D.E. Munson

A constitutive model for inelastic flow and damage evolution in solids under triaxial compression

Abstract A constitutive model for describing time-dependent, pressure-sensitive inelastic flow and damage evolution in crystalline solids under non-hydrostatic compression has been developed on the basis that the relevant damage and dislocation flow processes both contribute to the overall inelastic strain rate. A damage-based kinetic equation is first formulated using the work-conjugate approach and the continuum damage concept. That relation is then added to the dislocation-based kinetic equation of a multi-mechanism deformation (M-D) model to obtain the macroscopic inelastic strain rate. The proposed kinetic relation for the overall inelastic strain rate is shown to be derivable from a flow potential. The kinetic equation indicates plastic dilatancy under triaxial compression when the damage term is activated, and leads to plastic incompressibility when inelastic straining is primarily provided by dislocation flow mechanisms. The dependence of creep rate and plastic dilatancy on confining pressure shown by model calculations for rock salt is in accordance with experimental observations.

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.

Damage-induced nonassociated inelastic flow in rock salt

Abstract The multimechanism deformation coupled fracture model recently developed by Chan et al. [1992], for describing time-dependent, pressure-sensitive inelastic flow and damage evolution in crystalline solids was evaluated against triaxial creep experiments on rock salt. Guided by experimental observations, the kinetic equation and the flow law for damage-induced inelastic flow in the model were modified to account for the development of damage and inelastic dillation in the transient creep regime. The revised model was then utilized to obtain the creep response and damage evolution in rock salt as a function of confining pressure and stress difference. Comparison between model calculation and experiment revealed that damage-induced inelastic flow is nonassociated, dilational, and contributes significantly to the macroscopic strain rate observed in rock salt deformed at low confining pressures. The inelastic strain rate and volumetric strain due to damage decrease with increasing confining pressures, and all are suppressed at sufficiently high confining pressures.

Cleavage and creep fracture of rock salt

Abstract The dominant failure mechanism in rock salt at ambient temperature is either cleavage or creep fracture. Since the transition of creep fracture to cleavage in a compressive stress field is not well understood, failure of rock salt by cleavage and creep fracture is analyzed in this paper to elucidate the effect of stress state on the competition between these two fracture mechanisms. For cleavage fracture, a shear crack is assumed to cause the formation and growth of a symmetric pair of wing cracks in a predominantly compressive stress field. The conditions for wing-crack instability are derived and presented as the cleavage fracture boundary in the fracture mechanism map. Using an existing creep fracture model, stress conditions for the onset of creep fracture and isochronous failure curves of specified times-to-rupture are calculated and incorporated into the fracture mechanism map. The regimes of dominance by cleavage and creep fracture are established and compared with experimental data. The result indicates that unstable propagation of cleavage cracks occurs only in the presence of tensile stress. The onset of creep fracture is promoted by a tensile stress, but can be totally suppressed by a high confining pressure. Transition of creep fracture to cleavage occurs when critical conditions of stress difference and tensile stress for crack instability are exceeded.

Steady Wave Analysis of Wave Propagation in Laminates and Mechanical Mixtures

A mechanical theory is developed for the propagation of steady waves in laminated media. This analysis treats wave propagation parallel and perpendicular to the laminate plates. It predicts the response of the composite from a knowledge of the component vol ume fractions and mechanical equation of states. Under the restric tion of fluid or hydrodynamic materials, the results yield a hydro dynamic prediction which is independent of composite geometry. Consequently, the analysis is equally applicable to mechanical mix tures. Theoretical calculations are compared to experimental Hu goniot results for a cloth laminate quartz phenolic, a plate laminate and three mechanical mixtures of Al2O3 in epoxy. Excellent agree ment is obtained at low stresses, if the expected deviations caused by material strength are recognized. Thermodynamic effects caused by deviations of the loading path from that of a single shock become more predominant as the stress increases. Models describing both the strength and thermodynamic effects are discussed.

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.

Experimental evaluation of a constitutive model for inelastic flow and damage evolution in solids subjected to triaxial compression

Recent concern over the potential for creep induced development of a damaged rock zone adjacent to shafts and rooms at the Waste Isolation Pilot Plant (WIPP) has motivated the formulation of a coupled constitutive description of continuum salt creep and damage. This constitutive model gives time-dependent inelastic flow and pressure-sensitive damage in crystalline solids. Initially the constitutive model was successfully used to simulate multiaxial, i.e. true triaxial, experiments obtained at relatively high, 2.5 to 20 MPa, confining pressures. Predictions of the complete creep curve, including the heretofore unmodeled tertiary creep, were also demonstrated. However, comparisons of model predictions with data were hampered because the bulk of the creep data existing on WIPP salt was intentionally obtained under confining pressures typically greater than 15 MPa, in an attempt to match the underground in situ lithostatic pressure level. It was realized that the high confining pressures suppressed tertiary creep and resulted in better defined steady state creep responses. To address the tertiary creep process directly, a number of creep tests were conducted at lower confining pressures for the explicit purpose of creating dilatant behavior.

Approach to first principles model prediction of measured WIPP (Waste Isolation Pilot Plant) in situ room closure in salt

Abstract The discrepancies between predicted and measured Waste Isolation Pilot Plant (WIPP) in-situ Room D closures are markedly reduced through the use of a Tresca flow potential, an improved small strain constitutive model, an improved set of material parameters, and a modified stratigraphy.

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.