Sheet Thinning Research Articles

Thickness distribution and design of a multi-stage process for sheet metal incremental forming

Sheet incremental forming (ISF) is a promising technology. It is inexpensive and does not require particular dies. Sheet thinning, however, has always been one of the forming defects which impede the process’s wide application. Although a multi-stage forming process is supposed to be effective to deal with this problem, it is still uncertain how the process can reduce thickness thinning and there is no applicable rule to determine the favorable number of forming stages. In this work, based on a truncated cone, a finite element method (FEM) model for a double-pass forming was established first. Unlike simplifications in previous studies, with the process of the three-dimensional coordinates in numerical controlled (NC) machining code, the tool trajectory in this simulation model is the same as that in real work. With this approach, it was expected to gain reliability of the simulation result, and then this simulation result and a single-pass forming result were analyzed. The results of the analysis indicate that more uniform thickness distribution in the double-forming process largely benefits from the increase of the total plastic deformation zone. Finally, under the condition of constant volume in deformation, an equation was proposed to work out the right number of necessary forming stages and the rule of this equation was verified with a relatively complex product.

Experimental investigation and finite element modeling on profile forming of conical component using Al 3003(O) alloy

Profile forming of sheet metal is a special technique that offers flexibility and cost-effectiveness in the metal forming process, requiring no high capacity presses or set of dies, thus meeting the ever increasing demand for small batch production and rapid prototyping. This paper demonstrates the formation of sheet metal part using the CNC controlled hemispherical tool and analyses the various parameters underlying this mechanism – like maximum wall angle, surface roughness (Ra) and thinning of sheet. Analysis of the microstructure is carried out using Scanning electron microscopy and Energy-dispersive X-ray spectroscopy microanalysis test. In this study, Aluminum sheet of grade Al 3003(O) with 1mm and 1.25mm thickness is used as a work piece. The paper also presents an explicit numerical simulation using the standard finite element code ABAQUS and the experimental and numerical results are validated.

Magnetic reconnection associated fluctuations in the deep magnetotail: ARTEMIS results

Abstract. On the basis of ARTEMIS two-probe mission magnetic reconnection (MR) outflow associated magnetic fluctuations and turbulence are analyzed on 19 February 2011. In the deep-tail, at distances between X = 45 – 51 RE, evidence for reconnection associated plasma sheet thinning was found, accompanied by heating of the plasma sheet. Correlated flow and field reversals and the large-scale Hall-effect signatures indicated the presence of the reconnection X-line. Within fast reconnection plasma outflows, magnetic fluctuations exhibit the same spectral scaling features and kinked spectra as magnetic fluctuations in the solar wind or in various parts of geospace. It was shown that the proton scale magnetic fluctuations are constrained by oblique firehose, proton cyclotron and mirror instability thresholds. For parallel plasma β|| > 1, where the thresholds converge, perpendicular magnetic fluctuations are enhanced. Magnetic compressibility decreases with the distance to the neutral sheet, however, near the instability thresholds it is comparable to the values obtained in the solar wind.

Structure, force balance, and evolution of incompressible cross-tail current sheet thinning

[1] THEMIS five-point observations on April 8, 2009 were used to study thinning of the current sheet in the near-Earth tail that led to the onset of a small substorm. Taking advantage of a fortuitous alignment of the five spacecraft near 2300 LT and 11 RE and within 1.5 RE of the current sheet center, latitudinal gradients are analyzed. A significant latitudinal pressure gradient is present indicating the necessity of a (J × B)z force to maintain the pre-onset equilibrium state. During thinning the total pressure remained approximately constant at all spacecraft rather than increasing. Within the plasma sheet, magnetic field strength increased while plasma pressure decreased due to decreasing temperature. We present a comprehensive explanation for the relationship between the thinning, the stretched structure, and development of intense current density. Our analysis of this event suggests that (1) the thinning in this event is an MHD force-balanced self-evolving process and is not a forced process due to an increased lobe field; (2) the thinning changes flux tube structure in length and curvature but not significantly in volume; (3) the thinning evolves with a change of the radial plasma pressure profile in the near-Earth tail, which is associated with a locally intensified current sheet. The conclusion is that the increased lobe field strength is not the necessary and the primary cause for cross tail current sheet thinning but rather thinning can occur within the plasma sheet as a result of unknown internal processes.

