Fracture Characterization of Rolled Sheet Alloys in Shear Loading: Studies of Specimen Geometry,Anisotropy, and Rate Sensitivity

Two different shear sample geometries were employed to investigate the failure behaviour of two automotive alloy rolled sheets; a highly anisotropic magnesium alloy (ZEK100) and a relatively isotropic dual phase steel (DP780) at room temperature. The performance of the butterfly type specimen (Mohr and Henn Exp Mech 47:805–820, 16; Dunand and Mohr Eng Fract Mech 78:2919-2934, 17) was evaluated at quasi-static conditions along with that of the shear geometry of Peirs et al Exp Mech 52:729-741, (27) using in situ digital image correlation (DIC) strain measurement techniques. It was shown that both test geometries resulted in similar strain-paths; however, the fracture strains obtained using the butterfly specimen were lower for both alloys. It is demonstrated that ZEK100 exhibits strong anisotropy in terms of failure strain. In addition, the strain rate sensitivity of fracture for ZEK100 was studied in shear tests with strain rates from quasi-static (0.01 s^?1) to elevated strain rates of 10 and 100 s^?1, for which a reduction in fracture strain was observed with increasing strain rate.     

DESIRE: diagonally extended singly implicit Runge–Kutta effective order methods

To overcome known disadvantages in the use of singly-implicit methods in the solution of stiff differential equations, two generalizations have been recently introduced. These are the use of additional diagonally-implicit stages and the use of effective order as a weakening of the conditions on the method. In this paper, these two generalizations are combined into a unified scheme. The resulting DESIRE methods are very promising alternatives to standard methods for solving stiff problems. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Six-Pulse PASS MAS-NMR Technique Solved by a Phasor Method

The PASS MAS-NMR technique is capable of recovering full intensities of the central resonances of a spectrum by phase adjusting the spinning sidebands. This variant of the original PASS sequence by Dixon uses six π pulses instead of four. The addition of two π pulses provides more flexibility in choosing the spacing between pulses and therefore eliminates pulse overlap and receiver dead-time problems. The nonlinear, underdetermined PASS equations were solved using a graphical phasor method. All PASS sequences were successfully tested. A table of the six pulse delay times for different pitches is presented.     

Normal Forms for High Co-Dimension Bifurcations of Nonlinear Time-Periodic Systems with Nonsemisimple Eigenvalues

The normal forms for time-periodic nonlinear variational equations witharbitrary linear Jordan form undergoing bifurcations of highco-dimension are found. First, the equations are transformed via theLyapunov–Floquet (L–F) transformation into an equivalent form in whichthe linear matrix is constant with degenerate nonsemisimple lineareigenvalues while the nonlinear monomials have periodic coefficients. Byconsidering the resulting coupling of the bases of the near identitytransformation, the solvability condition for an arbitrary Jordan matrixis then derived. It is shown that time-independent and/or time-dependentnonlinear resonance terms remain in the normal form for various Jordanmatrices. Specifically, the normal forms for quadratic and cubicnonlinearities with the following linear Jordan forms are explicitlyderived: double zero eigenvalues (co-dimension two bifurcation), triplezero eigenvalues (co-dimension three bifurcation), and two repeatedpairs of purely imaginary eigenvalues (co-dimension two bifurcation). Acommutative system with cubic nonlinearities and a double inverted pendulum with a periodicfollower force are used as illustrative examples.     

Synthesis,spectroscopy, and X-ray crystal structures of copper(II) complexes of the tridentate ONS ligand formed by condensation of 4,4,4-trifluoro-1-(2-thienyl)-2,4-butanedione with S-benzyldithiocarbazate

A new tridentate ONS ligand, H₂L, has been synthesized by condensing thenoyltrifluoroacetone(4,4,4-trifluoro-1-(2-thienyl)-2,4butaneanedione) with S-benzyldithiocarbazate and its structure determined by X-ray diffraction. In the solid state, the Schiff base exists as the ketoamine-thioketo tautomer but in solution and in the presence of copper(II), it converts to the enol-thiol form and deprotonates to give copper(II) complexes of formula, [CuL] and [CuLL¹] (L = doubly deprotonated form of the ligand; L¹ = py, bipy or phen] which have been characterized by magnetic, spectroscopic, and X-ray diffraction studies. An X-ray crystallographic analysis shows that [CuL(py)] has a square-planar geometry with the ligand coordinated to the copper(II) center via the enolate oxygen, the azomethinic nitrogen and the thiolate sulfur, the fourth coordination position being occupied by pyridine. The [CuL(bipy)] complex is five-coordinate with a structure close to square-pyramidal in which the Schiff base acts as a doubly deprotonated tridentate ONS ligand and bipy is bidentate.     

Gallium and oxygen accumulations on gallium nitride surfaces following argon ion milling in ultra-high vacuum conditions

Metallic gallium was observed on the surfaces of GaN commercial samples following argon ion milling. SIMS measurements confirmed that the commercial GaN had approximately 0.02% bulk oxygen present. The SIMS signal was standardized using a specimen of known oxygen content, as determined by elastic recoil detection analysis using 200 MeV heavy ions of ¹⁹⁷Au. Despite this 2–5% oxygen was observed by XPS in the bulk of the GaN after the argon ion milling. This oxygen is believed to be from the original surface oxide that re-cycles on the GaN surface during the ion milling.