A note on post-failure stress-strain path dependence in norite

A strain-based forming limit criterion is widely used throughout the sheet-metal forming industry to gauge the stability of the deformed material with respect to the development of a localized neck prior to fracture. This criterion is strictly valid only when the strain path is linear throughout the deformation process. There is significant data that shows a strong and complex dependence of the limit criterion on the strain path. Unfortunately, the strain path is never linear in secondary forming and hydro-forming processes. Furthermore, the path is often found to be nonlinear in localized critical areas in the first draw die. Therefore, the conventional practice of using a path-independent strain-based forming limit criterion often leads to erroneous assessments of forming severity. Recently it has been reported that a stress-based forming limit criterion appears to exhibit no strain-path dependencies. Subsequently, it has been suggested that this effect is not real, but is due to the saturation of the stress-strain relation. This paper will review and compare the strain-based and stress-based forming limit criteria, looking at a number of factors that are involved in the definition of the stress-based forming limit, including the role of the stress-strain relation.

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

Journal of Engineering Materials and Technology ◽

10.1115/1.2931152 ◽

2008 ◽

Vol 130 (4) ◽

Cited By ~ 5

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.

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Strain path dependence of texture development in aluminum

Acta Metallurgica ◽

10.1016/0001-6160(89)90293-9 ◽

1989 ◽

Vol 37 (10) ◽

pp. 2595-2611 ◽

Cited By ~ 9

Author(s):

T. Takeshita ◽

U.F. Kocks ◽

H.-R. Wenk

Keyword(s):

Strain Path ◽

Path Dependence ◽

Texture Development

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Investigation of Critical Stress Concentration Factor in Analytical Stress Based Forming Limit Criterion

ASME 2009 International Manufacturing Science and Engineering Conference, Volume 1 ◽

10.1115/msec2009-84138 ◽

2009 ◽

Author(s):

Kyle R. McLaughlin ◽

Tugce Kasikci ◽

Igor Tsukrov ◽

Brad L. Kinsey

Keyword(s):

Stress Concentration ◽

Stress Concentration Factor ◽

Failure Criterion ◽

Concentration Factor ◽

Critical Stress ◽

Strain Path ◽

Path Dependence ◽

Forming Limit ◽

Concentration Factors ◽

Stress Concentration Factors

Tearing concerns in sheet metal forming have traditionally been predicted by comparing the strain state imposed on a material to its associated strain based Forming Limit Diagram. A shortcoming of this strain based failure criterion is that the Forming Limit Curves exhibit strain path dependence. Alternatively, a stress based failure criterion was introduced and shown analytically and numerically to exhibit less strain path dependence. In our past research, an analytical model was created to predict the stress based Forming Limit Curve. Inputs into the model include a material constitutive relationship, anisotropic yield criterion and a critical stress concentration factor, defined as the ratio of the effective stress in the base material to the effective stress in the necking region. This stress concentration factor is thought to be a material parameter, which characterizes a material’s ability to work harden and prevent the concentration of stress which produces the necking condition. In this paper, the critical stress concentration factors for steel and aluminum alloys were determined by comparing analytical model predictions and experimental data and found to be significantly different. A setup is then proposed to experimentally measure the critical stress concentration factors and initial results are presented.

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A numerical solution of cavity expansion problem in sand based directly on experimental stress-strain curves

Canadian Geotechnical Journal ◽

10.1139/t98-028 ◽

1998 ◽

Vol 35 (4) ◽

pp. 541-559 ◽

Cited By ~ 18

Author(s):

Branko Ladanyi ◽

Adolfo Foriero

Keyword(s):

Numerical Solution ◽

Strain Path ◽

Shear Resistance ◽

Cavity Expansion ◽

Large Strains ◽

Volume Changes ◽

Stress Strain ◽

Stress Variation ◽

Cylindrical Cavity Expansion ◽

State Of Stress

A numerical solution of a spherical and cylindrical cavity expansion problem in sand is presented herein. The underlying theory is unbiased in that it is based directly on experimentally determined stress-strain curves. The solution makes it possible to follow the continuous variation of strains, stresses, and volume changes produced by cavity expansion. It essentially uses the "strain path" approach to determine the state of stress around the cavity, taking into account large strains and the effect of spherical stress variation on the mobilized shear resistance and the associated volume strains. A limited comparison with experimental data shows a reasonable agreement between theory and measurements.Key words: cavities, expansion, sand, stress-strain curves, numerical solution.

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