An increase in crevasse extent, West Greenland: Hydrologic implications

[1] We compare high-resolution 1985 and 2009 imagery to assess changes in crevasse extent in the Sermeq Avannarleq ablation zone, West Greenland. The area occupied by crevasses >2 m wide significantly increased (13 ± 4%) over the 24-year period. This increase consists of an expansion of existing crevasse fields, and is accompanied by widespread changes in crevasse orientation (up to 45°). We suggest that a combination of ice sheet thinning and steepening are responsible for the increase in crevasse extent. We examine the potential impact of this change on the hydrology of the ice sheet. We provide a first-order demonstration that moulin-type drainage is more efficient in transferring meltwater fluctuations to the subglacial system than crevasse-type drainage. As enhanced basal sliding is associated with meltwater “pulses”, an increase in crevasse extent can therefore be expected to result in a net decrease in basal sliding sensitivity. An increase in crevasse extent may also accelerate cryo-hydrologic warming and enhance surface ablation.

Numerical simulation of non-circular spinning: a rotationally non-symmetric spinning process

This paper describes the peculiarities encountered in the numerical modeling of non-circular spinning processes using motion-controlled roller tools and applying the Finite Element Method (FEM). This process is suitable for producing non-circular, hollow components in small to medium-sized production lots. Numerical simulation can be used to optimize the process. Therefore, it is necessary to make a realistic sheet thinning and wrinkling calculation by using the FEM. This can be achieved through the definition of the real kinematics, a suitable flow curve and an optimal sheet meshing strategy using solid elements. An optimal sheet meshing strategy is particularly necessary in order to realistically calculate the process within an acceptable computing time. Reference experiments with the rotationally non-symmetric mandrel types, the “Tripode” and “Pagoda”, were carried out to compare simulations and experiments. A comparison of the reference experiments with the “Tripode” mandrel demonstrated that it is possible to simulate non-circular spinning with a deviation of less than 5% with respect to minimum sheet thickness. It is also possible to predict wrinkling in critical, non-circular spinning processes. This has been confirmed by comparing the “Pagoda” reference experiment with the FEM simulation.

An Experimental Investigation on Profile Forming of an End Cap Using Al 3003 (O)

The feasibility of using modern computers in manufacturing has evolved an era in the development of several new sheet metal forming process. The concept of profile forming technique has been investigated for production of sheet metal components. Profile forming is a very promising technology to manufacture sheet metal producs by CNC controlled movement with simple forming tool. Profile forming was developed as a flexible, alternative manufacturing method to effectively prototype stampings and produce in small lots. Cylindrical Cup is formed on Aluminium sheet of grade Al 3003 (O) without using punch and die. Formability of material, maximum wall angle, Surface roughness, thinning of sheet and Microstructural characteristics of Aluminium sheet are studied.

Representing Grounding Line Dynamics in Numerical Ice Sheet Models: Recent Advances and Outlook

Recent satellite observations of the Antarctic and Greenland ice sheets show accelerated ice flow and associated ice sheet thinning along coastal outlet glaciers in contact with the ocean. Both processes are the result of grounding line retreat due to melting at the grounding line (the grounding line is the contact of the ice sheet with the ocean, where it starts to float and forms an ice shelf or ice tongue). Such rapid ice loss is not yet included in large-scale ice sheet models used for IPCC projections, as most of the complex processes are poorly understood. Here we report on the state-of-the art of grounding line migration in marine ice sheets and address different ways in which grounding line migration can be attributed and represented in ice sheet models. Using one-dimensional ice flow models of the ice sheet/ice shelf system we carried out a number of sensitivity experiments with different spatial resolutions and stress approximations. These are verified with semi-analytical steady state solutions. Results show that, in large-scale finite-difference models, grounding line migration is dependent on the numerical treatment (e.g. staggered/non-staggered grid) and the level of physics involved (e.g. shallow-ice/shallow-shelf approximation).

Experimental and Numerical Modelling of Thermo-Forming of Anisotropic Thin Sheet

Coupled constitutive equations, formulated in the framework of the thermodynamics of irreversible processes accounting for isotropic hardening as well as the isotropic ductile damage are used to simulate numerically, by the Finite Element Analysis, 3D metal hydroforming processes. The experimental study is dedicated to the identification of stress-strain flow and damage parameters by using the Nelder-Mead simplex algorithm optimization from the global measure of displacement and force. Applications are made to the simulation of thin sheet thermohydroforming using different die geometry to show the efficiency of the proposed methodology and to localize plastic instability, thinning of sheet and damage initiation under different forming conditions.

