Elastic Springback Research Articles

Determination of springback gradient in the die on compacted polymer powders during high-velocity compaction

A uniaxial high-velocity compaction process for polymer powder using a cylindrical, hardened steel die and a new technique with relaxation assist was tested with various heights. The influences of the relaxation assist device on the process characteristics are discussed. Two bonded strain gauges and a high-speed video camera system were used to investigate the springback phenomenon during the compaction process. It was found that the relaxation assist improves the compaction of the polymer powder by locking the powder bed in the compacted form. It is shown that the high-velocity compaction process is an interruption process and that the delay times between the pressure waves can be reduced by increasing the height of the relaxation assist device. The delay times between the pressure waves are also strongly dependent on the strain rate. If the height of the relaxation assist device is increased, the first gross instantaneous springback, and the total elastic springback, are reduced. In addition, the density of the powder bed is increased. The relative times of the compacting stage, decompacting stage and the reorganisation of the particles can be also controlled by altering the height of the relaxation assist.

Transient Simulation of Electromagnetic Forming of Aluminium Tubes

The recent push to use more aluminium in automobiles has stimulated interest in understanding electromagnetic forming (EMF), which uses induced electromagnetic fields to generate high strain rates during the forming process. The high strain rates increase the formability of aluminum materials and might reduce elastic spring-back and wrinkling of the workpiece. Primary emphasis is placed on including of all relevant physical phenomena, which govern the process, as well as their numerical representation by means of simplified electrical equivalent circuits for the EMF machine and fully coupled field approach of the transient electromagnetic and mechanical phenomena. Moreover, the thermal effects due to Joule heating by eddy currents and plastic work are considered. The numerical model predicts the electromagnetic field, temperature, stress, and deformation properties that occur during the forming process. The numerical results of the tube deformation are compared with available experimental data.

Compensation of elastic strains in the determination of plastic strain ratio ( R) in sheet metals

Plastic strain ratios of AA8011 aluminum alloy and commercially pure titanium sheet with, respectively, low and high elastic spring-back were determined by digital imaging of marked tensile specimens with and without considering elastic strains. To calculate the actual R-values, a new method was proposed for the compensation of elastic strains. The essential feature in the approach proposed consists of defining elastic strains with respect to gage length before unloading. Comparison with experimental data shows that the new method is generally more accurate than the existing ones, especially in the cases where materials with very high elastic spring-back, such as titanium, are concerned. The results were discussed on the basis of elastic and yield behavior of the materials.

Molecular dynamics simulation of the effect of tool edge radius on cutting forces and cutting region in nanoscale ductile cutting of silicon

Unlike in conventional cutting processes, where the undeformed chip thickness is significant compared to the cutting tool edge radius, in nanoscale cutting processes, the undeformed chip thickness is very small, on the nanoscales. Therefore, the tool edge radius can not been ignored. It has been found that there is a brittle-ductile transition in cutting of brittle materials when the cutting tool edge radius is reduced to nanoscale and the undeformed chip thickness is smaller than the tool edge radius. In order to better understand the mechanism of the transition, a molecular dynamics (MD) method, which is different from continuous linear mechanics, is employed to model and simulate the nanoscale ductile mode cutting process of monocrystalline silicon wafer. The simulated variation of the cutting forces with the tool cutting edge radius is compared with the results of the cutting force from experimental cutting tests and they show a good agreement. In the simulated results, it can be seen that the thrust force is much larger than the cutting force in cutting. The simulated results also denote that the resultant force in the cutting process is not uniformly distributed along the cutting tool edge. In the simulation, the elastic springback of small thickness is observed on the machined workpiece surface.

Influence of some relevant process parameters on the dimensional accuracy in incremental forming: a numerical and experimental investigation

As known, incremental forming is a flexible and innovative sheet metal forming process which allows complex shape shells forming without the need for any die.For these reasons, incremental forming is nowadays suggested for rapid prototyping and customised products.The present paper is focused on material formability in incremental forming and, in particular, on the evaluation and compensation of elastic springback. The latter significantly modifies the imposed shape.For this purpose, a deeper assessment of the process was developed following three different approaches. First of all, a wide experimental investigation on the influence of some relevant process parameters was developed. At the same time, an explicit FEM analysis of incremental forming process was carried out in order to verify its effectiveness and, as a consequence, its ability to be used as a design tool. Furthermore, the obtained parts were analysed by a reverse engineering technique and the measured geometry was numerically compared with the desired one, with the aim to quantify the geometrical discrepancies.In this way, an integrated numerical/experimental procedure is proposed in order to limit the shape defects between the obtained geometry and the desired one.

