Deborah Hopkins

The implications of joint deformation in analyzing the properties and behavior of fractured rock masses, underground excavations, and faults

Abstract For a given stress state, joint deformation depends on the joint’s geometry, including surface roughness, spatial geometry of the contact area, and large-scale topographical features such as dips. Under normal stress, contacting asperities compress, and the half spaces bounding the joint are deformed. A very significant consequence of half-space deformation is that it allows mechanical interaction among all contact points between the joint surfaces. As a result, the contact area’s overall spatial geometry plays an important role in determining the distribution of stress across joint surfaces and the change in geometry of the void space between surfaces that occurs with changes in stress. Mechanical interaction among contact points is important in determining normal joint stiffness: two joints with the same total contact area can have substantially different stiffnesses depending on the spatial geometry of their contact areas. Modeling results indicate that joints with small contact areas uniformly distributed across the surfaces can be nearly as stiff as a perfectly mated interface. These results have significant implications for almost any endeavor in fractured rock, including designing underground excavations, predicting the hydraulic response of a rock mass to changes in stress, understanding the deformation and failure of joints under shear stress, and analyzing the stability of faults. In underground excavations, for example, deformation of the roof and floor means that the load acting on any supporting pillar and the distribution of stress throughout the pillar depend on: the pillar’s size and shape; the size, shape, and proximity of neighboring pillars; and the spatial geometry of the pillar array. Purely elastic deformation can lead to either catastrophic or progressive failure. Similarly, to accurately predict fluid flow through jointed rock, changes in void space geometry that result from changes in stress must be considered; these changes in geometry are not predicted by methods that assume that aperture changes uniformly across the joint. For joints and faults, the nonuniform distribution of normal and shear stresses resulting from surface roughness and mechanical interaction between contact points suggests a progressive form of shear failure. Failure is initiated at points of low normal stress and propagates as stress from failed asperities is redistributed to neighboring asperities. Consistent with observations on many faults, modeling and analytical results predict that earthquakes on a fault would be clustered in time and space because of mechanical interaction between persistent asperities.

Mapping fracture aperture as a function of normal stress using a combination of casting, image analysis and modeling techniques

Abstract A combination of casting, image analysis and modeling techniques have been used to produce aperture maps of natural fractures under a normal load. Images of the fracture casts are corrected for trends introduced by the inhomogeneity of the light source, and a precision-engineered mold is used to make a calibration wedge for each fracture that is used to determine the relationship between grey-level and aperture. The resulting aperture maps are input to an analytical model that analyzes how the void spaces deform under stress. For natural fractures in granite core samples, results from the model are compared to LVDT measurements of displacement across the fracture, and maps of contact area generated via image analysis of the fracture casts. The laboratory measurements and modeling results both indicate the importance of accounting for the deformation of fracture surfaces in calculating changes in fracture aperture with stress; the aperture maps obtained via image analysis alone, assuming that aperture changes uniformly across the fracture, over-estimate contact area and do not accurately portray changes in void geometry that occur under load. The research demonstrates the important role that image processing can play in understanding and modeling the hydromechanical behavior of natural fractures, and the importance of building a methodology for transforming images into physically meaningful data.

Inspection of Spot Welds Using an Ultrasonic Phased Array

Results are summarized for a series of experiments in which several hundred spot welds were inspected using high‐frequency phased‐array ultrasonic probes. Analysis of the signals in the Fourier domain allows identification of satisfactory, undersized and defective welds. Work is underway to develop analysis techniques that will allow dimensional analysis of the welds.

Surface-Adaptive Ultrasound (SAUL) for phased-array inspection of composite specimens with curved edges and complex geometry

Results from laboratory experiments and a fully automated industrial implementation are presented to demonstrate the ability of Surface-Adaptive Ultrasound (SAUL) to mitigate the challenges of complex geometry, variability of parts, and misaligned probes, while decreasing inspection times and costs. Shape-corrected scans are presented for a variety of parts demonstrating SAULs ability to adapt the incident wave to the geometry, even for tight radii measured with a linear probe. Results for a linear and a curved array demonstrate that SAUL can compensate for misaligned probes.

Comparison of Metallurgical and Ultrasonic Inspections of Galvanized Steel Resistance Spot Welds

Metallurgical examination of galvanized steel resistance spot welds was used to gauge the capabilities of two ultrasonic, non‐destructive, scanning techniques. One method utilized the amplitude of the echo from the weld faying surface, while the other used the spectral content of the echo train to map the fused area. The specimens were subsequently sectioned and etched, to distinguish the fused, zinc‐brazed, and non‐fused areas. The spectral maps better matched the metallurgical maps, while the interface‐amplitude method consistently overestimated the weld size.

