Thin Sheet Materials Research Articles

Uniform Ray Description for the PO Scattering by Vertices in Curved Surface With Curvilinear Edges and Relatively General Boundary Conditions

A new high-frequency analysis is presented for the scattering by vertices in a curved surface with curvilinear edges and relatively general boundary conditions, under the physical optics (PO) approximation. Both, impenetrable (e.g., impedance surface, coated conductor) as well as transparent thin sheet materials (e.g., thin dielectric, or frequency selective surface) are treated, via their Fresnel reflection and transmission coefficients. The PO scattered field is cast in a uniform theory of diffraction (UTD) ray format and comprises geometrical optics, edge and vertex diffracted rays. The contribution of this paper is twofold. First, we derive PO-based edge and vertex diffraction coefficients for sufficiently thin but relatively arbitrary materials, while in the literature most of the results (especially for vertex diffraction) are valid only for perfectly conducting objects. Second, the shadow boundary transitional behavior of edge and vertex diffracted fields is rigorously derived for the curved geometry case, as a function of various geometrical parameters such as the local radii of curvature of the surface, of its edges and of the incident ray wavefront. For edge diffracted rays, such a transitional behavior is found to be the same as that obtained heuristically in the original UTD. For vertex diffracted rays, the PO-based transitional behavior is a novel result providing offers clues to generalize a recent UTD solution for a planar vertex to treat the present curved vertex problem. Some numerical examples highlight the accuracy and the effectiveness of the proposed ray description.

Effect of Rolling Direction and Annealing Temperature on Mechanical Properties of Thin Stainless Steel Sheets

Thin stainless steel sheet has been widely used for the small sized and high strength mechanical parts. The materials are initially experienced either the TA (Tension Annealing) or heat treatment after cold rolling, then processed for the final products. Not only stainless steel but thin sheet materials basically have anisotropy in their physical and mechanical properties because of unidirectional rolling history. A few results were reported on the effect of the annealing temperature on those properties. In this paper, the effect of temperature annealing in the air on the anisotropy of mechanical properties of stainless steel thin sheet such as surface roughness, W-bending, Vickers hardness, Young's modulus, spring bending elastic limit and pulley-bendingtype fatigue limit were described.

Laser-Mig Hybrid Welding of aluminium to steel — A straightforward analytical model for wetting length

Laser-MIG hybrid welding was recently suggested as a feasible process for joining of aluminium to steel for both structural as well as tailored blank applications. In this process, the aluminium is molten to create a brazed bond to the zinc-coated steel sheet, which remains solid. Using thin-sheet materials in a thickness range of approximately 1 mm in butt joint configuration, this process allows a joining speed of more than 100 mm/s at a laser power of 4 kW whilst retaining some gap bridging ability. In such a case, the wetting length of the aluminium melt on the top and bottom sides of the zinc-coated steel sheet is of significance for the properties of the joint. Therefore, an understanding of the parameters governing wetting length is required. To promote this understanding, a model to calculate wetting length in dependence of processing conditions is suggested. Based on the assumption that there is a correlation between the temperature field on the steel sheet and wetting length, an analytical model for the temperature field is developed and correlated with experimental results on the material combination AA6016 T4 (thickness 1.15 mm) and DC05+ZE (1 mm). Both model and experiments show that the wetting length is correlated to the melting isotherm of the zinc coating (provided a sufficient amount of melt is created). These results shall contribute to an improved understanding of the process.

Fracture limit prediction for a double safety structure in cylindrical-type lithium secondary batteries

In this study, a double safety structure used for cylindrical-type lithium secondary batteries is newly introduced. The structure is necessary to prevent users and the cylindrical-type secondary batteries from unpredictable explosions due to a temporary increase in the inner pressure of the batteries. The double safety structure consists of a primary safety component as micro half-blanked component, and a secondary safety device as V-notched part. For the double safety device, both the mentioned components are considered by the micro half-blanking and the V-notch forming processes with numerical and experimental predictions for the fracture limit. The mechanical properties are investigated with both a raw and an annealed thin sheet material of 1050-H16 aluminum alloy. The main process parameters are considered to be the clearance and punch-die corner radius for the micro half-blanking process, and the remaining thickness, tip radius, and shape angle of the V-notch. In this study, finite element simulations are carried out to verify the manufacturing process with the mentioned process parameters. The ductile fracture criterion is also adopted to predict the fracture limit for each component. Furthermore, experimental investigations are included to verify the fracture limit predicted from the numerical approach. From the systematic approaches, it is confirmed that the fracture limit for the double safety structure is well predicted, and satisfies the required fracture limit.