Elastic strain at semi-isostatic compression of Scots pine (Pinus sylvestris)

Quarter-sawn and plain-sawn specimens of Scots pine were semi-isostatically compressed at 5, 15, 50, and 140 MPa in a Quintus press. Elastic strain was measured using a telescope device that was pushed together when wood was compressed and remained in this position at release of pressure. Delayed elastic and plastic strains were assessed through repeated callipering during 5 years after densification. At 140 MPa, wood reached an almost compact structure (ρ ≈ 1450 kg/m3) but as a result of elastic springback the density decreased to just below 1000 kg/m3. At 140 MPa, the elastic and delayed elastic strains were 14.6% and 1.8%, respectively, in quarter-sawn specimens, and were 13.1% and 0.8%, respectively, in plain-sawn specimens. The higher elastic strains in quarter-sawn specimens can be attributed to elastic springback in the tangentially deformed latewood bands.

The effect of statistical variability in material properties on springback

A major concern with manufacturing processes using metals is the accurate prediction of the response of the material to complex forming operations that shape a blank into a component. One of the more difficult problems is springback, which is the tendency of a metal to not maintain the desired shape after the forming process is terminated. Springback is more pronounced in high-strength steel and aluminium alloys than other metals. Unless springback is accurately estimated, manufactured parts may deviate excessively from the design specifications. The purpose of this paper is to use mechanistically based probability modelling to accurately estimate variability in the dimensions of a component and the adherence to design tolerances. It is assumed that the variability in the component dimensions is due to randomness in the material properties that directly affect the magnitude of the springback. The yield stress is the primary source of randomness and is most critical in the springback prediction. In order to assess the effects of variability, a simple model for elastic springback in a straight rectangular bar bent around a circular mandrel is considered. Explicit computations are made for a commercially available aluminium alloy for which material properties are readily available. The stress–strain behaviour of the alloy is assumed to be bilinear. The effects of the stress–strain behaviour, the model parameters, and the statistical variability in material properties on springback are assessed.

Nano-precision measurement of diamond tool edge radius for wafer fabrication

In this paper, a non-destructive nano-precision measurement method for diamond tool cutting edge radius is presented. The basis of the method is that the profile of a tool cutting edge can be copied by indenting the tool cutting edge into the surface of a selected material, and that the copy of the profile can be measured at nano-precision level using AFM. The selected material elastic error compensation coefficient has to be determined to cancel out the effect of elastic spring-back. Copper was selected as the indentation piece material due to its (1) high rigidity and high density, (2) large Young’s modulus and (3) low yield strength. The elastic error compensation coefficient for the copper material is determined through the indentation of a tungsten carbide tool edge on the copper surface. By comparing the actual tool edge radius measured using scanning electron microscope (SEM) on the sectional view of the tungsten carbide tool with the one measured from the copied profile of the tool edge on the copper surface, the coefficient is obtained. Three diamond tool edge radii were obtained using the proposed method. Analysis is given for the accuracy of the proposed method, showing that as far as the error elastic compensation coefficient is consistent with the copper material used, the only source of errors with the measurement will come from the device for measuring the indented profile on the surface.

Finite element simulation of cold isostatic pressing and sintering of SiC components

Finite element simulations were performed for cold isostatic pressing of SiC powder. To describe the compaction behaviour, the Drucker–Prager–Cap model implemented in ABAQUS/Explicit® computer program was applied. The influence of friction between powder and steel core as well as rubber bag on the density distribution was investigated for compacts with cylindrical and helical cores. Simulations with and without rubber bags were made showing that the effect of the bag on the density distribution is fairly small, at least for thin bags. Due to the presence of the steel core, density gradients develop during compaction, although the outer pressure is hydrostatic. The predicted density variation is consistent with experimental results. After the pressing cycle it may be difficult to remove the helical steel core from the powder compact. The simulation shows that the elastic spring-back leads to residual stresses which may reach the green strength of the powder compact, so that the part may crack during the unloading or removal of the helical core. Investigations of the sintering behaviour predict small shape distortions due to the slightly inhomogeneous density distribution of the green body. However, the differences between the ideal geometry and the predicted outline after sintering are small.

Vibration of Flex Circuits in Hard Disk Drives

A flex circuit connects the stationary electronic components in a hard disk drive to the rotating arm that carries the read/write heads and positions them above data tracks on the disk. Flex circuits are conventionally formed as a laminate of polyimide substrate, adhesive, and copper conductors. Deformation of a flex circuit is discussed in the context of the following stages: the initial unstressed shape, configurations in which stresses set and relax in response to elevated temperature, equilibrium, and small amplitude vibration. The model involves displacements of the flex circuit in the directions tangent and normal to the local equilibrium shape, and those motions couple with the arm’s dynamics. Nonlinearity associated with finite curvature, partial elastic springback, and the arm’s geometry and inertia properties are incorporated within the vibration model to predict system-level natural frequencies, mode shapes, and coupling factors between the circuit and the arm. Laboratory measurements using noncontact laser interferometry validate the model with respect to the circuit’s shape, stiffness, restoring moment, and natural frequencies. The primary degrees of freedom for optimizing flex circuit design are the thicknesses of the individual layers within the circuit, free length, and the locations and slopes of the circuit’s attachment points to the arm and electronics block. The model’s predictions and trends developed from a case study in free length are discussed with a view toward reducing coupling between the circuit and arm in certain vibration modes.