Thermographic and Acoustic Imaging of Spot-Welded and Weld-Bonded Joints

The work presented here is part of a research effort focused on developing nondestructive evaluation (NDE) and testing techniques that are sufficiently fast, robust, accurate, and cost effective for on-line inspection of automotive structures. A series of laboratory experiments was conducted to assess the feasibility of thermographic and acoustic methods for evaluating the quality of individual spot welds and the structural integrity of spot-welded and weld-bonded joints. Emphasis was placed on identifying structurally weak “stick” welds, which are much more difficult to detect than broken welds. After nondestructive evaluation, the samples were subjected to mechanical tests to determine the strength of individual spot welds. Analytical and numerical models are also being developed to help interpret results of the laboratory experiments. The insight gained from the data and modeling results are essential in moving from qualitative techniques that identify flaws to quantitative methods that assess the severity of defects.

DEFECT DETECTION IN BONDED STRUCTURES USING THE REVERBERANT WAVEFIELD

With the increasing use of adhesives in the automotive, aerospace, and manufacturing industries, there is a growing interest in developing nondestructive methods for locating defects in adhesive bonds. While conventional techniques which utilize ultrasonic waves and Lamb waves are likely candidates for obtaining high resolution images of defects, these methods may not be practical for assembly line applications where the time required to scan the bonds and the access to the bonds are often limited. The objective of this work is to develop an approach for detecting defects in bonds that requires only a limited number of measurements of the reverberant acoustic wavefield (i.e., waves that are multiply scattered off the boundaries of the structure) made over a band of frequencies.

USE OF METALLOGRAPHIC ANALYSIS AND STRENGTH TESTING TO IMPROVE ULTRASONIC PHASED‐ARRAY EVALUATION OF RESISTANCE SPOT WELDS

Results are summarized for a series of experiments in which one hundred spot welds were inspected using a high‐frequency phased‐array ultrasonic probe, and then sectioned, polished and etched to reveal the microstructure of the welds. The ultrasonic and metallographic results are analyzed in conjunction with the results of strength tests and the size of the weld buttons obtained from destructive tear‐down of the welded samples.

Model for Deformation, Stress and Contact at Interfaces — Implications for Ultrasonic Measurements

An analytical model is presented for calculating deformation, contact area, stiffness, and the distribution of stress across joints and interfaces that can be described as two rough surfaces in partial contact. Analytical, modeling, and experimental results are presented that demonstrate the role that deformation of the bulk material surrounding the joint and mechanical interaction between contact points play in joint properties and the propagation of acoustic waves across the interface. Results are applied to help interpret C‐scans of spot‐welded joints.

Complications of using resonance-frequency shifts to detect defects in adhesive joints

It is well known that introduction of a crack-like defect into a structure reduces its stiffness and results in a corresponding downward shift in resonance frequencies. This result is consistent with the Rayleigh-Ritz formulation, which predicts that a reduction in stiffness will decrease resonance frequencies for negligibly small perturbations in mass. Techniques based on frequency shifts and mode shape analysis are being investigated to determine their feasibility for characterizing defects in adhesive-bonded joints in automotive structures. Although counter intuitive, it has been observed that a structure containing a defective joint sometimes exhibits higher resonance frequencies for some modes than a structure with an undamaged joint. Such results have been observed in laboratory experiments on aluminum plates with adhesive-bonded T-joints, and in finite-element simulations for a variety of structures. In all cases, the defects are gaps in the adhesive layer of the joints. While the reduction in mass is very small, it appears that the mass effect can sometimes overwhelm the frequency-decreasing effect of the reduced stiffness. Such behavior depends on the location of the defect, and is speculated to occur when the mode shape corresponding to the frequency is very sensitive to the mass (inertia) but relatively insensitive to the change in stiffness.It is well known that introduction of a crack-like defect into a structure reduces its stiffness and results in a corresponding downward shift in resonance frequencies. This result is consistent with the Rayleigh-Ritz formulation, which predicts that a reduction in stiffness will decrease resonance frequencies for negligibly small perturbations in mass. Techniques based on frequency shifts and mode shape analysis are being investigated to determine their feasibility for characterizing defects in adhesive-bonded joints in automotive structures. Although counter intuitive, it has been observed that a structure containing a defective joint sometimes exhibits higher resonance frequencies for some modes than a structure with an undamaged joint. Such results have been observed in laboratory experiments on aluminum plates with adhesive-bonded T-joints, and in finite-element simulations for a variety of structures. In all cases, the defects are gaps in the adhesive layer of the joints. While the reduction in mass...