Revisit of ASTM Round-Robin Test Data for DeterminingRCurves of Thin-Sheet Materials

AbstractThis paper revisits the ASTM round-robin fracture test data obtained in 1979–1980 by ASTM Task Group E24.06.02 on Application of Fracture Analysis Methods. The fracture tests were conducted using thin-sheet compact tension [C(T)] specimens made of three materials—7075-T561 aluminum alloy, 2024-T351 aluminum alloy, and 304 stainless steel—and different specimen widths were employed in order to take account of in-plane specimen size effect on fracture toughness. Typical experimental data are reanalyzed, and crack growth resistance curves are developed in accordance with fracture test standards, ASTM E561-05 and ASTM E1820-08. Several useful results as well as the conditions under which the two standards can equivalently determine a geometry-independent resistance curve are obtained for the thin-sheet C(T) specimens.

Mixed-mode crack growth in ductile thin-sheet materials under combined in-plane and out-of-plane loading

Cracks in thin structures often are subjected to combined in-plane and out-of-plane loading conditions leading to complex mixed mode conditions in the crack tip region. When applied to ductile materials, large out-of-plane displacements make both experimentation and modeling difficult. In this work, the mixed-mode behavior of thin, ductile materials containing cracks undergoing combined in-plane tension (mode I) and out-of-plane shear (mode III) deformation is investigated experimentally. Mixed-mode fracture experiments are performed and full, three-dimensional (3D) surface deformations of thin-sheet specimens from aluminum alloy and steel are acquired using 3D digital image correlation. General characteristics of the fracture process are described and quantitative results are presented, including (a) the fracture surface, (b) crack path, (c) load-displacement response, (d) 3D full-field surface displacement and strain fields prior to crack growth, (e) radial and angular distributions of the crack-tip strain fields prior to crack growth and (f) singularity analysis of the crack-tip strains prior to crack growth. Results indicate that the introduction of a mode III component to the loading process (a) alters the crack tip fields relative to those measured during nominally mode I loading and (b) significantly increases the initial and stable critical crack-opening-displacement. The data on strain fields in both AL6061-T6 aluminum and GM6208 steel consistently show that for a given strain component, the normalized angular and radial strains at all load levels can be reasonably represented by a single functional form over the range of loading considered, confirming that the strain fields in highly ductile, thin-sheet material undergoing combined in-plane tension and out-of-plane shear loading can be expressed in terms of separable angular and radial functions. For both materials, the displacement and strain fields are (a) similar for both mixed-mode loading angles Φ = 30° and Φ = 60° and (b) different from the fields measured for Mode I loading angle Φ = 0°. Relative to the radial distribution, results indicate that the in-plane strain components do not uniformly exhibit the singularity trends implicit in the HRR theory.

Flow towards a guarded sampling probe: Modelling of a 2D flow cell

Analytic and numerical methods are used to predict fluid flow in a thin rectangular sheet of porous material when fluid is extracted through a port at the midpoint of one of the edges of the sheet. The aim is to model (in 2 dimensions) flow towards a sampling probe used to extract reservoir fluids from the rock surrounding a newly-drilled well. Such samples are usually contaminated with drilling fluid filtrate that saturates the rock adjacent to the wellbore, but a guarded probe can eliminate this contamination. Complex variable techniques are used to determine the flow of incompressible fluids when the interface between the two fluids is sharp, and filtrate and original pore fluid have identical viscosities. Results are compared against the predictions of a numerical reservoir simulator, and agreement is reasonable once numerical dispersion has been accounted for. Numerical results are also obtained for the case when the viscosities of the two fluids differ. The results give confidence in the use of 3-dimensional numerical computations to predict flow towards a guarded probe in a real wellbore, and thereby to optimize the design of such probes.

Morphing of curved corrugated shells

Thin sheet materials of low bending stiffness but high membrane stiffness are often corrugated in order to achieve improvements of several orders of magnitude in bending stiffness with only minimal increases in weight and cost. If these corrugated sheets are initially curved along the corrugations, much of this stiffness gain is lost. In return, the sheets are then capable of significant elastic changes in shape overall, including large changes in overall Gaussian curvature. These shape changes are described here by non-linear and coupled kinematical relationships, which are verified against experiment and finite-element simulations. It is found that gross simplifications can be made about the large displacement behaviour of such shells without a loss of accuracy.

