Single-crystal silicon test specimens, fabricated by lithography and deep reactive ion etching (DRIE), were used to measure microscale deformation and fracture properties. The mechanical properties of two specimen geometries, both in the form of a Greek letter H (theta), were measured using an instrumented indentation system. The DRIE process generated two different surface structures leading to two strength distributions that were specimen geometry independent: One distribution, centered about 2.1 GPa, was controlled by 35 nm surface roughness of scallops; the second distribution, centered about 1.4 GPa, was controlled by larger, 150 nm, pitting defects. Finite element analyses (FEA) converted measured loads into strengths; tensile elastic measurements validated the FEA. Fractographic observations verified failure locations. The theta specimen and testing protocols are shown to be extremely effective at testing statistically relevant (hundreds) numbers of samples to establish processing-structure-property relationships at ultrasmall scales and for determining design parameters for components of microelectromechanical systems.
Weak bedding planes create a unique mechanism for hydraulic fracture height containment, providing one possible explanation for unusual patterns of height growth in shale formations. This paper describes an investigation into how bedding planes modify the interactions between multiple, simultaneously propagating hydraulic fractures in a formation with weak horizontal interfaces with laterally varying properties. The investigation used a 3-D simulator that fully coupled geomechanics, fracture mechanics, and fluid behavior. Three equally spaced fractures were simulated along a horizontal trajectory. Fluid was injected simultaneously into all three locations, and partitioned according to maintain a specified total injection rate. Variations in perforation spacing, fluid viscosity and injection rate are modeled. The four designs investigated were: 1) 10-cp fluid, 20b-pm injection rate with 30-m cluster spacing. 2) 100-cp fluid and 20-bpm fluid injection rate with 30-m cluster spacing. 3) 10-cp fluid and 40-bpm injection rate with 30-m cluster spacing. 4) 10-cp fluid, 20-bpm and 45-m cluster spacing. Results showed how these changes affected fracture area and shape. The propped surface area for each scenario was also estimated. The results suggested that the presence of laterally varying weak interfaces can significantly affect fracture interference.
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