Interaction of process parameters, forming mechanisms, and residual stresses in single point incremental forming

The residual stress state of a sheet metal component manufactured by metal forming has a significant influence on the mechanical properties, and thus determines the time until the component fails, especially for dynamic loads. The origin of the resulting residual stress state of incrementally formed parts with regard to the forming mechanisms of shearing, bending, and the normal stress component is still under investigation. The relationship between the process parameters, the forming mechanisms, and the resulting residual stress state for a complex part geometry manufactured by single point incremental forming (SPIF) is presented in this publication. For this purpose, a validated numerical process model is used to analyze the influence of the step-down increment Δz for truncated cones on the characteristics of the forming mechanisms and the resulting residual stress state. For the first time the forming mechanisms are evaluated numerically on both sides of the formed component. A relationship between the process parameters, forming mechanisms, residual stresses, and the mechanical properties of an incrementally formed component is shown. Shearing-induced hardening is identified as a relevant influence on the residual stress state of cones

BKM Lie superalgebras from counting twisted CHL dyons

Following Sen[arXiv:0911.1563], we study the counting of (`twisted') BPS states that contribute to twisted helicity trace indices in four-dimensional CHL models with N=4 supersymmetry. The generating functions of half-BPS states, twisted as well as untwisted, are given in terms of multiplicative eta products with the Mathieu group, M_{24}, playing an important role. These multiplicative eta products enable us to construct Siegel modular forms that count twisted quarter-BPS states. The square-roots of these Siegel modular forms turn out be precisely a special class of Siegel modular forms, the dd-modular forms, that have been classified by Clery and Gritsenko[arXiv:0812.3962]. We show that each one of these dd-modular forms arise as the Weyl-Kac-Borcherds denominator formula of a rank-three Borcherds-Kac-Moody Lie superalgebra. The walls of the Weyl chamber are in one-to-one correspondence with the walls of marginal stability in the corresponding CHL model for twisted dyons as well as untwisted ones. This leads to a periodic table of BKM Lie superalgebras with properties that are consistent with physical expectations.Comment: LaTeX, 32 pages; (v2) matches published versio

Prediction of temperature induced shape deviations in dry milling

In this paper a model for a simulation based prediction of temperature induced shape deviations in dry milling is presented. A closed loop between Boolean material removal, process forces, heat flux and thermoelastic deformation is established. Therefore, an efficient dexel based machining simulation is extended by a contact zone analysis to model the local workpiece load. Based on the computed contact zone the cutting forces and heat flux are calculated using a semi-empirical process model. For a detailed consideration of the loads they are discretized and localized on the dexel-represented workpiece surface. A projection of the localized workpiece loads on the boundary of the finite element domain, taking into account the Boolean material removal during the process, allows the calculation of the current temperature and deformation of the workpiece. By transforming these thermomechanical characteristics back to the dexel-model a consideration in the machining simulation is possible. An extended contact zone analysis is developed for the prediction of the localized shape deviations. Finally, the results of the simulation are compared with measured data. The comparison shows that workpiece temperatures, workpiece deformation and shape deviations in different workpiece areas are predicted accurately.DFG/DE 447/90-2DFG/MA 1657/21-

Slip statistics of dislocation avalanches under different loading modes

Slowly compressed microcrystals deform via intermittent slip events, observed as displacement jumps or stress drops. Experiments often use one of two loading modes: an increasing applied stress (stress driven, soft), or a constant strain rate (strain driven, hard). In this work we experimentally test the influence of the deformation loading conditions on the scaling behavior of slip events. It is found that these common deformation modes strongly affect time series properties, but not the scaling behavior of the slip statistics when analyzed with a mean-field model. With increasing plastic strain, the slip events are found to be smaller and more frequent when strain driven, and the slip-size distributions obtained for both drives collapse onto the same scaling function with the same exponents. The experimental results agree with the predictions of the used mean-field model, linking the slip behavior under different loading modes

Micro-plasticity and intermittent dislocation activity in a simplified micro structural model

Here we present a model to study the micro-plastic regime of a stress-strain curve. In this model an explicit dislocation population represents the mobile dislocation content and an internal shear-stress field represents a mean-field description of the immobile dislocation content. The mobile dislocations are constrained to a simple dipolar mat geometry and modelled via a dislocation dynamics algorithm, whilst the shear-stress field is chosen to be a sinusoidal function of distance along the mat direction. The latter, defined by a periodic length and a shear-stress amplitude, represents a pre-existing micro-structure. These model parameters, along with the mobile dislocation density, are found to admit a diversity of micro-plastic behaviour involving intermittent plasticity in the form of a scale-free avalanche phenomenon, with an exponent for the strain burst magnitude distribution similar to those seen in experiment and more complex dislocation dynamics simulations.Comment: 30 pages, 12 figures, to appear in "Modelling and Simulation in Materials Science and Engineering

Generalized Kac-Moody Algebras from CHL dyons

We provide evidence for the existence of a family of generalized Kac-Moody(GKM) superalgebras, G_N, whose Weyl-Kac-Borcherds denominator formula gives rise to a genus-two modular form at level N, Delta_{k/2}(Z), for (N,k)=(1,10), (2,6), (3,4), and possibly (5,2). The square of the automorphic form is the modular transform of the generating function of the degeneracy of CHL dyons in asymmetric Z_N-orbifolds of the heterotic string compactified on T^6. The new generalized Kac-Moody superalgebras all arise as different `automorphic corrections' of the same Lie algebra and are closely related to a generalized Kac-Moody superalgebra constructed by Gritsenko and Nikulin. The automorphic forms, Delta_{k/2}(Z), arise as additive lifts of Jacobi forms of (integral) weight k/2 and index 1/2. We note that the orbifolding acts on the imaginary simple roots of the unorbifolded GKM superalgebra, G_1 leaving the real simple roots untouched. We anticipate that these superalgebras will play a role in understanding the `algebra of BPS states' in CHL compactifications.Comment: LaTeX, 35 pages; v2: improved referencing and discussion; typos corrected; v3 [substantial revision] 44 pages, modularity of additive lift proved, product representation of the forms also given; further references adde

