S. R. Bodner

Ballistic impact: The status of analytical and numerical modeling

Abstract Simulation of ballistic impact generally falls into one of two categories: analytical models which assume certain dominant physical phenomena and numerical simulations, where the general continuum conservation equations are integrated in time at all points in a spatial mesh to obtain the spatial time history of stresses, strains, velocities, etc., in the projectile and target. Analytical formulations model the mechanical processes over the full field of influence which leads to approximate conservation equations for the entire region in an impact event. These for mulations have met with considerable success so long as the assumptions inherent in the model are applicable. Numerical simulations (hydrocodes) compute the wave (shock) interactions important at early times. Mechanical effects, e.g. plugging, erosion, etc., require realistic constitutive modeling which includes failure criteria and failure propagation. This paper gives a broad overview of both analytical and hydrocode modeling and examines the technical issues, uncertainties and potential diffuculties for advancement in predictive capability.

A Damage Mechanics Treatment of Creep Failure in Rock Salt

Recent progress in the formulation of a constitutive model for describing coupled creep and damage development in rock salt is summarized. The constitutive model is based on the assumption that both dislocation slip and creep damage in the form of microcracks with possible wing-tips contribute to the macroscopic inelastic strain rate. The relevant kinetic equations, flow law, and damage evolution equation are presented. Evaluations are made of the coupled creep and fracture model against the measured creep response of clean salt from the Waste Isolation Pilot Plant (WIPP) site. In addition, the development of creep damage and the rupture of WIPP salt subjected to either triaxial compression or indirect tension have been analyzed to evaluate several creep rupture criteria.

Recovery and Healing of Damage in WIPP Salt

Creep damage in rock salt, which generally manifests in the form of microcracks, can be recovered or healed when subjected to sufficiently high pressures and temperatures. In this paper, the phenomena of damage recovery and healing in rock salt are treated using the continuum damage mechanics approach. A healing term is formulated and incorporated into an existing constitutive model for describing coupled creep, fracture, and healing in rock salt. The constitutive model is then evaluated against experimental data of rock salt from the Waste Isolation Pilot Plant (WIPP) site. Satisfactory results are obtained between model calculations and experimental measurements of axial, lateral, and volumetric strains, as well as acoustic wave velocity and attenuation recovered during damage healing. Furthermore, analyses of experimental data revealed that healing anisotropies exist in WIPP salt. Most, though not all, of the healing anisotropies can be modeled with an appropriate power-conjugate equivalent stress, kinetic equation, and evolution equation for damage healing based on a scalar damage variable. This work represents the first attempt to simulate healing of damaged intact WIPP salt; however, further evaluations and improvement of the model can be anticipated.

Permeability of WIPP Salt During Damage Evolution and Healing

The presence of damage in the form of microcracks can increase the permeability of salt. In this paper, an analytical formulation of the permeability of damaged rock salt is presented for both initially intact and porous conditions. The analysis shows that permeability is related to the connected (i.e., gas accessible) volumetric strain and porosity according to two different power-laws, which may be summed to give the overall behavior of a porous salt with damage. This relationship was incorporated into a constitutive model, known as the Multimechanism Deformation Coupled Fracture (MDCF) model, which has been formulated to describe the inelastic flow behavior of rock salt due to coupled creep, damage, and healing. The extended model was used to calculate the permeability of rock salt from the Waste Isolation Pilot Plant (WIPP) site under conditions where damage evolved with stress over a time period. Permeability changes resulting from both damage development under deviatoric stresses and damage healing under hydrostatic pressures were considered. The calculated results were compared against experimental data from the literature, which indicated that permeability in damaged intact WIPP salt depends on the magnitude of the gas accessible volumetric strain and not on the total volumetric strain. Consequently, the permeability of WIPP salt is significantly affected by the kinetics of crack closure, but shows little dependence on the kinetics of crack removal by sintering.

