Anelastic collapse of small cavities in metals

Engineering Fracture Mechanics, 1985

Composite materials made of a steel matrix and spherical alumina particles were prepared to study the growth of cavities nucleated from A1203 inclusions during deformation at room temperature. Two materials containing different volume fractions of A1z03 particles, i.e. f = 0.5% and 2%. were investigated. Axisymmetric notched specimens were employed to determine the effect of stress triaxiality on cavity growth rate. These specimens were calculated by finite element method. They were predeformed at room temperature and subsequently broken at -196°C. The experimental results are in broad agreement with the theoretical results derived from Rice and Tracey model. In particular it is observed that the cavity growth is proportional to the local strain obtained from the finite element calculations. Moreover the effect of stress triaxiality intervenes exponentially as predicted by the Rice and Tracey model. However, the theoretical proportionality factor in front of the exponential term is lower than the experimental one. The reasons for this discrepancy. especially the effect of interactions between neighbouring inclusions which are not taken into account in this model, are briefly discussed.

International Journal of Mechanical Sciences, 2007

Cavitation instabilities have been found for a single void in a ductile metal stressed under high triaxiality conditions. Here, the possibility of unstable cavity growth is studied for a metal containing many voids. The central cavity is discretely represented, while the surrounding voids are represented by a porous ductile material model in terms of a field quantity that specifies the variation of the void volume fraction in the surrounding metal. As the central void grows, the surrounding void volume fractions increase in nonuniform fields, where the strains grow very large near the void surface, while the high stress levels are reached at some distance from the void, and the interaction of these stress and strain fields determines the porosity evolution. In some cases analysed, the porosity is present initially in the metal matrix, while in other cases voids nucleate gradually during the deformation process. It is found that interaction with the neighbouring voids reduces the critical stress for unstable cavity growth.

Solid State Communications, 2006

In his recent paper, Shear modulus collapse of lattices at high pressure, J. Phys. Cond. Matt. 16 (2004) L125, V.V. Kechin claims that the zero temperature shear modulus of a metallic solid vanishes at a high critical pressure, and the critical pressures for this shear modulus collapse lie in the range 0-250 Mbar for elemental metals. Here we demonstrate that Kechin's arguments contain an erroneous assumption, and therefore, do not prove that all metals become mechanically unstable at high pressures. Ab initio calculations and experimental results on a number of solids are analyzed to confirm our conclusion.

Mechanics of Materials, 2005

Molecular dynamics calculations were performed using embedded atom method (EAM) potentials to study the localization of inelastic flow and crack initiation in fcc single crystal copper and nickel. We compared the atomic scale anisotropic inelastic response of the copper single crystals from EAM to the results of [Philos. Mag. 78 ] (experiments and finite element results using single crystal plasticity). Hollow circular cylinders of single crystals were loaded radially with a constant average velocity at a strain rate of 10 9 s À1 , inducing the collapse of the cylinder. Various initial orientations of the lattice are examined to study the localization of flow and crack initiation. Comparisons between EAM, experiments, and finite element simulations were in good agreement with each other illustrating that kinematic and localization effects are invariant to extremely large spatial and temporal regimes. Finally, similar dislocation nucleation patterns, localization sites, and crack initiation sites were observed when comparing copper to nickel.

European Journal of Mechanics - A/Solids, 2007

The elastoplastic field induced by quasi-static expansion in steady-state plane-strain conditions of a pressurized cylindrical cavity (cylindrical cavitation) is investigated. Material behavior is modeled by Mises and Tresca large strain flow theories formulated as hypoelastic. Both models account for elastic-compressibility and allow for arbitrary strain-hardening (or softening). For the Mises solid analysis centers on the axially-hydrostatic assumption (axial stress coincides with hydrostatic stress) in conjunction with a controlled error method. Introducing an error control parameter we arrive at a single-parameter-dependent quadrature expression for cavitation pressure. Available results are recovered with particular values of that parameter, and an optimal value is defined such that the cavitation pressure is predicted with high accuracy. For the Tresca solid we obtain an elegant solution with the standard model when no corner develops in the yield surface. Under certain conditions however a corner zone exists near the cavity and the solution is accordingly modified revealing a slight difference in cavitation pressure. Comparison with numerical solutions suggests that the present study establishes cylindrical cavitation analysis on equal footing with existing studies for spherical cavitation.

Key Engineering Materials, 2013

Damage of metals subjected to large plastic deformations typical for forming processes is mainly governed by void nucleation, growth and coalescence. An opposite process may occur in deformation processes with negative stress triaxialities: the closure of strain-induced defects under large hydrostatic pressure. Understanding the mechanisms of damage growth and healing under plastic deformation of metals is still an urgent problem. In order to solve it a theoretical framework for anisotropic ductile damage based on a physically motivated concept for changes in the void volume and shape was recently developed [6]. Strain-induced damage was experimentally determined during uniaxial compression of cylindrical metallic specimens with artificial voids represented by fully-trough drilled holes. It was revealed that the governing physical mechanism of failure is a change in void shapes due to compressive stresses at low negative stress triaxialities in contrast to the growth of voids volume due to high positive stress triaxialities in the processes with dominating tensile stresses. The tensorial model presented in proved to be able to describe kinetics of ductile damage, failure as the ultimate damage, and the closure of voids at negative stress triaxialities.

2005

Starting from a commensurate triangular thin solid strip, confined within two hard structureless walls, a stretch along its length introduces a rectangular distortion. Beyond a critical strain the solid fails through nucleation of "smectic"-like bands. We show using computer simulations and simple density functional based arguments, how a solid-smectic transition mediates the failure. Further, we show that the critical strain introducing failure is inversely proportional to the channel width i.e. thinner strips are stronger !

Doklady Physics, 2003

Journal of Engineering Materials and Technology, 2003

This paper deals with an experimental methodology of the large deformation of cylinders under constrained sides and end conditions. A specific arrangement of two geometrically identical cylinders compressed laterally is studied under different quasi-static strain rates. Several tests are performed using two different structural situations. In the first case, the two cylinders are made from superplastic tin-lead alloy, while in the second case, one cylinder is made from superplastic and the other from steel. Different cylindrical geometries are investigated having the same cross sectional area with different ratios of inner to outer diameter (di/do). The load-deflection curves are recorded and then the energy absorbed per unit volume is determined. The experiments show obviously the remarkable sensitivity of the utilized superplastic to the strain rate in the range of 10 Ϫ5 /s -10 Ϫ3 /s. A two-dimensional finite element simulation is also conducted describing the collapse behavior of these cylindrical geometries in both structural cases under different strain rates.

Procedia IUTAM, 2014

The failure of ductile materials subject to high loading rates is notably affected by material inertia. We analyze how strain localization and fracture are influenced by inertia through selected topics comprising dynamic necking, fragmentation, adiabatic shear banding and dynamic damage by micro-voiding. A multiscale modeling of the behavior of voided visco-plastic materials is proposed that extends classical models by including microscale inertia. Applications to spalling and dynamic fracture reveal that microscale inertia has first order effects on results.