Initial Plate Thickness Research Articles

Flattening aluminum plates with tuning asymmetric rolling parameters

The asymmetric rolling (ASR) process can introduce shear strains inside the plate, resulting in the improvements of microstructures and mechanical properties. Its industrial application for rolling the (mid-)thick plates is impeded by the uncontrollable bending behavior. In this study, the influences of rolling parameters on the bending behavior of the rolled AA 7050 aluminum alloy plates were investigated. It is found that the plate will bend towards the slower roll with larger speed ratios and initial plate thickness as well as lower thickness reduction. A flat plate can be obtained by choosing appropriate rolling parameters. The equivalent plastic strain rate distribution is considered to be critical to the plate bending, the downward bending (towards faster roll) would be associated with an obvious increase of the equivalent plastic strain rate at the top surface of the plate near the end of the deformation zone. Multi-pass asymmetric rolling routes considering bending optimization were proposed and verified through rolling trials. As the speed ratio increased from 1.1 to 1.2, the through-thickness plastic strain became more homogeneous and the total rolling pass numbers decreased by 33 % (from 9 passes to 6 passes).

Synergistic strengthening mechanism of gradient structure AZ31 magnesium alloy plate in hard plate rolling

Compared with homogeneous structural materials, gradient structural materials are easier to realize the strength-ductility optimization. Research on the strengthening mechanism of different gradient structure materials is a meaningful way to broaden the application of gradient structure materials. In this paper, the AZ31 magnesium alloy plate was rolled by hard plate rolling. The gradient structure was controlled by changing the initial plate thickness. When the initial plate thickness was 4 ​mm, AZ31 magnesium alloy shows excellent strength and ductility, the tensile strength was 282.2 ​MPa, and the ductility was 28.4 ​%. The change of the initial plate thickness changes the stress state which forming a gradient structure with different characteristic layers. The extra strengthening between different characteristic layers improves the properties of gradient structure, which makes the magnesium alloy change from a uniaxial stress state to a multi-axial stress state during the tensile process. The increase of the characteristic layer induces more geometrically necessary dislocation accumulation, improving the gradient structure's strength and ductility. This research provides a new design strategy for the forming and performance optimization of gradient structure magnesium alloy plate by hard plate rolling, which has good industrial production and application potential.

Birefringent phase masks for laser beams shaping during laser material processing at imaging plane

We present phase masks (PMs) made from birefringent CaCO3 crystal plates to create laser beams at an imaging plane with given shapes and intensity distributions close to flat-top distributions. The principle of PMs is based on creating the phase shift of π or 2π (depending on the initial plate thickness) in linearly polarized radiation passing through etched areas with given shapes. The phase shift in these areas is converted into the intensity distribution at an analyzer output, which can be projected with a demagnification by a high-quality lens into its imaging plane aligned with a microprocessing plane or target. In this research, we provide theoretical discussion of choosing PM configurations. PMs with the square and quadrating square shapes (such configurations are in demand in laser microprocessing and molecular optics) were fabricated by laser-induced microplasma and successfully tested in the experimental setup with a pulsed laser (with a wavelength of 1.06 μm and pulse duration of 120 ns). PMs were also used in this experimental setup for laser ablation of polished steel samples. Contours of footprints on samples were well matched with formed beam shapes.

An investigation of strength degradation due to thickness plate reduction on Ferry Ro-Ro Ship’s Hull

Old ships will experience a degradation of the structural strength after receiving repeated loads. Decreased strength performance is also caused by structure shape and structural dimensions changes. In steel ships, Dimensional changes will be discovered when the ship is docked, because the material undergo corrosion causing in thinning the shell plate. In this study, a thickness reduction of the shell plate has been simulated to determine the longitudinal response of the ship’s structure. A Finite element analysis of ferry Ro-Ro ship’s hull was carried out using ANSYS package program. The simulation was carried out to exceed the allowable limit for reducing the thickness plate by the Indonesian Classification Bureau (BKI), which is 20% of the initial plate thickness. Based on simulation result, it was found that an increase of stress at each variation of the reduction in hull plate thickness in hogging and sagging conditions.

