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.

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.

Experimental Researches on Nonlinear Strain Paths Forming for Dual Phase Steel

2014 ◽  
Vol 1004-1005 ◽  
pp. 209-213
Author(s):  
Li Bo Pan ◽  
Hong Chuan Zhu ◽  
Ze Hong Lei ◽  
Zhi Jian Zhang
Keyword(s):  
Plastic Strain ◽  
Dual Phase Steel ◽  
Forming Limit Diagram ◽  
Forming Limit ◽  
Strain Diagram ◽  
Dual Phase ◽  
Effective Plastic Strain ◽  
Nonlinear Strain ◽  
Precise Tool ◽  
Strain Paths

Strain paths during sheet metal forming are always complex and nonlinear. Forming limit diagram (FLD) is a common method to determine failure in the past decades. However, it is only suitable for linear strain path condition. Regarding dual phase steel DP780, a special experiment was designed and carried out on Zwick Cupping equipment to get nonlinear strain paths. And the strain status was analyzed in FLD. It was found that FLD cannot predict failure precisely in this case. A new approach proposed by Stoughton and Yoon which based on polar effective plastic strain was introduced to analyze this nonlinear strain paths condition, the result is in good agreement with experiment, which indicated that Polar Effective Plastic Strain Diagram was an effective and precise tool to determine failure especially for complex nonlinear strain paths forming.

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.

Void Nucleation Effects in Biaxially Stretched Sheets

1980 ◽  
Vol 102 (3) ◽  
pp. 249-256 ◽  
Author(s):  
C. C. Chu ◽  
A. Needleman
Keyword(s):  
Plastic Strain ◽  
Volume Fraction ◽  
Void Nucleation ◽  
Hydrostatic Stress ◽  
Forming Limit ◽  
Stress Theory ◽  
Out Of Plane ◽  
Necking Criterion ◽  
Controlled Nucleation ◽  
Forming Limit Curves

The effects of void nucleation occurring during the deformation history on forming limit curves are considered for both in-plane and punch stretching employing a constitutive model of a porous plastic solid. Both plastic strain controlled and stress controlled nucleation processes are simulated by a two parameter void nucleation criterion. For in-plane stretching, plastic strain controlled nucleation can have, in certain circumstances, a significantly destabilizing effect on the forming limit curve. However, within the framework of plane stress theory which neglects the enhancement of the hydrostatic stress due to necking, a stress controlled nucleation process is not found to be significantly destabilizing. In punch stretching a ductile rupture criterion, which limits the maximum volume fraction of voids, as well as the appearance of a well defined thickness trough, is adopted as a localized necking criterion. Only plastic strain controlled void nucleation is considered here in out-of-plane stretching. The resulting forming limit curves have the same shape as those obtained previously with void nucleation neglected.

Effect of Strain Paths on Formability Evaluation of TRIP Steels

2010 ◽  
Vol 89-91 ◽  
pp. 214-219 ◽  
Author(s):  
David Gutiérrez ◽  
A. Lara ◽  
Daniel Casellas ◽  
Jose Manuel Prado
Keyword(s):  
Strain Path ◽  
High Strength Steels ◽  
High Strength ◽  
Test Method ◽  
Forming Limit ◽  
Trip Steels ◽  
Advanced High Strength Steels ◽  
Strain Paths ◽  
Analysis System

The Forming Limit Diagrams (FLD) are widely used in the formability analysis of sheet metal to determine the maximum strain, which gives the Forming Limit Curve (FLC). It is well known that these curves depend on the strain path during forming and hence on the test method used to calculate them. In this paper, different stretching tests such as the Nakajima and the Marciniak tests were performed, with different sample geometries to obtain points in different areas of the FLD. An optical analysis system was used, which allows following the strain path during the test. The increasing use of advanced high-strength steels (AHSS) has created an interest in determining the mechanical properties of these materials. In this work, FLCs for a TRIP steel were determined using Nakajima and Marciniak tests, which revealed different strain paths depending on the type of test. Determination of the FLCs was carried out following the mathematical calculations indicated in the ISO 12004 standard and was also compared with an alternative mathematical method, which showed different FLCs. Finally, the tests were verified by comparing the strain paths of the Nakajima and Marciniak tests with a well-known mild steel.

