Elastic Springback Research Articles

Application of numerical simulation in the bending of aluminium-alloy profiles

This paper deals with 3D elasto-plastic finite-element analyses of the production bending of aluminium extrusions. The overall objective of the study is to determine the applicability of using the general purpose software MARC K5.2 in analysing industrial rotary draw bending and stretch bending. The main focus is placed on the effects of material behaviour, slenderness of cross-sectional members, and die geometry on geometrical tolerances. The influence of applying external pre-stretching and internal support for obtaining better tolerances is demonstrated also. The results have been validated by a number of tests carried out in the laboratory and using industrial bending machines. The results show that wrinkles and sagging, or ‘suck-in’ of the flanges, can be eliminated by applying a stationary internal mandrel in combination with an internal web, even with tight radii. Furthermore, external pre-stretching is shown to be advantageous in order to reduce local buckling and spring-back. It has been found that the thickness variation expected after extrusion is of the same importance as anisotropy with respect to sagging in stretch bending. Elastic spring-back is influenced by the strain-hardening characteristic and the amount of axial loading applied, both decreased strain hardening and increased tension ensuring reduced spring-back. The experimental and numerical results appear to be in excellent agreement, indicating that extrapolation of the results to cases, other than those tested, may be possible. It is concluded that finite-element analysis has proven to be a well-suited numerical tool for design and product optimisation in industrial bending.

The behaviour of thin-walled, aluminium alloy profiles in rotary draw bending—A comparison between numerical and experimental results

This paper deals with elasto-plastic finite element (FE) analysis of a rotary draw bending process using eight-node brick elements and contact elements. The objective of the study is to determine the applicability of using numerical simulation to predict bendability and elastic springback in industrial bending. Particular attention is paid to studying the effects of die radius and interface friction on flange sagging and springback. The computations have been validated by experiments conducted in a standard rotary draw bending machine. Single and double chambered cross-sectional shapes in alloy AA6063 were bent into different radii, with and without use of internal mandrels. The results show that by applying models that give an accurate description of material strain-hardening and interface friction, the simulated behaviour coincides well with the experimental behaviour. It is concluded that FE analysis has been used successfully to reproduce experimental results. The simulations appeared to be extremely time-consuming, even on a Cray Y-MP supercomputer, but in the near future it is to be expected that simulations are to be regularly used for die design and optimization purposes of bent aluminium alloy shapes.

The influence of powder packing on the rheology of fibre-loaded pastes

The effects of fibre addition on the extrusion rheology of ceramic particulate pastes has been investigated using model pastes containing chopped glass fibre and alumina powders. In these pastes where the fibre diameter was much larger than the alumina particle diameter, there was a decrease in the pressure required to extrude the paste as the powder component was replaced by fibre, up to a ratio of 0.4 powder to 0.6 fibre by volume. When the pastes were characterized using physically based models this behaviour was reflected in lower values of the derived rheological parameters. It is shown that this behaviour can largely be attributed to the packing behaviour of the fibre and powder-phase components. The results also suggest that the presence of fibres increases the die entry pressure drop relative to the die land pressure drop. It is shown that while the models proposed by Milewski in combination with the rheological models can be used to illustrate the expected behaviour of composite pastes, the observed behaviour was better predicted by using modified models proposed by Karlsson and Spring. At high fibre loadings (>60 vol%), extrudable materials could not be formed; this was attributed to packing and mixing problems leading to increased fibre-fibre interaction preventing flow. This is highlighted by materials in which the ratio of powder to fibre was 1 to 4 by volume, where the paste-like body was compressible and exhibited some elastic springback. For pastes where the solid phase contains <50 vol% fibre the rheological behaviour is predictable if the packing behaviour of the fibre and the rheological behaviour of the pastes containing only the powder are known. This can be used as a tool to aid the design of composite pastes and for the development of suitable process equipment.

Measurement and Control of a Straightening Process for Seamless Pipes

This paper deals with an automatic curing process for out-of-straightness of terminal ends of seamless pipes. The developed curing process is composed of a measuring stage and a controlling stage. In the measuring stage, the out-of-straightness pattern of each pipe is measured automatically, then reference pressure points and press strokes are determined to minimize the sum of squares of deflection angles. In the controlling stage, elastic springback of the pipe is predicted by an observer using the calculated press stroke, on-line measured values of reactive force, and deflection of the pipe. Through a series of experiments, the validity of the proposed process was verified.

Structural optimization with manufacturing considerations

Product design has traditionally been done in a sequential fashion. This often requires extensive iteration between product and manufacturing engineers to insure manufacturability long after the initial product design. Simultaneous engineering attempts to reduce design time by considering both the product and process from the earliest design stage. Toward this goal, we have extended a structural optimization program by incorporating manufacturability requirements for thin-wall beam type members formed by stamping. This was implemented using a new two-piece beam design element which accounts for thinning of the sidewalls during combined stretch and draw forming. Multiple material types and stamping processes are considered. Simple formulae for forming strain and elastic springback after stamping allow us to evaluate the formability of each beam member. The new capability was tested using both simple beam structures and a complete automotive frame structure. Minimum mass designs were then produced while considering both structural and formability requirements. In general, the mass of the optimal designs was near the mass of the same structures designed without manufacturing considerations. This was possible because of the additional design freedom offered by including the sidewall thinning effects.

