Todd S. Gross

Mode I stress intensity factors induced by fracture surface roughness under pure mode III loading: Application to the effect of loading modes on stress corrosion crack growth

A model to estimate the reduction of effective crack tip Mode III stress intensity factors by frictional and asperity interaction of an idealized fracture surface is described. An extension of the model is used to calculate the Mode I stress intensity factors due to the crack tip opening displacement induced by the mismatch of the fracture surface asperities. The results of calculations based on a “reasonable” fracture surface profile are used to analyze experimental studies designed to determine the relative significance of hydrogen embrittlement and crack tip dissolution in stress corrosion crack growth in Al alloys by comparison of Mode I and Mode III stress corrosion cracking (SCC) resistance. It is concluded that a pure Mode III stress state is not possible for cracks with microscopically rough surfaces and that the magnitude of the induced Mode I stress intensity factor is sufficient to cause stress corrosion crack growth.

Evidence of fracture surface interference for cracks loaded in shear detected by phase-shifted speckle interferometry

Interference of the asperities on a crack loaded in pure, remote shear wedges the crack faces open, thereby inducing a mode I stress intensity factor (SIF). The interference also shields the crack tip from the applied mode II SIF. Three-illumination beam, phase-shifted speckle interferometry was used to measure the three-dimensional incremental displacement fields in a 7×11 mm area around a mode I fatigue precrack in a Al 7075 specimen loaded in 94 increments of increasing shear. The displacement fields were accumulated relative to the unloaded state by sampling at appropriate locations in the incremental fields to optimize spatial resolution and compensate for large rigid body motions. The induced mode I SIF and the effective mode II SIF were estimated from the crack tip shear displacement (CTSD) and crack tip opening displacement (CTOD). A digitized fracture surface profile was numerically shifted according to the experimentally measured crack face displacements to determine the locations of fracture surface interference as a function of applied load.

Two-dimensional, electrostatic finite element study of tip–substrate interactions in electric force microscopy of high density interconnect structures

Two-dimensional electrostatic finite element modeling is used to estimate the variation of tip force as a function of potential, dielectric film thickness, and tip-substrate spacing when imaging using electric force microscopy. Blanket dielectric films and approximately 1000 nm thick interconnect structures were studied. We conclude that sidewall damage regions can be detected but will require special processing to make an unambiguous measurement.

The influence of composition on the properties of pH-swellable polymers for chemical sensors

Abstract Aminated polystyrene swells at low pH due to electrostatic repulsion between charged sites on the polymer. The effects of polymer formulation on the rate and degree of swelling and on the penetration modulus have been evaluated for porous aminated polystyrene beads prepared by suspension polymerization. The following parameters were varied in a 3×3×3×2 factorial experiment: 1) percent crosslinking, 2) percent porogenic solvent, 3) composition of porogenic solvent and 4) level of Kraton G1652, a styrene–ethylene, butylene–styrene triblock copolymer, added to toughen the polymer. The degree of swelling decreases at higher levels of crosslinking. Swelling is greater when the polymer morphology is continuous rather than consisting of connected small spheres. The percentage of xylene in the porogenic solvent affects the degree of swelling for underivatized beads in toluene but not for derivatized beads in acid. The rate of swelling of underivatized beads in toluene appears to involve toluene entering the pore space of the bead by capillary action. However, rates of swelling of derivatized bead in acid appear to be governed by the rate at which protons move through the bulk of the polymer rather than involving transport through pore space. The penetration moduli are small for all beads and depend on the degree of crosslinking, the amount of pore space in the bead and the polymer morphology.

Experimental–computational estimation of rough fracture surface contact stresses

Abstract This paper presents the preliminary results of a technique for estimating the contact stress distribution on the rough surfaces of cracks which are partially closed and loaded in shear. Phase shifted speckle interferrometric measurements of the crack face opening and sliding displacements of a crack in a four-point-bend mixed-mode fracture specimen under quasi-static cyclic loading are used as the initial data. An iterative computational process determines acceptable fits of the initial displacement data and the corresponding crack face contact stresses, which are found from a numerical model of the specimen and loading. Contact stress results are presented from one specimen at two load increments which suggest that the roughness causes an increase in the contact length compared to flat and smooth surfaces. More importantly, as the extent of sliding increases, the effective frictional resistance becomes localized and is a strong function of position along the contact. This cannot be modeled by Coulomb friction with a single value of the coefficient of friction. These are the first results of their kind ever presented for the local displacement and contact stress distributions across rough interacting fracture surfaces.

