Circle Grid Research Articles

The development of a forming limit surface for 5083 aluminum alloy sheet

A custom mechanical stretching setup based on the Nakazima method was designed and built for testing sheet metals at elevated temperatures. Specimens from a fine-grained 5083 aluminum alloy sheet were deformed at various temperatures, spanning between those associated with warm forming (250°C) and hot forming (550°C). Circle grid analysis of the deformed specimens produced the forming limit curves at each of the covered temperatures, hence revealing the great influences of forming temperature on the material’s formability limits. Finally, all the curves were combined to construct a unique three-dimensional forming limit surface, which we present here as a more comprehensive map for describing material formability limits at wide-ranging temperatures.

On the potential of single point incremental forming of sheet polymer parts

The aim of this paper is to provide an overview into the development and application of single point incremental forming in rapid prototyping and rapid manufacturing of polymer sheet products that will enable the readers to recognize the key influential variables, to identify the process feasibility window, to diagnose possible sources of failure and to understand the routes for selecting the most appropriate materials and operative conditions. The methodology draws from independent determination of mechanical properties and formability limits of polymers to rapid prototyping of truncated conical and pyramidal parts. The investigation is supported by circle grid analysis. Results and observations are explained in the light of theoretical framework based on membrane analysis that is capable of modelling the cold plastic deformation of polymers with pressure-sensitive yield surfaces. The results show that the single point incremental forming of polymer sheets, performed on conventional CNC machining centres, is a cost-effective innovative technology for product development in a manufacturing environment. Applications may span from products with very high depths, taking advantage of the excellent formability of polyethylene terephthalate, to applications in polycarbonate where transparency is kept during cold forming.

Hydroformability of Bulge Forming Light-Weight Tubes via Micro-Hardness Dependence

To evaluate the hydroformablility of tubular components in the tube hydroforming (THF) process, the conventional method is to measure the deformed square or circle grids printed on the surface of the tubular parts. However, the reliability of those measured data is affected greatly by the grid size and its measurement method on the curved surface. It is well-known that material hardness varies under different plastic deformation conditions, especially before and after the forming process. And it is more convenient to obtain the Vickers’ hardness values and distribution around the burst area of deformed components. This paper mainly presents an effective and reliable approach to evaluate the hydroformability of tubular components using micro-hardness measurement. At first, the Vickers’ hardness values and distribution around the burst area of the deformed components were obtained. The plastic strain, together with its distribution in such an area could then be derived by the measured micro-hardness through the developed equations. As a result, it was found to be more suitable to evaluate the hydroformability of tubes using this approach instead of the traditional grids measurement.

Sheet Formability and Performance of Metastable Austenitic Stainless Steels

The sheet formability of AISI Types 301, 304, and 305 stainless steels, ranked in order of increasing stability to strain‐induced martensite formation, was evaluated as a function of temperature between 15 and 60 °C. Forming limits spanning deep drawing, plane strain, and biaxial stretching strain states were determined by circle grid analysis of sheet specimens subjected to punch‐stretch testing at a constant punch displacement rate. Amounts of strain‐induced martensite were measured as a function of strain by magnetic measurement. Formability varied widely depending on test temperature and austenite stability, a result of temperature‐ and strain‐dependent formation of martensite that in some conditions was beneficial and in some conditions was detrimental to formability. These results are presented and discussed in detail.

Easy calibration technique for stereo vision using a circle grid

Combined with the digital image correlation (DIC), the stereo vision calibrated by a circle grid can be used to measure the surface deformation of a deformable body. The grid dot centers are taken as the calibration points. A subpixel localization technique was developed to precisely find the location of the edge points of a dot. A conical section was then fitted to the obtained edge points to locate the dot center so that the intrinsic and extrinsic camera parameters can be accurately extracted after the camera calibration. The baseline measurement error of the stereo vision was evaluated by performing rigid body translation tests. By using the DIC to find the conjugate pairs in stereo images, the calibrated stereo vision is used to measure the strain field of a tension test specimen to evaluate its applicability to the surface deformation measurement of a deformable body.