Control for Straightening Process of Seamless Pipe.

Seamless pipes have some terminal end bends which must be eliminated before shipment. This paper describes a real-time control system for a press straightening process. The straightening process must account for elastic springback, which is a strong function of the material properties of the pipe. On-line measurements of reactive forces and deflection of the pipe during the early part of the bending process are performed to form an elastic-plastic model in a microcomputer. The final correct die position to yield the desired unloaded shape is predicted using the elastic-plastic model. Through a series of experiments on different materials and different sizes and shapes, the resulting straightness of the pipes was within 0.18 mm, which is sufficiently smaller than product allowance.

Springback and residual stresses after stretch bending of workhardening sheet metal

Stretch-bending operations are widely used for the fabrication of airframe and automative structural components. The fabrication process involves bending of individual member to prescribed contour while applying of an initial stretch tension. Forming tools must be designed and buit in a form which that produce the required contour within sufficient accuracy and tolerances satisfactory to the user applications. After plastic stretch bending, the bent section contains residual stresses as a result of the forming process. The magnitude of these stresses significantly affect the load carrying capacity and the fatigue strength of the formed member. In this work, the primary emphasis is to evaluate the elastic springback and the residual stress after stretch bending of a rectangular section of 7075 Aluminum sheet. The variation of the amount of springback and the unfavorable residual stresses for elastic-plastic and fully plastic cases are given both in analytical and graphical form.

Springback and residual stresses after stretch bending of workhardening sheet metal

Stretch-bending operations are widely used for the fabrication of airframe and automative structural components. The fabrication process involves bending of individual member to prescribed contour while applying of an initial stretch tension. Forming tools must be designed and buit in a form which that produce the required contour within sufficient accuracy and tolerances satisfactory to the user applications. After plastic stretch bending, the bent section contains residual stresses as a result of the forming process. The magnitude of these stresses significantly affect the load carrying capacity and the fatigue strength of the formed member. In this work, the primary emphasis is to evaluate the elastic springback and the residual stress after stretch bending of a rectangular section of 7075 Aluminum sheet. The variation of the amount of springback and the unfavorable residual stresses for elastic-plastic and fully plastic cases are given both in analytical and graphical form.

Analysis of the dynamic phenomena during lamination of multilayer printed circuit board by the measurement of pressure distribution

In order to develop improved methods for manufacturing multilayer printed circuit boards (MLPCBs), it is necessary to understand the dynamic phenomena that occur during the lamination process. For this purpose, the authors have performed direct measurement of the pressure distribution in MLPCB laminates during curing by the application of their own force sensor technique and have concluded that the dynamic phenomena that occur during the lamination process can be explained on a large scale by the Newtonian fluid flow model, the friction affected mass model, and the elastic springback model. Synthesizing the knowledge acquired in this study makes it possible to manufacture MLPCBs with larger dimensions, higher density, and more layers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Control for straightening process of seamless pipe.

Seamless pipes have some terminal end bends which must be cured before shipment. This paper describes a real-time control system for a press straightening process. The straightening process must account for elastic springback, which is a strong function of the material properties of the pipe. On-line measurements of reactive force and deflection of the pipe during the early part of the bending process are performed to form an elastic-plastic model in a microcomputer. The final correct die position to yield the desired unloaded shape is predicted using the elastic-plastic model. Through a series of experiments on different materials and different sizes and shapes, the straightening process gave an accuracy of 0.18 mm/m, which is sufficiently smaller than product allowances.

Influence of admixing of lubricants on compressibility and compactibility of uranium dioxide powders

An instrumented compacting tool connected to a microcomputer system has been used to determine specific parameters characterizing the compaction process of powdered or granulated materials. With the aid of this system, the compaction behaviour of uranium dioxide granulates was investigated. The effects of variations of the type and method of mixing of lubricants on compressibility and compactibility are discussed, on the basis of density and strength of the compacts, elastic springback during pressure removal and ejection, distribution of stresses, components of compaction work, and parameters which characterize frictional phenomena such as the force transmission coefficient and the coefficients of wall and powder friction.

Residual stresses in cold-rolled profiles

Structural steel members obtained by cold-forming have become more and more popular in steel construction. They allow for lightening the weight and thus provide appreciable savings over conventional hot-rolled sections. Cold-forming leads to changes in the main structural characteristics of the virgin material. Among them the increase of the yield strength due to strain-hardening and of the ultimate strength due to strain-ageing and the birth of residual stresses which play an important role in the behaviour of the profiles under compression loads. The aim of the paper is to propose a theoretical method for predicting residual stresses due to cold-rolling. The numerical results obtained lead to a better knowledge of the characteristics of the cold-rolling (elastic spring-back, effect of the ratio of the thickness versus the radius of the corner, distribution and size of the residual stresses with respect to the dimensions of the profiles).