The effect of plasticity in crumpling of thin sheets

Crumpling a thin sheet of material into a small volume requires energy for creating a network of deformations such as vertices and ridges. Scaling properties of a single elastic vertex or ridge have been analysed theoretically, and crumpling of a sheet by numerical simulations. Real materials are however elasto-plastic and large local strains induce irreversible plastic deformations. Hence, a numerical model that can be purely elastic or elasto-plastic is introduced. In crumpled elastic sheets, the ridge patterns are found to be similar, independent of the width to thickness (L/h) ratio of the sheet, and the fractal dimension of crumpled sheets is given by scaling properties of the energy and average length of ridges. In crumpled elasto-plastic sheets, such a similarity does not appear as the L/h ratio affects the deformations, and the fractal dimension (Dpl) is thereby reduced. Evidence is also found of Dpl not being universal but dependent on the plastic yield point of the material.

Textiles, Cloth, and Skins: The Problem of Terminology and Relationship

The problem of terminology and relationship is something I first came across when researching cloth and skins in the societies of prehistoric Europe. I wanted to understand the relationship between animal skins, linen and wool textiles, netting and twined cloth, yet I found there was no adequate way of describing these as a group of related materials. I was faced with quite separate books and journals on “cloth” or “textiles” from those on “skins” or “leather.” The content of these publications were usually defined by raw materials, technology or style. Such a separation made it difficult to understand the relationship between these materials at any given time or place. From this problem, I recognized the value of classifying these related materials by their physical similarity and pattern of use. To do this I have used the term cloth-type material to refer to all flexible, thin sheets of material that can be wrapped, folded, and shaped, but excluding materials related through structure, technology or raw material that do not share these qualities. This classification is significant to consider how cloth-type materials have the potential to be used in similar ways, yet through cultural values and choices have distinct roles and values.

Recent developments in local concepts of fatigue assessment of welded joints

Several lately proposed modifications or variants of the structural stress or strain concepts, of the notch stress or strain concepts (also termed ‘local stress or strain concepts’) and of the fracture mechanics concepts of fatigue assessment of welded joints are reviewed, whereas the wider context is presented in a recently republished and actualised standard work. The structural stress concepts described first are based on a linearisation of the stress distribution across the plate thickness or along the anticipated crack path and, alternatively, on the structural stress 1 mm in depth below the weld toe. The structural stress is defined and set against design S– N curves. A further structural stress concept is presented for welded joints in thin-sheet steels and aluminium alloys. Among the elastic notch stress concepts, the variant with the reference notch radius, ρ r = 1 mm, recently verified also for welded joints in aluminium alloys with plate thicknesses t ⩾ 5 mm and the variant with a small-size reference notch radius, ρ r = 0.05 mm, applicable to welded joints in thin-sheet materials, are outlined. The elastic–plastic notch strain concept is applied to a spot-welded tensile-shear specimen starting from a small-size keyhole notch at the nugget edge. The novel notch stress intensity factor (NSIF) approach relating to crack initiation and extrapolated to final fracture of seam-welded joints in steels and in aluminium alloys is reviewed. A more recently developed crack propagation approach for spot welds is finally described.

Tear Strength of Five Elastomeric Impression Materials at Two Setting Times and Two Tearing Rates

