Gregg Fenton

Modeling of Electromagnetically Formed Sheet Metal

Abstract The intent of this paper is to show that a two-dimensional (2D) arbitrary Lagrangian Eulerian (ALE) finite-difference computer code can accurately predict the dynamics of the electromagnetic sheet metal forming process. The challenging aspect of simulating the deformation of thin metal parts which have been loaded by magnetic forces is solving a highly coupled system of partial differential equations. The material motion and the magnetic physics require two drastically different time steps to maintain numerical stability. The CALE computer code has the ability to solve such challenging problems. This paper highlights the CALE modeling of a number of electromagnetic sheet metal forming operations.

Pressure heterogeneity in small displacement electrohydraulic forming processes

Electrohydraulic (submerged arc discharge) forming of sheet metal parts has been used as a specialized high speed forming method since the 1960’s. The parts formed generally had a major dimension in the 5 to 25 cm range and required gross metal expansion in the centimeter range. In the descriptions of this process found in the literature, the pressure front emanating from the initial plasma generated by the arc is considered to be uniformly spherical in nature. At least one commercial system used this model to design hardware for pressure front focusing to optimize the forming process[1] and it has been the subject of continued research [2]. Recently, there has been commercial interest in adopting the electro-hydraulic method for the production of much smaller parts requiring very high die contact pressures but little gross sheet expansion. The forming of these small shallow parts required only a few kilojoules but proved to be problematic in other terms. The process development clearly showed indications of random patterns of large pressure heterogeneity across distances in the millimeter range. The apparent pressure heterogeneity produced unacceptable small scale variation in the part geometry. A test program was designed to verify and quantify this effect using a target (die) consisting of a flat plate having small closely spaced holes. This 50 mm diameter target proved very effective in clearly showing the extent of the heterogeneity as well as the approximate local pressures. Various discharge energies were investigated along with different chamber shapes and pressure transfer mediums. The pressure heterogeneity across the target face was a common feature to all experiments. These test results indicate that a uniform pressure front model can be seriously in error for the electrohydraulic process as implemented to date. The results of a qualitative hydro-code model of the test system including the discharge event are presented. The model results are similar enough to the experimental to imply that the coaxial electrode’s inherent off center discharge is a primary suspect among potential explanations for the observed heterogeneity in terms of asymmetric shock interaction. The absence of this phenomena in the earlier electrohydraulic forming literature is also discussed.

Shock Compression Modeling of Distended Mixtures

Development of material models to describe the thermodynamic shock states of distended mixtures is motivated by the need to understand how these materials respond over large compression ranges starting from low-pressure mechanical crush, extending into extreme thermodynamic states, and subsequent release to low-pressure. A material modeling approach is presented, which is comprised of a thermodynamically consistent equation-of-state (EOS) within a mixture-modeling framework. This modeling approach enables the investigator to describe the dynamic response of distended mixtures over a large compression range. The EOS model is applied to shock Hugoniot data on tungsten carbide, tantalum pentoxide, and calcite-water mixtures.

Equation of state for shock compression of distended solids

Shock Hugoniot data for full-density and porous compounds of boron carbide, silicon dioxide, tantalum pentoxide, uranium dioxide and playa alluvium are investigated for the purpose of equation-of-state representation of intense shock compression. Complications of multivalued Hugoniot behavior characteristic of highly distended solids are addressed through the application of enthalpy-based equations of state of the form originally proposed by Rice and Walsh in the late 1950s. Additive measures of cold and thermal pressure intrinsic to the Mie-Gruneisen EOS framework is replaced by isobaric additive functions of the cold and thermal specific volume components in the enthalpy-based formulation. Additionally, experimental evidence reveals enhancement of shock-induced phase transformation on the Hugoniot with increasing levels of initial distension for silicon dioxide, uranium dioxide and possibly boron carbide. Methods for addressing this experimentally observed feature of the shock compression are incorporated into the EOS model.

Intense shock compression of porous solids: Application to wc and ta2O5

The intense shock states achievable within granular or porous solids can be quantified through the application of continuum thermodynamic models. Here emphasis is on distended and granular solids for the purpose of calculating compression paths. In the present paper thermo-physical relations are developed and applied to the shock compression of aerogels and powders. These materials were selected because of previous studies available in the literature and recent high-pressure test results obtained at the Sandia National Laboratories Z-Machine. The relations developed herein have been implemented in the Sandia Laboratories CTH code, specifically within a newly modified version of the P-γ equation of state. Analytic equations of state similar to P-γ are usually considered inefficient for hydrocode computation because of the many subcycle calculations needed to determine the pressure. However, the main advantage of this newly modified EOS is it allows for the easy creation of novel heterogeneous mixture model...

SHOCK‐LESS HIGH RATE COMPACTION OF POROUS BRITTLE MATERIALS

The dynamic behavior of granular materials such as granular silica (sand), technical ceramics, and porous geological substances has importance to a variety of engineering applications. Although the mechanical behaviors of sand and other granular ceramics have been studied extensively for several decades, the dynamic behavior of such materials remains poorly understood. This paper describes how instrumented electromagnetic tube compression driven by capacitive discharge can be used to measure compaction of porous materials at high and controlled strain rates. The technique relies on electromagnetically crushing a powder‐filled conductive tube. By measuring the current as a function of time and the tube displacement through Photon Doppler Velocimetry (PDV) sufficient data can be obtained to reveal the behavior of the porous material. The method will be described in detail and example data will be shown for compaction of silica sand.