Prediction of residual stresses and springback after bending of a textured aluminium plate

In this work, we attempt to simulate residual stresses and springback of a deformed metal part based on a micro-macro modelling of the elastic and plastic strains. Samples cut out of an aluminium plate, under different angles relative to the rolling direction, have been bent around a die. The springback angle has been measured in order to estimate the accuracy of numerical simulations. To start, a finite element code with an isotropic material law is applied, showing that most plate sections deform under the action of a pure bending moment (i.e. shear forces are negligible). Using this result, the effect of texture on the elastic springback is simulated with a polycrystalline elastic-plastic theory. Here, the stress state is computed for different layers across the plate under the hypothesis of a homogeneously deforming polycrystal. Unloading is simulated subsequently by reducing the bending moment down to zero. The predictions are compared to the experimental results and the stress profile across the plate thickness is analysed during loading and after unloading. In the discussion, attention is paid to the effects of anisotropy and the relevance of implementing polycrystalline elasto-plasticity into finite element modelling.

On the measurement of the plasticity length scale parameter in LIGA nickel foils

This paper presents measurements of the plasticity length scale for polycrystalline LIGA nickel foils produced by electroplating in a sulfamate bath. The micro-bend test method developed by Stölken and Evans [Acta Mater. 46 (1998) 5109] is used to obtain a composite length scale parameter, l c that is primarily associated with rotational gradients. The micro-bend test utilizes the measurement of the curvature change associated with elastic spring-back of bent micro-beams in the extraction of a composite length scale parameter, l c. The length scale is measured to be ∼5.6 μm for foils between 25 and 175 μm thick. This is in the range (3–5 μm) reported from prior micro-bend experiments on nickel foils (loc. cit.). The measured length scale is also similar to values reported previously for polycrystalline copper wires using torsion tests in which rotation gradients dominate.

Tools of Change

This article discusses reconfigurable forming dies that increases the efficiency of small-lot production. Manufacturers have long desired single universal tools that could make many different shapes. Patents for reconfigurable “discrete-die” tooling—dies composed of movable elements such as pins or plates—date back nearly to the inception of the patent office. In forming large sheet metal parts, elastic springback can cause unacceptable part shape errors if the part is formed on a tool whose shape mirrors that of the finished part. Two approaches to tool shape correction have been developed for use with the reconfigurable tool. In one, an iterative technique calculates the correct die shape based on two initial guesses. In the other, a predictive technique uses finite element analysis to model and correct for elastic springback. Cost and benefit analysis has shown the attractiveness of reconfigurable tooling based on the initial investment alone. An even greater benefit could be realized through lowered assembly costs and shortened turnaround time for small production lots. Small-lot production shops are likely to profit by replacing fixed-shape forming tools with reconfigurable tools.

Design Optimization of Springback in a Deepdrawing Process

The design optimization of springback in a deepdrawing process is proposed to control the e nal shape of the workpiece. The manufacturing process design problem is formulated to minimize the difference between the shape of the desired workpiece geometry and the e nal analysis result after elastic springback. The rigid die shape and the workpiece thickness are treated as design variables. A nonlinear structural problem that includes e nitedeformation elastoplasticity withfrictional contactissolved usinga mesh-freemethod in which thestructural domain is discretized by a set of particles. Continuum-based design sensitivity analysis is carried out to obtain gradient information for the optimization efe ciently. The accuracy of the sensitivity result is compared with the e nite difference result with excellent agreement. The optimum deepdrawing process signie cantly improves the quality of the e nal product. ESPITE signie cant simulation and design capability developments in modern technology, gaps still remain between the simulation-based design and the manufacturing process itself. One major reason for these gaps is the lack of efe cient and accurate numerical methods in the design process. First, accurate numerical methods have to be used to simulate manufacturing processes, and these methods must take into account large deformations, complicated constitutive relations, and a sliding contact between workpiece and die. Second, efe cient numerical methods have to be used to make the deepdrawing optimization process practical. It is the purpose of this paper to demonstrate that these two obstacles can be resolved by using accurate numerical methods and an efe cient design sensitivity analysis (DSA). The deepdrawingprocessinvolvesa large degree ofplastic deformation and rigid-body rotations, as well as a complicated contact between workpiece and die. Many simplie ed approaches have been proposedinsimulationanddesignofthemetalformingprocess.One

Improving the Forming Characteristics of Aluminium Sheets for Aerospace Applications

The first part of this paper recalls the metallurgical principles applied to develop a new « high formability » 2024 alloy. The properties of this alloy are compared to those of standard 2024, in W and T351 tempers. « High formability » 2024 clearly displays a better formability. Secondly, the paper describes a series of experiments and calculations regarding elastic springback of various aluminium alloys after simple bending and stretch-bending. The modelling shows very good agreement with the experimental results.

