Simulation of springback: Through-thickness integration

The number of through-thickness integration points (N_IP) required for accurate springback analysis following sheet forming simulation using shell elements is a subject of confusion and controversy. Li and Wagoner recommended, in 1999, based on a finite element analysis (FEA) of draw-bending springback, the use of 25 integration points (IP), with up to 51 IP required to ensure accuracies of 1%. Several researchers have since reported that N_IP between 5 and 11 are adequate, or even that 7 or 9 IP are optimal, with reduced accuracy for more IP. These apparent contradictions are addressed with an analytical model of elasto-plastic bending under tension, followed by elastic springback. The fractional error in the evaluated bending moment, which is equal to the fractional error in springback, was determined by comparing three numerical integration schemes, with various N_IP, to the closed-form result. The results illustrate the oscillatory nature of numerical integration error with small parametric changes, such that fortuitous agreement can be obtained in isolated simulations where the number of integration points is inadequate. The concept of an assured error limit is introduced as well as a maximum error limit (for a range of generally unknown sheet tensions). The assured error limit varies with the integration scheme, N_IP, bending ratio (R/t), and sheet tension. Guidelines for the number of integration points required for given error tolerances are reported to allow practitioners to choose numerical parameters appropriately.     

Creep and anelasticity in the springback of aluminum

Draw-bend tests, devised to measure springback in previous work, revealed that the specimen shapes for aluminum alloys can continue to change for long periods following forming and unloading. Steels tested under identical conditions showed no such time-dependent springback. In order to quantify the effect and infer its basis, four aluminum alloys, 2008-T4, 5182-O, 6022-T4 and 6111-T4, were draw-bend tested under conditions promoting the time-dependent response (small tool radius and low sheet tension). Detailed measurements were made over 15 months following forming, after which the shape changes were difficult to separate from experimental scatter. Earlier tests were re-measured up to 7 years following forming. The shape changes are generally proportional to log(time) up to a few months, after which the kinetics become slower. In order to understand the basis of the phenomenon, two models were considered: residual stress-driven creep, and anelastic deformation. In the first case, creep properties of 6022-T4 were measured and used to simulate creep-based time-dependent springback. Qualitative agreement was obtained using a crude finite element model. For the second possibility, novel anelasticity tests following reverse-path loading were performed for 6022-T4 and drawing-quality silicon-killed (DQSK) steel. Based on the experiments and simulations, it appears that anelasticity is unlikely to play a large role in long-term time-dependent springback of aluminum alloys.     

Elastic fields of line defects in a cracked body

Elastic fields are presented for line forces and dislocations in the vicinity of a crack tip and of a contained, double-ended planar crack. The fields of line force couples are also derived. The corresponding stress intensity factors are listed. The use of these results as two-dimensional Green functions for more general cases is discussed.     

Calculation of a High Order QCD Process-gg to ttgg

We use the permutation group of order 4 to classify the fouith order tree QCD Feynman diagrams, which contribute to the gg to tfgg process. (There are 159 of them.) We also provide new methods to make the color sum, and to check the gauge symmetry of the matrix elements and Feynman parts.     

Influence of segregation on magnetic order in Cr75(Fe x Mn1−x )25, 0.64 ≤x ≤ 0.85

Mössbauer and magnetic measurements on Cr₇₅(Fe,Mn)₂₅ alloys, which were segregated and re-disordered by appropriate heat treatments, are reported. A primary factor for the kind of magnetic order which appears is the Cr concentration around the Mössbauer probe atom. At around 15 K, a transition to a re-entrant spin-glass state occurs. For this state, the hyperfine field distributions of all investigated disordered and re-disordered samples are independent of the Fe concentration.     

IMINIUM SALT BENZOCHLORINS: STRUCTURE-ACTIVITY RELATIONSHIP STUDIES

An iminium salt of copper(II) octaethylbenzochlorin (CDS1) is an effective new photosensitizer despite the fact that it does not produce singlet oxygen, does not fluoresce and the triplet state lifetime can only be less than 20 ns. A number of octaethylbenzochlorin derivatives were synthesized in order to determine the structural component(s) that is(are) responsible for the photodynamic action of these new photosensitizers. Studies utilizing the N -(4-[5-nitro-2-furyl]-2-thiazolyl)formamide-induced urothelial tumor revealed that the coexistence of the copper inside the aromatic ring and the iminium group at the meso position are required for the photodynamic effect.