Forming limit prediction of anisotropic material subjected to normal and through thickness shear stresses using a modified M–K model

Fatemi, Afshin; Dariani, Bijan Mollaei

doi:10.1007/s00170-015-7001-x

Cited by 22 publications

(11 citation statements)

References 29 publications

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“…8 demonstrate that the application of compressive normal stresses on a sheet allows its formability to be enhanced, especially in the range of positive strain paths. These results are consistent with several earlier investigations (see, e.g., [10,13,14]). a b Fig.…”

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confidence: 94%

“…As a result of this investigation, a new generalized forming limit diagram has been proposed, which highlights the influence of normal stress components on the formability limits. The numerical approach developed in Allwood and Shouler [13] has been extended by Fatemi and Dariani [14] by taking into account the plastic anisotropy of the sheet via the use of the Hill'48 yield criterion. In both of these contributions, the strain and stress distributions have been assumed to be homogeneous through the thickness of the sheet during the deformation.…”

Section: Introductionmentioning

confidence: 99%

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Numerical investigation of the combined effects of curvature and normal stress on sheet metal formability

2017

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A number of parts and components involved in the automotive industry are made of thin bent sheets, which are subjected to out-of-plane compressive stresses in addition to traditional in-plane stresses. Unfortunately, the classical predictions based on the conventional concept of Forming Limit Diagram (FLD) are no longer relevant when the strain distribution is heterogonous over the sheet thickness. Therefore, this conventional FLD concept is not capable of accounting for the effect of out-of-plane stresses on the onset of localized necking. The aim of the present contribution is to propose an extension of the well-known Marciniak-Kuczynski approach to simultaneously account for the effect of curvature and normal stress on formability prediction. The new developed tool allows predicting the limit strains for the whole range of strain paths. The mechanical behavior of the studied sheets follows the rigid-plastic flow theory. Through numerical results, it is shown that both curvature and normal stress tend to increase the formability limit of the sheet metal.

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confidence: 94%

Section: Introductionmentioning

confidence: 99%

Numerical investigation of the combined effects of curvature and normal stress on sheet metal formability

2017

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“…As a result of this earlier investigation, a new generalized forming limit diagram has been proposed, which highlights the influence of normal stress component on the formability limit. Note that a specifically designed linear paddle testing apparatus has been used in [9] to experimentally assess the increase in formability limits due to the application of normal compressive stresses. It is shown in this latter study that the use of simplifying assumptions, such as plastic isotropy, results in some discrepancies between numerical predictions and experimental results.…”

Section: Introductionmentioning

confidence: 99%

“…It is shown in this latter study that the use of simplifying assumptions, such as plastic isotropy, results in some discrepancies between numerical predictions and experimental results. To avoid this drawback, Fatemi and Dariani [9] extended the approach developed in [8] , by taking into account the plastic anisotropy of the sheet via the application of Hill '48 yield criterion. Another extension of the Marciniak and Kuczynski approach has been developed in [10] .…”

Section: Introductionmentioning

confidence: 99%

Theoretical and numerical investigation of the impact of out-of-plane compressive stress on sheet metal formability

Bettaieb

Abed‐Meraim

2017

International Journal of Mechanical Sciences

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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. In modern sheet metal forming processes, such as hydroforming and single point incremental forming, sheet metals are often subjected to out-of-plane compressive stresses in addition to traditional in-plane stresses. However, the effect of these out-of-plane stresses on the onset of plastic strain localization is not considered when classic necking criteria are used, as the latter are generally formulated based on the plane stress assumption. The main objective of the present investigation is to overcome this limitation by developing numerical tools and analytical relations that allow considering the influence of these compressive stresses on the prediction of localized necking. In the different tools developed, and for comparison purposes, finite strain versions of both the deformation theory of plasticity and the rigid-plastic flow theory are used to describe the mechanical behavior of the metal sheet. Furthermore, both the bifurcation theory and the initial imperfection approach are employed to predict the onset of strain localization. Various numerical predictions are reported to illustrate the effect of normal stress on the occurrence of localized necking in sheet metals. From these different results, it is clearly demonstrated that out-of-plane stresses may notably enhance sheet metal formability and, therefore, this property can be effectively used to avoid the initiation of early strain localization.

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“…When the tubes were bulged under the combined actions of internal and external pressures, the stress state must be treated as threedimensional stress state. Moreover, several forming limit theory models, which considering the effect of through-thickness normal stress, has been established based on the classical plastic instability theory and M-K approach, respectively [25][26][27]. So far, the mechanical properties of thin-walled anisotropic tubes under three-dimensional stress state have not yet been realized due to the challenge of experimental setup for doublesided tube hydro-bulging.…”

Section: Introductionmentioning

confidence: 99%

Determination of mechanical properties of anisotropic thin-walled tubes under three-dimensional stress state

Cui

Yuan

2016

Int J Adv Manuf Technol

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Tube hydro-bulging test is a specialized method to obtain the mechanical properties of tubes when they are deformed under bi-axial stress states. However, the normal stress cannot be ignored in double-sided tube hydroforming process. In order to investigate the mechanical properties of anisotropic thin-walled tubes under three-dimensional stress state, an analytical model for stress component calculation for fixed-end tube under internal and external pressures was proposed. Furthermore, the equivalent stress and the equivalent strain were derived using the Hill 1948 yield criterion through plastic increment theory. A thin-walled AA5052-O aluminum alloy tubes were bulged under different external pressures using a dedicated testing apparatus for double-sided tube hydrobulging tests. Then, hardening curves considering anisotropy were obtained for each external pressure condition, respectively. It is shown that the strain hardening exponent of AA5052 tube shows a slight increase with the increasing external pressure, and the external pressure of 85 MPa has little or no effects on the hardening behavior of tubes. Moreover, the anisotropy has a little effect on the strain hardening exponent, but has an obvious influence on the strength coefficient of the AA5052 tube. Therefore, for the measurement of the AA5052 tube's mechanical properties under three-dimensional stress state, the effect of external pressure can be ignored but the anisotropy of tubes must be considered.

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Forming limit prediction of anisotropic material subjected to normal and through thickness shear stresses using a modified M–K model

Cited by 22 publications

References 29 publications

Numerical investigation of the combined effects of curvature and normal stress on sheet metal formability

Numerical investigation of the combined effects of curvature and normal stress on sheet metal formability

Theoretical and numerical investigation of the impact of out-of-plane compressive stress on sheet metal formability

Determination of mechanical properties of anisotropic thin-walled tubes under three-dimensional stress state

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