New Utah Rule 26: A Blueprint for Proportionality Under the Federal Rules of Civil Procedure

Article published in the Michigan State Law Review

Measurement of opaque film thickness

The theoretical and experimental framework for thickness measurements of thin metal films by low frequency thermal waves is described. Although it is assumed that the films are opaque and the substrates are comparatively poor thermal conductors, the theory is easily extended to other cases of technological interest. A brief description is given of the thermal waves and the experimental arrangement and parameters. The usefulness of the technique is illustrated for making absolute measurements of the thermal diffusivities of isotropic substrate materials. This measurement on pure elemental solids provides a check on the three dimensional theory in the limiting case of zero film thickness. The theoretical framework is then presented, along with numerical calculations and corresponding experimental results for the case of copper films on a glass substrate

Thermal wave detection and analysis of defects in structural composite materials

One criticism which can be leveled at thermal wave images is that their resolution is often less than that of the very best ultrasonic images of similar targets. This reduction of the resolution arises from the transverse diffusion of heat in the thermal waves reflected from the subsurface defects in the sample. In this paper we describe a technique for removing the blurring of pulsed thermal wave images of planar defects through the reconstruction of the shape of the scatterer by use of inverse scattering techniques. Although the method at present is restricted to planar defects, this special class of defects includes delaminations and disbonds in layered materials, defects which are of great interest to a variety of industries. Therefore, the availability of a reconstruction algorithm provides a solution to an important problem in nondestructive evaluation. The algorithm produced we have developed is quite simple and very effective when it is applied to thermal wave images of such defects. The idea behind the design of the model is the manipulation of the equations of thermal wave scattering theory in such a way that the scattered wave at the surface of the sample ends up being expressed as a convolution of a “heat spread” function, with a function which describes the shape of the scatterer. The Fourier transform of the surface temperature contrast (the contrast in the image is essentially just a representation of the scattered wave) can then be expressed as a simple product of the Fourier transform of the heat spread function and the Fourier transform of the shape function of the scatterer. In principle, application of the algorithm consists of performing a two-dimensional spatial Fast Fourier Transform (FFT) on the experimental image of the (unknown) scatterer, dividing the resulting Fourier transform by the transform of the (known) theoretical heat spread function, and finally doing an inverse FFT to obtain the shape of the scatterer

Evaluation of Photoacoustic Microscopy Fatigue Crack Detection

The purpose of this paper is to evaluate the technique of scanning photoacoustic microscopy (SPAM) for the detection of fatigue cracks in metal alloys, and to describe an experimental arrangement for SPAM measurements on the inner surface of a cylindrical bolt hole. The experimental technique is based upon the physical mechanism of thermal wave imaging and has been described in detail at previous1, 2 Reviews of Progress in Quantitative NDE and elsewhere.3 In this paper we will also present some results of theoretical calculations for thermal wave scattering from closed, slanted cracks which intersect the surface of an opaque solid, and compare these results with our experimental data

Photoacoustic Microscopy

Recent advances in scanning photoacoustic microscopy (SPAM) for NDE are described. Conventional and phase-contrast modes are used to detect a well-characterized subsurface flaw in Al, and the results are shown to be in good agreement with calculations based upon a three-dimensional thermal diffusion model. Applications of the technique are given which demonstrate surface and subsurface flaw detection in complex-shaped ceramic turbine parts. Photoacoustic pictures are presented of an integrated circuit semiconductor chip and show 6 μm resolution

Thermal Wave Characterization of Coated Surfaces

The experimental techniques and theory for utilizing the mirage effect, or optical probe beam detection, of thermal waves in opaque solids for determining their thermal diffusivities have been described in detail elsewhere. [1–4] An application to a coated nickel-based alloy has also been described elsewhere. [1] In previous papers [5,6] we presented a theoretical expression which describes the mirage effect signal in a three-layer medium (gas-coating-sample system), taking into consideration the effects of the sizes of the heating and probe beams. In this paper we extend the results of numerical calculations from that expression to the case of films which are thermally very thin (thicknesses of the order of 10-3 thermal diffusion lengths). A model system of 100–500 nm thick Cu films on glass substrates was studied experimentally at thermal wave frequencies below 1kHz, and in this paper we compare the results of those measurements to the numerical calculations

Parallel Box-Car Imaging of Adhesion Defects in Plasma-Sprayed Coatings

Thermal wave techniques have been successfully used for the characterization of adhesion defects of plasma-sprayed coatings on metal substrates. [1–3] With the advent of thermal wave infrared video imaging,[4–6] it is now possible to image large surface areas at video frame rates using an IR video camera. In this work we describe a novel parallel box-car imaging system, using an IR video camera and WSU-designed pixel by pixel time-gating and averaging and we demonstrate the ability of this system to detect adhesion defects in plasma-sprayed coatings on metal substrates. A particular advantage of our system is that the entire image can be obtain in parallel, thus making it a much faster technique than the conventional cw thermal wave imaging techniques

Parallel Vector Lock-In Thermal Wave IR Video Imaging of Microcracks in Cu Foils Deposited on Polyimide

Recently, the concept of area-wide lock-in detection in infrared video imaging and its application to thermal wave imaging was demonstrated.[1] This technique combines the lock-in detection method with an IR video camera and almost real-time digital image processing to form a parallel vector lock-in thermal wave IR video imaging system. In this method each pixel of an image is processed in the manner similar to the lock-in detection method while the sample is excited (heated) synchronously with a square-wave modulated joule heating. The synchronous detection allows the non-synchronous background radiation to be subtracted from the signal resulting in an enhanced signal-to-noise ratio, thus allowing the signal of interest to be measured even in situations where it is completely masked by noise. The advantage of IR detection (8–12 µm) and high speed data acquisition combined with the area-wide lock-in detection makes this a unique thermal wave imaging technique for non-destructive evaluation. In this paper we report the application of this lock-in thermal wave IR video imaging technique using ac Joule heating to the imaging of microcracks in Cu foils deposited on polyimide substrates. Comparison of the lock-in video images of good and faulty samples are presented

Thermal Wave Imaging of Aircraft Stuructures

In a previous report [1], we introduced the application of thermal wave imaging to adhesion disbonds and corrosion in aircraft. In the present paper, we describe the application of pulse-echo thermal wave imaging to NDT of aging aircraft. The technique uses high-power photographic flash lamps as a heat source and an IR video camera as a detector. The flash lamps launch pulses of heat into the skin of the aircraft and the IR camera images the returning thermal wave reflections from subsurface defects. The system also includes electronic hardware and software for carrying out the time-gated imaging and real time analysis of the defects. It also has the ability to image large areas in short times. The current inspection speed enables the imaging of over 90 feet of a 16″ strip of aircraft per hour. Here we present some examples of airframe defects, both for metal and composite structures