Springback Analysis of the Stiffened Panel Milling from the Bent Plate

An analytical method considering the redistribution of residual stress in the bent plate is proposed to predict the springback of the stiffened panel when milling the panel layer by layer. Two types of stiffened panel, namely, a panel with crosswise stiffeners and a panel with lengthwise stiffeners, were selected as examples and were analyzed during the removal of each layer. Moreover, a finite-element simulation of the milling process was conducted to make comparisons with the analytical results, which demonstrates similar stress distribution and springback values. The maximum stress variation and springback value appeared when the milling depth reached the initial neutral surface. When the plate thickness decreased, the errors between analytical results and FEM results increased, and the lengthwise-stiffened panel was less affected by errors than the crosswise-stiffened panel because of a larger moment of inertia. The effects of different milling thicknesses per layer, initial plate thickness, and bending radius were also analyzed. Moreover, the milling experiment was performed to make verification. The results suggest that the analytical method can predict the springback of the stiffened panel effectively. The proposed method can also be applied to other similar forming conditions.

The forming simulation of flexible glass with silt down draw method

The slit down draw method is the main manufacturing process of flexible glass. In this study, Flow3DTM software was used to simulate the process of drawing and thinning glass slits during the slit down draw process. The influence of glass viscosity, initial plate thickness and initial plate speed on the glass spreading process was studied. The maximum pull-down force that the root can bear is linearly proportional to the viscosity, the initial thickness of 1.3837 power and the initial plate speed, respectively. The best way to improve the tensile strength of flexible glass is to increase the viscosity. Flexible glass was more easily to obtain with low viscosity, low thickness and low drawing speed.

Upper bound analysis of a shape-dependent criterion for closing central rectangular defects during hot rolling

• A shape-dependent closure criterion for closing central defects during hot plate rolling is proposed. • The decrease in initial plate thickness or the increases in relative reduction and in roller radius are in favor of defect closure. • A defect tends to be closed well if the actual shape factor reaches or exceeds the corresponding critical shape factor. • A flatter defect with larger value of aspect ratio can be closed much easier. A triangular velocity field for central defect closure is proposed in this paper. With the proposed velocity field, the minimum upper bound power is calculated. Then, the stress state coefficient as a function of defect thickness δ and aspect ratio η is obtained by the upper bound theorem. By applying the limit condition of the stress state coefficient with respect to defect size and letting the defect size be zero, the analytical solution of critical shape factor depending on aspect ratio solely is derived from a quadratic equation. Ultimately, a shape-dependent criterion for closing rectangular defects during hot rolling is established by relating the derived critical shape factor to the actual one. It is shown that as the aspect ratio increases, the critical defect size decreases and the applied energy required for closing central defects increases. The increases in relative reduction and roller radius or the decrease in initial plate thickness are in favor of defect closure. Validation of the present result with available simulation result and a current rolling schedule shows that the present analytical criterion matches well with the simulation result and can be used for optimizing rolling parameters to close central defects. Experimental research in laboratory shows that a defect can be closed well if the actual shape factor reaches or exceeds the corresponding critical shape factor.

A dynamic closure criterion for central defects in heavy plate during hot rolling

A new continuous velocity field used to analyze central defect closure for heavy plate rolling is proposed by modifying a two-dimensional velocity field. By using the proposed velocity field and mean yield criterion (or called MY criterion for short), the internal deformation energy rate is obtained. With co-line vector inner-product method, the frictional energy rate is then integrated. Ultimately, an analytical solution of the rolling torque and rolling force is obtained by minimizing the total energy rate with respect to neutral angle. Based on the assumption that when a central defect tends to be closed the stress state coefficient will obtain its critical value, a mathematical expression of critical shape factor together with a dynamic closure criterion for rectangular shape defects are derived. It is found that the critical shape factor is a function of initial plate thickness, relative reduction, work roll radius, and friction factor. The effects of independent rolling parameters such as plate thickness, relative reduction, work roll radius, and friction factor on the critical shape factor are discussed systematically. The results show that the increases in relative reduction, work roll radius and friction factor benefit defect closure, while a large value of initial plate thickness induces central burst formation. In addition, the proposed criterion is validated by comparison with available theoretical results and very good agreement is found.

Research on the Hole Shape Distortions Near the Bending Plastic Deformation Area

In this paper, a research work on the hole shape distortion of commercial-purity aluminum plates in the bending process was carried out. The bending process was simulated by using ABAQUS software in order to reveal the phenomenon and law of hole shape distortions near deformation area. A series of bending tests were conducted for the comparison of simulation results. By measuring the hole diameter under different conditions, the factors that affect distortion level were obtained, including hole distance and initial plate thickness. The rationality of this distortion law was proved by finite element simulation. This research provided the plate with a hole of theoretical basis for bending process selection of the most suitable process parameters.