Effective and flexible modeling approach to investigate various 3D Talbot carpets from a spatial finite mask

We present an effective modeling approach for a fast calculation of the Talbot carpet from an initially 2-dimensional mask pattern. The introduced numerical algorithm is based on a modified angular-spectrum method, in which it is possible to consider the border effects of the Talbot region from a mask with a finite aperture. The Bluestein’s fast Fourier transform (FFT) algorithm is applied to speed up the calculation. This approach allows as well to decouple the sampling points in the real space and the spatial frequency domain so that both parameters can be chosen independently. As a result an extended three-dimensional Talbot-carpet can be calculated with a minimized number of numerical steps and computation time, but still with high accuracy. The algorithm was applied to various 2-dimensional mask patterns and illumination setups. The influence of specific mask patterns to the resulting field intensity distribution is discussed

Ground State Electromagnetic Moments of ³⁷Ca

The hyperfine coupling constants of neutron deficient $^{37}$Ca were deduced from the atomic hyperfine spectrum of the $4s~^2S_{1/2}$ $\leftrightarrow$ $4p~^2P_{3/2}$ transition in Ca II, measured using the collinear laser spectroscopy technique. The ground-state magnetic-dipole and spectroscopic electric-quadrupole moments were determined for the first time as $\mu = +0.7453(72) \mu_N$ and $Q = -15(11)$ $e^2$fm$^2$, respectively. The experimental values agree well with nuclear shell model calculations using the universal sd model-space Hamiltonians versions A and B (USDA/B) in the $sd$-model space with a 95\% probability of the canonical nucleon configuration. It is shown that the magnetic moment of $^{39}$Ca requires a larger non-$sd$-shell component than that of $^{37}$Ca for good agreement with the shell-model calculation, indicating a more robust closed sub-shell structure of $^{36}$Ca at the neutron number $N$ = 16 than $^{40}$Ca. The results are also compared to valence-space in-medium similarity renormalization group calculations based on chiral two- and three-nucleon interactions

Exoproteomic profiling uncovers critical determinants for virulence of livestock-associated and human-originated Staphylococcus aureus ST398 strains

Staphylococcus aureus: with the sequence type (ST) 398 was previously associated with livestock carriage. However, in recent years livestock-independent S. aureus ST398 has emerged, representing a potential health risk for humans especially in nosocomial settings. Judged by whole-genome sequencing analyses, the livestock- and human originated strains belong to two different S. aureus ST398 clades but, to date, it was not known to what extent these clades differ in terms of actual virulence. Therefore, the objective of this study was to profile the exoproteomes of 30 representative S. aureus ST398 strains by mass spectrometry, to assess clade-specific differences in virulence factor secretion, and to correlate the identified proteins and their relative abundance to the strains' actual virulence. Although the human-originated strains are more heterogeneous at the genome level, our observations show that they are more homogeneous in terms of virulence factor production than the livestock-associated strains. To assess differences in virulence, infection models based on larvae of the wax moth Galleria mellonella and the human HeLa cell line were applied. Correlation of the exoproteome data to larval killing and toxicity toward HeLa cells uncovered critical roles of the staphylococcal Sbi, SpA, SCIN and CHIPS proteins in virulence. These findings were validated by showing that sbi or spa mutant bacteria are attenuated in G. mellonella and that the purified SCIN and CHIPS proteins are toxic for HeLa cells. Altogether, we show that exoproteome profiling allows the identification of critical determinants for virulence of livestock-associated and human-originated S. aureus ST398 strains

Negotiating different disciplinary discourses: biology students’ ritualized and exploratory participation in mathematical modeling activities

Non-mathematics specialists’ competence and confidence in mathematics in their disciplines have been highlighted as in need of improvement. We report from a collaborative, developmental research project which explores the conjecture that greater integration of mathematics and biology in biology study programs, for example through engaging students with Mathematical Modeling (MM) activities, is one way to achieve this improvement. We examine the evolution of 12 first-semester biology students’ mathematical discourse as they engage with such activities in four sessions which ran concurrently with their mandatory mathematics course and were taught by a mathematician with extensive experience with MM. The sessions involved brief introductions to different aspects of MM, followed by small-group work on tasks set in biological contexts. Our analyses use the theory of commognition to investigate the tensions between ritualized and exploratory participation in the students’ MM activity. We focus particularly on a quintessential routine in MM, assumption building: we trace attempts which start from ritualized engagement in the shape of “guesswork” and evolve into more productively exploratory formulations. We also identify signs of persistent commognitive conflict in the students’ activity, both intra-mathematical (concerning what is meant by a “math task”) and extra-mathematical (concerning what constitutes a plausible solution to the tasks in a biological sense). Our analyses show evidence of the fluid interplay between ritualized and exploratory engagement in the students’ discursive activity and contribute towards what we see as a much needed distancing from operationalization of the commognitive constructs of ritual and exploration as an unhelpfully dichotomous binary