scholarly journals Development of a Nakazima Test Suitable for Determining the Formability of Ultra-Thin Copper Sheets

Metals ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 1163 ◽  
Author(s):  
Nejia Ayachi ◽  
Noamen Guermazi ◽  
Cong Hanh Pham ◽  
Pierre-Yves Manach
Keyword(s):  
Pure Copper ◽  
Accurate Method ◽  
Forming Limit ◽  
Iso Standard ◽  
Metal Sheets ◽  
Dependent Measurement ◽  
Strain Paths ◽  
Planar Strain ◽  
Derivatives Of ◽  
Forming Limit Curves

The objective is to propose an accurate method for determining the forming limit curves (FLC) for ultra-thin metal sheets which are complex to obtain with conventional techniques. Nakazima tests are carried out to generate the FLCs of a pure copper and a copper beryllium alloy with a thickness of 0.1 mm. Because of the very small thickness of the sheets, the standard devices and the know-how of this test are no longer valid. Consequently, new tools have been designed in order to limit friction effect. Two different methods are used and compared to estimate the necking: the position-dependent measurement method (ISO Standard 12004-2), and the time-dependent method based on the analysis of the derivatives of the planar strain field. It is shown that the ISO standard method underestimates the forming limit curves. As the results present non linear strain paths, a compensation method is applied to correct the FLCs for the tested materials, which combines the effects of curvature, nonlinear strain paths and pressure. The curvature effect for such thickness and punch diameter on the FLCs is weak. The results show that this procedure enables to obtain FLCs that are close to those determined by the reference Marciniak method, leading to a minimum in major strain that converges to the plane strain state.

Orientation and Path Dependence of Formability in the Stress- and the Extended Stress-Based Forming Limit Curves

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
C. Hari Manoj Simha ◽  
Kaan Inal ◽  
Michael J. Worswick
Keyword(s):  
Strain Path ◽  
Path Dependence ◽  
Forming Limit ◽  
Stress Space ◽  
Forming Limit Diagrams ◽  
Metall Trans ◽  
Strain Paths ◽  
Strain Path Changes ◽  
Path Dependent ◽  
Forming Limit Curves

This article analyzes the formability data sets for aluminum killed steel (Laukonis, J. V., and Ghosh, A. K., 1978, “Effects of Strain Path Changes on the Formability of Sheet Metals,” Metall. Trans. A., 9, pp. 1849–1856), for Al 2008-T4 (Graf, A., and Hosford, W., 1993, “Effect of Changing Strain Paths on Forming Limit Diagrams of Al 2008-T4,” Metall. Trans. A, 24A, pp. 2503–2512) and for Al 6111-T4 (Graf, A., and Hosford, W., 1994, “The Influence of Strain-Path Changes on Forming Limit Diagrams of Al 6111 T4,” Int. J. Mech. Sci., 36, pp. 897–910). These articles present strain-based forming limit curves (ϵFLCs) for both as-received and prestrained sheets. Using phenomenological yield functions, and assuming isotropic hardening, the ϵFLCs are transformed into principal stress space to obtain stress-based forming limit curves (σFLCs) and the principal stresses are transformed into effective stress and mean stress space to obtain the extended stress-based forming limit curves (XSFLCs). A definition of path dependence for the σFLC and XSFLC is proposed and used to classify the obtained limit curves as path dependent or independent. The path dependence of forming limit stresses is observed for some of the prestrain paths. Based on the results, a novel criterion that, with a knowledge of the forming limit stresses of the as-received material, can be used to predict whether the limit stresses are path dependent or independent for a given prestrain path is proposed. The results also suggest that kinematic hardening and transient hardening effects may explain the path dependence observed in some of the prestrain paths.

Effects of Processing, Texture and Temperature on the Formability of AZ31 and ZE10 Sheets

2011 ◽  
Vol 690 ◽  
pp. 298-301 ◽  
Author(s):  
Dietmar Letzig ◽  
Lennart Stutz ◽  
Jan Bohlen ◽  
Karl Ulrich Kainer
Keyword(s):  
Metal Forming ◽  
Alloy Composition ◽  
Deformation Mechanisms ◽  
Forming Limit ◽  
Forming Limit Diagrams ◽  
Sheet Formability ◽  
Strain Paths ◽  
Twin Roll Cast ◽  
Twin Roll ◽  
Forming Limit Curves

Sheet metal forming experiments have been carried out on AZ31 and ZE10 sheets produced by rolling conventionally DC cast slabs as well as twin roll cast (TRC) strips. Nakajima tests were performed on the various sheet materials over the temperature range from RT to 200 °C using Hasek type samples of specified geometries to generate various strain paths. The strain path data were used to derive the forming limit curves as plotted in forming limit diagrams for the two alloys. The temperature dependence of the sheet formability is discussed in terms of the operating deformation mechanisms and the roles of alloy composition, initial texture and processing history.

scholarly journals A Cruciform Shape to Study the Influence of Strain Paths on Forming Limit Curves

2013 ◽  
Vol 554-557 ◽  
pp. 41-46 ◽  
Author(s):  
Lionel Leotoing ◽  
Dominique Guines ◽  
Shun Ying Zhang ◽  
Eric Ragneau
Keyword(s):  
Forming Limit ◽  
Strain Paths ◽  
Forming Limit Curves

Time Dependent FLC Determination Comparison of Different Algorithms to Detect the Onset of Unstable Necking before Fracture

