Dynamics of Necking and Fracture in Ductile Porous Materials

Zheng, Xiang; N'souglo, Komi Espoir; Rodríguez-Martínez, J.A.; Srivastava, Ankit

doi:10.1115/1.4045841

Cited by 8 publications

(8 citation statements)

References 41 publications

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“…Note that, as ∆ increases, the cumulative instability index I neck decreases (see also Fig. 10 of Zheng et al (2020) and the discussion therein, and Appendix C of N'souglo et al (2020)). As in Sections 6.1, 6.2 and 6.4, the imposed initial major strain rate isε 0…”

Section: The Effect Of Imperfection Amplitudementioning

confidence: 94%

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

N'souglo

Jacques

Rodríguez-Martínez

2021

Journal of the Mechanics and Physics of Solids

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In this paper, we have investigated the effect of material orthotropy on the formability of metallic sheets subjected to 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 Rodríguez-Martínez 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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Section: The Effect Of Imperfection Amplitudementioning

confidence: 94%

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

N'souglo

Jacques

Rodríguez-Martínez

2021

Journal of the Mechanics and Physics of Solids

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“…For the given range of initial equivalent strain rates, the parameter describing the inertial resistance to motionL −1 varies between 0.00166 and 0.333 (see equation (31)). Note that previous numerical results reported by N'souglo et al [36,35] and Zheng et al [54] indicated that dynamic effects start to play an important role in the inception of necks forL −1 in the range 0.06 − 0.1. The finite element results are compared with the predictions of the linear stability analysis.…”

Section: Effect Of the Third Invariant On The Formation Of Dynamic Necks In Materials With The Same Response In Tension And Compression Amentioning

confidence: 66%

Effect of the third invariant on the formation of necking instabilities in ductile plates subjected to plane strain tension

et al. 2021

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In this paper, we have investigated the effect of the third invariant of the stress deviator on the formation of necking instabilities in isotropic metallic plates subjected to plane strain tension. For that purpose, we have performed finite element calculations and linear stability analysis for initial equivalent strain rates ranging from 10 −4 s −1 to 8 • 10 4 s −1 . The plastic behavior of the material has been described with the isotropic Drucker yield criterion [11], which depends on both the second and third invariant of the stress deviator, and a parameter c which determines the ratio between the yield stresses in uniaxial tension and in pure shear σ T /τ Y . For c = 0, Drucker yield criterion [11] reduces to the von Mises yield criterion [32] while for c = 81/66, the Hershey-Hosford (m = 6) yield criterion [19,22] is recovered. The results obtained with both finite element calculations and linear stability analysis show the same overall trends and there is also quantitative agreement for most of the loading rates considered. In the quasi-static regime, while the specimen elongation when necking occurs is virtually insensitive to the value of the parameter c, both finite element results and analytical calculations using Considère criterion [10] show that the necking strain increases as the parameter c decreases, bringing out the effect of the third invariant of the stress deviator on the formation of quasi-static necks. In contrast, at high initial equivalent strain rates, when the influence of inertia on the necking process becomes important, both finite element simulations and linear stability analysis show that the effect of the third invariant is reversed, notably for long necking wavelengths, with the specimen elongation when necking occurs increasing as the parameter c increases, and the necking strain decreasing as the parameter c decreases.

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“…et al ( 2009), Golovashchenko et al (2013) and Li et al (2017), among others). Moreover, the numerical results reported by N'souglo et al (2020) and Zheng et al (2020) indicated that the effect of inertia on neck retardation starts to be important forL −1 in the range 0.06 − 0.1. Initial void volume fractions ranging from 0.01 to 0.1 are considered.…”

Section: The Effect Of Porosity 360mentioning

confidence: 83%

A new analytical model to predict the formation of necking instabilities in porous plates subjected to dynamic biaxial loading

Kumar¹,

N'souglo²,

Rodríguez-Martínez³

2021

Preprint

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In this paper, we have developed a linear stability analysis to predict the formation of necking instabilities in porous ductile plates subjected to dynamic biaxial stretching. The mechanical behavior of the material is described with the Gurson-Tvergaard-Needleman constitutive relation for progressively cavitating solids (Gurson, 1977; Tvergaard, 1981, 1982; Tvergaard and Needleman, 1984) which considers the voids to be spherical and the matrix material isotropic with yielding defined by the von Mises (1928) criterion. The analytical model is formulated in a two-dimensional framework in which the multiaxial stress state that develops inside the necked region is approximated with the Bridgman (1952) correction factor, superimposing a hydrostatic stress state to the uniform stress field that develops in the plate before localization. As opposed to the linear stability models published so far to model dynamic necking in ductile plates, which consider the material to be fully dense and incompressible, the approach developed in this paper provides new insights into the interplay between porosity and inertia on plastic localization. In addition, the predictions of the theoretical model for the critical strain leading to necking formation have been compared with unit-cell finite element calculations performed in ABAQUS/Explicit (2019). Satisfactory quantitative and qualitative agreement has been found between the theoretical and computational approach for loading paths ranging from plane strain tension to nearly equibiaxial tension, loading rates varying from 100 s−1 to 10000 s−1, and different values of the initial void volume fraction ranging from 0.01 to 0.1. Both analytical and finite element results suggest that the influence of porosity on necking localization increases, due to early voids coalescence, as the loading rate increases and the loading path approaches equibiaxial tension. The original formulation developed in this paper serves as a basis for analytically modeling the dynamic formability of porous ductile plates, and it can be readily extended to consider more complex porous plasticity theories, e.g. constitutive models which consider the anisotropy of the material (Benzerga and Besson, 2001) and/or voids with different shapes (Gologanu et al., 1993; Monchiet et al., 2008).

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Dynamics of Necking and Fracture in Ductile Porous Materials

Cited by 8 publications

References 41 publications

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

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

Effect of the third invariant on the formation of necking instabilities in ductile plates subjected to plane strain tension

A new analytical model to predict the formation of necking instabilities in porous plates subjected to dynamic biaxial loading

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