Multiple necking pattern in nonlinear elastic bars subjected to dynamic stretching: The role of defects and inertia

Vaz-Romero, A.; Rodríguez-Martínez, J.A.; Mercier, Sébastien; Molinari, A.

doi:10.1016/j.ijsolstr.2017.07.001

Cited by 26 publications

(39 citation statements)

References 27 publications

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“…To track the history of the growth rate of all the growing modes during the post-homogeneous deformation process (i.e. for strains greater than the Considère strain), we use the cumulative instability index I = t 0 η + dt [21,38,42,43]. The index I accumulates the growth rate of all the growing modes during the loading process, i.e.…”

Section: Theoretical Modelmentioning

confidence: 99%

Dynamics of Necking and Fracture in Ductile Porous Materials

Zheng

N'souglo

Rodríguez-Martínez

et al. 2020

Journal of Applied Mechanics

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bines the effects of loading rate, material properties and unit cell size. Our results show that low initial porosity levels favor necking before fracture, and high initial porosity levels favor fracture before necking, especially at high loading rates where inertia effects delay the onset of necking. The finite element results are also compared with the predictions of linear stability analysis of necking instabilities in porous ductile materials.

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Section: Theoretical Modelmentioning

confidence: 99%

Dynamics of Necking and Fracture in Ductile Porous Materials

Zheng

N'souglo

Rodríguez-Martínez

et al. 2020

Journal of Applied Mechanics

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“…To this end, following [18,22,45], we introduce the concept of cumulative instability index defined as I = t t considère η + dt, where t considère corresponds to the time at maximum force (onset of post-critical regime). Unlike the instantaneous perturbation growthη + , the cumulative index-which integrates the dimensional growth rate of the perturbation-tracks the history of the growth rate of all the growing modes during the post-critical deformation process and, as such, provides a more accurate description of the dominant necking modes which determine the localization pattern for each level of strain [22,35]. The reader is referred to the paper of Vaz-Romero et al [35] to see a comparison between the results obtained with the instantaneous perturbation growth and the cumulative instability index for the problem of a nonlinear elastic bar subjected to dynamic stretching.…”

Section: Comparison Between Linear Stability Analysis and Finite-elemmentioning

confidence: 99%

“…Unlike the instantaneous perturbation growthη + , the cumulative index-which integrates the dimensional growth rate of the perturbation-tracks the history of the growth rate of all the growing modes during the post-critical deformation process and, as such, provides a more accurate description of the dominant necking modes which determine the localization pattern for each level of strain [22,35]. The reader is referred to the paper of Vaz-Romero et al [35] to see a comparison between the results obtained with the instantaneous perturbation growth and the cumulative instability index for the problem of a nonlinear elastic bar subjected to dynamic stretching. The key point is the calibration of the cumulative index in such a manner that the predictive capabilities of the stability analysis can be exploited.…”

Section: Comparison Between Linear Stability Analysis and Finite-elemmentioning

confidence: 99%

Random distributions of initial porosity trigger regular necking patterns at high strain rates

et al. 2018

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At high strain rates, the fragmentation of expanding structures of ductile materials, in general, starts by the localization of plastic deformation in multiple necks. Two distinct mechanisms have been proposed to explain multiple necking and fragmentation process in ductile materials. One view is that the necking pattern is related to the distribution of material properties and defects. The second view is that it is due to the activation of specific instability modes of the structure. Following this, we investigate the emergence of necking patterns in porous ductile bars subjected to dynamic stretching at strain rates varying from 10 to 0.5×10 using finite-element calculations and linear stability analysis. In the calculations, the initial porosity (representative of the material defects) varies randomly along the bar. The computations revealed that, while the random distribution of initial porosity triggers the necking pattern, it barely affects the average neck spacing, especially, at higher strain rates. The average neck spacings obtained from the calculations are in close agreement with the predictions of the linear stability analysis. Our results also reveal that the necking pattern does not begin when the Considère condition is reached but is significantly delayed due to the stabilizing effect of inertia.

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“…Notice that Dudzinski and Molinari (1991) and Zaera et al (2015) relied on the instantaneous instability indexη + to determine when a neck is formed, in order to construct forming limit diagrams. However, in this paper we choose I because, as discussed by El Maï et al 2014and Vaz-Romero et al (2017), it provides predictions for necking formation which are generally closer to finite element results.…”

Section: Linear Stability Modelmentioning

confidence: 83%

A three-pronged approach to predict the effect of plastic orthotropy on the formability of thin sheets subjected to dynamic biaxial stretching

Rodríguez-Martínez¹,

N'souglo²,

Jacques³

2020

Preprint

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In this paper, we have investigated the effect of material orthotropy on the formability of metallic sheets subjectedto dynamic biaxial stretching. For that purpose, we have devised an original three-pronged methodology which includes a linear stability analysis, a nonlinear two-zone model and ?finite element calculations. We have studied 5 different materials whose mechanical behavior is described with an elastic isotropic, plastic anisotropic constitutive model with yielding based on Hill (1948) criterion. The linear stability analysis and the nonlinear two-zone model are extensions of the formulations developed by Zaera et al. (2015) and Jacques (2020), respectively, to consider Hill (1948) plasticity. The ?finite element calculations are performed with ABAQUS/Explicit (2016) using the unit-cell model developed by Rodriguez-Martinez et al. (2017), which includes a sinusoidal spatial imperfection to favor necking localization. The predictions of the stability analysis and the two-zone model are systematically compared against the ?finite element results --which are considered as the reference approach to validate the theoretical models-- for loading paths ranging from plane strain stretching to equibiaxial stretching, and for different strain rates ranging from 100 s-1 to 50000 s-1. The stability analysis and the two-zone model yield the same overall trends obtained with the ?finite element simulations for the 5 materials investigated, and for most of the strain rates and loading paths the agreement for the necking strains is also quantitative. Notably, the differences between the ?finite element results and the two-zone model rarely go beyond 5%. Altogether, the results presented in this work provide new insights into the mechanisms which control dynamic formability of anisotropic metallic sheets.

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Multiple necking pattern in nonlinear elastic bars subjected to dynamic stretching: The role of defects and inertia

Cited by 26 publications

References 27 publications

Dynamics of Necking and Fracture in Ductile Porous Materials

Dynamics of Necking and Fracture in Ductile Porous Materials

Random distributions of initial porosity trigger regular necking patterns at high strain rates

A three-pronged approach to predict the effect of plastic orthotropy on the formability of thin sheets subjected to dynamic biaxial stretching

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