Constitutive equations for granular materials : application to dry sand and powder metal

Abstract

Strain localization into shear bands is commonly observed in natural soil masses, as well as in human-built embankments, footings, retaining walls and other geotechnical structures. Although the onset of strain localization can be derived from standard bifurcation analyses, few numerical simulations of the complete process of strain localization in granular materials have been previously reported. Predictions for the onset and process of shear band formation are critically dependent upon the constitutive equations employed. In this thesis, a new physically based constitutive model is formulated for describing the plastic flow of cohesionless granular materials. This constitutive model has been implemented in the finite element package ABAQUS/explicit(1999) and is used to predict the strain localization in geomaterials. The numerical calculations are shown to be in good quantitative agreement with the recent corresponding experiments of Han and Drescher(1993) and Alsiny et al. (1992) on the localization in dry Ottawa sand under low pressure conditions. The physical description for the plastic flow enables the model to reproduce the macroscopic stress strain response and the complete strain localization process. The complex evolution of the strain localization from "Riedel shear" to "boundary shear" in the shearing experiment of a simulated gouge layer (Marone et al., 1990,1999) has been captured in our simulations. This physically based constitutive model is also able to predict the startling "stress dip" in a static sandpile - the vertical stress is not maximum under the apex of the pile, but shows a local dip there. Next, we shall focus on metal powders, which are commonly used in powder metallurgy industry to form net- or near-net-shaped components with high relative density by cold compaction. A new constitutive model for cold compaction of metal powders has been developed. The plastic flow of metal powders at the macroscopic level is assumed to be representable as a combination of a distortion mechanism, and a consolidation mechanism. For the distortion mechanism the model employs a pressure-sensitive, Mohr-Coulomb type yield condition, and a new physically based non-associated flow rule. For the consolidation mechanism the model employs a smooth yield function which has a quarter-elliptical shape in the mean-normal pressure and the equivalent shear stress plane, together with an associated flow rule. The constitutive model has been implemented in a finite element program. The material parameters in the constitutive model have been calibrated for MH-100 iron powder by fitting the model to reproduce data from true triaxial compression experiments, torsion ring-shear experiments, and simple compression experiments. The predictive capability of the constitutive model and computational procedure is checked by simulating two simple powder forming processes: (i) a uniaxial strain compression of a cylindrical sample, and (ii) forming of a conical shaped-charge liner. In both cases the predicted load-displacement curves and density variations in the compacted specimens are shown to compare well with corresponding experimental measurements.