PROBLEM/AIMS: Thin sections of impression materials are susceptible to tearing in gingival crevices and interproximal spaces. This study measures the tear strength of six fast and regular set impression materials after different setting times and at different tearing rates. Tear strength specimens were prepared of four addition silicone materials: Aquasil (Dentsply, Konstanz, Germany), Imprint 3 (3M ESPE, Seefeld, Germany), Stand Out (Kerr, Orange, CA, USA), Virtual (Ivoclar Vivadent, Schaan, Liechtenstein); one polyether material: Impregum (3M ESPE); and a new hybrid material: Senn (GC, Aichi, Japan) using a split mold. Specimens were divided into four groups (N = 5). Groups 1 and 2 were immediately removed from the mold and loaded in tension until failure using an Instron testing device (Instron Corp., Canton, MA, USA). Groups 3 and 4 were tested 24 hours after fabrication. Groups 1 and 3 were tested at 1 mm/minute, and groups 2 and 4 were tested at 500 mm/minute. A two-factor analysis of variance (ANOVA) and Tukey's test revealed differences among material brands (alpha = 0.05) in all experimental groups. The polyether and hybrid material were in the lowest statistically significant ranking group for all experimental groups. A three-factor ANOVA determined that a 500 mm/minute tearing rate and a 24-hour set time produced higher tear strengths and that fast set materials produced greater tear strength than regular set materials. Most addition silicone materials provide higher tear strengths than polyether and hybrid materials. Materials display higher tear strengths after longer set times and at faster tearing rates. Impressions should be removed from the mouth with the fastest possible speed. Addition silicone materials should be used in impressions requiring replication of gingival crevices or interproximal spaces to prevent tearing of thin sheets of material. Impressions should be removed from the mouth and separated from the model with the fastest possible speed.

The Nature and Geometry of the Light Echo from SN 2006X

We report on the discovery of the geometry producing the light echo emanating from supernova 2006X, a nearby but underluminous Type Ia supernova (SN Ia) in M100 (=NGC 4321). This offers a rare chance to study the environment of a SN Ia. Contrary to previous reports, there is little evidence of a circumstellar component in the light echo morphology or in the light curve of the unresolved SN point source. Instead, the obvious and dominant echo contribution comes from what is probably a relatively thin sheet of material some 26 pc in front of SN 2006X. Of the four known SN Ia light echoes, three show no evidence of a circumstellar echo and the fourth needs to be confirmed. We consider other evidence for circumstellar material around SN Ia, which may be rare.

Optical Pattern Inspection for Flex PCB — Challenges & Solution

Due to the material properties and technology advancement in printed circuit flex tapes, traditional PCB inspection algorithms using reference image cannot be used. Flex tapes are flexible circuits enabling the design and production of lighter, faster and smaller electronic products. A flex tape is made of flexible polymer film that is laminated onto a thin sheet of conductive material and etched to produce a circuit pattern. The width of fine pitch patterns can be of a few microns. Due to the material characteristics of printed circuit tapes, such as thinness and flexibility, the images captured during inspection are distorted (stretch or shrink, tilt, meandering, etc.). These anomalies and shining tape surface make the possibility of using conventional PCB inspection algorithms using referential methods for pattern inspection, difficult.The goal of pattern inspection is to identify pattern defects — open, short, nick, protrusion, island, pinholes and dust particles. Non-repetitive and non-uniform distortions are some of the main challenges in inspecting these flexible tapes. Some of the other challenges faced during the design of the defect detection algorithm are non-uniform lighting and the gamut of sizes, shapes & orientation of defects as well as features on the printed circuit. Moreover, the algorithms need to take into account the stringent defect tolerance limits followed by the industry.

Mixed-mode fracture of ductile thin-sheet materials under combined in-plane and out-of-plane loading

Mixed-mode fracture of ductile thin-sheet materials under combined in-plane and out-of-plane loading

Three-dimensional digital image correlation to quantify deformation and crack-opening displacement in ductile aluminum under mixed-mode I/III loading

Fractures in ductile thin-sheet structures, such as a fuselage or automobile panels, often occur under complex loading conditions. In particular, under remote mixed-mode I/III loading conditions, a cracked structure is subjected to a combination of in-plane tension and large out-of-plane tearing deformation, which may lead to crack tip fields consisting of all three fracture modes (modes I, II, and III). Understanding such fracture events in ductile materials is an important component of the structural integrity analysis of load-bearing structures containing ductile, thin sheets. Due to the complex nature of mixed-mode I/III fracture in ductile thin-sheet materials, reports of experimental investigations are very limited in the literature. We configure three-dimensional digital image correlation (3D-DIC) systems to acquire full-field deformations during the loading and stable tearing processes. The full-field deformation measurements are used to characterize the stable crack extension behavior of an aluminum alloy undergoing quasistatic and dynamic mixed-mode I/III loading. Results confirm that 3D-DIC is an excellent methodology for measuring 3-D deformations in the presence of large out-of-plane warping and motion, both dynamically and statically. Data obtained during the fracture process indicate that the introduction of a mode III component into the loading process alters the crack tip displacement and strain fields relative to those measured in the nominally mode I loading. Furthermore, the measured crack-opening displacement (COD) values during quasistatic and impact mixed-mode I/III fracture show that (1) COD is nearly constant for crack extension beyond 2 mm and (2) COD under combined-mode I/III loading is four times larger than observed during mixed-mode I/II or mode I fracture of the same material, indicating that the magnitude of the critical COD is a function of loading mode in highly ductile, thin-sheet materials.

