Fracture of materials undergoing solid-solid phase transformation

A large number of technologically important materials undergo solid-solid phase transformations. Examples range from ferroelectrics (transducers and memory devices), zirconia (Thermal Barrier Coatings) to nickel superalloys and (lithium) iron phosphate (Li-ion batteries). These transformations involve a change in the crystal structure either through diffusion of species or local rearrangement of atoms. This change of crystal structure leads to a macroscopic change of shape or volume or both and results in internal stresses during the transformation. In certain situations this stress field gives rise to cracks (tin, iron phosphate etc.) which continue to propagate as the transformation front traverses the material. In other materials the transformation modifies the stress field around cracks and effects crack growth behavior (zirconia, ferroelectrics). These observations serve as our motivation to study cracks in solids undergoing phase transformations. Understanding these effects will help in improving the mechanical reliability of the devices employing these materials.

In this thesis we present work on two problems concerning the interplay between cracks and phase transformations. First, we consider the directional growth of a set of parallel edge cracks due to a solid-solid transformation. We conclude from our analysis that phase transformations can lead to formation of parallel edge cracks when the transformation strain satisfies certain conditions and the resulting cracks grow all the way till their tips cross over the phase boundary. Moreover the cracks continue to grow as the phase boundary traverses into the interior of the body at a uniform spacing without any instabilities. There exists an optimal value for the spacing between the cracks. We ascertain these conclusion by performing numerical simulations using finite elements.

Second, we model the effect of the semiconducting nature and dopants on cracks in ferroelectric perovskite materials, particularly barium titanate. Traditional approaches to model fracture in these materials have treated them as insulators. In reality, they are wide bandgap semiconductors with oxygen vacancies and trace impurities acting as dopants. We incorporate the space charge arising due the semiconducting effect and dopant ionization in a phase field model for the ferroelectric. We derive the governing equations by invoking the dissipation inequality over a ferroelectric domain containing a crack. This approach also yields the driving force acting on the crack. Our phase field simulations of polarization domain evolution around a crack show the accumulation of electronic charge on the crack surface making it more permeable than was previously believed so, as seen in recent experiments. We also discuss the effect the space charge has on domain formation and the crack driving force.

Structural and clumped-isotope constraints on the mechanisms of displacement along low-angle detachments

Despite years of research on low-angle detachments, much about them remains enigmatic. This thesis addresses some of the uncertainty regarding two particular detachments, the Mormon Peak detachment in Nevada and the Heart Mountain detachment in Wyoming and Montana.

Constraints on the geometry and kinematics of emplacement of the Mormon Peak detachment are provided by detailed geologic mapping of the Meadow Valley Mountains, along with an analysis of structural data within the allochthon in the Mormon Mountains. Identifiable structures well suited to constrain the kinematics of the detachment include a newly mapped, Sevier-age monoclinal flexure in the hanging wall of the detachment. This flexure, including the syncline at its base and the anticline at its top, can be readily matched to the base and top of the frontal Sevier thrust ramp, which is exposed in the footwall of the detachment to the east in the Mormon Mountains and Tule Springs Hills. The ~12 km of offset of these structural markers precludes the radial sliding hypothesis for emplacement of the allochthon.

The role of fluids in the slip along faults is a widely investigated topic, but the use of carbonate clumped-isotope thermometry to investigate these fluids is new. Faults rocks from within ~1 m of the Mormon Peak detachment, including veins, breccias, gouges, and host rocks, were analyzed for carbon, oxygen, and clumped-isotope measurements. The data indicate that much of the carbonate breccia and gouge material along the detachment is comminuted host rock, as expected. Measurements in vein material indicate that the fluid system is dominated by meteoric water, whose temperature indicates circulation to substantial depths (c. 4 km) in the upper crust near the fault zone.

Slip along the subhorizontal Heart Mountain detachment is particularly enigmatic, and many different mechanisms for failure have been proposed, predominantly involving catastrophic failure. Textural evidence of multiple slip events is abundant, and include multiple brecciation events and cross-cutting clastic dikes. Footwall deformation is observed in numerous exposures of the detachment. Stylolitic surfaces and alteration textures within and around “banded grains” previously interpreted to be an indicator of high-temperature fluidization along the fault suggest their formation instead via low-temperature dissolution and alteration processes. There is abundant textural evidence of the significant role of fluids along the detachment via pressure solution. The process of pressure solution creep may be responsible for enabling multiple slip events on the low-angle detachment, via a local rotation of the stress field.

Clumped-isotope thermometry of fault rocks associated with the Heart Mountain detachment indicates that despite its location on the flanks of a volcano that was active during slip, the majority of carbonate along the Heart Mountain detachment does not record significant heating above ambient temperatures (c. 40-70°C). Instead, cold meteoric fluids infiltrated the detachment breccia, and carbonate precipitated under ambient temperatures controlled by structural depth. Locally, fault gouge does preserve hot temperatures (>200°C), as is observed in both the Mormon Peak detachment and Heart Mountain detachment areas. Samples with very hot temperatures attributable to frictional shear heating are present but rare. They appear to be best preserved in hanging wall structures related to the detachment, rather than along the main detachment.

Evidence is presented for the prevalence of relatively cold, meteoric fluids along both shallow crustal detachments studied, and for protracted histories of slip along both detachments. Frictional heating is evident from both areas, but is a minor component of the preserved fault rock record. Pressure solution is evident, and might play a role in initiating slip on the Heart Mountain fault, and possibly other low-angle detachments.

Finite-Element Simulations of Earthquakes

This thesis discusses simulations of earthquake ground motions using prescribed ruptures and dynamic failure. Introducing sliding degrees of freedom led to an innovative technique for numerical modeling of earthquake sources. This technique allows efficient implementation of both prescribed ruptures and dynamic failure on an arbitrarily oriented fault surface. Off the fault surface the solution of the three-dimensional, dynamic elasticity equation uses well known finite-element techniques. We employ parallel processing to efficiently compute the ground motions in domains containing millions of degrees of freedom.

Using prescribed ruptures we study the sensitivity of long-period near-source ground motions to five earthquake source parameters for hypothetical events on a strike-slip fault (M_w 7.0 to 7.1) and a thrust fault (M_w 6.6 to 7.0). The directivity of the ruptures creates large displacement and velocity pulses in the ground motions in the forward direction. We found a good match between the severity of the shaking and the shape of the near-source factor from the 1997 Uniform Building Code for strike-slip faults and thrust faults with surface rupture. However, for blind thrust faults the peak displacement and velocities occur up-dip from the region with the peak near-source factor. We assert that a simple modification to the formulation of the near-source factor improves the match between the severity of the ground motion and the shape of the near-source factor.

For simulations with dynamic failure on a strike-slip fault or a thrust fault, we examine what constraints must be imposed on the coefficient of friction to produce realistic ruptures under the application of reasonable shear and normal stress distributions with depth. We found that variation of the coefficient of friction with the shear modulus and the depth produces realistic rupture behavior in both homogeneous and layered half-spaces. Furthermore, we observed a dependence of the rupture speed on the direction of propagation and fluctuations in the rupture speed and slip rate as the rupture encountered changes in the stress field. Including such behavior in prescribed ruptures would yield more realistic ground motions.