Consequences of violation of frozen-in-flux: Evidence from OpenGGCM simulations

[1] It is widely believed that during a substorm, plasma instabilities occur before the onset of magnetic reconnection, signaling the end of the growth phase. Despite many years of effort, however, the details of how the instability and the onset of reconnection develop from closed field line configuration with finite normal magnetic field are not well understood. In this paper, we study an idealized simulation of a substorm that occurred on 23 March 2007, based on the Open Geospace General Circulation Model (OpenGGCM). Our analysis emphasizes the time development of the distribution of the entropy parameter and its convective time derivative, which should be zero in ideal MHD. In the late growth phase, the simulation exhibits, over a range of local times, a systematic violation of conservation of entropy that corresponds to what is called “antidiffusion.” Out of this background, a more localized disturbance develops in a region of high magnetic stretching, resulting in formation of a strong reduction of entropy (bubble) earthward of a local enhancement (blob). The process is accelerated when the current density exceeds a threshold for triggering an explicit resistivity in the code. The bubble moves earthward and the blob tailward, which leads to a reduction of the normal magnetic field and a thinning of the current sheet between them, making the magnetospheric configuration more conducive to tearing and other instabilities (we do not address specifically which instability has occurred). This positive feedback gives rise to increased violation of the perfect conductivity relation and eventually reconnection.

Parametric Investigation of Circular and Elliptical Bulge Tests in Warm Hydroforming Process for AA5754-O Sheet

This study numerically investigated the effects of process parameter variations such as blank holder forces (800kN-1200kN), strain rates (0.0013/sec, 0.013/sec, 0.13/sec), coefficient of friction (0.05-0.15), temperature (150 °C, 260 °C) and apex angles (0º, 60º, 90º,120º) on warm hydroforming of AA 5754-O sheet blanks. Warm hydroforming process was simulated through hydraulic bulge test with circular and elliptical die openings. Dome height and sheet thinning were selected as control parameters for formability of AA 5754-O sheet blanks. Results showed that the dome height and formed blank thicknesses did not change significantly with the variation of coefficient of friction and blank holder force. Moreover, increasing forming temperature and non-isothermal conditions yielded slightly better formability. On the other hand, increase in strain rate, and elliptical type of bulge test cavity led to significant decreases in dome height and formed part thinning. Another significant finding was that the elliptical bulge test model and isothermal analyses did not reveal the effect of anisotropy for the sheet material concerned.

Accelerated thinning of the near-Earth plasma sheet caused by a bubble-blob pair

[1] In the late stage of a substorm growth phase, the magnetic field in the near-Earth region is highly stretched. We assume that such conditions can lead to violation of the frozen-in-flux condition, allowing transfer of plasma from one flux tube to another and creating a plasma blob tailward of a plasma bubble. In this letter we present results of a simulation where we artificially impose a bubble-blob pair by introducing a disturbance in PV5/3 in the near-Earth plasma sheet. In the subsequent evolution, as calculated by the equilibrium version of the Rice Convection Model (RCM-E), the bubble surges earthward and the blob moves tailward, while the magnetic field between them weakens and the localized cross-tail current density increases. We speculate that, at substorm onset, there could be a positive feedback in which the breakdown of the frozen-in condition would increasingly make the current sheet thinner until magnetic reconnection occurs.

Multiscale‐multifluid simulations of the 26 February 2008 substorm: Evidence for internal triggering of a substorm

Multiscale‐multifluid simulations are used to provide high‐resolution (∼470 km) simulations of the 26 February 2008 substorm that was well observed by the THEMIS spacecraft to investigate whether the substorm was internally or externally triggered. This substorm occurred during an extended (1 h 45 min) period of weak (−2.5 to −1.5 nT) southward interplanetary magnetic field (IMF). Simulation results show that this substorm was internally triggered well before the IMF start to become more northerly. The southward IMF leads to an enhancement in the cross‐polar cap potential, strong thinning of the current sheet, and pseudo‐breakup in association with patchy reconnection. The southward IMF also produces an enhancement in the outflow of ionospheric oxygen into the current sheet. Because of the tilt of the magnetic field the strongest outflows originate from the southern polar cap. The arrival of these heavy ions in the tail occurs about 10 min prior to the observed substorm onset and leads to enhanced tail reconnection, including flux rope development and fast earthward flows. The interaction of these fast flows at the inner edge of the plasma sheet is closely associated with auroral onset, indicating that the substorm is internally triggered. Comparison with THEMIS data suggests that reconnection occurred earlier than THEMIS observations. The results show onset is associated with processes at the inner edge of the plasma sheet and is not directly related to the onset of reconnection. Comparison with THEMIS data indicates that processes at scale lengths less than 500 km are occurring.

