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In short-carbon-fiber-reinforced polyamide 66 articles shaped by 3D printing (3D-SCFRPA66), the interfaces between printed layers are often susceptible to damage, and the composite is excessively brittle. Therefore, a novel treatment for 3D-printed short-carbon-fiber-reinforced polyamide (3D-SCFRPA66) using homogeneous low-potential electron beam irradiation (HLEBI) to enhance tensile properties was investigated. In 3D-SCFRPA66 samples, ductility was measured based on the following parameters: strain at tensile strength (corresponding to homogeneous deformation) (εts) and resistance energy to homogeneous deformation, a measure of toughness (Ehd), which were both substantially increased. An HLEBI dose of 43.2 kGy at an acceleration potential of 210 kV for the finished 3D-SCFRPA66 samples increased the εts and Ehd values from 0.031 and 1.20 MPa·m for the untreated samples to 0.270 and 6.05 MPa·m for the treated samples, increases of 771% and 504%, respectively. Higher HLEBI doses of 86, 129, or 215 kGy also increased the εts and Ehd values to lesser degrees. Electron spin resonance (ESR) data in the literature show that HLEBI creates dangling bonds in Nylon 6. Since PA66 and Nylon 6 are constructed of C, N, and O and have similar molecular structures, HLEBI apparently severs the (-C-N-) bonds in the backbone of PA66, which have the lowest bond-dissociation energy (BDE) of ~326 to 335 kJ mol−1. This shortens the PA66 chains for higher ductility. In addition, for Nylon 6, X-ray photoelectron spectroscopy (XPS) data in the literature show that HLEBI reduces the N peak while increasing the C peak, indicating the occurrence of shortening chains via dangling bond formation accompanied by increases in crosslinking with carbon bonds. However, caution is advised, since HLEBI was found to decrease the tensile strength (σts) and initial elasticity ([dσ/dε]i) of 3D-SCFRPA66. This tradeoff can possibly allow the HLEBI dose to be adjusted for the desired ductility and strength while minimizing energy consumption. [ABSTRACT FROM AUTHOR]

We describe how one department moved from skepticism to wide-spread embrace of coordinated Calculus I. Data played a crucial role in this process. Details of this journey, including successful strategies and missteps, may provide insight and perspective to other departments starting on, or immersed in, similar transformational adventures.

CANWA (Comparative Analytical Numerical Wave Algorithm), written in MATLAB, provides a fast, direct comparison of a general finite volume solution to the 1+1 shallow water wave equations with a robust analytical solution recently presented by Nicolsky et al. (2018). The implementation of the method for data projection, introduced in Nicolsky et al. (2018), solves the initial value problem produced by the Carrier-Greenspan transformation, allows for highly accurate simulations of waves with nonzero initial velocities. Additionally, an L2analysis of error grants a comparison of solutions across the entire spatial domain. Simulations of both solitary and N-waves reveal that the numerical method consistently yields larger inundation zones than the analytical solution.

An edge-colored graph is properly connected if for every pair of vertices u and v there exists a properly colored uv-path (i.e. a uv-path in which no two consecutive edges have the same color). The proper connection number of a connected graph G, denoted pc(G), is the smallest number of colors needed to color the edges of G such that the resulting colored graph is properly connected. An edge-colored graph is flexibly connected if for every pair of vertices u and v there exist two properly colored paths between them, say P and Q, such that the first edges of P and Q have different colors and the last edges of P and Q have different colors. The flexible connection number of a connected graph G, denoted fpc(G), is the smallest number of colors needed to color the edges of G such that the resulting colored graph is flexibly connected. In this paper, we demonstrate several methods for constructing graphs with pc(G) = 2 and fpc(G) = 2. We describe several families of graphs such that pc(G) ≥ 2 and we settle a conjecture from [BFG+12]. We prove that if G is connected and bipartite, then pc(G) = 2 is equivalent to being 2-edge-connected and fpc(G) = 2 is equivalent to the existence of a path through all cut-edges. Finally, it is proved that every connected, k-regular, Class 1 graph has flexible connection number 2.

