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Research Papers

Smooth Yield Surface Constitutive Modeling for Granular Materials

[+] Author and Article Information
Youssef Hammi

Center for Advanced Vehicular Systems,
Box 5405,
Mississippi State, MS 39762-5405
e-mail: yhammi@cavs.msstate.edu

Tonya W. Stone

Mem. ASME
Department of Mechanical Engineering,
Mississippi State University,
Box 9552,
Mississippi State, MS 39762-9552
e-mail: stone@me.msstate.edu

Bhasker Paliwal

Center for Advanced Vehicular Systems,
Box 5405,
Mississippi State, MS 39762-5405
e-mail: bhasker@cavs.msstate.edu

Mark F. Horstemeyer

Mem. ASME
Department of Mechanical Engineering,
Mississippi State University,
Box 9552,
Mississippi State, MS 39762-9552
e-mail: mfhorst@me.msstate.edu

Paul G. Allison

Mem. ASME
Department of Mechanical Engineering,
University of Alabama,
Box 870276,
Tuscaloosa, AL 35487-0276
e-mail: pallison@eng.ua.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received June 13, 2016; final manuscript received October 14, 2016; published online November 14, 2016. Assoc. Editor: Curt Bronkhorst.

J. Eng. Mater. Technol 139(1), 011010 (Nov 14, 2016) (10 pages) Paper No: MATS-16-1181; doi: 10.1115/1.4034987 History: Received June 13, 2016; Revised October 14, 2016

In this paper, the authors present an internal state variable (ISV) cap plasticity model to provide a physical representation of inelastic mechanical behaviors of granular materials under pressure and shear conditions. The formulation is dependent on several factors: nonlinear elasticity, yield limit, stress invariants, plastic flow, and ISV hardening laws to represent various mechanical states. Constitutive equations are established based on a modified Drucker–Prager cap plasticity model to describe the mechanical densification process. To avoid potential numerical difficulties, a transition yield surface function is introduced to smooth the intersection between the failure and cap surfaces for different shapes and octahedral profiles of the shear failure yield surface. The ISV model for the test case of a linear-shaped shear failure surface with Mises octahedral profile is implemented into a finite element code. Numerical simulations using a steel metal powder are presented to demonstrate the capabilities of the ISV cap plasticity model to represent densification of a steel powder during compaction. The formulation is general enough to also apply to other powder metals and geomaterials.

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References

Figures

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Fig. 1

The ISV cap model showing the yield surface in the meridional (q, p) plane

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Fig. 2

Hyperbolic-shaped shear failure yield surface smoothly connected to a cap surface in the meridional (q, p) plane

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Fig. 3

Exponent-shaped shear failure yield surface smoothly connected to cap surface in the meridional (q, p) plane

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Fig. 4

Three-dimensional representation of the linear-, hyperbolic- and exponent-shaped shear yield surfaces smoothly connected to the cap surface with a Mises, Gudehus, William–Warnke, and Mohr–Coulomb octahedral profiles

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Fig. 5

Yield surface profile in the octahedral plane

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Fig. 6

Octahedral shear failure envelopes plotted at allowable values of strength ratio (a) with no smoothing and (b) with smoothing parameter, γ=0.995

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Fig. 15

Procedure to build pq-plots from different experiments

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Fig. 16

Isodensity curves in the p-q meridional plane representing the evolution of the ISV cap model with respect to relative density (% theoretical) for FC-0205 steel powders

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Fig. 14

Calibrated cap eccentricity versus green density for FC-0205 steel powders

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Fig. 13

Comparison of measured and finite element hoop strains for a 6.35 cm FC-0205 copper steel cylindrical sample

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Fig. 12

(a) Hoop strain contours on the cylindrical die after simulated compaction of a FC-0205 copper steel powder and (b) strain gauges located on cylindrical die to measure hoop strain during compaction of FC-0205 powder

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Fig. 11

Comparison of the elastic Young's modulus E as function of the porosity for the FC-0205 steel powder with the AS1000 metal powders (data from Ref. [51])

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Fig. 10

Interparticle friction (tan β) versus green density for FC-0205 steel cylindrical samples

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Fig. 9

Material cohesion (d) versus green density for FC-0205 steel cylindrical samples

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Fig. 8

Failure stress versus green density for FC-0205 steel cylindrical samples

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Fig. 7

Density–pressure compressibility curves associated with cap hardening for FC-0205 steel powders from isostatic compaction tests

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