistance to normal impact and tangential loads than the laser coating prepared with the 80 μm-WC particle additive. (3) The inherent WC initial crack and dense stress concentration in the 80 μm-WC laser coating could easily cause dislocations to accumulate, as shown both quantitatively and qualitatively, resulting in the formation of micro-crack nucleation. After the end of the running-in phase, the COF of the 2 μm-WC-Ysub.2Osub.3/Ni component samples stabilized at the minimum of the COF of the four samples. The numerical order of the four COF curves was stable from small to large as follows: 2 μm-WC-Ysub.2Osub.3/Ni, 2 μm-WC/Ni, 80 μm-WC/Ni, and 30CrMnSiNi2A. (4) The frictional volume loss rate of 2 μm-WC-Ysub.2Osub.3/Ni was 1.3, which was significantly lower than the corresponding values of the other three components: 2.4, 3.5, and 13.
In order to comprehensively understand the degradation of cementitious materials when subjected to the coupled action of calcium leaching and freezing/thawing, changes of the pore structure and the ...Vickers hardness of cement paste are investigated. In this study, the coupled action are designed as Case I (first leaching then freezing/thawing) and Case II (first freezing/thawing then leaching). The effects of Case I on the mechanical degradation are greater than Case II. This is further clarified by changes of the pore structure. For freezing/thawing, the level of deterioration qualified by hardness decrease is sensitive to the proportion of big pores (i.e., >100 nm). For calcium leaching, it is determined by the amount of CH and C-S-H. In addition, the hardness-porosity relationship is discussed. A quantitative prediction model from theoretical deviations considering influences of pore size is established.
Laser polishing, capable of polishing selective nonplanar areas, is exploited to improve the surface roughness of additive manufactured metal components. It offers a highly repeatable, higher speed ...polishing process as well as low labor costs compared with traditional mechanical abrasive polishing. In spite of the fact that many studies can be found on laser polishing processes, few have reported that focus on metal components, manufactured additively by selective laser melting (SLM) technology, with geometrically different complex surfaces. This paper presents a novel method to reduce the surface roughness of Cobalt Chromium (CoCr) components with complex surface geometry by using a layered polishing method which can constantly adjust the defocusing distance of the laser along with the surface shape of the components. The optimized laser polishing parameters used were firstly obtained from the test results on planar surfaces of CoCr alloy samples and samples with complex surface geometry were then polished based on the laser parameters. Characterizations for the laser polished samples were conducted using optical profiling and scanning electron microscopy, showing that the surface roughness was reduced significantly in comparison with the as-received samples. A reduction of up to 93% in surface roughness was achieved. The mechanical hardness was also characterized by testing for Vickers hardness, which indicated the surface hardness of the laser polished samples was enhanced by 8%. Moreover, a simple and effective model was developed to illustrate the method of laser polishing on the complex surface geometry of additive manufactured CoCr alloy components. The analytical model is helpful in understanding and evaluating the underlying mechanisms of laser polishing.
The meltdown test is an efficient tool widely and commonly used to characterize structural changes in frozen desserts resulting from different ingredients and processing conditions. The meltdown is ...commonly determined by a gravimetric test, and it is used to obtain the onset (Mon), rate (Mrate), and maximum (MMax) meltdown. However, these parameters are calculated ambiguously due to the inconsistency in the methodology. This work aims at modeling the meltdown curves (weight vs time) of different commercial samples (36 commercial samples). Samples of commercial frozen desserts (40–60 g) was placed on a 304 stainless wire cloth (1.50 mm opening size and 52% open area) suspended about 15 cm above of an analytical balance, and the dripped portion of the melted ice cream was continuously recorded throughout the duration of the test. The meltdown test was conducted at room temperature. Each meltdown test generated more between 3000 to 4000 data points and was modeled using 4 equations: The logistic model, the Gompertz model, the Richard model, and the Hill model. All the meltdown curves were sigmoidal in shape, regardless of the type of frozen dessert. The experimental meltdown curves were adequately represented by the Logistic model, judging by several criteria (R2 = 0.999, adjusted RAdj2 = 0.999, Akaike probability = 6582, and F-value = 1.88 × 106). Thus, the Logistic model was shown to be an effective tool for predicting the meltdown curves of frozen desserts, and it can be used to define unambiguously the onset, rate, and maximum meltdown. Moreover, a dimensionless response (meltdown behavior, MBe) that combines Mon, Mrate, and MMax was developed and used for mapping the meltdown of different commercial frozen desserts.
In this paper, mechanical properties of RB-SiC ceramics, such as hardness, elastic modulus and fracture toughness, are characterized through indentation technique using a Vickers indenter at elevated ...temperatures ranging from room temperature to1200 °C realized by laser heating. The indentation size effect, load-displacement curves and relationship between crack length and applied load are studied in order to determine hardness, elastic modulus and fracture toughness accurately. The results show that the Meyer’s index and Vickers hardness decrease with the increase temperature. It indicates that the permanent plastic deformation of RB-SiC ceramics is mainly responsible for the indentation size effect and the reduction of hardness at elevated temperature. Both material softening and plastic deformation will contribute to the indentation creep at elevated temperature as shown in the load-displacement curves. The elastic modulus decreases with the increase of temperature due to increase of contact depth as a result of less elastic recovery. In the indentation test for calculating fracture toughness, only radial-median cracks are identified by the relationship between crack length and applied load at all temperatures, although the fracture mode observed at the indent corner changes from transgranular at room temperature to intergranular at elevated temperature. As more energy is consumed by intergranular facture and cracking-healing takes place due to oxidation, only short crack length appears in the indentation test which implies an increase of fracture toughness with the increase of temperature. However, this tendency has an exception at the highest temperature of 1200 °C. This is because the free Si softening in RB-SiC specimen fails to resist crack propagation at extremely high temperature. Consequently, the crack length increases again which leads to the increase of the calculating fracture toughness at the highest temperature. These variations of hardness, elastic modulus and fracture toughness with temperatures will account for the possible change of material removal regimes occurred in some thermal-involved hybrid machining of RB-SiC ceramics.
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