Real-Time Control of Twist Deformation

In many areas of material production and basic manufacturing, it is necessary to impart a known twist contour to a long slender member. Also, in the production of aluminum extrusions, there is typically a high premium on straightness of the product, including “twist straightness.” The current method for the latter is a laborious, trial and error method that greatly limits the speed and accuracy of the process, and inevitably leads to conservative or wasteful design practice. This paper presents a method for placing the process of longitudinal twist deformation under real-time, closed-loop control so as to eliminate the inaccurate and costly iterative processes now used. The basic approach involves measuring the elastic springback in-process using appropriate torque and rate of twist measurements. Given these measurements in real time, a closed-loop twist servo can be constructed. The relevant mechanics of the process will be presented, and several scenarios for control of the twist process will be discussed. In particular, a method that applies the twist over a “long” length of material, but measures the relative twist over a very short distance, has been studied in detail. This control method has been investigated in a series of experiments using a computer controlled, closed-loop twisting machine constucted for this purpose.

Stamping and springback of circular plates deformed in hemispherical dies

Circular plates of mild steel with radius-to-thickness ratios between 30:1 and 60:1 were pressed or stamped into a hemispherical die by a matching punch. Measurements of the punch travel, the final curvature of the plates (i.e. after elastic springback) and a record of the wrinkling encountered during pressing are related to the punch force for a range of plate central deflection up to several plate thicknesses. A theoretical analysis, based on axisymmetric bending or stretching of rigid-perfectly plastic plates is presented. This analysis well accounts for the experimental variations in stamping force during pressing and the final curvature of the deformed plates.

Reverse springback: A curious manifestation of thermoelasticity

A new and rather unexpected phenomenon has been observed in the shape memory alloy, CuAlNi: a strip, having previously been plastically deformed, springs spontaneously to an even greater deformation strain when the deforming forces are removed—a reverse, elastic springback, opposite in direction to the expected movement. The effect is produced by cooling through M d (the temperature at which martensite can first be stress induced) while constraining the material in the deformation geometry. The effect is caused by a transformation momentum: the martensitic transformation, having been oriented in the early stages by the constraining forces, continues to transform in the same biased manner, even after the constraining geometry has been fully achieved and the constraining stress relaxed.

Cylindrical bending of metal strips

AbstractCopper, brass, and mild steel strips were deformed under elastic-plastic bending in cylindrical dies by matched cylindrical punches, without the use of any lubrication, to study the history of the enforced deformation. Separation between the punch and the strip, the punch load-displacement relationship, and the elastic springback are described. The deformation model is found to be dominated by the parameter (Y/E) (l/h), where Y is the material yield stress, E its Young's modulus, h the strip thickness, and I the strip length. When the value of this parameter is small, the strip is described as ‘stiff‘, and when it is large, ‘slender‘. The complete deformation process may be divided into several stages, each associated with a number of loading points. The phenomena of multi-point loading and the effects of largest punch load have been successfully incorporated into an explanation of the non-uniformity in final curvature of the strip after springback.

Closed-Loop Shape Control of a Roll-Bending Process

This paper describes a shape control system for a three roll bending process. The objective of this process is to impart a desired curvature to a workpiece at each point along the length of the part. Since final part shape is determined by the shape to which the workpiece is loaded and the amount of elastic springback, and since the latter is a strong function of the material properties of the workpiece, a truly closed-loop controller must account for these properties to insure consistent process performance. The scheme presented here accomplishes shape control by measuring both the loaded shape, the loading moment, and the effective beam rigidity of the material in real-time. As a result, a very accurate prediction of unloaded curvature can be made and an unloaded curvature control system can be designed. A series of experiments were performed to test this scheme by bending thin sheets of different materials to constant radii, specifying only the desired radius. The results indicate that the controller responds to the different material properties and produces accurate shapes regardless of variability in these properties.

Springback after the biaxial elastic-plastic pure bending of a rectangular plate—I

The elastic springback undergone by a rectangular plate after submitting it to biaxial elastic-plastic pure bending is determined. The analysis is first based on non-proportional loading using the Tresca criterion and then on proportional loading for both the Mises and Tresca criteria. Some numerical results and examples are given.

On springback after the pure bending of beams and plates of elastic work-hardening materials—III

Based on our previous work[1], the elastic springback undergone by elastic work-hardening beams and plates after submitting them to elastic-plastic pure bending is determined. The expressions for the final curvatures and some numerical results are given.

Elastic springback in plates and beams formed by bending

A plane-strain solution is presented to predict the springback of plates formed by bending. The solution assumes that the strains are small, that the material is an isotropichardening von Mises material, and either that the stress-strain diagrams for tension and compression are identical or that an average diagram can be employed. The plastic portion of each stress-strain diagram is approximated by a finite number of straight lines. Both analytical solutions and experimental evidence indicate that the much simpler plane-stress solution can be used to predict springback for both beams and plates. Experimental data confirm that the type of die has a pronounced effect on the springback for beams and plates if the material exhibits a yield point.