It is vital to maximize the safety of outdoor constructions, airplanes, and space vehicles by protecting against the impact of airborne debris from increasing winds due to climate change, or from bird strikes or micrometeoroids. In a widely-used compression-molded short glass fiber polyester bulk-molded compound (SGFRP-BMC) with 55% wt. CaCO3 filler, the center of the mother panel has lower impact strength than the outer sections with solidification texture angles and short glass fiber (SGF) orientations being random from 0 to 90 degrees. Therefore, a new double-step process of: (1) reducing commercial fiber length without change in molding equipment; followed by a (2) 0.86 MGy dose of homogeneous low-voltage electron beam irradiation (HLEBI) to both sides of the finished samples requiring no chemicals or additives, which is shown to increase the Charpy impact value (auc) about 50% from 6.26 to 9.59 kJm−2 at median-accumulative probability of fracture, Pf = 0.500. Shortening the SGFs results in higher fiber spacing density, Sf, as the thermal compressive stress site proliferation by action of the CTE difference between the matrix and SGF while the composite cools and shrinks. To boost impact strength further, HLEBI provides additional nano-compressive stresses by generating dangling bonds (DBs) creating repulsive forces while increasing SGF/matrix adhesion. Increased internal cracking apparently occurs, raising the auc. [ABSTRACT FROM AUTHOR]

A graph G is H-saturated if H is not a subgraph of G but the addition of any edge from G̅ to G results in a copy of H. The minimum size of an H-saturated graph on n vertices is denoted sat(n,H), while the maximum size is the well studied extremal number, ex(n,H). The saturation spectrum for a graph H is the set of sizes of H saturated graphs between sat(n,H) and ex(n,H). In this paper we completely determine the saturation spectrum of stars and we show the saturation spectrum of paths is continuous from sat(n, Pk) to within a constant of ex(n, Pk) when n is sufficiently large.

In an interlayered carbon fiber-reinforced polycarbonate polymer (CFRPC) composite composed of three sized of CF plies, alternating between four PC sheets, designated [PC]4[CF]3, and a new process of activating CF cross-weave cloth plies directly on both sides with homogeneous low-energy electron beam irradiation (HLEBI) before lamination assembly and hot pressing at 6.0 MPa and 537 K for 8 min was produced. Experimental results show that a dose of 215 kGy of HLEBI raised the bending strength, σb, at each experimental accumulative probability, Pa, with the σb at a median Pa of 0.50, increasing by 25% over that of the untreated sample. Three-parameter Weibull analysis showed that when quality can be controlled, a dose of 215 kGy of HLEBI can raise the statistically lowest bending strength, σs, at Pa = 0 (94.3 Mpa), with a high correlation coefficient. This is because, although it had a higher bending strength than that in the other experimental conditions, the weakest sample of the 215 kGy data set had a much lower σb value than that of the others. Electron spin resonance (ESR) of the CF showed that naturally occurring dangling bonds in CF were increased at 215 kGy. Charge transfer to the PC occurs, apparently generating stronger bonds, which are possibly covalent, resulting in enhanced adhesion at the CF–PC interface. [ABSTRACT FROM AUTHOR]

New types of hybrid aluminum joints: Al-acrylonitrile butadiene styrene (ABS) carbon fiber reinforced thermoplastic polymer (CFRTP) designated Al/Ni-CFP/ABS, and Al-18-8 Stainless steel, Al/Ni-CFP/18-8, by Ni-plated carbon fiber plug (Ni-CFP) insert not before seen in the literature have been fabricated. The goal is to take advantage of extremely high ~6 mm CF surface area for high adhesion, to enhance the safety level of aircraft and other parts. This is without fasteners, chemical treatment, or glue. First, the CFP is plated with Ni. Second, the higher melting point half-length is spot welded to the CFP; and third, the remaining half-length is fabricated. The ultimate tensile strength (UTS) of Al/Ni-CFP/ABS was raised 15 times over that of Al/ABS. Normalized cUTS according to CFP cross-section by Rule of Mixtures for cAl/Ni-CFP/18-8 was raised over that of cAl/Ni-CFP/18-8 from 140 to 360 MPa. Resistance energy to tensile deformation, UT, was raised 12 times from Al/ABS to Al/Ni-CFP/ABS, and 6 times from Al/CFP/18-8 to Al/Ni-CFP/18-8. Spot welding allows rapid melting followed by rapid solidification for amorphous metal structures minimizing grain boundaries. The Ni-coating lowers or counters the effects of brittle Al4C3 and FexC formation at the interface and prevents damage by impingement to CFs, allowing joints to take on more of the load. [ABSTRACT FROM AUTHOR]