Dislocation Microstructure in Copper Multicrystals Deformed under the Sequences: Rolling - Tension and Tension - Rolling

2006 ◽  
Vol 514-516 ◽  
pp. 589-593 ◽  
Author(s):  
Nataliya A. Sakharova ◽  
José Valdemar Fernandes
Keyword(s):  
Electron Microscopy ◽  
Strain Path ◽  
Deformation Mode ◽  
Slip Activity ◽  
Transmission Electron ◽  
Different Types ◽  
Strain Paths ◽  
Strain Path Change ◽  
Complex Strain ◽  
Types Of Change

The microstructure evolution of copper multicrystalline sheets, undergoing plastic deformation in the sequences of strain paths rolling – tension and tension – rolling, was studied in the present work. For both sequences, two different types of change of strain path were studied: the tensile and rolling directions were parallel and normal to each other. Samples submitted to these four complex strain paths were investigated by transmission electron microscopy (TEM). TEM observations have shown the typical dislocations microstructures for the prestrain paths in tension and rolling. The dislocation microstructures observed during the second path were analysed and discussed as a function of the sequence and of the type of strain path change (parallel and normal sequential paths). Special microbands features were observed during the second path, for both sequences, rolling – tension and tension – rolling. The appearance of such microstructural features is discussed in terms of the sequence and type of strain path change and it is linked with the slip activity during the second deformation mode.

Analysis of Stress Response to Various Strain-Paths in Axial-Torsional Deformation of Metals

1984 ◽  
Vol 106 (4) ◽  
pp. 361-366 ◽  
Author(s):  
Han C. Wu ◽  
Jen-Che Yao
Keyword(s):  
Stress Response ◽  
Plastic Strain ◽  
Strain Path ◽  
Sensitivity Study ◽  
Total Strain ◽  
Torsional Deformation ◽  
Torsional Strain ◽  
Straight Line ◽  
Phase Path ◽  
Strain Paths

The stress response to various axial-torsional strain paths is discussed. The modified endochronic plasticity theory, which is formulated based on plastic-strain is used for theoretical analysis. In a sensitivity study, it is shown that a substantial amount of change in the stress response is induced by a small perturbation on the plastic-strain path. Of this change a significant amount is due to perturbation in the direction of the plastic-strain path. Several stepwise strain paths, both total-strain and plastic-strain paths, are also included in the investigation. It has been found that, when the number of steps is increased to infinity such that the strain path converges to a straight line corresponding to an in-phase path, the stress response to such a path is wildly fluctuating in the stress space if the path is a plastic-strain path, and the stress response converges to that of the in-phase path if the path is a total-strain path.

A comparative study on determination of forming limit diagrams for industrial aluminium sheet alloys considering combined effect of strain path, anisotropy and yield locus

2012 ◽  
Vol 47 (6) ◽  
pp. 350-361 ◽  
Author(s):  
Milad Janbakhsh ◽  
Faramarz Djavanroodi ◽  
Mohammad Riahi
Keyword(s):  
Finite Element ◽  
Strain Path ◽  
Small Deviation ◽  
Axial Strain ◽  
Simulation Software ◽  
Forming Limit ◽  
Plastic Strain Ratio ◽  
Forming Limit Diagrams ◽  
Aluminium Sheet ◽  
Strain Paths

Suitability of AA2024-T3 and AA5083-H111 aluminium sheet alloys for forming operations in room temperature were examined by using forming limit diagrams with different strain paths. In the experimental part, circular bulge, non-grooved tensile as well as grooved tensile specimens were used. This was done to simulate the following: (a) biaxial stretching region (positive range of minor strain), (b) uni-axial strain path and (c) strain path from uni-axial tension to plane strain region of the forming limit diagram, respectively. The effects of combined strain paths coupled with material anisotropy were taken into account in each stage. Tensile properties as well as formability parameters were correlated in accordance with the attained forming limit diagrams. Average plastic strain ratio and planar anisotropy, in addition to work hardening exponents of the samples, were calculated from the test data and the effects on the forming limit diagrams were discussed. Moreover, comparisons were made between experimental and theoretical forming limit diagrams. It is shown that experimental forming limit diagrams are in very good agreement with the theoretical predictions, particularly when BBC2000 yield criteria are used for the M–K model. In addition, theoretical prediction by using the Hill93–Swift model showed small deviation with the experimental forming limit diagrams. Finally, finite element simulations were carried out to investigate the numerical forming limit diagrams through an industrial sheet metal forming simulation software. It was consequently shown that, due to frictional effects resulting from hemispherical-shaped punch, the finite element results depicted small deviation compared to the experimental data.

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