Forming of AISI 409 sheets for fan blade manufacturing

The necessity for adapting the standardised fan models to conditions of higher temperature has emerged due to the growth of concerning with the consequences of the Mont Blanc tunnel accident where 41 people died. The objective of this work is to present an alternative to standard fans by considering a new manufacturing procedure for producing fan blades. Experimentation on prototypes combined with circle grid analysis allows concluding that during the sheet metal forming process the zones undergoing more deformation are still below the formability limits and, therefore, the new process can be successful utilised for producing fan blades.

Aspects of automated measurement of proportional and non-proportional deformation in sheet metal forming

This paper evaluates techniques of surface strain analysis in sheet metal forming based on a two-dimensional grid. Deficiencies of circle grid analysis, which in general cannot be used to measure non-proportional deformation, are discussed. An improved technique utilising a grid of squares or quadrilaterals for the automatic measurement of strains and stresses is presented. The advantage of applying a stress limit curve (SLC), instead of the forming limit curve (FLC), in the experimental analysis of deformation and in the evaluation of forming severity is discussed.

A study on determining hardening curve for sheet metal

The hardening curve for sheet metal can be determined from the load–displacement curve of tensile specimen with rectangular cross-section. The previous researches, however, have paid little attention to its use in large deformation. Moreover, it varies with materials, deformation conditions and so on, and there are not enough hardening curves available in manuals. In order to study metal behavior, it is very important to establish a method to create a large strain hardening curve based on the normal mechanical test. In this paper, two new kinds of specimens are proposed, one is a multi-stepped specimen that can be traced to the three-stepped specimen, and the other is a tapered specimen which decreases the complexity of the multi-stepped specimen in manufacture. In this study, circle grids are imposed on the specimen surface to calculate true strains at different positions of the specimen. It is found that the load added to the different segments of specimen just before fracture can be determined by the maximum load and breaking load. True strains and corresponding true stresses can be determined after the specimen is pulled to fracture, so the hardening curve can be easily achieved. After a great deal of experiment, the results show that the tapered specimen has almost the same key parameters as the multi-stepped specimen, and the former is more easily used. Meanwhile, the work-hardening exponent ( n) and the coefficient of normal anisotropy ( r) can be obtained conveniently, and the forming limit line can also be approximately induced.

Effect of matrix constitutive behavior and inclusions on forming limits of Fe-42 pct Ni alloy sheet

The effects of matrix constitutive behavior and nonmetallic inclusions on forming limit strains have been examined with five laboratory heats of Fe-42 pct Ni alloy. The inclusion volume fraction was varied between approximately 0.01 and 1.59 pct by proper selection of Mn, S, and O contents. Each ingot was processed into 0.38-mm-thick sheets and heat treated to the recovered or the recrystallized condition. Forming limit strains were obtained from uniaxial tensile, plane-strain tensile, and hydraulic bulge tests by circle grid analysis. In any strain path, the limit strain increased with increasing the strain hardening exponent, n. The forming limit strains on the right-hand side of the forming limit diagram (FLD) decreased with inclusion volume fraction, while no effects of the inclusion volume fraction were observed on the left-hand side. A decrease in the slope of the FLD on the right-hand side due to an increase in the inclusion volume fraction qualitatively agrees with the theoretical calculation by Graf and Hosford, which was conducted on the basis of the Marciniak-Kuczynski (M-K) theory.

Circle grid analysis applied to the production problems of the car body panel

Production problems of the autobody door inner panel in the press shop is investigated with aid of the circle grid analysis. The aim is to reduce the scrap rate. The strain distribution and the strain history in the severe deformed area is determined. Strains are compared with the limit strains in the form of the forming limit diagrams. Two forming limit diagrams (FLDs) are determined for two sheet metal blank orientations to the rolling direction α=90° and α=0°, respectively. Mathematical statistics is used for evaluating of experimental data. Statistically significant difference between forming limit curves is appreciated and the formability stock in the range of various strain states through FLD is determined. Also strain history in the investigated area of the stamped part is determined.