Three-illumination-beam phase-shifted holographic interferometry study of thermally induced displacements on a printed wiring board

Spatially resolved measurement of thermally induced surface displacements of printed wiring boards using phase-shifted holographic interferometry is discussed. Three separate holograms with three linearly independent illumination beams were recorded. The interferograms were viewed in real time from a fixed detector location, and phase maps corresponding to each illumination direction were generated with the phase-shifting interferometer. The phase maps are then used to compute the displacements on a point by point basis. The measurement accuracy is estimated to be +/-0.004 microm out-of-plane and +/-0.02 microm in-plane over a temperature range of 40 degrees C. The system was tested on a through hole in a printed wiring board; the results of this test are discussed. Phase computation and unwrapping, data reduCtion, experimental geometry, surface preparation, and displacement computation are discussed.

An investigation of tire-wheel interface loads using ADINA

Aircraft wheels are designed to exhibit a fail-safe point so that a crack in the wheel can be detected before any catastrophic failure occurs. Presently, engineers use intrusive instrumentation to directly measure the tire-wheel interface pressure distribution. The goal of the current research is to demonstrate a nonintrusive methodology for using experimental displacement data in conjunction with the finite element method to back calculate this pressure distribution. The result is a well calibrated and credible finite element model which can be used to investigate the structural performance of the wheel.

Numerical Modeling of Grain Boundary Effects in the Diffusional Creep of Copper Interconnect Lines

We propose a numerical simulation technique to model the process of diffusional creep and stress relaxation that occurs in Cu-damascene interconnects of integrated circuit devices in processing stage. The mass flow problem is coupled to the stress analysis through vacancy flux and equilibrium vacancy concentration. The technique is implemented in a software package that seamlessly integrates the problem-oriented code with commercially available finite element program MSC.Marc. It is utilized to model the Coble creep phenomenon by introducing the nanoscale grain boundary region having the thickness on the order of several layers of atoms. As an illustration, the two-dimensional problem of stress relaxation in a single grain subjected to prescribed displacements and tractions is examined.

Detection of plasma-induced, nanoscale dielectric constant variations in carbon-doped CVD oxides by electrostatic force microscopy

Electrostatic force microscopy was used to detect nanoscale dielectric constant variations in two different, carbon-doped oxide low-k dielectrics deposited by plasma-enhanced chemical vapour deposition and subjected to oxidizing isotropic plasmas and inert gas isotropic plasmas. Samples were polished at 10\r{} to the sample normal to enhance the through-the-thickness spatial resolution. We observed that the technique was able to detect k{}~{}0.1 variations of dielectric constant with ~10 nm spatial resolution. We also observed that the oxidizing isotropic plasma caused damage to a depth of approximately 10-50 nm and that one of the carbon-doped oxides was more susceptible to plasma-induced damage. The estimated increase of dielectric constant from the oxidizing plasma was from k~2.5-3 to k>4-5. The damage from the inert gas plasma was observed to be deeper but less severe.

Finite Element Predictions of the Effect of Diffusion-Accommodated Interfacial Sliding on Thermal Stresses in Cu/Polymer Dielectric and Cu/Oxide Dielectric Single Level Damascene Interconnect Structures

The finite element method was used to estimate the stresses in single level, 1 mm thick Cu-dielectric interconnect line arrays with Ta liners resulting from heating from 20°C 400°C assuming that the structure was stress free at 20°C. Benzocyclobutene (BC SiO2 were chosen to represent typical polymer and ceramic dielectric materials b evaluated for Cu damascene interconnect structures. Experimentally observed Cu-T Cu-Cu interfacial sliding was incorporated into the model usin g a 1 nmthick creep element that was calibrated to match the predictions of a classical diffus accommodated sliding model. The effect of Cu-Ta and Cu-Cu interfacial sliding evaluated by comparing the relaxed and unrelaxed stresses. The effect of line wid thickness (w/t) ratio and Ta liner thickness on the shear, normal, and Ta liner-p stresses at the Cu-Ta-dielectric interface was investigated because this interface is a failure site. @DOI: 10.1115/1.1402629 #