Effect of rolling parameters on plate curvature during snake rolling

In order to predict the plate curvature during snake rolling, FE model was constructed based on plane strain assumption. The accuracy of the FE model was verified by the comparison between the plate curvature conducted by FE model and experiment respectively. By using FE model, the effect of offset distance, speed ratio, reduction, roll radius and initial plate thickness on the plate curvature during snake rolling was investigated. The experimental results show that, a proper offsetting distance can efficiently decrease plate curvature, however an excessive offsetting distance will increase plate curvature. A larger speed ratio, reduction will cause a large plate curvature, however a larger roll radius has effect to reduce plate curvature. Plate which undergoes a larger reduction and plate with a larger initial thickness always need a larger offset distance to keep the plate the minimum plate curvature, but for a larger roll radius a smaller offset distance is needed.

Pressure Welding of Thin Sheet Metals: Experimental Investigations and Analytical Modeling

Emerging applications, such as fuel cell, fuel processor, heat exchanger, microreactors, etc., require joining of thin metallic plates in confined places with small dimensions and minimal damage to the surrounding areas. In this study, the feasibility and modeling of pressure welding (solid state bonding) process are investigated, specifically for bonding of thin sheet metals. The effects of material type (e.g., copper, nickel, and stainless steel) and initial plate thickness (51–254 μm) as well as process conditions (e.g., welding pressure and temperature, 25–300°C) on the minimum welding pressure and the final bond strength are experimentally studied. A pressure welding apparatus was developed for testing of different materials and process conditions. Based on the experimental results, the effects of material and process conditions on the final bond quality are characterized. At room temperature, copper and nickel blanks were successfully bonded, while stainless steel blanks could only be joined at elevated temperature levels (150°C and 300°C). The material type (i.e., strength) and thickness were shown to have significant impact on the welding pressure; in that more pressure is required to bond the blanks with higher strength or thinner. To reduce the required welding pressure, the process can be carried out at elevated temperature levels. In this study, the bond strength of the welded blanks was characterized with uniaxial testing. The tensile test results showed that the bond strength could be increased by increasing the welding pressure or temperature. However, the increase in bond strength by increasing the welding pressure was shown to have an optimal point, after which the bond strength would decrease with further increase in pressure. This critical pressure value was found to be dependent on the material and process conditions. In addition, bond formation mechanisms for different materials were studied through microscopic analyses. The microscopy images of the weld spots showed that for a successful bonding to take place, the contaminant layers at the surfaces must be removed or broken to allow the virgin metal underneath to be extruded through. The metallic bonds only form at these locations where both surfaces are free of contaminant layers. Finally, a model for bond strength prediction in pressure welding was developed and validated. This model includes the sheet thickness parameter, which is shown to be a critical factor in bonding thin sheet metals with the sheet thickness in the range of a few hundred micrometers.

S0301-3-3 α黄銅超微細結晶粒材の創成とその疲労強度(疲労き裂進展と疲労強度)

Ultra-fine grain α-brass (UFG brass) thin plates were made by repletion of rolling and heat-treatment. The thickness and the grain size of the plates were 0.1 mm and 10 μm for the plate with the initial thickness of 6 mm, and those were 0.120 mm and 1.5 μm for the initial plate thickness of 3 mm, respectively. The fatigue tests were conducting using an electro-hydraulic testing machine with the loading frequency of 30 Hz and the stress ratio of -1 at room temperature. The tensile strength and the 0.2% proof stress of the UFG brass was twice and five times higher than those of normal grain size a-brass (NG brass), respectively, while the elongation of the UFG brass was 1/3 of the NG brass. The fatigue strength of the UFG brass was scarcely higher than that of the NG brass. In the UFG brass, fatigue cracks usually initiated from pits those were formed during electro-chemical polishing process although they were initiated from slip bands for the NG brass. It indicates that the fatigue strength of the UFG brass is very sensitive to defects. Except for the fatigue strength of the UFG brass, the strengths linearly increased with increasing of the inverse of the square root of the grain size (Hall-Petch relationship). Although the tensile strengths were lower for thinner plates, the 0.2% proof stress and the fatigue strength for 10^7 cycles were almost independent of the thickness.