Inelastic Flow Behavior of Argillaceous Salt

The effects of weak clay particles on the creep response of argillaceous salt have been analyzed by considering the particles as damage initiation sites where local tensile stresses and microcracks are induced under triaxial compression. The thermodynamic driving force for the damage process is formulated in terms of an appropriate power-conjucate equivalent stress measure, and the damage kinetics are described in terms of an evolution equation formulated on the basis of the conjugate equivalent stress and the scalar damage variable from Kachanov (1958). This treatment of clay particle effects is then incorporated into the Multimechanism Deformation Coupled Fracture (MDCF) constitutive model. A summary of the constitutive model is presented with an evaluation of the model calculations against experimental data of clean and argillaceous salt. The results suggest that the higher creep rate observed in argillaceous salt compared to clean salt is the consequence of increased damage growth in argillaceous salt due to the presence of weak clay particles.

Creep-induced cleavage fracture in WIPP salt under indirect tension

The phenomenon of cleavage fracture initiation in rock salt undergoing concurrent creep was studied experimentally using the Brazilian indirect tension test technique. The tensile creep and cleavage fracture behaviors were characterized for rock salt from the Waste Isolation Pilot Plant (WIPP) site. The Brazilian test consists of a compressive line load applied diametrically on a disk specimen to produce a region of tensile stress in the center of the disk. The damage processes were documented using video photography. The experimental results were analyzed in terms of a wing-crack fracture model and an independently developed, coupled time-dependent, mechanism-based constitutive model whose parameters were obtained from triaxial compression creep tests. Analytical results indicate that coupling between creep and cleavage fracture in WIPP salt results in a fracture behavior that exhibits time-dependent characteristics and obeys a failure criterion involving a combination of stress difference and tensile stress. Implications of creep-induced cleavage fracture to the integrity of WIPP structures are discussed.

A Damage Mechanics Approach to Life Prediction for a Salt Structure

Excavated rooms in natural bedded salt formations are being considered for use as repositories for nuclear waste. It is presumed that deformation of the rooms by creep will lead to loss of structural integrity and affect room life history and seal efficiency. At projected repository temperatures, two possible fracture mechanisms in salt are creep-induced microcracking in triaxial compression and cleavage in tension. Thus, an accurate prediction of the time of room life and seal degradation requires a reliable description of the creep and damage processes.

Application of Isochronous Healing Curves in Predicting Damage Evolution in a Salt Structure

A treatment of damage healing is present for rock salt, formulated within the framework of continuum damage mechanics. The concept of an isochronous healing surface, which is a locus of points in a stress space for which the times of healing are identical, is proposed and derived from the healing formulation in order to establish the initial stresses for the onset of healing and the evolution of healing with time and stress. The characteristics of the isochronous healing curves are identified and compared against those of isochronous failure curves and the dilatancy boundary. Isochronous healing curves for clean and argillaceous (containing clay particles) salt are developed and evaluated against laboratory data. Subsequently, the isochronous healing curves are used to predict the healing response of damage in the disturbed rock zone of an air intake shaft in a salt structure.

Fracture of cubical tungsten specimens under explosive loading

Abstract Tests have been conducted on cubical specimens of two tungsten alloys subject to explosive loading. One- and two-dimensional numerical simulations have been used in conjunction with experimental data to estimate the spall stress values of the two alloys. Capping the specimens with a thin layer of aluminum suppressed spallation, but led to fracture along the centerline of specimens of one of the two alloy materials; specimens of the other alloy maintained their integrity. Two-dimensional numerical simulations show large tensile stress along the centerline of the fragment due to the superposition of rarefaction waves from edge relief. The derived spall strengths of the two alloys were found to be consistent with the centerline fracture characteristics.

Shock propagation and damage in tungsten cubes subjected to explosive loading

Abstract A combined experimental and numerical study was performed on the dynamic response behavior of cubical specimens of a tungsten alloy. The locations of the first and second (incipient) spall planes were determined as a function of the height of explosive charge acting on one of the faces of the specimen. In the experimental program, the damaged specimens were soft recovered and post-test observations were performed. One-dimensional computer simulations using the WONDY program related the position of the first spall plane to the dynamic fracture strength in order to estimate the dynamic fracture strength of the alloy. A second, incipient spall fracture was observed in the recovered specimens. Detailed examination of the micrographs indicated that the damage occurred by void nucleation and growth. Based on the fracture strength inferred from the depth of the first spall plane, the one-dimensional analysis provided predictions for the incipient second fracture plane location that were in reasonable agreement with the experimental observations.