An efficient model for diffuse to localized necking transition in rate-dependent bifurcation analysis of metallic sheets

Zajkani, Asghar; Bandizaki, Ali

doi:10.1016/j.ijmecsci.2017.09.054

Cited by 13 publications

(3 citation statements)

References 24 publications

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“…On the one hand, the simultaneous activation of slip and twinning modes leads to a sharper yield locus (compared to the case of activation of slip mode only) and consequently promotes the occurrence of localized necking, especially in the range of positive strain paths (Barlat, 1987). However, the effect of such a curvature of the yield surface on the prediction of diffuse necking limit strains is very small, especially in the biaxial loading range, as has been demonstrated in several contributions (see, for instance, Kim et al, 2005;Zajkani and Bandizaki, 2017). On the other hand, the activation of the twinning deformation mode in addition to the slip mode leads to a significant increase in the evolution Fig.…”

Section: Sensitivity Studymentioning

confidence: 92%

Prediction of necking in HCP sheet metals using a two-surface plasticity model

Jedidi

Bettaieb

Abed‐Meraim

et al. 2020

International Journal of Plasticity

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In the present contribution, a two-surface plasticity model is coupled with several diffuse and localized necking criteria to predict the ductility limits of hexagonal closed packed sheet metals. The plastic strain is considered, in this two-surface constitutive framework, as the result of both slip and twinning deformation modes. This leads to a description of the plastic anisotropy by two separate yield functions: the Barlat yield function to model plastic anisotropy due to slip deformation modes, and the Cazacu yield function to model plastic anisotropy due to twinning deformation modes. Actually, the proposed two-surface model offers an accurate prediction of the plastic anisotropy as well as the tension-compression yield asymmetry for the material response. Furthermore, the current model allows incorporating the effect of distortional hardening resulting from the evolution of plastic anisotropy and tension-compression yield asymmetry. Diffuse necking is predicted by the general bifurcation criterion. As to localized necking, it is determined by the Rice bifurcation criterion as well as by the Marciniak & Kuczynski imperfection approach. To apply both bifurcation criteria, the expression of the continuum tangent modulus associated with this constitutive framework is analytically derived. The set of equations resulting from the coupling between the Marciniak & Kuczynski approach and the constitutive relations is solved by developing an efficient implicit algorithm. The numerical implementation of the two-surface model is assessed and validated through a comparative study between our numerical predictions and several experimental results from the literature. A sensitivity study is presented to analyze the effect of some mechanical parameters on the-2-prediction of diffuse and localized necking in thin sheet metals made of HCP materials. The effect of distortional hardening on the onset of plastic instability is also investigated.

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Section: Sensitivity Studymentioning

confidence: 92%

Prediction of necking in HCP sheet metals using a two-surface plasticity model

Jedidi

Bettaieb

Abed‐Meraim

et al. 2020

International Journal of Plasticity

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“…However, the ideal yield trajectory cannot accurately describe the deformation process in the deformation strengthening stage. This is because, in the subsequent yielding stage of the deformation process, singularity points must exist on the yield surface, resulting in regions of increased local stress [ 49 ]. Therefore, Storen and Rice believed that the deformation instability of materials is induced by the presence of singularity on the subsequent yield surface.…”

Section: Definition Of Deformation Instabilitymentioning

confidence: 99%

Theory, Method and Practice of Metal Deformation Instability: A Review

Wan

Yao

et al. 2023

Materials

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Deformation instability is a macroscopic and microscopic phenomenon of non-uniformity and unstable deformation of materials under stress loading conditions, and it is affected by the intrinsic characteristics of materials, the structural geometry of materials, stress state and environmental conditions. Whether deformation instability is positive and constructive or negative and destructive, it objectively affects daily life at all times and the deformation instability based on metal-bearing analysis in engineering design has always been the focus of attention. Currently, the literature on deformation instability in review papers mainly focuses on the theoretical analysis of deformation instability (instability criteria). However, there are a limited number of papers that comprehensively classify and review the subject from the perspectives of material characteristic response, geometric structure response, analysis method and engineering application. Therefore, this paper aims to provide a comprehensive review of the existing literature on metal deformation instability, covering its fundamental principles, analytical methods, and engineering practices. The phenomenon and definition of deformation instability, the principle and viewpoint of deformation instability, the theoretical analysis, experimental research and simulation calculation of deformation instability, and the engineering application and prospect of deformation instability are described. This will provide a reference for metal bearing analysis and deformation instability design according to material deformation instability, structural deformation instability and localization conditions of deformation instability, etc. From the perspective of practical engineering applications, regarding the key problems in researching deformation instability, using reverse thinking to deduce and analyze the characteristics of deformation instability is the main trend of future research.

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“…The NBA is limited by the strain magnitude. In this regard, Zajkani and Bandizaki 22 studied the transition of diffuse to localized necking in the context of an efficient rate-dependent bifurcation model. Another rate-dependent model can be found for evaluation of the non-linear strain paths.…”

Section: Introductionmentioning

confidence: 99%

Localized forming limit analysis of substrate-supported metals: Influence of yield-dependent necking bound angle

Bandizaki

Zajkani

Moulood

2021

Proceedings of the Institution of Mechanical Engineers, Part B:

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In this paper, the influence of functional elastomeric substrate-supported layers for enhancing potential resistance capability against localized plastic failure of advanced high strength steels is considered based on a localized necking model of vertex theory. Application of this structure leads to postponing the plastic instability of the metallic part. By defining diffuse and localized modes of deformation in a general framework, the theoretical models are developed to predict necking limits at several stress states. In addition, the results of the Hookean and neo-Hookean elastomers are compared in terms of strain hardening with the anisotropy parameter of Hill’s yield criteria. Since necking band angle (NBA) is a principal factor for the necking prediction, its effect on bifurcation events is evaluated specifically for different ratios of stress rate, and quadratic and non-quadratic yield criteria. This analysis is performed by proposing a supported and yield-dependent necking bound angle (YD-NBA). All considerations are done by providing equilibrium conditions governed over the NBA. Finally, obtained results indicate good agreements between several theoretical considerations and experimental data.

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An efficient model for diffuse to localized necking transition in rate-dependent bifurcation analysis of metallic sheets

Cited by 13 publications

References 24 publications

Prediction of necking in HCP sheet metals using a two-surface plasticity model

Prediction of necking in HCP sheet metals using a two-surface plasticity model

Theory, Method and Practice of Metal Deformation Instability: A Review

Localized forming limit analysis of substrate-supported metals: Influence of yield-dependent necking bound angle

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