Energy absorption and ductile failure in metal sheets under lateral indentation by a sphere

This paper is concerned with the mechanics of lateral indentation of a rigid sphere into a thin, ductile metal plate. The paper presents a study including experiments, analytical theories and finite element calculations. The focus is on the prediction plate failure and on the energy absorption up to this point. Load–displacement curves from experiments are presented for various plate geometries (circular, square, rectangular), indentor radii and locations of loading on the plate. The experiments show that the penetration to ductile fracture and the energy absorption is sensitive to both plate geometry, loading position and indentor geometry. The plate fails by localised necking followed closely by material fracture. Analytical theories are derived for the load–displacement behaviour of a plastic membrane up to failure. The point of plate failure is determined by a global stability criterion taking into account both the change of geometric and material stiffness during the indentation process. For the cases of axis-symmetric loading very good agreement between measured and theoretical load–displacement curves up to — and including — the point of initial plate failure is found. Curve fitting to the theoretical solutions produced the following expressions for the penetration and absorbed energy up to plate failure: δ f =1.41n 0.33R 0.48R b 0.52, E= πC 0t 0RR b 0.318 R b R 0.607−0.387R b/R+1.20(R b/R) 2 +0.067(n−0.2) where C 0 and n are the strength coefficient and the hardening exponent in the material power law, t 0 is the initial plate thickness, R b is the indentor radius and R is the plate radius. The tests were also modelled by the use of a commercially available finite element program. It is shown that the applied finite element method can accurately predict the response up to necking and fracture initiation for both symmetric and non-symmetric loading.

Analysis of the bending of the rolling material in asymmetrical sheet rolling

In asymmetric rolling the workpiece is often bent to an unexpected shape. Its curvature may be caused by a speed difference, by a lubrication mismatch or a radius difference of the work rolls, and depends on various rolling parameters, such as the ratio of the peripheral velocities of the upper roll and the lower roll, reduction ratio, average radius of the work rolls, initial plate thickness and friction between the rolls and the workpiece. A finite element simulation, which shows the influence of different diameters of the working rolls and of the degree of reduction on the bending of the workpiece, has been performed.

Necking in plane strain under bending with constant tension

A s part of a study of failure of plates at built-in supports, modes of plane strain failure under increasing bending with constant tension are calculated for an elastic, power-law plastic material with kinematic hardening. Under increasing bending, the moment reaches a maximum when the bending curvature (normalized by the initial plate thickness) is approximately twice the strain-hardening exponent. At the maximum moment, different boundary conditions result in different failures. Under applied bending moment, rotational instability occurs. Under applied bending angle, stable localized kinking occurs. Kinking leads to high curvatures and then tensile necking. Large further applied bending curvature gives tensile necking. For example, with a strain-hardening exponent of n = 0.1 and a constant tensile force of 90% of that for necking under pure tension, a bending curvature of 0.865 (normalized by the initial plate thickness) is required for tensile instability. For most practical cases (that is, for the radius of curvature greater than the order of thickness), bending decreases the tensile necking force by 7–17% for a strain-hardening exponent of n = 0.2–0.05. Reversal before reaching the maximum moment requires almost the same curvature change to reach a maximum moment as for monotonic loading.

Pressure Distribution in Plate Rolling

When analysing the stress distribution in the tool/workpiece interface in plate rolling, it is conventional to assume either Amontons friction law, τ = μp, or full stiction τ = k. Neither of these two laws are, however, generally valid. This paper presents an analysis by the slab method using a general friction model developed by Wanheim and Bay. The differential equation describing the pressure distribution in the roll gap is numerically solved on a computer using a fourth order Runge-Kutta method. Pressure and friction stress distributions as well as total load and torque are thereby estimated as functions of roll radius, initial plate thickness, reduction, friction factor, front tension, back tension and material stress strain hardening characteristic. Roll flattening is also taken into account. The results are in good accordance with experiments estimating the pressure distribution when rolling model material and load and torque when rolling aluminium. Especially the good torque predictions should be noticed since earlier analysis have failed at this point.

Diffusion during Deformation by Surface Intensity Methods

Equations are derived for the surface activity of a diffusion specimen for two cases: In the thin plate case (plane source at the origin of a semi-infinite slab), an analytical solution is obtained for a statically annealed sample and for a sample annealed during simultaneous deformation (either compression or tension normal to the free surface). In the thick plate case, solutions for similar situations are obtained (under proper experimental conditions) in the form of a definite integral convenient for evaluation on an automatic digital computer. Specific cases are shown (using nickel) to illustrate the range in which the thin- and thick-plate solutions are valid. When surface intensity methods are used with a plate sufficiently thick that considerable absorption takes place before diffusion, it is necessary to know precisely the initial plate thickness. This is true regardless of the diffusion time; this is not necessary when the sectioning method is used (with sufficiently long diffusion times). A discussion of a surface intensity experiment by Wazzan is given to illustrate this point.