Circle grids and bipartite graphs of distances

Fort fixed,n+t pointsA 1,A 2,...,A n andB 1,B 2,...,B t are constructed in the plane withO(√n) distinct distancesd(A i B j ) As a by-product we show that the graph of thek largest distances can contain a complete subgraphK t, n withn=Θ(k 2), which settles a problem of Erdős, Lovasz and Vesztergombi.

Sheared edge extension of high-strength cold-rolled steels

The edge formability of a spectrum of high-strength cold-rolled steels has been evaluated using the hole expansion test. The effects of edge condition, micro structure, and tensile properties on hole expansion performance were determined. Modification of stringer inclusions through rare-earth treatments caused the hole expansion response of these steels to be much less sensitive to edge condition, as-blanked vs de-burred. Independently of edge condition, rare-earth treatment also produced a significant increase in hole expansion performance compared to the same steel untreated. Circle grid analysis showed that deformation modes generated in a hole expansion test are drawing near the hole edge, stretching farther from the edge, and plane strain separating these two modes. Recovery annealed steels with low transverse ductility were observed to fail away from the edge in the plane strain region during hole expansion. The hole expansion performance of the entire range of steels tested was found to vary linearly with the product of the steels’ transverse total elongation and rm values. A phenomenological expression that determines hole expansion performance was derived using linear analysis. It predicts that for steels with total elongations of about 30 pct, each increase in rm of about 0.1 will increase its hole expansion performance by greater than 10 pct.

Forming limit curves: Out-of-plane and in-plane stretching

The study of deformation and failure of biaxially stretched sheets is of considerable practical interest in the area of sheet metal press forming. During biaxial stretching of sheet metal, the uniform plastic straining regime is often followed by a localised plastic straining regime which finally leads to fracture. The technique of analysing failures in sheet metal pressing through the use of circle grids and “forming limit curves” has gained considerable popularity. The forming limit curve describes the combination of the two principal surface strains of a biaxially stretched sheet metal at which a localised xone of thinning or necking is bound to occur. Forming limit curves thus provide excellent guidelines for adjusting material, tooling and lubrication conditions in the plant. In spite of their usefulness, however, in an actual forming operation, material parameters interact with the pressing process variables in a complex manner and comparison of different forming limit curves becomes difficult. Forming limit curves are strongly dependent on material parameters, such as the sheet thickness, the straining path and the strain gradients, and also on the geometry of the tooling. The type of stretching process can also influence the forming limit curve. In the present work, forming limit curves have been determined experimentally for annealed aluminium alloy sheets by two methods: out-of-plane stretching, where the sheet is bulged by lateral hydrostatic pressure, and in-plane stretching by tensile forces lying in the plane of the sheet. It is found that the former method produces higher limit strains than the latter under identical degrees of strain biaxiality and initial sheet thickness. A study of the various parameters present in each method which may influence the strain localisation process indicates that the overall strain gradient across the bulged testpiece is responsible for the higher strain limits.

The use of a square grid as an alternative to a circular grid in the determination of strains

The circle grid strain analysis method has hitherto been the most commonly used method to determine strains in sheet metal parts. This method has proved very successful in a number of applications. However, the method has drawbacks, some of which can be overcome by employing a grid strain analysis — the coefficient method — based on the measuring of a grid consisting of squares. The present paper compares the circle grid method and the coefficient method, the conclusions of which comparison are that the coefficient method (i) can yield the strain distribution much faster and more accurately, (ii) is very flexible with respect to choice of optimum reference area, (iii) can be used to analyse the influence of the strain path on the formability of sheet metal, and (iv) is very easy to computerize.

Two Circle Grid Charts for Measuring Visual Acuity and Astigmatism

The charts are described and their advantages enumerated. From the Psychological Laboratory, University of Michigan. The charts are described and their advantages enumerated. From the Psychological Laboratory, University of Michigan.

Effect of background on visual acuity of circle grids.

Effect of background on visual acuity of circle grids.