Constitutive behaviour of metal powder during hot forming.

Geindreau, Christian; Bouvard, D.; Dorémus, P.

doi:10.1016/s0997-7538(99)00101-1

Cited by 21 publications

(35 citation statements)

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“…In this particular case, for a given value of n, it can be shown (Abouaf, 1985;Geindreau et al, 1999b;Danas et al, 2008) that the macroscopic equivalent stress is written…”

Section: Macro-strain Paths Definition (Step 4)mentioning

confidence: 99%

“…As a first approximation, it seems reasonable to assume that the influence of the third invariant S 3 is negligible (Green, 1972;Abouaf, 1985;Geindreau et al, 1999b;Fritzen et al, 2012). Consequently, the macroscopic volumetric mechanical dissipation P v depends on the first and second stress and strain invariants and not only on the second ones as at the microscale 6.…”

Section: Macro-strain Paths Definition (Step 4)mentioning

confidence: 99%

“…5. Different expressions of the material functions f (φ) and c(φ) have been proposed in the past based on experimental data on metal powders (Abouaf, 1985;Abouaf and Chenot, 1988;Geindreau et al, 1999b), micromechanical modeling (cell model; Duva and Crow, 1992) or numerical simulations on simple microstructures (Sofronis and McMeeking, 1992). These functions have been identified in a restricted range of porosity (dense materials with φ < 0.4).…”

Section: Density Dependence Of the Iso-dissipation Curvesmentioning

confidence: 99%

“…These functions have been identified in a restricted range of porosity (dense materials with φ < 0.4). We propose to fit our numerical results using the expressions proposed by Geindreau et al (1999b). In order to account for the change in the porosity range between metal powders and snow, the relative density limit value of 0.57 is set equal to zero.…”

Section: Density Dependence Of the Iso-dissipation Curvesmentioning

confidence: 99%

“…Nevertheless, it can be shown that the exponent n is preserved at the macroscopic scale and that the macroscopic dissipation power is the volume average of the local one (Suquet, 1993). Using these properties, the macroscopic constitutive equation of snow is formulated within the framework defined by the theory of representation of anisotropic tensor functions (Smith, 1971;Liu, 1982) and by using macroscopic iso-dissipation surfaces (Green, 1972;Abouaf, 1985;Duva and Crow, 1992;Sofronis and McMeeking, 1992;Geindreau et al, 1999b;Storakers et al, 1999;Sanchez et al, 2002;Orgéas et al, 2007). The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

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Numerical homogenization of the viscoplastic behavior of snow based on X-ray tomography images

2017

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Abstract. While the homogenization of snow elastic properties has been widely reported in the literature, homogeneous rate-dependent behavior responsible for the densification of the snowpack has hardly ever been upscaled from snow microstructure. We therefore adapt homogenization techniques developed within the framework of elasticity to the study of snow viscoplastic behavior. Based on the definition of kinematically uniform boundary conditions, homogenization problems are applied to 3-D images obtained from X-ray tomography, and the mechanical response of snow samples is explored for several densities. We propose an original postprocessing approach in terms of viscous dissipated powers in order to formulate snow macroscopic behavior. Then, we show that Abouaf models are able to capture snow viscoplastic behavior and we formulate a homogenized constitutive equation based on a density parametrization. Eventually, we demonstrate the ability of the proposed models to account for the macroscopic mechanical response of snow for classical laboratory tests.

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“…In this particular case, for a given value of n, it can be shown (Abouaf, 1985;Geindreau et al, 1999b;Danas et al, 2008) that the macroscopic equivalent stress is written…”

Section: Macro-strain Paths Definition (Step 4)mentioning

confidence: 99%

Section: Macro-strain Paths Definition (Step 4)mentioning

confidence: 99%

Section: Density Dependence Of the Iso-dissipation Curvesmentioning

confidence: 99%

Section: Density Dependence Of the Iso-dissipation Curvesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical homogenization of the viscoplastic behavior of snow based on X-ray tomography images

2017

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Identification of the Norton‐Green Compaction Model for the Prediction of the Ti–6Al–4V Densification During the Spark Plasma Sintering Process

et al. 2016

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One of the main challenges for the industrialization of the spark plasma sintering (SPS) is to resolve issues linked to the compaction of real parts with complex shapes. The modeling of powder compaction is an interesting tool to predict how the densification field varies during sintering. However, expressing the behavior law which reflect the powder compaction is often a difficult and long step in the model establishment. In this paper, a simple methodology for the identification of the densification parameters is proposed. Dense and porous creep tests combined with SPS die compaction tests are employed to determine a complete densification law on a Ti-6Al-4V alloy directly in a SPS machine. The compaction model obtained is successfully validated through prediction of the densification of new SPSed samples.

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Two-phase thermo-mechanical and macrosegregation modelling of binary alloys solidification with emphasis on the secondary cooling stage of steel slab continuous casting processes

Fachinotti

Corre

Triolet³

et al. 2006

Int. J. Numer. Meth. Engng

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International audienceAs an approach towards a better modelling of solidification problems, we introduce a thermo-mechanical and macrosegregation model that considers a solidifying alloy as a binary mixture made of a liquid and a solid phase. Macroscopic conservation laws for mass, momentum and solute are obtained by spatial averaging of the respective microscopic conservation equations. Assuming local thermal equilibrium, a single equation for the conservation of the mixture energy is then written. A single equation can be obtained for the solute as well by invoking a proper microsegregation rule. The numerical implementation in a 2D finite element code is then detailed. Lastly, some examples of simulations of academic tests as well as industrial applications for continuous casting of steel slabs are discussed. They particularly enlighten the ability of the formulation to describe the formation of central macrosegregation during the secondary cooling of slab continuous casting processes

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Constitutive behaviour of metal powder during hot forming.

Cited by 21 publications

References 0 publications

Numerical homogenization of the viscoplastic behavior of snow based on X-ray tomography images

Numerical homogenization of the viscoplastic behavior of snow based on X-ray tomography images

Identification of the Norton‐Green Compaction Model for the Prediction of the Ti–6Al–4V Densification During the Spark Plasma Sintering Process

Two-phase thermo-mechanical and macrosegregation modelling of binary alloys solidification with emphasis on the secondary cooling stage of steel slab continuous casting processes

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