http://user.engineering.uiowa.edu/~sxiao/paper/stable_particleMethods.pdf

Stable particle methods based on Lagrangian kernels

In this series of papers, we investigate the mechanics and physics of necking and fragmentation in ductile materials. The behavior of ductile metals at strain rates of about 10,000 per second is considered. The expanding ring experiment is used as the vehicle for examining the material behavior in this range of strain rates. In the present paper, the details of the experiment and the experimental observations on Al 6061-O are reported. Specifically, the design of the expanding ring experiment is evaluated through an analysis of the electromagnetic and mechanical aspects of the problem. Then, through an innovative use of high-speed, high-spatial resolution imaging we determine the sequence of deformation and failure in the expanding ring. In particular, the high speed photographs reveal that multiple necks nucleate along the circumference of the ring near a critical strain level; this is followed by a sequence of fractures, and eventually the fragments are unloaded and move as a rigid body. The strain at the onset of localized deformation, the time of fracture initiation, and the sequence of fragmentation are~all quantified in these experiments. These experimental results facilitate detailed comparison to analytical and numerical models of the fragmentation process. Following this, quantitative interpretation of the experimental observations is pursued. First, the uniform expansion of the ring is considered; the observed radial expansion is shown to agree well with an analytical solution of the problem based on a strain-rate-independent plasticity model. The evolution of the strain in the specimen and the onset of necking are evaluated quantitatively and shown to exhibit no dependence on the applied strain rate for this material; the strain at final fracture, averaged over the entire ring, is shown to be an inadequate measure of the ductility of the material. The fragmentation process is modeled with finite element analysis, incorporating the concept of the Mott release waves; this simulation provides a detailed numerical characterization of the experimental observations. Finally, the statistics of the necking and fragmentation are evaluated; these are interpreted both with the predictions of the linear perturbation analysis and a Weibull/Mott model of necking and fragmentation. In the sequel, we will explore the effect of material ductility, strain rate dependence, the effect of geometry and constraint, and finally the effect of a compliant cladding or coating on the development of necking and fragmentation.

On the dynamics of necking and fragmentation – I. Real-time and post-mortem observations in Al 6061-O

Thin rings have been rapidly expanded using large, transient magnetic fields to study the effect of deformation velocity on strains to failure of ductile metals. A classical electrodynamics analysis similar to one developed previously by Gourdin was employed to estimate sample velocities. Within expansion velocities studied (50 to 300 m/s), the experimental results show that ductility of Al 6061 and OFHC Cu increases monotonically with increasing velocity. In each case, sample strain at failure is almost twice as great at 300 m/s as in the static condition. Comparison to a one-dimensional rigid-viscoplastic dynamic finite element method analysis suggests that inertial effects are mainly responsible for enhanced ductility over a wide range of velocity.

Increased ductility in high velocity electromagnetic ring expansion

Effect of velocity on flow localization in tension

The stability of discretizations by particle methods with corrected derivatives is analyzed. It is shown that the standard particle method (which is equivalent to the element-free Galerkin method with an Eulerian kernel and nodal quadrature) has two sources of instability: 1. rank deficiency of the discrete equations, and 2. distortion of the material instability. The latter leads to the so-called tensile instability. It is shown that a Lagrangian kernel with the addition of stress points eliminates both instabilities. Examples that verify the stability of the new formulation are given.

http://user.engineering.uiowa.edu/~sxiao/paper/particleMethod_stability.pdf

Stability Analysis of Particle Methods with Corrected Derivatives

This paper presents the results of an investigation to develop new techniques to enhance the moire method of mechanical interferometry. The program demonstrated the practicality of developing the use of orthogonal bicolored moire fringes with the unique capability to selectively display either set of fringes while obscuring the other set. An interpolation method for the determination of fractional fringe orders is also discussed.

E. I. Riegner

Papers

The development of orthogonal bicolored moiré fringes