Identification of substorm onset location and preonset sequence using Reimei, THEMIS GBO, PFISR, and Geotail

We present state‐of‐the‐art multiple instrument observations of an isolated substorm on October 12, 2007. The auroral breakup was observed simultaneously by Reimei, THEMIS ASI, and PFISR. The footprint of Geotail was also near the breakup. These observations allow for detailed study of the breakup location in terms of large‐ and small‐scale auroral morphology, particle precipitation, and ionospheric convection, which has not previously been achieved. It also allows for detailed identification of the sequence leading to the breakup. We report the first spaceborne high spatial and temporal resolution images of part of a breakup arc and a wave‐like auroral enhancement captured by Reimei. Observations suggest a sudden plasma sheet thinning initiated ∼10 min before the onset. Wave‐like auroral enhancements were observed twice at the most equatorward arc ∼3 min and ∼1 min before the breakup. These enhancements are likely due to some near‐Earth instability, such as ballooning instability. Unlike the usual substorm sequence, this most equatorward arc did not develop into the breakup arc but remained almost stable until being engulfed by the auroral equatorward expansion from higher latitude after onset. The wave‐like auroral enhancement was associated with three fine inverted V arcs and embedded within energetic ion precipitation. Following this enhancement, an arc, likely a poleward boundary intensification, formed at higher latitude just adjacent to the plasma sheet boundary layer (PSBL). This arc then extended southwestward and led to the breakup arc, which was located poleward of the wavy structures. Assuming longitudinal homogeneity of ion precipitation over 1°, this breakup arc was located in a region without ion precipitation just poleward of the energetic ion precipitation. These observations suggest the possible existence of a low‐entropy flow channel associated with the arc adjacent to the PSBL, which might be associated with instability in the near‐Earth plasma sheet responsible for the auroral breakup.

Evolution of the Kippenhahn–Schlüter Prominence Model Magnetic Field under Cowling Resistivity

Abstract We present the results from 1.5D diffusion simulations of the Kippenhahn–Schlüter prominence model magnetic field evolution under the influence of the ambipolar terms of Cowling resistivity. We show that initially the evolution is determined by the ratio of the horizontal and vertical magnetic fields, which gives current sheet thinning (thickening) when this ratio is small (large) and a marginal case where a new characteristic current sheet length scale is formed. After a timespan greater than the Cowling resistivity time, the current sheet thickens as a power law of $t$ independent of the ratio of the field strengths. These results imply that when Cowling resistivity is included in the model, the tearing instability time scale is reduced by more than one order of magnitude when the ratio of the horizontal field to the vertical field is 20% or less. These results imply that, over the course of its lifetime, the structure of the prominence can be significantly altered by Cowling resistivity, and in some cases will allow the tearing instability to occur.

Onset of magnetic reconnection in the presence of a normal magnetic field: Realistic ion to electron mass ratio

Two‐dimensional particle‐in‐cell simulations with a realistic ion to electron mass ratio are used to investigate the impact of an externally applied convection electric field on the stability of a moderately thick (1.6c/ωpi) current sheet configuration containing a nonzero Bz. The imposition of the electric field produces a thinning of the current sheet associated with the formation of an embedded electron current layer and a reduction in the normal magnetic field component. The time scale for these processes is found to be nearly independent of the electron mass. Once kxρen becomes of order unity (kx is the wave number for the maximally growing tearing mode, and ρen is the electron gyroradius in the normal field), fluctuations drive Bz southward over a subion‐inertia‐length scale region; further driving then leads to a conventional reconnection process featuring Bz pulses (dipolarization fronts) propagating away from the X line. Consistent with earlier results with heavier electrons, strong parallel electric fields and an electron current layer form on scales of about an ion inertia length in the outflow direction, while electron outflow jets extend over much larger distances downstream from the X line.

