Determination of the Forming Limit Stress Curve for Anisotropic Sheets

Arrieux, Robert; Boivin, M.; Maître, F

doi:10.1016/s0007-8506(07)62584-0

Cited by 71 publications

(18 citation statements)

References 2 publications

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“…The following four methods are employed in this paper: (i) de 11 (1)- (13). The Newton-Raphson iteration is used to solve the simultaneous equations because they are nonlinear.…”

Section: Methods Of Calculationmentioning

confidence: 99%

“…When rϽ0, w is not 0. In the following discussion, the forming stress or strain is defined as the minimized limit with respect to w among the limits defined by negative de 11 .…”

Section: Methods Of Calculationmentioning

confidence: 99%

“…Although many researchers, [10][11][12][13] have proposed this FLSD method in various ways from an early stage, it has taken time for this approach to gain wide acceptance. One reason may be the difficulty of measuring stresses in practical situations, whereas strains can easily be measured by using scribed circles.…”

Section: Introductionmentioning

confidence: 99%

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Evaluation of Ductile Forming Limit Stress in Sheet Forming Processes and Measurement of Actual Stress at Fracture

Iguchi¹

2007

ISIJ Int.

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A stress-based ductile forming limit theory applicable to nonlinear strain paths is investigated with a 11 % Cr steel which displays a highly anisotropic behavior in plastic deformation. The forming limit stress is evaluated by a theoretical method based on the M-K theory, and is also measured directly in some cases with nonlinear loading paths. The evaluated and measured stresses are compared with an experimentally-obtained forming limit stress diagram, where the stresses are converted from strains by Stoughton's method. The theoretically-evaluated limit stress corresponds not to the measured stress at the onset of fracture but to the stress at the onset of localized necking. The evaluated forming limit stress and experimentallyobtained localized necking stress demonstrate no dependency on strains paths, thus verifying the applicability of the theory to this particular material. The experimentally-obtained forming limit stress diagram was corrected using the above results, which has improved the discrepancies between the experimentally-and numerically-obtained forming limit stress.KEY WORDS: 11 % Cr steel; sheet forming; stress-based forming limit; nonlinear loading path. ISIJ International, Vol. 47 (2007), No. 3, pp. 493-501 493 © 2007 ISIJ et al. 14,15) verified this theory experimentally by actually measuring stresses in aluminum tube hydroforming. However, cases where stresses in the material can be measured directly during forming are rare.Considering the various problems outlined above, the author and a co-worker focused on an investigation of the applicability of the FLSD theory to a particular material, 11 % Cr steel. In a previous paper, 16) the ductile forming limit was measured in some nonlinear loading paths and was then converted to an FLSD. In this paper, the forming limit stress is evaluated by a numerical method using the M-K theory.17) The forming limit stress is also measured directly in experiments with some nonlinear loading paths. These stresses are compared with the above converted FLSD, and their relationships are discussed. The physical aspect of the FLSD theory is discussed on the basis of this investigation.Here, it must be stressed again that the stresses used to draw the experimental FLSD are values which have been converted from strains. The theoretically-evaluated FLSD is based on plastic theory as well. This means that the accuracy of the stresses depends on the accuracy of the plastic deformation theory, which requires modeling of a workhardening rule, a yield criterion, and anisotropic parameters such as the r-value of the material concerned. The problem is the same in theoretical evaluation of the forming limit stress because the plastic deformation theory is also used in the calculations. This is particularly important for the material investigated here because it demonstrates highly anisotropic behavior. The authors verified these models for this material in detail in a previous paper, 16) so it is now possible to corroborate the relationship between the converted and me...

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“…The following four methods are employed in this paper: (i) de 11 (1)- (13). The Newton-Raphson iteration is used to solve the simultaneous equations because they are nonlinear.…”

Section: Methods Of Calculationmentioning

confidence: 99%

“…When rϽ0, w is not 0. In the following discussion, the forming stress or strain is defined as the minimized limit with respect to w among the limits defined by negative de 11 .…”

Section: Methods Of Calculationmentioning

confidence: 99%

See 1 more Smart Citation

Evaluation of Ductile Forming Limit Stress in Sheet Forming Processes and Measurement of Actual Stress at Fracture

Iguchi¹

2007

ISIJ Int.

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“…2,3) One of the methods on which the authors are focusing to overcome this problem is the stress-based forming limit theory. [4][5][6][7] This theory determines a unique limit line for sheet forming in a principal stress field, not in the strain field, independently of strain paths. In this paper, the diagram for the stress field is called a Forming Limit Stress Diagram (FLSD).…”

Section: Introductionmentioning

confidence: 99%

“…In this case, the limit was verified mainly by stresses evaluated by transforming the strain limit using plastic deformation theory. [4][5][6][7] Some researchers have also evaluated and verified the stress limit by a numerical method 8,9) based on the M-K theory. 10) For example, Yoshida et al 9) directly measured the limit stress in the case of aluminum tube forming.…”

Section: Introductionmentioning

confidence: 99%

Ductile Forming Limit Stress in Sheet Forming Processes with Nonlinear Strain Path Involving Out-of-plane Forming

Iguchi¹

2007

ISIJ Int.

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Determination of Forming Limit Stress Diagrams for the Characterization of Material for Sheet Metal Forming

2002

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Forming limit diagrams (FLD) are usually used to predict the possible failure of the material in a sheet metal forming process. The FLD shows the maximum strain to failure as a function of the strain state. Another way of describing the deformation limit of a material is a forming limit stress diagram (FLSD), which shows the equivalent stress to failure as a function of the principal stresses. The FLSD is independent of the deformation history and the deformation path of the material, which is in contrast to the commonly used forming limit diagram (FLD). FLSDs for five different deep drawing steel grades have been calculated from data of previously determined FLDs, flow curves, and anisotropy coefficients.

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Determination of the Forming Limit Stress Curve for Anisotropic Sheets

Cited by 71 publications

References 2 publications

Evaluation of Ductile Forming Limit Stress in Sheet Forming Processes and Measurement of Actual Stress at Fracture

Evaluation of Ductile Forming Limit Stress in Sheet Forming Processes and Measurement of Actual Stress at Fracture

Ductile Forming Limit Stress in Sheet Forming Processes with Nonlinear Strain Path Involving Out-of-plane Forming

Determination of Forming Limit Stress Diagrams for the Characterization of Material for Sheet Metal Forming

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