The construction of ultimate strain diagrams for textured thin sheet materials taking into account their physical inhomogeneity

The paper presents results obtained in studying the influence of the inhomogeneity of mechanical property distribution over the surface of a thin sheet material on its ultimate strain. An algorithm for constructing ultimate strain diagrams for thin sheet materials is suggested. Data for calculating ultimate strain diagrams were obtained by the impact indentation and acoustic methods.

Imaging inert fluorinated gases in cracks: perhaps in David's ankles

Inspired by the challenge of determining the nature of cracks on the ankles of Michelangelo's statue David, we discovered that one can image SF(6) gas in cracks in marble samples with alacrity. The imaging method produces images of gas with a signal-to-noise ratio (SNR) of 100-250, which is very high for magnetic resonance imaging (MRI) in general, let alone for an image of a gas at thermal equilibrium polarization. To put this unusual SNR in better perspective, we imaged SF(6) in a crack in a marble sample and imaged the lung tissue of a live rat (a more familiar variety of sample to many MRI scientists) using the same pulse sequence, the same size coils and the same MRI system. In both cases, we try to image subvoxel thin sheets of material that should appear bright against a darker background. By choosing imaging parameters appropriate for the different relaxation properties of SF(6) gas versus lung tissue and by choosing voxel sizes appropriate for the different goals of detecting subvoxel cracks on marble versus resolving subvoxel thin sheets of tissue, the SNR for voxels full of material was 220 and 14 for marble and lung, respectively. A major factor is that we chose large voxels to optimize SNR for detecting small cracks and we chose small voxels for resolving lung features at the expense of SNR. Imaging physics will cooperate to provide detection of small cracks on marble, but David's size poses a challenge for magnet designers. For the modest goal of imaging cracks in the left ankle, we desire a magnet with an approximately 32-cm gap and a flux density of approximately 0.36 T that weighs <500 kg.

Variational eigenstrain analysis of residual stresses in a welded plate

We present the formulation for finding the distribution of eigenstrains, i.e. the sources of residual stress, from a set of measurements of residual elastic strain (e.g. by diffraction), or residual stress, or stress redistribution, or distortion. The variational formulation employed seeks to achieve the best agreement between the model prediction and some measured parameters in the sense of a minimum of a functional given by a sum over the entire set of measurements. The advantage of this approach lies in its flexibility: different sets of measurements and information about different components of the stress-strain state can be incorporated. We demonstrate the power of the technique by analysing experimental data for welds in thin sheet of a nickel superalloy aerospace material. Very good agreement can be achieved between the prediction and the measurement results without the necessity of using iterative solution. In practice, complete characterisation of residual stress states is often very difficult, due to limitations of facility access, measurement time or specimen dimensions. Implications of the new technique for experimental analysis are all the more significant, since it allows the reconstruction of the entire stress state from incomplete sets of data.

Development of a heterogeneous microstructurally based finite element model for the prediction of forming limit diagram for sheet material

A heterogeneous finite element model with randomly distributed inhomogeneities has been developed for the determination of the forming limit diagram (FLD) for thin aluminum sheet material based on the prediction of localized necking. The strength difference between the inhomogeneities and the matrix is ascertained either from the fluctuation of the experimental stress-strain curve or from a micromechanical analysis that uses a representative particle field. By changing the specimen geometry and friction conditions, different stress states (or strain paths) are achieved. A plot of the critical Oyane fracture parameter is used to identify the limit strain state. Also, a plot of equivalent plastic strain rate is used to distinguish the boundary of intense shear bands and hence to identify where to take the measurement point. Both a plane stress model and a three-dimensional (3-D) model are adopted to predict the shear banding phenomenon and hence the FLD. The predicted FLD agrees well with the measurements from a recent round robin experimental FLD involving several independent research laboratories. The Taguchi method is applied to assess how the various parameters involved in the heterogeneous model affect the calculated forming limit strain.