For a fixed graph F, a graph G is F-saturated if there is no copy of F in G, but for any edge e ∉ G, there is a copy of F in G + e. The minimum number of edges in an F-saturated graph of order n will be denoted by sat(n, F). A graph G is weakly F-saturated if there is an ordering of the missing edges of G so that if they are added one at a time, each edge added creates a new copy of F. The minimum size of a weakly F-saturated graph G of order n will be denoted by wsat(n, F). The graphs of order n that are weakly F-saturated will be denoted by wSAT(n, F), and those graphs in wSAT(n, F) with wsat(n, F) edges will be denoted by wSAT(n, F). The precise value of wsat(n, T) for many families of sparse graphs, and in particular for many trees, will be determined. More specifically, families of trees for which wsat(n, T) = |T|−2 will be determined. The maximum and minimum values of wsat(n, T) for the class of all trees will be given. Some properties of wsat(n, T) and wSAT(n, T) for trees will be discussed. Keywords: saturated graphs, sparse graphs, weak saturation.

We say that a graph G is maximal Kp-free if G does not contain Kp but if we add any new edge e ∈ E(G) to G, then the graph G + e contains Kp. We study the minimum and maximum size of non-(p − 1)-partite maximal Kp-free graphs with n vertices. We also answer the interpolation question: for which values of n and m are there any n-vertex maximal Kp-free graphs of size m?

Impact by hailstone, volcanic rock, bird strike, or also dropping tools can cause damage to aircraft materials. For maximum safety, the goal is to increase Charpy impact strength (auc) of a carbon-fiber-reinforced thermoplastic polyphenylene sulfide polymer (CFRTP-PPS) composite for potential application to commercial aircraft parts. The layup was three cross-weave CF plies alternating between four PPS plies, [PPS-CF-PPS-CF-PPS-CF-PPS], designated [PPS]4[CF]3. To strengthen, a new process for CFRP-PPS was employed applying homogeneous low voltage electron beam irradiation (HLEBI) to both sides of PPS plies prior to lamination assembly with untreated CF, followed by hot press under 4.0 MPa at 573 K for 8 min. Experimental results showed a 5 kGy HLEBI dose was at or near optimum, increasing auc at each accumulative probability, Pf. Optical microscopy of 5 kGy sample showed a reduction in main crack width with significantly reduced CF separation and pull-out; while, scanning electron microscopy (SEM) and electron dispersive X-ray (EDS) mapping showed PPS adhering to CF. Electron spin resonance (ESR) of a 5 kGy sample indicated lengthening of PPS chains as evidenced by a reduction in dangling bond peak. It Is assumed that 5 kGy HLEBI creates strong bonds at the interface while strengthening the PPS bulk. A model is proposed to illustrate the possible strengthening mechanism. [ABSTRACT FROM AUTHOR]

Strong adhesion between recyclable thermoplastic (TP) polymer and carbon fiber (CF) has always been highly sought after. Therefore, for an interlayered CF reinforced TP polypropylene (CFRTPP) composite composed of 3 sized CF plies, alternating between 4 PP sheets, designated [PP]4[CF]3, a process of activating CF plies directly on both sides with homogeneous low energy electron beam irradiation (EBI) under N2 gas, prior to lamination assembly and hot press of 4.0 MPa at 493 K for 3 min was carried out. Experimental results showed EBI dose of 43.2, 129, or 216 kGy significantly raised Charpy impact values, auc at all fracture probabilities, Pf. The 129 kGy dose appeared to be at or near optimum increasing auc 103%, 83%, and 65% at low-, median-, and high-Pf = 0.07, 0.50, and 0.93; while raising statistically lowest impact value, as at Pf = 0 calculated by 3-dimensional Weibull equation about 110%, indicating increased safety and reliability. It is assumed dangling bonds generated by the EBI rapidly form covalent bonds CF: C:O:C :PP and CF: C:C :PP at the interface, along with cross-linking in the PP near the CF. This is by charge transfer from CF to PP. [ABSTRACT FROM AUTHOR]