Evaluation of constitutive models for voided solids

Ragab, Ahmed; Saleh, Ch.A.R.

doi:10.1016/s0749-6419(99)00024-8

Cited by 43 publications

(25 citation statements)

References 19 publications

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“…[18] An extension to include anisotropy of the matrix material of the voided solid is presented by Ragab and Saleh. [19,20] Orthotropic anisotropy as introduced by Hill [21] is adopted here such that the macroscopic effective stress in terms of the principal stresses ( 1 , 2 , 3 ) is given by [1] where…”

Section: A Constitutive Laws For Anisotropic Voided Solidsmentioning

confidence: 99%

“…Combining Eq. [1] with a simplified form of the GursonTvergaard yield function [18,19,20] gives the effective matrix stress as [2] where f is the void volume fraction and the mean stress m ϭ ( 1 ϩ 2 ϩ 3 )/3. According to several works as listed in the article by Ragab, [23] the semiempirical parameters q 1 and q 2 , previously adopted by Tvergaard, [18] are selected to be q 1 ϭ 2 and q 2 ϭ 1.…”

Section: A Constitutive Laws For Anisotropic Voided Solidsmentioning

confidence: 99%

“…Contact e-mail: a.r.ragab@link.net Manuscript submitted April 6, 2005. model deals with the materials as being initially defected with voids nucleated at inclusions. The analysis is thus based on a Gurson-Tvergaard yield function [18] for voided solids, which is modified [19,20] to include Hill's model of orthotropic anisotropy, [21] a factor that is largely overlooked in most analyses. The limit strains are generally predicted at the onset of formation of shear bands within the ligaments joining growing voids of spheroidal shapes according to a condition given by McClintock.…”

Section: Introductionmentioning

confidence: 99%

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An approach to predict free surface fracture in bulk forming

Ragab

2006

Metall Mater Trans A

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This work presents a unified approach to predict surface strains at failure in bulk forming processes. The approach does not deal with a specific process but rather with prescribed strain and stress paths. The material to be processed is assumed to possess an initial void volume fraction that grows and coalesces with straining, ending by fracture. The predictions are based on a formulation for voided solids according to the Gurson-Tvergaard yield function adapted to include orthotropic anisotropy. The incident of fracture is characterized by shear band formation within the ligaments of the matrix material among spheroidal voids as described by McClintock. The results are represented by a straight line plot of tensile limit strain versus the compressive strain for different loading paths. These limit curves are shown to be dependent on the initial void fraction, hardening, and anisotropy of the matrix material. Alloys with lower initial void fractions as well as those of higher hardening show better workability. The model is applied to predict bulk formability curves for steels AISI 1040 and 1045, Aluminum Al 7075-T6, and copper, based on the proper selection of micromechanical parameters for these alloys. The validity of the model is ensured through fairly favorable comparison with experimentally determined limit curves. The current failure conditions are suitable to predict the experimental dual slope fracture line that may exist for some alloys such as cold-drawn steel AISI 1045 and aluminum 2024-T6 by considering two mechanisms of failure: internal necking in the ligament material between voids, followed by transition to shear band formation.

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Section: A Constitutive Laws For Anisotropic Voided Solidsmentioning

confidence: 99%

Section: A Constitutive Laws For Anisotropic Voided Solidsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An approach to predict free surface fracture in bulk forming

Ragab

2006

Metall Mater Trans A

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“…Since the above yield function involving a hyperbolic cosine term becomes unattractive in further analytical manipulations, the hyperbolic cosine term is expanded into a series. In most plastic deformation processes (κσ m /σ M ) is of the order of unity or less; hence it is acceptable to neglect powers higher than 2, as discussed by Ragab and Saleh (30) .…”

Section: Yield Function For Anisotropic Materials Withmentioning

confidence: 99%

Effect of Void Shape and Its Growth on Forming Limits for Anisotropic Sheets Containing Non-Spherical Voids

Son

Kim

et al. 2004

JSME Int. J., Ser. A

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2-15) to a ductile material containing an oblate ellipsoidal cavity. And, they proposed a new approximate yield function incorporating the initial void shape effects, which is significant especially at low stress triaxiality. In the present work, the Gologanu-Leblond-Devaux's yield function for anisotropic sheet materials containing axisymmetric prolate ellipsoidal cavities is adopted in evaluating analytically forming limits of sheet metals under biaxial stretching by Marciniak and Kuczynski (M-K) model. The effect of a void shape and growth on the forming limits of sheet metals under biaxial tensile loading is introduced and examined within the framework of the M-K model, along with the effect of including a first-order strain gradient term in the flow stress. To confirm the validity of the proposed model, the predicted FLDs were compared with experimental results for steel sheets. The predicted forming limits for the voided sheets were found to agree well with the experimental data.

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“…foams), considering applications, experimental tests and different approaches for modeling [1][2][3][4][5] . To identify and determine the mechanical properties of cellular materials, standards and consolidated experimental methods developed for solid homogenous materials can be applied.…”

Section: Introductionmentioning

confidence: 99%

Study of an anisotropic polymeric cellular material under compression loading

et al. 2012

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This paper emphasizes the influence of micro mechanisms of failure of a cellular material on its phenomenological response. Most of the applications of cellular materials comprise a compression loading. Thus, the study focuses on the influence of the anisotropy in the mechanical behavior of cellular material under cyclic compression loadings. For this study, a Digital Image Correlation (DIC) technique (named Correli) was applied, as well as SEM (Scanning Electron Microscopy) images were analyzed. The experimental results are discussed in detail for a closed-cell rigid poly (vinyl chloride) (PVC) foam, showing stress-strain curves in different directions and why the material can be assumed as transversely isotropic. Besides, the present paper shows elastic and plastic Poisson's ratios measured in different planes, explaining why the plastic Poisson's ratios approach to zero. Yield fronts created by the compression loadings in different directions and the influence of spring-back phenomenon on hardening curves are commented, also.

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Evaluation of constitutive models for voided solids

Cited by 43 publications

References 19 publications

An approach to predict free surface fracture in bulk forming

An approach to predict free surface fracture in bulk forming

Effect of Void Shape and Its Growth on Forming Limits for Anisotropic Sheets Containing Non-Spherical Voids

Study of an anisotropic polymeric cellular material under compression loading

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