Empirical modeling of a CIR‐driven magnetic storm

The empirical analysis of structure and evolution of the geomagnetic field and underlying electric currents during the 8–11 March 2008 magnetospheric storm, driven by a corotating interaction region, is presented. It is based on the high‐resolution geomagnetic field model TS07D (http://geomag_field.jhuapl.edu/model/) and the low‐altitude mapping of field‐aligned currents obtained using Iridium satellites. Compared to storms, driven by coronal mass ejections, the equatorial currents are found to be overall more dawn‐dusk symmetric. Only in the early main phase a moderate hook‐like westward current flowing from the Region‐2 inflow area on the dawn side to the dusk/afternoon magnetopause is detected, along with an eastward current near the pre‐noon magnetopause. New tail‐type currents are found to dominate the storm‐time magnetosphere in early main and recovery phases at the moments of strong peaks of the solar wind dynamic pressure. Similar effects, found in CME‐driven storms, coincide in time with the plasma sheet density bursts. A clear distinction between the periods dominated by the partial ring current and the tail‐type currents seen in the model agrees with the Iridium data that indicate a significant reduction and contraction of the field‐aligned current pattern in the latter case. Overall small magnitudes of the total field‐aligned currents, with rather transient enhancements, appear to be the most distinctive feature of CIR‐driven storms. Comparison between the model and observations made by five THEMIS probes shows good agreement on storm timescales. Moreover, every deviation arising during a substorm reveals characteristic signatures of the tail current sheet thinning and dipolarization.

Inflow of Warm Circumpolar Deep Water in the Central Amundsen Shelf*

Abstract The thinning and acceleration of the West Antarctic Ice Sheet has been attributed to basal melting induced by intrusions of relatively warm salty water across the continental shelf. A hydrographic section including lowered acoustic Doppler current profiler measurements showing such an inflow in the channel leading to the Getz and Dotson Ice Shelves is presented here. The flow rate was 0.3–0.4 Sv (1 Sv ≡ 106 m3 s−1), and the subsurface heat loss was estimated to be 1.2–1.6 TW. Assuming that the inflow persists throughout the year, it corresponds to an ice melt of 110–130 km3 yr−1, which exceeds recent estimates of the net ice glacier ice volume loss in the Amundsen Sea. The results also show a 100–150-m-thick intermediate water mass consisting of Circumpolar Deep Water that has been modified (cooled and freshened) by subsurface melting of ice shelves and/or icebergs. This water mass has not previously been reported in the region, possibly because of the paucity of historical data.

A geometrical model of the kinematics of incremental sheet forming for the prediction of membrane strains and sheet thickness

The sine law is a simple geometrical model for incremental sheet metal forming (ISF). It is based on the assumption that the deformation is a projection of the undeformed sheet onto the surface of the final part. The sine law provides approximations of sheet thinning for shear spinning and ISF at negligible computational cost, but as a plane strain model it can be applied only when plane strain deformation prevails. In this paper, a new model for the process kinematics of ISF is presented that is more general than the sine law. The model treats ISF as an evolution of a surface from the undeformed sheet to the final shape. It computes trajectories of surface points based on idealized intermediate shapes, assuming that the deformation between intermediate shapes proceeds by displacements along the surface normal of the current shape. For 2D and axisymmetrical problems, an analytical solution of the model is developed, which is useful for visualizing and discussing the kinematics of ISF. In order to use the new model with arbitrary parts, it was cast into a computer program that calculates membrane strains and the sheet thickness on a triangular mesh. For a benchmark shape, the model is compared to the sine law and experimental results. It is shown that the new model yields better thickness estimates than the sine law, especially in non-flat part areas where strains parallel to the direction of tool motion are significant.

Deglacial history of the West Antarctic Ice Sheet in the Weddell Sea embayment: Constraints on past ice volume change

The retreat history of the West Antarctic Ice Sheet (WAIS) since the Last Glacial Maximum is important for understanding the process of rapid deglaciation, constraining models that seek to predict the future trajectory of the ice sheet, and for estimating rates of sea-level change. Here we report new glacial geologic data from the southwestern Weddell Sea embayment that demonstrate that this part of the WAIS was thinner than previously suggested, and that there was progressive thinning of the ice sheet by 230–480 m since ca. 15 ka. We use geomorphological data and a numerical ice sheet model to reconstruct the ice sheet in the Weddell Sea at the Last Glacial Maximum. The volume of this ice would have added between 1.4 and 2.0 m to postglacial sea-level rise and would not have been sufficient to contribute significantly to meltwater pulse 1A, a rapid rise in sea level ∼14,200 yr ago.