D. K. Rehbein

The interaction of ultrasound with contacting asperities: Applications to crack closure and fatigue crack growth

The partial contact of two rough fatigue crack surfaces leads to transmission, reflection, diffraction, and mode conversion of an acoustic signal at those contacts. This paper reviews recent experimental and theoretical efforts to understand and quantify such contact on actual fatigue cracks in greater detail. It is shown that the size and density of individual contacts, or asperities, can be estimated from acoustic measurements. Furthermore, it is shown that this information is useful to provide the static stress across a partially closed crack as well as the “effective” stress intensity range which activates fatigue crack propagation.

Nonlinear Acoustics, a Technique to Determine Microstructural Changes in Materials

An important aspect of nondestructive evaluation is materials characterization, in particular, detection of changes in the microstructure, affecting the mechanical properties. The goal of this project is to correlate the mechanical properties of high strength alloys with nonlinear acoustical properties of the materials. Many high strength alloys are precipitation hardened, and therefore, their mechanical properties are dependent on microstructural changes during thermal aging. Since the precipitates are formed by diffusion a property sensitive to the precipitation changes is the electrical resistivity. Standard ultrasonic techniques, on the other hand, have been unreliable in microstructural characterization, since in these alloys linear acoustic properties (e.g. sound velocity, attenuation) change by no more than 1%. Literature indicates however that nonlinear acoustical properties change by roughly 50% [1]. From this evidence it appears a nonlinear acoustic technique would be an additional method to examine microstructural changes in precipitation hardened materials.

Acoustic harmonic generation at diffusion bonds

The distortion of a sinusoidal acoustic wave at unbonded interfaces has been determined in terms of the first and second harmonic amplitudes. The results demonstrate for the first time that the second harmonic can reach the theoretically predicted maximum value. As also predcted, the harmonic generation efficiency at unbonded interfaces first increases and then decreases with an externally applied compressive load. The technique has been applied to diffusion bonded specimens in an attempt to quantify their achieved strength. As already demonstrated earlier, the energy reflected from such diffusion bonds is also useful to characterize their strength. Indications are that a combination of reflected energy and harmonic generation data could be a powerful tool to quantify the strength of diffusion bonds, particularly those of nearly perfect strength. A strength determination of diffusion bonds by nondestructive evaluation is a necessity for the qualification of such bonds in critical applications.

Nondestructive characterization of the mechanical strength of diffusion bonds. I. Experimental results

The application of ultrasonic reflectivity for the characterization of a variety of copper diffusion bonds is described. The quality of each diffusion bond has been described by its ultimate tensile strength. Furthermore, fractography of the failed bonds provided information on the relative fraction of bonded areas as well as the geometry of the bonds. This paper provides the experimental results obtained as well as empirical correlations between the quantities determined.

Nondestructive characterization of the mechanical strength of diffusion bonds. II. Application of a quasi-static spring model

It has been shown that the acoustic response of imperfect interfaces may be described by a quasi-static spring model. In the present paper, experimental data on the geometry of the contacts between two diffusion-bonded blocks have been used to determine the “spring stiffness” of such interfaces which have been correlated with experimentally determined ultrasonic reflection coefficients. The correlation between the theoretical reflection coefficient and the “spring stiffness” was found to be in excellent agreement with experimentally-observed values, if the disbonds are of infinitesimally small thickness. For disbonds of finite thickness, the agreement is less satisfactory. Reasons for the discrepancy in the latter case are unknown at the present time.

Crack tip shielding by asperity contact as determined by acoustic measurements

Abstract Asperity contact along the fracture surface of a crack is one of the mechanisms of crack closure. This contact shields the crack tip, in part, from the externally applied driving force. We have now succeeded in using information from acoustic transmission and diffraction experiments, obtained under plane strain conditions, to determine the size and density of the contacting asperities in the closure region. We have also succeeded in estimating values for the static stress across a partially closed crack as well as the stress intensity factor,KI (local), which shields the crack tip below the stress intensity factor KIclosure at which the first contact during unloading occurs. It is suggested that when crack closure has an important influence on crack propagation, the shielding stress intensity factor provides information that can be used to estimate the fatigue crack propagation rate.

Interaction of Ultrasonic Waves with Simulated and Real Fatigue Cracks

It is now well accepted that the partial contact of fracture surfaces can have significant effects on the ultrasonic response of fatigue cracks. The authors and colleagues1–4 have developed an approximate model for this effect in which the array of contacts is replaced by an equivalent distributed spring with stiffness per unit area, K. A result of this model, the frequency dependent transmission and reflection coefficients, has been verified by comparison to exact solutions for special cases.5,6 Of particular note is the comparison to the transmission and reflection at a periodic array of strip contacts, as analyzed by Angel and Achenbach7, which is in good agreement with that of the spring model when the wavelength is large with respect to the contact spacing. Comparison to static elasticity solutions allows K to be determined for a variety of interesting interfacial topographies.5,6

Contacting surfaces: A problem in fatigue and diffusion bonding

Contact between surfaces usually occurs at asperities under compression or at connecting ligaments, depending on how the interface is formed. This paper deals with the nondestructive evaluation of the topology of contact and with the use of this information to predict the effects that loads borne by these contacts have on mechanical properties. Two specific examples are discussed: a fatigue crack and a diffusion bond. Asperity contact along the fracture surface of a fatigue crack partially shields the crack tip from the externally applied driving force. Using information from acoustic experiments, the geometry of the asperities, the contacting stress, and the shielding stress intensity factor have been estimated. Acoustically, a diffusion bonded interface looks very similar to that joining the two sides of a partially closed crack. In this particular case, the acoustically determined geometry of well-bonded ligaments can be verified by fractography of destructively tested samples whose bond strength has also been determined. Models to determine the bond strength from the ligament geometry are being suggested.

Strength and Ultrasonic Characterization of Metallic Interfaces

In recent years, the process of diffusion bonding has found considerable usage in both the nuclear power and aerospace industries. This process requires the compression of mating surfaces at an elevated temperature for a given time. If optimum conditions of time, temperature, pressure and surface cleanliness are achieved, diffusion of material across the interface will occur, yielding interfacial mechanical properties identical to those of the bulk material. The use of insufficient bonding conditions may result in void formation, precipitation of undesired phases or lack of grain growth across the interface. The consequence will be an interface that is less than fully bonded, which will result in severe degradation of the mechanical properties. Applications of diffusion bonding to nuclear reactor fuel elements, helicopter rotor hubs, jet engine turbine blades, etc., thus make the ability to characterize the strength of these interfaces highly desirable.

Ultrasonic measurements of crack tip shielding by closure

Abstract During fatigue, an existing crack closes partially owing to the compressive stresses set up by the deformed material. It is well established that this crack closure can have pronounced effects on the rate of crack propagation and thus on fatigue life. The present paper deals mainly with our recent efforts which have been concerned with the characterization of crack closure acoustically and the determination of the mechanical effects of closure on the crack tip. Results indicate that closure occurs by asperity contact along the fracture surface and it is this asperity contact which shields the crack tip, in part, from the externally applied driving force on the crack tip. Consequences of this research on the effective stress intensity range and thus on the driving force on a crack will be discussed.