Forming limit diagrams for anisotropic metal sheets with different yield criteria

Kuroda, Mitsutoshi; Tvergaard, Viggo

doi:10.1016/s0020-7683(99)00200-0

Cited by 152 publications

(67 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…7. It should be noted, that if strain-gradient effects are excluded within this material model a conventional anisotropic plasticity theory arises which can be used with high accuracy for M-K analyses [52].…”

Section: Resultsmentioning

confidence: 99%

Necking of anisotropic micro-films with strain-gradient effects

Legarth

2008

Acta Mech Sin

View full text Add to dashboard Cite

Necking of stubby micro-films of aluminum is investigated numerically by considering tension of a specimen with an initial imperfection used to onset localisation. Plastic anisotropy is represented by two different yield criteria and strain-gradient effects are accounted for using the visco-plastic finite strain model. Furthermore, the model is extended to isotropic anisotropic hardening (evolving anisotropy). For isotropic hardening plastic anisotropy affects the predicted overall nominal stress level, while the peak stress remains at an overall logarithmic strain corresponding to the hardening exponent. This holds true for both local and nonlocal materials. Anisotropic hardening delays the point of maximum overall nominal stress.

show abstract

Section: Resultsmentioning

confidence: 99%

Necking of anisotropic micro-films with strain-gradient effects

Legarth

2008

Acta Mech Sin

View full text Add to dashboard Cite

show abstract

“…Nevertheless, Gotoh's yield function has only been considered occasionally in sheet metal modeling analyses since its first introduction more than forty years ago [8,9,10,11,12,13], but rarely outside Japan [14,15]. In comparison, associated non-quadratic yield functions such as Yld2000-2d and non-associated quadratic anisotropic sheet metal plasticity modeling that have only been proposed and developed since 2000s [16,17] are much more widely appeared nowadays in the literature.…”

Section: Related Contentmentioning

confidence: 99%

On the Certification of Positive and Convex Gotoh’s Fourth-Order Yield Function

Tong

2018

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Abstract. Gotoh proposed in 1977 a fourth-order homogeneous polynomial of three plane stress components as a yield function to model anisotropic yielding and plastic flow of sheet metals. The yield function admits up to eight experimental inputs from uniaxial tension tests and one measurement from an equal biaxial tension test for calibrating its nine material constants and can model the formation of up to eight ears in deep cup drawing. However, the superior Gotoh's yield function has not been widely adopted in sheet metal forming analyses in both academy and industry, especially outside Japan. One major concern is uncertain about the positivity and convexity of a calibrated Gotoh's yield function. Here the problem of certifying a calibrated Gotoh's yield function to be strictly positive and convex is first described and its resolutions are summarized based on some very recent research results. Algebraic necessary and sufficient conditions for a positive and convex Gotoh's yield function with only two nonzero stress components are first presented. Sufficient conditions in terms of semi-algebraic and algebraic inequalities for establishing the positivity and convexity of tri-component plane stress Gotoh's yield function are then summarized. Finally, the complete necessary and sufficient conditions for a positive and convex Gotoh's yield function in plane stress are realized as a fully numerical minimization problem. Examples of successfully applying those conditions in certifying positive and convex Gotoh's yield functions of various sheet metals are also given.

show abstract

“…Accordingly, a wide range of phenomenological constitutive models have been coupled with several localization criteria to investigate the effect on the predicted FLDs of various mechanical features, such as plastic anisotropy (Neale and Chater, 1980;Cao et al, 2000;Kuroda and Tvergaard, 2000;Wu et al, 2004;Zhang and Wang, 2012), strain-rate sensitivity (Ghosh, 1977;Hutchinson and Neale, 1978b;Neale and Chater, 1980;Khan and Baig, 2011;Manopulo et al, 2015), temperature (Khan and Baig, 2011;Manopulo et al, 2015) and damage-induced softening (Haddag et al, 2009;Abed-Meraim et al, 2014;Mansouri et al, 2014). However, a major shortcoming in the phenomenological constitutive models is their inability to consider accurately many of the salient microstructural aspects of the material behavior, such as crystallographic texture (Hosford and Caddell, 1993;Raabe et al, 2005).…”

Section: Introductionmentioning

confidence: 99%

Computationally efficient predictions of crystal plasticity based forming limit diagrams using a spectral database

Gupta

Bettaieb

Abed‐Meraim

et al. 2018

International Journal of Plasticity

View full text Add to dashboard Cite

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible.This is an author-deposited version published in: https://sam.ensam.eu Handle ID: .http://hdl.handle.net/10985/13136 To cite this version :Akash GUPTA, Mohamed BEN BETTAIEB, Farid ABED-MERAIM, Surya KALIDINDIComputationally efficient predictions of crystal plasticity based forming limit diagrams using a spectral database -International Journal of Plasticity -Vol. 103, p.168-187 -2018 Any correspondence concerning this service should be sent to the repository A B S T R A C TThe present investigation focuses on the development of a fast and robust numerical tool for the prediction of the forming limit diagrams (FLDs) for thin polycrystalline metal sheets using a Taylor-type (full constraints) crystal plasticity model. The incipience of localized necking is numerically determined by the well-known Marciniak-Kuczynski model. The crystal plasticity constitutive equations, on which these computations are based, are known to be highly nonlinear, thus involving computationally very expensive solutions. This presents a major impediment to the wider adoption of crystal plasticity theories in the computation of FLDs. In this work, this limitation is addressed by using a recently developed spectral database approach based on discrete Fourier transforms (DFTs). Significant improvements were made to the prior approach and a new database was created to address this challenge successfully. These extensions are detailed in the present paper. It is shown that the use of the database allows a significant reduction in the computational cost involved in crystal plasticity based FLD predictions (a reduction of about 96% in terms of CPU time).

show abstract

Forming limit diagrams for anisotropic metal sheets with different yield criteria

Cited by 152 publications

References 32 publications

Necking of anisotropic micro-films with strain-gradient effects

Necking of anisotropic micro-films with strain-gradient effects

On the Certification of Positive and Convex Gotoh’s Fourth-Order Yield Function

Computationally efficient predictions of crystal plasticity based forming limit diagrams using a spectral database

Contact Info

Product

Resources

About