2013 ◽  
Vol 549 ◽  
pp. 397-404 ◽  
Author(s):  
Walter Hotz ◽  
Marion Merklein ◽  
Andreas Kuppert ◽  
Harald Friebe ◽  
Markus Klein
Keyword(s):  
Correlation Coefficient ◽  
Work Group ◽  
Time History ◽  
Time Dependent ◽  
Forming Limit ◽  
Iso Standard ◽  
Modified Method ◽  
History Of ◽  
Forming Limit Curves

The ISO standard 12004-2:2008E for the determination of forming limit curves based on the section method was approved in 2008. About 4 years of measuring experience in different laboratories has shown advantages and weaknesses of the standard and is leading to some minor changes in the specification. In the years from the development of this standard until today a further technical development of the optical measuring devices occurred, so that it is now possible to determine forming limit curves using the time history of the test. This procedure of determination is referred to a time dependent technique and could be the basis of the ISO 12004 part 2 proposal worked out by the work group Erweiterung FLC ISO 12004 of the German group of the IDDRG. This publication recapitulates existing work which was carried out from the IDDRG work group regarding the determination of forming limit curves for sheet metal materials. On one hand known issues with the current section based approach are discussed and on the other hand it deals with a comparison of different algorithms to determine the FLC from the time history of the Nakajima test using strategies to identify the instant of onset of instable necking. The different time dependent algorithms [ utilised are automatically selecting the area where necking is leading to fracture and then analyze the time history of such points using the first or the second time derivative of the true major strain, or of the true thinning strain using methods like: correlation coefficient (modified method based on [2]), gliding correlation coefficient, linear best fit (modified method based on [3]) and gliding difference of mean to median. The resulting experimental FLC points are compared with the results from the section technique described in ISO 12004 part 2 and with the maximum strain values measured in each test. Further a large number of forming limit curves were determined and used for a comparison of these different methods to define the most promising time dependent algorithm, which was selected as a suggestion for the working group defining the new proposed ISO standard 12004 part 2.

Forming Limit Curves for Complex Strain Paths

2013 ◽  
Vol 58 (2) ◽  
pp. 587-593 ◽  
Author(s):  
J. Rojek ◽  
D. Lumelskyy ◽  
R. Pęcherski ◽  
F. Grosman ◽  
M. Tkocz ◽  
...  
Keyword(s):  
Plastic Strain ◽  
Strain Path ◽  
Experimental Studies ◽  
Polar Coordinates ◽  
Forming Limit ◽  
Effective Plastic Strain ◽  
Steel Blank ◽  
Strain Paths ◽  
Complex Strain ◽  
Forming Limit Curves

This paper presents results of experimental studies of forming limit curves (FLC) for sheet forming under complex strain paths. The Nakazima-type formability tests have been performed for the as-received steel blank and for the blank pre-strained by13%. Prestraining leads to abrupt change of strain path in the blank deformation influencing the forming limit curve. The experimental FLC of the pre-strained blank has been compared with the FLC constructed by transformation of the as-received FLC. Quite a good agreement has been found out. The concept of strain-path independent FLCs in polar coordinates has been verified. Two types of the polar diagrams have been considered, the first one with the strain-path angle and effective plastic strain as the polar coordinates, and the second one originally proposed in this work in which the thickness strain has been used instead of the effective plastic strain as one of the polar coordinates. The second transformation based on our own concept has given a better agreement between the transformed FLCs, which allows us to propose this type of polar diagrams as a new strain-path in dependent criterion to predict sheet failure in forming processes.

Multiscale Modelling of Plastic Deformation of Polycrystals: Implementation of Texture-Based Anisotropy in Engineering Applications (FE Codes for Forming, Prediction of Forming Limit Curves)

2007 ◽  
Vol 539-543 ◽  
pp. 3454-3459
Author(s):  
Paul van Houtte ◽  
Albert Van Bael ◽  
Marc Seefeldt
Keyword(s):  
Metal Forming ◽  
Multilevel Models ◽  
Sheet Material ◽  
Forming Limit ◽  
Engineering Applications ◽  
Macro Scale ◽  
Scale Models ◽  
Strain Paths ◽  
Forming Limit Curves ◽  
Meso Scale

Finite element models for metal forming are used to design and optimise industrial forming processes. The limit strain in sheet metal forming can be predicted for monotonic loading or strain paths with changes. Models like these should be as accurate as possible in order to be useful, and hence take the texture, microstructure and substructure (dislocation patterns) into account. To achieve this, a hierarchical type of modelling is proposed in order to maintain the balance between calculation speed (required for engineering applications) and accuracy. In that case, FE models to be used at the engineering length scale work with an analytical constitutive model, the parameters of which are identified using results of multilevel models (meso-scale with an homogenisation procedure). The analytical model to be used at macro-scale will be discussed, as well as the identifications procedure. The later make use of meso-scale models. Finally an example will be given (formability of a sheet material).

scholarly journals A sheet metal necking formability diagram for nonlinear strain paths

2017 ◽  
Vol 233 (7) ◽  
pp. 1287-1294
Author(s):  
Peter Christiansen ◽  
Mikkel RB Jensen ◽  
Grethe Winther
Keyword(s):  
Sheet Metal ◽  
Theoretical Basis ◽  
Reasonable Agreement ◽  
Forming Limit ◽  
Limit Curve ◽  
Forming Limit Curve ◽  
Forming Limits ◽  
Nonlinear Strain ◽  
Strain Paths ◽  
Forming Limit Curves

A new procedure for drawing forming limit curves is suggested. The theoretical basis for computing the forming limit curve due to diffuse necking, for nonlinear strain paths, is derived. The theoretically determined forming limit curve is compared with experimentally determined forming limits for both linear and bilinear strain paths. Reasonable agreement is observed. The procedure can also be utilized for nonlinear strain paths in general.

Sign in / Sign up

Export Citation Format

Share Document