Reliability-based analysis of a stretch-bending process for aluminium extrusions

The paper presents reliability analyses of a plastic forming process. Stretch-bending of extruded aluminium square hollow sections was studied through finite element analysis. The profiles were axially fixed and given a specified curvature by means of a bending die. Important response parameters in stretch-bending of extruded profiles are flange sagging and elastic springback. The sensitivity of the predicted response parameters was investigated with respect to variations in the material properties of the aluminium alloy, i.e. yield stress, strain hardening and plastic anisotropy. The material parameters were modelled as random variables with given statistical properties. The probability of the response parameters staying within specified limits could then be calculated by means of response surface methods and FORM/SORM. Finally, the consequences of the specified response limits on allowable variations of the material properties were established. The paper shows how reliability-based methods can be used to establish relations between the variation of model parameters (e.g. material properties, cross-sectional geometry and process parameters) and the resulting variation of characteristic response parameters for a given forming process.

The evaluation of springback in 3D stamping and coining processes

An effective predictive technique of the elastic springback in a fully 3D 90° V-punch V-die bending process is presented. This is based on a combined approach in which an explicit finite element code was used to simulate the loading phase of the process whilst an implicit procedure was used to analyse the springback phase. Two different punches with a nose radius of 4 and 8 mm were used. An increase in the springback ratio with the coining load was observed with the lower nose radius. Conversely, an increase in the springback ratio with the coining load up to a peak value (>1), corresponding to a force of about 20 kN, followed by a decrease in the springback ratio with increasing the coining load, was observed for the larger punch nose radius. This ‘negative springback', namely, the increase in the bend angle after unloading, for coining loads higher than about 13 kN, takes place because during coining the bend angle under loading is higher than the desired one. Therefore, in the final stage of the coining, the sheet blank is unbent and after unloading undergoes an inward springback. The comparison between the finite element method (FEM) results and experimental data obtained by laboratory tests carried out under similar conditions shows an excellent agreement.

Control of the Fabrication of Long Slender Workpieces of Arbitrary Shape—Part I: Open-Loop Control of the Multi-Axis Bending Process

Computer numerically controlled (CNC) multi-axis bending is a new metal-forming process used to fabricate long slender workpieces of arbitrary shape and cross section. This process can achieve higher productivity and flexibility than conventional forming processes. However, a manual trial-and-error process has been adopted to find control commands that would produce accurate part shape in mass production. This traditional approach which completely relies on the skills of the machine operator often results in long lead-times and great cost in setting up the bender for a new part. A new methodology has been developed, using the geometrical concept of intrinsic part representation, to model the workpiece and fabricating process. The process model compensates for elastic and fabricating process. The process model compensates for elastic springback, and can be used to predict a set of initial multi-axis control commands which will eventually converge to the final commands through a feedback process. The effectiveness of the method has been demonstrated experimentally.

Computer aided engineering of the sheet bending process

The effects of the punch nose radius and sheet thickness on the elastic springback and residual stresses in the 90° V-punch and U-die bending process of AA 5083 aluminium alloy have been extensively studied by numerical simulations based on the finite element method. The results show that, irrespective of the sheet thickness and punch stroke, the springback ratio is not affected by the punch nose radius. Such results are in excellent agreement with the experimental ones obtained in similar conditions. As far as punch nose radius effects on the residual stresses are considered, significant differences were observed between residual stresses predicted with different nose radii. In particular, the shifting of the neutral layer and increase in the magnitude of the residual stresses predicted by the FEM code were found with decreasing punch nose radius.

Local flange buckling and its relation to elastic springback in forming of aluminium extrusions

This paper presents a numerical and experimental investigation of interactions between local buckling and elastic springback in forming of thin-walled aluminium extrusions. The cross sectional distortions that are present in typical aluminium sections prior to elastic unloading cannot be disregarded. This is the case even when these beams are bent with relative large radii. The numerical analyses presented herein have shown that both element type and formulation have to be chosen carefully in order to correctly predict elastic recovery. Full integration tri-linear brick elements in combination with the assumed strain formulation have proven to be preferable to linear thick-shell, conventional full integration brick elements as well as reduced integration elements.